{"text": "Title: Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints\nAbstract: We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity of fair allocations. We study the problem of finding an allocation that is Pareto-optimal. While it is easy to find an efficient allocation when the underlying graph is a path or a star, the problem is NP-hard for many other graph topologies, even for trees of bounded pathwidth or of maximum degree 3. We show that on a path, there are instances where no Pareto-optimal allocation satisfies envy-freeness up to one good, and that it is NP-hard to decide whether such an allocation exists, even for binary valuations. We also show that, for a path, it is NP-hard to find a Pareto-optimal allocation that satisfies maximin share, but show that a moving-knife algorithm can find such an allocation when agents have binary valuations that have a non-nested interval structure.", "field": "cs", "label": 1}
{"text": "Title: Taming the Beast: Fully Automated Unit Testing with Coyote C++\nAbstract: In this paper, we present Coyote C++, a fully automated white-box unit testing tool for C and C++. Whereas existing tools have struggled to realize unit test generation for C++, Coyote C++ is able to produce high coverage results from unit test generation at a testing speed of over 10,000 statements per hour. This impressive feat is made possible by the combination of a powerful concolic execution engine with sophisticated automated test harness generation. Additionally, the GUI of Coyote C++ displays detailed code coverage visualizations and provides various configuration features for users seeking to manually optimize their coverage results. Combining potent one-click automated testing with rich support for manual tweaking, Coyote C++ is the first automated testing tool that is practical enough to make automated testing of C++ code truly viable in industrial applications.", "field": "cs", "label": 0}
{"text": "Title: Two remarks on graph norms\nAbstract: For a graph $H$, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions $W$ in $L^p$, $p\\geq e(H)$, denoted by $t(H,W)$. One may then define corresponding functionals $\\|W\\|_{H}:=|t(H,W)|^{1/e(H)}$ and $\\|W\\|_{r(H)}:=t(H,|W|)^{1/e(H)}$ and say that $H$ is (semi-)norming if $\\|.\\|_{H}$ is a (semi-)norm and that $H$ is weakly norming if $\\|.\\|_{r(H)}$ is a norm. We obtain two results that contribute to the theory of (weakly) norming graphs. Firstly, answering a question of Hatami, who estimated the modulus of convexity and smoothness of $\\|.\\|_{H}$, we prove that $\\|.\\|_{r(H)}$ is not uniformly convex nor uniformly smooth, provided that $H$ is weakly norming. Secondly, we prove that every graph $H$ without isolated vertices is (weakly) norming if and only if each component is an isomorphic copy of a (weakly) norming graph. This strong factorisation result allows us to assume connectivity of $H$ when studying graph norms. In particular, we correct an error in the original statement of the aforementioned theorem by Hatami.", "field": "math", "label": 1}
{"text": "Title: Low regularity estimates of the Lie-Totter time-splitting Fourier spectral method for the logarithmic Schrödinger equation\nAbstract: In this paper, we conduct rigorous error analysis of the Lie-Totter time-splitting Fourier spectral scheme for the nonlinear Schr\\\"odinger equation with a logarithmic nonlinear term $f(u)=u\\ln|u|^2$ (LogSE) and periodic boundary conditions on a $d$-dimensional torus $\\mathbb T^d$. Different from existing works based on regularisation of the nonlinear term $ f(u)\\approx f^\\varepsilon(u)=u\\ln (|u| + \\varepsilon )^2,$ we directly discretize the LogSE with the understanding $f(0)=0.$ Remarkably, in the time-splitting scheme, the solution flow map of the nonlinear part: $g(u)= u {\\rm e}^{-{\\rm} i t \\ln|u|^{2}}$ has a higher regularity than $f(u)$ (which is not differentiable at $u=0$ but H\\\"older continuous), where $g(u)$ is Lipschitz continuous and possesses a certain fractional Sobolev regularity with index $0<s<1$. Accordingly, we can derive the $L^2$-error estimate: $O\\big((\\tau^{s/2} + N^{-s})\\ln\\! N\\big)$ of the proposed scheme for the LogSE with low regularity solution $u\\in C((0,T]; H^s( \\mathbb{T}^d)\\cap L^\\infty( \\mathbb{T}^d)).$ Moreover, we can show that the estimate holds for $s=1$ with more delicate analysis of the nonlinear term and the associated solution flow maps. Furthermore, we provide ample numerical results to demonstrate such a fractional-order convergence for initial data with low regularity. This work is the first one devoted to the analysis of splitting scheme for the LogSE without regularisation in the low regularity setting, as far as we can tell.", "field": "math", "label": 0}
{"text": "Title: On the standing waves of the NLS-log equation with point interaction on a star graph\nAbstract: We study a nonlinear Schr\\\"odinger equation with logarithmic nonlinearity on a star graph $\\mathcal{G}$. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\\alpha\\in \\mathbb{R}$. We investigate orbital stability and spectral instability of the standing wave solutions $e^{i\\omega t}\\mathbf{\\Phi}(x)$ to the equation when the profile $\\mathbf\\Phi(x)$ has mixed structure (i.e. has bumps and tails). In our approach we essentially use the extension theory of symmetric operators by Krein - von Neumann, and the analytic perturbations theory.", "field": "math", "label": 1}
{"text": "Title: Deep Automated Mechanism Design for Integrating Ad Auction and Allocation in Feed\nAbstract: E-commerce platforms usually present an ordered list, mixed with several organic items and an advertisement, in response to each user's page view request. This list, the outcome of ad auction and allocation processes, directly impacts the platform's ad revenue and gross merchandise volume (GMV). Specifically, the ad auction determines which ad is displayed and the corresponding payment, while the ad allocation decides the display positions of the advertisement and organic items. The prevalent methods of segregating the ad auction and allocation into two distinct stages face two problems: 1) Ad auction does not consider externalities, such as the influence of actual display position and context on ad Click-Through Rate (CTR); 2) The ad allocation, which utilizes the auction-winning ad's payment to determine the display position dynamically, fails to maintain incentive compatibility (IC) for the advertisement. For instance, in the auction stage employing the traditional Generalized Second Price (GSP) , even if the winning ad increases its bid, its payment remains unchanged. This implies that the advertisement cannot secure a better position and thus loses the opportunity to achieve higher utility in the subsequent ad allocation stage. Previous research often focused on one of the two stages, neglecting the two-stage problem, which may result in suboptimal outcomes...", "field": "cs", "label": 0}
{"text": "Title: An eigenvalue problem for self-similar patterns in Hele-Shaw flows\nAbstract: Hele-Shaw problems are prototypes to study the interface dynamics. Linear theory suggests the existence of self-similar patterns in a Hele-Shaw flow. That is, with a specific injection flux the interface shape remains unchanged while its size increases. In this paper, we explore the existence of self-similar patterns in the nonlinear regime and develop a rigorous nonlinear theory characterizing their fundamental features. Using a boundary integral formulation, we pose the question of self-similarity as a generalized nonlinear eigenvalue problem, involving two nonlinear integral operators. The flux constant $C$ is the eigenvalue and the corresponding self-similar pattern $\\mathbf{x}$ is the eigenvector. We develop a quasi-Newton method to solve the problem and show the existence of nonlinear shapes with $k$-fold dominated symmetries. The influence of initial guesses on the self-similar patterns is investigated. We are able to obtain a desired self-similar shape once the initial guess is properly chosen. Our results go beyond the predictions of linear theory and establish a bridge between the linear theory and simulations.", "field": "math", "label": 0}
{"text": "Title: Compact Group Actions on Topological and Noncommutative Joins\nAbstract: We consider the Type 1 and Type 2 noncommutative Borsuk-Ulam conjectures of Baum, D$\\k{a}$browski, and Hajac: there are no equivariant morphisms $A \\to A \\circledast_\\delta H$ or $H \\to A \\circledast_\\delta H$, respectively, when $H$ is a nontrivial compact quantum group acting freely on a unital $C^*$-algebra $A$. Here $A \\circledast_\\delta H$ denotes the equivariant noncommutative join of $A$ and $H$; this join procedure is a modification of the topological join that allows a free action of $H$ on $A$ to produce a free action of $H$ on $A \\circledast_\\delta H$. For the classical case $H = \\mathcal{C}(G)$, $G$ a compact group, we present a reduction of the Type 1 conjecture and counterexamples to the Type 2 conjecture. We also present some examples and conditions under which the Type 2 conjecture does hold.", "field": "math", "label": 1}
{"text": "Title: Reliability of k-out-of-n Data Storage System with Deterministic Parallel and Serial Repair\nAbstract: In this paper, we find the Laplace Stieltjes transform of the probability of data loss for the k-out-of-n distributed storage system with deterministic repair times. We consider two repair models, namely the serial and parallel repair. We show that for failure rate much lower than the repair rate, mean time of data loss for the two models is the same unlike the case for exponential repair models.", "field": "cs", "label": 1}
{"text": "Title: On Virasoro Constraints for Orbifold Gromov-Witten Theory\nAbstract: Virasoro constraints for orbifold Gromov-Witten theory are described. These constraints are applied to the degree zreo, genus zero orbifold Gromov-Witten potentials of the weighted projective stacks $\\mathbb{P}(1,N)$, $\\mathbb{P}(1,1,N)$ and $\\mathbb{P}(1,1,1,N)$ to obtain formulas of descendant cyclic Hurwitz-Hodge integrals.", "field": "math", "label": 1}
{"text": "Title: Parametric change point detection with random occurrence of the change point\nAbstract: We are concerned with the problem of detecting a single change point in the model parameters of time series data generated from an exponential family. In contrast to the existing literature, we allow that the true location of the change point is itself random, possibly depending on the data. Under the alternative, we study the case when the size of the change point converges to zero while the sample size goes to infinity. Moreover, we concentrate on change points in the \"middle of the data\", i.e., we assume that the change point fraction (the location of the change point relative to the sample size) converges weakly to a random variable $\\lambda^*$ which takes its values almost surely in a closed subset of $(0,1).$ We show that the known statistical results from the literature also transfer to this setting. We substantiate our theoretical results with a simulation study.", "field": "math", "label": 1}
{"text": "Title: Shadow Blade: A tool to interact with attack vectors\nAbstract: The increased demand of cyber security professionals has also increased the development of new platforms and tools that help those professionals to improve their offensive skills. One of these platforms is HackTheBox, an online cyber security training platform that delivers a controlled and safe environment for those professionals to explore virtual machines in a Capture the Flag (CTF) competition style. Most of the tools used in a CTF, or even on real-world Penetration Testing (Pentest), were developed for specific reasons so each tool usually has different input and output formats. These different formats make it hard for cyber security professionals and CTF competitors to develop an attack graph. In order to help cyber security professionals and CTF competitors to discover, select and exploit an attack vector, this paper presents Shadow Blade, a tool to aid users to interact with their attack vectors.", "field": "cs", "label": 0}
{"text": "Title: Two open problems in the fixed point theory of contractive type mappings on first-countable quasimetric spaces\nAbstract: Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., {\\it Generalized distances and their associate metrics. Impact on fixed point theory}, Creat. Math. Inform. {\\bf 22} (2013), no. 1, 23--32] are considered. We give a complete answer to the first problem, a partial answer to the second one, and also illustrate the complexity and relevance of these problems by means of four very interesting and comprehensive examples.", "field": "math", "label": 1}
{"text": "Title: Exploring Boundary of GPT-4V on Marine Analysis: A Preliminary Case Study\nAbstract: Large language models (LLMs) have demonstrated a powerful ability to answer various queries as a general-purpose assistant. The continuous multi-modal large language models (MLLM) empower LLMs with the ability to perceive visual signals. The launch of GPT-4 (Generative Pre-trained Transformers) has generated significant interest in the research communities. GPT-4V(ison) has demonstrated significant power in both academia and industry fields, as a focal point in a new artificial intelligence generation. Though significant success was achieved by GPT-4V, exploring MLLMs in domain-specific analysis (e.g., marine analysis) that required domain-specific knowledge and expertise has gained less attention. In this study, we carry out the preliminary and comprehensive case study of utilizing GPT-4V for marine analysis. This report conducts a systematic evaluation of existing GPT-4V, assessing the performance of GPT-4V on marine research and also setting a new standard for future developments in MLLMs. The experimental results of GPT-4V show that the responses generated by GPT-4V are still far away from satisfying the domain-specific requirements of the marine professions. All images and prompts used in this study will be available at https://github.com/hkust-vgd/Marine_GPT-4V_Eval", "field": "cs", "label": 0}
{"text": "Title: Energy based diffusion generator for efficient sampling of Boltzmann distributions\nAbstract: We introduce a novel sampler called the energy based diffusion generator for generating samples from arbitrary target distributions. The sampling model employs a structure similar to a variational autoencoder, utilizing a decoder to transform latent variables from a simple distribution into random variables approximating the target distribution, and we design an encoder based on the diffusion model. Leveraging the powerful modeling capacity of the diffusion model for complex distributions, we can obtain an accurate variational estimate of the Kullback-Leibler divergence between the distributions of the generated samples and the target. Moreover, we propose a decoder based on generalized Hamiltonian dynamics to further enhance sampling performance. Through empirical evaluation, we demonstrate the effectiveness of our method across various complex distribution functions, showcasing its superiority compared to existing methods.", "field": "cs", "label": 0}
{"text": "Title: Local Discontinuous Galerkin Methods for Solving Convection-Diffusion and Cahn-Hilliard Equations on Surfaces\nAbstract: Local discontinuous Galerkin methods are developed for solving second order and fourth order time-dependent partial differential equations defined on static 2D manifolds. These schemes are second-order accurate with surfaces triangulized by planar triangles and careful design of numerical fluxes. The schemes are proven to be energy stable. Various numerical experiments are provided to validate the new schemes.", "field": "math", "label": 0}
{"text": "Title: Homotopy Algebras are Homotopy Algebras\nAbstract: We prove that strongly homotopy algebras (such as $A_\\infty$, $C_\\infty$, sh Lie, $B_\\infty$, $G_\\infty$,...) are homotopically invariant in the category of chain complexes. An important consequence is a rigorous proof that `strongly homotopy structures transfer over chain homotopy equivalences.'", "field": "math", "label": 1}
{"text": "Title: A Steinberg type decomposition theorem for higher level Demazure modules\nAbstract: We study Demazure modules which occur in a level $\\ell$ irreducible integrable representation of an affine Lie algebra. We also assume that they are stable under the action of the standard maximal parabolic subalgebra of the affine Lie algebra. We prove that such a module is isomorphic to the fusion product of \"prime\" \\ Demazure modules, where the prime factors are indexed by dominant integral weights which are either a multiple of $\\ell$ or take value less than $\\ell$ on all simple coroots. Our proof depends on a technical result which we prove in all the classical cases and $G_2$. Calculations with mathematica show that this result is correct for small values of the level. Using our result, we show that there exist generalizations of $Q$--systems to pairs of weights where one of the weights is not necessarily rectangular and is of a different level. Our results also allow us to compare the multiplicities of an irreducible representation occuring in the tensor product of certian pairs of irreducible representations, i.e., we establish a version of Schur positvity for such pairs of irreducible modules for a simple Lie algebra.", "field": "math", "label": 1}
{"text": "Title: Path-based Explanation for Knowledge Graph Completion\nAbstract: Graph Neural Networks (GNNs) have achieved great success in Knowledge Graph Completion (KGC) by modelling how entities and relations interact in recent years. However, the explanation of the predicted facts has not caught the necessary attention. Proper explanations for the results of GNN-based KGC models increase model transparency and help researchers develop more reliable models. Existing practices for explaining KGC tasks rely on instance/subgraph-based approaches, while in some scenarios, paths can provide more user-friendly and interpretable explanations. Nonetheless, the methods for generating path-based explanations for KGs have not been well-explored. To address this gap, we propose Power-Link, the first path-based KGC explainer that explores GNN-based models. We design a novel simplified graph-powering technique, which enables the generation of path-based explanations with a fully parallelisable and memory-efficient training scheme. We further introduce three new metrics for quantitative evaluation of the explanations, together with a qualitative human evaluation. Extensive experiments demonstrate that Power-Link outperforms the SOTA baselines in interpretability, efficiency, and scalability.", "field": "cs", "label": 0}
{"text": "Title: On the behavior of adjoint ideals under pure morphisms\nAbstract: We characterize adjoint ideal sheaves via ultraproducts and, utilizing this characterization, study their behavior under pure morphisms. In particular, given a pure morphism $f:Y \\to X$ between normal quasi-projective complex varieties, a reduced divisor $D$ and an effective $\\mathbb{Q}$-Weil divisor $\\Gamma$ on $X$ without common components, we have the following result: if the cycle-theoretic pullback $E:=f^{\\natural}D$ is reduced and $(Y, E+f^*\\Gamma)$ is of plt type along $E$, then $(X, D+\\Gamma)$ is of plt type along $D$. This provides an affirmative answer to a question posed by Z. Zhuang.", "field": "math", "label": 0}
{"text": "Title: Radar-Camera Pixel Depth Association for Depth Completion\nAbstract: While radar and video data can be readily fused at the detection level, fusing them at the pixel level is potentially more beneficial. This is also more challenging in part due to the sparsity of radar, but also because automotive radar beams are much wider than a typical pixel combined with a large baseline between camera and radar, which results in poor association between radar pixels and color pixel. A consequence is that depth completion methods designed for LiDAR and video fare poorly for radar and video. Here we propose a radar-to-pixel association stage which learns a mapping from radar returns to pixels. This mapping also serves to densify radar returns. Using this as a first stage, followed by a more traditional depth completion method, we are able to achieve image-guided depth completion with radar and video. We demonstrate performance superior to camera and radar alone on the nuScenes dataset. Our source code is available at https://github.com/longyunf/rc-pda.", "field": "cs", "label": 1}
{"text": "Title: Rectilinear Shortest Paths Among Transient Obstacles\nAbstract: This paper presents an optimal $\\Theta(n \\log n)$ algorithm for determining time-minimal rectilinear paths among $n$ transient rectilinear obstacles. An obstacle is transient if it exists in the scene only for a specific time interval, i.e., it appears and then disappears at specific times. Given a point robot moving with bounded speed among transient rectilinear obstacles and a pair of points $s$, $d$, we determine a time-minimal, obstacle-avoiding path from $s$ to $d$. The main challenge in solving this problem arises as the robot may be required to wait for an obstacle to disappear, before it can continue moving toward the destination. Our algorithm builds on the continuous Dijkstra paradigm, which simulates propagating a wavefront from the source point. We also solve a query version of this problem. For this, we build a planar subdivision with respect to a fixed source point, so that minimum arrival time to any query point can be reported in $O(\\log n)$ time, using point location for the query point in this subdivision.", "field": "cs", "label": 1}
{"text": "Title: LSTMs Exploit Linguistic Attributes of Data\nAbstract: While recurrent neural networks have found success in a variety of natural language processing applications, they are general models of sequential data. We investigate how the properties of natural language data affect an LSTM's ability to learn a nonlinguistic task: recalling elements from its input. We find that models trained on natural language data are able to recall tokens from much longer sequences than models trained on non-language sequential data. Furthermore, we show that the LSTM learns to solve the memorization task by explicitly using a subset of its neurons to count timesteps in the input. We hypothesize that the patterns and structure in natural language data enable LSTMs to learn by providing approximate ways of reducing loss, but understanding the effect of different training data on the learnability of LSTMs remains an open question.", "field": "cs", "label": 1}
{"text": "Title: Signed Latent Factors for Spamming Activity Detection\nAbstract: Due to the increasing trend of performing spamming activities (e.g., Web spam, deceptive reviews, fake followers, etc.) on various online platforms to gain undeserved benefits, spam detection has emerged as a hot research issue. Previous attempts to combat spam mainly employ features related to metadata, user behaviors, or relational ties. These works have made considerable progress in understanding and filtering spamming campaigns. However, this problem remains far from fully solved. Almost all the proposed features focus on a limited number of observed attributes or explainable phenomena, making it difficult for existing methods to achieve further improvement. To broaden the vision about solving the spam problem and address long-standing challenges (class imbalance and graph incompleteness) in the spam detection area, we propose a new attempt of utilizing signed latent factors to filter fraudulent activities. The spam-contaminated relational datasets of multiple online applications in this scenario are interpreted by the unified signed network. Two competitive and highly dissimilar algorithms of latent factors mining (LFM) models are designed based on multi-relational likelihoods estimation (LFM-MRLE) and signed pairwise ranking (LFM-SPR), respectively. We then explore how to apply the mined latent factors to spam detection tasks. Experiments on real-world datasets of different kinds of Web applications (social media and Web forum) indicate that LFM models outperform state-of-the-art baselines in detecting spamming activities. By specifically manipulating experimental data, the effectiveness of our methods in dealing with incomplete and imbalanced challenges is valida", "field": "cs", "label": 1}
{"text": "Title: Coalition Formation Games for Collaborative Spectrum Sensing\nAbstract: Collaborative Spectrum Sensing (CSS) between secondary users (SUs) in cognitive networks exhibits an inherent tradeoff between minimizing the probability of missing the detection of the primary user (PU) and maintaining a reasonable false alarm probability (e.g., for maintaining a good spectrum utilization). In this paper, we study the impact of this tradeoff on the network structure and the cooperative incentives of the SUs that seek to cooperate for improving their detection performance. We model the CSS problem as a non-transferable coalitional game, and we propose distributed algorithms for coalition formation. First, we construct a distributed coalition formation (CF) algorithm that allows the SUs to self-organize into disjoint coalitions while accounting for the CSS tradeoff. Then, the CF algorithm is complemented with a coalitional voting game for enabling distributed coalition formation with detection probability guarantees (CF-PD) when required by the PU. The CF-PD algorithm allows the SUs to form minimal winning coalitions (MWCs), i.e., coalitions that achieve the target detection probability with minimal costs. For both algorithms, we study and prove various properties pertaining to network structure, adaptation to mobility and stability. Simulation results show that CF reduces the average probability of miss per SU up to 88.45% relative to the non-cooperative case, while maintaining a desired false alarm. For CF-PD, the results show that up to 87.25% of the SUs achieve the required detection probability through MWC", "field": "cs", "label": 1}
{"text": "Title: A profile decomposition for the limiting Sobolev embedding\nAbstract: For many known non-compact embeddings of two Banach spaces $E\\hookrightarrow F$, every bounded sequence in $E$ has a subsequence that takes form of a profile decomposition - a sum of clearly structured terms with asymptotically disjoint supports plus a remainder that vanishes in the norm of $F$. In this note we construct a profile decomposition for arbitrary sequences in the Sobolev space $H^{1,2}(M)$ of a compact Riemannian manifold, relative to the embedding of $H^{1,2}(M)$ into $L^{2^*}(M)$, generalizing the well-known profile decomposition of Struwe ([Proposition 2.1]{Struwe}) to the case of arbitrary bounded sequences.", "field": "math", "label": 1}
{"text": "Title: VGA: Vision and Graph Fused Attention Network for Rumor Detection\nAbstract: With the development of social media, rumors have been spread broadly on social media platforms, causing great harm to society. Beside textual information, many rumors also use manipulated images or conceal textual information within images to deceive people and avoid being detected, making multimodal rumor detection be a critical problem. The majority of multimodal rumor detection methods mainly concentrate on extracting features of source claims and their corresponding images, while ignoring the comments of rumors and their propagation structures. These comments and structures imply the wisdom of crowds and are proved to be crucial to debunk rumors. Moreover, these methods usually only extract visual features in a basic manner, seldom consider tampering or textual information in images. Therefore, in this study, we propose a novel Vision and Graph Fused Attention Network (VGA) for rumor detection to utilize propagation structures among posts so as to obtain the crowd opinions and further explore visual tampering features, as well as the textual information hidden in images. We conduct extensive experiments on three datasets, demonstrating that VGA can effectively detect multimodal rumors and outperform state-of-the-art methods significantly.", "field": "cs", "label": 0}
{"text": "Title: Dense triangle-free $(n, d, λ)$-graphs for all orders\nAbstract: In 1994, Alon construct a triangle-free $(n,d,\\lambda)$-graph with $d = \\Omega(n^{2/3})$ and $\\lambda = O(d^{1/2})$ for an exponentially increasing sequence of integers $n$. Using his ingenious construction, we deduce that there exist triangle-free $(n,d,\\lambda)$-graphs with $d = \\Omega(n^{2/3})$ and $\\lambda = O( (d \\log n)^{1/2} )$ for all sufficiently large $n$.", "field": "math", "label": 0}
{"text": "Title: A Remark on Nonlinear Dirac Equations\nAbstract: For a $n$-dimensional spin manifold $M$ with a fixed spin structure and a spinor bundle $\\Sigma M$, we prove an $\\epsilon$-regularity theorem for weak solutions to the nonlinear Dirac equation of cubic nonlinearity. This, in particular, answers a regularity question raised by Chen-Jost-Wang when $n=2$.", "field": "math", "label": 1}
{"text": "Title: Ballistic random walks in random environment as rough paths: convergence and area anomaly\nAbstract: Annealed functional CLT in the rough path topology is proved for the standard class of ballistic random walks in random environment. Moreover, the `area anomaly', i.e. a deterministic linear correction for the second level iterated integral of the rescaled path, is identified in terms of a stochastic area on a regeneration interval. The main theorem is formulated in more general settings, namely for any discrete process with uniformly bounded increments which admits a regeneration structure where the regeneration times have finite moments. Here the largest finite moment translates into the degree of regularity of the rough path topology. In particular, the convergence holds in the $\\alpha$-H\\\"older rough path topology for all $\\alpha<1/2$ whenever all moments are finite, which is the case for the class of ballistic random walks in random environment. The latter may be compared to a special class of random walks in Dirichlet environments for which the regularity $\\alpha<1/2$ is bounded away from $1/2$, explicitly in terms of the corresponding trap parameter.", "field": "math", "label": 1}
{"text": "Title: The weak categorical quiver minor theorem and its applications: matchings, multipaths, and magnitude cohomology\nAbstract: Building upon previous works of Proudfoot and Ramos, and using the categorical framework of Sam and Snowden, we extend the weak categorical minor theorem from undirected graphs to quivers. As case of study, we investigate the consequences on the homology of multipath complexes; eg. on its torsion. Further, we prove a comparison result: we show that, when restricted to directed graphs without oriented cycles, multipath complexes and matching complexes yield functors which commute up to a blow-up operation on directed graphs. We use this fact to compute the homotopy type of matching complexes for a certain class of bipartite graphs also known as half-graphs or ladders. We complement the work with a study of the (representation) category of cones, and with analysing related consequences on magnitude cohomology of quivers.", "field": "math", "label": 0}
{"text": "Title: From a Kac algebra subfactor to Drinfeld double\nAbstract: Given a finite-index and finite-depth subfactor, we define the notion of \\textit{quantum double inclusion} - a certain unital inclusion of von Neumann algebras constructed from the given subfactor - which is closely related to that of Ocneanu's asymptotic inclusion. We show that the quantum double inclusion when applied to the Kac algebra subfactor $R^H \\subset R$ produces Drinfeld double of $H$ where $H$ is a finite-dimensional Kac algebra acting outerly on the hyperfinite $II_1$ factor $R$ and $R^H$ denotes the fixed-point subalgebra. More precisely, quantum double inclusion of $R^H \\subset R$ is isomorphic to $R \\subset R \\rtimes D(H)^{cop}$ for some outer action of $D(H)^{cop}$ on $R$ where $D(H)$ denotes the Drinfeld double of $H$.", "field": "math", "label": 1}
{"text": "Title: Convex Clustering via Optimal Mass Transport\nAbstract: We consider approximating distributions within the framework of optimal mass transport and specialize to the problem of clustering data sets. Distances between distributions are measured in the Wasserstein metric. The main problem we consider is that of approximating sample distributions by ones with sparse support. This provides a new viewpoint to clustering. We propose different relaxations of a cardinality function which penalizes the size of the support set. We establish that a certain relaxation provides the tightest convex lower approximation to the cardinality penalty. We compare the performance of alternative relaxations on a numerical study on clustering.", "field": "cs", "label": 1}
{"text": "Title: First order sensitivity analysis of symplectic eigenvalues\nAbstract: For every $2n \\times 2n$ positive definite matrix $A$ there are $n$ positive numbers $d_1(A) \\leq \\ldots \\leq d_n(A)$ associated with $A$ called the symplectic eigenvalues of $A.$ It is known that $d_m$ are continuous functions of $A$ but are not differentiable in general. In this paper, we show that the directional derivative of $d_m$ exists and derive its expression. We also discuss various subdifferential properties of $d_m$ such as Clarke and Michel-Penot subdifferentials.", "field": "math", "label": 1}
{"text": "Title: The Molecular Characterizations of Variable Triebel-Lizorkin Spaces Associated with the Hermite Operator and Its Applications\nAbstract: In this article, we introduce inhomogeneous variable Triebel-Lizorkin spaces, $F_{p(\\cdot),q(\\cdot)}^{\\alpha(\\cdot),H}(\\mathbb R^n)$, associated with the Hermite operator $H:=-\\Delta+|x|^2$, where $\\Delta$ is the Laplace operator on $\\mathbb R^n$, and mainly establish the molecular characterization of this space. As applications, we obtain some regularity results to fractional Hermite equations $$(-\\Delta+|x|^2)^\\sigma u=f,\\quad (-\\Delta+|x|^2+I)^\\sigma u=f,$$ and the boundedness of spectral multiplier associated to the operator $H$ on the variable Triebel-Lizorkin space $F_{p(\\cdot),q(\\cdot)}^{\\alpha(\\cdot),H}(\\mathbb R^n)$. Furthermore, we explain the relationship between $F_{p(\\cdot),q(\\cdot)}^{\\alpha(\\cdot),H}(\\mathbb R^n)$ and the variable Triebel-Lizorkin spaces $F_{p(\\cdot),q(\\cdot)}^{\\alpha(\\cdot)}(\\mathbb R^n)$ (introduced in Diening t al. J. Funct. Anal. 256(2009), 1731-1768.) via the atomic decomposition.", "field": "math", "label": 0}
{"text": "Title: Rough metrics on manifolds and quadratic estimates\nAbstract: We study the persistence of quadratic estimates related to the Kato square root problem across a change of metric on smooth manifolds by defining a class of Riemannian-like metrics that are permitted to be of low regularity and degenerate on sets of measure zero. We also demonstrate how to transmit quadratic estimates between manifolds which are homeomorphic and locally bi-Lipschitz. As a consequence, we demonstrate the invariance of the Kato square root problem under Lipschitz transformations of the space and obtain solutions to this problem on functions and forms on compact manifolds with a continuous metric. Furthermore, we show that a lower bound on the injectivity radius is not a necessary condition to solve the Kato square root problem.", "field": "math", "label": 1}
{"text": "Title: Nonconvex bundle method with application to a delamination problem\nAbstract: Delamination is a typical failure mode of composite materials caused by weak bonding. It arises when a crack initiates and propagates under a destructive loading. Given the physical law characterizing the properties of the interlayer adhesive between the bonded bodies, we consider the problem of computing the propagation of the crack front and the stress field along the contact boundary. This leads to a hemivariational inequality, which after discretization by finite elements we solve by a nonconvex bundle method, where upper-$C^1$ criteria have to be minimized. As this is in contrast with other classes of mechanical problems with non-monotone friction laws and in other applied fields, where criteria are typically lower-$C^1$, we propose a bundle method suited for both types of nonsmoothness. We prove its global convergence in the sense of subsequences and test it on a typical delamination problem of material sciences.", "field": "math", "label": 1}
{"text": "Title: Comptage des quiddit{é}s sur les corps finis et sur quelques anneaux $\\mathbb{Z}/N\\mathbb{Z}$\nAbstract: The $\\lambda$-quiddities of size $n$ are $n$-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter friezes. These can be considered on various sets with very different structures from one set to another. The main objective of this text is to obtain explicit formulas giving the number of $\\lambda$-quiddities of size $n$ over finite fields and over the rings $\\mathbb{Z}/N\\mathbb{Z}$ with $N=4m$ and $m$ square free. We will also give some elements about the asymptotic behavior of the number of $\\lambda$-quiddities verifying an irreducibility condition over $\\mathbb{Z}/N\\mathbb{Z}$ when $N$ goes to the infinity.", "field": "math", "label": 0}
{"text": "Title: Euclidean algorithms are Gaussian over imaginary quadratic fields\nAbstract: The distributional analysis of Euclidean algorithms was carried out by Baladi and Vall\\'{e}e. They showed the asymptotic normality of the number of division steps and associated costs in the Euclidean algorithm as a random variable on the set of rational numbers with bounded denominator based on the transfer operator methods. We extend their result to the Euclidean algorithm over appropriate imaginary quadratic fields by studying dynamics of the nearest integer complex continued fraction map, which is piecewise analytic and expanding but not a full branch map. By observing a finite Markov partition with a regular CW-structure, which enables us to associate the transfer operator acting on a direct sum of spaces of $C^1$-functions, we obtain the limit Gaussian distribution as well as residual equidistribution.", "field": "math", "label": 0}
{"text": "Title: On grids in point-line arrangements in the plane\nAbstract: The famous Szemer\\'{e}di-Trotter theorem states that any arrangement of $n$ points and $n$ lines in the plane determines $O(n^{4/3})$ incidences, and this bound is tight. In this paper, we prove the following Tur\\'an-type result for point-line incidence. Let $\\mathcal{L}_1$ and $\\mathcal{L}_2$ be two sets of $t$ lines in the plane and let $P=\\{\\ell_1 \\cap \\ell_2 : \\ell_1 \\in \\mathcal{L}_1, \\ell_2 \\in \\mathcal{L}_2\\}$ be the set of intersection points between $\\mathcal{L}_1$ and $\\mathcal{L}_2$. We say that $(P, \\mathcal{L}_1 \\cup \\mathcal{L}_2)$ forms a \\emph{natural $t\\times t$ grid} if $|P| =t^2$, and $conv(P)$ does not contain the intersection point of some two lines in $\\mathcal{L}_i,$ for $i = 1,2.$ For fixed $t > 1$, we show that any arrangement of $n$ points and $n$ lines in the plane that does not contain a natural $t\\times t$ grid determines $O(n^{\\frac{4}{3}- \\varepsilon})$ incidences, where $\\varepsilon = \\varepsilon(t)$. We also provide a construction of $n$ points and $n$ lines in the plane that does not contain a natural $2 \\times 2$ grid and determines at least $\\Omega({n^{1+\\frac{1}{14}}})$ incidences.", "field": "math", "label": 1}
{"text": "Title: The line bundles on the moduli stack of principal bundles on families of curves\nAbstract: Given a connected reductive algebraic group G, we investigate the Picard group of the moduli stack of principal G-bundles over an arbitrary family of smooth curves.", "field": "math", "label": 0}
{"text": "Title: Optimal Economic Operation of Liquid Petroleum Products Pipeline Systems\nAbstract: The majority of overland transport needs for crude petroleum and refined petroleum products are met using pipelines. Numerous studies have developed optimization methods for design of these systems in order to minimize construction costs while meeting capacity requirements. Here, we formulate problems to optimize the operations of existing single liquid commodity pipeline systems subject to physical flow and pump engineering constraints. The objectives are to maximize the economic value created for users of the system and to minimize operating costs. We present a general computational method for this class of continuous, non-convex nonlinear programs, and examine the use of pump operating settings and flow allocations as decision variables. The approach is applied to compute optimal operating regimes and perform engineering economic sensitivity analyses for a case study of a crude oil pipeline developed using publicly available data.", "field": "math", "label": 1}
{"text": "Title: Optimal Synthesis of Finite State Machines with Universal Gates using Evolutionary Algorithm\nAbstract: This work presents an optimization method for the synthesis of finite state machines. The focus is on the reduction in the on-chip area and the cost of the circuit. A list of finite state machines from MCNC91 benchmark circuits have been evolved using Cartesian Genetic Programming. On the average, almost 30% of reduction in the total number of gates has been achieved. The effects of some parameters on the evolutionary process have also been discussed in the paper.", "field": "cs", "label": 0}
{"text": "Title: How many digits are needed?\nAbstract: Let $X_1,X_2,...$ be the digits in the base-$q$ expansion of a random variable $X$ defined on $[0,1)$ where $q\\ge2$ is an integer. For $n=1,2,...$, we study the probability distribution $P_n$ of the (scaled) remainder $T^n(X)=\\sum_{k=n+1}^\\infty X_k q^{n-k}$: If $X$ has an absolutely continuous CDF then $P_n$ converges in the total variation metric to the Lebesgue measure $\\mu$ on the unit interval. Under weak smoothness conditions we establish first a coupling between $X$ and a non-negative integer valued random variable $N$ so that $T^N(X)$ follows $\\mu$ and is independent of $(X_1,...,X_N)$, and second exponentially fast convergence of $P_n$ and its PDF $f_n$. We discuss how many digits are needed and show examples of our results. The convergence results are extended to the case of a multivariate random variable defined on a unit cube.", "field": "math", "label": 0}
{"text": "Title: On the relations between Auerbach or almost Auberbach Markushevich systems and Schauder bases\nAbstract: We establish that the summability of the series $\\sum\\varepsilon_n$ is the necessary and sufficient criterion ensuring that every $(1+\\varepsilon_n)$ Markushevich basis in a separable Hilbert space is a Riesz basis. Further we show that if $n\\varepsilon_n\\to \\infty$, then in $\\ell_2$ there exists a $(1+\\varepsilon_n)$ Markushevich basis that under any permutation is non-equivalent to a Schauder basis. We extend this result to any separable Banach space. Finally we provide examples of Auerbach bases in 1-symmetric separable Banach spaces whose no permutations are equivalent to any Schauder basis or (depending on the space) any unconditional Schauder basis.", "field": "math", "label": 0}
{"text": "Title: Edge statistics for random band matrices\nAbstract: Consider Hermitian and symmetric random band matrices $H=(\\sigma_{xy}A_{xy})$ on the $d$-dimensional lattice $\\left(\\mathbb{Z}/{L\\mathbb{Z}}\\right)^d$, where $A_{xy}=\\overline{A_{yx}}$ are independent uniformly distributed random variables on $S^1$ or $\\{+1, -1\\}$, and the variance profile $\\sigma^{2}_{xy}$ is characterized by the bandwidth $W$ and $\\alpha$-stable density with $\\alpha\\in (0,2]$. We investigate local eigenvalue statistics at the spectral edge as $W\\to \\infty$ and observe the critical dimension $d_c=3\\alpha$ and the critical bandwidth $W_c=L^{(1-\\frac{d}{3\\alpha})_{+}}$, possibly with a $\\log L$ correction when $d=\\alpha$ or $2\\alpha$. In the Hermitian case, we establish that (i) when $d<2\\alpha$, GUE edge, interpolating, and Poisson statistics emerge in the supercritical ($W\\gg W_c$), critical ($W\\sim W_c$), and subcritical ($W\\ll W_c$) regimes, respectively; (ii) when $d\\ge 2\\alpha$, as long as $W\\ge L^{\\frac{1}{3}+\\epsilon}$ for a small constant $\\epsilon>0$, GUE edge universality holds. In the symmetric case, we also establish similar but subtle phenomena. In both $d=1$ and $\\alpha=2$, the subcritical and supercritical results have been proven by Sodin for the band model with a cutoff variance profile \\cite{sodin2010spectral}. Our proof builds upon Sodin's program and new techniques of taming the singularity of Feynman diagrams and graph integrals through a connection to the $\\phi^3$ model.", "field": "math", "label": 0}
{"text": "Title: HawkRover: An Autonomous mmWave Vehicular Communication Testbed with Multi-sensor Fusion and Deep Learning\nAbstract: Connected and automated vehicles (CAVs) have become a transformative technology that can change our daily life. Currently, millimeter-wave (mmWave) bands are identified as the promising CAV connectivity solution. While it can provide high data rate, their realization faces many challenges such as high attenuation during mmWave signal propagation and mobility management. Existing solution has to initiate pilot signal to measure channel information, then apply signal processing to calculate the best narrow beam towards the receiver end to guarantee sufficient signal power. This process takes significant overhead and time, hence not suitable for vehicles. In this study, we propose an autonomous and low-cost testbed to collect extensive co-located mmWave signal and other sensors data such as LiDAR (Light Detection and Ranging), cameras, ultrasonic, etc, traditionally for ``automated'', to facilitate mmWave vehicular communications. Intuitively, these sensors can build a 3D map around the vehicle and signal propagation path can be estimated, eliminating iterative the process via pilot signals. This multimodal data fusion, together with AI, is expected to bring significant advances in ``connected'' research.", "field": "cs", "label": 0}
{"text": "Title: On a conjecture of George Beck\nAbstract: In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts.", "field": "math", "label": 1}
{"text": "Title: Composition method for chromatic symmetric functions: Neat noncommutative analogs\nAbstract: This work is inspired by Shareshian and Wachs's exquisite formula for the chromatic symmetric function of paths. We develop a composition method to unearth neat noncommutative analogs of chromatic symmetric functions. A symmetric function is $e$-positive if and only if it has a $\\Lambda$-positive noncommutative analog. We bring to light short and sweet $\\Lambda$-positive noncommutative analogs for the chromatic symmetric functions of tadpoles and barbells, with cycles and lollipops as specifications. Using these elegant formulas and the composition method, we discover a new family of $e$-positive graphs and call them hats, which are the unicyclic graphs obtained by adding an edge to a path. A compact ribbon Schur analog for cycles is also obtained as a by-product.", "field": "math", "label": 0}
{"text": "Title: Trajectory-Oriented Policy Optimization with Sparse Rewards\nAbstract: Deep reinforcement learning (DRL) remains challenging in tasks with sparse rewards. These sparse rewards often only indicate whether the task is partially or fully completed, meaning that many exploration actions must be performed before the agent obtains useful feedback. Hence, most existing DRL algorithms fail to learn feasible policies within a reasonable time frame. To overcome this problem, we develop an approach that exploits offline demonstration trajectories for faster and more efficient online RL in sparse reward settings. Our key insight is that by regarding offline demonstration trajectories as guidance, instead of imitating them, our method learns a policy whose state-action visitation marginal distribution matches that of offline demonstrations. Specifically, we introduce a novel trajectory distance based on maximum mean discrepancy (MMD) and formulate policy optimization as a distance-constrained optimization problem. Then, we show that this distance-constrained optimization problem can be reduced into a policy-gradient algorithm with shaped rewards learned from offline demonstrations. The proposed algorithm is evaluated on extensive discrete and continuous control tasks with sparse and deceptive rewards. The experimental results indicate that our proposed algorithm is significantly better than the baseline methods regarding diverse exploration and learning the optimal policy.", "field": "cs", "label": 0}
{"text": "Title: Stable cohomology of congruence subgroups\nAbstract: We describe the $\\mathbb{F}_p$-cohomology of the congruence subgroups $SL_n(\\mathbb{Z}, p^m)$ in degrees $* < p$, for all large enough $n$, establishing a formula proposed by F. Calegari. Along the way, we also establish a formula for the stable cohomology of $SL_n(\\mathbb{Z}/p)$ with certain twisted coefficients.", "field": "math", "label": 1}
{"text": "Title: Introducing an experimental distortion-tolerant speech encryption scheme for secure voice communication\nAbstract: The current increasing need for privacy-preserving voice communications is leading to new ideas for securing voice transmission. This paper refers to a relatively new concept of sending encrypted speech as pseudo-speech in the audio domain over digital voice communication infrastructures, like 3G cellular network and VoIP. This work presents a novel distortion-tolerant speech encryption scheme for secure voice communications over voice channels that combines the robustness of analog speech scrambling and elevated security offered by digital ciphers like AES-CTR. The system scrambles vocal parameters of a speech signal (loudness, pitch, timbre) using distance-preserving pseudo-random translations and rotations on a hypersphere of parameters. Next, scrambled parameters are encoded to a pseudo-speech signal adapted to transmission over digital voice channels equipped with voice activity detection. Upon reception of this pseudo-speech signal, the legitimate receiver restores distorted copies of the initial vocal parameters. Despite some deciphering errors, an integrated neural-based vocoder based on the LPCNet architecture reconstructs an intelligible speech. The experimental implementation of this speech encryption scheme has been tested by simulations and sending an encrypted signal over FaceTime between two iPhones 6 connected to the same WiFi network. Moreover, speech excerpts restored from encrypted signals were evaluated by a speech quality assessment on a group of about 40 participants. The experiments demonstrated that the proposed scheme produces intelligible speech with a gracefully progressive quality degradation depending on the channel noise. Finally, the preliminary computational analysis suggested that the presented setting may operate on high-end portable devices in nearly real-time.", "field": "cs", "label": 1}
{"text": "Title: Kempe equivalence and quadratic toric rings\nAbstract: Perfectly contractile graphs form a typical class of perfect graphs. In particular, all $k$-colorings of a perfectly contractile graph are Kempe equivalent. Everett and Reed conjectured that a graph is perfectly contractile if and only if it contains no odd holes, no antiholes and no odd prisms. On the other hand the authors and Shibata conjectured that a perfect graph is perfectly contractile if and only if its toric ring, which is called the stable set ring, is quadratic. In the present paper, we characterize when the stable set ring of a (not necessarily perfect) graph is quadratic by using Kempe equivalence. As applications of this characterization, we can claim that if Everett and Reed conjecture is true, then the conjecture of the authors and Shibata is also true. Moreover, we can show that for several important classes of perfectly contractile graphs, the stable set rings are quadratic.", "field": "math", "label": 0}
{"text": "Title: Generalised Dirac-Schrödinger operators and the Callias Theorem\nAbstract: We consider generalised Dirac-Schr\\\"odinger operators, consisting of a self-adjoint elliptic first-order differential operator D with a skew-adjoint 'potential' given by a (suitable) family of unbounded operators on an auxiliary Hilbert module. The index of such an operator represents the pairing (Kasparov product) of the K-theory class of the potential with the K-homology class of D. Our main result in this paper is a generalisation of the Callias Theorem: the index of the Dirac-Schr\\\"odinger operator can be computed from its restriction to a hypersurface. Our theorem simultaneously generalises (and is inspired by) the well-known result that the spectral flow of a path of relatively compact perturbations depends only on the endpoints.", "field": "math", "label": 0}
{"text": "Title: Hyperbolic Graph Diffusion Model\nAbstract: Diffusion generative models (DMs) have achieved promising results in image and graph generation. However, real-world graphs, such as social networks, molecular graphs, and traffic graphs, generally share non-Euclidean topologies and hidden hierarchies. For example, the degree distributions of graphs are mostly power-law distributions. The current latent diffusion model embeds the hierarchical data in a Euclidean space, which leads to distortions and interferes with modeling the distribution. Instead, hyperbolic space has been found to be more suitable for capturing complex hierarchical structures due to its exponential growth property. In order to simultaneously utilize the data generation capabilities of diffusion models and the ability of hyperbolic embeddings to extract latent hierarchical distributions, we propose a novel graph generation method called, Hyperbolic Graph Diffusion Model (HGDM), which consists of an auto-encoder to encode nodes into successive hyperbolic embeddings, and a DM that operates in the hyperbolic latent space. HGDM captures the crucial graph structure distributions by constructing a hyperbolic potential node space that incorporates edge information. Extensive experiments show that HGDM achieves better performance in generic graph and molecule generation benchmarks, with a $48\\%$ improvement in the quality of graph generation with highly hierarchical structures.", "field": "cs", "label": 0}
{"text": "Title: Semifinite harmonic functions on branching graphs\nAbstract: We study semifinite harmonic functions on arbitrary branching graphs. We give a detailed exposition of an algebraic method which allows one to classify semifinite indecomposable harmonic functions on some multiplicative branching graphs. This method was proposed by A. Wassermann in terms of operator algebras, while we rephrase, clarify, and simplify the main arguments, working only with combinatorial objects. This work was inspired by the theory of traceable factor representations of the infinite symmetric group $S(\\infty)$.", "field": "math", "label": 1}
{"text": "Title: Higher convexity and iterated sum sets\nAbstract: Let $f$ be a smooth real function with strictly monotone first $k$ derivatives. We show that for a finite set $A$, with $|A+A|\\leq K|A|$, $|2^kf(A)-(2^k-1)f(A)|\\gg_k |A|^{k+1-o(1)}/K^{O_k(1)}$. We deduce several new sum-product type implications, e.g. that $A+A$ being small implies unbounded growth for a many enough times iterated product set $A \\cdots A$.", "field": "math", "label": 1}
{"text": "Title: Frequency-Adaptive Pan-Sharpening with Mixture of Experts\nAbstract: Pan-sharpening involves reconstructing missing high-frequency information in multi-spectral images with low spatial resolution, using a higher-resolution panchromatic image as guidance. Although the inborn connection with frequency domain, existing pan-sharpening research has not almost investigated the potential solution upon frequency domain. To this end, we propose a novel Frequency Adaptive Mixture of Experts (FAME) learning framework for pan-sharpening, which consists of three key components: the Adaptive Frequency Separation Prediction Module, the Sub-Frequency Learning Expert Module, and the Expert Mixture Module. In detail, the first leverages the discrete cosine transform to perform frequency separation by predicting the frequency mask. On the basis of generated mask, the second with low-frequency MOE and high-frequency MOE takes account for enabling the effective low-frequency and high-frequency information reconstruction. Followed by, the final fusion module dynamically weights high-frequency and low-frequency MOE knowledge to adapt to remote sensing images with significant content variations. Quantitative and qualitative experiments over multiple datasets demonstrate that our method performs the best against other state-of-the-art ones and comprises a strong generalization ability for real-world scenes. Code will be made publicly at \\url{https://github.com/alexhe101/FAME-Net}.", "field": "cs", "label": 0}
{"text": "Title: Stability and instability of Kelvin waves\nAbstract: The $m$-waves of Kelvin are uniformly rotating patch solutions of the 2D Euler equations with $m$-fold rotational symmetry for $m\\geq 2$. For Kelvin waves sufficiently close to the disc, we prove a nonlinear stability result up to an arbitrarily long time in the $L^1$ norm of the vorticity, for $m$-fold symmetric perturbations. To obtain this result, we first prove that the Kelvin wave is a strict local maximizer of the energy functional in some admissible class of patches, which had been claimed by Wan in 1986. This gives an orbital stability result with a support condition on the evolution of perturbations, but using a Lagrangian bootstrap argument which traces the particle trajectories of the perturbation, we are able to drop the condition on the evolution. Based on this unconditional stability result, we establish that long time filamentation, or formation of long arms, occurs near the Kelvin waves, which have been observed in various numerical simulations. Additionally, we discuss stability of annular patches in the same variational framework.", "field": "math", "label": 1}
{"text": "Title: Stability of strong viscous shock wave under periodic perturbation for 1-D isentropic Navier-Stokes system in the half space\nAbstract: In this paper, a viscous shock wave under space-periodic perturbation of 1-D isentropic Navier-Stokes system in the half space is investigated. It is shown that if the initial periodic perturbation around the viscous shock wave is small, then the solution time asymptotically tends to a viscous shock wave with a shift partially determined by the periodic oscillations. Moreover, the strength of {the} shock wave could be arbitrarily large. This result essentially improves the previous work \" A. Matsumura, M. Mei, Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary. Arch. Ration. Mech. Anal. 146 (1999), no. 1, 1-22.\" where the strength of shock wave is sufficiently small and the initial periodic oscillations vanish.", "field": "math", "label": 0}
{"text": "Title: A bridge between the circular and linear normal distributions\nAbstract: In this short note, we present a refined approximation for the log-ratio of the density of the von Mises$(\\mu,\\kappa)$ distribution (also called the circular normal distribution) to the standard (linear) normal distribution when the concentration parameter \\k{appa} is large. Our work complements the one of Hill (1976), who obtained a very similar approximation along with quantile couplings, using earlier approximations by Hill & Davis (1968) of Cornish-Fisher type. One motivation for this note is to highlight the connection between the circular and linear normal distributions through their circular variance and (linear) variance.", "field": "math", "label": 0}
{"text": "Title: Linear subspaces of the intersection of two quadrics via Kuznetsov component\nAbstract: Let $Q_i(i=1,2)$ be $2g$ dimensional quadrics in $\\mathbb{P}^{2g+1}$ and let $Y$ be the smooth intersection $Q_1\\cap Q_2$. We associate the linear subspace in $Y$ with vector bundles on the hyperelliptic curve $C$ of genus $g$ by the left adjoint functor of $\\Phi:D^b(C)\\rightarrow D^b(Y)$. As an application, we give a different proof of the classification of line bundles and stable bundles of rank $2$ on hyperelliptic curves given by Desale and Ramanan. When $g=3$, we show that the projection functor induces a closed embedding $\\alpha:Y\\rightarrow SU^s_C(4,h)$ into the moduli space of stable bundles on $C$ of rank $4$ of fixed determinant.", "field": "math", "label": 0}
{"text": "Title: Reciprocity formulas for certain generalized Hardy sums\nAbstract: In this paper, we establish some reciprocity formulas for certain generalized Hardy sums by using the Fourier series technique and some properties of the periodic zeta function and Lerch zeta function. It turns out that one of Hardy's reciprocity theorems is deduced as a special case.", "field": "math", "label": 0}
{"text": "Title: A fractional conformal curvature flow on the unit sphere\nAbstract: We study a fractional conformal curvature flow on the standard unit sphere and prove a perturbation result of the fractional Nirenberg problem with fractional exponent $\\sigma \\in (1/2,1)$. This extends the result of Chen-Xu (Invent. Math. 187, no. 2, 395-506, 2012) for the scalar curvature flow on the standard unit sphere.", "field": "math", "label": 1}
{"text": "Title: Predicting parametric spatiotemporal dynamics by multi-resolution PDE structure-preserved deep learning\nAbstract: Pure data-driven deep learning models suffer from high training costs, error accumulation, and poor generalizability when predicting complex physical processes. A more promising way is to leverage our prior physics knowledge in scientific deep learning models, known as physics-informed deep learning (PiDL). In most PiDL frameworks, the physics prior is utilized to regularize neural network training by incorporating governing equations into the loss function. The resulting physical constraint, imposed in a soft manner, relies heavily on a proper setting of hyperparameters that weigh each loss term. To this end, we propose a new direction to leverage physics prior knowledge by ``baking'' the mathematical structure of governing equations into the neural network architecture, namely PDE-preserved neural network (PPNN). The discretized PDE is preserved in PPNN as convolutional residual networks formulated in a multi-resolution setting. This physics-inspired learning architecture endows PPNN with excellent generalizability and long-term prediction accuracy compared to the state-of-the-art black-box baselines. The effectiveness and merit of the proposed methods have been demonstrated over a handful of spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers', and Navier-Stokes equations.", "field": "cs", "label": 1}
{"text": "Title: Two dimensional gravity waves at low regularity II: Global solutions\nAbstract: This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such solutions have been proved to exist earlier in [15, 7, 10, 12] in much higher regularity. Our goal in this paper is to improve these results and prove global well-posedness under minimal regularity and decay assumptions for the initial data. One key ingredient here is represented by the balanced cubic estimates in our first paper. Another is the nonlinear vector field Sobolev inequalities, an idea first introduced by the last two authors in the context of the Benjamin-Ono equations [14].", "field": "math", "label": 1}
{"text": "Title: Analyticity of Entropy Rate of Hidden Markov Chains\nAbstract: We prove that under mild positivity assumptions the entropy rate of a hidden Markov chain varies analytically as a function of the underlying Markov chain parameters. A general principle to determine the domain of analyticity is stated. An example is given to estimate the radius of convergence for the entropy rate. We then show that the positivity assumptions can be relaxed, and examples are given for the relaxed conditions. We study a special class of hidden Markov chains in more detail: binary hidden Markov chains with an unambiguous symbol, and we give necessary and sufficient conditions for analyticity of the entropy rate for this case. Finally, we show that under the positivity assumptions the hidden Markov chain {\\em itself} varies analytically, in a strong sense, as a function of the underlying Markov chain parameters.", "field": "math", "label": 1}
{"text": "Title: On the non-transverse homoclinic channel of a center manifold\nAbstract: We consider a scenario when a stable and unstable manifolds of compact center manifold of a saddle-center coincide. The normal form of the ODE governing the system near the center manifold is derived and so is the normal form of the return map to the neighbourhood of the center manifold. The limit dynamics of the return map is investigated by showing that it might take the form of a Henon-like map possessing a Lorenz-like attractor or satisfy 'cone-field condition' resulting in partial hyperbolicity. We consider also motivating example from game theory.", "field": "math", "label": 1}
{"text": "Title: On the Lebesgue measure of the Feigenbaum Julia set\nAbstract: We show that the Julia set of the Feigenbaum polynomial has Hausdorff dimension less than~2 (and consequently it has zero Lebesgue measure). This solves a long-standing open question.", "field": "math", "label": 1}
{"text": "Title: Bounded diameter tree-decompositions\nAbstract: When does a graph admit a tree-decomposition in which every bag has small diameter? For finite graphs, this is a property of interest in algorithmic graph theory, where it is called having bounded ``tree-length''. We will show that this is equivalent to being ``boundedly quasi-isometric to a tree'', which for infinite graphs is a much-studied property from metric geometry. One object of this paper is to tie these two areas together. We will prove that there is a tree-decomposition in which each bag has small diameter, if and only if there is a map $\\phi$ from $V(G)$ into the vertex set of a tree $T$, such that for all $u,v\\in V(G)$, the distances $d_G(u,v), d_T(\\phi(u),\\phi(v))$ differ by at most a constant. A ``geodesic loaded cycle'' in $G$ is a pair $(C,F)$, where $C$ is a cycle of $G$ and $F\\subseteq E(C)$, such that for every pair $u,v$ of vertices of $C$, one of the paths of $C$ between $u,v$ contains at most $d_G(u,v)$ $F$-edges, where $d_G(u,v)$ is the distance between $u,v$ in $G$. We will show that a graph $G$ admits a tree-decomposition in which every bag has small diameter, if and only if $|F|$ is small for every geodesic loaded cycle $(C,F)$. Our proof is an extension of an algorithm to approximate tree-length in finite graphs by Dourisboure and Gavoille. In metric geometry, there is a similar theorem that characterizes when a graph is quasi-isometric to a tree, ``Manning's bottleneck criterion''. The goal of this paper is to tie all these concepts together, and add a few more related ideas. For instance, we prove a conjecture of Rose McCarty, that $G$ admits a tree-decomposition in which every bag has small diameter, if and only if for all vertices $u,v,w$ of $G$, some ball of small radius meets every path joining two of $u,v,w$.", "field": "math", "label": 0}
{"text": "Title: A Survey of Protocol Fuzzing\nAbstract: Communication protocols form the bedrock of our interconnected world, yet vulnerabilities within their implementations pose significant security threats. Recent developments have seen a surge in fuzzing-based research dedicated to uncovering these vulnerabilities within protocol implementations. However, there still lacks a systematic overview of protocol fuzzing for answering the essential questions such as what the unique challenges are, how existing works solve them, etc. To bridge this gap, we conducted a comprehensive investigation of related works from both academia and industry. Our study includes a detailed summary of the specific challenges in protocol fuzzing, and provides a systematic categorization and overview of existing research efforts. Furthermore, we explore and discuss potential future research directions in protocol fuzzing. This survey serves as a foundational guideline for researchers and practitioners in the field.", "field": "cs", "label": 0}
{"text": "Title: Supervised learning on heterogeneous, attributed entities interacting over time\nAbstract: Most physical or social phenomena can be represented by ontologies where the constituent entities are interacting in various ways with each other and with their environment. Furthermore, those entities are likely heterogeneous and attributed with features that evolve dynamically in time as a response to their successive interactions. In order to apply machine learning on such entities, e.g., for classification purposes, one therefore needs to integrate the interactions into the feature engineering in a systematic way. This proposal shows how, to this end, the current state of graph machine learning remains inadequate and needs to be be augmented with a comprehensive feature engineering paradigm in space and time.", "field": "cs", "label": 1}
{"text": "Title: Fringe Analysis of Plane Trees Related to Cutting and Pruning\nAbstract: Rooted plane trees are reduced by four different operations on the fringe. The number of surviving nodes after reducing the tree repeatedly for a fixed number of times is asymptotically analyzed. The four different operations include cutting all or only the leftmost leaves or maximal paths. This generalizes the concept of pruning a tree. The results include exact expressions and asymptotic expansions for the expected value and the variance as well as central limit theorems.", "field": "math", "label": 1}
{"text": "Title: Weaving continuous generalized frames for operators\nAbstract: Recently, Bemrose et al. \\cite{BE} developed a theory of weaving frames, which was motivated by a problem regarding distributed signal processing. In this present article, we introduce the atomic $g$-system and we generalize some of the known results in continuous $L$-frames, weaving continuous and weaving continuous $ g$-frames, also we study weaving continuous $ L$-$g$-frames in Hilbert spaces. Moreover, we study the behaviour continuous $ L$-$g$-frames under some perturbations, and we show that approximate $L$-duals are stable under small perturbation and that it is possible to remove some elements of a woven continuous $ L$-$g$-frame and still have a woven continuous $ L$-$g$-frame.", "field": "math", "label": 0}
{"text": "Title: Economics Arena for Large Language Models\nAbstract: Large language models (LLMs) have been extensively used as the backbones for general-purpose agents, and some economics literature suggest that LLMs are capable of playing various types of economics games. Following these works, to overcome the limitation of evaluating LLMs using static benchmarks, we propose to explore competitive games as an evaluation for LLMs to incorporate multi-players and dynamicise the environment. By varying the game history revealed to LLMs-based players, we find that most of LLMs are rational in that they play strategies that can increase their payoffs, but not as rational as indicated by Nash Equilibria (NEs). Moreover, when game history are available, certain types of LLMs, such as GPT-4, can converge faster to the NE strategies, which suggests higher rationality level in comparison to other models. In the meantime, certain types of LLMs can win more often when game history are available, and we argue that the winning rate reflects the reasoning ability with respect to the strategies of other players. Throughout all our experiments, we observe that the ability to strictly follow the game rules described by natural languages also vary among the LLMs we tested. In this work, we provide an economics arena for the LLMs research community as a dynamic simulation to test the above-mentioned abilities of LLMs, i.e. rationality, strategic reasoning ability, and instruction-following capability.", "field": "cs", "label": 0}
{"text": "Title: Chebyshev Subdivision and Reduction Methods for Solving Multivariable Systems of Equations\nAbstract: We present a new algorithm for finding isolated zeros of a system of real-valued functions in a bounded interval in $\\mathbb{R}^n$. It uses the Chebyshev proxy method combined with a mixture of subdivision, reduction methods, and elimination checks that leverage special properties of Chebyshev polynomials. We prove the method has R-quadratic convergence locally near simple zeros of the system. We also analyze the temporal complexity and the numerical stability of the algorithm and provide numerical evidence in dimensions up to three that the method is both fast and accurate on a wide range of problems. The algorithm should also work well in higher dimensions. Our tests show that the algorithm outperforms other standard methods on this problem of finding all real zeros in a bounded domain. Our Python implementation of the algorithm is publicly available.", "field": "math", "label": 0}
{"text": "Title: High-Resolution Image Inpainting with Iterative Confidence Feedback and Guided Upsampling\nAbstract: Existing image inpainting methods often produce artifacts when dealing with large holes in real applications. To address this challenge, we propose an iterative inpainting method with a feedback mechanism. Specifically, we introduce a deep generative model which not only outputs an inpainting result but also a corresponding confidence map. Using this map as feedback, it progressively fills the hole by trusting only high-confidence pixels inside the hole at each iteration and focuses on the remaining pixels in the next iteration. As it reuses partial predictions from the previous iterations as known pixels, this process gradually improves the result. In addition, we propose a guided upsampling network to enable generation of high-resolution inpainting results. We achieve this by extending the Contextual Attention module to borrow high-resolution feature patches in the input image. Furthermore, to mimic real object removal scenarios, we collect a large object mask dataset and synthesize more realistic training data that better simulates user inputs. Experiments show that our method significantly outperforms existing methods in both quantitative and qualitative evaluations. More results and Web APP are available at https://zengxianyu.github.io/iic.", "field": "cs", "label": 1}
{"text": "Title: Privacy concerns from variances in spatial navigability in VR\nAbstract: Current Virtual Reality (VR) input devices make it possible to navigate a virtual environment and record immersive, personalized data regarding the user's movement and specific behavioral habits, which brings the question of the user's privacy concern to the forefront. In this article, the authors propose to investigate Machine Learning driven learning algorithms that try to learn with human users co-operatively and can be used to countermand existing privacy concerns in VR but could also be extended to Augmented Reality (AR) platforms.", "field": "cs", "label": 1}
{"text": "Title: Joint distribution in residue classes of families of polynomially-defined additive functions\nAbstract: Let $g_1, \\dots , g_M$ be additive functions for which there exist nonconstant polynomials $G_1, \\dots , G_M$ satisfying $g_i(p) = G_i(p)$ for all primes $p$ and all $i \\in \\{1, \\dots , M\\}$. Under fairly general and nearly optimal hypotheses, we show that the functions $g_1, \\dots , g_M$ are jointly equidistributed among the residue classes to moduli $q$ varying uniformly up to a fixed but arbitrary power of $\\log x$. Thus, we obtain analogues of the Siegel-Walfisz Theorem for primes in arithmetic progressions, but with primes replaced by values of such additive functions. Our results partially extend work of Delange from fixed moduli to varying moduli, and also generalize recent work done for a single additive function.", "field": "math", "label": 0}
{"text": "Title: Event-Object Reasoning with Curated Knowledge Bases: Deriving Missing Information\nAbstract: The broader goal of our research is to formulate answers to why and how questions with respect to knowledge bases, such as AURA. One issue we face when reasoning with many available knowledge bases is that at times needed information is missing. Examples of this include partially missing information about next sub-event, first sub-event, last sub-event, result of an event, input to an event, destination of an event, and raw material involved in an event. In many cases one can recover part of the missing knowledge through reasoning. In this paper we give a formal definition about how such missing information can be recovered and then give an ASP implementation of it. We then discuss the implication of this with respect to answering why and how questions.", "field": "cs", "label": 1}
{"text": "Title: Simplified Information Geometry Approach for Massive MIMO-OFDM Channel Estimation -- Part II: Convergence Analysis\nAbstract: In Part II of this two-part paper, we prove the convergence of the simplified information geometry approach (SIGA) proposed in Part I. For a general Bayesian inference problem, we first show that the iteration of the common second-order natural parameter (SONP) is separated from that of the common first-order natural parameter (FONP). Hence, the convergence of the common SONP can be checked independently. We show that with the initialization satisfying a specific but large range, the common SONP is convergent regardless of the value of the damping factor. For the common FONP, we establish a sufficient condition of its convergence and prove that the convergence of the common FONP relies on the spectral radius of a particular matrix related to the damping factor. We give the range of the damping factor that guarantees the convergence in the worst case. Further, we determine the range of the damping factor for massive MIMO-OFDM channel estimation by using the specific properties of the measurement matrices. Simulation results are provided to confirm the theoretical results.", "field": "cs", "label": 0}
{"text": "Title: Improving Approximate Optimal Transport Distances using Quantization\nAbstract: Optimal transport (OT) is a popular tool in machine learning to compare probability measures geometrically, but it comes with substantial computational burden. Linear programming algorithms for computing OT distances scale cubically in the size of the input, making OT impractical in the large-sample regime. We introduce a practical algorithm, which relies on a quantization step, to estimate OT distances between measures given cheap sample access. We also provide a variant of our algorithm to improve the performance of approximate solvers, focusing on those for entropy-regularized transport. We give theoretical guarantees on the benefits of this quantization step and display experiments showing that it behaves well in practice, providing a practical approximation algorithm that can be used as a drop-in replacement for existing OT estimators.", "field": "cs", "label": 1}
{"text": "Title: Do the Hodge spectra distinguish orbifolds from manifolds? Part 2\nAbstract: In \\cite{GGKM-SSS} we examined the relationship between the singular set of a compact Riemannian orbifold and the spectrum of the Hodge Laplacian on $p$-forms by computing the heat invariants associated to the $p$-spectrum. We showed that the heat invariants of the $0$-spectrum together with those of the $1$-spectrum for the corresponding Hodge Laplacians are sufficient to distinguish orbifolds from manifolds as long as the singular sets have codimension $\\le 3.$ This is enough to distinguish orbifolds from manifolds for dimension $\\le 3.$ Here we give both positive and negative inverse spectral results for the individual $p$-spectra considered separately. For example, we give conditions on the codimension of the singular set which guarantee that the volume of the singular set is determined, and in many cases we show by providing counterexamples that the conditions are sharp.", "field": "math", "label": 0}
{"text": "Title: Looking forwards and backwards: dynamics and genealogies of locally regulated populations\nAbstract: We introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial position and local population density, defined via the convolution of the point measure with a nonnegative kernel. We pass to three different scaling limits: an interacting superprocess, a nonlocal partial differential equation (PDE), and a classical PDE. The classical PDE is obtained both by first scaling time and population size to pass to the nonlocal PDE, and then scaling the kernel that determines local population density; and also (when the limit is a reaction-diffusion equation) by simultaneously scaling the kernel width, timescale and population size in our individual based model. A novelty of our model is that we explicitly model a juvenile phase: offspring are thrown off in a Gaussian distribution around the location of the parent, and reach (instant) maturity with a probability that can depend on the population density at the location at which they land. Although we only record mature individuals, a trace of this two-step description remains in our population models, resulting in novel limits governed by a nonlinear diffusion. Using a lookdown representation, we retain information about genealogies and, in the case of deterministic limiting models, use this to deduce the backwards in time motion of the ancestral lineage of a sampled individual. We observe that knowing the history of the population density is not enough to determine the motion of ancestral lineages in our model. We also investigate the behaviour of lineages for three different deterministic models of a population expanding its range as a travelling wave: the Fisher-KPP equation, the Allen-Cahn equation, and a porous medium equation with logistic growth.", "field": "math", "label": 0}
{"text": "Title: From Bi-immunity to Absolute Undecidability\nAbstract: An infinite binary sequence A is absolutely undecidable if it is impossible to compute A on a set of positions of positive upper density. Absolute undecidability is a weakening of bi-immunity. Downey, Jockusch and Schupp asked whether, unlike the case for bi-immunity, there is an absolutely undecidable set in every non-zero Turing degree. We provide a positive answer to this question by applying techniques from coding theory. We show how to use Walsh-Hadamard codes to build a truth-table functional which maps any sequence A to a sequence B, such that given any restriction of B to a set of positive upper density, one can recover A. This implies that if A is non-computable, then B is absolutely undecidable. Using a forcing construction, we show that this result cannot be strengthened in any significant fashion.", "field": "math", "label": 1}
{"text": "Title: Stress and Adaptation: Applying Anna Karenina Principle in Deep Learning for Image Classification\nAbstract: Image classification with deep neural networks has reached state-of-art with high accuracy. This success is attributed to good internal representation features that bypasses the difficulties of the non-convex optimization problems. We have little understanding of these internal representations, let alone quantifying them. Recent research efforts have focused on alternative theories and explanations of the generalizability of these deep networks. We propose the alternative perturbation of deep models during their training induces changes that lead to transitions to different families. The result is an Anna Karenina Principle AKP for deep learning, in which less generalizable models unhappy families vary more in their representation than more generalizable models happy families paralleling Leo Tolstoy dictum that all happy families look alike, each unhappy family is unhappy in its own way. Anna Karenina principle has been found in systems in a wide range: from the surface of endangered corals exposed to harsh weather to the lungs of patients suffering from fatal diseases of AIDs. In our paper, we have generated artificial perturbations to our model by hot-swapping the activation and loss functions during the training. In this paper, we build a model to classify cancer cells from non-cancer ones. We give theoretical proof that the internal representations of generalizable happy models are similar in the asymptotic limit. Our experiments verify similar representations of generalizable models.", "field": "cs", "label": 1}
{"text": "Title: Some Aspects on Solving Transportation Problem\nAbstract: In this paper, we consider a class of transportation problems which arises in sample surveys and other areas of statistics. The associated cost matrices of these transportation problems are of special structure. We observe that the optimality of North West corner solution holds for the general problem where cost component is replaced by a convex function. We revisit assignment problem and present a weighted version of K$\\ddot{o}$nig-Egerv$\\acute{a}$ry theorem and Hungarian method. The weighted Hungarian method proposed in the paper can be used for solving transportation problem.", "field": "math", "label": 1}
{"text": "Title: Fractal geometry of the space-time difference profile in the directed landscape via construction of geodesic local times\nAbstract: The Directed Landscape, a random directed metric on the plane (where the first and the second coordinates are termed spatial and temporal respectively), was constructed in the breakthrough work of Dauvergne, Ortmann, and Vir\\'ag, and has since been shown to be the scaling limit of various integrable models of Last Passage percolation, a central member of the Kardar-Parisi-Zhang universality class. It exhibits several scale invariance properties making it a natural source of rich fractal behavior. Such a study was initiated in Basu-Ganguly-Hammond, where the difference profile i.e., the difference of passage times from two fixed points (say $(\\pm 1,0)$), was considered. Owing to geodesic geometry, it turns out that this difference process is almost surely locally constant. The set of non-constancy is connected to disjointness of geodesics and inherits remarkable fractal properties. In particular, it has been established that when only the spatial coordinate is varied, the set of non-constancy of the difference profile has Hausdorff dimension $1/2$, and bears a rather strong resemblance to the zero set of Brownian motion. The arguments crucially rely on a monotonicity property, which is absent when the temporal structure of the process is probed, necessitating the development of new methods. In this paper, we put forth several new ideas, and show that the set of non-constancy of the 2D difference profile and the 1D temporal process (when the spatial coordinate is fixed and the temporal coordinate is varied) have Hausdorff dimensions $5/3$ and $2/3$ respectively. A particularly crucial ingredient in our analysis is the novel construction of a local time process for the geodesic akin to Brownian local time, supported on the \"zero set\" of the geodesic. Further, we show that the latter has Hausdorff dimension $1/3$ in contrast to the zero set of Brownian motion which has dimension $1/2.$", "field": "math", "label": 1}
{"text": "Title: On the error term in a mixed moment of L-functions\nAbstract: There has recently been some interest in optimizing the error term in the asymptotic for the fourth moment of Dirichlet L-functions and a closely related mixed moment of L-functions involving automorphic L-functions twisted by Dirichlet characters. We obtain an improvement for the error term of the latter.", "field": "math", "label": 0}
{"text": "Title: A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario\nAbstract: We study the weak solvability of a quasilinear reaction-diffusion system nonlinearly coupled with an linear elliptic system posed in a domain with distributed microscopic balls in $2D$. The size of these balls are governed by an ODE with direct feedback on the overall problem. The system describes the diffusion, aggregation, fragmentation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of the problem relies on a suitable application of Schauder's fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.", "field": "math", "label": 1}
{"text": "Title: Towards dense volumetric pancreas segmentation in CT using 3D fully convolutional networks\nAbstract: Pancreas segmentation in computed tomography imaging has been historically difficult for automated methods because of the large shape and size variations between patients. In this work, we describe a custom-build 3D fully convolutional network (FCN) that can process a 3D image including the whole pancreas and produce an automatic segmentation. We investigate two variations of the 3D FCN architecture; one with concatenation and one with summation skip connections to the decoder part of the network. We evaluate our methods on a dataset from a clinical trial with gastric cancer patients, including 147 contrast enhanced abdominal CT scans acquired in the portal venous phase. Using the summation architecture, we achieve an average Dice score of 89.7 $\\pm$ 3.8 (range [79.8, 94.8]) % in testing, achieving the new state-of-the-art performance in pancreas segmentation on this dataset.", "field": "cs", "label": 1}
{"text": "Title: Watkins' conjecture for elliptic curves over function fields\nAbstract: In 2002 Watkins conjectured that given an elliptic curve defined over $\\mathbb{Q}$, its Mordell-Weil rank is at most the $2$-adic valuation of its modular degree. We consider the analogous problem over function fields of positive characteristic, and we prove it in several cases. More precisely, every modular semi-stable elliptic curve over $\\mathbb{F}_q(T)$ after extending constant scalars, and every quadratic twist of a modular elliptic curve over $\\mathbb{F}_q(T)$ by a polynomial with sufficiently many prime factors satisfy the analogue of Watkins' conjecture. Furthermore, for a well-known family of elliptic curves with unbounded rank due to Ulmer, we prove the analogue of Watkins' conjecture.", "field": "math", "label": 1}
{"text": "Title: Speeding up the Euler scheme for killed diffusions\nAbstract: Let $X$ be a linear diffusion taking values in $(\\ell,r)$ and consider the standard Euler scheme to compute an approximation to $\\mathbb{E}[g(X_T)\\mathbf{1}_{[T<\\zeta]}]$ for a given function $g$ and a deterministic $T$, where $\\zeta=\\inf\\{t\\geq 0: X_t \\notin (\\ell,r)\\}$. It is well-known since \\cite{GobetKilled} that the presence of killing introduces a loss of accuracy and reduces the weak convergence rate to $1/\\sqrt{N}$ with $N$ being the number of discretisatons. We introduce a drift-implicit Euler method to bring the convergence rate back to $1/N$, i.e. the optimal rate in the absence of killing, using the theory of recurrent transformations developed in \\cite{rectr}. Although the current setup assumes a one-dimensional setting, multidimensional extension is within reach as soon as a systematic treatment of recurrent transformations is available in higher dimensions.", "field": "math", "label": 1}
{"text": "Title: Enumerating m-Length Walks in Directed Graphs with Constant Delay\nAbstract: In this paper, we provide a novel enumeration algorithm for the set of all walks of a given length within a directed graph. Our algorithm has worst-case constant delay between outputting succinct representations of such walks, after a preprocessing step requiring linear time relative to the size of the graph. We apply these results to the problem of enumerating succinct representations of the strings of a given length from a prefix-closed regular language (languages accepted by a finite automaton which has final states only).", "field": "cs", "label": 0}
{"text": "Title: Adaptive estimation of a function from its Exponential Radon Transform in presence of noise\nAbstract: In this article we propose a locally adaptive strategy for estimating a function from its Exponential Radon Transform (ERT) data, without prior knowledge of the smoothness of functions that are to be estimated. We build a non-parametric kernel type estimator and show that for a class of functions comprising a wide Sobolev regularity scale, our proposed strategy follows the minimax optimal rate up to a $\\log{n}$ factor. We also show that there does not exist an optimal adaptive estimator on the Sobolev scale when the pointwise risk is used and in fact the rate achieved by the proposed estimator is the adaptive rate of convergence.", "field": "math", "label": 1}
{"text": "Title: Structure of betweenness uniform graphs with low values of betweenness centrality\nAbstract: This work deals with undirected graphs that have the same betweenness centrality for each vertex, so-called betweenness uniform graphs (or BUGs). The class of these graphs is not trivial and its classification is still an open problem. Recently, Gago, Coroni\\v{c}ov\\'a-Hurajov\\'a and Madaras conjectured that for every rational $\\alpha\\ge 3/4$ there exists a BUG having betweenness centrality~$\\alpha$. We disprove this conjecture, and provide an alternative view of the structure of betweenness-uniform graphs from the point of view of their complement. This allows us to characterise all the BUGs with betweennes centrality at most 9/10, and show that their betweenness centrality is equal to $\\frac{\\ell}{\\ell+1}$ for some integer $\\ell\\le 9$. We conjecture that this characterization extends to all the BUGs with betweenness centrality smaller than~1.", "field": "math", "label": 0}
{"text": "Title: Boson Operator Ordering Identities from Generalized Stirling and Eulerian Numbers\nAbstract: Ordering identities in the Weyl-Heisenberg algebra generated by single-mode boson operators are investigated. A boson string composed of creation and annihilation operators can be expanded as a linear combination of other such strings, the simplest example being a normal ordering. The case when each string contains only one annihilation operator is already combinatorially nontrivial. Two kinds of expansion are derived: (i) that of a power of a string $\\Omega$ in lower powers of another string $\\Omega'$, and (ii) that of a power of $\\Omega$ in twisted versions of the same power of $\\Omega'$. The expansion coefficients are shown to be, respectively, generalized Stirling numbers of Hsu and Shiue, and certain generalized Eulerian numbers. Many examples are given. These combinatorial numbers are binomial transforms of each other, and their theory is developed, emphasizing schemes for computing them: summation formulas, Graham-Knuth-Patashnik (GKP) triangular recurrences, terminating hypergeometric series, and closed-form expressions. The results on the first type of expansion subsume a number of previous results on the normal ordering of boson strings.", "field": "math", "label": 0}
{"text": "Title: Harvesting of a stochastic population under a mixed regular-singular control formulation\nAbstract: This work focuses on optimal harvesting-renewing for a stochastic population. A mixed regular-singular control formulation with a state constraint and regime-switching is introduced. The decision-makers either harvest or renew with finite or infinite harvesting/renewing rates. The payoff functions depend on the harvesting/renewing rates. Several properties of the value functions are established. The limiting value function as the white noise intensity approaches infinity is identified. The Markov chain approximation method is used to find a numerical approximation of the value function and optimal strategies.", "field": "math", "label": 1}
{"text": "Title: Team Semantics and Independence Notions in Quantum Physics\nAbstract: We study dependence and independence concepts found in quantum physics, especially those related to hidden variables and non-locality, through the lens of team semantics and probabilistic team semantics, adapting a relational framework introduced by the first author in a prior paper. This leads to new developments also in independence logic and probabilistic independence logic.", "field": "math", "label": 1}
{"text": "Title: Spin systems with hyperbolic symmetry: a survey\nAbstract: Spin systems with hyperbolic symmetry originated as simplified models for the Anderson metal--insulator transition, and were subsequently found to exactly describe probabilistic models of linearly reinforced walks and random forests. In this survey we introduce these models, discuss their origins and main features, some existing tools available for their study, recent probabilistic results, and relations to other well-studied probabilistic models. Along the way we discuss some of the (many) open questions that remain.", "field": "math", "label": 1}
{"text": "Title: Convergence of the discrete Redner-Ben-Avraham-Kahng coagulation equation\nAbstract: This article looks at the relationship between the discrete and the continuous Redner-Ben-Avraham-Kahng (RBK) coagulation models. On the basis of a priori estimation, a weak stability principle and the weak compactness in $L_1$ for the continuous RBK model is shown. By employing a sequence of discrete models to approximate the continuous one, we show that how discrete model eventually converges to the the modified continuous one using the stability principle.", "field": "math", "label": 0}
{"text": "Title: Beyond Regrets: Geometric Metrics for Bayesian Optimization\nAbstract: Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the performance of Bayesian optimization is assessed by regret-based metrics such as instantaneous, simple, and cumulative regrets. These metrics only rely on function evaluations, so that they do not consider geometric relationships between query points and global solutions, or query points themselves. Notably, they cannot discriminate if multiple global solutions are successfully found. Moreover, they do not evaluate Bayesian optimization's abilities to exploit and explore a search space given. To tackle these issues, we propose four new geometric metrics, i.e., precision, recall, average degree, and average distance. These metrics allow us to compare Bayesian optimization algorithms considering the geometry of both query points and global optima, or query points. However, they are accompanied by an extra parameter, which needs to be carefully determined. We therefore devise the parameter-free forms of the respective metrics by integrating out the additional parameter. Finally, we empirically validate that our proposed metrics can provide more convincing interpretation and understanding of Bayesian optimization algorithms from distinct perspectives, compared to the conventional metrics.", "field": "cs", "label": 0}
{"text": "Title: Hereditary completeness of Exponential systems $\\{e^{λ_n t}\\}_{n=1}^{\\infty}$ in their closed span in $L^2 (a, b)$ and Spectral Synthesis\nAbstract: Suppose that $\\{\\lambda_n\\}_{n=1}^{\\infty}$ is a sequence of distinct positive real numbers satisfying the conditions inf$\\{\\lambda_{n+1}-\\lambda_n \\}>0,$ and $\\sum_{n=1}^{\\infty}\\lambda_n^{-1}<\\infty.$ We prove that the exponential system $\\{e^{\\lambda_n t}\\}_{n=1}^{\\infty}$ is hereditarily complete in the closure of the subspace spanned by $\\{e^{\\lambda_n t}\\}_{n=1}^{\\infty}$ in the space $L^2 (a,b)$. We also give an example of a class of compact non-normal operators defined on this closure which admit spectral synthesis.", "field": "math", "label": 0}
{"text": "Title: NODEC: Neural ODE For Optimal Control of Unknown Dynamical Systems\nAbstract: Controlling complex dynamical systems is generally associated with minimizing certain control objectives with known dynamics under the variational calculus framework. For systems with unknown dynamics, an additional step of dynamics modeling is required. However, any inaccuracy in dynamics modeling will lead to sub-optimality in the resulting control function. Another set of approaches for controlling unknown dynamical systems - reinforcement learning, folds the dynamics modeling into controller training via value function approximation or policy gradient through extensively interacting with the environment, but it suffers from low data efficiency. To address these, we introduce NODEC, a novel framework for controlling unknown dynamical systems, which combines dynamics modelling and controller training using a coupled neural ODE model. Through an intriguing interplay between the two coupled neural networks, NODEC learns system dynamics as well as optimal controls that guides the unknown dynamical system towards target states. Our experiments demonstrate the effectiveness and data efficiency of NODEC for learning optimal control of unknown dynamical systems.", "field": "cs", "label": 0}
{"text": "Title: Feature Selection for Discovering Distributional Treatment Effect Modifiers\nAbstract: Finding the features relevant to the difference in treatment effects is essential to unveil the underlying causal mechanisms. Existing methods seek such features by measuring how greatly the feature attributes affect the degree of the {\\it conditional average treatment effect} (CATE). However, these methods may overlook important features because CATE, a measure of the average treatment effect, cannot detect differences in distribution parameters other than the mean (e.g., variance). To resolve this weakness of existing methods, we propose a feature selection framework for discovering {\\it distributional treatment effect modifiers}. We first formulate a feature importance measure that quantifies how strongly the feature attributes influence the discrepancy between potential outcome distributions. Then we derive its computationally efficient estimator and develop a feature selection algorithm that can control the type I error rate to the desired level. Experimental results show that our framework successfully discovers important features and outperforms the existing mean-based method.", "field": "cs", "label": 1}
{"text": "Title: Uncertainty in GNN Learning Evaluations: A Comparison Between Measures for Quantifying Randomness in GNN Community Detection\nAbstract: (1) The enhanced capability of Graph Neural Networks (GNNs) in unsupervised community detection of clustered nodes is attributed to their capacity to encode both the connectivity and feature information spaces of graphs. The identification of latent communities holds practical significance in various domains, from social networks to genomics. Current real-world performance benchmarks are perplexing due to the multitude of decisions influencing GNN evaluations for this task. (2) Three metrics are compared to assess the consistency of algorithm rankings in the presence of randomness. The consistency and quality of performance between the results under a hyperparameter optimisation with the default hyperparameters is evaluated. (3) The results compare hyperparameter optimisation with default hyperparameters, revealing a significant performance loss when neglecting hyperparameter investigation. A comparison of metrics indicates that ties in ranks can substantially alter the quantification of randomness. (4) Ensuring adherence to the same evaluation criteria may result in notable differences in the reported performance of methods for this task. The $W$ Randomness coefficient, based on the Wasserstein distance, is identified as providing the most robust assessment of randomness.", "field": "cs", "label": 0}
{"text": "Title: Characterizing Fake News Targeting Corporations\nAbstract: Misinformation proliferates in the online sphere, with evident impacts on the political and social realms, influencing democratic discourse and posing risks to public health and safety. The corporate world is also a prime target for fake news dissemination. While recent studies have attempted to characterize corporate misinformation and its effects on companies, their findings often suffer from limitations due to qualitative or narrative approaches and a narrow focus on specific industries. To address this gap, we conducted an analysis utilizing social media quantitative methods and crowd-sourcing studies to investigate corporate misinformation across a diverse array of industries within the S\\&P 500 companies. Our study reveals that corporate misinformation encompasses topics such as products, politics, and societal issues. We discovered companies affected by fake news also get reputable news coverage but less social media attention, leading to heightened negativity in social media comments, diminished stock growth, and increased stress mentions among employee reviews. Additionally, we observe that a company is not targeted by fake news all the time, but there are particular times when a critical mass of fake news emerges. These findings hold significant implications for regulators, business leaders, and investors, emphasizing the necessity to vigilantly monitor the escalating phenomenon of corporate misinformation.", "field": "cs", "label": 0}
{"text": "Title: SPHARMA approximations for stationary functional time series on the sphere\nAbstract: In this paper, we focus on isotropic and stationary sphere-cross-time random fields. We first introduce the class of spherical functional autoregressive-moving average processes (SPHARMA), which extend in a natural way the spherical functional autoregressions (SPHAR) recently studied in [8, 7]; more importantly, we then show that SPHAR and SPHARMA processes of sufficiently large order can be exploited to approximate every isotropic and stationary sphere-cross-time random field, thus generalizing to this infinite-dimensional framework some classical results on real-valued stationary processes. Further characterizations in terms of functional spectral representation theorems and Wold-like decompositions are also established.", "field": "math", "label": 1}
{"text": "Title: On a variety of right-symmetric algebras\nAbstract: We construct a finite-dimensional metabelian right-symmetric algebra over an arbitrary field that does not have a finite basis of identities.", "field": "math", "label": 0}
{"text": "Title: Limit pretrees for free group automorphisms: existence\nAbstract: To any free group automorphism, we associate a real pretree with several nice properties. First, it has a rigid/non-nesting action of the free group with trivial arc stabilizers. Secondly, there is an expanding pretree-automorphism of the real pretree that represents the free group automorphism. Finally and crucially, the loxodromic elements are exactly those whose (conjugacy class) length grows exponentially under iteration of the automorphism; thus, the action on the real pretree is able to detect the growth type of an element. This construction extends the theory of metric trees that has been used to study free group automorphisms. The new idea is that one can equivariantly blow up an isometric action on a real tree with respect to other real trees and get a rigid action on a treelike structure known as a real pretree. Topology plays no role in this construction as all the work is done in the language of pretrees.", "field": "math", "label": 1}
{"text": "Title: Attacks in Adversarial Machine Learning: A Systematic Survey from the Life-cycle Perspective\nAbstract: Adversarial machine learning (AML) studies the adversarial phenomenon of machine learning, which may make inconsistent or unexpected predictions with humans. Some paradigms have been recently developed to explore this adversarial phenomenon occurring at different stages of a machine learning system, such as backdoor attack occurring at the pre-training, in-training and inference stage; weight attack occurring at the post-training, deployment and inference stage; adversarial attack occurring at the inference stage. However, although these adversarial paradigms share a common goal, their developments are almost independent, and there is still no big picture of AML. In this work, we aim to provide a unified perspective to the AML community to systematically review the overall progress of this field. We firstly provide a general definition about AML, and then propose a unified mathematical framework to covering existing attack paradigms. According to the proposed unified framework, we build a full taxonomy to systematically categorize and review existing representative methods for each paradigm. Besides, using this unified framework, it is easy to figure out the connections and differences among different attack paradigms, which may inspire future researchers to develop more advanced attack paradigms. Finally, to facilitate the viewing of the built taxonomy and the related literature in adversarial machine learning, we further provide a website, \\ie, \\url{http://adversarial-ml.com}, where the taxonomies and literature will be continuously updated.", "field": "cs", "label": 0}
{"text": "Title: Fluctuation of the Largest Eigenvalue of a Kernel Matrix with application in Graphon-based Random Graphs\nAbstract: In this article, we explore the spectral properties of general random kernel matrices $[K(U_i,U_j)]_{1\\leq i\\neq j\\leq n}$ from a Lipschitz kernel $K$ with $n$ independent random variables $U_1,U_2,\\ldots, U_n$ distributed uniformly over $[0,1]$. In particular we identify a dichotomy in the extreme eigenvalue of the kernel matrix, where, if the kernel $K$ is degenerate, the largest eigenvalue of the kernel matrix (after proper normalization) converges weakly to a weighted sum of independent chi-squared random variables. In contrast, for non-degenerate kernels, it converges to a normal distribution extending and reinforcing earlier results from Koltchinskii and Gin\\'e (2000). Further, we apply this result to show a dichotomy in the asymptotic behavior of extreme eigenvalues of $W$-random graphs, which are pivotal in modeling complex networks and analyzing large-scale graph behavior. These graphs are generated using a kernel $W$, termed as graphon, by connecting vertices $i$ and $j$ with probability $W(U_i, U_j)$. Our results show that for a Lipschitz graphon $W$, if the degree function is constant, the fluctuation of the largest eigenvalue (after proper normalization) converges to the weighted sum of independent chi-squared random variables and an independent normal distribution. Otherwise, it converges to a normal distribution.", "field": "math", "label": 0}
{"text": "Title: The uniform companion for fields with free operators in characteristic zero\nAbstract: Generalising the uniform companion for large fields with a single derivation, we construct a theory $\\text{UC}_{\\mathcal{D}}$ of fields of characteristic $0$ with free operators -- operators determined by a homomorphism from the field to its tensor product with $\\mathcal{D}$, a finite-dimensional $\\mathbb{Q}$-algebra -- which is the model companion of any theory of a field with free operators whose associated difference field is difference large and model complete. Under the assumption that $\\mathcal{D}$ is a local ring, we show that simplicity is transferred from the theory of the underlying field to the theory of the field with operators, and we use this to study the model theory of bounded, PAC fields with free operators.", "field": "math", "label": 0}
{"text": "Title: A stratification of moduli of arbitrarily singular curves\nAbstract: We introduce a new moduli stack $\\mathscr{E}_{g,n}$ of ``equinormalized curves\" which is a minor modification of the moduli space of all reduced, connected curves. We construct a stratification $\\bigsqcup_\\Gamma \\mathscr{E}_\\Gamma$ of $\\mathscr{E}_{g,n}$ indexed by generalized dual graphs and prove that each stratum $\\mathscr{E}_{\\Gamma}$ is a fiber bundle over a finite quotient of a product of $\\mathcal{M}_{g,n}$'s. The fibers are moduli schemes parametrizing subalgebras of a fixed algebra, and are in principle explicitly computable as locally closed subschemes of products of Grassmannians. We thus obtain a remarkably explicit geometric description of moduli of reduced curves with arbitrary singularities.", "field": "math", "label": 0}
{"text": "Title: On the construction of Cohn's universal localization\nAbstract: For an associative ring we investigate a construction of Cohn's universal ring of fractions defined relative to a multiplicative set of matrices. The construction avoids the Ore condition, which is necessary to construct a ring of fractions relative to a multiplicative set of elements. But a similar condition, which we call the ``pseudo-Ore'' condition, plays an important role in the construction of Cohn's localization. We show that this condition in fact determines the equivalence relation used in the construction.", "field": "math", "label": 0}
{"text": "Title: Minimum Weight Pairwise Distance Preservers\nAbstract: In this paper, we study the Minimum Weight Pairwise Distance Preservers (MWPDP) problem. Consider a positively weighted undirected/directed connected graph $G = (V, E, c)$ and a subset $P$ of pairs of vertices, also called demand pairs. A subgraph $G'$ is a distance preserver with respect to $P$ if and only if every pair $(u, w) \\in P$ satisfies $dist_{G'} (u, w) = dist_{G}(u, w)$. In MWPDP problem, we aim to find the minimum-weight subgraph $G^*$ that is a distance preserver with respect to $P$. Taking a shortest path between each pair in $P$ gives us a trivial solution with the weight of at most $U=\\sum_{(u,v) \\in P} dist_{G} (u, w)$. Subsequently, we ask how much improvement we can make upon $U$. In other words, we opt to find a distance preserver $G^*$ that maximizes $U-c(G^*)$. Denote this problem as Cost Sharing Pairwise Distance Preservers (CSPDP), which has several applications in the planning and operations of transportation systems. The only known work that can provide a nontrivial solution for CSPDP is that of Chlamt\\'a\\v{c} et al. (SODA, 2017). This algorithm works for unweighted graphs and guarantees a non-zero objective only if the optimal solution is extremely sparse with respect to the trivial solution. We address this issue by proposing an $O(|E|^{1/2+\\epsilon})$-approximation algorithm for CSPDP in weighted graphs that runs in $O((|P||E|)^{2.38} (1/\\epsilon))$ time. Moreover, we prove CSPDP is at least as hard as $\\text{LABEL-COVER}_{\\max}$. This implies that CSPDP cannot be approximated within $O(|E|^{1/6-\\epsilon})$ factor in polynomial time, unless there is an improvement in the notoriously difficult $\\text{LABEL-COVER}_{\\max}$.", "field": "cs", "label": 1}
{"text": "Title: On the delooping of (framed) embedding spaces\nAbstract: It is known that the bimodule derived mapping spaces between two operads have a delooping in terms of the operadic mapping space. We show a relative version of that statement. The result has applications to the spaces of disc embeddings fixed near the boundary and framed disc embeddings.", "field": "math", "label": 1}
{"text": "Title: Prompt Decoupling for Text-to-Image Person Re-identification\nAbstract: Text-to-image person re-identification (TIReID) aims to retrieve the target person from an image gallery via a textual description query. Recently, pre-trained vision-language models like CLIP have attracted significant attention and have been widely utilized for this task due to their robust capacity for semantic concept learning and rich multi-modal knowledge. However, recent CLIP-based TIReID methods commonly rely on direct fine-tuning of the entire network to adapt the CLIP model for the TIReID task. Although these methods show competitive performance on this topic, they are suboptimal as they necessitate simultaneous domain adaptation and task adaptation. To address this issue, we attempt to decouple these two processes during the training stage. Specifically, we introduce the prompt tuning strategy to enable domain adaptation and propose a two-stage training approach to disentangle domain adaptation from task adaptation. In the first stage, we freeze the two encoders from CLIP and solely focus on optimizing the prompts to alleviate domain gap between the original training data of CLIP and downstream tasks. In the second stage, we maintain the fixed prompts and fine-tune the CLIP model to prioritize capturing fine-grained information, which is more suitable for TIReID task. Finally, we evaluate the effectiveness of our method on three widely used datasets. Compared to the directly fine-tuned approach, our method achieves significant improvements.", "field": "cs", "label": 0}
{"text": "Title: Locally differentially private estimation of nonlinear functionals of discrete distributions\nAbstract: We study the problem of estimating non-linear functionals of discrete distributions in the context of local differential privacy. The initial data $x_1,\\ldots,x_n \\in [K]$ are supposed i.i.d. and distributed according to an unknown discrete distribution $p = (p_1,\\ldots,p_K)$. Only $\\alpha$-locally differentially private (LDP) samples $z_1,...,z_n$ are publicly available, where the term 'local' means that each $z_i$ is produced using one individual attribute $x_i$. We exhibit privacy mechanisms (PM) that are interactive (i.e. they are allowed to use already published confidential data) or non-interactive. We describe the behavior of the quadratic risk for estimating the power sum functional $F_{\\gamma} = \\sum_{k=1}^K p_k^{\\gamma}$, $\\gamma >0$ as a function of $K, \\, n$ and $\\alpha$. In the non-interactive case, we study two plug-in type estimators of $F_{\\gamma}$, for all $\\gamma >0$, that are similar to the MLE analyzed by Jiao et al. (2017) in the multinomial model. However, due to the privacy constraint the rates we attain are slower and similar to those obtained in the Gaussian model by Collier et al. (2020). In the interactive case, we introduce for all $\\gamma >1$ a two-step procedure which attains the faster parametric rate $(n \\alpha^2)^{-1/2}$ when $\\gamma \\geq 2$. We give lower bounds results over all $\\alpha$-LDP mechanisms and all estimators using the private samples.", "field": "math", "label": 1}
{"text": "Title: Kronecker coefficients and noncommutative super Schur functions\nAbstract: The theory of noncommutative Schur functions can be used to obtain positive combinatorial formulae for the Schur expansion of various classes of symmetric functions, as shown by Fomin and Greene. We develop a theory of noncommutative super Schur functions and use it to prove a positive combinatorial rule for the Kronecker coefficients where one of the partitions is a hook, recovering previous results of the two authors. This method also gives a precise connection between this rule and a heuristic for Kronecker coefficients first investigated by Lascoux.", "field": "math", "label": 1}
{"text": "Title: Cross-linguistically Consistent Semantic and Syntactic Annotation of Child-directed Speech\nAbstract: While corpora of child speech and child-directed speech (CDS) have enabled major contributions to the study of child language acquisition, semantic annotation for such corpora is still scarce and lacks a uniform standard. We compile two CDS corpora with sentential logical forms, one in English and the other in Hebrew. In compiling the corpora we employ a methodology that enforces a cross-linguistically consistent representation, building on recent advances in dependency representation and semantic parsing. The corpora are based on a sizable portion of Brown's Adam corpus from CHILDES (about 80% of its child-directed utterances), and to all child-directed utterances from Berman's Hebrew CHILDES corpus Hagar. We begin by annotating the corpora with the Universal Dependencies (UD) scheme for syntactic annotation, motivated by its applicability to a wide variety of domains and languages. We then proceed by applying an automatic method for transducing sentential logical forms (LFs) from UD structures. The two representations have complementary strengths: UD structures are language-neutral and support direct annotation, whereas LFs are neutral as to the interface between syntax and semantics, and transparently encode semantic distinctions. We verify the quality of the annotated UD annotation using an inter-annotator agreement study. We then demonstrate the utility of the compiled corpora through a longitudinal corpus study of the prevalence of different syntactic and semantic phenomena.", "field": "cs", "label": 1}
{"text": "Title: Borel structurability on the 2-shift of a countable group\nAbstract: We show that for any infinite countable group $G$ and for any free Borel action $G \\curvearrowright X$ there exists an equivariant class-bijective Borel map from $X$ to the free part $\\mathrm{Free}(2^G)$ of the $2$-shift $G \\curvearrowright 2^G$. This implies that any Borel structurability which holds for the equivalence relation generated by $G \\curvearrowright \\mathrm{Free}(2^G)$ must hold a fortiori for all equivalence relations coming from free Borel actions of $G$. A related consequence is that the Borel chromatic number of $\\mathrm{Free}(2^G)$ is the maximum among Borel chromatic numbers of free actions of $G$. This answers a question of Marks. Our construction is flexible and, using an appropriate notion of genericity, we are able to show that in fact the generic $G$-equivariant map to $2^G$ lands in the free part. As a corollary we obtain that for every $\\epsilon > 0$, every free pmp action of $G$ has a free factor which admits a $2$-piece generating partition with Shannon entropy less than $\\epsilon$. This generalizes a result of Danilenko and Park.", "field": "math", "label": 1}
{"text": "Title: On metric dimension of cube of trees\nAbstract: Let $G=(V,E)$ be a connected graph and $d_{G}(u,v)$ be the shortest distance between the vertices $u$ and $v$ in $G$. A set $S=\\{s_{1},s_{2},\\cdots,s_{n}\\}\\subset V(G)$ is said to be a {\\em resolving set} if for all distinct vertices $u,v$ of $G$, there exist an element $s\\in S$ such that $d(s,u)\\neq d(s,v)$. The minimum cardinality of a resolving set for a graph $G$ is called the {\\em metric dimension} of $G$ and it is denoted by $\\beta{(G)}$. A resolving set having $\\beta{(G)}$ number of vertices is named as {\\em metric basis} of $G$. The metric dimension problem is to find a metric basis in a graph $G$, and it has several real-life applications in network theory, telecommunication, image processing, pattern recognition, and many other fields. In this article, we consider {\\em cube of trees} $T^{3}=(V, E)$, where any two vertices $u,v$ are adjacent if and only if the distance between them is less than equal to three in $T$. We establish the necessary and sufficient conditions of a vertex subset of $V$ to become a resolving set for $T^{3}$. This helps determine the tight bounds (upper and lower) for the metric dimension of $T^{3}$. Then, for certain well-known cubes of trees, such as caterpillars, lobsters, spiders, and $d$-regular trees, we establish the boundaries of the metric dimension. Further, we characterize some restricted families of cube of trees satisfying $\\beta{(T^{3})}=\\beta{(T)}$. We provide a construction showing the existence of a cube of tree attaining every positive integer value as their metric dimension.", "field": "math", "label": 0}
{"text": "Title: On the computation of coarse cohomology\nAbstract: The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the boundedly supported cohomology. Boundedly supported cohomology coincides with compactly supported Alexander--Spanier cohomology if the space is proper and contractible. Our work generalizes an earlier result of Roe which says that the coarse cohomology is isomorphic to the compactly supported Alexander-Spanier cohomology if the space is uniformly contractible. As an application of our main theorem, we obtain that coarse cohomology of the complement can be computed in terms of Alexander-Spanier cohomology for many spaces.", "field": "math", "label": 0}
{"text": "Title: Performance Analysis of Clustered LoRa Networks\nAbstract: In this paper, we investigate the uplink transmission performance of low-power wide-area (LPWA) networks with regards to coexisting radio modules. We adopt long range (LoRa) radio technique as an example of the network of focus even though our analysis can be easily extended to other situations. We exploit a new topology to model the network, where the node locations of LoRa follow a Poisson cluster process (PCP) while other coexisting radio modules follow a Poisson point process (PPP). Unlike most of the performance analysis based on stochastic geometry, we take noise into consideration. More specifically, two models, with a fixed and a random number of active LoRa nodes in each cluster, respectively, are considered. To obtain insights, both the exact and simple approximated expressions for coverage probability are derived. Based on them, area spectral efficiency and energy efficiency are obtained. From our analysis, we show how the performance of LPWA networks can be enhanced through adjusting the density of LoRa nodes around each LoRa receiver. Moreover, the simulation results unveil that the optimal number of active LoRa nodes in each cluster exists to maximize the area spectral efficiency.", "field": "cs", "label": 1}
{"text": "Title: Noncompact $n$-dimensional Einstein spaces as attractors for the Einstein flow\nAbstract: We prove that along with the Einstein flow, any small perturbations of an $n(n \\geq 4)$-dimensional, non-compact negative Einstein space with some \"non-positive Weyl tensor\" lead to a unique and global solution, and the solution will be attracted to a noncompact Einstein space that is close to the background one. The $n=3$ case has been addressed in [30], while in dimension $n \\geq 4$, as we know, negative Einstein metrics in general have non-trivial moduli spaces. This fact is reflected on the structure of Einstein equations, which further indicates no decay for the spatial Weyl tensor. Furthermore, it is suggested in the proof that the mechanic preventing the metric from flowing back to the original Einstein metric lies in the non-decaying character of spatial Weyl tensor. In contrary to the compact case considered in Andersson-Moncrief [4], our proof is independent of the theory of infinitesimal Einstein deformations. Instead, we take advantage of the inherent geometric structures of Einstein equations and develop an approach of energy estimates for a hyperbolic system of Maxwell type.", "field": "math", "label": 0}
{"text": "Title: Wasserstein Nonnegative Tensor Factorization with Manifold Regularization\nAbstract: Nonnegative tensor factorization (NTF) has become an important tool for feature extraction and part-based representation with preserved intrinsic structure information from nonnegative high-order data. However, the original NTF methods utilize Euclidean or Kullback-Leibler divergence as the loss function which treats each feature equally leading to the neglect of the side-information of features. To utilize correlation information of features and manifold information of samples, we introduce Wasserstein manifold nonnegative tensor factorization (WMNTF), which minimizes the Wasserstein distance between the distribution of input tensorial data and the distribution of reconstruction. Although some researches about Wasserstein distance have been proposed in nonnegative matrix factorization (NMF), they ignore the spatial structure information of higher-order data. We use Wasserstein distance (a.k.a Earth Mover's distance or Optimal Transport distance) as a metric and add a graph regularizer to a latent factor. Experimental results demonstrate the effectiveness of the proposed method compared with other NMF and NTF methods.", "field": "cs", "label": 0}
{"text": "Title: Beyond Self-Promotion: How Software Engineering Research Is Discussed on LinkedIn\nAbstract: LinkedIn is the largest professional network in the world. As such, it can serve to build bridges between practitioners, whose daily work is software engineering (SE), and researchers, who work to advance the field of software engineering. We know that such a metaphorical bridge exists: SE research findings are sometimes shared on LinkedIn and commented on by software practitioners. Yet, we do not know what state the bridge is in. Therefore, we quantitatively and qualitatively investigate how SE practitioners and researchers approach each other via public LinkedIn discussions and what both sides can contribute to effective science communication. We found that a considerable proportion of LinkedIn posts on SE research are written by people who are not the paper authors (39%). Further, 71% of all comments in our dataset are from people in the industry, but only every second post receives at least one comment at all. Based on our findings, we formulate concrete advice for researchers and practitioners to make sharing new research findings on LinkedIn more fruitful.", "field": "cs", "label": 0}
{"text": "Title: Formal manifolds: foundations, function spaces, and Poincaré's lemma\nAbstract: This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the notion of formal manifolds in the context of differential geometry, inspired by the notion of formal schemes in algebraic geometry. We develop the basic theory for formal manifolds, including a generalization of the theory of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. Additionally, we establish Poincar\\'e's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions.", "field": "math", "label": 0}
{"text": "Title: Mechanism Design for Time Critical and Cost Critical Task Execution via Crowdsourcing\nAbstract: An exciting application of crowdsourcing is to use social networks in complex task execution. In this paper, we address the problem of a planner who needs to incentivize agents within a network in order to seek their help in executing an {\\em atomic task} as well as in recruiting other agents to execute the task. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner's goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We identify a set of desirable properties that should ideally be satisfied by a crowdsourcing mechanism. In particular, {\\em sybil-proofness} and {\\em collapse-proofness} are two complementary properties in our desiderata. We prove that no mechanism can satisfy all the desirable properties simultaneously. This leads us naturally to explore approximate versions of the critical properties. We focus our attention on approximate sybil-proofness and our exploration leads to a parametrized family of payment mechanisms which satisfy collapse-proofness. We characterize the approximate versions of the desirable properties in cost critical and time critical domain.", "field": "cs", "label": 1}
{"text": "Title: Reference-less Measure of Faithfulness for Grammatical Error Correction\nAbstract: We propose USim, a semantic measure for Grammatical Error Correction (GEC) that measures the semantic faithfulness of the output to the source, thereby complementing existing reference-less measures (RLMs) for measuring the output's grammaticality. USim operates by comparing the semantic symbolic structure of the source and the correction, without relying on manually-curated references. Our experiments establish the validity of USim, by showing that (1) semantic annotation can be consistently applied to ungrammatical text; (2) valid corrections obtain a high USim similarity score to the source; and (3) invalid corrections obtain a lower score.", "field": "cs", "label": 1}
{"text": "Title: A Note on Minimax Robustness of Designs Against Correlated or Heteroscedastic Responses\nAbstract: We present a result according to which certain functions of covariance matrices are maximized at scalar multiples of the identity matrix. This is used to show that experimental designs that are optimal under an assumption of independent, homoscedastic responses can be minimax robust, in broad classes of alternate covariance structures. In particular it can justify the common practice of disregarding possible dependence, or heteroscedasticity, at the design stage of an experiment.", "field": "math", "label": 0}
{"text": "Title: The Cayley Plane and the Witten Genus\nAbstract: This paper defines a new genus, the Cayley plane genus. By definition it is the universal multiplicative genus for oriented Cayley plane bundles. The main result (Theorem 2) is that it factors (tensor Q) through the product of the Ochanine elliptic genus and the Witten genus---revealing a synergy between these two genera---and that its image is the homogeneous coordinate ring Q[Kum,HP^2,HP^3,CaP^2]/(CaP^3).(HP^3,CaP^2-(HP^2)^2) of the union of the curve of Ochanine elliptic genera and the surface of Witten genera meeting with multiplicity 2 at the point CaP^2=HP^3=HP^2=0 corresponding to the \\^A-genus. This all remains true if the word \"oriented\" is replaced with the word \"spin\" (Theorem 3). This paper also characterizes the Witten genus (tensor Q) as the universal genus vanishing on total spaces of Cayley plane bundles (Theorem 1, a result proved independently by Dessai in [Des09].)", "field": "math", "label": 1}
{"text": "Title: Universality in block dependent linear models with applications to nonparametric regression\nAbstract: Over the past decade, characterizing the exact asymptotic risk of regularized estimators in high-dimensional regression has emerged as a popular line of work. This literature considers the proportional asymptotics framework, where the number of features and samples both diverge, at a rate proportional to each other. Substantial work in this area relies on Gaussianity assumptions on the observed covariates. Further, these studies often assume the design entries to be independent and identically distributed. Parallel research investigates the universality of these findings, revealing that results based on the i.i.d.~Gaussian assumption extend to a broad class of designs, such as i.i.d.~sub-Gaussians. However, universality results examining dependent covariates so far focused on correlation-based dependence or a highly structured form of dependence, as permitted by right rotationally invariant designs. In this paper, we break this barrier and study a dependence structure that in general falls outside the purview of these established classes. We seek to pin down the extent to which results based on i.i.d.~Gaussian assumptions persist. We identify a class of designs characterized by a block dependence structure that ensures the universality of i.i.d.~Gaussian-based results. We establish that the optimal values of the regularized empirical risk and the risk associated with convex regularized estimators, such as the Lasso and ridge, converge to the same limit under block dependent designs as they do for i.i.d.~Gaussian entry designs. Our dependence structure differs significantly from correlation-based dependence, and enables, for the first time, asymptotically exact risk characterization in prevalent nonparametric regression problems in high dimensions. Finally, we illustrate through experiments that this universality becomes evident quite early, even for relatively moderate sample sizes.", "field": "math", "label": 0}
{"text": "Title: Stable sets of primes in number fields\nAbstract: We define a new class of sets -- stable sets -- of primes in number fields. For example, Chebotarev sets $P_{M/K}(\\sigma)$, with $M/K$ Galois and $\\sigma \\in \\Gal(M/K)$, are very often stable. These sets have positive (but arbitrary small) Dirichlet density and generalize sets with density 1 in the sense that arithmetic theorems like certain Hasse principles, the Grunwald-Wang theorem, the Riemann's existence theorem, etc. hold for them. Geometrically this allows to give examples of infinite sets $S$ with arbitrary small positive density such that $\\Spec \\mathcal{O}_{K,S}$ is algebraic $K(\\pi,1)$ (for all $p$ simultaneous).", "field": "math", "label": 1}
{"text": "Title: Counting Finite Topologies\nAbstract: In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.", "field": "math", "label": 0}
{"text": "Title: Eigenvalues Distributions and Control Theory\nAbstract: This work deals with the isogeometric Galerkin discretization of the eigenvalue problem related to the Laplace operator subject to homogeneous Dirichlet boundary conditions on bounded intervals. This paper uses GLT theory to study the behavior of the gap of discrete spectra toward the uniform gap condition needed for the uniform boundary observability/controllability problems. The analysis refers to a regular $B$-spline basis and concave or convex reparametrizations. Under suitable assumptions on the reparametrization transformation, we prove that structure emerges within the distribution of the eigenvalues once we reframe the problem into GLT-symbol analysis. We also demonstrate numerically, that the necessary average gap condition proposed in \\cite{bianchi2018spectral} is not equivalent to the uniform gap condition. However, by improving the result in \\cite{bianchi2021analysis} we construct sufficient criteria that guarantee the uniform gap property.", "field": "math", "label": 0}
{"text": "Title: Generalizations of quasielliptic curves\nAbstract: We generalize the notion of quasielliptic curves, which have infinitesimal symmetries and exist only in characteristic two and three, to a remarkable hierarchy of regular curves having infinitesimal symmetries, defined in all characteristics and having higher genera. This relies on the study of certain infinitesimal group schemes acting on the affine line and certain compactifications. The group schemes are defined in terms of invertible additive polynomials over rings with nilpotent elements, and the compactification is constructed with the theory of numerical semigroups. The existence of regular twisted forms relies on Brion's recent theory of equivariant normalization. Furthermore, extending results of Serre from the realm of group cohomology, we describe non-abelian cohomology for semidirect products, to compute in special cases the collection of all twisted forms.", "field": "math", "label": 0}
{"text": "Title: Tuple-Independent Representations of Infinite Probabilistic Databases\nAbstract: Probabilistic databases (PDBs) are probability spaces over database instances. They provide a framework for handling uncertainty in databases, as occurs due to data integration, noisy data, data from unreliable sources or randomized processes. Most of the existing theory literature investigated finite, tuple-independent PDBs (TI-PDBs) where the occurrences of tuples are independent events. Only recently, Grohe and Lindner (PODS '19) introduced independence assumptions for PDBs beyond the finite domain assumption. In the finite, a major argument for discussing the theoretical properties of TI-PDBs is that they can be used to represent any finite PDB via views. This is no longer the case once the number of tuples is countably infinite. In this paper, we systematically study the representability of infinite PDBs in terms of TI-PDBs and the related block-independent disjoint PDBs. The central question is which infinite PDBs are representable as first-order views over tuple-independent PDBs. We give a necessary condition for the representability of PDBs and provide a sufficient criterion for representability in terms of the probability distribution of a PDB. With various examples, we explore the limits of our criteria. We show that conditioning on first order properties yields no additional power in terms of expressivity. Finally, we discuss the relation between purely logical and arithmetic reasons for (non-)representability.", "field": "cs", "label": 1}
{"text": "Title: The multicolour size-Ramsey number of powers of paths\nAbstract: Given a positive integer $s$, a graph $G$ is $s$-Ramsey for a graph $H$, denoted $G\\rightarrow (H)_s$, if every $s$-colouring of the edges of $G$ contains a monochromatic copy of $H$. The $s$-colour size-Ramsey number ${\\hat{r}}_s(H)$ of a graph $H$ is defined to be ${\\hat{r}}_s(H)=\\min\\{|E(G)|\\colon G\\rightarrow (H)_s\\}$. We prove that, for all positive integers $k$ and $s$, we have ${\\hat{r}}_s(P_n^k)=O(n)$, where $P_n^k$ is the $k$th power of the $n$-vertex path $P_n$.", "field": "math", "label": 1}
{"text": "Title: Improved Training of Sparse Coding Variational Autoencoder via Weight Normalization\nAbstract: Learning a generative model of visual information with sparse and compositional features has been a challenge for both theoretical neuroscience and machine learning communities. Sparse coding models have achieved great success in explaining the receptive fields of mammalian primary visual cortex with sparsely activated latent representation. In this paper, we focus on a recently proposed model, sparse coding variational autoencoder (SVAE) (Barello et al., 2018), and show that the end-to-end training scheme of SVAE leads to a large group of decoding filters not fully optimized with noise-like receptive fields. We propose a few heuristics to improve the training of SVAE and show that a unit $L_2$ norm constraint on the decoder is critical to produce sparse coding filters. Such normalization can be considered as local lateral inhibition in the cortex. We verify this claim empirically on both natural image patches and MNIST dataset and show that projection of the filters onto unit norm drastically increases the number of active filters. Our results highlight the importance of weight normalization for learning sparse representation from data and suggest a new way of reducing the number of inactive latent components in VAE learning.", "field": "cs", "label": 1}
{"text": "Title: Use of Jordan forms for convection-pressure split Euler solvers\nAbstract: In this study, we analyze convection-pressure split Euler flux functions which contain genuine weakly hyperbolic convection subsystems. A system is said to be a genuine weakly hyperbolic if all eigenvalues are real with no complete set of linearly independent (LI) eigenvectors. To construct an upwind solver based on flux difference splitting (FDS) framework, we require to generate complete set of LI eigenvectors. This can be done through addition of generalized eigenvectors which can be computed from theory of Jordan canonical forms. Once we have complete set of LI generalized eigenvectors, we construct upwind solvers in convection-pressure splitting framework. Since generalized eigenvectors are not unique, we take extra care to ensure no direct contribution of generalized eigenvectors in the final formulation of both the newly developed numerical schemes. First scheme is based on Zha and Bilgen type splitting approach, while second is based on Toro and V\\'azquez splitting. Both the schemes are tested on several bench-mark test problems on 1-D and one of them is tested on some typical 2-D test problems which involve shock instabilities. The concept of generalized eigenvector based on Jordan forms is found to be useful in dealing with the genuine weakly hyperbolic parts of the considered Euler systems.", "field": "math", "label": 1}
{"text": "Title: Void Shape Identification in a 2D Point Distribution\nAbstract: We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm. Our methodology initiates with the computational determination of the Convex Hull vertices within the point cloud, followed by a systematic selection of optimal line segments, strategically chosen for their likelihood of intersecting internal void regions. We then utilize Delaunay triangulation in conjunction with Voronoi diagrams to ascertain the initial points for the construction of the maximal internal curve envelope by adopting a pseudo-recursive approach for higher-order void identification. In each iteration, the existing collection of maximal internal curve envelope points serves as a basis for identifying additional candidate points. This iterative process is inherently self-converging, ensuring progressive refinement of the void's shape with each successive computation cycle. The mathematical robustness of this method allows for an efficient convergence to a stable solution, reflecting both the geometric intricacies and the topological characteristics of the voids within the point cloud. Our findings introduce a method that aims to balance geometric accuracy with computational practicality. The approach is designed to improve the understanding of void shapes within point clouds and suggests a potential framework for exploring more complex, multi-dimensional data analysis.", "field": "cs", "label": 0}
{"text": "Title: An invariant for homogeneous spaces of compact quantum groups\nAbstract: The central notion in Connes' formulation of non commutative geometry is that of a spectral triple. Given a homogeneous space of a compact quantum group, restricting our attention to all spectral triples that are `well behaved' with respect to the group action, we construct a certain dimensional invariant. In particular, taking the (quantum) group itself as the homogeneous space, this gives an invariant for a compact quantum group. Computations of this invariant in several cases, including all type A quantum groups, are given.", "field": "math", "label": 1}
{"text": "Title: Somos-4 and a quartic Surface in $\\mathbb{RP}^{3}$\nAbstract: The Somos-4 equation defines the sequences with this name. Looking at these sequences with an additional property we get a quartic polynomial in 4 variables. This polynomial defines a rational, projective surface in $\\mathbb{RP}^{3}$. Here some generators of the subgroup of $Cr_3 (\\mathbb{R})$ are determined, whose birational maps are automorphisms of the quartic surface.", "field": "math", "label": 0}
{"text": "Title: Synchronized CTL over One-Counter Automata\nAbstract: We consider the model-checking problem of Synchronized Computation-Tree Logic (CTL+Sync) over One-Counter Automata (OCAs). CTL+Sync augments CTL with temporal operators that require several paths to satisfy properties in a synchronous manner, e.g., the property \"all paths should eventually see $p$ at the same time\". The model-checking problem for CTL+Sync over finite-state Kripke structures was shown to be in $\\mathsf{P}^{\\mathsf{NP}^{\\mathsf{NP}}}$. OCAs are labelled transition systems equipped with a non-negative counter that can be zero-tested. Thus, they induce infinite-state systems whose computation trees are not regular. The model-checking problem for CTL over OCAs was shown to be $\\mathsf{PSPACE}$-complete. We show that the model-checking problem for CTL+Sync over OCAs is decidable. However, the upper bound we give is non-elementary. We therefore proceed to study the problem for a central fragment of CTL+Sync, extending CTL with operators that require all paths to satisfy properties in a synchronous manner, and show that it is in $\\mathsf{EXP}^\\mathsf{NEXP}$ (and in particular in $\\mathsf{EXPSPACE}$), by exhibiting a certain \"segmented periodicity\" in the computation trees of OCAs.", "field": "cs", "label": 0}
{"text": "Title: Taking Complete Finite Prefixes To High Level, Symbolically\nAbstract: Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of a P/T Petri net's unfolding contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. We evaluate this extended algorithm through a prototype implementation on four novel benchmark families. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.", "field": "cs", "label": 0}
{"text": "Title: Monotonicity Formulas for Bakry-Emery Ricci Curvature\nAbstract: Motivated and inspired by the recent work of Colding [5] and Colding-Minicozzi [6] we derive several families of monotonicity formulas for manifolds with nonnegative Bakry-Emery Ricci curvature, extending the formulas in [5, 6].", "field": "math", "label": 1}
{"text": "Title: Subtraction games in more than one dimension\nAbstract: This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966), with finite subtraction sets. In case of two move rulesets we find a complete solution, via a certain \\P-to-\\P\\ principle (where \\P \\ means that the previous player wins). Namely $x \\in \\P$ if and only if $x +a +b \\in \\P$, where $a$ and $b$ are the two move options. Flammenkamp 1997 observed that, already in one dimension, rulesets with three moves can be hard to analyze, and still today his related conjecture remains open. Here, we solve instances of rulesets with three moves in two dimensions, and conjecture that they all have regular outcomes. Through several computer visualizations of outcomes of multi-move two-dimensional rulesets, we observe that they tend to partition the game board into periodic mosaics on very few regions/segments, which can depend on the number of moves in a ruleset. For example, we have found a five-move ruleset with an outcome segmentation into six semi-infinite slices. In this spirit, we develop a coloring automaton that generalizes the \\P-to-\\P\\ principle. Given an initial set of colored positions, it quickly paints the \\P-positions in segments of the game board. Moreover, we prove that two-dimensional rulesets have row/column eventually periodic outcomes. We pose open problems on the generic hardness of two-dimensional rulesets; several regularity conjectures are provided, but we also conjecture that not all rulesets have regular outcomes.", "field": "math", "label": 0}
{"text": "Title: Topological Data Analysis for Neural Network Analysis: A Comprehensive Survey\nAbstract: This survey provides a comprehensive exploration of applications of Topological Data Analysis (TDA) within neural network analysis. Using TDA tools such as persistent homology and Mapper, we delve into the intricate structures and behaviors of neural networks and their datasets. We discuss different strategies to obtain topological information from data and neural networks by means of TDA. Additionally, we review how topological information can be leveraged to analyze properties of neural networks, such as their generalization capacity or expressivity. We explore practical implications of deep learning, specifically focusing on areas like adversarial detection and model selection. Our survey organizes the examined works into four broad domains: 1. Characterization of neural network architectures; 2. Analysis of decision regions and boundaries; 3. Study of internal representations, activations, and parameters; 4. Exploration of training dynamics and loss functions. Within each category, we discuss several articles, offering background information to aid in understanding the various methodologies. We conclude with a synthesis of key insights gained from our study, accompanied by a discussion of challenges and potential advancements in the field.", "field": "cs", "label": 0}
{"text": "Title: Modeling and analysis of pooled stepped chutes\nAbstract: We consider an application of pooled stepped chutes where the transport in each pooled step is described by the shallow--water equations. Such systems can be found for example at large dams in order to release overflowing water. We analyze the mathematical conditions coupling the flows between different chutes taken from the engineering literature. We present the solution to a Riemann problem in the large and also a well--posedness result for the coupled problem. We finally report on some numerical experiments.", "field": "math", "label": 1}
{"text": "Title: On the intermittency front of stochastic heat equation driven by colored noises\nAbstract: We study the propagation of high peaks (intermittency front) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in $\\mathbb{R}^d$. The noise is assumed to have a general homogeneous covariance in both time and space, and the solution is interpreted in the senses of the Wick product. We give some estimates for the upper and lower bounds of the propagation speed, based on a moment formula of the solution. When the space covariance is given by a Riesz kernel, we give more precise bounds for the propagation speed.", "field": "math", "label": 1}
{"text": "Title: Online codes for analog signals\nAbstract: This paper revisits a classical scenario in communication theory: a waveform sampled at regular intervals is to be encoded so as to minimize distortion in its reconstruction, despite noise. This transformation must be online (causal), to enable real-time signaling; and should use no more power than the original signal. The noise model we consider is an \"atomic norm\" convex relaxation of the standard (discrete alphabet) Hamming-weight-bounded model: namely, adversarial $\\ell_1$-bounded. In the \"block coding\" (noncausal) setting, such encoding is possible due to the existence of large almost-Euclidean sections in $\\ell_1$ spaces, a notion first studied in the work of Dvoretzky in 1961. Our main result is that an analogous result is achievable even causally. Equivalently, our work may be seen as a \"lower triangular\" version of $\\ell_1$ Dvoretzky theorems. In terms of communication, the guarantees are expressed in terms of certain time-weighted norms: the time-weighted $\\ell_2$ norm imposed on the decoder forces increasingly accurate reconstruction of the distant past signal, while the time-weighted $\\ell_1$ norm on the noise ensures vanishing interference from distant past noise. Encoding is linear (hence easy to implement in analog hardware). Decoding is performed by an LP analogous to those used in compressed sensing.", "field": "cs", "label": 1}
{"text": "Title: Large volume limit fibrations over fanifolds\nAbstract: We lift the stratified torus fibration over a fanifold constructed by Gammage--Shende to the associated Weinstein manifold-with-boundary, which is homotopic to a filtered stratified integrable system with noncompact fibers. When the fanifold admits a dual stratified space in a suitable sense, we give a stratified fibration over it completing SYZ picture. For the fanifold associated with a very affine hypersurface, we realize the latter fibration as a restriction of SYZ fibrations over the tropical hypersurface proposed by Abouzaid--Auroux--Katzarkov.", "field": "math", "label": 0}
{"text": "Title: Neural Network Complexity of Chaos and Turbulence\nAbstract: Chaos and turbulence are complex physical phenomena, yet a precise definition of the complexity measure that quantifies them is still lacking. In this work we consider the relative complexity of chaos and turbulence from the perspective of deep neural networks. We analyze a set of classification problems, where the network has to distinguish images of fluid profiles in the turbulent regime from other classes of images such as fluid profiles in the chaotic regime, various constructions of noise and real world images. We analyze incompressible as well as weakly compressible fluid flows. We quantify the complexity of the computation performed by the network via the intrinsic dimensionality of the internal feature representations, and calculate the effective number of independent features which the network uses in order to distinguish between classes. In addition to providing a numerical estimate of the complexity of the computation, the measure also characterizes the neural network processing at intermediate and final stages. We construct adversarial examples and use them to identify the two point correlation spectra for the chaotic and turbulent vorticity as the feature used by the network for classification.", "field": "cs", "label": 1}
{"text": "Title: To Save Mobile Crowdsourcing from Cheap-talk: A Game Theoretic Learning Approach\nAbstract: Today mobile crowdsourcing platforms invite users to provide anonymous reviews about service experiences, yet many reviews are found biased to be extremely positive or negative. The existing methods find it difficult to learn from biased reviews to infer the actual service state, as the state can also be extreme and the platform cannot verify the truthfulness of reviews immediately. Further, reviewers can hide their (positive or negative) bias types and proactively adjust their anonymous reviews against the platform's inference. To our best knowledge, we are the first to study how to save mobile crowdsourcing from cheap-talk and strategically learn from biased users' reviews. We formulate the problem as a dynamic Bayesian game, including users' service-type messaging and the platform's follow-up rating/inference. Our closed-form PBE shows that an extremely-biased user may still honestly message to convince the platform of listening to his review. Such Bayesian game-theoretic learning obviously outperforms the latest common schemes especially when there are multiple diversely-biased users to compete. For the challenging single-user case, we further propose a time-evolving mechanism with the platform's commitment inferences to ensure the biased user's truthful messaging all the time, whose performance improves with more time periods to learn from more historical data.", "field": "cs", "label": 0}
{"text": "Title: Support theorem for the transverse ray transform of tensor fields of rank 2\nAbstract: Let (M, g) be a simple, real analytic, Riemannian manifold with boundary and of dimension n>=3. In this work, we prove a support theorem for the transverse ray transform of tensor fields of rank 2 defined over such manifolds. More specifically, given a symmetric tensor field f of rank 2, we show that if the transverse ray transform of f vanishes over an appropriate open set of maximal geodesics of M , then the support of f vanishes on the points of M that lie on the union of the aforementioned open set of geodesics.", "field": "math", "label": 1}
{"text": "Title: From transient elastic linkages to friction: a complete study of a penalized fourth order equation with delay\nAbstract: In this paper we consider a fourth order nonlinear parabolic delayed problem modelling a quasi-instantaneous turn-over of linkages in the context of cell-motility. The model depends on a small parameter $\\epsilon$ which represents a typical time scale of the memory effect. We first prove global existence and uniqueness of solutions for $\\epsilon$ fixed. This is achieved by combining suitable fixed-point and energy arguments and by uncovering a nonlocal in time, integral conserved quantity. After giving a complete classification of steady states in terms of elliptic functions, we next show that every solution converges to a steady state as $t \\to \\infty$. When $\\epsilon \\to 0$, we then establish convergence results on finite time intervals, showing that the solution tends in a suitable sense towards the solution of a parabolic problem without delay. Moreover, we establish the convergence of energies as $\\epsilon \\to 0$, which enables us to show that, for $\\epsilon$ small enough, the $\\epsilon$-dependent problem inherits part of the large time asymptotics of the limiting parabolic problem.", "field": "math", "label": 0}
{"text": "Title: Temporal Matrix Factorization for Tracking Concept Drift in Individual User Preferences\nAbstract: The matrix factorization (MF) technique has been widely adopted for solving the rating prediction problem in recommender systems. The MF technique utilizes the latent factor model to obtain static user preferences (user latent vectors) and item characteristics (item latent vectors) based on historical rating data. However, in the real world user preferences are not static but full of dynamics. Though there are several previous works that addressed this time varying issue of user preferences, it seems (to the best of our knowledge) that none of them is specifically designed for tracking concept drift in individual user preferences. Motivated by this, we develop a Temporal Matrix Factorization approach (TMF) for tracking concept drift in each individual user latent vector. There are two key innovative steps in our approach: (i) we develop a modified stochastic gradient descent method to learn an individual user latent vector at each time step, and (ii) by the Lasso regression we learn a linear model for the transition of the individual user latent vectors. We test our method on a synthetic dataset and several real datasets. In comparison with the original MF, our experimental results show that our temporal method is able to achieve lower root mean square errors (RMSE) for both the synthetic and real datasets. One interesting finding is that the performance gain in RMSE is mostly from those users who indeed have concept drift in their user latent vectors at the time of prediction. In particular, for the synthetic dataset and the Ciao dataset, there are quite a few users with that property and the performance gains for these two datasets are roughly 20% and 5%, respectively.", "field": "cs", "label": 1}
{"text": "Title: Predators and altruists arriving on jammed Riviera\nAbstract: The Riviera model is a combinatorial model for a settlement along a coastline, introduced recently by the authors. Of most interest are the so-called jammed states, where no more houses can be built without violating the condition that every house needs to have free space to at least one of its sides. In this paper, we introduce new agents (predators and altruists) that want to build houses once the settlement is already in the jammed state. Their behavior is governed by a different set of rules, and this allows them to build new houses even though the settlement is jammed. Our main focus is to detect jammed configurations that are resistant to predators, to altruists, and to both predators and altruists. We provide bivariate generating functions, and complexity functions (configurational entropies) for such jammed configurations. We also discuss this problem in the two-dimensional setting of a combinatorial settlement planning model that was also recently introduced by the authors, and of which the Riviera model is just a special case.", "field": "math", "label": 0}
{"text": "Title: The Local Queue Number of Graphs with Bounded Treewidth\nAbstract: A queue layout of a graph $G$ consists of a vertex ordering of $G$ and a partition of the edges into so-called queues such that no two edges in the same queue nest, i.e., have their endpoints ordered in an ABBA-pattern. Continuing the research on local ordered covering numbers, we introduce the local queue number of a graph $G$ as the minimum $\\ell$ such that $G$ admits a queue layout with each vertex having incident edges in no more than $\\ell$ queues. Similarly to the local page number [Merker, Ueckerdt, GD'19], the local queue number is closely related to the graph's density and can be arbitrarily far from the classical queue number. We present tools to bound the local queue number of graphs from above and below, focusing on graphs of treewidth $k$. Using these, we show that every graph of treewidth $k$ has local queue number at most $k+1$ and that this bound is tight for $k=2$, while a general lower bound is $\\lceil k/2\\rceil+1$. Our results imply, inter alia, that the maximum local queue number among planar graphs is either 3 or 4.", "field": "math", "label": 1}
{"text": "Title: Balancing Continual Learning and Fine-tuning for Human Activity Recognition\nAbstract: Wearable-based Human Activity Recognition (HAR) is a key task in human-centric machine learning due to its fundamental understanding of human behaviours. Due to the dynamic nature of human behaviours, continual learning promises HAR systems that are tailored to users' needs. However, because of the difficulty in collecting labelled data with wearable sensors, existing approaches that focus on supervised continual learning have limited applicability, while unsupervised continual learning methods only handle representation learning while delaying classifier training to a later stage. This work explores the adoption and adaptation of CaSSLe, a continual self-supervised learning model, and Kaizen, a semi-supervised continual learning model that balances representation learning and down-stream classification, for the task of wearable-based HAR. These schemes re-purpose contrastive learning for knowledge retention and, Kaizen combines that with self-training in a unified scheme that can leverage unlabelled and labelled data for continual learning. In addition to comparing state-of-the-art self-supervised continual learning schemes, we further investigated the importance of different loss terms and explored the trade-off between knowledge retention and learning from new tasks. In particular, our extensive evaluation demonstrated that the use of a weighting factor that reflects the ratio between learned and new classes achieves the best overall trade-off in continual learning.", "field": "cs", "label": 0}
{"text": "Title: On Completely Edge-Independent Spanning Trees in Locally Twisted Cubes\nAbstract: A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if any two of them are pairwisely edge-disjoint, they are called completely edge-independent spanning trees (CEISTs for short). CEISTs can facilitate many network functionalities, and constructing CEISTs as maximally allowed as possible in a given network is a worthy undertaking. In this paper, we establish the maximal number of CEISTs in the locally twisted cube network, and propose an algorithm to construct $\\lfloor \\frac{n}{2} \\rfloor$ CEISTs in $LTQ_n$, the $n$-dimensional locally twisted cube. The proposed algorithm has been actually implemented, and we present the outputs. Network broadcasting in the $LTQ_n$ was simulated using $\\lfloor\\frac{n}{2}\\rfloor$ CEISTs, and the performance compared with broadcasting using a single tree.", "field": "cs", "label": 0}
{"text": "Title: Membrane-Dependent Neuromorphic Learning Rule for Unsupervised Spike Pattern Detection\nAbstract: Several learning rules for synaptic plasticity, that depend on either spike timing or internal state variables, have been proposed in the past imparting varying computational capabilities to Spiking Neural Networks. Due to design complications these learning rules are typically not implemented on neuromorphic devices leaving the devices to be only capable of inference. In this work we propose a unidirectional post-synaptic potential dependent learning rule that is only triggered by pre-synaptic spikes, and easy to implement on hardware. We demonstrate that such a learning rule is functionally capable of replicating computational capabilities of pairwise STDP. Further more, we demonstrate that this learning rule can be used to learn and classify spatio-temporal spike patterns in an unsupervised manner using individual neurons. We argue that this learning rule is computationally powerful and also ideal for hardware implementations due to its unidirectional memory access.", "field": "cs", "label": 1}
{"text": "Title: Specific Emitter Identification Based on Joint Variational Mode Decomposition\nAbstract: Specific emitter identification (SEI) technology is significant in device administration scenarios, such as self-organized networking and spectrum management, owing to its high security. For nonlinear and non-stationary electromagnetic signals, SEI often employs variational modal decomposition (VMD) to decompose the signal in order to effectively characterize the distinct device fingerprint. However, the trade-off of VMD between the robustness to noise and the ability to preserve signal information has not been investigated in the current literature. Moreover, the existing VMD algorithm does not utilize the stability of the intrinsic distortion of emitters within a certain temporal span, consequently constraining its practical applicability in SEI. In this paper, we propose a joint variational modal decomposition (JVMD) algorithm, which is an improved version of VMD by simultaneously implementing modal decomposition on multi-frame signals. The consistency of multi-frame signals in terms of the central frequencies and the inherent modal functions (IMFs) is exploited, which effectively highlights the distinctive characteristics among emitters and reduces noise. Additionally, the complexity of JVMD is analyzed, which is proven to be more computational-friendly than VMD. Simulations of both modal decomposition and SEI that involve real-world datasets are presented to illustrate that when compared with VMD, the JVMD algorithm improves the accuracy of device classification and the robustness towards noise.", "field": "cs", "label": 0}
{"text": "Title: Imperfect Delayed CSIT can be as Useful as Perfect Delayed CSIT: DoF Analysis and Constructions for the BC\nAbstract: In the setting of the two-user broadcast channel, where a two-antenna transmitter communicates information to two single-antenna receivers, recent work by Maddah-Ali and Tse has shown that perfect knowledge of delayed channel state information at the transmitter (perfect delayed CSIT) can be useful, even in the absence of any knowledge of current CSIT. Similar benefits of perfect delayed CSIT were revealed in recent work by Kobayashi et al., Yang et al., and Gou and Jafar, which extended the above to the case of perfect delayed CSIT and imperfect current CSIT. The work here considers the general problem of communicating, over the aforementioned broadcast channel, with imperfect delayed and imperfect current CSIT, and reveals that even substantially degraded and imperfect delayed-CSIT is in fact sufficient to achieve the aforementioned gains previously associated to perfect delayed CSIT. The work proposes novel multi-phase broadcasting schemes that properly utilize knowledge of imperfect delayed and imperfect current CSIT, to match in many cases the optimal degrees-of-freedom (DoF) region achieved with perfect delayed CSIT. In addition to the theoretical limits and explicitly constructed precoders, the work applies towards gaining practical insight as to when it is worth improving CSIT quality.", "field": "cs", "label": 1}
{"text": "Title: A Hybrid Neural Network Model For Predicting The Nitrate Concentration In The Recirculating Aquaculture System\nAbstract: This study was groundbreaking in its application of neural network models for nitrate management in the Recirculating Aquaculture System (RAS). A hybrid neural network model was proposed, which accurately predicted daily nitrate concentration and its trends using six water quality parameters. We conducted a 105-day aquaculture experiment, during which we collected 450 samples from five sets of RAS to train our model (C-L-A model) which incorporates Convolutional Neural Network (CNN), Long Short-Term Memory (LSTM), and self-Attention. Furthermore, we obtained 90 samples from a standalone RAS as the testing data to evaluate the performance of the model in practical applications. The experimental results proved that the C-L-A model accurately predicted nitrate concentration in RAS and maintained good performance even with a reduced proportion of training data. We recommend using water quality parameters from the past 7 days to forecast future nitrate concentration, as this timeframe allows the model to achieve maximum generalization capability. Additionally, we compared the performance of the C-L-A model with three basic neural network models (CNN, LSTM, self-Attention) as well as three hybrid neural network models (CNN-LSTM, CNN-Attention, LSTM-Attention). The results demonstrated that the C-L-A model (R2=0.956) significantly outperformed the other neural network models (R2=0.901-0.927). Our study suggests that the utilization of neural network models, specifically the C-L-A model, could potentially assist the RAS industry in conserving resources for daily nitrate monitoring.", "field": "cs", "label": 0}
{"text": "Title: Efficient Continuous Relaxations for Dense CRF\nAbstract: Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range interactions, dense CRFs provide a more detailed labelling compared to their sparse counterparts. Variational inference in these dense models is performed using a filtering-based mean-field algorithm in order to obtain a fully-factorized distribution minimising the Kullback-Leibler divergence to the true distribution. In contrast to the continuous relaxation-based energy minimisation algorithms used for sparse CRFs, the mean-field algorithm fails to provide strong theoretical guarantees on the quality of its solutions. To address this deficiency, we show that it is possible to use the same filtering approach to speed-up the optimisation of several continuous relaxations. Specifically, we solve a convex quadratic programming (QP) relaxation using the efficient Frank-Wolfe algorithm. This also allows us to solve difference-of-convex relaxations via the iterative concave-convex procedure where each iteration requires solving a convex QP. Finally, we develop a novel divide-and-conquer method to compute the subgradients of a linear programming relaxation that provides the best theoretical bounds for energy minimisation. We demonstrate the advantage of continuous relaxations over the widely used mean-field algorithm on publicly available datasets.", "field": "cs", "label": 1}
{"text": "Title: The configuration category of a covering space\nAbstract: We investigate the relationship between the configuration category of a manifold and the configuration category of a covering space of that manifold.", "field": "math", "label": 0}
{"text": "Title: Characterizing Boundedness in Chase Variants\nAbstract: Existential rules are a positive fragment of first-order logic that generalizes function-free Horn rules by allowing existentially quantified variables in rule heads. This family of languages has recently attracted significant interest in the context of ontology-mediated query answering. Forward chaining, also known as the chase, is a fundamental tool for computing universal models of knowledge bases, which consist of existential rules and facts. Several chase variants have been defined, which differ on the way they handle redundancies. A set of existential rules is bounded if it ensures the existence of a bound on the depth of the chase, independently from any set of facts. Deciding if a set of rules is bounded is an undecidable problem for all chase variants. Nevertheless, when computing universal models, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound remains unknown or even very large. Hence, we investigate the decidability of the k-boundedness problem, which asks whether the depth of the chase for a given set of rules is bounded by an integer k. We identify a general property which, when satisfied by a chase variant, leads to the decidability of k-boundedness. We then show that the main chase variants satisfy this property, namely the oblivious, semi-oblivious (aka Skolem), and restricted chase, as well as their breadth-first versions. This paper is under consideration for publication in Theory and Practice of Logic Programming.", "field": "cs", "label": 1}
{"text": "Title: Signal reconstruction from the magnitude of subspace components\nAbstract: We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature conditions, that require at least a quadratic number of subspaces. Moreover, we address reconstruction under the erasure of a subset of the norms; using the concepts of $p$-fusion frames and list decoding, we propose an algorithm that outputs a finite list of candidate signals, one of which is the correct one. In the random setting, we show that a set of subspaces chosen at random and of cardinality scaling linearly in the ambient dimension allows for exact reconstruction with high probability by solving the feasibility problem of a semidefinite program.", "field": "math", "label": 1}
{"text": "Title: Reconstruction from Substrings with Partial Overlap\nAbstract: This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous works considered two extreme cases in which \\emph{all} substrings of some fixed length are read or substrings are read with no overlap, this work considers the setup in which consecutive substrings are read with some given minimum overlap. First, upper bounds are provided on the attainable rates of codes that guarantee unique reconstruction. Then, we present efficient constructions of asymptotically optimal codes that meet the upper bound.", "field": "cs", "label": 1}
{"text": "Title: Continuous Credit Networks and Layer 2 Blockchains: Monotonicity and Sampling\nAbstract: To improve transaction rates, many cryptocurrencies have implemented so-called ''Layer-2'' transaction protocols, where payments are routed across networks of private payment channels. However, for a given transaction, not every network state provides a feasible route to perform the payment; in this case, the transaction must be put on the public ledger. The payment channel network thus multiplies the transaction rate of the overall system; the less frequently it fails, the higher the multiplier. We build on earlier work on credit networks and show that this network liquidity problem is connected to the combinatorics of graphical matroids. Earlier work could only analyze the (unnatural) scenario where transactions had discrete sizes. Superficially, it might seem like the continuous case would be harder to examine. However, removing this assumption lets us make progress in two important directions. First, we give a partial answer to the ``monotonicity conjecture'' that previous work left open. This conjecture asks that the network's performance not degrade as capacity on any edge increases. And second, we construct here a network state sampling procedure with much faster asymptotic performance than off-the-shelf Markov chains ($O(\\vert E\\vert \\beta(\\vert E\\vert))$, where $\\beta(x)$ is the complexity of solving a linear program on $x$ constraints.) We obtain our results by mapping the underlying graphs to convex bodies and then showing that the liquidity and sampling problems reduce to bounding and computing the volumes of these bodies. The transformation relies crucially on the combinatorial properties of the underlying graphic matroid, as do the proofs of monotonicity and fast sampling.", "field": "cs", "label": 1}
{"text": "Title: The relationship between Biological and Artificial Intelligence\nAbstract: Intelligence can be defined as a predominantly human ability to accomplish tasks that are generally hard for computers and animals. Artificial Intelligence [AI] is a field attempting to accomplish such tasks with computers. AI is becoming increasingly widespread, as are claims of its relationship with Biological Intelligence. Often these claims are made to imply higher chances of a given technology succeeding, working on the assumption that AI systems which mimic the mechanisms of Biological Intelligence should be more successful. In this article I will discuss the similarities and differences between AI and the extent of our knowledge about the mechanisms of intelligence in biology, especially within humans. I will also explore the validity of the assumption that biomimicry in AI systems aids their advancement, and I will argue that existing similarity to biological systems in the way Artificial Neural Networks [ANNs] tackle tasks is due to design decisions, rather than inherent similarity of underlying mechanisms. This article is aimed at people who understand the basics of AI (especially ANNs), and would like to be better able to evaluate the often wild claims about the value of biomimicry in AI.", "field": "cs", "label": 1}
{"text": "Title: Jumping numbers of a unibranch curve on a smooth surface\nAbstract: A formula for the jumping numbers of a curve unibranch at a singular point is established. The jumping numbers are expressed in terms of the Enriques diagram of the log resolution of the singularity, or equivalently in terms of the canonical set of generators of the semigroup of the curve at the singular point.", "field": "math", "label": 1}
{"text": "Title: Harvesting of interacting stochastic populations\nAbstract: We analyze the optimal harvesting problem for an ecosystem of species that experience environmental stochasticity. Our work generalizes the current literature significantly by taking into account non-linear interactions between species, state-dependent prices, and species injections. The key generalization is making it possible to not only harvest, but also `seed' individuals into the ecosystem. This is motivated by how fisheries and certain endangered species are controlled. The harvesting problem becomes finding the optimal harvesting-seeding strategy that maximizes the expected total income from the harvest minus the lost income from the species injections. Our analysis shows that new phenomena emerge due to the possibility of species injections. It is well-known that multidimensional harvesting problems are very hard to tackle. We are able to make progress, by characterizing the value function as a viscosity solution of the associated Hamilton-Jacobi-Bellman (HJB) equations. Moreover, we provide a verification theorem, which tells us that if a function has certain properties, then it will be the value function. This allows us to show heuristically, as was shown in Lungu and $\\O$ksendal (Bernoulli '01), that it is almost surely never optimal to harvest or seed from more than one population at a time. We approximate the continuous-time systems by Markov chains and show that the optimal harvesting-seeding strategies of the Markov chain approximations converge to the correct optimal harvesting strategy. This is used to provide numerical approximations to the optimal harvesting-seeding strategies and is a first step towards a full understanding of the intricacies of how one should harvest and seed interacting species. In particular, we look at three examples: one species modeled by a Verhulst-Pearl diffusion, two competing species and a two-species predator-prey system.", "field": "math", "label": 1}
{"text": "Title: A 3-skeleton for a classifying space for the symmetric group\nAbstract: We construct a 3-dimensional cell complex that is the 3-skeleton for an Eilenberg--MacLane classifying space for the symmetric group $\\mathfrak{S}_n$. Our complex starts with the presentation for $\\mathfrak{S}_n$ with $n-1$ adjacent transpositions with squaring, commuting, and braid relations, and adds seven classes of 3-cells that fill in certain 2-spheres bounded by these relations. We use a rewriting system and a combinatorial method of K. Brown to prove the correctness of our construction. Our main application is a computation of the second cohomology of $\\mathfrak{S}_n$ in certain twisted coefficient modules; we use this computation in a companion paper to study splitting of extensions related to braid groups. As another application, we give a concrete description of the third homology of $\\mathfrak{S}_n$ with untwisted coefficients in $\\mathbb{Z}$.", "field": "math", "label": 0}
{"text": "Title: Improving Deep Pancreas Segmentation in CT and MRI Images via Recurrent Neural Contextual Learning and Direct Loss Function\nAbstract: Deep neural networks have demonstrated very promising performance on accurate segmentation of challenging organs (e.g., pancreas) in abdominal CT and MRI scans. The current deep learning approaches conduct pancreas segmentation by processing sequences of 2D image slices independently through deep, dense per-pixel masking for each image, without explicitly enforcing spatial consistency constraint on segmentation of successive slices. We propose a new convolutional/recurrent neural network architecture to address the contextual learning and segmentation consistency problem. A deep convolutional sub-network is first designed and pre-trained from scratch. The output layer of this network module is then connected to recurrent layers and can be fine-tuned for contextual learning, in an end-to-end manner. Our recurrent sub-network is a type of Long short-term memory (LSTM) network that performs segmentation on an image by integrating its neighboring slice segmentation predictions, in the form of a dependent sequence processing. Additionally, a novel segmentation-direct loss function (named Jaccard Loss) is proposed and deep networks are trained to optimize Jaccard Index (JI) directly. Extensive experiments are conducted to validate our proposed deep models, on quantitative pancreas segmentation using both CT and MRI scans. Our method outperforms the state-of-the-art work on CT [11] and MRI pancreas segmentation [1], respectively.", "field": "cs", "label": 1}
{"text": "Title: Cross-Layer Modeling of Randomly Spread CDMA Using Stochastic Network Calculus\nAbstract: Code-division multiple-access (CDMA) has the potential to support traffic sources with a wide range of quality of service (QoS) requirements. The traffic carrying capacity of CDMA channels under QoS constraints (such as delay guarantee) is, however, less well-understood. In this work, we propose a method based on stochastic network calculus and large system analysis to quantify the maximum traffic that can be carried by a multiuser CDMA network under the QoS constraints. At the physical layer, we have linear minimum-mean square error receivers and adaptive modulation and coding, while the channel service process is modeled by using a finite-state Markov chain. We study the impact of delay requirements, violation probability and the user load on the traffic carrying capacity under different signal strengths. A key insight provided by the numerical results is as to how much one has to back-off from capacity under the different delay requirements.", "field": "cs", "label": 1}
{"text": "Title: Neural Ensemble Search via Bayesian Sampling\nAbstract: Recently, neural architecture search (NAS) has been applied to automate the design of neural networks in real-world applications. A large number of algorithms have been developed to improve the search cost or the performance of the final selected architectures in NAS. Unfortunately, these NAS algorithms aim to select only one single well-performing architecture from their search spaces and thus have overlooked the capability of neural network ensemble (i.e., an ensemble of neural networks with diverse architectures) in achieving improved performance over a single final selected architecture. To this end, we introduce a novel neural ensemble search algorithm, called neural ensemble search via Bayesian sampling (NESBS), to effectively and efficiently select well-performing neural network ensembles from a NAS search space. In our extensive experiments, NESBS algorithm is shown to be able to achieve improved performance over state-of-the-art NAS algorithms while incurring a comparable search cost, thus indicating the superior performance of our NESBS algorithm over these NAS algorithms in practice.", "field": "cs", "label": 1}
{"text": "Title: Polynomial Bound and Nonlinear Smoothing for the Benjamin-Ono Equation on the Circle\nAbstract: For initial data in Sobolev spaces $H^s(\\mathbb T)$, $\\frac 12 < s \\leqslant 1$, the solution to the Cauchy problem for the Benjamin-Ono equation on the circle is shown to grow at most polynomially in time at a rate $(1+t)^{3(s-\\frac 12) + \\epsilon}$, $0<\\epsilon \\ll 1$. Key to establishing this result is the discovery of a nonlinear smoothing effect for the Benjamin-Ono equation, according to which the solution to the equation satisfied by a certain gauge transform, which is widely used in the well-posedness theory of the Cauchy problem, becomes smoother once its free solution is removed.", "field": "math", "label": 1}
{"text": "Title: How to Apply Markov Chains for Modeling Sequential Edit Patterns in Collaborative Ontology-Engineering Projects\nAbstract: With the growing popularity of large-scale collaborative ontology-engineering projects, such as the creation of the 11th revision of the International Classification of Diseases, we need new methods and insights to help project- and community-managers to cope with the constantly growing complexity of such projects. In this paper, we present a novel application of Markov chains to model sequential usage patterns that can be found in the change-logs of collaborative ontology-engineering projects. We provide a detailed presentation of the analysis process, describing all the required steps that are necessary to apply and determine the best fitting Markov chain model. Amongst others, the model and results allow us to identify structural properties and regularities as well as predict future actions based on usage sequences. We are specifically interested in determining the appropriate Markov chain orders which postulate on how many previous actions future ones depend on. To demonstrate the practical usefulness of the extracted Markov chains we conduct sequential pattern analyses on a large-scale collaborative ontology-engineering dataset, the International Classification of Diseases in its 11th revision. To further expand on the usefulness of the presented analysis, we show that the collected sequential patterns provide potentially actionable information for user-interface designers, ontology-engineering tool developers and project-managers to monitor, coordinate and dynamically adapt to the natural development processes that occur when collaboratively engineering an ontology. We hope that presented work will spur a new line of ontology-development tools, evaluation-techniques and new insights, further taking the interactive nature of the collaborative ontology-engineering process into consideration.", "field": "cs", "label": 1}
{"text": "Title: Wittgenstein, Peirce, and paradoxes of mathematical proof\nAbstract: Wittgenstein's paradoxical theses that unproved propositions are meaningless, proofs form new concepts and rules, and contradictions are of limited concern, led to a variety of interpretations, most of them centered on the rule-following skepticism. We argue that his intuitions rather reflect resistance to treating meaning as fixed content, and are better understood in the light of C.S. Peirce's distinction between corollarial and theorematic proofs. We show how Peirce's insight that \"all necessary reasoning is diagrammatic\", vindicated in modern epistemic logic and semantic information theory, helps explain the paradoxical ability of deduction to generate new knowledge and meaning.", "field": "math", "label": 1}
{"text": "Title: U-Mixer: An Unet-Mixer Architecture with Stationarity Correction for Time Series Forecasting\nAbstract: Time series forecasting is a crucial task in various domains. Caused by factors such as trends, seasonality, or irregular fluctuations, time series often exhibits non-stationary. It obstructs stable feature propagation through deep layers, disrupts feature distributions, and complicates learning data distribution changes. As a result, many existing models struggle to capture the underlying patterns, leading to degraded forecasting performance. In this study, we tackle the challenge of non-stationarity in time series forecasting with our proposed framework called U-Mixer. By combining Unet and Mixer, U-Mixer effectively captures local temporal dependencies between different patches and channels separately to avoid the influence of distribution variations among channels, and merge low- and high-levels features to obtain comprehensive data representations. The key contribution is a novel stationarity correction method, explicitly restoring data distribution by constraining the difference in stationarity between the data before and after model processing to restore the non-stationarity information, while ensuring the temporal dependencies are preserved. Through extensive experiments on various real-world time series datasets, U-Mixer demonstrates its effectiveness and robustness, and achieves 14.5\\% and 7.7\\% improvements over state-of-the-art (SOTA) methods.", "field": "cs", "label": 0}
{"text": "Title: Hot Streaks on Social Media\nAbstract: Measuring the impact and success of human performance is common in various disciplines, including art, science, and sports. Quantifying impact also plays a key role on social media, where impact is usually defined as the reach of a user's content as captured by metrics such as the number of views, likes, retweets, or shares. In this paper, we study entire careers of Twitter users to understand properties of impact. We show that user impact tends to have certain characteristics: First, impact is clustered in time, such that the most impactful tweets of a user appear close to each other. Second, users commonly have 'hot streaks' of impact, i.e., extended periods of high-impact tweets. Third, impact tends to gradually build up before, and fall off after, a user's most impactful tweet. We attempt to explain these characteristics using various properties measured on social media, including the user's network, content, activity, and experience, and find that changes in impact are associated with significant changes in these properties. Our findings open interesting avenues for future research on virality and influence on social media.", "field": "cs", "label": 1}
{"text": "Title: Density estimation using the perceptron\nAbstract: We propose a new density estimation algorithm. Given $n$ i.i.d. samples from a distribution belonging to a class of densities on $\\mathbb{R}^d$, our estimator outputs any density in the class whose ''perceptron discrepancy'' with the empirical distribution is at most $O(\\sqrt{d/n})$. The perceptron discrepancy between two distributions is defined as the largest difference in mass that they place on any halfspace of $\\mathbb{R}^d$. It is shown that this estimator achieves expected total variation distance to the truth that is almost minimax optimal over the class of densities with bounded Sobolev norm and Gaussian mixtures. This suggests that regularity of the prior distribution could be an explanation for the efficiency of the ubiquitous step in machine learning that replaces optimization over large function spaces with simpler parametric classes (e.g. in the discriminators of GANs). We generalize the above to show that replacing the ''perceptron discrepancy'' with the generalized energy distance of Sz\\'ekeley-Rizzo further improves total variation loss. The generalized energy distance between empirical distributions is easily computable and differentiable, thus making it especially useful for fitting generative models. To the best of our knowledge, it is the first example of a distance with such properties for which there are minimax statistical guarantees.", "field": "math", "label": 0}
{"text": "Title: The Impact of Distance on Performance and Scalability of Distributed Database Systems in Hybrid Clouds\nAbstract: The increasing need for managing big data has led the emergence of advanced database management systems. There has been increased efforts aimed at evaluating the performance and scalability of NoSQL and Relational databases hosted by either private or public cloud datacenters. However, there has been little work on evaluating the performance and scalability of these databases in hybrid clouds, where the distance between private and public cloud datacenters can be one of the key factors that can affect their performance. Hence, in this paper, we present a detailed evaluation of throughput, scalability, and VMs size vs. VMs number for six modern databases in a hybrid cloud, consisting of a private cloud in Adelaide and Azure based datacenter in Sydney, Mumbai, and Virginia regions. Based on results, as the distance between private and public clouds increases, the throughput performance of most databases reduces. Second, MongoDB obtains the best throughput performance, followed by MySQL C luster, whilst Cassandra exposes the most fluctuation in through performance. Third, vertical scalability improves the throughput of databases more than the horizontal scalability. Forth, exploiting bigger VMs rather than more VMs with less cores can increase throughput performance for Cassandra, Riak, and Redis.", "field": "cs", "label": 1}
{"text": "Title: Precise Regret Bounds for Log-loss via a Truncated Bayesian Algorithm\nAbstract: We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper bounds for the sequential minimax regret that are defined as the excess loss it incurs over a class of experts. After proving a general upper bound, we consider some specific classes of experts from Lipschitz class to bounded Hessian class and derive matching lower and upper bounds with provably optimal constants. Our bounds work for a wide range of values of the data dimension and the number of rounds. To derive lower bounds, we use tools from information theory (e.g., Shtarkov sum) and for upper bounds, we resort to new \"smooth truncated covering\" of the class of experts. This allows us to find constructive proofs by applying a simple and novel truncated Bayesian algorithm. Our proofs are substantially simpler than the existing ones and yet provide tighter (and often optimal) bounds.", "field": "cs", "label": 1}
{"text": "Title: A note on $t$-designs in isodual codes\nAbstract: In the present paper, we construct 3-designs using extended binary quadratic residue codes and their dual codes.", "field": "math", "label": 0}
{"text": "Title: Agile Behaviour Design: A Design Approach for Structuring Game Characters and Interactions\nAbstract: In this paper, a novel design methodology-Agile Behaviour Design-is presented that accommodates the requirements for developing complex game agents suitable for industrial environments. An essential part of the design approach is to support independent work of both designers and programmers by reducing bottleneck situations. The approach fosters the creation of more loose and fluid interactions between design and implementation, leaving more freedom for creative expression.", "field": "cs", "label": 1}
{"text": "Title: Inference with System W Satisfies Syntax Splitting\nAbstract: In this paper, we investigate inductive inference with system W from conditional belief bases with respect to syntax splitting. The concept of syntax splitting for inductive inference states that inferences about independent parts of the signature should not affect each other. This was captured in work by Kern-Isberner, Beierle, and Brewka in the form of postulates for inductive inference operators expressing syntax splitting as a combination of relevance and independence; it was also shown that c-inference fulfils syntax splitting, while system P inference and system Z both fail to satisfy it. System W is a recently introduced inference system for nonmonotonic reasoning that captures and properly extends system Z as well as c-inference. We show that system W fulfils the syntax splitting postulates for inductive inference operators by showing that it satisfies the required properties of relevance and independence. This makes system W another inference operator besides c-inference that fully complies with syntax splitting, while in contrast to c-inference, also extending rational closure.", "field": "cs", "label": 1}
{"text": "Title: On the use of the M-quantiles for outlier detection in multivariate data\nAbstract: Defining a successful notion of a multivariate quantile has been an open problem for more than half a century, motivating a plethora of possible solutions. Of these, the approach of [8] and [25] leading to M-quantiles, is very appealing for its mathematical elegance combining elements of convex analysis and probability theory. The key idea is the description of a convex function (the K-function) whose gradient (the K-transform) is in one-to-one correspondence between all of R^d and the unit ball in R^d. By analogy with the d=1 case where the K-transform is a cumulative distribution function-like object (an M-distribution), the fact that its inverse is guaranteed to exist lends itself naturally to providing the basis for the definition of a quantile function for all d>=1. Over the past twenty years the resulting M-quantiles have seen applications in a variety of fields, primarily for the purpose of detecting outliers in multidimensional spaces. In this article we prove that for odd d>=3, it is not the gradient but a poly-Laplacian of the K-function that is (almost everywhere) proportional to the density function. For d even one cannot establish a differential equation connecting the K-function with the density. These results show that usage of the K-transform for outlier detection in higher odd-dimensions is in principle flawed, as the K-transform does not originate from inversion of a true M-distribution. We demonstrate these conclusions in two dimensions through examples from non-standard asymmetric distributions. Our examples illustrate a feature of the K-transform whereby regions in the domain with higher density map to larger volumes in the co-domain, thereby producing a magnification effect that moves inliers closer to the boundary of the co-domain than outliers. This feature obviously disrupts any outlier detection mechanism that relies on the inverse K-transform.", "field": "math", "label": 0}
{"text": "Title: Properties of Mean Value Sets: Angle Conditions, Blowup Solutions, and Nonconvexity\nAbstract: We study the mean values sets of the second order divergence form elliptic operator with principal coefficients defined as $$a^{ij}_k(x):= \\begin{cases} \\alpha_k \\delta^{ij}(x) &x_n>0 \\beta_k \\delta^{ij}(x) &x_n<0. \\end{cases}$$ In particular, we will show that the mean value sets associated to such an operator need not be convex as $\\alpha_k$ and $\\beta_k$ converge to 1. This example then leads to an example of nonconvex mean value sets for smooth $a^{ij}(x)$.", "field": "math", "label": 1}
{"text": "Title: Moduli of non-commutative polarized schemes\nAbstract: We construct, using geometric invariant theory, a quasi-projective Deligne-Mumford stack of stable graded algebras. We also construct a derived enhancement, which classifies twisted bundles of stable graded A-infinity-algebras. The tangent complex of the derived scheme is given by graded Hochschild cohomology, which we relate to ordinary Hochschild cohomology. We obtain a version of Hilbert stability for non-commutative projective schemes.", "field": "math", "label": 1}
{"text": "Title: Approximating Numerical Flux by Fourier Neural Operators for the Hyperbolic Conservation Laws\nAbstract: Classical numerical schemes exist for solving PDEs numerically, and recently, neural network-based methods have been developed. However, methodologies using neural networks, such as PINN and neural operators, lack robustness and generalization power. To compensate for such drawbacks, there are many types of research combining classical numerical schemes and machine learning methods by replacing a small portion of the numerical schemes with neural networks. In this work, we focus on hyperbolic conservation laws and replace numerical fluxes in the numerical schemes by neural operator. For this, we construct losses that are motivated by numerical schemes for conservation laws and approximate numerical flux by FNO. Through experiments, we show that our methodology has advantages of both numerical schemes and FNO by comparing with original methods. For instance, we demonstrate our method gains robustness, resolution invariance property, and feasibility of a data-driven method. Our method especially has the ability to predict continuously in time and generalization power on the out-of-distribution samples, which are challenges to be tackled for existing neural operator methods.", "field": "math", "label": 0}
{"text": "Title: Mining Temporal Attack Patterns from Cyberthreat Intelligence Reports\nAbstract: Defending from cyberattacks requires practitioners to operate on high-level adversary behavior. Cyberthreat intelligence (CTI) reports on past cyberattack incidents describe the chain of malicious actions with respect to time. To avoid repeating cyberattack incidents, practitioners must proactively identify and defend against recurring chain of actions - which we refer to as temporal attack patterns. Automatically mining the patterns among actions provides structured and actionable information on the adversary behavior of past cyberattacks. The goal of this paper is to aid security practitioners in prioritizing and proactive defense against cyberattacks by mining temporal attack patterns from cyberthreat intelligence reports. To this end, we propose ChronoCTI, an automated pipeline for mining temporal attack patterns from cyberthreat intelligence (CTI) reports of past cyberattacks. To construct ChronoCTI, we build the ground truth dataset of temporal attack patterns and apply state-of-the-art large language models, natural language processing, and machine learning techniques. We apply ChronoCTI on a set of 713 CTI reports, where we identify 124 temporal attack patterns - which we categorize into nine pattern categories. We identify that the most prevalent pattern category is to trick victim users into executing malicious code to initiate the attack, followed by bypassing the anti-malware system in the victim network. Based on the observed patterns, we advocate organizations to train users about cybersecurity best practices, introduce immutable operating systems with limited functionalities, and enforce multi-user authentications. Moreover, we advocate practitioners to leverage the automated mining capability of ChronoCTI and design countermeasures against the recurring attack patterns.", "field": "cs", "label": 0}
{"text": "Title: Reproducing formulas for generalized translation invariant systems on locally compact abelian groups\nAbstract: In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let $\\Gamma_j$, $j \\in J$, be a countable family of closed, co-compact subgroups of a second countable locally compact abelian group $G$ and study systems of the form $\\cup_{j \\in J}\\{g_{j,p}(\\cdot - \\gamma)\\}_{\\gamma \\in \\Gamma_j, p \\in P_j}$ with generators $g_{j,p}$ in $L^2(G)$ and with each $P_j$ being a countable or an uncountable index set. We refer to systems of this form as generalized translation invariant (GTI) systems. Many of the familiar transforms, e.g., the wavelet, shearlet and Gabor transform, both their discrete and continuous variants, are GTI systems. Under a technical $\\alpha$ local integrability condition ($\\alpha$-LIC) we characterize when GTI systems constitute tight and dual frames that yield reproducing formulas for $L^2(G)$. This generalizes results on generalized shift invariant systems, where each $P_j$ is assumed to be countable and each $\\Gamma_j$ is a uniform lattice in $G$, to the case of uncountably many generators and (not necessarily discrete) closed, co-compact subgroups. Furthermore, even in the case of uniform lattices $\\Gamma_j$, our characterizations improve known results since the class of GTI systems satisfying the $\\alpha$-LIC is strictly larger than the class of GTI systems satisfying the previously used local integrability condition. As an application of our characterization results, we obtain new characterizations of translation invariant continuous frames and Gabor frames for $L^2(G)$. In addition, we will see that the admissibility conditions for the continuous and discrete wavelet and Gabor transform in $L^2(\\mathbb{R}^n)$ are special cases of the same general characterizing equations.", "field": "math", "label": 1}
{"text": "Title: Center of Mass Technique and Affine Geometry\nAbstract: The notion of center of mass, which is very useful in kinematics, proves to be very handy in geometry (see [1]-[2]). Countless applications of center of mass to geometry go back to Archimedes. Unfortunately, the center of mass cannot be defined for sets whose total mass equals zero. In the paper we improve this disadvantage and assign to an n-dimensional affine space L over any field k the (n+1)-dimensional vector space over the field k of weighty points and mass dipoles in L. In this space, the sum of weighted points with nonzero total mass is equal to the center of mass of these points equipped with their total mass. We present several interpretations of the space of weighty points and mass dipoles in L, and a couple of its applications to geometry. The paper is self-contained and is accessible for undergraduate students.", "field": "math", "label": 0}
{"text": "Title: Profinite equivariant spectra and their tensor-triangular geometry\nAbstract: We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all other models in the literature. We describe the Balmer spectrum of finite $G$-spectra up to the ambiguity that is present in the finite group case; in particular, we obtain a thick subcategory theorem when $G$ is abelian. By verifying the bijectivity hypothesis for $\\mathsf{Sp}_G$, we prove a nilpotence theorem for all profinite groups. Our study then moves to the realm of rational $G$-equivariant spectra. By exploiting the continuity of our model, we construct an equivalence between the category of rational $G$-spectra and the algebraic model of the second author and Sugrue, which improves their result to the symmetric monoidal and $\\infty$-categorical level. Furthermore, we prove that the telescope conjecture holds in this category. Finally, we characterize when the category of rational $G$-spectra is stratified, resulting in a classification of the localizing ideals in terms of conjugacy classes of subgroups. To facilitate these results, we develop some foundational aspects of pro-tt-geometry. For instance, we establish and use the continuity of the homological spectrum and introduce a notion of von Neumann regular tt-categories, of which rational $G$-spectra is an example.", "field": "math", "label": 0}
{"text": "Title: Theory of sexes by Geodakian as it is advanced by Iskrin\nAbstract: In 1960s V.Geodakian proposed a theory that explains sexes as a mechanism for evolutionary adaptation of the species to changing environmental conditions. In 2001 V.Iskrin refined and augmented the concepts of Geodakian and gave a new and interesting explanation to several phenomena which involve sex, and sex ratio, including the war-years phenomena. He also introduced a new concept of the \"catastrophic sex ratio.\" This note is an attempt to digest technical aspects of the new ideas by Iskrin.", "field": "cs", "label": 1}
{"text": "Title: Cambrian triangulations and their tropical realizations\nAbstract: This paper develops a Cambrian extension of the work of C. Ceballos, A. Padrol and C. Sarmiento on $\\nu$-Tamari lattices and their tropical realizations. For any signature $\\varepsilon \\in \\{\\pm\\}^n$, we consider a family of $\\varepsilon$-trees in bijection with the triangulations of the $\\varepsilon$-polygon. These $\\varepsilon$-trees define a flag regular triangulation $\\mathcal{T}^\\varepsilon$ of the subpolytope $\\operatorname{conv} \\{(\\mathbf{e}_{i_\\bullet}, \\mathbf{e}_{j_\\circ}) \\, | \\, 0 \\le i_\\bullet < j_\\circ \\le n+1 \\}$ of the product of simplices $\\triangle_{\\{0_\\bullet, \\dots, n_\\bullet\\}} \\times \\triangle_{\\{1_\\circ, \\dots, (n+1)_\\circ\\}}$. The oriented dual graph of the triangulation $\\mathcal{T}^\\varepsilon$ is the Hasse diagram of the (type $A$) $\\varepsilon$-Cambrian lattice of N. Reading. For any $I_\\bullet \\subseteq \\{0_\\bullet, \\dots, n_\\bullet\\}$ and $J_\\circ \\subseteq \\{1_\\circ, \\dots, (n+1)_\\circ\\}$, we consider the restriction $\\mathcal{T}^\\varepsilon_{I_\\bullet, J_\\circ}$ of the triangulation $\\mathcal{T}^\\varepsilon$ to the face $\\triangle_{I_\\bullet} \\times \\triangle_{J_\\circ}$. Its dual graph is naturally interpreted as the increasing flip graph on certain $(\\varepsilon, I_\\bullet, J_\\circ)$-trees, which is shown to be a lattice generalizing in particular the $\\nu$-Tamari lattices in the Cambrian setting. Finally, we present an alternative geometric realization of $\\mathcal{T}^\\varepsilon_{I_\\bullet, J_\\circ}$ as a polyhedral complex induced by a tropical hyperplane arrangement.", "field": "math", "label": 1}
{"text": "Title: Three term rational function progressions in finite fields\nAbstract: Let $F(t),G(t)\\in \\mathbb{Q}(t)$ be rational functions such that $F(t),G(t)$ and the constant function $1$ are linearly independent over $\\mathbb{Q}$, we prove an asymptotic formula for the number of the three term rational function progressions of the form $x,x+F(y),x+G(y)$ in subsets of $\\mathbb{F}_p$. The main new ingredient is an algebraic geometry version of PET induction that bypasses Weyl's differencing. This answers a question of Bourgain and Chang.", "field": "math", "label": 0}
{"text": "Title: Quantiles on global non-positive curvature spaces\nAbstract: This paper develops a notion of geometric quantiles on Hadamard spaces, also known as global non-positive curvature spaces. After providing some definitions and basic properties, including scaled isometry equivariance and a necessary condition on the gradient of the quantile loss function at quantiles on Hadamard manifolds, we investigate asymptotic properties of sample quantiles on Hadamard manifolds, such as strong consistency and joint asymptotic normality. We provide a detailed description of how to compute quantiles using a gradient descent algorithm in hyperbolic space and, in particular, an explicit formula for the gradient of the quantile loss function, along with experiments using simulated and real single-cell RNA sequencing data.", "field": "math", "label": 0}
{"text": "Title: Spatiotemporal Attention for Multivariate Time Series Prediction and Interpretation\nAbstract: Multivariate time series modeling and prediction problems are abundant in many machine learning application domains. Accurate interpretation of such prediction outcomes from a machine learning model that explicitly captures temporal correlations can significantly benefit the domain experts. In this context, temporal attention has been successfully applied to isolate the important time steps for the input time series. However, in multivariate time series problems, spatial interpretation is also critical to understand the contributions of different variables on the model outputs. We propose a novel deep learning architecture, called spatiotemporal attention mechanism (STAM) for simultaneous learning of the most important time steps and variables. STAM is a causal (i.e., only depends on past inputs and does not use future inputs) and scalable (i.e., scales well with an increase in the number of variables) approach that is comparable to the state-of-the-art models in terms of computational tractability. We demonstrate our models' performance on two popular public datasets and a domain-specific dataset. When compared with the baseline models, the results show that STAM maintains state-of-the-art prediction accuracy while offering the benefit of accurate spatiotemporal interpretability. The learned attention weights are validated from a domain knowledge perspective for these real-world datasets.", "field": "cs", "label": 1}
{"text": "Title: Symplectic period for a representation of $GL_n(D)$\nAbstract: In this paper, we study the irreducible admissible representations of $GL_{n}(D)$ with a symplectic period for $n = 3$ and $4$, i.e., those representations which have a linear functional invariant under $Sp_n(D)$, where $D$ is a quaternion division algebra over a non-archimedean local field $k$ of characteristic zero and $Sp_n(D)$ is the unique non-split inner form of the symplectic group $Sp_{2n}(k)$. Our results contain all distinguished unitary representations stated in Prasad's conjecture.", "field": "math", "label": 0}
{"text": "Title: First International HARTING Open Source Prize Winner: The igus Humanoid Open Platform\nAbstract: The use of standard platforms in the field of humanoid robotics can lower the entry barrier for new research groups, and accelerate research by the facilitation of code sharing. Numerous humanoid standard platforms exist in the lower size ranges of up to 60cm, but beyond that humanoid robots scale up quickly in weight and price, becoming less affordable and more difficult to operate, maintain and modify. The igus Humanoid Open Platform is an affordable, fully open-source platform for humanoid research. At 92cm, the robot is capable of acting in an environment meant for humans, and is equipped with enough sensors, actuators and computing power to support researchers in many fields. The structure of the robot is entirely 3D printed, leading to a lightweight and visually appealing design. This paper covers the mechanical and electrical aspects of the robot, as well as the main features of the corresponding open-source ROS software. At RoboCup 2016, the platform was awarded the first International HARTING Open Source Prize.", "field": "cs", "label": 1}
{"text": "Title: Reconstructing almost all of a point set in $\\mathbb{R}^d$ from randomly revealed pairwise distances\nAbstract: Let $V$ be a set of $n$ points in $\\mathbb{R}^d$, and suppose that the distance between each pair of points is revealed independently with probability $p$. We study when this information is sufficient to reconstruct large subsets of $V$, up to isometry. Strong results for $d=1$ have been obtained by Gir\\~ao, Illingworth, Michel, Powierski, and Scott. In this paper, we investigate higher dimensions, and show that if $p>n^{-2/(d+4)}$, then we can reconstruct almost all of $V$ up to isometry, with high probability. We do this by relating it to a polluted graph bootstrap percolation result, for which we adapt the methods of Balogh, Bollob\\'as, and Morris.", "field": "math", "label": 0}
{"text": "Title: A New Criterion on Normal Bases of Finite Field Extensions\nAbstract: A new criterion on normal bases of finite field extension $\\mathbb{F}_{q^n} / \\mathbb{F}_{q}$ is presented and explicit criterions for several particular finite field extensions are derived from this new criterion.", "field": "math", "label": 1}
{"text": "Title: Non-commutative ambits and equivariant compactifications\nAbstract: We prove that an action $\\rho:A\\to M(C_0(\\mathbb{G})\\otimes A)$ of a locally compact quantum group on a $C^*$-algebra has a universal equivariant compactification, and prove a number of other category-theoretic results on $\\mathbb{G}$-equivariant compactifications: that the categories compactifications of $\\rho$ and $A$ respectively are locally presentable (hence complete and cocomplete), that the forgetful functor between them is a colimit-creating left adjoint, and that epimorphisms therein are surjective and injections are regular monomorphisms. When $\\mathbb{G}$ is regular coamenable we also show that the forgetful functor from unital $\\mathbb{G}$-$C^*$-algebras to unital $C^*$-algebras creates finite limits and is comonadic, and that the monomorphisms in the former category are injective.", "field": "math", "label": 1}
{"text": "Title: Minimum $2$-vertex strongly biconnected spanning directed subgraph problem\nAbstract: A directed graph $G=(V,E)$ is strongly biconnected if $G$ is strongly connected and its underlying graph is biconnected. A strongly biconnected directed graph $G=(V,E)$ is called $2$-vertex-strongly biconnected if $|V|\\geq 3$ and the induced subgraph on $V\\setminus\\left\\lbrace w\\right\\rbrace $ is strongly biconnected for every vertex $w\\in V$. In this paper we study the following problem. Given a $2$-vertex-strongly biconnected directed graph $G=(V,E)$, compute an edge subset $E^{2sb} \\subseteq E$ of minimum size such that the subgraph $(V,E^{2sb})$ is $2$-vertex-strongly biconnected.", "field": "cs", "label": 1}
{"text": "Title: Toward 6G: From New Hardware Design to Wireless Semantic and Goal-Oriented Communication Paradigms\nAbstract: Several speculative visions are conjecturing on what 6G services will be able to offer at the horizon of 2030. Nevertheless, the 6G design process is at its preliminary stages. The reality today is that hardware, technologies and new materials required to effectively meet the unprecedented performance targets required for future 6G services and network operation, have not been designed, tested or even do not exist yet. Today, a solid vision on the cost-benefit trade-offs of machine learning and artificial intelligence support for 6G network and services operation optimization is missing. This includes the possible support from hardware efficiency, operation effectiveness and, the immeasurable cost due to data acquisition-transfer-processing. The contribution of this paper is three-fold. This is the first paper deriving crucial 6G key performance indicators on hardware and technology design. Second, we present a new hardware technologies design methodology conceived to enable the effective software-hardware components integration required to meet the challenging performance envisioned for future 6G networks. Third, we suggest a paradigm shift towards goal-oriented and semantic communications, in which a totally new opportunity of joint design of hardware, artificial intelligence and effective communication is offered. The proposed vision is consolidated by our recent results on hardware, technology and machine learning performance.", "field": "cs", "label": 1}
{"text": "Title: Differentially Private Sketches for Jaccard Similarity Estimation\nAbstract: This paper describes two locally-differential private algorithms for releasing user vectors such that the Jaccard similarity between these vectors can be efficiently estimated. The basic building block is the well known MinHash method. To achieve a privacy-utility trade-off, MinHash is extended in two ways using variants of Generalized Randomized Response and the Laplace Mechanism. A theoretical analysis provides bounds on the absolute error and experiments show the utility-privacy trade-off on synthetic and real-world data. The paper ends with a critical discussion of related work.", "field": "cs", "label": 1}
{"text": "Title: Introducing Packet-Level Analysis in Programmable Data Planes to Advance Network Intrusion Detection\nAbstract: Programmable data planes offer precise control over the low-level processing steps applied to network packets, serving as a valuable tool for analysing malicious flows in the field of intrusion detection. Albeit with limitations on physical resources and capabilities, they allow for the efficient extraction of detailed traffic information, which can then be utilised by Machine Learning (ML) algorithms responsible for identifying security threats. In addressing resource constraints, existing solutions in the literature rely on compressing network data through the collection of statistical traffic features in the data plane. While this compression saves memory resources in switches and minimises the burden on the control channel between the data and the control plane, it also results in a loss of information available to the Network Intrusion Detection System (NIDS), limiting access to packet payload, categorical features, and the semantic understanding of network communications, such as the behaviour of packets within traffic flows. This paper proposes P4DDLe, a framework that exploits the flexibility of P4-based programmable data planes for packet-level feature extraction and pre-processing. P4DDLe leverages the programmable data plane to extract raw packet features from the network traffic, categorical features included, and to organise them in a way that the semantics of traffic flows are preserved. To minimise memory and control channel overheads, P4DDLe selectively processes and filters packet-level data, so that only the features required by the NIDS are collected. The experimental evaluation with recent Distributed Denial of Service (DDoS) attack data demonstrates that the proposed approach is very efficient in collecting compact and high-quality representations of network flows, ensuring precise detection of DDoS attacks.", "field": "cs", "label": 0}
{"text": "Title: Faster optimal univariate microgaggregation\nAbstract: Microaggregation is a method to coarsen a dataset, by optimally clustering data points in groups of at least $k$ points, thereby providing a $k$-anonymity type disclosure guarantee for each point in the dataset. Previous algorithms for univariate microaggregation had a $O(k n)$ time complexity. By rephrasing microaggregation as an instance of the concave least weight subsequence problem, in this work we provide improved algorithms that provide an optimal univariate microaggregation on sorted data in $O(n)$ time and space. We further show that our algorithms work not only for sum of squares cost functions, as typically considered, but seamlessly extend to many other cost functions used for univariate microaggregation tasks. In experiments we show that the presented algorithms lead to real world performance improvements.", "field": "cs", "label": 0}
{"text": "Title: DHOT-GM: Robust Graph Matching Using A Differentiable Hierarchical Optimal Transport Framework\nAbstract: Graph matching is one of the most significant graph analytic tasks in practice, which aims to find the node correspondence across different graphs. Most existing approaches rely on adjacency matrices or node embeddings when matching graphs, whose performances are often sub-optimal because of not fully leveraging the multi-modal information hidden in graphs, such as node attributes, subgraph structures, etc. In this study, we propose a novel and effective graph matching method based on a differentiable hierarchical optimal transport (HOT) framework, called DHOT-GM. Essentially, our method represents each graph as a set of relational matrices corresponding to the information of different modalities. Given two graphs, we enumerate all relational matrix pairs and obtain their matching results, and accordingly, infer the node correspondence by the weighted averaging of the matching results. This method can be implemented as computing the HOT distance between the two graphs -- each matching result is an optimal transport plan associated with the Gromov-Wasserstein (GW) distance between two relational matrices, and the weights of all matching results are the elements of an upper-level optimal transport plan defined on the matrix sets. We propose a bi-level optimization algorithm to compute the HOT distance in a differentiable way, making the significance of the relational matrices adjustable. Experiments on various graph matching tasks demonstrate the superiority and robustness of our method compared to state-of-the-art approaches.", "field": "cs", "label": 0}
{"text": "Title: Higher Descent Data as a Homotopy Limit\nAbstract: We define the 2-groupoid of descent data assigned to a cosimplicial 2-groupoid and present it as the homotopy limit of the cosimplicial space gotten after applying the 2-nerve in each cosimplicial degree. This can be applied also to the case of $n$-groupoids thus providing an analogous presentation of \"descent data\" in higher dimensions.", "field": "math", "label": 1}
{"text": "Title: On the Theoretical Gap of Channel Hopping Sequences with Maximum Rendezvous Diversity in the Multichannel Rendezvous Problem\nAbstract: In the literature, there are several well-known periodic channel hopping (CH) sequences that can achieve maximum rendezvous diversity in a cognitive radio network (CRN). For a CRN with $N$ channels, it is known that the period of such a CH sequence is at least $N^2$. The asymptotic approximation ratio, defined as the ratio of the period of a CH sequence to the lower bound $N^2$ when $N \\to \\infty$, is still 2.5 for the best known CH sequence in the literature. An open question in the multichannel rendezvous problem is whether it is possible to construct a periodic CH sequence that has the asymptotic approximation ratio 1. In this paper, we tighten the theoretical gap by proposing CH sequences, called IDEAL-CH, that have the asymptotic approximation ratio 2. For a weaker requirement that only needs the two users to rendezvous on one commonly available channel in a period, we propose channel hopping sequences, called ORTHO-CH, with period $(2p +1)p$, where $p$ is the smallest prime not less than $N$.", "field": "cs", "label": 1}
{"text": "Title: Some Fibonacci-Related Sequences\nAbstract: We discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the Walnut theorem-prover. We also prove two new results about synchronized sequences.", "field": "math", "label": 0}
{"text": "Title: On instability of Type (II) Lawson-Osserman Cones\nAbstract: We obtain the instability of Type (II) Lawson-Osserman cones in Euclidean spaces, and thus provide a family of (uncountably many) unstable solutions with singularity to the Dirichlet problem for minimal graphs of high codimension versus smooth unstable ones by Lawson-Osserman through a min-max technique. To our knowledge, these are the first examples of non-smooth unstable minimal graphs and unlikely detectible through the mean curvature flow or min-max theory.", "field": "math", "label": 1}
{"text": "Title: Ramsey Partial Orders from Acyclic Graphs\nAbstract: We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that class of acyclic graphs has the Ramsey property and uses the partite construction.", "field": "math", "label": 1}
{"text": "Title: On a reduction map for Drinfeld modules\nAbstract: In this paper we investigate a local to global principle for Mordell-Weil group defined over a ring of integers ${\\cal O}_K$ of $t$-modules that are products of the Drinfeld modules ${\\widehat\\varphi}={\\phi}_{1}^{e_1}\\times \\dots \\times {\\phi}_{t}^{e_{t}}.$ Here $K$ is a finite extension of the field of fractions of $A={\\mathbb F}_{q}[t].$ We assume that the ${\\mathrm{rank}}(\\phi)_{i})=d_{i}$ and endomorphism rings of the involved Drinfeld modules of generic characteristic are the simplest possible, i.e. ${\\mathrm{End}}({\\phi}_{i})=A$ for $ i=1,\\dots , t.$ Our main result is the following numeric criterion. Let ${N}={N}_{1}^{e_1}\\times\\dots\\times {N}_{t}^{e_t}$ be a finitely generated $A$ submodule of the Mordell-Weil group ${\\widehat\\varphi}({\\cal O}_{K})={\\phi}_{1}({\\cal O}_{K})^{e_{1}}\\times\\dots\\times {\\phi}_{t}({\\cal O}_{K})^{{e}_{t}},$ and let ${\\Lambda}\\subset N$ be an $A$ - submodule. If we assume $d_{i}\\geq e_{i}$ and $P\\in N$ such that $r_{\\cal W}(P)\\in r_{\\cal W}({\\Lambda}) $ for almost all primes ${\\cal W}$ of ${\\cal O}_{K},$ then $P\\in {\\Lambda}+N_{tor}.$ We also build on the recent results of S.Bara{\\'n}czuk \\cite{b17} concerning the dynamical local to global principle in Mordell-Weil type groups and the solvability of certain dynamical equations to the aforementioned $t$-modules.", "field": "math", "label": 1}
{"text": "Title: Murre's conjectures for certain product varieties\nAbstract: We consider Murre's conjectures on Chow groups for a fourfold which is a product of two curves and a surface. We give a result which concerns Conjecture D:the kernel of a certain projector is equal to the homologically trivial part of the Chow group. We also give a proof of Conjecture B for a product of two surfaces.", "field": "math", "label": 1}
{"text": "Title: Approximate Approximations from scattered data\nAbstract: The aim of this paper is to extend the approximate quasi-interpolation on a uniform grid by dilated shifts of a smooth and rapidly decaying function on a uniform grid to scattered data quasi-interpolation. It is shown that high order approximation of smooth functions up to some prescribed accuracy is possible, if the basis functions, which are centered at the scattered nodes, are multiplied by suitable polynomials such that their sum is an approximate partition of unity. For Gaussian functions we propose a method to construct the approximate partition of unity and describe the application of the new quasi-interpolation approach to the cubature of multi-dimensional integral operators.", "field": "math", "label": 1}
{"text": "Title: Counterexamples to the local-global principle associated with Swinnerton-Dyer's cubic form\nAbstract: In this paper, we imitate a classical construction of a counterexample to the local-global principle of cubic forms of 4 variables which was discovered first by Swinnerton-Dyer (Mathematica (1962)). Our construction gives new explicit families of counterexamples in homogeneous forms of $4, 5, 6, ..., 2n+2$ variables of degree $2n+1$ for infinitely many integers $n$. It is contrastive to Swinnerton-Dyer's original construction that we do not need any concrete calculation in the proof of local solubility.", "field": "math", "label": 1}
{"text": "Title: On the linear complexity for multidimensional sequences\nAbstract: In this paper, we define the linear complexity for multidimensional sequences over finite fields, generalizing the one-dimensional case. We give some lower and upper bounds, valid with large probability, for the linear complexity and $k$-error linear complexity of multidimensional periodic sequences.", "field": "math", "label": 1}
{"text": "Title: PEGASUS: Physically Enhanced Gaussian Splatting Simulation System for 6DOF Object Pose Dataset Generation\nAbstract: We introduce Physically Enhanced Gaussian Splatting Simulation System (PEGASUS) for 6DOF object pose dataset generation, a versatile dataset generator based on 3D Gaussian Splatting. Environment and object representations can be easily obtained using commodity cameras to reconstruct with Gaussian Splatting. PEGASUS allows the composition of new scenes by merging the respective underlying Gaussian Splatting point cloud of an environment with one or multiple objects. Leveraging a physics engine enables the simulation of natural object placement within a scene through interaction between meshes extracted for the objects and the environment. Consequently, an extensive amount of new scenes - static or dynamic - can be created by combining different environments and objects. By rendering scenes from various perspectives, diverse data points such as RGB images, depth maps, semantic masks, and 6DoF object poses can be extracted. Our study demonstrates that training on data generated by PEGASUS enables pose estimation networks to successfully transfer from synthetic data to real-world data. Moreover, we introduce the Ramen dataset, comprising 30 Japanese cup noodle items. This dataset includes spherical scans that captures images from both object hemisphere and the Gaussian Splatting reconstruction, making them compatible with PEGASUS.", "field": "cs", "label": 0}
{"text": "Title: Real-Time 2D Temperature Field Prediction in Metal Additive Manufacturing Using Physics-Informed Neural Networks\nAbstract: Accurately predicting the temperature field in metal additive manufacturing (AM) processes is critical to preventing overheating, adjusting process parameters, and ensuring process stability. While physics-based computational models offer precision, they are often time-consuming and unsuitable for real-time predictions and online control in iterative design scenarios. Conversely, machine learning models rely heavily on high-quality datasets, which can be costly and challenging to obtain within the metal AM domain. Our work addresses this by introducing a physics-informed neural network framework specifically designed for temperature field prediction in metal AM. This framework incorporates a physics-informed input, physics-informed loss function, and a Convolutional Long Short-Term Memory (ConvLSTM) architecture. Utilizing real-time temperature data from the process, our model predicts 2D temperature fields for future timestamps across diverse geometries, deposition patterns, and process parameters. We validate the proposed framework in two scenarios: full-field temperature prediction for a thin wall and 2D temperature field prediction for cylinder and cubic parts, demonstrating errors below 3% and 1%, respectively. Our proposed framework exhibits the flexibility to be applied across diverse scenarios with varying process parameters, geometries, and deposition patterns.", "field": "cs", "label": 0}
{"text": "Title: A macroscopic model for a system of swarming agents using curvature control\nAbstract: In this paper, we study the macroscopic limit of a new model of collective displacement. The model, called PTWA, is a combination of the Vicsek alignment model and the Persistent Turning Walker (PTW) model of motion by curvature control. The PTW model was designed to fit measured trajectories of individual fish. The PTWA model (Persistent Turning Walker with Alignment) describes the displacements of agents which modify their curvature in order to align with their neighbors. The derivation of its macroscopic limit uses the non-classical notion of generalized collisional invariant. The macroscopic limit of the PTWA model involves two physical quantities, the density and the mean velocity of individuals. It is a system of hyperbolic type but is non-conservative due to a geometric constraint on the velocity. This system has the same form as the macroscopic limit of the Vicsek model (the 'Vicsek hydrodynamics') but for the expression of the model coefficients. The numerical computations show that the numerical values of the coefficients are very close. The 'Vicsek Hydrodynamic model' appears in this way as a more generic macroscopic model of swarming behavior as originally anticipated.", "field": "math", "label": 1}
{"text": "Title: $F$-finiteness of homomorphisms and its descent\nAbstract: Let $p$ be a prime number. We define the notion of $F$-finiteness of homomorphisms of $\\mathbb F_p$-algebras, and discuss some basic properties. In particular, we prove a sort of descent theorem on $F$-finiteness of homomorphisms of $\\mathbb F_p$-algebras. As a corollary, we prove the following. Let $g:B\\to C$ be a homomorphism of Noetherian $\\mathbb F_p$-algebras. If $g$ is faithfully flat reduced, and $C$ is $F$-finite, then $B$ is $F$-finite. This is a generalization of Seydi's result on excellent local rings of characteristic $p$.", "field": "math", "label": 1}
{"text": "Title: Improving Automated Program Repair with Domain Adaptation\nAbstract: Automated Program Repair (APR) is defined as the process of fixing a bug/defect in the source code, by an automated tool. APR tools have recently experienced promising results by leveraging state-of-the-art Neural Language Processing (NLP) techniques. APR tools such as TFix and CodeXGLUE combine text-to-text transformers with software-specific techniques are outperforming alternatives, these days. However, in most APR studies the train and test sets are chosen from the same set of projects. In reality, however, APR models are meant to be generalizable to new and different projects. Therefore, there is a potential threat that reported APR models with high effectiveness perform poorly when the characteristics of the new project or its bugs are different than the training set's(Domain Shift). In this study, we first define and measure the domain shift problem in automated program repair. Then, we then propose a domain adaptation framework that can adapt an APR model for a given target project. We conduct an empirical study with three domain adaptation methods FullFineTuning, TuningWithLightWeightAdapterLayers, and CurriculumLearning using two state-of-the-art domain adaptation tools (TFix and CodeXGLUE) and two APR models on 611 bugs from 19 projects. The results show that our proposed framework can improve the effectiveness of TFix by 13.05% and CodeXGLUE by 23.4%. Another contribution of this study is the proposal of a data synthesis method to address the lack of labelled data in APR. We leverage transformers to create a bug generator model. We use the generated synthetic data to domain adapt TFix and CodeXGLUE on the projects with no data (Zero-shot learning), which results in an average improvement of 5.76% and 24.42% for TFix and CodeXGLUE, respectively.", "field": "cs", "label": 1}
{"text": "Title: Learning Knowledge Representation with Meta Knowledge Distillation for Single Image Super-Resolution\nAbstract: Knowledge distillation (KD), which can efficiently transfer knowledge from a cumbersome network (teacher) to a compact network (student), has demonstrated its advantages in some computer vision applications. The representation of knowledge is vital for knowledge transferring and student learning, which is generally defined in hand-crafted manners or uses the intermediate features directly. In this paper, we propose a model-agnostic meta knowledge distillation method under the teacher-student architecture for the single image super-resolution task. It provides a more flexible and accurate way to help the teachers transmit knowledge in accordance with the abilities of students via knowledge representation networks (KRNets) with learnable parameters. In order to improve the perception ability of knowledge representation to students' requirements, we propose to solve the transformation process from intermediate outputs to transferred knowledge by employing the student features and the correlation between teacher and student in the KRNets. Specifically, the texture-aware dynamic kernels are generated and then extract texture features to be improved and the corresponding teacher guidance so as to decompose the distillation problem into texture-wise supervision for further promoting the recovery quality of high-frequency details. In addition, the KRNets are optimized in a meta-learning manner to ensure the knowledge transferring and the student learning are beneficial to improving the reconstructed quality of the student. Experiments conducted on various single image super-resolution datasets demonstrate that our proposed method outperforms existing defined knowledge representation related distillation methods, and can help super-resolution algorithms achieve better reconstruction quality without introducing any inference complexity.", "field": "cs", "label": 1}
{"text": "Title: Index theory for traveling waves in reaction diffusion systems with skew gradient structure\nAbstract: A unified geometric approach for the stability analysis of traveling pulse solutions for reaction-diffusion equations with skew-gradient structure has been established in a previous paper [9], but essentially no results have been found in the case of traveling front solutions. In this work, we will bridge this gap. For such cases, a Maslov index of the traveling wave is well-defined, and we will show how it can be used to provide the spectral information of the waves. As an application, we use the same index providing the exact number of unstable eigenvalues of the traveling front solutions of FitzHugh-Nagumo equation.", "field": "math", "label": 1}
{"text": "Title: Generating synthetic data for neural operators\nAbstract: Numerous developments in the recent literature show the promising potential of deep learning in obtaining numerical solutions to partial differential equations (PDEs) beyond the reach of current numerical solvers. However, data-driven neural operators all suffer from the same problem: the data needed to train a network depends on classical numerical solvers such as finite difference or finite element, among others. In this paper, we propose a new approach to generating synthetic functional training data that does not require solving a PDE numerically. The way we do this is simple: we draw a large number $N$ of independent and identically distributed `random functions' $u_j$ from the underlying solution space (e.g., $H_0^1(\\Omega)$) in which we know the solution lies according to classical theory. We then plug each such random candidate solution into the equation and get a corresponding right-hand side function $f_j$ for the equation, and consider $(f_j, u_j)_{j=1}^N$ as supervised training data for learning the underlying inverse problem $f \\rightarrow u$. This `backwards' approach to generating training data only requires derivative computations, in contrast to standard `forward' approaches, which require a numerical PDE solver, enabling us to generate a large number of such data points quickly and efficiently. While the idea is simple, we hope that this method will expand the potential for developing neural PDE solvers that do not depend on classical numerical solvers.", "field": "cs", "label": 0}
{"text": "Title: Online minimum search for Brownian motion and the Cauchy process: Multiple approache\nAbstract: The distribution for the minimum of Brownian motion or the Cauchy process is well-known using the reflection principle. Here we consider the problem of finding the sample-by-sample minimum, which we call the online minimum search. We consider the possibility of the golden search method, but we show quantitatively that the bisection method is more efficient. In the bisection method there is a hierarchical parameter, which tunes the depth to which each sub-search is conducted, somewhat similarly to how a depth-first search works to generate a topological ordering on nodes. Finally, we consider the possibility of using harmonic measure, which is a novel idea that has so far been unexplored.", "field": "math", "label": 0}
{"text": "Title: Presentations of Kauffman bracket skein algebras of planar surfaces\nAbstract: Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface $\\Sigma_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by explicit generators and relations. The presentation is independent of $R$, and can be considered as a quantization of the trace algebra of $n$ generic $2\\times 2$ unimodular matrices.", "field": "math", "label": 0}
{"text": "Title: Globalizing and stabilizing global $\\infty$-categories\nAbstract: We consider the question of cocompleting partially presentable parametrized $\\infty$-categories in the sense of arXiv:2307.11001. As our main result we show that in certain cases one may compute such relative cocompletions via a very explicit formula given in terms of partially lax limits. We then apply this to equivariant homotopy theory, building on the work of op. cit. and arXiv:2301.08240, to conclude that the global $\\infty$-category of globally equivariant spectra is the relative cocompletion of the global $\\infty$-category of equivariant spectra. Evaluating at a group $G$ we obtain a description of the $\\infty$-category of $G$-global spectra as a partially lax limit, extending the main result of arXiv:2206.01556 for finite groups to $G$-global homotopy theory. Finally we investigate the question of stabilizing global $\\infty$-categories by inverting the action of representation spheres, and deduce a second universal property for the global $\\infty$-category of globally equivariant spectra, similar to that of arXiv:2302.06207.", "field": "math", "label": 0}
{"text": "Title: Know Your Limits: Uncertainty Estimation with ReLU Classifiers Fails at Reliable OOD Detection\nAbstract: A crucial requirement for reliable deployment of deep learning models for safety-critical applications is the ability to identify out-of-distribution (OOD) data points, samples which differ from the training data and on which a model might underperform. Previous work has attempted to tackle this problem using uncertainty estimation techniques. However, there is empirical evidence that a large family of these techniques do not detect OOD reliably in classification tasks. This paper gives a theoretical explanation for said experimental findings and illustrates it on synthetic data. We prove that such techniques are not able to reliably identify OOD samples in a classification setting, since their level of confidence is generalized to unseen areas of the feature space. This result stems from the interplay between the representation of ReLU networks as piece-wise affine transformations, the saturating nature of activation functions like softmax, and the most widely-used uncertainty metrics.", "field": "cs", "label": 1}
{"text": "Title: Dynamic Local Regret for Non-convex Online Forecasting\nAbstract: We consider online forecasting problems for non-convex machine learning models. Forecasting introduces several challenges such as (i) frequent updates are necessary to deal with concept drift issues since the dynamics of the environment change over time, and (ii) the state of the art models are non-convex models. We address these challenges with a novel regret framework. Standard regret measures commonly do not consider both dynamic environment and non-convex models. We introduce a local regret for non-convex models in a dynamic environment. We present an update rule incurring a cost, according to our proposed local regret, which is sublinear in time T. Our update uses time-smoothed gradients. Using a real-world dataset we show that our time-smoothed approach yields several benefits when compared with state-of-the-art competitors: results are more stable against new data; training is more robust to hyperparameter selection; and our approach is more computationally efficient than the alternatives.", "field": "cs", "label": 1}
{"text": "Title: Galois subspaces for smooth projective curves\nAbstract: Given an embedding of a smooth projective curve $X$ of genus $g\\geq1$ into $\\mathbb{P}^N$, we study the locus of linear subspaces of $\\mathbb{P}^N$ of codimension 2 such that projection from said subspace, composed with the embedding, gives a Galois morphism $X\\to\\mathbb{P}^1$. For genus $g\\geq2$ we prove that this locus is a smooth projective variety with components isomorphic to projective spaces. If $g=1$ and the embedding is given by a complete linear system, we prove that this locus is also a smooth projective variety whose positive-dimensional components are isomorphic to projective bundles over \\'etale quotients of the elliptic curve, and we describe these components explicitly.", "field": "math", "label": 1}
{"text": "Title: Pseudorandom Hashing for Space-bounded Computation with Applications in Streaming\nAbstract: We revisit Nisan's classical pseudorandom generator (PRG) for space-bounded computation (STOC 1990) and its applications in streaming algorithms. We describe a new generator, HashPRG, that can be thought of as a symmetric version of Nisan's generator over larger alphabets. Our generator allows a trade-off between seed length and the time needed to compute a given block of the generator's output. HashPRG can be used to obtain derandomizations with much better update time and \\emph{without sacrificing space} for a large number of data stream algorithms, such as $F_p$ estimation in the parameter regimes $p > 2$ and $0 < p < 2$ and CountSketch with tight estimation guarantees as analyzed by Minton and Price (SODA 2014) which assumed access to a random oracle. We also show a recent analysis of Private CountSketch can be derandomized using our techniques. For a $d$-dimensional vector $x$ being updated in a turnstile stream, we show that $\\|x\\|_{\\infty}$ can be estimated up to an additive error of $\\varepsilon\\|x\\|_{2}$ using $O(\\varepsilon^{-2}\\log(1/\\varepsilon)\\log d)$ bits of space. Additionally, the update time of this algorithm is $O(\\log 1/\\varepsilon)$ in the Word RAM model. We show that the space complexity of this algorithm is optimal up to constant factors. However, for vectors $x$ with $\\|x\\|_{\\infty} = \\Theta(\\|x\\|_{2})$, we show that the lower bound can be broken by giving an algorithm that uses $O(\\varepsilon^{-2}\\log d)$ bits of space which approximates $\\|x\\|_{\\infty}$ up to an additive error of $\\varepsilon\\|x\\|_{2}$. We use our aforementioned derandomization of the CountSketch data structure to obtain this algorithm, and using the time-space trade off of HashPRG, we show that the update time of this algorithm is also $O(\\log 1/\\varepsilon)$ in the Word RAM model.", "field": "cs", "label": 0}
{"text": "Title: Random walk on the high-dimensional IIC\nAbstract: We study the asymptotic behavior the exit times of random walk from Euclidean balls around the origin of the incipient infinite cluster in a manner inspired by [26]. We do this by obtaining bounds on the effective resistance between the origin and the boundary of these Euclidean balls. We show that the geometric properties of long-range percolation clusters are significantly different from those of finite-range clusters. We also study the behavior of random walk on the backbone of the IIC and we prove that the Alexander-Orbach conjecture holds for the incipient infinite cluster in high dimensions, both for long-range percolation and for finite-range percolation.", "field": "math", "label": 1}
{"text": "Title: Matroid Products in Tropical Geometry\nAbstract: Symmetric powers of matroids were first introduced by Lovasz and Mason in the 1970s, where it was shown that not all matroids admit higher symmetric powers. Since these initial findings, the study of matroid symmetric powers has remained largely unexplored. In this paper, we establish an equivalence between valuated matroids with arbitrarily large symmetric powers and tropical linear spaces that appear as the variety of a tropical ideal. In establishing this equivalence, we additionally show that all tropical linear spaces are connected through codimension one. These results provide additional geometric and algebraic connections to the study of matroid symmetric powers, which we leverage to prove that the class of matroids with second symmetric power is minor closed and has infinitely many forbidden minors.", "field": "math", "label": 0}
{"text": "Title: Permawound Unipotent Groups\nAbstract: We introduce the class of permawound unipotent groups, and show that they simultaneously satisfy certain \"ubiquity\" and \"rigidity\" properties that in combination render them very useful in the study of general wound unipotent groups. As an illustration of their utility, we present two applications: We prove that nonsplit smooth unipotent groups over (infinite) finitely-generated fields have infinite first cohomology; and we show that every commutative p-torsion wound unipotent group over a field of degree of imperfection 1 is the maximal unipotent quotient of a commutative pseudo-reductive group, thus partially answering a question of Totaro.", "field": "math", "label": 0}
{"text": "Title: Linking forms of amphichiral knots\nAbstract: We give a simple obstruction for a knot to be amphichiral, in terms of the homology of the 2-fold branched cover. We work with unoriented knots, and so obstruct both positive and negative amphichirality.", "field": "math", "label": 1}
{"text": "Title: Beck modules and alternative algebras\nAbstract: We set out the general theory of \"Beck modules\" in a variety of algebras and describe them as modules over suitable \"universal enveloping\" unital associative algebras. We pay particular attention to the somewhat nonstandard case of \"alternative algebras,\" defined by a restricted associative law, and determine the Poincar\\'e polynomial of the universal enveloping algebra in the homogenous case.", "field": "math", "label": 0}
{"text": "Title: Detecting Hostile Posts using Relational Graph Convolutional Network\nAbstract: This work is based on the submission to the competition Hindi Constraint conducted by AAAI@2021 for detection of hostile posts in Hindi on social media platforms. Here, a model is presented for detection and classification of hostile posts and further classify into fake, offensive, hate and defamation using Relational Graph Convolutional Networks. Unlike other existing work, our approach is focused on using semantic meaning along with contextutal information for better classification. The results from AAAI@2021 indicates that the proposed model is performing at par with Google's XLM-RoBERTa on the given dataset. Our best submission with RGCN achieves an F1 score of 0.97 (7th Rank) on coarse-grained evaluation and achieved best performance on identifying fake posts. Among all submissions to the challenge, our classification system with XLM-Roberta secured 2nd rank on fine-grained classification.", "field": "cs", "label": 1}
{"text": "Title: Smoothing cones over K3 surfaces\nAbstract: We prove that the affine cone over a general primitively polarised K3 surface of genus g is smoothable if and only if g\\le 10 or g=12. We also give several examples of singularities with special behaviour, such as surfaces whose affine cone is smoothable even though the projective cone is not.", "field": "math", "label": 1}
{"text": "Title: Non-isogenous superelliptic jacobians II\nAbstract: Let $\\ell$ be an odd prime and $K$ a field of characteristic different from $\\ell$. Let $\\bar{K}$ be an algebraic closure of $K$. Assume that $K$ contains a primitive $\\ell$th root of unity. Let $n \\ne \\ell$ be another odd prime. Let $f(x)$ and $h(x)$ be degree $n$ polynomials with coefficients in $K$ and without repeated roots. Let us consider superelliptic curves $C_{f,\\ell}: y^{\\ell}=f(x)$ and $C_{h,\\ell}: y^{\\ell}=h(x)$ of genus $(n-1)(\\ell-1)/2$, and their jacobians $J^{(f,\\ell)}$ and $J^{(h,\\ell)}$, which are $(n-1)(\\ell-1)/2$-dimensional abelian varieties over $\\bar{K}$. Suppose that one of the polynomials is irreducible and the other reducible over $K$. We prove that if $J^{(f,\\ell)}$ and $J^{(h,\\ell)}$ are isogenous over $\\bar{K}$ then both endomorphism algebras $\\mathrm{End}^{0}(J^{(f,\\ell)})$ and $\\mathrm{End}^{0}(J^{(h,\\ell)})$ contain an invertible element of multiplicative order $n$.", "field": "math", "label": 0}
{"text": "Title: Structural properties of weak cotype 2 spaces\nAbstract: Several characterizations of weak cotype 2 and weak Hilbert spaces are given in terms of basis constants and other structural invariants of Banach spaces. For finite-dimensional spaces, characterizations depending on subspaces of fixed proportional dimension are proved.", "field": "math", "label": 1}
{"text": "Title: Pre-trained Recommender Systems: A Causal Debiasing Perspective\nAbstract: Recent studies on pre-trained vision/language models have demonstrated the practical benefit of a new, promising solution-building paradigm in AI where models can be pre-trained on broad data describing a generic task space and then adapted successfully to solve a wide range of downstream tasks, even when training data is severely limited (e.g., in zero- or few-shot learning scenarios). Inspired by such progress, we investigate in this paper the possibilities and challenges of adapting such a paradigm to the context of recommender systems, which is less investigated from the perspective of pre-trained model. In particular, we propose to develop a generic recommender that captures universal interaction patterns by training on generic user-item interaction data extracted from different domains, which can then be fast adapted to improve few-shot learning performance in unseen new domains (with limited data). However, unlike vision/language data which share strong conformity in the semantic space, universal patterns underlying recommendation data collected across different domains (e.g., different countries or different E-commerce platforms) are often occluded by both in-domain and cross-domain biases implicitly imposed by the cultural differences in their user and item bases, as well as their uses of different e-commerce platforms. As shown in our experiments, such heterogeneous biases in the data tend to hinder the effectiveness of the pre-trained model. To address this challenge, we further introduce and formalize a causal debiasing perspective, which is substantiated via a hierarchical Bayesian deep learning model, named PreRec. Our empirical studies on real-world data show that the proposed model could significantly improve the recommendation performance in zero- and few-shot learning settings under both cross-market and cross-platform scenarios.", "field": "cs", "label": 0}
{"text": "Title: A note on a flip-connected class of generalized domino tilings of the box $[0,2]^n$\nAbstract: Let $n,d\\in \\mathbb{N}$ and $n>d$. An $(n-d)$-domino is a box $I_1\\times \\cdots \\times I_n$ such that $I_j\\in \\{[0,1],[1,2]\\}$ for all $j\\in N\\subset [n]$ with $|N|=d$ and $I_i=[0,2]$ for every $i\\in [n]\\setminus N$. If $A$ and $B$ are two $(n-d)$-dominoes such that $A\\cup B$ is an $(n-(d-1))$-domino, then $A,B$ is called a twin pair. If $C,D$ are two $(n-d)$-dominoes which form a twin pair such that $A\\cup B=C\\cup D$ and $\\{C,D\\}\\neq \\{A,B\\}$, then the pair $C,D$ is called a flip of $A,B$. A family $\\mathscr{D}$ of $(n-d)$-dominoes is a tiling of the box $[0,2]^n$ if interiors of every two members of $\\mathscr{D}$ are disjoint and $\\bigcup_{B\\in \\mathscr{D}}B=[0,2]^n$. An $(n-d)$-domino tiling $\\mathscr{D}'$ is obtained from an $(n-d)$-domino tiling $\\mathscr{D}$ by a flip, if there is a twin pair $A,B\\in \\mathscr{D}$ such that $\\mathscr{D}'=(\\mathscr{D}\\setminus \\{A,B\\})\\cup \\{C,D\\}$, where $C,D$ is a flip of $A,B$. A family of $(n-d)$-domino tilings of the box $[0,2]^n$ is flip-connected, if for every two members $\\mathscr{D},\\mathscr{E}$ of this family the tiling $\\mathscr{E}$ can be obtained from $\\mathscr{D}$ by a sequence of flips. In the paper some flip-connected class of $(n-d)$-domino tilings of the box $[0,2]^n$ is described.", "field": "math", "label": 0}
{"text": "Title: Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games\nAbstract: We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional instances of MFGs that are beyond reach with existing solution methods. We achieve this in two steps. First, we take advantage of the underlying variational primal-dual structure that MFGs exhibit and phrase it as a convex-concave saddle point problem. Second, we parameterize the value and density functions by two neural networks, respectively. By phrasing the problem in this manner, solving the MFG can be interpreted as a special case of training a generative adversarial network (GAN). We show the potential of our method on up to 100-dimensional MFG problems.", "field": "cs", "label": 1}
{"text": "Title: Projections, Embeddings and Stability\nAbstract: In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and practical implications; the theory applies even if the boundary operator is rank deficient, or near rank deficient. If desired, the pseudoinverse can be implemented directly using standard tools like Matlab. We also introduce a new and simplified version of the semidiscrete approximation of the linear PDE system, which completely avoids taking the time derivative of the boundary data. The stability results are valid for general, nondiagonal summation-by-parts norms. Another key result is the extension of summation-by-parts operators to multi-domains by means of carefully crafted embedding operators. No extra numerical boundary conditions are required at the grid interfaces. The aforementioned pseudoinverse allows for a compact representation of these multi-block operators, which preserves all relevant properties of the single-block operators. The embedding operators can be constructed for multiple space dimensions. Numerical results for the two-dimensional Maxwell's equations are presented, and they show very good agreement with theory.", "field": "math", "label": 0}
{"text": "Title: Set-valued prediction in hierarchical classification with constrained representation complexity\nAbstract: Set-valued prediction is a well-known concept in multi-class classification. When a classifier is uncertain about the class label for a test instance, it can predict a set of classes instead of a single class. In this paper, we focus on hierarchical multi-class classification problems, where valid sets (typically) correspond to internal nodes of the hierarchy. We argue that this is a very strong restriction, and we propose a relaxation by introducing the notion of representation complexity for a predicted set. In combination with probabilistic classifiers, this leads to a challenging inference problem for which specific combinatorial optimization algorithms are needed. We propose three methods and evaluate them on benchmark datasets: a na\\\"ive approach that is based on matrix-vector multiplication, a reformulation as a knapsack problem with conflict graph, and a recursive tree search method. Experimental results demonstrate that the last method is computationally more efficient than the other two approaches, due to a hierarchical factorization of the conditional class distribution.", "field": "cs", "label": 1}
{"text": "Title: Stable Set Polytopes with High Lift-and-Project Ranks for the Lovász-Schrijver SDP Operator\nAbstract: We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lov{\\'a}sz--Schrijver SDP operator $\\LS_+$, with a particular focus on a search for relatively small graphs with high $\\LS_+$-rank (the least number of iterations of the $\\LS_+$ operator on the fractional stable set polytope to compute the stable set polytope). We provide families of graphs whose $\\LS_+$-rank is asymptotically a linear function of its number of vertices, which is the best possible up to improvements in the constant factor (previous best result in this direction, from 1999, yielded graphs whose $\\LS_+$-rank only grew with the square root of the number of vertices).", "field": "math", "label": 0}
{"text": "Title: Quotients of the braid group that are extensions of the symmetric group\nAbstract: We consider normal subgroups $N$ of the braid group $B_n$ such that the quotient $B_n/N$ is an extension of the symmetric group by an abelian group. We show that, if $n\\geq 4$, then there are exactly 8 commensurability classes of such subgroups. We define a Specht subgroup to be a subgroup of this form that is maximal in its commensurability class. We give descriptions of the Specht subgroups in terms of winding numbers and in terms of infinite generating sets. The quotient of the pure braid group by a Specht subgroup is a module over the symmetric group. We show that the modules arising this way are closely related to Specht modules for the partitions $(n-1,1)$ and $(n-2,2)$, working over the integers. We compute the second cohomology of the symmetric group with coefficients in both of these Specht modules, working over an arbitrary commutative ring. Finally, we determine which of the extensions of the symmetric group arising from Specht subgroups are split extensions.", "field": "math", "label": 0}
{"text": "Title: Real-and-Present: Investigating the Use of Life-Size 2D Video Avatars in HMD-Based AR Teleconferencing\nAbstract: Augmented Reality (AR) teleconferencing allows separately located users to interact with each other in 3D through agents in their own physical environments. Existing methods leveraging volumetric capturing and reconstruction can provide a high-fidelity experience but are often too complex and expensive for everyday usage. Other solutions target mobile and effortless-to-setup teleconferencing on AR Head Mounted Displays (HMD). They directly transplant the conventional video conferencing onto an AR-HMD platform or use avatars to represent remote participants. However, they can only support either a high fidelity or a high level of co-presence. Moreover, the limited Field of View (FoV) of HMDs could further influence users' immersive experience. To achieve a balance between fidelity and co-presence, we explore using life-size 2D video-based avatars (video avatars for short) in AR teleconferencing. Specifically, with the potential effect of FoV on users' perception of proximity, we first conduct a pilot study to explore the local-user-centered optimal placement of video avatars in small-group AR conversations. With the placement results, we then implement a proof-of-concept prototype of video-avatar-based teleconferencing. We conduct user evaluations with the prototype to verify its effectiveness in balancing fidelity and co-presence. Following the indication in the pilot study, we further quantitatively explore the effect of FoV size on the video avatar's optimal placement through a user study involving more FoV conditions in a VR-simulated environment. We regress placement models to serve as references for computationally determining video avatar placements in such teleconferencing applications on various existing AR HMDs and future ones with bigger FoVs.", "field": "cs", "label": 0}
{"text": "Title: Brown representability for directed graphs\nAbstract: We prove that any contravariant functor from the homotopy category of finite directed graphs to abelian groups satisfying the additivity axiom and the Mayer-Vietoris axiom is representable.", "field": "math", "label": 1}
{"text": "Title: An Achievable Rate-Distortion Region for the Multiple Descriptions Problem\nAbstract: A multiple-descriptions (MD) coding strategy is proposed and an inner bound to the achievable rate-distortion region is derived. The scheme utilizes linear codes. It is shown in two different MD set-ups that the linear coding scheme achieves a larger rate-distortion region than previously known random coding strategies. Furthermore, it is shown via an example that the best known random coding scheme for the set-up can be improved by including additional randomly generated codebooks.", "field": "cs", "label": 1}
{"text": "Title: Will 6G be Semantic Communications? Opportunities and Challenges from Task Oriented and Secure Communications to Integrated Sensing\nAbstract: This paper explores opportunities and challenges of task (goal)-oriented and semantic communications for next-generation (NextG) communication networks through the integration of multi-task learning. This approach employs deep neural networks representing a dedicated encoder at the transmitter and multiple task-specific decoders at the receiver, collectively trained to handle diverse tasks including semantic information preservation, source input reconstruction, and integrated sensing and communications. To extend the applicability from point-to-point links to multi-receiver settings, we envision the deployment of decoders at various receivers, where decentralized learning addresses the challenges of communication load and privacy concerns, leveraging federated learning techniques that distribute model updates across decentralized nodes. However, the efficacy of this approach is contingent on the robustness of the employed deep learning models. We scrutinize potential vulnerabilities stemming from adversarial attacks during both training and testing phases. These attacks aim to manipulate both the inputs at the encoder at the transmitter and the signals received over the air on the receiver side, highlighting the importance of fortifying semantic communications against potential multi-domain exploits. Overall, the joint and robust design of task-oriented communications, semantic communications, and integrated sensing and communications in a multi-task learning framework emerges as the key enabler for context-aware, resource-efficient, and secure communications ultimately needed in NextG network systems.", "field": "cs", "label": 0}
{"text": "Title: Explicit separations between randomized and deterministic Number-on-Forehead communication\nAbstract: We study the power of randomness in the Number-on-Forehead (NOF) model in communication complexity. We construct an explicit 3-player function $f:[N]^3 \\to \\{0,1\\}$, such that: (i) there exist a randomized NOF protocol computing it that sends a constant number of bits; but (ii) any deterministic or nondeterministic NOF protocol computing it requires sending about $(\\log N)^{1/3}$ many bits. This exponentially improves upon the previously best-known such separation. At the core of our proof is an extension of a recent result of the first and third authors on sets of integers without 3-term arithmetic progressions into a non-arithmetic setting.", "field": "cs", "label": 0}
{"text": "Title: Joint symbolic aggregate approximation of time series\nAbstract: The increasing availability of temporal data poses a challenge to time-series and signal-processing domains due to its high numerosity and complexity. Symbolic representation outperforms raw data in a variety of engineering applications due to its storage efficiency, reduced numerosity, and noise reduction. The most recent symbolic aggregate approximation technique called ABBA demonstrates outstanding performance in preserving essential shape information of time series and enhancing the downstream applications. However, ABBA cannot handle multiple time series with consistent symbols, i.e., the same symbols from distinct time series are not identical. Also, working with appropriate ABBA digitization involves the tedious task of tuning the hyperparameters, such as the number of symbols or tolerance. Therefore, we present a joint symbolic aggregate approximation that has symbolic consistency, and show how the hyperparameter of digitization can itself be optimized alongside the compression tolerance ahead of time. Besides, we propose a novel computing paradigm that enables parallel computing of symbolic approximation. The extensive experiments demonstrate its superb performance and outstanding speed regarding symbolic approximation and reconstruction.", "field": "cs", "label": 0}
{"text": "Title: Development of An Autonomous Bridge Deck Inspection Robotic System\nAbstract: The threat to safety of aging bridges has been recognized as a critical concern to the general public due to the poor condition of many bridges in the U.S. Currently, the bridge inspection is conducted manually, and it is not efficient to identify bridge condition deterioration in order to facilitate implementation of appropriate maintenance or rehabilitation procedures. In this paper, we report a new development of the autonomous mobile robotic system for bridge deck inspection and evaluation. The robot is integrated with several nondestructive evaluation (NDE) sensors and a navigation control algorithm to allow it to accurately and autonomously maneuver on the bridge deck to collect visual images and conduct NDE measurements. The developed robotic system can reduce the cost and time of the bridge deck data collection and inspection. For efficient bridge deck monitoring, the crack detection algorithm to build the deck crack map is presented in detail. The impact-echo (IE), ultrasonic surface waves (USW) and electrical resistivity (ER) data collected by the robot are analyzed to generate the delamination, concrete elastic modulus, corrosion maps of the bridge deck, respectively. The presented robotic system has been successfully deployed to inspect numerous bridges in more than ten different states in the U.S.", "field": "cs", "label": 1}
{"text": "Title: Sharing Non-Anonymous Costs of Multiple Resources Optimally\nAbstract: In cost sharing games, the existence and efficiency of pure Nash equilibria fundamentally depends on the method that is used to share the resources' costs. We consider a general class of resource allocation problems in which a set of resources is used by a heterogeneous set of selfish users. The cost of a resource is a (non-decreasing) function of the set of its users. Under the assumption that the costs of the resources are shared by uniform cost sharing protocols, i.e., protocols that use only local information of the resource's cost structure and its users to determine the cost shares, we exactly quantify the inefficiency of the resulting pure Nash equilibria. Specifically, we show tight bounds on prices of stability and anarchy for games with only submodular and only supermodular cost functions, respectively, and an asymptotically tight bound for games with arbitrary set-functions. While all our upper bounds are attained for the well-known Shapley cost sharing protocol, our lower bounds hold for arbitrary uniform cost sharing protocols and are even valid for games with anonymous costs, i.e., games in which the cost of each resource only depends on the cardinality of the set of its users.", "field": "cs", "label": 1}
{"text": "Title: No solitary waves in 2-d gravity and capillary waves in deep water\nAbstract: A fundamental question in the study of water waves is the existence and stability of solitary waves. Solitary waves have been proved to exist and have been studied in many interesting situations, and often arise from the balance of different forces/factors influencing the fluid dynamics, e.g. gravity, surface tension or the fluid bottom. However, the existence of solitary waves has remained an open problem in two of the simplest cases, namely for either pure gravity waves or pure capillary waves in infinite depth. In this article we settle both of these questions in two space dimensions. Precisely, we consider incompressible, irrotational, infinite depth water wave equation, either with gravity and without surface tension, or without gravity but with surface tension. In both of these cases we prove that there are no solitary waves.", "field": "math", "label": 1}
{"text": "Title: Efficient Private SCO for Heavy-Tailed Data via Clipping\nAbstract: We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Prior work on this problem is restricted to the gradient descent (GD) method, which is inefficient for large-scale problems. In this paper, we resolve this issue and derive the first high-probability bounds for the private stochastic method with clipping. For general convex problems, we derive excess population risks $\\Tilde{O}\\left(\\frac{d^{1/7}\\sqrt{\\ln\\frac{(n \\epsilon)^2}{\\beta d}}}{(n\\epsilon)^{2/7}}\\right)$ and $\\Tilde{O}\\left(\\frac{d^{1/7}\\ln\\frac{(n\\epsilon)^2}{\\beta d}}{(n\\epsilon)^{2/7}}\\right)$ under bounded or unbounded domain assumption, respectively (here $n$ is the sample size, $d$ is the dimension of the data, $\\beta$ is the confidence level and $\\epsilon$ is the private level). Then, we extend our analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H$\\ddot{\\text{o}}$lder-continuous gradients). We establish new excess risk bounds without bounded domain assumption. The results above achieve lower excess risks and gradient complexities than existing methods in their corresponding cases. Numerical experiments are conducted to justify the theoretical improvement.", "field": "cs", "label": 1}
{"text": "Title: Core equality of real sequences\nAbstract: Given an ideal $\\mathcal{I}$ on $\\omega$ and a bounded real sequence $\\textbf{x}$, we denote by $\\text{core}_{\\textbf{x}}(\\mathcal{I})$ the smallest interval $[a,b]$ such that $\\{n \\in \\omega: x_n \\notin [a-\\varepsilon,b+\\varepsilon]\\} \\in \\mathcal{I}$ for all $\\varepsilon>0$ (which corresponds to the interval $[\\,\\liminf \\textbf{x}, \\limsup \\textbf{x}\\,]$ if $\\mathcal{I}$ is the ideal $\\text{Fin}$ of finite subsets of $\\omega$). First, we characterize all the infinite real matrices $A$ such that $$ \\text{core}_{A\\textbf{x}}(\\mathcal{J})=\\text{core}_{\\textbf{x}}(\\mathcal{I}) $$ for all bounded sequences $\\textbf{x}$, provided that $\\mathcal{J}$ is a countably generated ideal on $\\omega$ and $A$ maps bounded sequences into bounded sequences. Such characterization fails if both $\\mathcal{I}$ and $\\mathcal{J}$ are the ideal of asymptotic density zero sets. Next, we show that such equality is possible for distinct ideals $\\mathcal{I}, \\mathcal{J}$, answering an open question in [J.~Math.~Anal.~Appl.~\\textbf{321} (2006), 515--523]. Lastly, we prove that, if $\\mathcal{J}=\\text{Fin}$, the above equality holds for some matrix $A$ if and only if $\\mathcal{I}=\\text{Fin}$ or $\\mathcal{I}=\\text{Fin}\\oplus \\mathcal{P}(\\omega)$.", "field": "math", "label": 0}
{"text": "Title: Hybrid Learning of Time-Series Inverse Dynamics Models for Locally Isotropic Robot Motion\nAbstract: Applications of force control and motion planning often rely on an inverse dynamics model to represent the high-dimensional dynamic behavior of robots during motion. The widespread occurrence of low-velocity, small-scale, locally isotropic motion (LIMO) typically complicates the identification of appropriate models due to the exaggeration of dynamic effects and sensory perturbation caused by complex friction and phenomena of hysteresis, e.g., pertaining to joint elasticity. We propose a hybrid model learning base architecture combining a rigid body dynamics model identified by parametric regression and time-series neural network architectures based on multilayer-perceptron, LSTM, and Transformer topologies. Further, we introduce novel joint-wise rotational history encoding, reinforcing temporal information to effectively model dynamic hysteresis. The models are evaluated on a KUKA iiwa 14 during algorithmically generated locally isotropic movements. Together with the rotational encoding, the proposed architectures outperform state-of-the-art baselines by a magnitude of 10$^3$ yielding an RMSE of 0.14 Nm. Leveraging the hybrid structure and time-series encoding capabilities, our approach allows for accurate torque estimation, indicating its applicability in critically force-sensitive applications during motion sequences exceeding the capacity of conventional inverse dynamics models while retaining trainability in face of scarce data and explainability due to the employed physics model prior.", "field": "cs", "label": 1}
{"text": "Title: Solving Almost all Systems of Random Quadratic Equations\nAbstract: This paper deals with finding an $n$-dimensional solution $x$ to a system of quadratic equations of the form $y_i=|\\langle{a}_i,x\\rangle|^2$ for $1\\le i \\le m$, which is also known as phase retrieval and is NP-hard in general. We put forth a novel procedure for minimizing the amplitude-based least-squares empirical loss, that starts with a weighted maximal correlation initialization obtainable with a few power or Lanczos iterations, followed by successive refinements based upon a sequence of iteratively reweighted (generalized) gradient iterations. The two (both the initialization and gradient flow) stages distinguish themselves from prior contributions by the inclusion of a fresh (re)weighting regularization technique. The overall algorithm is conceptually simple, numerically scalable, and easy-to-implement. For certain random measurement models, the novel procedure is shown capable of finding the true solution $x$ in time proportional to reading the data $\\{(a_i;y_i)\\}_{1\\le i \\le m}$. This holds with high probability and without extra assumption on the signal $x$ to be recovered, provided that the number $m$ of equations is some constant $c>0$ times the number $n$ of unknowns in the signal vector, namely, $m>cn$. Empirically, the upshots of this contribution are: i) (almost) $100\\%$ perfect signal recovery in the high-dimensional (say e.g., $n\\ge 2,000$) regime given only an information-theoretic limit number of noiseless equations, namely, $m=2n-1$ in the real-valued Gaussian case; and, ii) (nearly) optimal statistical accuracy in the presence of additive noise of bounded support. Finally, substantial numerical tests using both synthetic data and real images corroborate markedly improved signal recovery performance and computational efficiency of our novel procedure relative to state-of-the-art approaches.", "field": "math", "label": 1}
{"text": "Title: Joint Multi-Facts Reasoning Network For Complex Temporal Question Answering Over Knowledge Graph\nAbstract: Temporal Knowledge Graph (TKG) is an extension of regular knowledge graph by attaching the time scope. Existing temporal knowledge graph question answering (TKGQA) models solely approach simple questions, owing to the prior assumption that each question only contains a single temporal fact with explicit/implicit temporal constraints. Hence, they perform poorly on questions which own multiple temporal facts. In this paper, we propose \\textbf{\\underline{J}}oint \\textbf{\\underline{M}}ulti \\textbf{\\underline{F}}acts \\textbf{\\underline{R}}easoning \\textbf{\\underline{N}}etwork (JMFRN), to jointly reasoning multiple temporal facts for accurately answering \\emph{complex} temporal questions. Specifically, JMFRN first retrieves question-related temporal facts from TKG for each entity of the given complex question. For joint reasoning, we design two different attention (\\ie entity-aware and time-aware) modules, which are suitable for universal settings, to aggregate entities and timestamps information of retrieved facts. Moreover, to filter incorrect type answers, we introduce an additional answer type discrimination task. Extensive experiments demonstrate our proposed method significantly outperforms the state-of-art on the well-known complex temporal question benchmark TimeQuestions.", "field": "cs", "label": 0}
{"text": "Title: Probabilistic Modeling for Sequences of Sets in Continuous-Time\nAbstract: Neural marked temporal point processes have been a valuable addition to the existing toolbox of statistical parametric models for continuous-time event data. These models are useful for sequences where each event is associated with a single item (a single type of event or a \"mark\") -- but such models are not suited for the practical situation where each event is associated with a set of items. In this work, we develop a general framework for modeling set-valued data in continuous-time, compatible with any intensity-based recurrent neural point process model. In addition, we develop inference methods that can use such models to answer probabilistic queries such as \"the probability of item $A$ being observed before item $B$,\" conditioned on sequence history. Computing exact answers for such queries is generally intractable for neural models due to both the continuous-time nature of the problem setting and the combinatorially-large space of potential outcomes for each event. To address this, we develop a class of importance sampling methods for querying with set-based sequences and demonstrate orders-of-magnitude improvements in efficiency over direct sampling via systematic experiments with four real-world datasets. We also illustrate how to use this framework to perform model selection using likelihoods that do not involve one-step-ahead prediction.", "field": "cs", "label": 0}
{"text": "Title: New Generalizations of the Bethe Approximation via Asymptotic Expansion\nAbstract: The Bethe approximation, discovered in statistical physics, gives an efficient algorithm called belief propagation (BP) for approximating a partition function. BP empirically gives an accurate approximation for many problems, e.g., low-density parity-check codes, compressed sensing, etc. Recently, Vontobel gives a novel characterization of the Bethe approximation using graph cover. In this paper, a new approximation based on the Bethe approximation is proposed. The new approximation is derived from Vontobel's characterization using graph cover, and expressed by using the edge zeta function, which is related with the Hessian of the Bethe free energy as shown by Watanabe and Fukumizu. On some conditions, it is proved that the new approximation is asymptotically better than the Bethe approximation.", "field": "cs", "label": 1}
{"text": "Title: Large Language Models Relearn Removed Concepts\nAbstract: Advances in model editing through neuron pruning hold promise for removing undesirable concepts from large language models. However, it remains unclear whether models have the capacity to reacquire pruned concepts after editing. To investigate this, we evaluate concept relearning in models by tracking concept saliency and similarity in pruned neurons during retraining. Our findings reveal that models can quickly regain performance post-pruning by relocating advanced concepts to earlier layers and reallocating pruned concepts to primed neurons with similar semantics. This demonstrates that models exhibit polysemantic capacities and can blend old and new concepts in individual neurons. While neuron pruning provides interpretability into model concepts, our results highlight the challenges of permanent concept removal for improved model \\textit{safety}. Monitoring concept reemergence and developing techniques to mitigate relearning of unsafe concepts will be important directions for more robust model editing. Overall, our work strongly demonstrates the resilience and fluidity of concept representations in LLMs post concept removal.", "field": "cs", "label": 0}
{"text": "Title: From Spot 2.0 to Spot 2.10: What's New?\nAbstract: Spot is a C ++ 17 library for LTL and $\\omega$-automata manipulation, with command-line utilities, and Python bindings. This paper summarizes its evolution over the past six years, since the release of Spot 2.0, which was the first version to support $\\omega$-automata with arbitrary acceptance conditions, and the last version presented at a conference. Since then, Spot has been extended with several features such as acceptance transformations, alternating automata, games, LTL synthesis, and more. We also shed some lights on the data-structure used to store automata.", "field": "cs", "label": 1}
{"text": "Title: Homological properties of the relative Frobenius morphism\nAbstract: This work concerns maps of commutative noetherian local rings containing a field of positive characteristic. Given such a map $\\varphi$ of finite flat dimension, the results relate homological properties of the relative Frobenius of $\\varphi$ to those of the fibers of $\\varphi$. The focus is on the complete intersection property and the Gorenstein property.", "field": "math", "label": 0}
{"text": "Title: Stationary solutions and large time asymptotics to a cross-diffusion-Cahn-Hilliard system\nAbstract: We study some properties of a multi-species degenerate Ginzburg-Landau energy and its relation to a cross-diffusion Cahn-Hilliard system. The model is motivated by multicomponent mixtures where crossdiffusion effects between the different species are taken into account, and where only one species does separate from the others. Using a comparison argument, we obtain strict bounds on the minimizers from which we can derive first-order optimality conditions, revealing a link with the single-species energy, and providing enough regularity to qualify the minimizers as stationary solutions of the evolution system. We also discuss convexity properties of the energy as well as long time asymptotics of the time-dependent problem. Lastly, we introduce a structure-preserving finite volume scheme for the time-dependent problem and present several numerical experiments in one and two spatial dimensions.", "field": "math", "label": 0}
{"text": "Title: Distribution of primes represented by polynomials and Multiple Dedekind zeta functions\nAbstract: n this paper, we state several conjectures regarding distribution of primes and of pairs of primes represented by irreducible homogeneous polynomial in two variables $f(a,b)$. We formulate conjectures with respect to the slope $t=b/a$ for any irreducible polynomial $f$. Here, we formulate a conjecture for all irreducible polynomials. We also consider conjectures for distribution of pairs of primes. It show unexpected relation to multiple Dedekind zeta function - at $s=2$ for one prime and at $(s_1,s_2)=(2,2)$ for pairs of primes. We tested the conjecture for pairs of primes for several quadratic fields. The conjecture for pairs of primes and multiple Dedekind zeta function over the Gaussian integers provide error less than a tenth of a percent. We also tested conjectures that compare sets of primes in a pair of different quadratic fields. Numerically, such quotients can be expressed in terms of regulators and class numbers. Some of the data, together with the code, is available on GitHub, (see \\cite{Zouberou}).", "field": "math", "label": 1}
{"text": "Title: Rellich inequalities in bounded domains\nAbstract: We find necessary and sufficient conditions for the validity of weighted Rellich inequalities in Lp for functions in bounded domains vanishing at the boundary. General operators like L = Delta+ c\\|x|^2x nabla-b\\|x|^2 are considered. Critical cases and remainder terms are also investigated.", "field": "math", "label": 1}
{"text": "Title: Enhancing RAW-to-sRGB with Decoupled Style Structure in Fourier Domain\nAbstract: RAW to sRGB mapping, which aims to convert RAW images from smartphones into RGB form equivalent to that of Digital Single-Lens Reflex (DSLR) cameras, has become an important area of research. However, current methods often ignore the difference between cell phone RAW images and DSLR camera RGB images, a difference that goes beyond the color matrix and extends to spatial structure due to resolution variations. Recent methods directly rebuild color mapping and spatial structure via shared deep representation, limiting optimal performance. Inspired by Image Signal Processing (ISP) pipeline, which distinguishes image restoration and enhancement, we present a novel Neural ISP framework, named FourierISP. This approach breaks the image down into style and structure within the frequency domain, allowing for independent optimization. FourierISP is comprised of three subnetworks: Phase Enhance Subnet for structural refinement, Amplitude Refine Subnet for color learning, and Color Adaptation Subnet for blending them in a smooth manner. This approach sharpens both color and structure, and extensive evaluations across varied datasets confirm that our approach realizes state-of-the-art results. Code will be available at ~\\url{https://github.com/alexhe101/FourierISP}.", "field": "cs", "label": 0}
{"text": "Title: Characterization of commuting graphs of finite groups having small genus\nAbstract: In this paper we first show that among all double-toroidal and triple-toroidal finite graphs only $K_8 \\sqcup 9K_1$, $K_8 \\sqcup 5K_2$, $K_8 \\sqcup 3K_4$, $K_8 \\sqcup 9K_3$, $K_8\\sqcup 9(K_1 \\vee 3K_2)$, $3K_6$ and $3K_6 \\sqcup 4K_4 \\sqcup 6K_2$ can be realized as commuting graphs of finite groups. As consequences of our results we also show that for any finite non-abelian group $G$ if the commuting graph of $G$ (denoted by $\\Gamma_c(G)$) is double-toroidal or triple-toroidal then $\\Gamma_c(G)$ and its complement satisfy Hansen-Vuki{\\v{c}}evi{\\'c} Conjecture and E-LE conjecture. In the process we find a non-complete graph, namely the non-commuting graph of the group $(\\mathbb{Z}_3 \\times \\mathbb{Z}_3) \\rtimes Q_8$, that is hyperenergetic. This gives a new counter example to a conjecture of Gutman regarding hyperenergetic graphs.", "field": "math", "label": 0}
{"text": "Title: Contravariant Pseudo-Hessian manifolds and their associated Poisson structures\nAbstract: A contravariant pseudo-Hessian manifold is a manifold $M$ endowed with a pair $(\\nabla,h)$ where $\\nabla$ is a flat connection and $h$ is a symmetric bivector field satisfying a contravariant Codazzi equation. When $h$ is invertible we recover the known notion of pseudo-Hessian manifold. Contravariant pseudo-Hessian manifolds have properties similar to Poisson manifolds and, in fact, to any contravariant pseudo-Hessian manifold $(M,\\nabla,h)$ we associate naturally a Poisson tensor on $TM$. We investigate these properties and we study in details many classes of such structures in order to highlight the richness of the geometry of these manifolds.", "field": "math", "label": 1}
{"text": "Title: On the conductor of cohomological transforms\nAbstract: In the analytic study of trace functions of $\\ell$-adic sheaves over finite fields, a crucial issue is to control the conductor of sheaves constructed in various ways. We consider cohomological transforms on the affine line over a finite field which have trace functions given by linear operators with an additive character of a rational function in two variables as a kernel. We prove that the conductor of such a transform is bounded in terms of the complexity of the input sheaf and of the rational function defining the kernel, and discuss applications of this result, including motivating examples arising from the Polymath8 project.", "field": "math", "label": 1}
{"text": "Title: Expressive Speech-driven Facial Animation with controllable emotions\nAbstract: It is in high demand to generate facial animation with high realism, but it remains a challenging task. Existing approaches of speech-driven facial animation can produce satisfactory mouth movement and lip synchronization, but show weakness in dramatic emotional expressions and flexibility in emotion control. This paper presents a novel deep learning-based approach for expressive facial animation generation from speech that can exhibit wide-spectrum facial expressions with controllable emotion type and intensity. We propose an emotion controller module to learn the relationship between the emotion variations (e.g., types and intensity) and the corresponding facial expression parameters. It enables emotion-controllable facial animation, where the target expression can be continuously adjusted as desired. The qualitative and quantitative evaluations show that the animation generated by our method is rich in facial emotional expressiveness while retaining accurate lip movement, outperforming other state-of-the-art methods.", "field": "cs", "label": 0}
{"text": "Title: $p$-numerical semigroups of Pell triples\nAbstract: For a nonnegative integer $p$, the $p$-numerical semigroup $S_p$ is defined as the set of integers whose nonnegative integral linear combinations of given positive integers $a_1,a_2,\\dots,a_\\kappa$ with $\\gcd(a_1,a_2,\\dots,a_\\kappa)=1$ are expressed in more than $p$ ways. When $p=0$, $S=S_0$ is the original numerical semigroup. The largest element and the cardinality of $\\mathbb N_0\\backslash S_p$ are called the $p$-Frobenius number and the $p$-genus, respectively. Their explicit formulas are known for $\\kappa=2$, but those for $\\kappa\\ge 3$ have been found only in some special cases. For some known cases, such as the Fibonacci and the Jacobsthal triplets, similar techniques could be applied and explicit formulas such as the $p$-Frobenius number could be found. In this paper, we give explicit formulas for the $p$-Frobenius number and the $p$-genus of Pell numerical semigroups $\\bigl(P_i(u),P_{i+2}(u),P_{i+k}(u)\\bigr)$. Here, for a given positive integer $u$, Pell-type numbers $P_n(u)$ satisfy the recurrence relation $P_n(u)=u P_{n-1}(u)+P_{n-2}(u)$ ($n\\ge 2$) with $P_0(u)=0$ and $P_1(u)=1$. The $p$-Ap\\'ery set is used to find the formulas, but it shows a different pattern from those in the known results, and some case by case discussions are necessary.", "field": "math", "label": 0}
{"text": "Title: Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets\nAbstract: Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this paper, we establish a generalized notion of convexity. By defining generalised $\\phi_{h-s}$ convex functions, we extend the well known concepts of generalised convex functions, $P$-functions, Breckner $s$-convex functions, $h$-convex functions amongst others. With this definition, we prove Hermite-Hadamard type inequalities for generalized $\\phi_{h-s}$ convex mappings onto fractal sets. Our results are then applied to probability theory.", "field": "math", "label": 0}
{"text": "Title: The Slepian model based independent interval approximation of persistency and zero-level exceedance distributions\nAbstract: In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed switching times. The approach matched the covariance of the clipped Gaussian process with the one for the stationary switching process and the distribution of the latter was used as the so-called independent interval approximation (IIA). The approach successfully assessed the persistency exponent for many physically important processes but left an unanswered question when such an approach leads to a mathematically meaningful and proper exceedance distribution. Here we address this question by proposing an alternative matching of the expected values of the clipped Slepian process and the corresponding switched process initiated at the origin. The method has allowed resolving the mathematical correctness of the matching method for a large subclass of the Gaussian processes with monotonic covariance, for which we provide a sufficient condition for the validity of the IIA. Within this class, the IIA produces a valid distribution for the excursion time and is represented in an explicit stochastic form that connects directly to the covariance of the underlying Gaussian process. We compare the excursion level distributions as well as the corresponding persistency exponents obtained through the IIA method with numerically computed exact distributions, and the simulated distribution for several important Gaussian models. We also argue that for stationary Gaussian processes with a non-monotonic covariance, the IIA fails and should not be used.", "field": "math", "label": 0}
{"text": "Title: Vanishing Cycles in Holomorphic Foliations by Curves and Foliated Shells\nAbstract: The purpose of this paper is the study of vanishing cycles in holomorphic foliations by complex curves on compact complex manifolds. The main result consists in showing that a vanishing cycle comes together with a much richer complex geometric object - we call this object a foliated shell.", "field": "math", "label": 1}
{"text": "Title: Sharper Bounds for $\\ell_p$ Sensitivity Sampling\nAbstract: In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension $d$ and the total sensitivity $\\mathfrak S$ in remarkably general settings. However, guarantees going beyond this general bound of $\\mathfrak S d$ are known in perhaps only one setting, for $\\ell_2$ subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for $\\ell_p$ subspace embeddings for $p > 2$ that improve over the general $\\mathfrak S d$ bound, achieving a bound of roughly $\\mathfrak S^{2-2/p}$ for $2<p<\\infty$. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly $d$ for $1\\leq p<2$, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly $d^{2/p}\\mathfrak S^{2-4/p}$ for $2<p<\\infty$. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small $\\ell_p$ sensitivity.", "field": "cs", "label": 0}
{"text": "Title: Twinless articulation points and some related problems\nAbstract: Let $G=(V,E)$ be a twinless strongly connected graph. a vertex $v\\in V$ is a twinless articulation point if the subrgraph obtained from $G$ by removing the vertex $v$ is not twinless strongly connected. An edge $e\\in E$ is a twinless bridge if the subgraph obtained from $G$ by deleting $e$ is not twiless strongly connected graph. In this paper we study twinless articulation points and twinless bridges. We also study the problem of finding a minimum cardinality edge subset $E_{1} \\subseteq E$ such that the subgraph $(V,E_{1})$ is twinless strongly connected. Moreover, we present an algorithm for computing the $2$-vertex-twinless connected components of $G$.", "field": "cs", "label": 1}
{"text": "Title: The Wave Equation on Lattices and Oscillatory Integrals\nAbstract: In this paper, we establish sharp dispersive estimates for the linear wave equation on the lattice $\\mathbb{Z}^d$ with dimension $d=4$. Combining the singularity theory with results in uniform estimates of oscillatory integrals, we prove that the optimal time decay rate of the fundamental solution is of order $|t|^{-\\frac{3}{2}}\\log |t|$, which is the first extension of P. Schultz's \\cite{S98} results in $d=2,3$ to the higher dimension. We also observe that the decay rate for $d=2,3,4$ can be well interpreted by the Newton polyhedra. Moreover, we prove $l^p\\rightarrow l^q$ estimates as well as Strichartz estimates and give applications to nonlinear wave equations.", "field": "math", "label": 0}
{"text": "Title: Magnitude function identifies generic finite metric spaces\nAbstract: We show that a ``generic'' finite metric space can be identified by the asymptotic behavior of the magnitude function. In particular, almost every finite set in Euclidean space can be determined by the magnitude function.", "field": "math", "label": 0}
{"text": "Title: Source-Free Online Domain Adaptive Semantic Segmentation of Satellite Images under Image Degradation\nAbstract: Online adaptation to distribution shifts in satellite image segmentation stands as a crucial yet underexplored problem. In this paper, we address source-free and online domain adaptation, i.e., test-time adaptation (TTA), for satellite images, with the focus on mitigating distribution shifts caused by various forms of image degradation. Towards achieving this goal, we propose a novel TTA approach involving two effective strategies. First, we progressively estimate the global Batch Normalization (BN) statistics of the target distribution with incoming data stream. Leveraging these statistics during inference has the ability to effectively reduce domain gap. Furthermore, we enhance prediction quality by refining the predicted masks using global class centers. Both strategies employ dynamic momentum for fast and stable convergence. Notably, our method is backpropagation-free and hence fast and lightweight, making it highly suitable for on-the-fly adaptation to new domain. Through comprehensive experiments across various domain adaptation scenarios, we demonstrate the robust performance of our method.", "field": "cs", "label": 0}
{"text": "Title: More on Arago'n Artacho - Campoy's Algorithm\nAbstract: The Arago'n Artacho-Campoy algorithm (AACA) is a new method for finding zeros of sums of monotone operators. In this paper we complete the analysis of [2] and[1] by providing study of the two possible Arago'n Artacho-Campoy operators.", "field": "math", "label": 0}
{"text": "Title: A taxonomy of estimator consistency on discrete estimation problems\nAbstract: We describe a four-level hierarchy mapping both all discrete estimation problems and all estimators on these problems, such that the hierarchy describes each estimator's consistency guarantees on each problem class. We show that no estimator is consistent for all estimation problems, but that some estimators, such as Maximum A Posteriori, are consistent for the widest possible class of discrete estimation problems. For Maximum Likelihood and Approximate Maximum Likelihood estimators we show that they do not provide consistency on as wide a class, but define a sub-class of problems characterised by their consistency. Lastly, we show that some popular estimators, specifically Strict Minimum Message Length, do not provide consistency guarantees even within the sub-class.", "field": "math", "label": 1}
{"text": "Title: On the number of hyperbolic Dehn fillings of a given volume\nAbstract: Let M be a 1-cusped hyperbolic 3-manifold whose cusp shape is quadratic. We show that there exists c=c(M) such that the number of hyperbolic Dehn fillings of M with any given volume v is uniformly bounded by c.", "field": "math", "label": 1}
{"text": "Title: Transformer Neural Autoregressive Flows\nAbstract: Density estimation, a central problem in machine learning, can be performed using Normalizing Flows (NFs). NFs comprise a sequence of invertible transformations, that turn a complex target distribution into a simple one, by exploiting the change of variables theorem. Neural Autoregressive Flows (NAFs) and Block Neural Autoregressive Flows (B-NAFs) are arguably the most perfomant members of the NF family. However, they suffer scalability issues and training instability due to the constraints imposed on the network structure. In this paper, we propose a novel solution to these challenges by exploiting transformers to define a new class of neural flows called Transformer Neural Autoregressive Flows (T-NAFs). T-NAFs treat each dimension of a random variable as a separate input token, using attention masking to enforce an autoregressive constraint. We take an amortization-inspired approach where the transformer outputs the parameters of an invertible transformation. The experimental results demonstrate that T-NAFs consistently match or outperform NAFs and B-NAFs across multiple datasets from the UCI benchmark. Remarkably, T-NAFs achieve these results using an order of magnitude fewer parameters than previous approaches, without composing multiple flows.", "field": "cs", "label": 0}
{"text": "Title: On the convergence of stochastic transport equations to a deterministic parabolic one\nAbstract: A stochastic transport linear equation (STLE) with multiplicative space-time dependent noise is studied. It is shown that, under suitable assumptions on the noise, a multiplicative renormalization leads to convergence of the solutions of STLE to the solution of a deterministic parabolic equation. Existence and uniqueness for STLE are also discussed. Our method works in dimension $d\\geq 2$; the case $d=1$ is also investigated but no conclusive answer is obtained.", "field": "math", "label": 1}
{"text": "Title: Concentration of maximum degree in random planar graphs\nAbstract: Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $[n]:=\\left\\{1, \\ldots, n\\right\\}$ with $m=m(n)$ edges. We show that in the sparse regime, when $m/n\\leq 1$, with high probability the maximum degree of $P(n,m)$ takes at most two different values. In contrast, this is not true anymore in the dense regime, when $m/n>1$, where the maximum degree of $P(n,m)$ is not concentrated on any subset of $[n]$ with bounded size.", "field": "math", "label": 1}
{"text": "Title: Effective descent morphisms of filtered preorders\nAbstract: We characterize effective descent morphisms of what we call filtered preorders, and apply these results to slightly improve a known result, due to the first author and F. Lucatelli Nunes, on the effective descent morphisms in lax comma categories of preorders. A filtered preorder, over a fixed preorder $X$, is defined as a preorder $A$ equipped with a profunctor $X\\to A$ and, equivalently, as a set $A$ equipped with a family $(A_x)_{x\\in X}$ of upclosed subsets of $A$ with $x'\\leqslant x\\Rightarrow A_x\\subseteq A_{x'}$.", "field": "math", "label": 0}
{"text": "Title: On a new method for the stochastic perturbation of the disease transmission coefficient in SIS Models\nAbstract: In this study we investigate a novel approach to stochastically perturb the disease transmission coefficient, which is a key parameter in susceptible-infected-susceptible (SIS) models. Motivated by the papers [2] and [5], we perturb the disease transmission coefficient with a Gaussian white noise, formally modelled as the time derivative of a mean reverting Ornstein-Uhlenbeck process. We remark that, thanks to a suitable representation of the solution to the deterministic SIS model, this perturbation is rigorous and supported by a Wong-Zakai approximation argument that consists in smoothing the singular Gaussian white noise and then taking limit of the solution from the approximated model. We prove that the stochastic version of the classic SIS model obtained this way preserves a crucial feature of the deterministic equation: the reproduction number dictating the two possible asymptotic regimes for the infection, i.e. extinction and persistence, remains unchanged. We then identify the class of perturbing noises for which this property holds and propose simple sufficient conditions for that. All the theoretical discoveries are illustrated and discussed with the help of several numerical simulations.", "field": "math", "label": 1}
{"text": "Title: Probabilistic Trajectory Design Via Approximate Gaussian Mixture Steering\nAbstract: A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a distribution steering problem. Typical distribution steering problems rely on the underlying uncertainties to be Gaussian distributions. This work expands on previous developments by embedding Gaussian mixture distributions into the formulation to better handle the uncertainty propagation and chance constraints involved. The method is applied to a finite-thrust Earth-to-Mars transfer problem. Evaluation via Monte Carlo analysis shows a greater satisfaction of constraints under non-Gaussian distributions of the state and a statistically lower cost.", "field": "math", "label": 0}
{"text": "Title: A General Implicit Framework for Fast NeRF Composition and Rendering\nAbstract: A variety of Neural Radiance Fields (NeRF) methods have recently achieved remarkable success in high render speed. However, current accelerating methods are specialized and incompatible with various implicit methods, preventing real-time composition over various types of NeRF works. Because NeRF relies on sampling along rays, it is possible to provide general guidance for acceleration. To that end, we propose a general implicit pipeline for composing NeRF objects quickly. Our method enables the casting of dynamic shadows within or between objects using analytical light sources while allowing multiple NeRF objects to be seamlessly placed and rendered together with any arbitrary rigid transformations. Mainly, our work introduces a new surface representation known as Neural Depth Fields (NeDF) that quickly determines the spatial relationship between objects by allowing direct intersection computation between rays and implicit surfaces. It leverages an intersection neural network to query NeRF for acceleration instead of depending on an explicit spatial structure.Our proposed method is the first to enable both the progressive and interactive composition of NeRF objects. Additionally, it also serves as a previewing plugin for a range of existing NeRF works.", "field": "cs", "label": 0}
{"text": "Title: Calderon-Zygmund theory for strongly coupled linear system of nonlocal equations with Holder-regular coefficient\nAbstract: We extend the Calder\\'on-Zygmund theory for nonlocal equations to strongly coupled system of linear nonlocal equations $\\mathcal{L}^{s}_{A} u = f$, where the operator $\\mathcal{L}^{s}_{A}$ is formally given by \\[ \\mathcal{L}^s_{A}u = \\int_{\\mathbb{R}^n}\\frac{A(x, y)}{\\vert x-y\\vert ^{n+2s}} \\frac{(x-y)\\otimes (x-y)}{\\vert x-y\\vert ^2}(u(x)-u(y))dy. \\] For $0 < s < 1$ and $A:\\mathbb{R}^{n} \\times \\mathbb{R}^{n} \\to \\mathbb{R}$ taken to be symmetric and serving as a variable coefficient for the operator, the system under consideration is the fractional version of the classical Navier-Lam\\'e linearized elasticity system. The study of the coupled system of nonlocal equations is motivated by its appearance in nonlocal mechanics, primarily in peridynamics. Our regularity result states that if $A(\\cdot, y)$ is uniformly Holder continuous and $\\inf_{x\\in \\mathbb{R}^n}A(x, x) > 0$, then for $f\\in L^{p}_{loc},$ for $p\\geq 2$, the solution vector $u\\in H^{2s-\\delta,p}_{loc}$ for some $\\delta\\in (0, s)$.", "field": "math", "label": 0}
{"text": "Title: Tangent categories of algebras over operads\nAbstract: Associated to a presentable $\\infty$-category $\\mathcal{C}$ and an object $X \\in \\mathcal{C}$ is the tangent $\\infty$-category $\\mathcal{T}_X\\mathcal{C}$, consisting of parameterized spectrum objects over $X$. This gives rise to a cohomology theory, called Quillen cohomology, whose category of coefficients is $\\mathcal{T}_X\\mathcal{C}$. When $\\mathcal{C}$ consists of algebras over a nice $\\infty$-operad in a stable $\\infty$-category, $\\mathcal{T}_X\\mathcal{C}$ is equivalent to the $\\infty$-category of operadic modules, by work of Basterra--Mandell, Schwede and Lurie. In this paper we develop the model-categorical counterpart of this identification and extend it to the case of algebras over an enriched operad, taking values in a model category which is not necessarily stable. This extended comparison can be used, for example, to identify the cotangent complex of enriched categories, an application we take up in a subsequent paper.", "field": "math", "label": 1}
{"text": "Title: Hilbert space operators with compatible off-diagonal corners\nAbstract: Given a complex, separable Hilbert space $\\mathcal{H}$, we characterize those operators for which $\\| P T (I-P) \\| = \\| (I-P) T P \\|$ for all orthogonal projections $P$ on $\\mathcal{H}$. When $\\mathcal{H}$ is finite-dimensional, we also obtain a complete characterization of those operators for which $\\mathrm{rank}\\, (I-P) T P = \\mathrm{rank}\\, P T (I-P)$ for all orthogonal projections $P$. When $\\mathcal{H}$ is infinite-dimensional, we show that any operator with the latter property is normal, and its spectrum is contained in either a line or a circle in the complex plane.", "field": "math", "label": 1}
{"text": "Title: Anchor Pruning for Object Detection\nAbstract: This paper proposes anchor pruning for object detection in one-stage anchor-based detectors. While pruning techniques are widely used to reduce the computational cost of convolutional neural networks, they tend to focus on optimizing the backbone networks where often most computations are. In this work we demonstrate an additional pruning technique, specifically for object detection: anchor pruning. With more efficient backbone networks and a growing trend of deploying object detectors on embedded systems where post-processing steps such as non-maximum suppression can be a bottleneck, the impact of the anchors used in the detection head is becoming increasingly more important. In this work, we show that many anchors in the object detection head can be removed without any loss in accuracy. With additional retraining, anchor pruning can even lead to improved accuracy. Extensive experiments on SSD and MS COCO show that the detection head can be made up to 44% more efficient while simultaneously increasing accuracy. Further experiments on RetinaNet and PASCAL VOC show the general effectiveness of our approach. We also introduce `overanchorized' models that can be used together with anchor pruning to eliminate hyperparameters related to the initial shape of anchors. Code and models are available at https://github.com/Mxbonn/anchor_pruning.", "field": "cs", "label": 1}
{"text": "Title: Primitive elements in infinitesimal bialgebras\nAbstract: For any set S, the free magmatic algebra spanned by card(S) binary products is the vector space spanned by the set of all planar rooted binary trees with the internal nodes colored by the elements of S, graded by the number of leaves of a tree. We show that it has a unique structure of coassociative coalgebra such that the coproduct satisfies the unital infinitesimal condition with each magmatic product, and prove an analog of Aguiar-Sottile formula in this context, describing the coproduct in terms of the Moebius basis for the Tamari order. The last result allows us to compute the subspace of primitive elements of any unital infinitesimal S-magmatic bialgebra. As an example, we construct a set of generators of the dual of Pilaud and Pons bialgebra of integer relations and compute an explicit basis of its subspace of primitive elements.", "field": "math", "label": 0}
{"text": "Title: Nonlinear Young integrals via fractional calculus\nAbstract: For H\\\"older continuous functions $W(t,x)$ and $\\varphi_t$, we define nonlinear integral $\\int_a^b W(dt, \\varphi_t)$ via fractional calculus. This nonlinear integral arises naturally in the Feynman-Kac formula for stochastic heat equations with random coefficients. We also define iterated nonlinear integrals.", "field": "math", "label": 1}
{"text": "Title: An exact test for renewal increasing mean residual life\nAbstract: In this paper, we develop an exact test for testing exponentiality against renewal increasing mean residual life class. Pitman's asymptotic efficacy value shows that our test perform well. Some numerical results are presented to demonstrate the performance of the testing method. We also discuss how the proposed method incorporates the right censored observations.", "field": "math", "label": 1}
{"text": "Title: Fundamental Theorem of Projective Geometry over Semirings\nAbstract: We state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra setup over semirings. We also provide more explicit results to understand the implications of our main theorem on maps between tropical lines in the tropical plane. Along with this we also look at geometrical connections to the rich theory of tropical geometry", "field": "math", "label": 1}
{"text": "Title: Close to Human-Level Agreement: Tracing Journeys of Violent Speech in Incel Posts with GPT-4-Enhanced Annotations\nAbstract: This study investigates the prevalence of violent language on incels.is. It evaluates GPT models (GPT-3.5 and GPT-4) for content analysis in social sciences, focusing on the impact of varying prompts and batch sizes on coding quality for the detection of violent speech. We scraped over 6.9M posts from incels.is and categorized a random sample into non-violent, explicitly violent, and implicitly violent content. Two human coders annotated 3,028 posts, which we used to tune and evaluate GPT-3.5 and GPT-4 models across different prompts and batch sizes regarding coding reliability. The best-performing GPT-4 model annotated an additional 30,000 posts for further analysis. Our findings indicate an overall increase in violent speech overtime on incels.is, both at the community and individual level, particularly among more engaged users. While directed violent language decreases, non-directed violent language increases, and self-harm content shows a decline, especially after 2.5 years of user activity. We find substantial agreement between both human coders (K = .65), while the best GPT-4 model yields good agreement with both human coders (K = 0.54 for Human A and K = 0.62 for Human B). Weighted and macro F1 scores further support this alignment. Overall, this research provides practical means for accurately identifying violent language at a large scale that can aid content moderation and facilitate next-step research into the causal mechanism and potential mitigations of violent expression and radicalization in communities like incels.is.", "field": "cs", "label": 0}
{"text": "Title: Multi-Source Domain Adaptation with Transformer-based Feature Generation for Subject-Independent EEG-based Emotion Recognition\nAbstract: Although deep learning-based algorithms have demonstrated excellent performance in automated emotion recognition via electroencephalogram (EEG) signals, variations across brain signal patterns of individuals can diminish the model's effectiveness when applied across different subjects. While transfer learning techniques have exhibited promising outcomes, they still encounter challenges related to inadequate feature representations and may overlook the fact that source subjects themselves can possess distinct characteristics. In this work, we propose a multi-source domain adaptation approach with a transformer-based feature generator (MSDA-TF) designed to leverage information from multiple sources. The proposed feature generator retains convolutional layers to capture shallow spatial, temporal, and spectral EEG data representations, while self-attention mechanisms extract global dependencies within these features. During the adaptation process, we group the source subjects based on correlation values and aim to align the moments of the target subject with each source as well as within the sources. MSDA-TF is validated on the SEED dataset and is shown to yield promising results.", "field": "cs", "label": 0}
{"text": "Title: Bayesian Intrinsic Groupwise Image Registration: Unsupervised Disentanglement of Anatomy and Geometry\nAbstract: This article presents a general Bayesian learning framework for multi-modal groupwise registration on medical images. The method builds on probabilistic modelling of the image generative process, where the underlying common anatomy and geometric variations of the observed images are explicitly disentangled as latent variables. Thus, groupwise registration is achieved through the solution to Bayesian inference. We propose a novel hierarchical variational auto-encoding architecture to realize the inference procedure of the latent variables, where the registration parameters can be calculated in a mathematically interpretable fashion. Remarkably, this new paradigm can learn groupwise registration in an unsupervised closed-loop self-reconstruction process, sparing the burden of designing complex intensity-based similarity measures. The computationally efficient disentangled architecture is also inherently scalable and flexible, allowing for groupwise registration on large-scale image groups with variable sizes. Furthermore, the inferred structural representations from disentanglement learning are capable of capturing the latent anatomy of the observations with visual semantics. Extensive experiments were conducted to validate the proposed framework, including four datasets from cardiac, brain and abdominal medical images. The results have demonstrated the superiority of our method over conventional similarity-based approaches in terms of accuracy, efficiency, scalability and interpretability.", "field": "cs", "label": 0}
{"text": "Title: Coded Beam Training\nAbstract: In extremely large-scale multiple input multiple output (XL-MIMO) systems for future sixth-generation (6G) communications, codebook-based beam training stands out as a promising technology to acquire channel state information (CSI). Despite their effectiveness, when the pilot overhead is limited, existing beam training methods suffer from significant achievable rate degradation for remote users with low signal-to-noise ratio (SNR). To tackle this challenge, leverging the error-correcting capability of channel codes, we introduce channel coding theory into hierarchical beam training to extend the coverage area. Specifically, we establish the duality between hierarchical beam training and channel coding, and the proposed coded beam training scheme serves as a general framework. Then, we present two specific implementations exemplified by coded beam training methods based on Hamming codes and convolutional codes, during which the beam encoding and decoding processes are refined respectively to better accommodate to the beam training problem. Simulation results have demonstrated that, the proposed coded beam training method can enable reliable beam training performance for remote users with low SNR, while keeping training overhead low.", "field": "cs", "label": 0}
{"text": "Title: List-Coloring Packing and Correspondence-Coloring Packing of Planar Graphs\nAbstract: For a graph $G$ and a list assignment $L$ with $|L(v)|=k$ for all $v$, an $L$-packing consists of $L$-colorings $\\varphi_1,\\cdots,\\varphi_k$ such that $\\varphi_i(v)\\ne\\varphi_j(v)$ for all $v$ and all distinct $i,j\\in\\{1,\\ldots,k\\}$. Let $\\chi^{\\star}_{\\ell}(G)$ denote the smallest $k$ such that $G$ has an $L$-packing for every $L$ with $|L(v)|=k$ for all $v$. Let $\\mathcal{P}_k$ denote the set of all planar graphs with girth at least $k$. We show that (i) $\\chi^{\\star}_{\\ell}(G)\\le 8$ for all $G\\in \\mathcal{P}_3$ and (ii) $\\chi^{\\star}_{\\ell}(G)\\le 5$ for all $G\\in \\mathcal{P}_4$ and (iii) $\\chi^{\\star}_{\\ell}(G)\\le 4$ for all $G\\in \\mathcal{P}_5$. Part (i) makes progress on a problem of Cambie, Cames van Batenburg, Davies, and Kang. We also construct outerplanar graphs $G$ such that $\\chi^{\\star}_{\\ell}(G)=4$, which matches the known upper bound $\\chi^{\\star}_{\\ell}(G)\\le 4$ for all outerplanar graphs. Finally, we consider the analogue of $\\chi^{\\star}_{\\ell}$ for correspondence coloring, $\\chi^{\\star}_c$. In fact, all bounds stated above for $\\chi^{\\star}_{\\ell}$ also hold for $\\chi^{\\star}_c$.", "field": "math", "label": 0}
{"text": "Title: A note on a question of Shioda about integral sections\nAbstract: We consider a rational elliptic surface with a relatively minimal fibration. We compute the number of integral sections in the above rational elliptic surface. As an application, we obtain an estimate of polynomial solutions of some equations.", "field": "math", "label": 0}
{"text": "Title: Training Single-Layer Morphological Perceptron Using Convex-Concave Programming\nAbstract: This paper concerns the training of a single-layer morphological perceptron using disciplined convex-concave programming (DCCP). We introduce an algorithm referred to as K-DDCCP, which combines the existing single-layer morphological perceptron (SLMP) model proposed by Ritter and Urcid with the weighted disciplined convex-concave programming (WDCCP) algorithm by Charisopoulos and Maragos. The proposed training algorithm leverages the disciplined convex-concave procedure (DCCP) and formulates a non-convex optimization problem for binary classification. To tackle this problem, the constraints are expressed as differences of convex functions, enabling the application of the DCCP package. The experimental results confirm the effectiveness of the K-DDCCP algorithm in solving binary classification problems. Overall, this work contributes to the field of morphological neural networks by proposing an algorithm that extends the capabilities of the SLMP model.", "field": "cs", "label": 0}
{"text": "Title: On semigroups of orientation-preserving partial permutations with restricted range\nAbstract: Let $\\Omega_n$ be a finite chain with $n$ elements $(n\\in\\mathbb{N})$, and let $\\mathcal{POPI}_{n}$ be the semigroup of all injective orientation-preserving partial transformations of $\\Omega_n$. In this paper, for any nonempty subset $Y$ of $\\Omega_n$, we consider the subsemigroup $\\mathcal{POPI}_{n}(Y)$ of $\\mathcal{POPI}_{n}$ of all transformations with range contained in $Y$. We describe the Green's relations and study the regularity of $\\mathcal{POPI}_{n}(Y)$. Moreover, we calculate the rank of $\\mathcal{POPI}_{n}(Y)$ and determine when two semigroups of this type are isomorphic.", "field": "math", "label": 0}
{"text": "Title: Hamiltonicity of Schrijver graphs and stable Kneser graphs\nAbstract: For integers $k\\geq 1$ and $n\\geq 2k+1$, the Schrijver graph $S(n,k)$ has as vertices all $k$-element subsets of $[n]:=\\{1,2,\\ldots,n\\}$ that contain no two cyclically adjacent elements, and an edge between any two disjoint sets. More generally, for integers $k\\geq 1$, $s\\geq 2$, and $n \\geq sk+1$, the $s$-stable Kneser graph $S(n,k,s)$ has as vertices all $k$-element subsets of $[n]$ in which any two elements are in cyclical distance at least $s$. We prove that all the graphs $S(n,k,s)$, in particular Schrijver graphs $S(n,k)=S(n,k,2)$, admit a Hamilton cycle that can be computed in time $\\mathcal{O}(n)$ per generated vertex.", "field": "math", "label": 0}
{"text": "Title: Non-trivial higher homotopy of first-order theories\nAbstract: Let $T$ be the theory of dense cyclically ordered sets with at least two elements. We determine the classifying space of $\\mathsf{Mod}(T)$ to be homotopically equivalent to $\\mathbb{CP}^\\infty$. In particular, $\\pi_2(\\lvert\\mathsf{Mod}(T)\\rvert)=\\mathbb{Z}$, which answers a question in our previous work. The computation is based on Connes' cycle category $\\Lambda$.", "field": "math", "label": 0}
{"text": "Title: On some permanence properties of (derived) splinters\nAbstract: We show that Noetherian splinters ascend under essentially \\'etale homomorphisms. Along the way, we also prove that the henselization of a Noetherian local splinter is always a splinter and that the completion of a local splinter with geometrically regular formal fibers is a splinter. Finally, we give an example of a (non-excellent) Gorenstein local splinter with mild singularities whose completion is not a splinter. Our results provide evidence for a strengthening of the direct summand theorem, namely that regular maps preserve the splinter property.", "field": "math", "label": 1}
{"text": "Title: Multiplicative and additive compounds via Kronecker products and Kronecker sums\nAbstract: Compound matrices play an important role in many fields of mathematics and have recently found new applications in systems and control theory. However, the explicit formulas for these compounds are non-trivial and not always easy to use. Here, we derive new formulas for the multiplicative and additive compounds of a matrix using Kronecker products and sums. This provides a new approach to matrix compounds based on the well-known and powerful theory of Kronecker products and sums. We demonstrate several applications of these new formulas, including deriving a new expression for the additive compound of the product of two matrices.", "field": "math", "label": 0}
{"text": "Title: InstructTA: Instruction-Tuned Targeted Attack for Large Vision-Language Models\nAbstract: Large vision-language models (LVLMs) have demonstrated their incredible capability in image understanding and response generation. However, this rich visual interaction also makes LVLMs vulnerable to adversarial examples. In this paper, we formulate a novel and practical gray-box attack scenario that the adversary can only access the visual encoder of the victim LVLM, without the knowledge of its prompts (which are often proprietary for service providers and not publicly available) and its underlying large language model (LLM). This practical setting poses challenges to the cross-prompt and cross-model transferability of targeted adversarial attack, which aims to confuse the LVLM to output a response that is semantically similar to the attacker's chosen target text. To this end, we propose an instruction-tuned targeted attack (dubbed InstructTA) to deliver the targeted adversarial attack on LVLMs with high transferability. Initially, we utilize a public text-to-image generative model to \"reverse\" the target response into a target image, and employ GPT-4 to infer a reasonable instruction $\\boldsymbol{p}^\\prime$ from the target response. We then form a local surrogate model (sharing the same visual encoder with the victim LVLM) to extract instruction-aware features of an adversarial image example and the target image, and minimize the distance between these two features to optimize the adversarial example. To further improve the transferability, we augment the instruction $\\boldsymbol{p}^\\prime$ with instructions paraphrased from an LLM. Extensive experiments demonstrate the superiority of our proposed method in targeted attack performance and transferability.", "field": "cs", "label": 0}
{"text": "Title: Approximating the Shapley Value without Marginal Contributions\nAbstract: The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is due to axiomatic properties that only the Shapley value satisfies, which, however, comes at the expense of an exact computation growing exponentially with the number of agents. Accordingly, a number of works are devoted to the efficient approximation of the Shapley value, most of them revolve around the notion of an agent's marginal contribution. In this paper, we propose with SVARM and Stratified SVARM two parameter-free and domain-independent approximation algorithms based on a representation of the Shapley value detached from the notion of marginal contribution. We prove unmatched theoretical guarantees regarding their approximation quality and provide empirical results including synthetic games as well as common explainability use cases comparing ourselves with state-of-the-art methods.", "field": "cs", "label": 0}
{"text": "Title: Continuity of composition operators in Sobolev spaces\nAbstract: We prove that all the composition operators $T_f(g):= f\\circ g$, which take the Adams-Frazier space $W^{m}_{p}\\cap \\dot{W}^{1}_{mp}(\\mathbb{R}^n)$ to itself, are continuous mappings from $W^{m}_{p}\\cap \\dot{W}^{1}_{mp}(\\mathbb{R}^n)$ to itself, for every integer $m\\geq 2$ and every real number $1\\leq p<+\\infty$. The same automatic continuity property holds for Sobolev spaces $W^m_p(\\mathbb{R}^n)$ for $m\\geq 2$ and $1\\leq p<+\\infty$.", "field": "math", "label": 1}
{"text": "Title: Formal multiple Eisenstein series and their derivations\nAbstract: We introduce the algebra of formal multiple Eisenstein series and study its derivations. This algebra is motivated by the classical multiple Eisenstein series, introduced by Gangl-Kaneko-Zagier as a hybrid of classical Eisenstein series and multiple zeta values. In depth one, we obtain formal versions of the Eisenstein series satisfying the same algebraic relations as the classical Eisenstein series. In particular, they generate an algebra whose elements we call formal quasimodular forms. We show that the algebra of formal multiple Eisenstein series is an $\\mathfrak{sl}_2$-algebra by formalizing the usual derivations for quasimodular forms and extending them naturally to the whole algebra. Additionally, we introduce some families of derivations for general quasi-shuffle algebras, providing a broader context for these derivations. Further, we prove that a quotient of this algebra is isomorphic to the algebra of formal multiple zeta values. This gives a novel and purely formal approach to classical (quasi)modular forms and builds a new link between (formal) multiple zeta values and modular forms.", "field": "math", "label": 0}
{"text": "Title: Logit-Q Dynamics for Efficient Learning in Stochastic Teams\nAbstract: We present two logit-Q learning dynamics combining the classical and independent log-linear learning updates with an on-policy value iteration update for efficient learning in stochastic games. We show that the logit-Q dynamics presented reach (near) efficient equilibrium in stochastic teams. We quantify a bound on the approximation error. We also show the rationality of the logit-Q dynamics against agents following pure stationary strategies and the convergence of the dynamics in stochastic games where the reward functions induce potential games, yet only a single agent controls the state transitions beyond stochastic teams. The key idea is to approximate the dynamics with a fictional scenario where the Q-function estimates are stationary over finite-length epochs only for analysis. We then couple the dynamics in the main and fictional scenarios to show that these two scenarios become more and more similar across epochs due to the vanishing step size.", "field": "cs", "label": 0}
{"text": "Title: Multiplicity of normalized solutions for the fractional Schrödinger equation with potentials\nAbstract: We get multiplicity of normalized solutions for the fractional Schr\\\"{o}dinger equation $$ (-\\Delta)^su+V(\\varepsilon x)u=\\lambda u+h(\\varepsilon x)f(u)\\quad \\mbox{in $\\mathbb{R}^N$}, \\qquad\\int_{\\mathbb{R}^N}|u|^2dx=a, $$ where $(-\\Delta)^s$ is the fractional Laplacian, $s\\in(0,1)$, $a,\\varepsilon>0$, $\\lambda\\in\\mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier, $V,h:\\mathbb{R}^N\\rightarrow[0,+\\infty)$ are bounded and continuous, and $f$ is continuous function with $L^2$-subcritical growth. We prove that the numbers of normalized solutions are at least the numbers of global maximum points of $h$ when $\\varepsilon$ is small enough.", "field": "math", "label": 0}
{"text": "Title: Complex structures on stratified Lie algebras\nAbstract: This paper investigates some properties of complex structures on Lie algebras. In particular, we focus on $\\textit{nilpotent}$ $\\textit{complex structures}$ that are characterized by a suitable $J$-invariant ascending or descending central series $\\mathfrak{d}^j$ and $\\mathfrak{d}_j$ respectively. In this article, we introduce a new descending series $\\mathfrak{p}_j$ and use it to give proof of a new characterization of nilpotent complex structures. We examine also whether nilpotent complex structures on stratified Lie algebras preserve the strata. We find that there exists a $J$-invariant stratification on a step $2$ nilpotent Lie algebra with a complex structure.", "field": "math", "label": 1}
{"text": "Title: Shrinking unit: a Graph Convolution-Based Unit for CNN-like 3D Point Cloud Feature Extractors\nAbstract: 3D point clouds have attracted increasing attention in architecture, engineering, and construction due to their high-quality object representation and efficient acquisition methods. Consequently, many point cloud feature detection methods have been proposed in the literature to automate some workflows, such as their classification or part segmentation. Nevertheless, the performance of point cloud automated systems significantly lags behind their image counterparts. While part of this failure stems from the irregularity, unstructuredness, and disorder of point clouds, which makes the task of point cloud feature detection significantly more challenging than the image one, we argue that a lack of inspiration from the image domain might be the primary cause of such a gap. Indeed, given the overwhelming success of Convolutional Neural Networks (CNNs) in image feature detection, it seems reasonable to design their point cloud counterparts, but none of the proposed approaches closely resembles them. Specifically, even though many approaches generalise the convolution operation in point clouds, they fail to emulate the CNNs multiple-feature detection and pooling operations. For this reason, we propose a graph convolution-based unit, dubbed Shrinking unit, that can be stacked vertically and horizontally for the design of CNN-like 3D point cloud feature extractors. Given that self, local and global correlations between points in a point cloud convey crucial spatial geometric information, we also leverage them during the feature extraction process. We evaluate our proposal by designing a feature extractor model for the ModelNet-10 benchmark dataset and achieve 90.64% classification accuracy, demonstrating that our innovative idea is effective. Our code is available at github.com/albertotamajo/Shrinking-unit.", "field": "cs", "label": 1}
{"text": "Title: Relating the Roe algebra of a space to the uniform Roe algebras of its discretizations\nAbstract: The Roe algebra $C^*(X)$ is a non-commutative $C^*$-algebra reflecting metric properties of a space $X$, and it is interesting to understand relation between the Roe algebra of $X$ and the uniform Roe algebra of its discretizations. Here we construct, for a simplicial space $X$, a continuous field of $C^*$-algebras over $\\mathbb N\\cup\\{\\infty\\}$ with the fibers over finite points the uniform $C^*$-algebras of discretizations of $X$, and the fiber over $\\infty$ the Roe algebra of $X$. We also construct the direct limit of the uniform Roe algebras of discretizations and its embedding into the Roe algebra of $X$.", "field": "math", "label": 0}
{"text": "Title: A small time approximation for the solution to the Zakai Equation\nAbstract: We propose a novel small time approximation for the solution to the Zakai equation from nonlinear filtering theory. We prove that the unnormalized filtering density is well described over short time intervals by the solution of a deterministic partial differential equation of Kolmogorov type; the observation process appears in a pathwise manner through the degenerate component of the Kolmogorov's type operator. The rate of convergence of the approximation is of order one in the lenght of the interval. Our approach combines ideas from Wong-Zakai-type results and Wiener chaos approximations for the solution to the Zakai equation. The proof of our main theorem relies on the well-known Feynman-Kac representation for the unnormalized filtering density and careful estimates which lead to completely explicit bounds.", "field": "math", "label": 1}
{"text": "Title: Convergence of Stochastic Gradient Descent for PCA\nAbstract: We consider the problem of principal component analysis (PCA) in a streaming stochastic setting, where our goal is to find a direction of approximate maximal variance, based on a stream of i.i.d. data points in $\\reals^d$. A simple and computationally cheap algorithm for this is stochastic gradient descent (SGD), which incrementally updates its estimate based on each new data point. However, due to the non-convex nature of the problem, analyzing its performance has been a challenge. In particular, existing guarantees rely on a non-trivial eigengap assumption on the covariance matrix, which is intuitively unnecessary. In this paper, we provide (to the best of our knowledge) the first eigengap-free convergence guarantees for SGD in the context of PCA. This also partially resolves an open problem posed in \\cite{hardt2014noisy}. Moreover, under an eigengap assumption, we show that the same techniques lead to new SGD convergence guarantees with better dependence on the eigengap.", "field": "cs", "label": 1}
{"text": "Title: The bar derived category of a curved dg algebra\nAbstract: Curved A-infinity algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A-infinity algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras via the bar construction and produce Quillen model structures on their module categories. We define the analogue of the relative derived category for a curved dg algebra.", "field": "math", "label": 1}
{"text": "Title: Free resolution of the logarithmic derivation modules of close to free arrangements\nAbstract: This paper studies the algebraic structure of a new class of hyperplane arrangement $A$ obtained by deleting two hyperplanes from a free arrangement. We provide information on the minimal free resolutions of the logarithmic derivation module of $A$, which can be used to compute a lower bound for the graded Betti numbers of the resolution. Specifically, for the three-dimensional case, we determine the minimal free resolution of the logarithmic derivation module of $A$. We present illustrative examples of our main theorems to provide insights into the relationship between algebraic and combinatorial properties for close-to-free arrangements.", "field": "math", "label": 0}
{"text": "Title: Self-adjointness of the Gaffney Laplacian on vector bundles\nAbstract: We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.", "field": "math", "label": 1}
{"text": "Title: Entropy and sampling numbers of classes of ridge functions\nAbstract: We study properties of ridge functions $f(x)=g(a\\cdot x)$ in high dimensions $d$ from the viewpoint of approximation theory. The considered function classes consist of ridge functions such that the profile $g$ is a member of a univariate Lipschitz class with smoothness $\\alpha > 0$ (including infinite smoothness), and the ridge direction $a$ has $p$-norm $\\|a\\|_p \\leq 1$. First, we investigate entropy numbers in order to quantify the compactness of these ridge function classes in $L_{\\infty}$. We show that they are essentially as compact as the class of univariate Lipschitz functions. Second, we examine sampling numbers and face two extreme cases. In case $p=2$, sampling ridge functions on the Euclidean unit ball faces the curse of dimensionality. It is thus as difficult as sampling general multivariate Lipschitz functions, a result in sharp contrast to the result on entropy numbers. When we additionally assume that all feasible profiles have a first derivative uniformly bounded away from zero in the origin, then the complexity of sampling ridge functions reduces drastically to the complexity of sampling univariate Lipschitz functions. In between, the sampling problem's degree of difficulty varies, depending on the values of $\\alpha$ and $p$. Surprisingly, we see almost the entire hierarchy of tractability levels as introduced in the recent monographs by Novak and Wo\\'zniakowski.", "field": "math", "label": 1}
{"text": "Title: Enumeration of nonisomorphic Hamiltonian cycles on square grid graphs\nAbstract: The enumeration of Hamiltonian cycles on 2n*2n grids of nodes is a longstanding problem in combinatorics. Previous work has concentrated on counting all cycles. The current work enumerates nonisomorphic cycles -- that is, the number of isomorphism classes (up to all symmetry operations of the square). It is shown that the matrix method used previously can be modified to count cycles with all combinations of reflective and 180-degree rotational symmetry. Cycles with 90-degree rotational symmetry were counted by a direct search, using a modification of Knuth's Dancing Links algorithm. From these counts, the numbers of nonisomorphic cycles were calculated for n<=10.", "field": "math", "label": 1}
{"text": "Title: Diabetic Retinopathy Using Gaussian Filter\nAbstract: The retina is an essential component of the visual system, and maintaining eyesight depends on the timely and correct detection of disorders. This research specifically addresses the early-stage detection and severity classification of diabetic retinopathy (DR), a serious public health hazard. We compare the results of different deep learning models such as InceptionV3, DenseNet121 and other CNN based models by using different image filters, such as Gaussian, grayscale and Gabor. These models could detect subtle pathological alterations and use that information to estimate the risk of retinal illnesses. The objective is to improve the diagnostic processes for diabetic retinopathy, the primary cause of diabetes-related blindness, by utilizing deep learning models. A comparative analysis between Greyscale, Gaussian and Gabor filters has been provided after applying these filters on the retinal images. The Gaussian filter resulted to be the most promising filter giving the best accuracies for all the models. The best performing model was InceptionV3 which gave an accuracy of 96% on Gaussian images, therefore Gaussian filter emerged as our most promising filter.", "field": "cs", "label": 0}
{"text": "Title: What You See is What You GAN: Rendering Every Pixel for High-Fidelity Geometry in 3D GANs\nAbstract: 3D-aware Generative Adversarial Networks (GANs) have shown remarkable progress in learning to generate multi-view-consistent images and 3D geometries of scenes from collections of 2D images via neural volume rendering. Yet, the significant memory and computational costs of dense sampling in volume rendering have forced 3D GANs to adopt patch-based training or employ low-resolution rendering with post-processing 2D super resolution, which sacrifices multiview consistency and the quality of resolved geometry. Consequently, 3D GANs have not yet been able to fully resolve the rich 3D geometry present in 2D images. In this work, we propose techniques to scale neural volume rendering to the much higher resolution of native 2D images, thereby resolving fine-grained 3D geometry with unprecedented detail. Our approach employs learning-based samplers for accelerating neural rendering for 3D GAN training using up to 5 times fewer depth samples. This enables us to explicitly \"render every pixel\" of the full-resolution image during training and inference without post-processing superresolution in 2D. Together with our strategy to learn high-quality surface geometry, our method synthesizes high-resolution 3D geometry and strictly view-consistent images while maintaining image quality on par with baselines relying on post-processing super resolution. We demonstrate state-of-the-art 3D gemetric quality on FFHQ and AFHQ, setting a new standard for unsupervised learning of 3D shapes in 3D GANs.", "field": "cs", "label": 0}
{"text": "Title: Constrained quantization for the Cantor distribution with a family of constraints\nAbstract: In this paper, for a given family of constraints and the classical Cantor distribution we determine the optimal sets of $n$-points, $n$th constrained quantization errors for all positive integers $n$. We also calculate the constrained quantization dimension and the constrained quantization coefficient, and see that the constrained quantization dimension $D(P)$ exists as a finite positive number, but the $D(P)$-dimensional constrained quantization coefficient does not exist.", "field": "math", "label": 0}
{"text": "Title: Post-Processed Posteriors for Banded Covariances\nAbstract: We consider Bayesian inference of banded covariance matrices and propose a post-processed posterior. The post-processing of the posterior consists of two steps. In the first step, posterior samples are obtained from the conjugate inverse-Wishart posterior which does not satisfy any structural restrictions. In the second step, the posterior samples are transformed to satisfy the structural restriction through a post-processing function. The conceptually straightforward procedure of the post-processed posterior makes its computation efficient and can render interval estimators of functionals of covariance matrices. We show that it has nearly optimal minimax rates for banded covariances among all possible pairs of priors and post-processing functions. Furthermore, we prove that the expected coverage probability of the $(1-\\alpha)100\\%$ highest posterior density region of the post-processed posterior is asymptotically $1-\\alpha$ with respect to a conventional posterior distribution. It implies that the highest posterior density region of the post-processed posterior is, on average, a credible set of a conventional posterior. The advantages of the post-processed posterior are demonstrated by a simulation study and a real data analysis.", "field": "math", "label": 1}
{"text": "Title: Shadow Generation with Decomposed Mask Prediction and Attentive Shadow Filling\nAbstract: Image composition refers to inserting a foreground object into a background image to obtain a composite image. In this work, we focus on generating plausible shadows for the inserted foreground object to make the composite image more realistic. To supplement the existing small-scale dataset, we create a large-scale dataset called RdSOBA with rendering techniques. Moreover, we design a two-stage network named DMASNet with decomposed mask prediction and attentive shadow filling. Specifically, in the first stage, we decompose shadow mask prediction into box prediction and shape prediction. In the second stage, we attend to reference background shadow pixels to fill the foreground shadow. Abundant experiments prove that our DMASNet achieves better visual effects and generalizes well to real composite images.", "field": "cs", "label": 0}
{"text": "Title: Principle of Relevant Information for Graph Sparsification\nAbstract: Graph sparsification aims to reduce the number of edges of a graph while maintaining its structural properties. In this paper, we propose the first general and effective information-theoretic formulation of graph sparsification, by taking inspiration from the Principle of Relevant Information (PRI). To this end, we extend the PRI from a standard scalar random variable setting to structured data (i.e., graphs). Our Graph-PRI objective is achieved by operating on the graph Laplacian, made possible by expressing the graph Laplacian of a subgraph in terms of a sparse edge selection vector $\\mathbf{w}$. We provide both theoretical and empirical justifications on the validity of our Graph-PRI approach. We also analyze its analytical solutions in a few special cases. We finally present three representative real-world applications, namely graph sparsification, graph regularized multi-task learning, and medical imaging-derived brain network classification, to demonstrate the effectiveness, the versatility and the enhanced interpretability of our approach over prevalent sparsification techniques. Code of Graph-PRI is available at https://github.com/SJYuCNEL/PRI-Graphs", "field": "cs", "label": 1}
{"text": "Title: The generalized Pythagorean theorem on the compactifications of certain dually flat spaces via toric geometry\nAbstract: In this paper we study dually flat spaces arising from Delzant polytopes equipped with a symplectic potential together with their corresponding toric K\\\"ahler manifolds as their torifications.We introduce a dually flat structure and the associated Bregman divergence on the boundary from the viewpoint of toric K\\\"ahler geometry. We show a continuity and a generalized Pythagorean theorem for the divergence on the boundary. We also provide a characterization for a toric K\\\"ahler manifold to become a torification of a mixture family on a finite set.", "field": "math", "label": 0}
{"text": "Title: Embedding Hypertrees into Steiner Triple Systems\nAbstract: In this paper we are interested in the following question: Given an arbitrary Steiner triple system $S$ on $m$ vertices and any 3-uniform hypertree $T$ on $n$ vertices, is it necessary that $S$ contains $T$ as a subgraph provided $m \\geq (1+\\mu)n$? We show the answer is positive for a class of hypertrees and conjecture that the answer is always positive.", "field": "math", "label": 1}
{"text": "Title: Predicting Post-Route Quality of Results Estimates for HLS Designs using Machine Learning\nAbstract: Machine learning (ML) has been widely used to improve the predictability of EDA tools. The use of CAD tools that express designs at higher levels of abstraction makes machine learning even more important to highlight the performance of various design steps. Behavioral descriptions used during the high-level synthesis (HLS) are completely technology independent making it hard for designers to interpret how changes in the synthesis options affect the resultant circuit. FPGA design flows are completely embracing HLS based methodologies so that software engineers with almost no hardware design skills can easily use their tools. HLS tools allow design space exploration by modifying synthesis options, however, they lack accuracy in the Quality of Results (QoR) reported right after HLS. This lack of correctness results in sub-optimal designs with problems in timing closure. This paper presents a robust ML based design flow that can accurately predict post-route QoR for a given behavioral description without the need to synthesize the design. The model is an important design exploration tool where a designer can quickly view the impact on overall design quality when local and global optimization directives are changed. The proposed methodology presents two strong advantages: (i) Accurate prediction of the design quality (QoR), and (ii) complete elimination of the need to execute high-level synthesis for each design option. We predict three post route parameters, (i). Area, (ii). Latency and (iii). Clock Period of a design just by analyzing the high level behavioral code and some intermediate representation codes. We have integrated the methodology with Xilinx HLS tools and have demonstrated accurate estimation on a variety of FPGA families. Our estimated results are within 10\\% of actual computed values", "field": "cs", "label": 1}
{"text": "Title: Clairaut Anti-invariant Riemannian maps from/to Kähler manifolds admitting Ricci soliton\nAbstract: The aim of this article is to study the Clairaut anti-invariant Riemannian maps from/to K\\\"ahler manifolds admitting Ricci solitons. We find the curvature relations and calculate the Ricci tensor under different conditions. We obtain conditions for the range and kernel of these maps to be Einstein. Next, we find the scalar curvature for range. Finally, we give some non-trivial examples of Clairaut anti-invariant Riemannian maps from/to K\\\"ahler manifolds admitting Ricci solitons.", "field": "math", "label": 0}
{"text": "Title: Explicit construction of a plane sextic model for genus-five Howe curves, II\nAbstract: A Howe curve is defined as the normalization of the fiber product over a projective line of two hyperelliptic curves. Howe curves are very useful to produce important classes of curves over fields of positive characteristic, e.g., maximal, superspecial, or supersingular ones. Determining their feasible equations explicitly is a basic problem, and it has been solved in the hyperelliptic case and in the non-hyperelliptic case with genus not greater than $4$. In this paper, we construct an explicit plane sextic model for non-hyperelliptic Howe curves of genus $5$. We also determine the number and type of singularities on our sextic model, and prove that the singularities are generically $4$ double points. Our results together with Moriya-Kudo's recent ones imply that for each $s \\in \\{2,3,4,5\\}$, there exists a non-hyperellptic curve $H$ of genus $5$ with $\\mathrm{Aut}(H) \\supset \\mathbf{V}_4$ such that its associated plane sextic has $s$ double points.", "field": "math", "label": 0}
{"text": "Title: Computing higher symplectic capacities I\nAbstract: We present recursive formulas which compute the recently defined \"higher symplectic capacities\" for all convex toric domains. In the special case of four-dimensional ellipsoids, we apply homological perturbation theory to the associated filtered L-infinity algebras and prove that the resulting structure coefficients count punctured pseudoholomorphic curves in cobordisms between ellipsoids. As sample applications, we produce new previously inaccessible obstructions for stabilized embeddings of ellipsoids and polydisks, and we give new counts of curves with tangency constraints.", "field": "math", "label": 1}
{"text": "Title: Assessing the Impact of a User-Item Collaborative Attack on Class of Users\nAbstract: Collaborative Filtering (CF) models lie at the core of most recommendation systems due to their state-of-the-art accuracy. They are commonly adopted in e-commerce and online services for their impact on sales volume and/or diversity, and their impact on companies' outcome. However, CF models are only as good as the interaction data they work with. As these models rely on outside sources of information, counterfeit data such as user ratings or reviews can be injected by attackers to manipulate the underlying data and alter the impact of resulting recommendations, thus implementing a so-called shilling attack. While previous works have focused on evaluating shilling attack strategies from a global perspective paying particular attention to the effect of the size of attacks and attacker's knowledge, in this work we explore the effectiveness of shilling attacks under novel aspects. First, we investigate the effect of attack strategies crafted on a target user in order to push the recommendation of a low-ranking item to a higher position, referred to as user-item attack. Second, we evaluate the effectiveness of attacks in altering the impact of different CF models by contemplating the class of the target user, from the perspective of the richness of her profile (i.e., cold v.s. warm user). Finally, similar to previous work we contemplate the size of attack (i.e., the amount of fake profiles injected) in examining their success. The results of experiments on two widely used datasets in business and movie domains, namely Yelp and MovieLens, suggest that warm and cold users exhibit contrasting behaviors in datasets with different characteristics.", "field": "cs", "label": 1}
{"text": "Title: Global Invariant Branches of Non-degenerate Foliations on Projective Toric Surfaces\nAbstract: We show that the isolated invariant branches globalize to algebraic curves, when we consider weak toric type complex hyperbolic foliations on projective toric ambient surfaces. To do it, we pass through a characterization of weak toric type foliations in terms of \"non-degeneracy\" conditions, associated to Newton polygons. We also give a description of the relationship between invariant algebraic curves and isolated invariant branches, valid for the case of toric type, by means of the following dichotomy. Either there is a rational first integral and there are no isolated invariant branches or we have only finitely many global invariant curves, all of them extending isolated invariant branches.", "field": "math", "label": 1}
{"text": "Title: SENS3: Multisensory Database of Finger-Surface Interactions and Corresponding Sensations\nAbstract: The growing demand for natural interactions with technology underscores the importance of achieving realistic touch sensations in digital environments. Realizing this goal highly depends on comprehensive databases of finger-surface interactions, which need further development. Here, we present SENS3, an extensive open-access repository of multisensory data acquired from fifty surfaces when two participants explored them with their fingertips through static contact, pressing, tapping, and sliding. SENS3 encompasses high-fidelity visual, audio, and haptic information recorded during these interactions, including videos, sounds, contact forces, torques, positions, accelerations, skin temperature, heat flux, and surface photographs. Additionally, it incorporates thirteen participants' psychophysical sensation ratings while exploring these surfaces freely. We anticipate that SENS3 will be valuable for advancing multisensory texture rendering, user experience development, and touch sensing in robotics.", "field": "cs", "label": 0}
{"text": "Title: Summing a family of generalized Pell numbers\nAbstract: A new family of generalized Pell numbers was recently introduced and studied by Br\\'od \\cite{Dorota}. These number possess, as Fibonacci numbers, a Binet formula. Using this, partial sums of arbitrary powers of generalized Pell numbers can be summed explicitly. For this, as a first step, a power $P_n^l$ is expressed as a linear combination of $P_{mn}$. The summation of such expressions is then manageable using generating functions. Since the new family contains a parameter $R=2^r$, the relevant manipulations are quite involved, and computer algebra produced huge expressions that where not trivial to handle at times.", "field": "math", "label": 1}
{"text": "Title: Convergence rate of alternating projection method for the intersection of an affine subspace and the second-order cone\nAbstract: We study the convergence rate of the alternating projection method (APM) applied to the intersection of an affine subspace and the second-order cone. We show that when they intersect non-transversally, the convergence rate is $O(k^{-1/2})$, where $k$ is the number of iterations of the APM. In particular, when the intersection is not at the origin or forms a half-line with the origin as the endpoint, the obtained convergence rate can be exact because a lower bound of the convergence rate is evaluated. These results coincide with the worst-case convergence rate obtained from the error bound discussed in [Borwein et al., SIOPT, 2014] and [Drusvyatskiy et al., Math. Prog., 2017]. Moreover, we consider the convergence rate of the APM for the intersection of an affine subspace and the product of two second-order cones. We provide an example that the worst-case convergence rate of the APM is better than the rate expected from the error bound for the example.", "field": "math", "label": 0}
{"text": "Title: Inferring relevant features: from QFT to PCA\nAbstract: In many-body physics, renormalization techniques are used to extract aspects of a statistical or quantum state that are relevant at large scale, or for low energy experiments. Recent works have proposed that these features can be formally identified as those perturbations of the states whose distinguishability most resist coarse-graining. Here, we examine whether this same strategy can be used to identify important features of an unlabeled dataset. This approach indeed results in a technique very similar to kernel PCA (principal component analysis), but with a kernel function that is automatically adapted to the data, or \"learned\". We test this approach on handwritten digits, and find that the most relevant features are significantly better for classification than those obtained from a simple gaussian kernel.", "field": "cs", "label": 1}
{"text": "Title: Ordered Ramsey numbers of powers of paths\nAbstract: Given two vertex-ordered graphs $G$ and $H$, the ordered Ramsey number $R_<(G,H)$ is the smallest $N$ such that whenever the edges of a vertex-ordered complete graph $K_N$ are red/blue-coloured, then there is a red (ordered) copy of $G$ or a blue (ordered) copy of $H$. Let $P_n^t$ denote the $t$-th power of a monotone path on $n$ vertices. The ordered Ramsey numbers of powers of paths have been extensively studied. We prove that there exists an absolute constant $C$ such that $R_<(K_s,P_n^t)\\leq R(K_s,K_t)^{C} \\cdot n$ holds for all $s,t,n$, which is tight up to the value of $C$. As a corollary, we obtain that there is an absolute constant $C$ such that $R_<(K_n,P_n^t)\\leq n^{Ct}$. These results resolve a problem and a conjecture of Gishboliner, Jin and Sudakov. Furthermore, we show that $R_<(P_n^t,P_n^t)\\leq n^{4+o(1)}$ for any fixed $t$. This answers questions of Balko, Cibulka, Kr\\'al and Kyn\\v{c}l, and of Gishboliner, Jin and Sudakov.", "field": "math", "label": 0}
{"text": "Title: Recursive sequences attached to modular representations of finite groups\nAbstract: The core of a finite-dimensional modular representation $M$ of a finite group $G$ is its largest non-projective summand. We prove that the dimensions of the cores of $M^{\\otimes n}$ have algebraic Hilbert series when $M$ is Omega-algebraic, in the sense that the non-projective summands of $M^{\\otimes n}$ fall into finitely many orbits under the action of the syzygy operator $\\Omega$. Similarly, we prove that these dimension sequences are eventually linearly recursive when $M$ is what we term $\\Omega^{+}$-algebraic. This partially answers a conjecture by Benson and Symonds. Along the way, we also prove a number of auxiliary permanence results for linear recurrence under operations on multi-variable sequences.", "field": "math", "label": 1}
{"text": "Title: Dirac geometry II: Coherent cohomology\nAbstract: Whatever it is that animates anima and breathes life into higher algebra, this something leaves its trace in the structure of a Dirac ring on the homotopy groups of a commutative algebra in spectra. In the prequel to this paper, we developed the commutative algebra of Dirac rings and defined the category of Dirac schemes. Here, we first embed this category in the larger infinity-category of Dirac stacks, which also contains formal Dirac schemes. We next develop the coherent cohomology of Dirac stacks, which amounts to a functor that to a Dirac stack X assigns a presentably symmetric monoidal stable infinity-category QCoh(X) of quasi-coherent sheaves together with a compatible t-structure. Finally, as applications of the general theory to stable homotopy theory, we use Quillen's theorem on complex cobordism and Milnor's theorem on the dual Steenrod algebra to identify the Dirac stacks corresponding to MU and F_p in terms of their functors of points. In the appendix, we develop a rudimentary theory of accessible presheaves of anima on coaccessible infinity-categories.", "field": "math", "label": 0}
{"text": "Title: Variance Reduction is an Antidote to Byzantines: Better Rates, Weaker Assumptions and Communication Compression as a Cherry on the Top\nAbstract: Byzantine-robustness has been gaining a lot of attention due to the growth of the interest in collaborative and federated learning. However, many fruitful directions, such as the usage of variance reduction for achieving robustness and communication compression for reducing communication costs, remain weakly explored in the field. This work addresses this gap and proposes Byz-VR-MARINA - a new Byzantine-tolerant method with variance reduction and compression. A key message of our paper is that variance reduction is key to fighting Byzantine workers more effectively. At the same time, communication compression is a bonus that makes the process more communication efficient. We derive theoretical convergence guarantees for Byz-VR-MARINA outperforming previous state-of-the-art for general non-convex and Polyak-Lojasiewicz loss functions. Unlike the concurrent Byzantine-robust methods with variance reduction and/or compression, our complexity results are tight and do not rely on restrictive assumptions such as boundedness of the gradients or limited compression. Moreover, we provide the first analysis of a Byzantine-tolerant method supporting non-uniform sampling of stochastic gradients. Numerical experiments corroborate our theoretical findings.", "field": "cs", "label": 1}
{"text": "Title: The Chern class for $K_3$ and the cyclic quantum dilogarithm\nAbstract: In this note we confirm the conjecture of Calegari, Garoufalidis and Zagier in their recent paper in Ann. Sci. \\'{E}cole Normale Sup. that $R_\\zeta=c_\\zeta^2$, where $R_\\zeta$ is their map on $K_3$ defined using the cyclic quantum dilogarithm and $c_\\zeta$ is the Chern class map on $K_3$.", "field": "math", "label": 1}
{"text": "Title: On the parametrized Tate construction and two theories of real $p$-cyclotomic spectra\nAbstract: We give a new formula for $p$-typical real topological cyclic homology that refines the fiber sequence formula discovered by Nikolaus and Scholze for $p$-typical topological cyclic homology to one involving genuine $C_2$-spectra. To accomplish this, we give a new definition of the $\\infty$-category of real $p$-cyclotomic spectra that replaces the usage of genuinely equivariant dihedral spectra with the parametrized Tate construction $(-)^{t_{C_2} \\mu_p}$ associated to the dihedral group $D_{2p} = \\mu_p \\rtimes C_2$. We then define a $p$-typical and $\\infty$-categorical version of H{\\o}genhaven's $O(2)$-orthogonal cyclotomic spectra, construct a forgetful functor relating the two theories, and show that this functor restricts to an equivalence between full subcategories of appropriately bounded below objects.", "field": "math", "label": 1}
{"text": "Title: Level-set based design of Wang tiles for modelling complex microstructures\nAbstract: Microstructural geometry plays a critical role in the response of heterogeneous materials. Consequently, methods for generating microstructural samples are increasingly crucial to advanced numerical analyses. We extend Sonon et al.'s unified framework, developed originally for generating particulate and foam-like microstructural geometries of Periodic Unit Cells, to non-periodic microstructural representations based on the formalism of Wang tiles. This formalism has been recently proposed in order to generalize the Periodic Unit Cell approach, enabling a fast synthesis of arbitrarily large, stochastic microstructural samples from a handful of domains with predefined compatibility constraints. However, a robust procedure capable of designing complex, three-dimensional, foam-like and cellular morphologies of Wang tiles has not yet been proposed. This contribution fills the gap by significantly broadening the applicability of the tiling concept. Since the original Sonon et al.'s framework builds on a random sequential addition of particles enhanced with an implicit representation of particle boundaries by the level-set field, we first devise an analysis based on a connectivity graph of a tile set, resolving the question where a particle should be copied when it intersects a tile boundary. Next, we introduce several modifications to the original algorithm that are necessary to ensure microstructural compatibility in the generalized periodicity setting of Wang tiles. Having established a universal procedure for generating tile morphologies, we compare strictly aperiodic and stochastic sets with the same cardinality in terms of reducing the artificial periodicity in reconstructed microstructural samples. We demonstrate the superiority of the vertex-defined tile sets for two-dimensional problems and illustrate the capabilities of the algorithm with two- and three-dimensional examples.", "field": "cs", "label": 1}
{"text": "Title: A Tutorial on Extremely Large-Scale MIMO for 6G: Fundamentals, Signal Processing, and Applications\nAbstract: Extremely large-scale multiple-input-multiple-output (XL-MIMO), which offers vast spatial degrees of freedom, has emerged as a potentially pivotal enabling technology for the sixth generation (6G) of wireless mobile networks. With its growing significance, both opportunities and challenges are concurrently manifesting. This paper presents a comprehensive survey of research on XL-MIMO wireless systems. In particular, we introduce four XL-MIMO hardware architectures: uniform linear array (ULA)-based XL-MIMO, uniform planar array (UPA)-based XL-MIMO utilizing either patch antennas or point antennas, and continuous aperture (CAP)-based XL-MIMO. We comprehensively analyze and discuss their characteristics and interrelationships. Following this, we introduce several electromagnetic characteristics and general distance boundaries in XL-MIMO. Given the distinct electromagnetic properties of near-field communications, we present a range of channel models to demonstrate the benefits of XL-MIMO. We further discuss and summarize signal processing schemes for XL-MIMO. It is worth noting that the low-complexity signal processing schemes and deep learning empowered signal processing schemes are reviewed and highlighted to promote the practical implementation of XL-MIMO. Furthermore, we explore the interplay between XL-MIMO and other emergent 6G technologies. Finally, we outline several compelling research directions for future XL-MIMO wireless communication systems.", "field": "cs", "label": 0}
{"text": "Title: Visual Relationship Forecasting in Videos\nAbstract: Real-world scenarios often require the anticipation of object interactions in unknown future, which would assist the decision-making process of both humans and agents. To meet this challenge, we present a new task named Visual Relationship Forecasting (VRF) in videos to explore the prediction of visual relationships in a reasoning manner. Specifically, given a subject-object pair with H existing frames, VRF aims to predict their future interactions for the next T frames without visual evidence. To evaluate the VRF task, we introduce two video datasets named VRF-AG and VRF-VidOR, with a series of spatio-temporally localized visual relation annotations in a video. These two datasets densely annotate 13 and 35 visual relationships in 1923 and 13447 video clips, respectively. In addition, we present a novel Graph Convolutional Transformer (GCT) framework, which captures both object-level and frame-level dependencies by spatio-temporal Graph Convolution Network and Transformer. Experimental results on both VRF-AG and VRF-VidOR datasets demonstrate that GCT outperforms the state-of-the-art sequence modelling methods on visual relationship forecasting.", "field": "cs", "label": 1}
{"text": "Title: Propagation of Input Tail Uncertainty in Rare-Event Estimation: A Light versus Heavy Tail Dichotomy\nAbstract: We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical approximation assuming the model is accurately specified. In this paper, we study a distinct direction on the propagation of model uncertainty and how it impacts the reliability of rare-event estimates. Specifically, we consider the basic setup of the exceedance of i.i.d. sum, and investigate how the lack of tail information of each input summand can affect the output probability. We argue that heavy-tailed problems are much more vulnerable to input uncertainty than light-tailed problems, reasoned through their large deviations behaviors and numerical evidence. We also investigate some approaches to quantify model errors in this problem using a combination of the bootstrap and extreme value theory, showing some positive outcomes but also uncovering some statistical challenges.", "field": "math", "label": 0}
{"text": "Title: Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence\nAbstract: We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.", "field": "math", "label": 1}
{"text": "Title: An extremal problem for the convolution of logarithmically concave functions\nAbstract: A new position is introduced and studied for the convolution of log-concave functions, which may be regarded as a functional analogue of the maximum intersection position of convex bodies introduced and studied by Artstein-Avidan and Katzin (2018) and Artstein-Avidan and Putterman (2022). Our main result is a John-type theorem for the maximal intersection position of a pair of log-concave functions, including the corresponding decomposition of the identity. The main result holds under very weak assumptions on the functions; in particular, the functions considered may both have unbounded supports.", "field": "math", "label": 0}
{"text": "Title: Constructing Approximate Single-Source Distance Sensitivity Oracles in Nearly Linear Time\nAbstract: For an input graph $G=(V, E)$ and a source vertex $s \\in V$, the \\emph{$\\alpha$-approximate vertex fault-tolerant distance sensitivity oracle} (\\emph{$\\alpha$-VSDO}) answers an $\\alpha$-approximate distance from $s$ to $t$ in $G-x$ for any query $(x, t)$. It is a data structure version of the so-called single-source replacement path problem (SSRP). In this paper, we present a new \\emph{nearly linear time} algorithm of constructing the $(1 + \\epsilon)$-VSDO for any weighted directed graph of $n$ vertices and $m$ edges with integer weights in range $[1, W]$, and any positive constant $\\epsilon \\in (0, 1]$. More precisely, the presented oracle attains $\\tilde{O}(m / \\epsilon + n /\\epsilon^2)$ construction time, $\\tilde{O}(n/ \\epsilon)$ size, and $\\tilde{O}(1/\\epsilon)$ query time for any polynomially-bounded $W$. To the best of our knowledge, this is the first non-trivial result for SSRP/VSDO beating the trivial $\\tilde{O}(mn)$ computation time for directed graphs with polynomially-bounded edge weights. Such a result has been unknown so far even for the setting of $(1 + \\epsilon)$-approximation. It also implies that the known barrier of $\\Omega(m\\sqrt{n})$ time for the exact SSRP by Chechik and Magen~[ICALP2020] does not apply to the case of approximation.", "field": "cs", "label": 0}
{"text": "Title: Linguistic Profiling of Deepfakes: An Open Database for Next-Generation Deepfake Detection\nAbstract: The emergence of text-to-image generative models has revolutionized the field of deepfakes, enabling the creation of realistic and convincing visual content directly from textual descriptions. However, this advancement presents considerably greater challenges in detecting the authenticity of such content. Existing deepfake detection datasets and methods often fall short in effectively capturing the extensive range of emerging deepfakes and offering satisfactory explanatory information for detection. To address the significant issue, this paper introduces a deepfake database (DFLIP-3K) for the development of convincing and explainable deepfake detection. It encompasses about 300K diverse deepfake samples from approximately 3K generative models, which boasts the largest number of deepfake models in the literature. Moreover, it collects around 190K linguistic footprints of these deepfakes. The two distinguished features enable DFLIP-3K to develop a benchmark that promotes progress in linguistic profiling of deepfakes, which includes three sub-tasks namely deepfake detection, model identification, and prompt prediction. The deepfake model and prompt are two essential components of each deepfake, and thus dissecting them linguistically allows for an invaluable exploration of trustworthy and interpretable evidence in deepfake detection, which we believe is the key for the next-generation deepfake detection. Furthermore, DFLIP-3K is envisioned as an open database that fosters transparency and encourages collaborative efforts to further enhance its growth. Our extensive experiments on the developed benchmark verify that our DFLIP-3K database is capable of serving as a standardized resource for evaluating and comparing linguistic-based deepfake detection, identification, and prompt prediction techniques.", "field": "cs", "label": 0}
{"text": "Title: Atomistic modelling of near-crack-tip plasticity\nAbstract: An atomistic model of near-crack-tip plasticity on a square lattice under anti-plane shear kinematics is formulated and studied. The model is based upon a new geometric and functional framework of a lattice manifold complex, which ensures that the crack surface is fully taken into account, while preserving the crucial notion of duality. As a result, existence of locally stable equilibrium configurations containing both a crack opening and dislocations is established. Notably, with the boundary in the form of a crack surface accounted for, no minimum separation between a dislocation core and the crack surface or the crack tip is required. The work presented here constitutes a foundation for several further studies aiming to put the phenomenon of near-crack-tip plasticity on a rigorous footing.", "field": "math", "label": 1}
{"text": "Title: An Asymmetric Contrastive Loss for Handling Imbalanced Datasets\nAbstract: Contrastive learning is a representation learning method performed by contrasting a sample to other similar samples so that they are brought closely together, forming clusters in the feature space. The learning process is typically conducted using a two-stage training architecture, and it utilizes the contrastive loss (CL) for its feature learning. Contrastive learning has been shown to be quite successful in handling imbalanced datasets, in which some classes are overrepresented while some others are underrepresented. However, previous studies have not specifically modified CL for imbalanced datasets. In this work, we introduce an asymmetric version of CL, referred to as ACL, in order to directly address the problem of class imbalance. In addition, we propose the asymmetric focal contrastive loss (AFCL) as a further generalization of both ACL and focal contrastive loss (FCL). Results on the FMNIST and ISIC 2018 imbalanced datasets show that AFCL is capable of outperforming CL and FCL in terms of both weighted and unweighted classification accuracies. In the appendix, we provide a full axiomatic treatment on entropy, along with complete proofs.", "field": "cs", "label": 1}
{"text": "Title: Flip Graphs on Self-Complementary Ideals of Chain Products\nAbstract: In this paper, we introduce a flip operation on self-complementary ideals of chain product posets and study the resulting flip graphs. We give asymptotics for the number of vertices in these graphs, compute their diameters, and give bounds for their radii. We also define similar flip operations on self-complementary ideals of the chain product $[2r]\\times [2r]\\times [2r]$ satisfying additional symmetries, and we achieve similar results for the resulting flip graphs.", "field": "math", "label": 0}
{"text": "Title: Dynamic Service Placement for Mobile Micro-Clouds with Predicted Future Costs\nAbstract: Mobile micro-clouds are promising for enabling performance-critical cloud applications. However, one challenge therein is the dynamics at the network edge. In this paper, we study how to place service instances to cope with these dynamics, where multiple users and service instances coexist in the system. Our goal is to find the optimal placement (configuration) of instances to minimize the average cost over time, leveraging the ability of predicting future cost parameters with known accuracy. We first propose an offline algorithm that solves for the optimal configuration in a specific look-ahead time-window. Then, we propose an online approximation algorithm with polynomial time-complexity to find the placement in real-time whenever an instance arrives. We analytically show that the online algorithm is $O(1)$-competitive for a broad family of cost functions. Afterwards, the impact of prediction errors is considered and a method for finding the optimal look-ahead window size is proposed, which minimizes an upper bound of the average actual cost. The effectiveness of the proposed approach is evaluated by simulations with both synthetic and real-world (San Francisco taxi) user-mobility traces. The theoretical methodology used in this paper can potentially be applied to a larger class of dynamic resource allocation problems.", "field": "cs", "label": 1}
{"text": "Title: Kernel Search approach to solve the Minimum Spanning Tree Problem with conflicting edge pairs\nAbstract: The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this problem using a tailored Kernel Search heuristic method, which consists in solving iteratively improved restrictions of the problem. The main novelty of the approach consists in using an independent set of the conflict graph within the algorithm. We test our approach on the benchmark instances and we compare our results with the ones obtained by other heuristics available in the literature.", "field": "math", "label": 0}
{"text": "Title: A Case Study on Software Vulnerability Coordination\nAbstract: Context: Coordination is a fundamental tenet of software engineering. Coordination is required also for identifying discovered and disclosed software vulnerabilities with Common Vulnerabilities and Exposures (CVEs). Motivated by recent practical challenges, this paper examines the coordination of CVEs for open source projects through a public mailing list. Objective: The paper observes the historical time delays between the assignment of CVEs on a mailing list and the later appearance of these in the National Vulnerability Database (NVD). Drawing from research on software engineering coordination, software vulnerabilities, and bug tracking, the delays are modeled through three dimensions: social networks and communication practices, tracking infrastructures, and the technical characteristics of the CVEs coordinated. Method: Given a period between 2008 and 2016, a sample of over five thousand CVEs is used to model the delays with nearly fifty explanatory metrics. Regression analysis is used for the modeling. Results: The results show that the CVE coordination delays are affected by different abstractions for noise and prerequisite constraints. These abstractions convey effects from the social network and infrastructure dimensions. Particularly strong effect sizes are observed for annual and monthly control metrics, a control metric for weekends, the degrees of the nodes in the CVE coordination networks, and the number of references given in NVD for the CVEs archived. Smaller but visible effects are present for metrics measuring the entropy of the emails exchanged, traces to bug tracking systems, and other related aspects. The empirical signals are weaker for the technical characteristics. Conclusion: [...]", "field": "cs", "label": 1}
{"text": "Title: Comparative Analysis of Obstacle Approximation Strategies for the Steady Incompressible Navier-Stokes Equations\nAbstract: This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization approximation and an approximation method utilizing high viscosity inside the obstacle region, as well as their composition. Analytical results concerning the convergence rate of these approaches are provided, and extensive numerical experiments are conducted to validate their performance.", "field": "math", "label": 0}
{"text": "Title: Notes on Nonrepetitive Graph Colouring\nAbstract: A vertex colouring of a graph is \\emph{nonrepetitive on paths} if there is no path $v_1,v_2,...,v_{2t}$ such that v_i and v_{t+i} receive the same colour for all i=1,2,...,t. We determine the maximum density of a graph that admits a k-colouring that is nonrepetitive on paths. We prove that every graph has a subdivision that admits a 4-colouring that is nonrepetitive on paths. The best previous bound was 5. We also study colourings that are nonrepetitive on walks, and provide a conjecture that would imply that every graph with maximum degree $\\Delta$ has a $f(\\Delta)$-colouring that is nonrepetitive on walks. We prove that every graph with treewidth k and maximum degree $\\Delta$ has a $O(k\\Delta)$-colouring that is nonrepetitive on paths, and a $O(k\\Delta^3)$-colouring that is nonrepetitive on walks.", "field": "math", "label": 1}
{"text": "Title: The continuum disordered pinning model\nAbstract: Any renewal processes on $\\mathbb{N}$ with a polynomial tail, with exponent $\\alpha \\in (0,1)$, has a non-trivial scaling limit, known as the $\\alpha$-stable regenerative set. In this paper we consider Gibbs transformations of such renewal processes in an i.i.d. random environment, called disordered pinning models. We show that for $\\alpha \\in (1/2, 1)$ these models have a universal scaling limit, which we call the continuum disordered pinning model (CDPM). This is a random closed subset of $\\mathbb{R}$ in a white noise random environment, with subtle features: -Any fixed a.s. property of the $\\alpha$-stable regenerative set (e.g., its Hausdorff dimension) is also an a.s. property of the CDPM, for almost every realization of the environment. -Nonetheless, the law of the CDPM is singular with respect to the law of the $\\alpha$-stable regenerative set, for almost every realization of the environment. The existence of a disordered continuum model, such as the CDPM, is a manifestation of disorder relevance for pinning models with $\\alpha \\in (1/2, 1)$.", "field": "math", "label": 1}
{"text": "Title: On some anabelian properties of arithmetic curves\nAbstract: In this paper we generalize an argument of Neukirch from birational anabelian geometry to the case of arithmetic curves. In contrast to the function field case, it seems to be more complicate to describe the position of decomposition groups of points at the boundary of the scheme $\\Spec \\caO_{K,S}$, where $K$ is a number field and $S$ a set of primes of $K$, intrinsically in terms of the fundamental group. We prove that it is equivalent to give the following pieces of information additionally with the fundamental group $\\pi_1(\\Spec \\caO_{K,S})$: the location of decomposition groups of boundary points inside it, the $p$-part of the cyclotomic character, the number of points on the boundary of all finite etale covers, etc. Under certain finiteness hypothesis on Tate-Shafarevich groups with divisible coefficients, one can reconstruct all this quantities from the fundamental group alone.", "field": "math", "label": 1}
{"text": "Title: Parallel Algorithms Align with Neural Execution\nAbstract: Neural algorithmic reasoners are parallel processors. Teaching them sequential algorithms contradicts this nature, rendering a significant share of their computations redundant. Parallel algorithms however may exploit their full computational power, therefore requiring fewer layers to be executed. This drastically reduces training times, as we observe when comparing parallel implementations of searching, sorting and finding strongly connected components to their sequential counterparts on the CLRS framework. Additionally, parallel versions achieve (often strongly) superior predictive performance.", "field": "cs", "label": 0}
{"text": "Title: Hyperbolicity and non-conservativity of a hydrodynamic model of swarming rigid bodies\nAbstract: In this paper, we study a nonlinear system of first order partial differential equations describing the macroscopic behavior of an ensemble of interacting self-propelled rigid bodies. Such system may be relevant for the modelling of bird flocks, fish schools or fleets of drones. We show that the system is hyperbolic and can be approximated by a conservative system through relaxation. We also derive viscous corrections to the model from the hydrodynamic limit of a kinetic model. This analysis prepares the future development of numerical approximations of this system.", "field": "math", "label": 1}
{"text": "Title: The Rotation of Eigenspaces of Perturbed Matrix Pairs\nAbstract: We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates are a natural way to obtain sharp --- as functions of the parameter indexing the family of matrix pairs --- estimates for the rotation of spectral subspaces.", "field": "math", "label": 1}
{"text": "Title: CURE Dataset: Ladder Networks for Audio Event Classification\nAbstract: Audio event classification is an important task for several applications such as surveillance, audio, video and multimedia retrieval etc. There are approximately 3M people with hearing loss who can't perceive events happening around them. This paper establishes the CURE dataset which contains curated set of specific audio events most relevant for people with hearing loss. We propose a ladder network based audio event classifier that utilizes 5s sound recordings derived from the Freesound project. We adopted the state-of-the-art convolutional neural network (CNN) embeddings as audio features for this task. We also investigate extreme learning machine (ELM) for event classification. In this study, proposed classifiers are compared with support vector machine (SVM) baseline. We propose signal and feature normalization that aims to reduce the mismatch between different recordings scenarios. Firstly, CNN is trained on weakly labeled Audioset data. Next, the pre-trained model is adopted as feature extractor for proposed CURE corpus. We incorporate ESC-50 dataset as second evaluation set. Results and discussions validate the superiority of Ladder network over ELM and SVM classifier in terms of robustness and increased classification accuracy. While Ladder network is robust to data mismatches, simpler SVM and ELM classifiers are sensitive to such mismatches, where the proposed normalization techniques can play an important role. Experimental studies with ESC-50 and CURE corpora elucidate the differences in dataset complexity and robustness offered by proposed approaches.", "field": "cs", "label": 1}
{"text": "Title: On the Girth of Graph Lifts\nAbstract: The size of the smallest $k$-regular graph of girth $g$ is denoted by the well studied function $n(k,g)$. We suggest generalizing this function to $n(H,g)$, defined as the smallest size girth $g$ graph covering the, possibly non-regular, graph $H$. We prove that the two main combinatorial bounds on $n(k,g)$, the Moore lower bound and the Erd\\\"{o}s Sachs upper bound, carry over to the new setting of lifts, even in their non-asymptotic form. We also consider two other generalizations of $n(k,g)$: i) The smallest size girth $g$ graph sharing a universal cover with $H$. We prove that it is the same as $n(H,g)$ up to a multiplicative constant. ii) The smallest size girth $g$ graph with a prescribed degree distribution. We discuss this known generalization and argue that the new suggested definitions are superior. We conclude with experimental results for a specific base graph and with some conjectures and open problems.", "field": "math", "label": 0}
{"text": "Title: A survey on divisibility of ultrafilters\nAbstract: An extension of the divisibility relation on $\\mathbb{N}$ to the set $\\beta\\mathbb{N}$ of ultrafilters on $\\mathbb{N}$ was defined and investigated in several papers during the last ten years. Here we make a survey of results obtained so far, adding a few simple results connecting the themes of different stages of the research. The main highlights include: separation into the lower part $L$ (with its division into levels) and the upper part; identifying basic ingredients (powers of primes) and fragmentation of each ultrafilter into them; finding the corresponding upward closed sets belonging to an ultrafilter; estimating cardinalities of divisibility-equivalence classes; extending the congruence relation (in two ways) and checking properties of the obtained relations.", "field": "math", "label": 0}
{"text": "Title: Simple loops on 2-bridge spheres in Heckoid orbifolds for the trivial knot\nAbstract: In this paper, we give a necessary and sufficient condition for an essential simple loop on a $2$-bridge sphere in an even Heckoid orbifold for the trivial knot to be null-homotopic, peripheral or torsion in the orbifold. We also give a necessary and sufficient condition for two essential simple loops on a $2$-bridge sphere in an even Heckoid orbifold for the trivial knot to be homotopic in the orbifold.", "field": "math", "label": 1}
{"text": "Title: Asymptotic probability for connectedness\nAbstract: We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of other derivative combinatorial classes. The general result applies to rapidly growing combinatorial structures, which we call gargantuan, that also admit a sequence decomposition. The result is then applied to several models of graphs, of surfaces (square-tiled surfaces, combinatorial maps), and to geometric models of higher dimension (constellations, graph encoded manifolds). The corresponding derivative combinatorial classes are irreducible (multi)tournaments, indecomposable (multi)permutations and indecomposable perfect (multi)matchings.", "field": "math", "label": 0}
{"text": "Title: Strong asymptotic expansions in a multidirection\nAbstract: In this paper we prove that, for asymptotically bounded holomorphic functions defined in a polysector in ${\\mathbb C}^n$, the existence of a strong asymptotic expansion in Majima's sense following a single multidirection towards the vertex entails (global) asymptotic expansion in the whole polysector. Moreover, we specialize this result for Gevrey strong asymptotic expansions. This is a generalization of a result proved by A. Fruchard and C. Zhang for asymptotic expansions in one variable, but the proof, mainly in the Gevrey case, involves different techniques of a functional-analytic nature.", "field": "math", "label": 1}
{"text": "Title: Quadratic Discontinuous Galerkin methods for Unilateral Contact Problem\nAbstract: In this article, we employ discontinuous Galerkin (DG) methods for the finite element approximation of the frictionless unilateral contact problem using quadratic finite elements over simplicial triangulation. We first establish an optimal \\textit{a priori} error estimates under the appropriate regularity assumption on the exact solution $\\b{u}$. Further, we analyze \\textit{a posteriori} error estimates in the DG norm wherein, the reliability and efficiency of the proposed \\textit{a posteriori} error estimator is addressed. The suitable construction of discrete Lagrange multiplier $\\b{\\lambda_h}$ and some intermediate operators play a key role in developing \\textit{a posteriori} error analysis. Numerical results presented on uniform and adaptive meshes illustrate and confirm the theoretical findings.", "field": "math", "label": 0}
{"text": "Title: TinyLlama: An Open-Source Small Language Model\nAbstract: We present TinyLlama, a compact 1.1B language model pretrained on around 1 trillion tokens for approximately 3 epochs. Building on the architecture and tokenizer of Llama 2, TinyLlama leverages various advances contributed by the open-source community (e.g., FlashAttention), achieving better computational efficiency. Despite its relatively small size, TinyLlama demonstrates remarkable performance in a series of downstream tasks. It significantly outperforms existing open-source language models with comparable sizes. Our model checkpoints and code are publicly available on GitHub at https://github.com/jzhang38/TinyLlama.", "field": "cs", "label": 0}
{"text": "Title: On the Performance of Large-Scale Wireless Networks in the Finite Block-Length Regime\nAbstract: Ultra-Reliable Low-Latency Communications have stringent delay constraints, and hence use codes with small block length (short codewords). In these cases, classical models that provide good approximations to systems with infinitely long codewords become imprecise. To remedy this, in this paper, an average coding rate expression is derived for a large scale network with short codewords using stochastic geometry and the theory of coding in the finite blocklength regime. The average coding rate and upper and lower bounds on the outage probability of the large-scale network are derived, and a tight approximation of the outage probability is presented. Then, simulations are presented to study the effect of network parameters on the average coding rate and the outage probability of the network, which demonstrate that results in the literature derived for the infinite blocklength regime overestimate the network performance, whereas the results in this paper provide a more realistic performance evaluation.", "field": "cs", "label": 1}
{"text": "Title: Flip colouring of graphs II\nAbstract: We give results concerning two problems on the recently introduced flip colourings of graphs, a new class of local v. global phenomena. We prove that for $(b, r)$-flip sequences with $4 \\leq b < r < b + 2 \\left\\lfloor\\frac{b+2}{6}\\right\\rfloor^2$, small constructions of $(b,r)$-flip graphs on $O(b+r)$ vertices are possible. Furthermore, we prove that there exists $k$-flip sequences $(a_1, \\dots, a_k)$ where $k > 4$, such that $a_k$ can be arbitrarily large whilst $a_i$ is constant for $1 \\leq i < \\frac{k}{4}$.", "field": "math", "label": 0}
{"text": "Title: Hessian of the Ricci Calabi functional\nAbstract: The Ricci Calabi functional is a functional on the space of K\\\"ahler metrics of Fano manifolds. Its critical points are called generalized K\\\"ahler Einstein metrics. In this article, we show that the Hessian of the Ricci Calabi functional is non-negative at generalized K\\\"ahler Einstein metrics. As its application, we give another proof of a Matsushima's type decomposition theorem for holomorphic vector fields, which was originally proved by Mabuchi. We also discuss a relation to the inverse Monge-Amp\\`ere flow developed recently by Collins-Hisamoto-Takahashi.", "field": "math", "label": 1}
{"text": "Title: Sphere-like isoparametric hypersurfaces in Damek-Ricci spaces\nAbstract: Locally harmonic manifolds are Riemannian manifolds in which small geodesic spheres are isoparametric hypersurfaces, i.e., hypersurfaces whose nearby parallel hypersurfaces are of constant mean curvature. Flat and rank one symmetric spaces are examples of harmonic manifolds. Damek-Ricci spaces are non-compact harmonic manifolds, most of which are non-symmetric. Taking the limit of an \"inflating\" sphere through a point $p$ in a Damek-Ricci space as the center of the sphere runs out to infinity along a geodesic half-line $\\gamma$ starting from $p$, we get a horosphere. Similarly to spheres, horospheres are also isoparametric hypersurfaces. In this paper, we define the sphere-like hypersurfaces obtained by \"overinflating the horospheres\" by pushing the center of the sphere beyond the point at infinity of $\\gamma$ along a virtual prolongation of $\\gamma$. They give a new family of isoparametric hypersurfaces in Damek-Ricci spaces connecting geodesic spheres to some of the isoparametric hypersurfaces constructed by J. C. D\\'iaz-Ramos and M. Dom\\'inguez-V\\'azquez [arXiv:1111.0264] in Damek-Ricci spaces. We study the geometric properties of these isoparametric hypersurfaces, in particular their homogeneity and the totally geodesic condition for their focal varieties.", "field": "math", "label": 0}
{"text": "Title: Simpler Specifications and Easier Proofs of Distributed Algorithms Using History Variables\nAbstract: This paper studies specifications and proofs of distributed algorithms when only message history variables are used, using the Basic Paxos and Multi-Paxos algorithms for distributed consensus as precise case studies. We show that not using and maintaining other state variables yields simpler specifications that are more declarative and easier to understand. It also allows easier proofs to be developed by needing fewer invariants and facilitating proof derivations. Furthermore, the proofs are mechanically checked more efficiently. We show that specifications in TLA+, Lamport's temporal logic of actions, and proofs in TLAPS, the TLA+ Proof System (TLAPS) are reduced by a quarter or more for single-value Paxos and by about half or more for multi-value Paxos. Overall we need about half as many manually written invariants and proof obligations. Our proof for Basic Paxos takes about 25% less time for TLAPS to check, and our proofs for Multi-Paxos are checked within 1.5 minutes whereas prior proofs fail to be checked by TLAPS.", "field": "cs", "label": 1}
{"text": "Title: A reciprocity relation for the twisted second moment of the Riemman Zeta function\nAbstract: We prove a reciprocity relation for the twisted second moment of the Riemann Zeta function. This provides an analogue to a formula of Conrey for Dirichlet L-functions", "field": "math", "label": 0}
{"text": "Title: Applications of machine learning and IoT for Outdoor Air Pollution Monitoring and Prediction: A Systematic Literature Review\nAbstract: According to the World Health Organization (WHO), air pollution kills seven million people every year. Outdoor air pollution is a major environmental health problem affecting low, middle, and high-income countries. In the past few years, the research community has explored IoT-enabled machine learning applications for outdoor air pollution prediction. The general objective of this paper is to systematically review applications of machine learning and Internet of Things (IoT) for outdoor air pollution prediction and the combination of monitoring sensors and input features used. Two research questions were formulated for this review. 1086 publications were collected in the initial PRISMA stage. After the screening and eligibility phases, 37 papers were selected for inclusion. A cost-based analysis was conducted on the findings to highlight high-cost monitoring, low-cost IoT and hybrid enabled prediction. Three methods of prediction were identified: time series, feature-based and spatio-temporal. This review's findings identify major limitations in applications found in the literature, namely lack of coverage, lack of diversity of data and lack of inclusion of context-specific features. This review proposes directions for future research and underlines practical implications in healthcare, urban planning, global synergy and smart cities.", "field": "cs", "label": 0}
{"text": "Title: Mobile ALOHA: Learning Bimanual Mobile Manipulation with Low-Cost Whole-Body Teleoperation\nAbstract: Imitation learning from human demonstrations has shown impressive performance in robotics. However, most results focus on table-top manipulation, lacking the mobility and dexterity necessary for generally useful tasks. In this work, we develop a system for imitating mobile manipulation tasks that are bimanual and require whole-body control. We first present Mobile ALOHA, a low-cost and whole-body teleoperation system for data collection. It augments the ALOHA system with a mobile base, and a whole-body teleoperation interface. Using data collected with Mobile ALOHA, we then perform supervised behavior cloning and find that co-training with existing static ALOHA datasets boosts performance on mobile manipulation tasks. With 50 demonstrations for each task, co-training can increase success rates by up to 90%, allowing Mobile ALOHA to autonomously complete complex mobile manipulation tasks such as sauteing and serving a piece of shrimp, opening a two-door wall cabinet to store heavy cooking pots, calling and entering an elevator, and lightly rinsing a used pan using a kitchen faucet. Project website: https://mobile-aloha.github.io", "field": "cs", "label": 0}
{"text": "Title: Cosemisimple Hopf algebras are faithfully flat over Hopf subalgebras\nAbstract: The question of whether or not a Hopf algebra $H$ is faithfully flat over a Hopf subalgebra $A$ has received positive answers in several particular cases: when $H$ (or more generally, just $A$) is commutative, or cocommutative, or pointed, or when $K$ contains the coradical of $H$. We prove the statement in the title, adding the class of cosemisimple Hopf algebras to those known to be faithfully flat over all Hopf subalgebras. We also show that the third term of the resulting \"exact sequence\" $A\\to H\\to C$ is always a cosemisimple coalgebra, and that the expectation $H\\to A$ is positive when $H$ is a CQG algebra.", "field": "math", "label": 1}
{"text": "Title: On friendship and cyclic parking functions\nAbstract: In parking problems, a given number of cars enter a one-way street sequentially, and try to park according to a specified preferred spot in the street. Various models are possible depending on the chosen rule for collisions, when two cars have the same preferred spot. In classical parking functions, if a car's preferred spot is already occupied by a previous car, it drives forward and looks for the first unoccupied spot to park. In this work, we introduce a variant of classical parking functions, called \"friendship parking functions\", which imposes additional restrictions on where cars can park. Namely, a car can only end up parking next to cars which are its friends (friendship will correspond to adjacency in an underlying graph). We characterise and enumerate such friendship parking functions according to their outcome permutation, which describes the final configuration when all cars have parked. We apply this to the case where the underlying friendship graph is the cycle graph. Finally, we consider a subset of classical parking functions, called \"cyclic parking functions\", where cars end up in an increasing cyclic order. We enumerate these cyclic parking functions and exhibit a bijection to permutation components.", "field": "math", "label": 0}
{"text": "Title: Towards Unsupervised Open World Semantic Segmentation\nAbstract: For the semantic segmentation of images, state-of-the-art deep neural networks (DNNs) achieve high segmentation accuracy if that task is restricted to a closed set of classes. However, as of now DNNs have limited ability to operate in an open world, where they are tasked to identify pixels belonging to unknown objects and eventually to learn novel classes, incrementally. Humans have the capability to say: I don't know what that is, but I've already seen something like that. Therefore, it is desirable to perform such an incremental learning task in an unsupervised fashion. We introduce a method where unknown objects are clustered based on visual similarity. Those clusters are utilized to define new classes and serve as training data for unsupervised incremental learning. More precisely, the connected components of a predicted semantic segmentation are assessed by a segmentation quality estimate. connected components with a low estimated prediction quality are candidates for a subsequent clustering. Additionally, the component-wise quality assessment allows for obtaining predicted segmentation masks for the image regions potentially containing unknown objects. The respective pixels of such masks are pseudo-labeled and afterwards used for re-training the DNN, i.e., without the use of ground truth generated by humans. In our experiments we demonstrate that, without access to ground truth and even with few data, a DNN's class space can be extended by a novel class, achieving considerable segmentation accuracy.", "field": "cs", "label": 1}
{"text": "Title: A dimension reduction approach for loss valuation in credit risk modelling\nAbstract: This paper addresses the ``curse of dimensionality'' in the loss valuation of credit risk models. A dimension reduction methodology based on the Bayesian filter and smoother is proposed. This methodology is designed to achieve a fast and accurate loss valuation algorithm in credit risk modelling, but it can also be extended to valuation models of other risk types. The proposed methodology is generic, robust and can easily be implemented. Moreover, the accuracy of the proposed methodology in the estimation of expected loss and value-at-risk is illustrated by numerical experiments. The results suggest that, compared to the currently most used PCA approach, the proposed methodology provides more accurate estimation of expected loss and value-at-risk of a loss distribution.", "field": "cs", "label": 0}
{"text": "Title: Machine Learning in Robotic Ultrasound Imaging: Challenges and Perspectives\nAbstract: This article reviews the recent advances in intelligent robotic ultrasound (US) imaging systems. We commence by presenting the commonly employed robotic mechanisms and control techniques in robotic US imaging, along with their clinical applications. Subsequently, we focus on the deployment of machine learning techniques in the development of robotic sonographers, emphasizing crucial developments aimed at enhancing the intelligence of these systems. The methods for achieving autonomous action reasoning are categorized into two sets of approaches: those relying on implicit environmental data interpretation and those using explicit interpretation. Throughout this exploration, we also discuss practical challenges, including those related to the scarcity of medical data, the need for a deeper understanding of the physical aspects involved, and effective data representation approaches. Moreover, we conclude by highlighting the open problems in the field and analyzing different possible perspectives on how the community could move forward in this research area.", "field": "cs", "label": 0}
{"text": "Title: Betting strategies with bounded splits\nAbstract: We show that a pair of Kolmogorov-Loveland betting strategies cannot win on every non-Martin-L\\\"of random sequence if either of the two following conditions is true: (I) There is an unbounded computable function $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\\ell$, bet on at most $\\ell-g(\\ell)$ positions among the first $\\ell$ positions of the sequence. (II) There is a sublinear function $g$ such that both betting strategies, when betting on an infinite binary sequence, almost surely, for almost all $\\ell$, bet on at least $\\ell-g(\\ell)$ positions among the first $\\ell$ positions of the sequence.", "field": "cs", "label": 1}
{"text": "Title: Nilpotent polynomials over $\\mathbb{Z}$\nAbstract: For a polynomial $u(x)$ in $\\mathbb{Z}[x]$ and $r\\in\\mathbb{Z}$, we consider the orbit of $u$ at $r$ denoted and defined by $\\mathcal{O}_u(r):=\\{u^{(n)}(r)~|~n\\in\\mathbb{N}\\}$. Here we study polynomials for which $0$ is in the orbit for a given $r$. We provide a complete classification of these polynomials when $|r|\\le 4$, with $|r|\\le 1$ already done in \\cite{SS23}. The central goal of this paper is to study the following questions: (i) relationship between the integers $r$ and $m$, for a polynomial $u$ in $N_{r,m}$; (ii) classification of the polynomials with nilpotency index $|r|$ for large enough $|r|$; and (iii) integer sequences with a generating polynomial.", "field": "math", "label": 0}
{"text": "Title: Fading memory as inductive bias in residual recurrent networks\nAbstract: Residual connections have been proposed as an architecture-based inductive bias to mitigate the problem of exploding and vanishing gradients and increased task performance in both feed-forward and recurrent networks (RNNs) when trained with the backpropagation algorithm. Yet, little is known about how residual connections in RNNs influence their dynamics and fading memory properties. Here, we introduce weakly coupled residual recurrent networks (WCRNNs) in which residual connections result in well-defined Lyapunov exponents and allow for studying properties of fading memory. We investigate how the residual connections of WCRNNs influence their performance, network dynamics, and memory properties on a set of benchmark tasks. We show that several distinct forms of residual connections yield effective inductive biases that result in increased network expressivity. In particular, those are residual connections that (i) result in network dynamics at the proximity of the edge of chaos, (ii) allow networks to capitalize on characteristic spectral properties of the data, and (iii) result in heterogeneous memory properties. In addition, we demonstrate how our results can be extended to non-linear residuals and introduce a weakly coupled residual initialization scheme that can be used for Elman RNNs.", "field": "cs", "label": 0}
{"text": "Title: Minimizing The Maximum Distance Traveled To Form Patterns With Systems of Mobile Robots\nAbstract: In the pattern formation problem, robots in a system must self-coordinate to form a given pattern, regardless of translation, rotation, uniform-scaling, and/or reflection. In other words, a valid final configuration of the system is a formation that is \\textit{similar} to the desired pattern. While there has been no shortage of research in the pattern formation problem under a variety of assumptions, models, and contexts, we consider the additional constraint that the maximum distance traveled among all robots in the system is minimum. Existing work in pattern formation and closely related problems are typically application-specific or not concerned with optimality (but rather feasibility). We show the necessary conditions any optimal solution must satisfy and present a solution for systems of three robots. Our work also led to an interesting result that has applications beyond pattern formation. Namely, a metric for comparing two triangles where a distance of $0$ indicates the triangles are similar, and $1$ indicates they are \\emph{fully dissimilar}.", "field": "cs", "label": 1}
{"text": "Title: Phototactic bioconvection in an algal suspension with a free top wall due to diffuse flux in the absence of direct collimated flux\nAbstract: In this article, the effect of diffuse flux in the absence of direct collimated flux on the onset of phototactic bioconvection is investigated. The main effect of diffuse flux in the absence of collimated flux is on the swimming behaviour of microorganisms in the suspension. At higher diffuse flux, the horizontal component of swimming orientation exhibits a higher magnitude, which slows the rate of pattern formation in the suspension. Also, the linear stability of the suspension predicts that the most unstable mode of disturbance transits from stationary (oscillatory) to oscillatory (stationary) at the variation in the magnitude of diffuse flux for some fixed parameters. The overstable nature of disturbance is mostly observed at the high value of swimming speed and extinction coefficient. Moreover, the suspension shows a more stable behaviour at the higher magnitude of diffuse flux.", "field": "math", "label": 0}
{"text": "Title: Whittaker modules and hyperbolic Toda lattices\nAbstract: Let $\\sg$ be a complex finite-dimensional simple Lie algebra and let $\\sg_l$ be the corresponding generalized Takiff algebra. This paper studies the affine variety $\\ssf+\\sb_l$ where $\\ssf$ is similar to a principal nilpotent element of $\\sg$ and $\\sb_l$ is a subalgebra corresponding to the Borel subalgebra $\\sb$ of $\\sg$. Inspired by Kostant's work then we deal with two questions. One of them is to construct the Whittaker model for the $G_l$-invariants of symmetric algebra $S(\\sg_l)$ where $G_l$ is the adjoint group of $\\sg_l$ and $G_l$ acts on $S(\\sg_l)$ by coadjoint action, and then to classify all nonsingular Whittaker modules over $\\sg_l$. Another one is to describe the symplectic structure of the manifold $Z\\subseteq\\ssf+\\sb_l$ of normalized Jacobi elements. Then the Hamiltonian corresponding to a fundamental invariant provides a class of hyperbolic Toda lattices. In particular, a simplest example describes the state of a dynamical system consisting of a positive mass particle and a negative mass particle.", "field": "math", "label": 0}
{"text": "Title: On Memorization and Privacy Risks of Sharpness Aware Minimization\nAbstract: In many recent works, there is an increased focus on designing algorithms that seek flatter optima for neural network loss optimization as there is empirical evidence that it leads to better generalization performance in many datasets. In this work, we dissect these performance gains through the lens of data memorization in overparameterized models. We define a new metric that helps us identify which data points specifically do algorithms seeking flatter optima do better when compared to vanilla SGD. We find that the generalization gains achieved by Sharpness Aware Minimization (SAM) are particularly pronounced for atypical data points, which necessitate memorization. This insight helps us unearth higher privacy risks associated with SAM, which we verify through exhaustive empirical evaluations. Finally, we propose mitigation strategies to achieve a more desirable accuracy vs privacy tradeoff.", "field": "cs", "label": 0}
{"text": "Title: A leaf as a convex domain containing eigenvalues of a linear transformation on a real inner product space\nAbstract: We define a leaf which is a domain in the closure $\\overline{\\mathfrak{H}}=\\mathfrak{H}\\cup\\mathbb{R}\\cup\\{\\infty\\}$ of the complex upper half plane $\\mathfrak{H} = \\{z\\in\\mathbb{C}\\mid{\\mathrm{Im}\\,} z>0\\}$ for any linear transformation of an inner product space over the real number field $\\mathbb{R}$. If the dimension of the inner product space is at least 3, the leaf is convex on the Poincar\\'e metric, and then simply connected, and contains all eigenvalues with nonnegative imaginary part. Moreover, if the linear transformation is normal, the leaf is the eigenvalue geodesic polygon, which is the minimum convex domain in $\\overline{\\mathfrak{H}}$ containing all eigenvalues with nonnegative imaginary part. We discuss the application of the geometric properties of a leaf to the operator norm.", "field": "math", "label": 0}
{"text": "Title: Federated Calibration and Evaluation of Binary Classifiers\nAbstract: We address two major obstacles to practical use of supervised classifiers on distributed private data. Whether a classifier was trained by a federation of cooperating clients or trained centrally out of distribution, (1) the output scores must be calibrated, and (2) performance metrics must be evaluated -- all without assembling labels in one place. In particular, we show how to perform calibration and compute precision, recall, accuracy and ROC-AUC in the federated setting under three privacy models (i) secure aggregation, (ii) distributed differential privacy, (iii) local differential privacy. Our theorems and experiments clarify tradeoffs between privacy, accuracy, and data efficiency. They also help decide whether a given application has sufficient data to support federated calibration and evaluation.", "field": "cs", "label": 1}
{"text": "Title: Some remarks on infinitesimals in MV-algebras\nAbstract: Replacing $\\{0\\}$ by the whole ideal of infinitesimals yields a weaker notion of \\emph{archimedean element} that we call \\emph{quasiarchimedean}. It is known that semisimple MV-algebras with compact maximal spectrum (in the co-Zarisky topology) are exactly the hyperarchimedean algebras. We characterise all the algebras with compact maximal spectrum as being \\emph{quasihyperarchimedean} \\mbox{MV-algebras,} which in a sense are non semisimple hyperarchimedean algebras. We develop some basic facts in the theory of MV-algebras along the lines of algebraic geometry, where infinitesimals play the role of nilpotent elements, and prove a MV-algebra version of Hilbert's Nullstellensatz. Finally we consider the relations (some inedited) between several elementary classes of MV-algebras in terms of the ideals that characterise them, and present elementary (first order with denumerable disjunctions) proofs in place of the \\mbox{set-theoretical} usually found in the literature.", "field": "math", "label": 1}
{"text": "Title: Towards Safe and Collaborative Robotic Ultrasound Tissue Scanning in Neurosurgery\nAbstract: Intraoperative ultrasound imaging is used to facilitate safe brain tumour resection. However, due to challenges with image interpretation and the physical scanning, this tool has yet to achieve widespread adoption in neurosurgery. In this paper, we introduce the components and workflow of a novel, versatile robotic platform for intraoperative ultrasound tissue scanning in neurosurgery. An RGB-D camera attached to the robotic arm allows for automatic object localisation with ArUco markers, and 3D surface reconstruction as a triangular mesh using the ImFusion Suite software solution. Impedance controlled guidance of the US probe along arbitrary surfaces, represented as a mesh, enables collaborative US scanning, i.e., autonomous, teleoperated and hands-on guided data acquisition. A preliminary experiment evaluates the suitability of the conceptual workflow and system components for probe landing on a custom-made soft-tissue phantom. Further assessment in future experiments will be necessary to prove the effectiveness of the presented platform.", "field": "cs", "label": 0}
{"text": "Title: Abacus models for parabolic quotients of affine Weyl groups\nAbstract: We introduce abacus diagrams that describe minimal length coset representatives in affine Weyl groups of types B, C, and D. These abacus diagrams use a realization of the affine Weyl group of type C due to Eriksson to generalize a construction of James for the symmetric group. We also describe several combinatorial models for these parabolic quotients that generalize classical results in affine type A related to core partitions.", "field": "math", "label": 1}
{"text": "Title: Eulerian 2-Complexes\nAbstract: It is shown that Euler's theorem for graphs can be generalized for 2-complexes. Two notions that generalize cycle and Eulerian tour are introduced (``circlet'' and ``Eulerian cover''), and we show that for a strongly-connected, pure 2-complex, the following are equivalent: (i) each edge meets a positive even number of 2-cells (faces), (ii) the complex can be decomposed as the face-disjoint union of circlets, and (iii) the complex has an Eulerian cover. A number of examples are provided.", "field": "math", "label": 0}
{"text": "Title: Unified Descriptive Intensional Logic\nAbstract: UDIL (unified descriptive intensional logic) aims to be an alternative and improved version of Bealer's logic fulfilling the goal of unifying Bealer's systems T1 and T2 together with adding features to deal with definite descriptions and singular terms and their related philosophical problems (there are interesting connections to Zalta's more restricted parallel second-order version in his book \\emph{Axiomatic Metaphysics}). UDIL also allows a much shorter and transparent proof of soundness, in particular with regards to a notoriously difficult preliminary lemma. UDIL stands out as being both formally and philosophically distinct from mainstream approaches to intensionality. One motivation for UDIL is to contribute to the Leibnizean goal of a formal philosophy, that is, a philosophy in which arguments and proofs are carried out entirely within a formal system.", "field": "math", "label": 0}
{"text": "Title: The singular limit of the Water-Waves equations in the rigid lid regime\nAbstract: The re-scaled Water-Waves equations depend strongly on the ratio epsilon between the amplitude of the wave and the depth of the water. We investigate in this paper the convergence as epsilon goes to zero of the free surface Euler equations to the so called rigid lid model. We first prove that the only solutions of this model are zero. Due to the conservation of the Hamiltonian, the solutions of the free surface Euler equations converge weakly to zero, but not strongly in the general case, as epsilon goes to zero. We then study this default of convergence. More precisely, we show a strong convergence result of the solutions of the water waves equations in the Zakharov-Craig-Sulem formulation to the solutions of the linear water-waves equations. It is then easy to observe that these latter converge weakly to zero. The simple structure of this system also allows us to explain the mechanisms of the weak convergence to zero. Finally, we show that this convergence to the rigid lid model also holds for the solutions of the Euler equations. To this end we give a new proof of the equivalence of the free surface Euler equations and of the Zakharov-Craig-Sulem equation by building an extension of the velocity and pressure fields.", "field": "math", "label": 1}
{"text": "Title: Quota Trees\nAbstract: We introduce the notion of quota trees in directed graphs. Given a nonnegative integer ``quota'' for each vertex of a directed multigraph $G$, a quota tree is an immersed rooted tree which hits each vertex of $G$ the prescribed number of times. When the quotas are all one, the tree is actually embedded and we recover the usual notion of a spanning arborescence (directed spanning tree). The usual algorithms which produce spanning arborescences with various properties typically have (sometimes more complicated) ``quota'' analogues. Our original motivation for studying quota trees was the problem of characterizing the sizes of the Myhill-Nerode equivalence classes in a connected deterministic finite-state automaton recognizing a given regular language. We show that the obstruction to realizing a given set of M-N class sizes is precisely the existence of a suitable quota tree. In this paper we develop the basic theory of quota trees. We give necessary and sufficient conditions for the existence of a quota tree (or forest) over a given directed graph with specified quotas, solving the M-N class size problem as a special case. We discuss some potential applications of quota trees and forests, and connect them to the $k$ lightest paths problem. We give two proofs of the main theorem: one based on an algorithmic loop invariant, and one based on direct enumeration of quota trees. For the latter, we use Lagrange inversion to derive a formula which vastly generalizes both the matrix-tree theorem and Cayley's formula for counting labeled trees. We give an efficient algorithm to sample uniformly from the set of forests with given quotas, as well as a generalization of Edmonds' algorithm for computing a minimum-weight quota forest.", "field": "math", "label": 0}
{"text": "Title: Method for Solving State-Path Constrained Optimal Control Problems Using Adaptive Radau Collocation\nAbstract: A new method is developed for accurately approximating the solution to state-variable inequality path constrained optimal control problems using a multiple-domain adaptive Legendre-Gauss-Radau collocation method. The method consists of the following parts. First, a structure detection method is developed to estimate switch times in the activation and deactivation of state-variable inequality path constraints. Second, using the detected structure, the domain is partitioned into multiple-domains where each domain corresponds to either a constrained or an unconstrained segment. Furthermore, additional decision variables are introduced in the multiple-domain formulation, where these additional decision variables represent the switch times of the detected active state-variable inequality path constraints. Within a constrained domain, the path constraint is differentiated with respect to the independent variable until the control appears explicitly, and this derivative is set to zero along the constrained arc while all preceding derivatives are set to zero at the start of the constrained arc. The time derivatives of the active state-variable inequality path constraints are computed using automatic differentiation and the properties of the chain rule. The method is demonstrated on two problems, the first being a benchmark optimal control problem which has a known analytical solution and the second being a challenging problem from the field of aerospace engineering in which there is no known analytical solution. When compared against previously developed adaptive Legendre-Gauss-Radau methods, the results show that the method developed in this paper is capable of computing accurate solutions to problems whose solution contain active state-variable inequality path constraints.", "field": "math", "label": 0}
{"text": "Title: Disjointness for measurably distal group actions and applications\nAbstract: We generalize Berg's notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure preserving system. As a corollary we obtain easy to check necessary and sufficient conditions for two systems to be disjoint, provided one of them is measurably distal. We also obtain a Wiener--Wintner type theorem for countable amenable groups with distal weights and applications to weighted multiple ergodic averages and multiple recurrence.", "field": "math", "label": 1}
{"text": "Title: Sobolev spaces on hypergroups Gelfand pairs\nAbstract: This paper introduces Sobolev spaces over Gelfand pairs in the framework of hypergroups. The Sobolev spaces in question are constructed from the Fourier transform on hypergroup Gelfand pairs. Mainly, the paper focuses on the investigation of Sobolev embedding results.", "field": "math", "label": 0}
{"text": "Title: From Language to Programs: Bridging Reinforcement Learning and Maximum Marginal Likelihood\nAbstract: Our goal is to learn a semantic parser that maps natural language utterances into executable programs when only indirect supervision is available: examples are labeled with the correct execution result, but not the program itself. Consequently, we must search the space of programs for those that output the correct result, while not being misled by spurious programs: incorrect programs that coincidentally output the correct result. We connect two common learning paradigms, reinforcement learning (RL) and maximum marginal likelihood (MML), and then present a new learning algorithm that combines the strengths of both. The new algorithm guards against spurious programs by combining the systematic search traditionally employed in MML with the randomized exploration of RL, and by updating parameters such that probability is spread more evenly across consistent programs. We apply our learning algorithm to a new neural semantic parser and show significant gains over existing state-of-the-art results on a recent context-dependent semantic parsing task.", "field": "cs", "label": 1}
{"text": "Title: Cyclic codes from low differentially uniform functions\nAbstract: Cyclic codes have many applications in consumer electronics, communication and data storage systems due to their efficient encoding and decoding algorithms. An efficient approach to constructing cyclic codes is the sequence approach. In their articles [Discrete Math. 321, 2014] and [SIAM J. Discrete Math. 27(4), 2013], Ding and Zhou constructed several classes of cyclic codes from almost perfect nonlinear (APN) functions and planar functions over finite fields and presented some open problems on cyclic codes from highly nonlinear functions. This article focuses on these exciting works by investigating new insights in this research direction. Specifically, its objective is twofold. The first is to provide a complement with some former results and present correct proofs and statements on some known ones on the cyclic codes from the APN functions. The second is studying the cyclic codes from some known functions processing low differential uniformity. Along with this article, we shall provide answers to some open problems presented in the literature. The first one concerns Open Problem 1, proposed by Ding and Zhou in Discrete Math. 321, 2014. The two others are Open Problems 5.16 and 5.25, raised by Ding in [SIAM J. Discrete Math. 27(4), 2013].", "field": "cs", "label": 1}
{"text": "Title: Strongly minimal Steiner Systems III: Path graphs and sparse configurations\nAbstract: We introduce a uniform method of proof for the following results. For {\\em each} of the following conditions, there are $2^{\\aleph_0}$ families of Steiner systems, satisfying that condition: i) Theorem~2.2.4: (extending \\cite{Chicoetal}) each Steiner triple system is $\\infty$-sparse and has a uniform but not perfect path graph; ii) (Theorem~5.4.2: (extending \\cite{CameronWebb}) each Steiner $k$-system (for $k=p^n$) is $2$-transitive and has a uniform path graph (infinite cycles only); iii) Theorem~2.1.5: (extending \\cite{Fujiwaramitre}, each is anti-Pasch (anti-mitre); iv) Theorem~3.6 has an explicit quasi-group structure. In each case all members of the family satisfy the same complete strongly minimal theory and it has $\\aleph_0$ countable models and one model of each uncountable cardinal.", "field": "math", "label": 1}
{"text": "Title: Pixel personality for dense object tracking in a 2D honeybee hive\nAbstract: Tracking large numbers of densely-arranged, interacting objects is challenging due to occlusions and the resulting complexity of possible trajectory combinations, as well as the sparsity of relevant, labeled datasets. Here we describe a novel technique of collective tracking in the model environment of a 2D honeybee hive in which sample colonies consist of $N\\sim10^3$ highly similar individuals, tightly packed, and in rapid, irregular motion. Such a system offers universal challenges for multi-object tracking, while being conveniently accessible for image recording. We first apply an accurate, segmentation-based object detection method to build initial short trajectory segments by matching object configurations based on class, position and orientation. We then join these tracks into full single object trajectories by creating an object recognition model which is adaptively trained to recognize honeybee individuals through their visual appearance across multiple frames, an attribute we denote as pixel personality. Overall, we reconstruct ~46% of the trajectories in 5 min recordings from two different hives and over 71% of the tracks for at least 2 min. We provide validated trajectories spanning 3000 video frames of 876 unmarked moving bees in two distinct colonies in different locations and filmed with different pixel resolutions, which we expect to be useful in the further development of general-purpose tracking solutions.", "field": "cs", "label": 1}
{"text": "Title: UpFusion: Novel View Diffusion from Unposed Sparse View Observations\nAbstract: We propose UpFusion, a system that can perform novel view synthesis and infer 3D representations for an object given a sparse set of reference images without corresponding pose information. Current sparse-view 3D inference methods typically rely on camera poses to geometrically aggregate information from input views, but are not robust in-the-wild when such information is unavailable/inaccurate. In contrast, UpFusion sidesteps this requirement by learning to implicitly leverage the available images as context in a conditional generative model for synthesizing novel views. We incorporate two complementary forms of conditioning into diffusion models for leveraging the input views: a) via inferring query-view aligned features using a scene-level transformer, b) via intermediate attentional layers that can directly observe the input image tokens. We show that this mechanism allows generating high-fidelity novel views while improving the synthesis quality given additional (unposed) images. We evaluate our approach on the Co3Dv2 and Google Scanned Objects datasets and demonstrate the benefits of our method over pose-reliant sparse-view methods as well as single-view methods that cannot leverage additional views. Finally, we also show that our learned model can generalize beyond the training categories and even allow reconstruction from self-captured images of generic objects in-the-wild.", "field": "cs", "label": 0}
{"text": "Title: Tailor: Size Recommendations for High-End Fashion Marketplaces\nAbstract: In the ever-changing and dynamic realm of high-end fashion marketplaces, providing accurate and personalized size recommendations has become a critical aspect. Meeting customer expectations in this regard is not only crucial for ensuring their satisfaction but also plays a pivotal role in driving customer retention, which is a key metric for the success of any fashion retailer. We propose a novel sequence classification approach to address this problem, integrating implicit (Add2Bag) and explicit (ReturnReason) user signals. Our approach comprises two distinct models: one employs LSTMs to encode the user signals, while the other leverages an Attention mechanism. Our best model outperforms SFNet, improving accuracy by 45.7%. By using Add2Bag interactions we increase the user coverage by 24.5% when compared with only using Orders. Moreover, we evaluate the models' usability in real-time recommendation scenarios by conducting experiments to measure their latency performance.", "field": "cs", "label": 0}
{"text": "Title: Parsing using a grammar of word association vectors\nAbstract: This paper was was first drafted in 2001 as a formalization of the system described in U.S. patent U.S. 7,392,174. It describes a system for implementing a parser based on a kind of cross-product over vectors of contextually similar words. It is being published now in response to nascent interest in vector combination models of syntax and semantics. The method used aggressive substitution of contextually similar words and word groups to enable product vectors to stay in the same space as their operands and make entire sentences comparable syntactically, and potentially semantically. The vectors generated had sufficient representational strength to generate parse trees at least comparable with contemporary symbolic parsers.", "field": "cs", "label": 1}
{"text": "Title: Functional Inequalities for Brownian Motion on Riemannian Manifolds with Sticky-Reflecting Boundary Diffusion\nAbstract: We prove geometric upper bounds for the Poincar\\'e and Logarithmic Sobolev constants for Brownian motion on manifolds with sticky reflecting boundary diffusion i.e. extended Wentzell-type boundary condition under general curvature assumptions on the manifold and its boundary. The method is based on an interpolation involving energy interactions between the boundary and the interior of the manifold. As side results we obtain explicit geometric bounds on the first nontrivial Steklov eigenvalue, for the norm of the boundary trace operator on Sobolev functions, and on the boundary trace logarithmic Sobolev constant. The case of Brownian motion with pure sticky reflection is also treated.", "field": "math", "label": 0}
{"text": "Title: More on homotopy continuation method and discounted zero-sum stochastic game with ARAT structure\nAbstract: In this paper, we introduce a homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of two-person zero-sum discounted stochastic ARAT game. We show that the algorithm has the higher order of convergence. For the proposed algorithm, the homotopy path approaching the solution is smooth and bounded. Two numerical examples are illustrated to show the effectiveness of the proposed algorithm.", "field": "math", "label": 1}
{"text": "Title: The cube axiom and resolutions in homotopy theory\nAbstract: We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model structure. As an application, classical theorems in unstable homotopy theory are extended to this context.", "field": "math", "label": 1}
{"text": "Title: Learned Image Downscaling for Upscaling using Content Adaptive Resampler\nAbstract: Deep convolutional neural network based image super-resolution (SR) models have shown superior performance in recovering the underlying high resolution (HR) images from low resolution (LR) images obtained from the predefined downscaling methods. In this paper we propose a learned image downscaling method based on content adaptive resampler (CAR) with consideration on the upscaling process. The proposed resampler network generates content adaptive image resampling kernels that are applied to the original HR input to generate pixels on the downscaled image. Moreover, a differentiable upscaling (SR) module is employed to upscale the LR result into its underlying HR counterpart. By back-propagating the reconstruction error down to the original HR input across the entire framework to adjust model parameters, the proposed framework achieves a new state-of-the-art SR performance through upscaling guided image resamplers which adaptively preserve detailed information that is essential to the upscaling. Experimental results indicate that the quality of the generated LR image is comparable to that of the traditional interpolation based method, but the significant SR performance gain is achieved by deep SR models trained jointly with the CAR model. The code is publicly available on: URL https://github.com/sunwj/CAR.", "field": "cs", "label": 1}
{"text": "Title: Spiking NeRF: Representing the Real-World Geometry by a Discontinuous Representation\nAbstract: A crucial reason for the success of existing NeRF-based methods is to build a neural density field for the geometry representation via multiple perceptron layers (MLPs). MLPs are continuous functions, however, real geometry or density field is frequently discontinuous at the interface between the air and the surface. Such a contrary brings the problem of unfaithful geometry representation. To this end, this paper proposes spiking NeRF, which leverages spiking neurons and a hybrid Artificial Neural Network (ANN)-Spiking Neural Network (SNN) framework to build a discontinuous density field for faithful geometry representation. Specifically, we first demonstrate the reason why continuous density fields will bring inaccuracy. Then, we propose to use the spiking neurons to build a discontinuous density field. We conduct a comprehensive analysis for the problem of existing spiking neuron models and then provide the numerical relationship between the parameter of the spiking neuron and the theoretical accuracy of geometry. Based on this, we propose a bounded spiking neuron to build the discontinuous density field. Our method achieves SOTA performance. The source code and the supplementary material are available at https://github.com/liaozhanfeng/Spiking-NeRF.", "field": "cs", "label": 0}
{"text": "Title: Pursuing the double affine Grassmannian III: Convolution with affine Zastava\nAbstract: This is the third paper of a series (started by arXiv:0711.2083, arXiv:0908.3390) which describes a conjectural analog of the affine Grassmannian for affine Kac-Moody groups (also known as the double affine Grassmannian). The current paper is dedicated to describing a conjectural analog of the convolution diagram for the double affine Grassmannian and affine Zastava.", "field": "math", "label": 1}
{"text": "Title: Free unitary groups are (almost) simple\nAbstract: We show that the quotients of Wang and Van Daele's universal quantum groups by their centers are simple in the sense that they have no normal quantum subgroups, thus providing the first examples of simple compact quantum groups with non-commutative fusion rings.", "field": "math", "label": 1}
{"text": "Title: Capacity Bounds and User Identification Costs in Rayleigh-Fading Many-Access Channel\nAbstract: Many-access channel (MnAC) model allows the number of users in the system and the number of active users to scale as a function of the blocklength and as such is suited for dynamic communication systems with massive number of users such as the Internet of Things. Existing MnAC models assume a priori knowledge of channel gains which is impractical since acquiring Channel State Information (CSI) for massive number of users can overwhelm the available radio resources. This paper incorporates Rayleigh fading effects to the MnAC model and derives an upper bound on the symmetric message-length capacity of the Rayleigh-fading Gaussian MnAC. Furthermore, a lower bound on the minimum number of channel uses for discovering the active users is established. In addition, the performance of Noisy Combinatorial Orthogonal Matching Pursuit (N-COMP) based group testing (GT) is studied as a practical strategy for active device discovery. Simulations show that, for a given SNR, as the number of users increase, the required number of channel uses for N-COMP GT scales approximately the same way as the lower bound on minimum user identification cost. Moreover, in the low SNR regime, for sufficiently large population sizes, the number of channel uses required by N-COMP GT was observed to be within a factor of two of the lower bound when the expected number of active users scales sub-linearly with the total population size.", "field": "cs", "label": 1}
{"text": "Title: Model theory and the Tannakian formalism\nAbstract: We draw the connection between the model theoretic notions of internality and the binding group on one hand, and the Tannakian formalism on the other. More precisely, we deduce the fundamental results of the Tannakian formalism by associating to a Tannakian category a first order theory, and applying the results on internality there. We also formulate the notion of a differential tensor category, and a version of the Tannakian formalism for differential linear groups, and show how the same techniques can be used to deduce the analogous results in that context.", "field": "math", "label": 1}
{"text": "Title: Sampling unknown large networks restricted by low sampling rates\nAbstract: Graph sampling plays an important role in data mining for large networks. Specifically, larger networks often correspond to lower sampling rates. Under the situation, traditional traversal-based samplings for large networks usually have an excessive preference for densely-connected network core nodes. Aim at this issue, this paper proposes a sampling method for unknown networks at low sampling rates, called SLSR, which first adopts a random node sampling to evaluate a degree threshold, utilized to distinguish the core from periphery, and the average degree in unknown networks, and then runs a double-layer sampling strategy on the core and periphery. SLSR is simple that results in a high time efficiency, but experimental evaluation confirms that the proposed method can accurately preserve many critical structures of unknown large networks with low sampling rates and low variances.", "field": "cs", "label": 0}
{"text": "Title: Global topology of the Hitchin system\nAbstract: Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic mixture of ideas originating in theoretical physics such as gauge theory and mirror symmetry, Weil conjectures in arithmetic algebraic geometry, representation theory of finite groups of Lie type and Langlands duality in number theory.", "field": "math", "label": 1}
{"text": "Title: Every closed surface of genus at least $17$ is Loewner\nAbstract: In this paper, we obtain an improved upper bound involving the systole and area for the volume entropy of a Riemannian surface. As a result, we show that every orientable and closed Riemannian surface of genus $g\\geq 17$ satisfies Loewner's systolic ratio inequality.", "field": "math", "label": 0}
{"text": "Title: Optimal transport for types and convex analysis for definable predicates in tracial $\\mathrm{W}^*$-algebras\nAbstract: We investigate the connections between continuous model theory, free probability, and optimal transport/convex analysis in the context of tracial von Neumann algebras. In particular, we give an analog of Monge-Kantorovich duality for optimal couplings where the role of probability distributions on $\\mathbb{C}^n$ is played by model-theoretic types, the role of real-valued continuous functions is played by definable predicates, and the role of continuous function $\\mathbb{C}^n \\to \\mathbb{C}^n$ is played by definable functions. In the process, we also advance the understanding of definable predicates and definable functions by showing that all definable predicates can be approximated by \"$C^1$ definable predicates\" whose gradients are definable functions. As a consequence, we show that every element in the definable closure of $\\mathrm{W}^*(x_1,\\dots,x_n)$ can be expressed as a definable function of $(x_1,\\dots,x_n)$. We give several classes of examples showing that the definable closure can be much larger than $\\mathrm{W}^*(x_1,\\dots,x_n)$ in general.", "field": "math", "label": 0}
{"text": "Title: Consistent estimation of non-bandlimited spectral density from uniformly spaced samples\nAbstract: In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular (uniform) sampling. A major reason for this preference is the well-known problem of inconsistency of estimators based on regular sampling, when the underlying power spectral density is not bandlimited. It is argued in this paper that, in consideration of a large sample property like consistency, it is natural to allow the sampling rate to go to infinity as the sample size goes to infinity. Through appropriate asymptotic calculations under this scenario, it is shown that the smoothed periodogram based on regularly spaced data is a consistent estimator of the spectral density, even when the latter is not band-limited. It transpires that, under similar assumptions, the estimators based on uniformly sampled and Poisson-sampled data have about the same rate of convergence. Apart from providing this reassuring message, the paper also gives a guideline for practitioners regarding appropriate choice of the sampling rate. Theoretical calculations for large samples and Monte-Carlo simulations for small samples indicate that the smoothed periodogram based on uniformly sampled data have less variance and more bias than its counterpart based on Poisson sampled data.", "field": "math", "label": 1}
{"text": "Title: A Universal Lipschitz Extension Property of Gromov Hyperbolic Spaces\nAbstract: A metric space has the universal Lipschitz extension property if for each subspace S embedded quasi-isometrically into an arbitrary metric space M there exists a continuous linear extension of Banach-valued Lipschitz functions on S to those on all of M. We show that the finite direct sum of Gromov hyperbolic spaces of bounded geometry is universal in the sense of this definition.", "field": "math", "label": 1}
{"text": "Title: A Generative AI Assistant to Accelerate Cloud Migration\nAbstract: We present a tool that leverages generative AI to accelerate the migration of on-premises applications to the cloud. The Cloud Migration LLM accepts input from the user specifying the parameters of their migration, and outputs a migration strategy with an architecture diagram. A user study suggests that the migration LLM can assist inexperienced users in finding the right cloud migration profile, while avoiding complexities of a manual approach.", "field": "cs", "label": 0}
{"text": "Title: Extreme statistics of non-intersecting Brownian paths\nAbstract: We consider finite collections of $N$ non-intersecting Brownian paths on the line and on the half-line with both absorbing and reflecting boundary conditions (corresponding to Brownian excursions and reflected Brownian motions) and compute in each case the joint distribution of the maximal height of the top path and the location at which this maximum is attained. The resulting formulas are analogous to the ones obtained in [MFQR13] for the joint distribution of $\\mathcal{M}={\\rm max}_{x\\in\\mathbb{R}}\\{\\mathcal{A}_2(x)-x^2\\}$ and $\\mathcal{T}={\\rm argmax}_{x\\in\\mathbb{R}}\\{\\mathcal{A}_2(x)-x^2\\}$, where $\\mathcal{A}_2$ is the Airy$_2$ process, and we use them to show that in the three cases the joint distribution converges, as $N\\to\\infty$, to the joint distribution of $\\mathcal{M}$ and $\\mathcal{T}$. In the case of non-intersecting Brownian bridges on the line, we also establish small deviation inequalities for the argmax which match the tail behavior of $\\mathcal{T}$. Our proofs are based on the method introduced in [CQR13,BCR15] for obtaining formulas for the probability that the top line of these line ensembles stays below a given curve, which are given in terms of the Fredholm determinant of certain \"path-integral\" kernels.", "field": "math", "label": 1}
{"text": "Title: Representing maps for semibounded forms and their Lebesgue type decompositions\nAbstract: For a semibounded sesquilinear form ${\\mathfrak t}$ in a Hilbert space ${\\mathfrak H}$ there exists a representing map $Q$ from ${\\mathfrak H}$ to another Hilbert space ${\\mathfrak K}$, such that ${\\mathfrak t}[\\varphi, \\psi]-c(\\varphi, \\psi)=(Q\\varphi,Q\\psi)$, $\\varphi,\\psi \\in {\\rm dom\\,}{\\mathfrak t}$, with $c \\in {\\mathbb R}$ a lower bound of ${\\mathfrak t}$. Representing maps offer a simplifying tool to study general semibounded forms. By means of representing maps closedness, closability, and singularity of ${\\mathfrak t}$ are immediately translated into the corresponding properties of the operator $Q$, and vice versa. Also properties of sum decompositions ${\\mathfrak t}={\\mathfrak t}_1+{\\mathfrak t}_2$ of a nonnegative form ${\\mathfrak t}$ with two other nonnegative forms ${\\mathfrak t}_1$ and ${\\mathfrak t}_2$ in ${\\mathfrak H}$ can be analyzed by means of associated nonnegative contractions $K\\in {\\mathbf B}({\\mathfrak K})$. This helps, for instance, to establish an explicit operator theoretic characterization for the summands ${\\mathfrak t}_1$ and ${\\mathfrak t}_2$ to be, or not to be, mutually singular. Such sum decompositions are used to study characteristic properties of the so-called Lebesgue type decompositions of semibounded forms ${\\mathfrak t}$, where ${\\mathfrak t}_1$ is closable and ${\\mathfrak t}_2$ singular; in particular, this includes the Lebesgue decomposition of a semibounded form due to B. Simon. Furthermore, for a semibounded form ${\\mathfrak t}$ with its representing map $Q$ it will be shown that the corresponding semibounded selfadjoint relation $Q^*Q^{**} +c$ is uniquely determined by a limit version of the classical representation theorem for the form ${\\mathfrak t}$, being studied by W. Arendt and T. ter Elst in a sectorial context. Via representing maps a full treatment is given of the convergence of monotone sequences of semibounded forms.", "field": "math", "label": 0}
{"text": "Title: L3Cube-IndicNews: News-based Short Text and Long Document Classification Datasets in Indic Languages\nAbstract: In this work, we introduce L3Cube-IndicNews, a multilingual text classification corpus aimed at curating a high-quality dataset for Indian regional languages, with a specific focus on news headlines and articles. We have centered our work on 10 prominent Indic languages, including Hindi, Bengali, Marathi, Telugu, Tamil, Gujarati, Kannada, Odia, Malayalam, and Punjabi. Each of these news datasets comprises 10 or more classes of news articles. L3Cube-IndicNews offers 3 distinct datasets tailored to handle different document lengths that are classified as: Short Headlines Classification (SHC) dataset containing the news headline and news category, Long Document Classification (LDC) dataset containing the whole news article and the news category, and Long Paragraph Classification (LPC) containing sub-articles of the news and the news category. We maintain consistent labeling across all 3 datasets for in-depth length-based analysis. We evaluate each of these Indic language datasets using 4 different models including monolingual BERT, multilingual Indic Sentence BERT (IndicSBERT), and IndicBERT. This research contributes significantly to expanding the pool of available text classification datasets and also makes it possible to develop topic classification models for Indian regional languages. This also serves as an excellent resource for cross-lingual analysis owing to the high overlap of labels among languages. The datasets and models are shared publicly at https://github.com/l3cube-pune/indic-nlp", "field": "cs", "label": 0}
{"text": "Title: Induction of quantum group representations\nAbstract: Induced representations for quantum groups are defined starting from coisotropic quantum subgroups and their main properties are proved. When the coisotropic quantum subgroup has a suitably defined section such representations can be realized on associated quantum bundles on general embeddable quantum homogeneous spaces.", "field": "math", "label": 1}
{"text": "Title: Edge detection with trigonometric polynomial shearlets\nAbstract: In this paper we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vall\\'{e}e Poussin type wavelets are able to detect singularities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of corresponding inner products. In the proof we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.", "field": "math", "label": 1}
{"text": "Title: On the Hankel Transform of Bessel Functions on Complex Numbers and Explicit Spectral Formulae over the Gaussian Field\nAbstract: In this paper, on the complex field $\\mathbb{C}$, we prove two integral formulae for the Hankel-Mellin transform and the double Fourier-Mellin transform of Bessel functions, both resulting the hypergeometric function. As two applications, we use the former integral formula to make explicit the spectral formula of Bruggeman and Motohashi for the fourth moment of Dedekind zeta function over the Gaussian number field $\\mathbb{Q}(i)$ and to establish a spectral formula for the Hecke-eigenvalue twisted second moment of central $L$-values for the Picard group $\\mathrm{PGL}_2 (\\mathbb{Z}[i])$. Moreover, we develop the theory of distributional Hankel transform on $\\mathbb{C} \\smallsetminus \\{0\\}$.", "field": "math", "label": 0}
{"text": "Title: Global uniqueness of small representations\nAbstract: We prove that automorphic representations whose local components are certain small representations have multiplicity one. The proof is based on the multiplicity-one theorem for certain functionals of small representations, also proved in this paper.", "field": "math", "label": 1}
{"text": "Title: Linearly shellable complexes\nAbstract: We introduce the class of linearly shellable pure simplicial complexes. The characterizing property is the existence of a labeling of their vertices such that all linear extensions of the Bruhat order on the set of facets are shelling orders. Coxeter complexes of weak intervals in Coxeter groups of finite rank are proved to be linearly shellable. We also introduce the notion of linear strong shellability.", "field": "math", "label": 0}
{"text": "Title: Parameterized Verification of Disjunctive Timed Networks\nAbstract: We introduce new techniques for the parameterized verification of disjunctive timed networks (DTNs), i.e., networks of timed automata (TAs) that communicate via location guards that enable a transition only if there is another process in a given location. This computational model has been considered in the literature before, example applications are gossiping clock synchronization protocols or planning problems. We address the minimum-time reachability problem (Minreach) in DTNs, and show how to efficiently solve it based on a novel zone graph algorithm. We further show that solving Minreach allows us to construct a summary TA capturing exactly the possible behaviors of a single TA within a DTN of arbitrary size. The combination of these two results enables the parameterized verification of DTNs, while avoiding the construction of an exponential-size cutoff system required by existing results. Additionally, we develop sufficient conditions for solving Minreach and parameterized verification problems even in certain cases where locations that appear in location guards can have clock invariants, a case that has usually been excluded in the literature. Our techniques are also implemented, and experiments show their practicality.", "field": "cs", "label": 0}
{"text": "Title: Algorithms Transcending the SAT-Symmetry Interface\nAbstract: Dedicated treatment of symmetries in satisfiability problems (SAT) is indispensable for solving various classes of instances arising in practice. However, the exploitation of symmetries usually takes a black box approach. Typically, off-the-shelf external, general-purpose symmetry detection tools are invoked to compute symmetry groups of a formula. The groups thus generated are a set of permutations passed to a separate tool to perform further analyzes to understand the structure of the groups. The result of this second computation is in turn used for tasks such as static symmetry breaking or dynamic pruning of the search space. Within this pipeline of tools, the detection and analysis of symmetries typically incurs the majority of the time overhead for symmetry exploitation. In this paper we advocate for a more holistic view of what we call the SAT-symmetry interface. We formulate a computational setting, centered around a new concept of joint graph/group pairs, to analyze and improve the detection and analysis of symmetries. Using our methods, no information is lost performing computational tasks lying on the SAT-symmetry interface. Having access to the entire input allows for simpler, yet efficient algorithms. Specifically, we devise algorithms and heuristics for computing finest direct disjoint decompositions, finding equivalent orbits, and finding natural symmetric group actions. Our algorithms run in what we call instance-quasi-linear time, i.e., almost linear time in terms of the input size of the original formula and the description length of the symmetry group returned by symmetry detection tools. Our algorithms improve over both heuristics used in state-of-the-art symmetry exploitation tools, as well as theoretical general-purpose algorithms.", "field": "cs", "label": 0}
{"text": "Title: Logarithmic prismatic cohomology, motivic sheaves, and comparison theorems\nAbstract: We prove that (logarithmic) prismatic and (logarithmic) syntomic cohomology are representable in the category of logarithmic motives. As an application, we obtain Gysin maps for prismatic and syntomic cohomology, and we explicitly identify their cofibers. We also prove a smooth blow-up formula and we compute prismatic and syntomic cohomology of Grassmannians. In the second part of the paper, we develop a descent technique inspired by the work of Nizio\\l~ on log $K$-theory. Using the resulting \\emph{saturated descent}, we prove de Rham and crystalline comparison theorems for log prismatic cohomology, and the existence of Gysin maps for $A_{\\inf}$-cohomology.", "field": "math", "label": 0}
{"text": "Title: Bernstein components via Bernstein center\nAbstract: Let G be a reductive p-adic group. Let $\\Phi$ be an invariant distribution on G lying in the Bernstein center Z(G). We prove that $\\Phi$ is supported on compact elements in G if and only if it defines a constant function on every component of the set Irr(G); in particular, we show that the space of all elements of Z(G) supported on compact elements is a subalgebra of Z(G). Our proof is a slight modiification of the arguments of J.F.Dat who proved our result in one direction.", "field": "math", "label": 1}
{"text": "Title: Playing Atari with Six Neurons\nAbstract: Deep reinforcement learning, applied to vision-based problems like Atari games, maps pixels directly to actions; internally, the deep neural network bears the responsibility of both extracting useful information and making decisions based on it. By separating the image processing from decision-making, one could better understand the complexity of each task, as well as potentially find smaller policy representations that are easier for humans to understand and may generalize better. To this end, we propose a new method for learning policies and compact state representations separately but simultaneously for policy approximation in reinforcement learning. State representations are generated by an encoder based on two novel algorithms: Increasing Dictionary Vector Quantization makes the encoder capable of growing its dictionary size over time, to address new observations as they appear in an open-ended online-learning context; Direct Residuals Sparse Coding encodes observations by disregarding reconstruction error minimization, and aiming instead for highest information inclusion. The encoder autonomously selects observations online to train on, in order to maximize code sparsity. As the dictionary size increases, the encoder produces increasingly larger inputs for the neural network: this is addressed by a variation of the Exponential Natural Evolution Strategies algorithm which adapts its probability distribution dimensionality along the run. We test our system on a selection of Atari games using tiny neural networks of only 6 to 18 neurons (depending on the game's controls). These are still capable of achieving results comparable---and occasionally superior---to state-of-the-art techniques which use two orders of magnitude more neurons.", "field": "cs", "label": 1}
{"text": "Title: Synthetic projective lines, geometric closure and AB-sets\nAbstract: In this note, we introduce a new approach to abstract ``synthetic'' projective lines. We discuss various aspects of our approach, and compare these aspects with the classical one. A number of intriguing questions arise. Amongst these aspects, we discuss geometric closures, and introduce automorphism-blocking sets. We also construct a number of (counter) examples in infinite cases.", "field": "math", "label": 1}
{"text": "Title: Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought\nAbstract: Large language models (LLMs) have shown remarkable reasoning capabilities given chain-of-thought prompts (examples with intermediate reasoning steps). Existing benchmarks measure reasoning ability indirectly, by evaluating accuracy on downstream tasks such as mathematical reasoning. However, it is unclear how these models obtain the answers and whether they rely on simple heuristics rather than the generated chain-of-thought. To enable systematic exploration of the reasoning ability of LLMs, we present a new synthetic question-answering dataset called PrOntoQA, where each example is generated from a synthetic world model represented in first-order logic. This allows us to parse the generated chain-of-thought into symbolic proofs for formal analysis. Our analysis on InstructGPT and GPT-3 shows that LLMs are quite capable of making correct individual deduction steps, and so are generally capable of reasoning, even in fictional contexts. However, they have difficulty with proof planning: When multiple valid deduction steps are available, they are not able to systematically explore the different options.", "field": "cs", "label": 1}
{"text": "Title: An Edge-Cloud Collaboration Framework for Generative AI Service Provision with Synergetic Big Cloud Model and Small Edge Models\nAbstract: Generative artificial intelligence (GenAI) offers various services to users through content creation, which is believed to be one of the most important components in future networks. However, training and deploying big artificial intelligence models (BAIMs) introduces substantial computational and communication overhead.This poses a critical challenge to centralized approaches, due to the need of high-performance computing infrastructure and the reliability, secrecy and timeliness issues in long-distance access of cloud services. Therefore, there is an urging need to decentralize the services, partly moving them from the cloud to the edge and establishing native GenAI services to enable private, timely, and personalized experiences. In this paper, we propose a brand-new bottom-up BAIM architecture with synergetic big cloud model and small edge models, and design a distributed training framework and a task-oriented deployment scheme for efficient provision of native GenAI services. The proposed framework can facilitate collaborative intelligence, enhance adaptability, gather edge knowledge and alleviate edge-cloud burden. The effectiveness of the proposed framework is demonstrated through an image generation use case. Finally, we outline fundamental research directions to fully exploit the collaborative potential of edge and cloud for native GenAI and BAIM applications.", "field": "cs", "label": 0}
{"text": "Title: Which Quantum Circuit Mutants Shall Be Used? An Empirical Evaluation of Quantum Circuit Mutations\nAbstract: As a new research area, quantum software testing lacks systematic testing benchmarks to assess testing techniques' effectiveness. Recently, some open-source benchmarks and mutation analysis tools have emerged. However, there is insufficient evidence on how various quantum circuit characteristics (e.g., circuit depth, number of quantum gates), algorithms (e.g., Quantum Approximate Optimization Algorithm), and mutation characteristics (e.g., mutation operators) affect the most mutant detection in quantum circuits. Studying such relations is important to systematically design faulty benchmarks with varied attributes (e.g., the difficulty in detecting a seeded fault) to facilitate assessing the cost-effectiveness of quantum software testing techniques efficiently. To this end, we present a large-scale empirical evaluation with more than 700K faulty benchmarks (quantum circuits) generated by mutating 382 real-world quantum circuits. Based on the results, we provide valuable insights for researchers to define systematic quantum mutation analysis techniques. We also provide a tool to recommend mutants to users based on chosen characteristics (e.g., a quantum algorithm type) and the required difficulty of killing mutants. Finally, we also provide faulty benchmarks that can already be used to assess the cost-effectiveness of quantum software testing techniques.", "field": "cs", "label": 0}
{"text": "Title: Mean Oriented Riesz Features for Micro Expression Classification\nAbstract: Micro-expressions are brief and subtle facial expressions that go on and off the face in a fraction of a second. This kind of facial expressions usually occurs in high stake situations and is considered to reflect a human's real intent. There has been some interest in micro-expression analysis, however, a great majority of the methods are based on classically established computer vision methods such as local binary patterns, histogram of gradients and optical flow. A novel methodology for micro-expression recognition using the Riesz pyramid, a multi-scale steerable Hilbert transform is presented. In fact, an image sequence is transformed with this tool, then the image phase variations are extracted and filtered as proxies for motion. Furthermore, the dominant orientation constancy from the Riesz transform is exploited to average the micro-expression sequence into an image pair. Based on that, the Mean Oriented Riesz Feature description is introduced. Finally the performance of our methods are tested in two spontaneous micro-expressions databases and compared to state-of-the-art methods.", "field": "cs", "label": 1}
{"text": "Title: Perfect numbers and Fibonacci primes\nAbstract: In this paper, we introduce the concept of $F$-perfect number, which is a positive integer $n$ such that $\\sum_{d|n,d<n}d^2=3n$. We prove that all the $F$-perfect numbers are of the form $n=F_{2k-1}F_{2k+1}$, where both $F_{2k-1}$ and $F_{2k+1}$ are Fibonacci primes. Moreover, we obtain other interesting results and raise a new conjecture on perfect numbers.", "field": "math", "label": 1}
{"text": "Title: An upwind method for genuine weakly hyperbolic systems\nAbstract: In this article, we attempted to develop an upwind scheme based on Flux Difference Splitting using Jordan canonical forms to simulate genuine weakly hyperbolic systems. Theory of Jordan Canonical Forms is being used to complete defective set of linear independent eigenvectors. Proposed FDS-J scheme is capable of recognizing various shocks accurately.", "field": "math", "label": 1}
{"text": "Title: Forced translational symmetry-breaking for abstract evolution equations: the organizing center for blocking of travelling waves\nAbstract: We consider two parameter families of differential equations on a Banach space X, where the parameters c and $\\epsilon$ are such that: (1) when $\\epsilon=0$, the differential equations are symmetric under the action of the group of one-dimensional translations SE(1) acting on X, whereas when $\\epsilon\\neq 0$, this translation symmetry is broken, (2) when $\\epsilon=0$, the symmetric differential equations admit a smooth family of relative equilibria (travelling waves) parametrized by the drift speed c, with $c=0$ corresponding to steady-states. Under certain hypotheses on the differential equations and on the Banach space X, we use the center manifold theorem of Sandstede, Scheel and Wulff to study the effects of the symmetry-breaking perturbation on the above family of relative equilibria. In particular, we show that the phenomenon commonly referred to as propagation failure, or wave blocking occurs in a cone in the $(c,\\epsilon)$ parameter space which emanates from the point $(c,\\epsilon)=(0,0)$. We also discuss how our methods can be adapted to perturbations of parameter-independent differential equations (such as the Fisher-KPP) which admit families of relative equilibria parametrized by drift speed.", "field": "math", "label": 1}
{"text": "Title: Cohomology of fixed point sets of anti-symplectic involutions in the Hilbert scheme of points on a surface\nAbstract: Let $S$ be a smooth, quasi-projective complex surface with complex symplectic form $\\omega \\in H^0(S, K_S)$. This determines a symplectic form $\\omega_n$ on the Hilbert scheme of points $S^{[n]}$ for $n \\geq 1$. Let $\\tau$ be an anti-symplectic involution of $(S,\\omega)$: an order two automorphism of $S$ such that $ \\tau^*\\omega=-\\omega$. Then $\\tau$ induces an anti-symplectic involution on $(S^{[n]},\\omega_n)$ and the fixed point set $(S^{[n]})^\\tau$ is a smooth Lagrangian subvariety of $S^{[n]}$. In this paper, we calculate the mixed Hodge structure of $H^*( (S^{[n]})^\\tau; \\mathbb{Q})$ in terms of the mixed Hodge structures of $H^*( S^\\tau;\\mathbb{Q})$ and of $H^*( S / \\tau; \\mathbb{Q})$. We also classify the connected components of $(S^{[n]})^\\tau$ and determine their mixed Hodge structures. Our results apply more generally whenever $S$ is a smooth quasi-projective surface, and $\\tau$ is an involution of $S$ for which $S^\\tau$ is a curve.", "field": "math", "label": 0}
{"text": "Title: Recognition of Unit Segment and Polyline Graphs is $\\exists\\mathbb{R}$-Complete\nAbstract: Given a set of objects O in the plane, the corresponding intersection graph is defined as follows. A vertex is created for each object and an edge joins two vertices whenever the corresponding objects intersect. We study here the case of unit segments and polylines with exactly k bends. In the recognition problem, we are given a graph and want to decide whether the graph can be represented as the intersection graph of certain geometric objects. In previous work it was shown that various recognition problems are $\\exists\\mathbb{R}$-complete, leaving unit segments and polylines as few remaining natural cases. We show that recognition for both families of objects is $\\exists\\mathbb{R}$-complete.", "field": "cs", "label": 0}
{"text": "Title: Paraconsistent Existential Graphs Gamma Peirce System\nAbstract: In this paper, the paraconsistent propositional logic LG is presented, along with its semantic characterization. It is shown that LG's set of theorems corresponds to the set of valid existential graphs, GET, which turns out to be an extension of Peirce's Gamma system, without becoming Zeman's gamma-4 system. All evidence is presented in a complete, rigorous, and detailed manner. This result is generalized by constructing the paraconsistent system of existential graphs GET4, and its semantic-deductive characterization. Finally, Zeman's Gamma-4, Gamma-4.2, and Gamma-5 existential graph systems are proven to be paraconsistent.", "field": "math", "label": 0}
{"text": "Title: Mixing Homomorphisms, Recolourings, and Extending Circular Precolourings\nAbstract: This work brings together ideas of mixing graph colourings, discrete homotopy, and precolouring extension. A particular focus is circular colourings. We prove that all the $(k,q)$-colourings of a graph $G$ can be obtained by successively recolouring a single vertex provided $k/q\\geq 2col(G)$ along the lines of Cereceda, van den Heuvel and Johnson's result for $k$-colourings. We give various bounds for such mixing results and discuss their sharpness, including cases where the bounds for circular and classical colourings coincide. As a corollary, we obtain an Albertson-type extension theorem for $(k,q)$-precolourings of circular cliques. Such a result was first conjectured by Albertson and West. General results on homomorphism mixing are presented, including a characterization of graphs $G$ for which the endomorphism monoid can be generated through the mixing process. As in similar work of Brightwell and Winkler, the concept of dismantlability plays a key role.", "field": "math", "label": 1}
{"text": "Title: Parabolic bifurcation loci in the spaces of rational functions\nAbstract: We give a geometric description of the parabolic bifurcation locus in the space $\\operatorname{Rat}_d$ of all rational functions on $\\mathbb{P}^1$ of degree $d>1$, generalizing the study by Morton and Vivaldi in the case of monic polynomials. The results are new even for quadratic rational functions.", "field": "math", "label": 0}
{"text": "Title: Longest and shortest cycles in random planar graphs\nAbstract: Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $\\{1, \\ldots, n\\}$ with $m=m(n)$ edges. We study the cycle and block structure of $P(n,m)$ when $m\\sim n/2$. More precisely, we determine the asymptotic order of the length of the longest and shortest cycle in $P(n,m)$ in the critical range when $m=n/2+o(n)$. In addition, we describe the block structure of $P(n,m)$ in the weakly supercritical regime when $n^{2/3}\\ll m-n/2\\ll n$.", "field": "math", "label": 1}
{"text": "Title: Rewrite Caption Semantics: Bridging Semantic Gaps for Language-Supervised Semantic Segmentation\nAbstract: Vision-Language Pre-training has demonstrated its remarkable zero-shot recognition ability and potential to learn generalizable visual representations from language supervision. Taking a step ahead, language-supervised semantic segmentation enables spatial localization of textual inputs by learning pixel grouping solely from image-text pairs. Nevertheless, the state-of-the-art suffers from clear semantic gaps between visual and textual modality: plenty of visual concepts appeared in images are missing in their paired captions. Such semantic misalignment circulates in pre-training, leading to inferior zero-shot performance in dense predictions due to insufficient visual concepts captured in textual representations. To close such semantic gap, we propose Concept Curation (CoCu), a pipeline that leverages CLIP to compensate for the missing semantics. For each image-text pair, we establish a concept archive that maintains potential visually-matched concepts with our proposed vision-driven expansion and text-to-vision-guided ranking. Relevant concepts can thus be identified via cluster-guided sampling and fed into pre-training, thereby bridging the gap between visual and textual semantics. Extensive experiments over a broad suite of 8 segmentation benchmarks show that CoCu achieves superb zero-shot transfer performance and greatly boosts language-supervised segmentation baseline by a large margin, suggesting the value of bridging semantic gap in pre-training data.", "field": "cs", "label": 0}
{"text": "Title: The cardinality of orthogonal exponentials of planar self-affine measures with three-element digit sets\nAbstract: In this paper, we consider the planar self-affine measures $\\mu_{M,D}$ generated by an expanding matrix $M\\in M_2(\\mathbb{Z})$ and an integer digit set $ D=\\left\\{ {\\left( {\\begin{array}{*{20}{c}} 0\\\\ 0 \\end{array}} \\right),\\left( {\\begin{array}{*{20}{c}} \\alpha_1\\\\ \\alpha_2 \\end{array}} \\right),\\left( {\\begin{array}{*{20}{c}} \\beta_1\\\\ \\beta_2 \\end{array}} \\right)} \\right\\} $ with $\\alpha_1\\beta_2-\\alpha_2\\beta_1\\neq0$. We show that if $\\det(M)\\notin 3\\mathbb{Z}$, then the mutually orthogonal exponential functions in $L^2(\\mu_{M,D})$ is finite, and the exact maximal cardinality is given.", "field": "math", "label": 1}
{"text": "Title: Gromov-Witten Invariants of Bielliptic Surfaces\nAbstract: Bielliptic surfaces appear as quotient of a product of two elliptic curves and were classified by Bagnera-Franchis. We give a concrete way of computing their GW-invariants with point insertions using a floor diagram algorithm. Using the latter, we are able to prove the quasi-modularity of their generating series by relating them to generating series of graphs for which we also prove quasi-modularity results. We propose a refinement of these invariants by inserting a {\\lambda}-class in the considered GW-invariants.", "field": "math", "label": 0}
{"text": "Title: A note on the equidistribution of $3$-colour partitions\nAbstract: In this short note, we prove equidistribution results regarding three families of three-colour partitions recently introduced by Schlosser and Zhou. To do so, we prove an asymptotic formula for the infinite product $F_{a,c}(\\zeta ; {\\rm e}^{-z}) := \\prod_{n \\geq 0} \\big(1- \\zeta {\\rm e}^{-(a+cn)z}\\big)$ ($a,c \\in \\mathbb{N}$ with $0<a\\leq c$ and $\\zeta$ a root of unity) when $z$ lies in certain sectors in the right half-plane, which may be useful in studying similar problems. As a corollary, we obtain the asymptotic behaviour of the three-colour partition families at hand.", "field": "math", "label": 0}
{"text": "Title: Continuum dynamics of the intention field under weakly cohesive social interactions\nAbstract: We investigate the long-time dynamics of an opinion formation model inspired by a work by Borghesi, Bouchaud and Jensen. Firstly, we derive a Fokker-Planck type equation under the assumption that interactions between individuals produce little consensus of opinion (grazing collision approximation). Secondly, we study conditions under which the Fokker-Planck equation has non-trivial equilibria and derive the macroscopic limit (corresponding to the long-time dynamics and spatially localized interactions) for the evolution of the mean opinion. Finally, we compare two different types of interaction rates: the original one given in the work of Borghesi, Bouchaud and Jensen (symmetric binary interactions) and one inspired from works by Motsch and Tadmor (non-symmetric binary interactions). We show that the first case leads to a conservative model for the density of the mean opinion whereas the second case leads to a non-conservative equation. We also show that the speed at which consensus is reached asymptotically for these two rates has fairly different density dependence.", "field": "math", "label": 1}
{"text": "Title: Global well-posedness for the Euler alignment system with mildly singular interactions\nAbstract: We consider the Euler alignment system with mildly singular interaction kernels. When the local repulsion term is of the fractional type, global in time existence of smooth solutions was proved in\\cite{do2018global,shvydkoy2017eulerian1,shvydkoy2017eulerian2,shvydkoy2017eulerian3}. Here, we consider a class of less singular interaction kernels and establish the global regularity of solutions as long as the interaction kernels are not integrable. The proof relies on modulus of continuity estimates for a class of parabolic integro-differential equations with a drift and mildly singular kernels.", "field": "math", "label": 1}
{"text": "Title: Roth-type Theorem for high-power system in Piatetski-Shapiro primes (II)\nAbstract: We consider the nonlinear system $c_1p_1^d +c_2p_2^d + \\dots + c_s p_s^d = 0$ with $c_1, c_2,\\dots, c_s\\in\\mathbb Z$ being nonzero and satisfying $c_1 +c_2 + \\dots + c_s = 0$. We show that for $s\\ge 2\\lfloor \\frac{d^2}2\\rfloor+1$ and $c\\in\\left(1, 1+c(d,s)\\right)$, if the system has only $K$-trivial solutions in subset $\\mathcal{A}$ of Piatetski-Shapiro primes up to $x$ and corresponding to $c$, then $|\\mathcal{A}| \\ll \\frac{x^{\\frac1c}}{\\log x} $$\\left(\\log \\log \\log \\log x\\right)^{\\frac{2-s}{dc}+\\varepsilon}$.", "field": "math", "label": 0}
{"text": "Title: Theoretical guarantees on the best-of-n alignment policy\nAbstract: A simple and effective method for the alignment of generative models is the best-of-$n$ policy, where $n$ samples are drawn from a base policy, and ranked based on a reward function, and the highest ranking one is selected. A commonly used analytical expression in the literature claims that the KL divergence between the best-of-$n$ policy and the base policy is equal to $\\log (n) - (n-1)/n.$ We disprove the validity of this claim, and show that it is an upper bound on the actual KL divergence. We also explore the tightness of this upper bound in different regimes. Finally, we propose a new estimator for the KL divergence and empirically show that it provides a tight approximation through a few examples.", "field": "cs", "label": 0}
{"text": "Title: On the heavy-tail behavior of the distributionally robust newsvendor\nAbstract: Since the seminal work of Scarf (1958) [A min-max solution of an inventory problem, Studies in the Mathematical Theory of Inventory and Production, pages 201-209] on the newsvendor problem with ambiguity in the demand distribution, there has been a growing interest in the study of the distributionally robust newsvendor problem. The model is criticized at times for being overly conservative since the worst-case distribution is discrete with a few support points. However, it is the order quantity prescribed from the model that is of practical relevance. A simple calculation shows that the optimal order quantity in Scarf's model with known first and second moment is also optimal for a censored student-t distribution with parameter 2. In this paper, we generalize this \"heavy-tail optimality\" property of the distributionally robust newsvendor to an ambiguity set where information on the first and the $\\alpha$th moment is known, for any real number $\\alpha > 1$. We show that the optimal order quantity for the distributionally robust newsvendor problem is also optimal for a regularly varying distribution with roughly a power law tail with tail index $\\alpha$. We illustrate the usefulness of the model in the high service level regime with numerical experiments, by showing that when a standard distribution such as the exponential or lognormal distribution is contaminated with a heavy-tailed (regularly varying) distribution, the distributionally robust optimal order quantity outperforms the optimal order quantity of the original distribution, even with a small amount of contamination.", "field": "math", "label": 1}
{"text": "Title: Toroidal orbifolds, destackification, and Kummer blowings up\nAbstract: We show that any toroidal DM stack $X$ with finite diagonalizable inertia possesses a maximal toroidal coarsening $X_{tcs}$ such that the morphism $X\\to X_{tcs}$ is logarithmically smooth. Further, we use torification results of [AT17] to construct a destackification functor, a variant of the main result of Bergh [Ber17], on the category of such toroidal stacks $X$. Namely, we associate to $X$ a sequence of blowings up of toroidal stacks $\\widetilde{\\mathcal{F}}_X\\:Y\\longrightarrow X$ such that $Y_{tc}$ coincides with the usual coarse moduli space $Y_{cs}$. In particular, this provides a toroidal resolution of the algebraic space $X_{cs}$. Both $X_{tcs}$ and $\\widetilde{\\mathcal{F}}_X$ are functorial with respect to strict inertia preserving morphisms $X'\\to X$. Finally, we use coarsening morphisms to introduce a class of non-representable birational modifications of toroidal stacks called Kummer blowings up. These modifications, as well as our version of destackification, are used in our work on functorial toroidal resolution of singularities.", "field": "math", "label": 1}
{"text": "Title: Radio Network Lower Bounds Made Easy\nAbstract: Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among an unknown set of nodes) and broadcast (message dissemination through an unknown network topology). In this paper, we introduce a new technique for proving this type of bound, based on reduction from a probabilistic hitting game, that simplifies and strengthens much of this existing work. In more detail, in this single paper we prove new expected time and high probability lower bounds for wake-up and global broadcast in single and multichannel versions of the radio network model both with and without collision detection. In doing so, we are able to reproduce results that previously spanned a half-dozen papers published over a period of twenty-five years. In addition to simplifying these existing results, our technique, in many places, also improves the state of the art: of the eight bounds we prove, four strictly strengthen the best known previous result (in terms of time complexity and/or generality of the algorithm class for which it holds), and three provide the first known non-trivial bound for the case in question. The fact that the same technique can easily generate this diverse collection of lower bounds indicates a surprising unity underlying communication tasks in the radio network model---revealing that deep down, below the specifics of the problem definition and model assumptions, communication in this setting reduces to finding efficient strategies for a simple game.", "field": "cs", "label": 1}
{"text": "Title: Rigidity And Unirational Groups\nAbstract: We prove a rigidity theorem for morphisms from products of open subschemes of the projective line into solvable groups not containing a copy of $\\Ga$ (for example, wound unipotent groups). As a consequence, we deduce several structural results about unirational group schemes, including that unirationality for group schemes descends through separable extensions. We also apply the main result to prove that permawound unipotent groups are unirational and -- when wound -- commutative.", "field": "math", "label": 0}
{"text": "Title: A parametricity-based formalization of semi-simplicial and semi-cubical sets\nAbstract: Semi-simplicial and semi-cubical sets are commonly defined as presheaves over respectively, the semi-simplex or semi-cube category. Homotopy Type Theory then popularized an alternative definition, where the set of n-simplices or n-cubes are instead regrouped into the families of the fibers over their faces, leading to a characterization we call indexed. Moreover, it is known that semi-simplicial and semi-cubical sets are related to iterated Reynolds parametricity, respectively in its unary and binary variants. We exploit this correspondence to develop an original uniform indexed definition of both augmented semi-simplicial and semi-cubical sets, and fully formalize it in Coq.", "field": "cs", "label": 0}
{"text": "Title: Dynamically Masked Discriminator for Generative Adversarial Networks\nAbstract: Training Generative Adversarial Networks (GANs) remains a challenging problem. The discriminator trains the generator by learning the distribution of real/generated data. However, the distribution of generated data changes throughout the training process, which is difficult for the discriminator to learn. In this paper, we propose a novel method for GANs from the viewpoint of online continual learning. We observe that the discriminator model, trained on historically generated data, often slows down its adaptation to the changes in the new arrival generated data, which accordingly decreases the quality of generated results. By treating the generated data in training as a stream, we propose to detect whether the discriminator slows down the learning of new knowledge in generated data. Therefore, we can explicitly enforce the discriminator to learn new knowledge fast. Particularly, we propose a new discriminator, which automatically detects its retardation and then dynamically masks its features, such that the discriminator can adaptively learn the temporally-vary distribution of generated data. Experimental results show our method outperforms the state-of-the-art approaches.", "field": "cs", "label": 0}
{"text": "Title: Communication games, sequential equilibrium, and mediators\nAbstract: We consider $k$-resilient sequential equilibria, strategy profiles where no player in a coalition of at most $k$ players believes that it can increase its utility by deviating, regardless of its local state. We prove that all $k$-resilient sequential equilibria that can be implemented with a trusted mediator can also be implemented without the mediator in a synchronous system of $n$ players if $n >3k$. In asynchronous systems, where there is no global notion of time and messages may take arbitrarily long to get to their recipient, we prove that a $k$-resilient sequential equilibrium with a mediator can be implemented without the mediator if $n > 4k$. These results match the lower bounds given by Abraham, Dolev, and Halpern (2008) and Geffner and Halpern (2023) for implementing a Nash equilibrium without a mediator (which are easily seen to apply to implementing a sequential equilibrium) and improve the results of Gerardi, who showed that, in the case that $k=1$, a sequential equilibrium can be implemented in synchronous systems if $n \\ge 5$.", "field": "cs", "label": 0}
{"text": "Title: Training-free Content Injection using h-space in Diffusion Models\nAbstract: Diffusion models (DMs) synthesize high-quality images in various domains. However, controlling their generative process is still hazy because the intermediate variables in the process are not rigorously studied. Recently, the bottleneck feature of the U-Net, namely $h$-space, is found to convey the semantics of the resulting image. It enables StyleCLIP-like latent editing within DMs. In this paper, we explore further usage of $h$-space beyond attribute editing, and introduce a method to inject the content of one image into another image by combining their features in the generative processes. Briefly, given the original generative process of the other image, 1) we gradually blend the bottleneck feature of the content with proper normalization, and 2) we calibrate the skip connections to match the injected content. Unlike custom-diffusion approaches, our method does not require time-consuming optimization or fine-tuning. Instead, our method manipulates intermediate features within a feed-forward generative process. Furthermore, our method does not require supervision from external networks. The code is available at https://curryjung.github.io/InjectFusion/", "field": "cs", "label": 0}
{"text": "Title: Multi-task learning for Joint Language Understanding and Dialogue State Tracking\nAbstract: This paper presents a novel approach for multi-task learning of language understanding (LU) and dialogue state tracking (DST) in task-oriented dialogue systems. Multi-task training enables the sharing of the neural network layers responsible for encoding the user utterance for both LU and DST and improves performance while reducing the number of network parameters. In our proposed framework, DST operates on a set of candidate values for each slot that has been mentioned so far. These candidate sets are generated using LU slot annotations for the current user utterance, dialogue acts corresponding to the preceding system utterance and the dialogue state estimated for the previous turn, enabling DST to handle slots with a large or unbounded set of possible values and deal with slot values not seen during training. Furthermore, to bridge the gap between training and inference, we investigate the use of scheduled sampling on LU output for the current user utterance as well as the DST output for the preceding turn.", "field": "cs", "label": 1}
{"text": "Title: Stable matchings with correlated Preferences\nAbstract: The stable matching problem has been the subject of intense theoretical and empirical study since the seminal 1962 paper by Gale and Shapley. The number of stable matchings for different systems of preferences has been studied in many contexts, going back to Donald Knuth in the 1970s. In this paper, we consider a family of distributions defined by the Mallows permutations and show that with high probability the number of stable matchings for these preferences is exponential in the number of people.", "field": "math", "label": 0}
{"text": "Title: Noncentral moderate deviations for time-changed Lévy processes with inverse of stable subordinators\nAbstract: In this paper we present some extensions of recent noncentral moderate deviation results in the literature. In the first part we generalize the results in \\cite{BeghinMacciSPL2022} by considering a general L\\'evy process $\\{S(t):t\\geq 0\\}$ instead of a compound Poisson process. In the second part we assume that $\\{S(t):t\\geq 0\\}$ has bounded variation and it is not a subordinator; thus, in some sense, we have the difference of two independent non-null subordinators. In this way we generalize the results in \\cite{LeeMacci} for Skellam processes.", "field": "math", "label": 0}
{"text": "Title: A Complete Landscape for the Price of Envy-Freeness\nAbstract: We study the efficiency of fair allocations using the well-studied price of fairness concept, which quantitatively measures the worst-case efficiency loss when imposing fairness constraints. Previous works provided partial results on the price of fairness with well-known fairness notions such as envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX). In this paper, we give a complete characterization for the price of envy-freeness in various settings. In particular, we first consider the two-agent case under the indivisible-goods setting and present tight ratios for the price of EF1 (for scaled utility) and EFX (for unscaled utility), which resolve questions left open in the literature. Next, we consider the mixed goods setting which concerns a mixture of both divisible and indivisible goods. We focus on envy-freeness for mixed goods (EFM), which generalizes both envy-freeness and EF1, as well as its strengthening called envy-freeness up to any good for mixed goods (EFXM), which generalizes envy-freeness and EFX. To this end, we settle the price of EFM and EFXM by providing a complete picture of tight bounds for two agents and asymptotically tight bounds for $n$ agents, for both scaled and unscaled utilities.", "field": "cs", "label": 0}
{"text": "Title: Energy Identity for Stationary Harmonic Maps\nAbstract: In this paper we consider sequences $u_j:B_2\\subseteq M\\to N$ of stationary harmonic maps between smooth Riemannian manifolds with uniformly bounded energy $E[u_j]\\equiv \\int |\\nabla u_j|^2\\leq \\Lambda$ . After passing to a subsequence it is known one can limit $u_j\\to u:B_1\\to N$ with the associated defect measure $|\\nabla u_j|^2 dv_g \\to |\\nabla u|^2dv_g+\\nu$, where $\\nu = e(x)\\, H^{m-2}_S$ is an $m-2$ rectifiable measure \\cite{lin_stat}. For a.e. $x\\in S=\\operatorname{supp}(\\nu)$ one can produce a finite number of bubble maps $b_j:S^2\\to N$ by blowing up the sequence $u_j$ near $x$. We prove the energy identity in this paper. Namely, we have at a.e. $x\\in S$ that $e(x)=\\sum_j E[b_j]$ for a complete set of such bubbles. That is, the energy density of the defect measure $\\nu$ is precisely the sum of the energies of the bubbling maps.", "field": "math", "label": 0}
{"text": "Title: Group actions on stacks and applications to equivariant string topology for stacks\nAbstract: This paper is a continuations of the project initiated in the book string topology for stacks. We construct string operations on the SO(2)-equivariant homology of the (free) loop space $L(X)$ of an oriented differentiable stack $X$ and show that $H^{SO(2)}_{*+dim(X) -2}(L(X))$ is a graded Lie algebra. In the particular case where $X$ is a 2-dimensional orbifold we give a Goldman-type description for the string bracket. To prove these results, we develop a machinery of (weak) group actions on topological stacks which should be of independent interest. We explicitly construct the quotient stack of a group acting on a stack and show that it is a topological stack. Then use its homotopy type to define equivariant (co)homology for stacks, transfer maps, and so on.", "field": "math", "label": 1}
{"text": "Title: 3D printed architected lattice structures by material jetting\nAbstract: High-precision 3D printing technology opens to almost endless opportunities to design complex shapes present in tailored architected materials. The scope of this work is to review the latest studies regarding 3D printed lattice structures that involve the use of photopolymers fabricated by Material Jetting (MJ), with a focus on the widely used Polyjet and MultiJet techniques. The main aspects governing this printing process are introduced to determine their influence during the fabrication of 3D printed lattices. Performed experimental studies, considered assumptions, and constitutive models for the respective numerical simulations are analyzed. Furthermore, an overview of the latest extensively studied 3D printed architected lattice materials is exposed by emphasizing their achieved mechanical performances through the use of Ashby plots. Then, we highlight the advantages, limitations, and challenges of the material jetting technology to manufacture tunable architected materials for innovative devices, oriented to several engineering applications. Finally, possible approaches for future works and gaps to be covered by further research are indicated, including cost and environmental-related issues.", "field": "cs", "label": 1}
{"text": "Title: Bases for free Lie superalgebras\nAbstract: We describe a basis for free Lie superalgebras which uses the theory of basic commutators. The only description for bases for free Lie superalgebras that I have found in the literature is in the book \"Infinite dimensional Lie superalgebras\" by Bahturin et al. Their bases make use of the theory of Shirshov bases in free Lie algebras, and I believe that there is a case for writing up an alternative approach using basic commutators.", "field": "math", "label": 0}
{"text": "Title: Symplectic reduction and lagrangian submanifolds in Gr(1, n)\nAbstract: We study lagrangian submanifolds of algebraic variety Gr(1, n) equipped with the Kahler form given by the Plucker embedding. We use the correspondence between lagrangian submanifolds of Gr(1, n) and lagrangian submanifolds of variety M_{n-2}, given by symplectic reduction Gr(1, n)//T^2 for some specially chosen moment maps, which generate T^2 action on Gr(1, n). We establish that in this way one finds many topological types, realized by lagrangian submanifolds, and then one counts that Gr(1, n) admits more than n different topological types of smooth lagrangian submanifolds.", "field": "math", "label": 0}
{"text": "Title: HEAP: Unsupervised Object Discovery and Localization with Contrastive Grouping\nAbstract: Unsupervised object discovery and localization aims to detect or segment objects in an image without any supervision. Recent efforts have demonstrated a notable potential to identify salient foreground objects by utilizing self-supervised transformer features. However, their scopes only build upon patch-level features within an image, neglecting region/image-level and cross-image relationships at a broader scale. Moreover, these methods cannot differentiate various semantics from multiple instances. To address these problems, we introduce Hierarchical mErging framework via contrAstive grouPing (HEAP). Specifically, a novel lightweight head with cross-attention mechanism is designed to adaptively group intra-image patches into semantically coherent regions based on correlation among self-supervised features. Further, to ensure the distinguishability among various regions, we introduce a region-level contrastive clustering loss to pull closer similar regions across images. Also, an image-level contrastive loss is present to push foreground and background representations apart, with which foreground objects and background are accordingly discovered. HEAP facilitates efficient hierarchical image decomposition, which contributes to more accurate object discovery while also enabling differentiation among objects of various classes. Extensive experimental results on semantic segmentation retrieval, unsupervised object discovery, and saliency detection tasks demonstrate that HEAP achieves state-of-the-art performance.", "field": "cs", "label": 0}
{"text": "Title: AERIAL-CORE: AI-Powered Aerial Robots for Inspection and Maintenance of Electrical Power Infrastructures\nAbstract: Large-scale infrastructures are prone to deterioration due to age, environmental influences, and heavy usage. Ensuring their safety through regular inspections and maintenance is crucial to prevent incidents that can significantly affect public safety and the environment. This is especially pertinent in the context of electrical power networks, which, while essential for energy provision, can also be sources of forest fires. Intelligent drones have the potential to revolutionize inspection and maintenance, eliminating the risks for human operators, increasing productivity, reducing inspection time, and improving data collection quality. However, most of the current methods and technologies in aerial robotics have been trialed primarily in indoor testbeds or outdoor settings under strictly controlled conditions, always within the line of sight of human operators. Additionally, these methods and technologies have typically been evaluated in isolation, lacking comprehensive integration. This paper introduces the first autonomous system that combines various innovative aerial robots. This system is designed for extended-range inspections beyond the visual line of sight, features aerial manipulators for maintenance tasks, and includes support mechanisms for human operators working at elevated heights. The paper further discusses the successful validation of this system on numerous electrical power lines, with aerial robots executing flights over 10 kilometers away from their ground control stations.", "field": "cs", "label": 0}
{"text": "Title: Domination structure in 3-connected graphs\nAbstract: From a recent perspective, the structure of a 3-connected graph is studied in this paper. It stipulates the minimum dominating set of a 3-connected graph. Also, we count the number of structures, as a consequence, the upper bound is obtained. By it, the minimum dominating set of a 3-connected graph is determined in polynomial time.", "field": "math", "label": 1}
{"text": "Title: Directional flow in perivascular networks: Mixed finite elements for reduced-dimensional models on graphs\nAbstract: The flow of cerebrospinal fluid through the perivascular spaces of the brain is believed to play a crucial role in eliminating toxic waste proteins. While the driving forces of this flow have been enigmatic, experiments have shown that arterial wall motion is central. In this work, we present a network model for simulating pulsatile fluid flow in perivascular networks. We establish the well-posedness of this model in the primal and dual mixed variational settings, and show how it can be discretized using mixed finite elements. Further, we utilize this model to investigate fundamental questions concerning the physical mechanisms governing perivascular fluid flow. Notably, our findings reveal that arterial pulsations can induce directional flow in branching perivascular networks.", "field": "math", "label": 0}
{"text": "Title: Radon-type transforms for holomorphic and Hermitian monogenic functions\nAbstract: The standard Radon transform of holomorphic functions is not always well defined, as the integration of such functions over planes may not converge. In this paper, we introduce new Radon-type transforms of co-(real)dimension $2$ for harmonic and holomorphic functions on the unit ball. These transforms are abstractly defined as orthogonal projections onto spaces of complex harmonic and holomorphic plane waves, respectively. The inversion formulas are derived based on the dual transform, while the latter is defined as an integration on a complex Stiefel manifold. Our transforms are extended to the Fock space and give rise to a new transform defined on the entire $L^{2}(\\mathbb{R}^{n})$ through the Segal-Bargmann transform. Furthermore, we develop these transforms for Hermitian monogenic functions on the unit ball, thereby refining the Szeg\\\"o-Radon transform for monogenic functions introduced by Colombo, Sabadini and Sommen.", "field": "math", "label": 0}
{"text": "Title: Dispersive decay of small data solutions for the KdV equation\nAbstract: We consider the Korteweg-de Vries (KdV) equation, and prove that small localized data yields solutions which have dispersive decay on a quartic time-scale. This result is optimal, in view of the emergence of solitons at quartic time, as predicted by inverse scattering theory.", "field": "math", "label": 1}
{"text": "Title: Reuse-Aware Cache Partitioning Framework for Data-Sharing Multicore Systems\nAbstract: Multi-core processors improve performance, but they can create unpredictability owing to shared resources such as caches interfering. Cache partitioning is used to alleviate the Worst-Case Execution Time (WCET) estimation by isolating the shared cache across each thread to reduce interference. It does, however, prohibit data from being transferred between parallel threads running on different cores. In this paper we present (SRCP) a cache replacement mechanism for partitioned caches that is aware of data being shared across threads, prevents shared data from being replicated across partitions and frequently used data from being evicted from caches. Our technique outperforms TA-DRRIP and EHC, which are existing state-of-the-art cache replacement algorithms, by 13.34% in cache hit-rate and 10.4% in performance over LRU (least recently used) cache replacement policy.", "field": "cs", "label": 1}
{"text": "Title: Norm inflation for the Boussinesq system\nAbstract: We prove the norm inflation phenomena for the Boussinesq system on $\\mathbb T^3$. For arbitrarily small initial data $(u_0,\\rho_0)$ in the negative-order Besov spaces $\\dot{B}^{-1}_{\\infty, \\infty} \\times \\dot{B}^{-1}_{\\infty, \\infty}$, the solution can become arbitrarily large in a short time. Such largeness can be detected in $\\rho$ in Besov spaces of any negative order: $\\dot{B}^{-s}_{\\infty, \\infty}$ for any $s>0$. Notice that our initial data space is scaling critical for $u$ and is scaling subcritical for $\\rho$.", "field": "math", "label": 1}
{"text": "Title: Deep Learning based Multi-Label Image Classification of Protest Activities\nAbstract: With the rise of internet technology amidst increasing rates of urbanization, sharing information has never been easier thanks to globally-adopted platforms for digital communication. The resulting output of massive amounts of user-generated data can be used to enhance our understanding of significant societal issues particularly for urbanizing areas. In order to better analyze protest behavior, we enhanced the GSR dataset and manually labeled all the images. We used deep learning techniques to analyze social media data to detect social unrest through image classification, which performed good in predict multi-attributes, then also used map visualization to display protest behaviors across the country.", "field": "cs", "label": 1}
{"text": "Title: Distributed convergence detection based on global residual error under asynchronous iterations\nAbstract: Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations, blocking communication requests are avoided, which makes it hard to isolate and handle any global vector. While some termination protocols were proposed for asynchronous iterations, only very few of them are based on global residual computation and guarantee effective convergence. But the most effective and efficient existing solutions feature two reduction operations, which constitutes an important factor of termination delay. In this paper, we present new, non-intrusive, protocols to compute a residual error under asynchronous iterations, requiring only one reduction operation. Various communication models show that some heuristics can even be introduced and formally evaluated. Extensive experiments with up to 5600 processor cores confirm the practical effectiveness and efficiency of our approach.", "field": "cs", "label": 0}
{"text": "Title: Approximating Single-Source Personalized PageRank with Absolute Error Guarantees\nAbstract: Personalized PageRank (PPR) is an extensively studied and applied node proximity measure in graphs. For a pair of nodes $s$ and $t$ on a graph $G=(V,E)$, the PPR value $\\pi(s,t)$ is defined as the probability that an $\\alpha$-discounted random walk from $s$ terminates at $t$, where the walk terminates with probability $\\alpha$ at each step. We study the classic Single-Source PPR query, which asks for PPR approximations from a given source node $s$ to all nodes in the graph. Specifically, we aim to provide approximations with absolute error guarantees, ensuring that the resultant PPR estimates $\\hat{\\pi}(s,t)$ satisfy $\\max_{t\\in V}\\big|\\hat{\\pi}(s,t)-\\pi(s,t)\\big|\\le\\varepsilon$ for a given error bound $\\varepsilon$. We propose an algorithm that achieves this with high probability, with an expected running time of - $\\widetilde{O}\\big(\\sqrt{m}/\\varepsilon\\big)$ for directed graphs, where $m=|E|$; - $\\widetilde{O}\\big(\\sqrt{d_{\\mathrm{max}}}/\\varepsilon\\big)$ for undirected graphs, where $d_{\\mathrm{max}}$ is the maximum node degree in the graph; - $\\widetilde{O}\\left(n^{\\gamma-1/2}/\\varepsilon\\right)$ for power-law graphs, where $n=|V|$ and $\\gamma\\in\\left(\\frac{1}{2},1\\right)$ is the extent of the power law. These sublinear bounds improve upon existing results. We also study the case when degree-normalized absolute error guarantees are desired, requiring $\\max_{t\\in V}\\big|\\hat{\\pi}(s,t)/d(t)-\\pi(s,t)/d(t)\\big|\\le\\varepsilon_d$ for a given error bound $\\varepsilon_d$, where the graph is undirected and $d(t)$ is the degree of node $t$. We give an algorithm that provides this error guarantee with high probability, achieving an expected complexity of $\\widetilde{O}\\left(\\sqrt{\\sum_{t\\in V}\\pi(s,t)/d(t)}\\big/\\varepsilon_d\\right)$. This improves over the previously known $O(1/\\varepsilon_d)$ complexity.", "field": "cs", "label": 0}
{"text": "Title: Capacity of Lorentzian polynomials and distance to binomial distributions\nAbstract: In this paper we study the capacity of Lorentzian polynomials. We give a new proof of a theorem of Br\\\"and\\'en, Leake and Pak. Our approach is probabilistic in nature and uses a lemma about a certain distance of binomial distributions to distributions with fixed expected value.", "field": "math", "label": 1}
{"text": "Title: Power-law bounds for increasing subsequences in Brownian separable permutons and homogeneous sets in Brownian cographons\nAbstract: The Brownian separable permutons are a one-parameter family -- indexed by $p\\in(0,1)$ -- of universal limits of random constrained permutations. We show that for each $p\\in (0,1)$, there are explicit constants $1/2 < \\alpha_*(p) \\leq \\beta^*(p) < 1$ such that the length of the longest increasing subsequence in a random permutation of size $n$ sampled from the Brownian separable permuton is between $n^{\\alpha_*(p) - o(1)}$ and $n^{\\beta^*(p) + o(1)}$ with probability tending to 1 as $n\\to\\infty$. In the symmetric case $p=1/2$, we have $\\alpha_*(p) \\approx 0.812$ and $\\beta^*(p)\\approx 0.975$. We present numerical simulations which suggest that the lower bound $\\alpha_*(p)$ is close to optimal in the whole range $p\\in(0,1)$. Our results work equally well for the closely related Brownian cographons. In this setting, we show that for each $p\\in (0,1)$, the size of the largest clique (resp. independent set) in a random graph on $n$ vertices sampled from the Brownian cographon is between $n^{\\alpha_*(p) - o(1)}$ and $n^{\\beta^*(p) + o(1)}$ (resp. $n^{\\alpha_*(1-p) - o(1)}$ and $n^{\\beta^*(1-p) + o(1)}$) with probability tending to 1 as $n\\to\\infty$. Our proofs are based on the analysis of a fragmentation process embedded in a Brownian excursion introduced by Bertoin (2002). We expect that our techniques can be extended to prove similar bounds for uniform separable permutations and uniform cographs.", "field": "math", "label": 0}
{"text": "Title: A convergence result for a local planning problem for mean field games and rigorous proof of a Freidlin-Ventchel-type Large Deviations Principle for the $1+1$ KPZ equation\nAbstract: We prove the convergence of a viscous approximation to an one dimensional local mean field type planning problem with singular initial and terminal measures. Then we use this result to give a rigorous proof to a Freidlin-Ventchel-type Large Deviations Principle for the height of the $1+1$ KPZ equation.", "field": "math", "label": 0}
{"text": "Title: On the Stability Functional for Conservation Laws\nAbstract: This note is devoted to the explicit construction of a functional defined on all pairs of $\\L1$ functions with small total variation, which is equivalent to the $\\L1$ distance and non increasing along the trajectories of a given system of conservation laws. Two different constructions are provided, yielding an extension of the original stability functional by Bressan, Liu and Yang.", "field": "math", "label": 1}
{"text": "Title: Large Language Model Capabilities in Perioperative Risk Prediction and Prognostication\nAbstract: We investigate whether general-domain large language models such as GPT-4 Turbo can perform risk stratification and predict post-operative outcome measures using a description of the procedure and a patient's clinical notes derived from the electronic health record. We examine predictive performance on 8 different tasks: prediction of ASA Physical Status Classification, hospital admission, ICU admission, unplanned admission, hospital mortality, PACU Phase 1 duration, hospital duration, and ICU duration. Few-shot and chain-of-thought prompting improves predictive performance for several of the tasks. We achieve F1 scores of 0.50 for ASA Physical Status Classification, 0.81 for ICU admission, and 0.86 for hospital mortality. Performance on duration prediction tasks were universally poor across all prompt strategies. Current generation large language models can assist clinicians in perioperative risk stratification on classification tasks and produce high-quality natural language summaries and explanations.", "field": "cs", "label": 0}
{"text": "Title: Singular SPDEs in domains with boundaries\nAbstract: We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent. Math. 198, 2014) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a \"boundary renormalisation\" takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf-Cole solution to the KPZ equation with a different boundary condition.", "field": "math", "label": 1}
{"text": "Title: Characters and chromatic symmetric functions\nAbstract: Let $P$ be a poset, $inc(P)$ its incomparability graph, and $X_{inc(P)}$ the corresponding chromatic symmetric function, as defined by Stanley in {\\em Adv. Math.}, {\\bf 111} (1995) pp.~166--194. Certain conditions on $P$ imply that the expansions of $X_{inc(P)}$ in standard symmetric function bases yield coefficients which have simple combinatorial interpretations. By expressing these coefficients as character evaluations, we extend several of these interpretations to {\\em all} posets $P$. Consequences include new combinatorial interpretations of the permanent and other immanants of totally nonnegative matrices, and of the sum of elementary coefficients in the Shareshian-Wachs chromatic quasisymmetric function $X_{inc(P),q}$ when $P$ is a unit interval order.", "field": "math", "label": 1}
{"text": "Title: Strong Equivalence Relations for Iterated Models\nAbstract: The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical representation, has become standard for applying topological reasoning to distributed computing. Its modular structure makes it easier to analyze than the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS). It is known that AS and IIS are equivalent with respect to \\emph{wait-free task} computability: a distributed task is solvable in AS if and only if it solvable in IIS. We observe, however, that this equivalence is not sufficient in order to explore solvability of tasks in \\emph{sub-models} of AS (i.e. proper subsets of its runs) or computability of \\emph{long-lived} objects, and a stronger equivalence relation is needed. In this paper, we consider \\emph{adversarial} sub-models of AS and IIS specified by the sets of processes that can be \\emph{correct} in a model run. We show that AS and IIS are equivalent in a strong way: a (possibly long-lived) object is implementable in AS under a given adversary if and only if it is implementable in IIS under the same adversary. %This holds whether the object is one-shot or long-lived. Therefore, the computability of any object in shared memory under an adversarial AS scheduler can be equivalently investigated in IIS.", "field": "cs", "label": 1}
{"text": "Title: Sharp weighted inequalities for iterated commutators of a class of multilinear operators\nAbstract: In this paper, the sharp quantitative weighted bounds for the iterated commutators of a class of multilinear operators were systematically studied. This class of operators contains multilinear Calder\\'{o}n-Zygmund operators, multilinear Fourier integral operators, and multilinear Littlewood-Paley square operators as its typical examples. These were done only under two pretty much general assumptions of pointwise sparse domination estimates. We first established local decay estimates and quantitative weak $A_\\infty$ decay estimates for iterated commutators of this class of operators. Then, we considered the corresponding Coifman-Fefferman inequalities and the mixed weak type estimates associated with Sawyer's conjecture. Beyond that, the Fefferman-Stein inequalities with respect to arbitrary weights and weighted modular inequalities were also given. As applications, it was shown that all the conclusions aforementioned can be applied to multilinear $\\omega$-Calder\\'{o}n-Zygmund operators, multilinear maximal singular integral operators, multilinear pseudo-differential operators, Stein's square functions, and higher order Calder\\'{o}n commutators.", "field": "math", "label": 0}
{"text": "Title: Morita Equivalence and Spectral Triples on Noncommutative Orbifolds\nAbstract: Let $G$ be a finite group. Noncommutative geometry of unital $G$-algebras is studied. A geometric structure is determined by a spectral triple on the crossed product algebra associated with the group action. This structure is to be viewed as a representative of a noncommutative orbifold. Based on a study of classical orbifold groupoids, a Morita equivalence for the crossed product spectral triples is developed. Noncommutative orbifolds are Morita equivalence classes of the crossed product spectral triples. As a special case of this Morita theory one can study freeness of the $G$-action on the noncommutative level. In the case of a free action, the crossed product formalism reduced to the usual spectral triple formalism on the algebra of $G$-invariant functions.", "field": "math", "label": 1}
{"text": "Title: Quantum Team Logic and Bell's Inequalities\nAbstract: A logical approach to Bell's Inequalities of quantum mechanics has been introduced by Abramsky and Hardy [2]. We point out that the logical Bell's Inequalities of [2] are provable in the probability logic of Fagin, Halpern and Megiddo [4]. Since it is now considered empirically established that quantum mechanics violates Bell's Inequalities, we introduce a modified probability logic, that we call quantum team logic, in which Bell's Inequalities are not provable, and prove a Completeness Theorem for this logic. For this end we generalise the team semantics of dependence logic [7] first to probabilistic team semantics, and then to what we call quantum team semantics.", "field": "math", "label": 1}
{"text": "Title: Balancing Specialization and Adaptation in a Transforming Scientific Landscape\nAbstract: How scientists navigate between the need to capitalize on their prior knowledge by specializing, and the urge to adapt to evolving research opportunities? Drawing from diverse perspectives on adaptation, in particular from institutional change and cultural evolution, this paper proposes a Bayesian model of the evolution of scientists' research portfolios in response to transformations in their field. The model relies on scientific abstracts and authorship data to evaluate the influence of intellectual, social, and institutional resources on scientists' trajectories within a cohort of $2\\,195$ high-energy physicists between 2000 and 2019. The reallocation of research efforts is shown to be structured by learning costs, thus enhancing the utility of the scientific capital disseminated among scientists. Two dimensions of social capital, namely ``diversity'' and ``power'', have opposite effects on the magnitude of change in scientists' research interests: while ``diversity'' disrupts and expands research interests, ``power'' stabilizes physicists' research agendas -- as does institutional stability. Social capital plays a more crucial role in shifts between cognitively distant research areas.", "field": "cs", "label": 0}
{"text": "Title: A Novel Dual-Stage Evolutionary Algorithm for Finding Robust Solutions\nAbstract: In robust optimization problems, the magnitude of perturbations is relatively small. Consequently, solutions within certain regions are less likely to represent the robust optima when perturbations are introduced. Hence, a more efficient search process would benefit from increased opportunities to explore promising regions where global optima or good local optima are situated. In this paper, we introduce a novel robust evolutionary algorithm named the dual-stage robust evolutionary algorithm (DREA) aimed at discovering robust solutions. DREA operates in two stages: the peak-detection stage and the robust solution-searching stage. The primary objective of the peak-detection stage is to identify peaks in the fitness landscape of the original optimization problem. Conversely, the robust solution-searching stage focuses on swiftly identifying the robust optimal solution using information obtained from the peaks discovered in the initial stage. These two stages collectively enable the proposed DREA to efficiently obtain the robust optimal solution for the optimization problem. This approach achieves a balance between solution optimality and robustness by separating the search processes for optimal and robust optimal solutions. Experimental results demonstrate that DREA significantly outperforms five state-of-the-art algorithms across 18 test problems characterized by diverse complexities. Moreover, when evaluated on higher-dimensional robust optimization problems (100-$D$ and 200-$D$), DREA also demonstrates superior performance compared to all five counterpart algorithms.", "field": "cs", "label": 0}
{"text": "Title: Fast and Continual Learning for Hybrid Control Policies using Generalized Benders Decomposition\nAbstract: Hybrid model predictive control with both continuous and discrete variables is widely applicable to robotic control tasks, especially those involving contact with the environment. Due to the combinatorial complexity, the solving speed of hybrid MPC can be insufficient for real-time applications. In this paper, we proposed a hybrid MPC solver based on Generalized Benders Decomposition (GBD). The algorithm enumerates and stores cutting planes online inside a finite buffer. After a short cold-start phase, the stored cuts provide warm-starts for the new problem instances to enhance the solving speed. Despite the disturbance and randomly changing environment, the solving speed maintains. Leveraging on the sparsity of feasibility cuts, we also propose a fast algorithm for Benders master problems. Our solver is validated through controlling a cart-pole system with randomly moving soft contact walls, and a free-flying robot navigating around obstacles. The results show that with significantly less data than previous works, the solver reaches competitive speeds to the off-the-shelf solver Gurobi despite the Python overhead.", "field": "cs", "label": 0}
{"text": "Title: An Experimental Study of ILP Formulations for the Longest Induced Path Problem\nAbstract: Given a graph $G=(V,E)$, the longest induced path problem asks for a maximum cardinality node subset $W\\subseteq V$ such that the graph induced by $W$ is a path. It is a long established problem with applications, e.g., in network analysis. We propose novel integer linear programming (ILP) formulations for the problem and discuss efficient implementations thereof. Comparing them with known formulations from literature, we prove that they are beneficial in theory, yielding stronger relaxations. Moreover, our experiments show their practical superiority.", "field": "cs", "label": 1}
{"text": "Title: On a class of stochastic hyperbolic equations with double characteristics\nAbstract: We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients of our partial differential operator depend polynomially on the space variables, while the noise is additive, white in time and coloured in space. We provide a sufficient condition on the spectral measure of the covariance functional describing the noise that allows for the existence of a random field solution for the resulting stochastic partial differential equation. Our approach is based on explicit computations for the fundamental solution of the partial differential operator and its Fourier transform.", "field": "math", "label": 1}
{"text": "Title: Representations of Lie groups\nAbstract: These are notes of a graduate course on representations of non-compact semisimple Lie groups given by the author at MIT.", "field": "math", "label": 0}
{"text": "Title: Where You Are Is Who You Are: User Identification by Matching Statistics\nAbstract: Most users of online services have unique behavioral or usage patterns. These behavioral patterns can be exploited to identify and track users by using only the observed patterns in the behavior. We study the task of identifying users from statistics of their behavioral patterns. Specifically, we focus on the setting in which we are given histograms of users' data collected during two different experiments. We assume that, in the first dataset, the users' identities are anonymized or hidden and that, in the second dataset, their identities are known. We study the task of identifying the users by matching the histograms of their data in the first dataset with the histograms from the second dataset. In recent works, the optimal algorithm for this user identification task is introduced. In this paper, we evaluate the effectiveness of this method on three different types of datasets and in multiple scenarios. Using datasets such as call data records, web browsing histories, and GPS trajectories, we show that a large fraction of users can be easily identified given only histograms of their data; hence these histograms can act as users' fingerprints. We also verify that simultaneous identification of users achieves better performance compared to one-by-one user identification. We show that using the optimal method for identification gives higher identification accuracy than heuristics-based approaches in practical scenarios. The accuracy obtained under this optimal method can thus be used to quantify the maximum level of user identification that is possible in such settings. We show that the key factors affecting the accuracy of the optimal identification algorithm are the duration of the data collection, the number of users in the anonymized dataset, and the resolution of the dataset. We analyze the effectiveness of k-anonymization in resisting user identification attacks on these datasets.", "field": "cs", "label": 1}
{"text": "Title: Efficient Checking of Timed Order Compliance Rules over Graph-encoded Event Logs\nAbstract: Validation of compliance rules against process data is a fundamental functionality for business process management. Over the years, the problem has been addressed for different types of process data, i.e., process models, process event data at runtime, and event logs representing historical execution. Several approaches have been proposed to tackle compliance checking over process logs. These approaches have been based on different data models and storage technologies including relational databases, graph databases, and proprietary formats. Graph-based encoding of event logs is a promising direction that turns several process analytics tasks into queries on the underlying graph. Compliance checking is one class of such analysis tasks. In this paper, we argue that encoding log data as graphs alone is not enough to guarantee efficient processing of queries on this data. Efficiency is important due to the interactive nature of compliance checking. Thus, compliance checking would benefit from sub-linear scanning of the data. Moreover, as more data are added, e.g., new batches of logs arrive, the data size should grow sub-linearly to optimize both the space of storage and time for querying. We propose two encoding methods using graph representation, realized in Neo4J, and show the benefits of these encoding on a special class of queries, namely timed order compliance rules. Compared to a baseline encoding, our experiments show up to 5x speed up in the querying time as well as a 3x reduction in the graph size.", "field": "cs", "label": 1}
{"text": "Title: Optimal Decay Estimates for the Radially Symmetric Compressible Navier-Stokes Equations\nAbstract: We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution. This allows us to obtain a bound from below for the time-decay of the solution in $L^\\infty$, proving that our decay estimate in that space is sharp. The decay rate is the same as that of the linear problem for curl-free flow. We also obtain an estimate for a scalar system related to curl-free solutions to the compressible Navier-Stokes equations in a weighted Lebesgue space.", "field": "math", "label": 0}
{"text": "Title: Adams spectral sequences and Franke's algebraicity conjecture\nAbstract: To any well-behaved homology theory we associate a derived $\\infty$-category which encodes its Adams spectral sequence. As applications, we prove a conjecture of Franke on algebraicity of certain homotopy categories and establish homotopy-coherent monoidality of the Adams filtration.", "field": "math", "label": 1}
{"text": "Title: Non-contractible closed geodesics on compact Finsler space forms without self-intersections\nAbstract: Let $M=S^n/ \\Gamma$ and $h \\in \\pi_1(M)$ be a non-trivial element of finite order $p$, where the integers $n, p\\geq2$ and $\\Gamma$ is a finite abelian group which acts on the sphere freely and isometrically. Therefore $M$ is diffeomorphic to a compact space form which is a typical non-simply connected manifold. For $\\Gamma =\\mathbb{Z}_2$, we obtain there are at least two non-contractible closed geodesics on $\\mathbb{R}P^2$ whose lengths are bounded by geometry of the manifold from above. Moreover, suppose $g_0$ is standard Riemannian metric. We prove that there exists at least $n$ prime non-contractible closed geodesics on $(M,F)$ of prescribed class $[h]$ without self-intersections, provided $F^2 <(\\frac{\\lambda+1}{\\lambda})^2 g_0$ and \\[(\\frac{\\lambda}{\\lambda+1})^2 < K \\leq 1 \\text{ for $n$ is odd or }\\; 0<K \\leq 1 \\text{ for $n$ is even}, \\] where $\\lambda$ is the reversibility and $K$ is the flag curvature. Some results on stability are obtained.", "field": "math", "label": 0}
{"text": "Title: Lookahead: An Inference Acceleration Framework for Large Language Model with Lossless Generation Accuracy\nAbstract: As Large Language Models (LLMs) have made significant advancements across various tasks, such as question answering, translation, text summarization, and dialogue systems, the need for accuracy in information becomes crucial, especially for serious financial products serving billions of users like Alipay. To address this, Alipay has developed a Retrieval-Augmented Generation (RAG) system that grounds LLMs on the most accurate and up-to-date information. However, for a real-world product serving millions of users, the inference speed of LLMs becomes a critical factor compared to a mere experimental model. Hence, this paper presents a generic framework for accelerating the inference process, resulting in a substantial increase in speed and cost reduction for our RAG system, with lossless generation accuracy. In the traditional inference process, each token is generated sequentially by the LLM, leading to a time consumption proportional to the number of generated tokens. To enhance this process, our framework, named \\textit{lookahead}, introduces a \\textit{multi-branch} strategy. Instead of generating a single token at a time, we propose a \\textit{Trie-based Retrieval} (TR) process that enables the generation of multiple branches simultaneously, each of which is a sequence of tokens. Subsequently, for each branch, a \\textit{Verification and Accept} (VA) process is performed to identify the longest correct sub-sequence as the final output. Our strategy offers two distinct advantages: (1) it guarantees absolute correctness of the output, avoiding any approximation algorithms, and (2) the worst-case performance of our approach is equivalent to the conventional process. We conduct extensive experiments to demonstrate the significant improvements achieved by applying our inference acceleration framework. Code is avaliable: https://github.com/alipay/PainlessInferenceAcceleration.", "field": "cs", "label": 0}
{"text": "Title: Closed categories vs. closed multicategories\nAbstract: We prove that the 2-category of closed categories of Eilenberg and Kelly is equivalent to a suitable full 2-subcategory of the 2-category of closed multicategories.", "field": "math", "label": 1}
{"text": "Title: Unsupervised Learning of the Total Variation Flow\nAbstract: The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images such as sharp edges and enables spectral, scale, and texture analysis. The standard numerical approach for TV flow requires solving multiple non-smooth optimisation problems. Even with state-of-the-art convex optimisation techniques, this is often prohibitively expensive and strongly motivates the use of alternative, faster approaches. Inspired by and extending the framework of physics-informed neural networks (PINNs), we propose the TVflowNET, a neural network approach to compute the solution of the TV flow given an initial image and a time instance. We significantly speed up the computation time by more than one order of magnitude and show that the TVflowNET approximates the TV flow solution with high fidelity. This is a preliminary report, more details are to follow.", "field": "cs", "label": 1}
{"text": "Title: Conformal invariants of $3$-Braids and Counting Functions\nAbstract: We consider a conformal invariant of braids, the extremal length with totally real horizontal boundary values $\\lambda_{tr}$. The invariant descends to an invariant of elements of $\\mathcal{B}_n\\diagup\\mathcal{Z}_n$, the braid group modulo its center. We prove that the number of elements of $\\mathcal{B}_3\\diagup\\mathcal{Z}_3$ of positive $\\lambda_{tr}$ grows exponentially. The estimate applies to obtain effective finiteness theorems in the spirit of the geometric Shafarevich conjecture over Riemann surfaces of second kind. As a corollary we obtain another proof of the exponential growth of the number of conjugacy classes of $\\mathcal{B}_3\\diagup\\mathcal{Z}_3$ with positive entropy not exceeding $Y$.", "field": "math", "label": 1}
{"text": "Title: Almost dominant generalized slices and convolution diagrams over them\nAbstract: Let $G$ be a connected reductive complex algebraic group with a maximal torus $T$. We denote by $\\Lambda$ the cocharacter lattice of $(T,G)$. Let $\\Lambda^+ \\subset \\Lambda$ be the submonoid of dominant coweights. For $\\lambda \\in \\Lambda^+,\\,\\mu \\in \\Lambda,\\,\\mu \\leqslant \\lambda$, in arXiv:1604.03625, authors defined a generalized transversal slice $\\overline{\\mathcal{W}}^\\lambda_\\mu$. This is an algebraic variety of the dimension $\\langle 2\\rho^{\\vee}, \\lambda-\\mu \\rangle$, where $2\\rho^{\\vee}$ is the sum of positive roots of $G$. In this paper, we construct an isomorphism $\\overline{\\mathcal{W}}^\\lambda_\\mu \\simeq \\overline{\\mathcal{W}}^\\lambda_{\\mu^+} \\times {\\mathbb{A}}^{\\langle 2\\rho^{\\vee},\\, \\mu^+-\\mu\\rangle}$ for $\\mu \\in \\Lambda$ such that $\\langle \\alpha^{\\vee},\\mu\\rangle \\geqslant -1$ for any positive root $\\alpha^{\\vee}$, here $\\mu^+ \\in W\\mu$ is the dominant representative in the Weyl group orbit of $\\mu$. We consider the example when $\\lambda$ is minuscule, $\\mu \\in W\\lambda$ and describe natural coordinates, Poisson structure on $\\overline{\\mathcal{W}}^\\lambda_\\mu \\simeq {\\mathbb{A}}^{\\langle 2\\rho^\\vee,\\,\\lambda-\\mu \\rangle}$ and its $T\\times {\\mathbb{C}}^\\times$-character. We apply these results to compute $T \\times {\\mathbb{C}}^\\times$-characters of tangent spaces at fixed points of convolution diagrams $\\widetilde{\\mathcal{W}}^{\\underline{\\lambda}}_\\mu$ with minuscule $\\lambda_i$. We also apply our results to construct open coverings by affine spaces of convolution diagrams $\\widetilde{\\mathcal{W}}^{\\underline{\\lambda}}_\\mu$ over slices with $\\mu$ such that $\\langle \\alpha^{\\vee},\\mu\\rangle \\geqslant -1$ for any positive root $\\alpha^{\\vee}$ and minuscule $\\lambda_i$ and to compute Poincar\\'e polynomials of such convolution diagrams $\\widetilde{\\mathcal{W}}^{\\underline{\\lambda}}_{\\mu}$.", "field": "math", "label": 1}
{"text": "Title: Hurewicz sets of reals without perfect subsets\nAbstract: We show that even for subsets X of the real line which do not contain perfect sets, the Hurewicz property does not imply the property S1(Gamma,Gamma), asserting that for each countable family of open gamma-covers of X, there is a choice function whose image is a gamma-cover of X. This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszynski and Tsaban, and implies that for C_p(X), the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskii's property alpha_2.", "field": "math", "label": 1}
{"text": "Title: Parametric robust structured control design\nAbstract: We present a new approach to parametric robust controller design, where we compute controllers of arbitrary order and structure which minimize the worst-case $H_\\infty$ norm over a pre-specified set of uncertain parameters. At the core of our method is a nonsmooth minimization method tailored to functions which are semi-infinite minima of smooth functions. A rich test bench and a more detailed example illustrate the potential of the technique, which can deal with complex problems involving multiple possibly repeated uncertain parameters.", "field": "math", "label": 1}
{"text": "Title: Towards Multi-Objective High-Dimensional Feature Selection via Evolutionary Multitasking\nAbstract: Evolutionary Multitasking (EMT) paradigm, an emerging research topic in evolutionary computation, has been successfully applied in solving high-dimensional feature selection (FS) problems recently. However, existing EMT-based FS methods suffer from several limitations, such as a single mode of multitask generation, conducting the same generic evolutionary search for all tasks, relying on implicit transfer mechanisms through sole solution encodings, and employing single-objective transformation, which result in inadequate knowledge acquisition, exploitation, and transfer. To this end, this paper develops a novel EMT framework for multiobjective high-dimensional feature selection problems, namely MO-FSEMT. In particular, multiple auxiliary tasks are constructed by distinct formulation methods to provide diverse search spaces and information representations and then simultaneously addressed with the original task through a multi-slover-based multitask optimization scheme. Each task has an independent population with task-specific representations and is solved using separate evolutionary solvers with different biases and search preferences. A task-specific knowledge transfer mechanism is designed to leverage the advantage information of each task, enabling the discovery and effective transmission of high-quality solutions during the search process. Comprehensive experimental results demonstrate that our MO-FSEMT framework can achieve overall superior performance compared to the state-of-the-art FS methods on 26 datasets. Moreover, the ablation studies verify the contributions of different components of the proposed MO-FSEMT.", "field": "cs", "label": 0}
{"text": "Title: A Hybrid Neural Coding Approach for Pattern Recognition with Spiking Neural Networks\nAbstract: Recently, brain-inspired spiking neural networks (SNNs) have demonstrated promising capabilities in solving pattern recognition tasks. However, these SNNs are grounded on homogeneous neurons that utilize a uniform neural coding for information representation. Given that each neural coding scheme possesses its own merits and drawbacks, these SNNs encounter challenges in achieving optimal performance such as accuracy, response time, efficiency, and robustness, all of which are crucial for practical applications. In this study, we argue that SNN architectures should be holistically designed to incorporate heterogeneous coding schemes. As an initial exploration in this direction, we propose a hybrid neural coding and learning framework, which encompasses a neural coding zoo with diverse neural coding schemes discovered in neuroscience. Additionally, it incorporates a flexible neural coding assignment strategy to accommodate task-specific requirements, along with novel layer-wise learning methods to effectively implement hybrid coding SNNs. We demonstrate the superiority of the proposed framework on image classification and sound localization tasks. Specifically, the proposed hybrid coding SNNs achieve comparable accuracy to state-of-the-art SNNs, while exhibiting significantly reduced inference latency and energy consumption, as well as high noise robustness. This study yields valuable insights into hybrid neural coding designs, paving the way for developing high-performance neuromorphic systems.", "field": "cs", "label": 0}
{"text": "Title: On the 2D Yang-Mills/Hurwitz Correspondence\nAbstract: In this paper, we show that in the large $N$ limit two-dimensional Yang-Mills theory with $U(N)$ gauge group becomes mixed Hurwitz theory, in the sense that the $1/N$ expansion of the chiral partition function receives contributions from both classical and monotone Hurwitz theory for all but finitely many compact orientable spacetimes.", "field": "math", "label": 0}
{"text": "Title: Strong Products of Hypergraphs: Unique Prime Factorization Theorems and Algorithms\nAbstract: It is well-known that all finite connected graphs have a unique prime factor decomposition (PFD) with respect to the strong graph product which can be computed in polynomial time. Essential for the PFD computation is the construction of the so-called Cartesian skeleton of the graphs under investigation. In this contribution, we show that every connected thin hypergraph H has a unique prime factorization with respect to the normal and strong (hypergraph) product. Both products coincide with the usual strong graph product whenever H is a graph. We introduce the notion of the Cartesian skeleton of hypergraphs as a natural generalization of the Cartesian skeleton of graphs and prove that it is uniquely defined for thin hypergraphs. Moreover, we show that the Cartesian skeleton of hypergraphs can be determined in O(|E|^2) time and that the PFD can be computed in O(|V|^2|E|) time, for hypergraphs H = (V,E) with bounded degree and bounded rank.", "field": "cs", "label": 1}
{"text": "Title: Significance of Anatomical Constraints in Virtual Try-On\nAbstract: The system of Virtual Try-ON (VTON) allows a user to try a product virtually. In general, a VTON system takes a clothing source and a person's image to predict the try-on output of the person in the given clothing. Although existing methods perform well for simple poses, in case of bent or crossed arms posture or when there is a significant difference between the alignment of the source clothing and the pose of the target person, these methods fail by generating inaccurate clothing deformations. In the VTON methods that employ Thin Plate Spline (TPS) based clothing transformations, this mainly occurs for two reasons - (1)~the second-order smoothness constraint of TPS that restricts the bending of the object plane. (2)~Overlaps among different clothing parts (e.g., sleeves and torso) can not be modeled by a single TPS transformation, as it assumes the clothing as a single planar object; therefore, disregards the independence of movement of different clothing parts. To this end, we make two major contributions. Concerning the bending limitations of TPS, we propose a human AnaTomy-Aware Geometric (ATAG) transformation. Regarding the overlap issue, we propose a part-based warping approach that divides the clothing into independently warpable parts to warp them separately and later combine them. Extensive analysis shows the efficacy of this approach.", "field": "cs", "label": 0}
{"text": "Title: Good Things Come to Those Who Swap Objects on Paths\nAbstract: We study a simple exchange market, introduced by Gourv\\'{e}s, Lesca and Wilczynski (IJCAI-17), where every agent initially holds a single object. The agents have preferences over the objects, and two agents may swap their objects if they both prefer the object of the other agent. The agents live in an underlying social network that governs the structure of the swaps: Two agents can only swap their objects if they are adjacent. We investigate the REACHABLE OBJECT problem, which asks whether a given starting situation can ever lead, by means of a sequence of swaps, to a situation where a given agent obtains a given object. Our results answer several central open questions on the complexity of REACHABLE OBJECT. First, the problem is polynomial-time solvable if the social network is a path. Second, the problem is NP-hard on cliques and generalized caterpillars. Finally, we establish a three-versus-four dichotomy result for preference lists of bounded length: The problem is easy if all preference lists have length at most three, and the problem becomes NP-hard even if all agents have preference lists of length at most four.", "field": "cs", "label": 1}
{"text": "Title: Enabling Digitalization in Modular Robotic Systems Integration\nAbstract: Integrating robot systems into manufacturing lines is a time-consuming process. In the era of digitalization, the research and development of new technologies is crucial for improving integration processes. Numerous challenges, including the lack of standardization, as well as intricate stakeholder relationships, complicate the process of robotic systems integration. This process typically consists of acquisition, integration, and deployment of the robot systems. This thesis focuses on three areas that help automate and simplify robotic systems integration. In the first area, related to acquisition, a constraint-based configurator is demonstrated that resolves compatibility challenges between robot devices, and automates the configuration process. This reduces the risk of integrating incompatible devices and decreases the need for experts during the configuration phase. In the second area, related to integration, the interoperable modeling format, Unified Robot Description Format (URDF), is investigated, where a detailed analysis is performed, revealing significant inconsistencies and critical improvements. This format is widely used for kinematic modeling and 3D visualization of robots, and its models can be reused across simulation tools. Improving this format benefits a wide range of users, including robotics engineers, researchers, and students. In the third area, related to deployment, Digital Twins (DTs) for robot systems are explored, as these improve efficiency and reduce downtime. A comprehensive literature review of DTs is conducted, and a case study of modular robot systems is developed. This research can accelerate the adoption of DTs in the robotics industry. These insights and approaches improve the process of robotic systems integration, offering valuable contributions that future research can build upon, ultimately driving efficiency, and reducing costs.", "field": "cs", "label": 0}
{"text": "Title: A survey on set-theoretical solutions to the pentagon equation\nAbstract: This survey aims to collect the main results of the theory of the set-theoretical solutions to the pentagon equation obtained up to now in the literature. In particular, we present some classes of these solutions and raise some questions.", "field": "math", "label": 0}
{"text": "Title: MULTI-CASE: A Transformer-based Ethics-aware Multimodal Investigative Intelligence Framework\nAbstract: AI-driven models are increasingly deployed in operational analytics solutions, for instance, in investigative journalism or the intelligence community. Current approaches face two primary challenges: ethical and privacy concerns, as well as difficulties in efficiently combining heterogeneous data sources for multimodal analytics. To tackle the challenge of multimodal analytics, we present MULTI-CASE, a holistic visual analytics framework tailored towards ethics-aware and multimodal intelligence exploration, designed in collaboration with domain experts. It leverages an equal joint agency between human and AI to explore and assess heterogeneous information spaces, checking and balancing automation through Visual Analytics. MULTI-CASE operates on a fully-integrated data model and features type-specific analysis with multiple linked components, including a combined search, annotated text view, and graph-based analysis. Parts of the underlying entity detection are based on a RoBERTa-based language model, which we tailored towards user requirements through fine-tuning. An overarching knowledge exploration graph combines all information streams, provides in-situ explanations, transparent source attribution, and facilitates effective exploration. To assess our approach, we conducted a comprehensive set of evaluations: We benchmarked the underlying language model on relevant NER tasks, achieving state-of-the-art performance. The demonstrator was assessed according to intelligence capability assessments, while the methodology was evaluated according to ethics design guidelines. As a case study, we present our framework in an investigative journalism setting, supporting war crime investigations. Finally, we conduct a formative user evaluation with domain experts in law enforcement. Our evaluations confirm that our framework facilitates human agency and steering in security-sensitive applications.", "field": "cs", "label": 0}
{"text": "Title: Co-compact Gabor systems on locally compact abelian groups\nAbstract: In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We formulate the concept of rationally oversampling of Gabor systems in an LCA group and prove corresponding characterization results via the Zak transform. From these results we derive non-existence results for critically sampled continuous Gabor frames. We obtain general characterizations in time and in frequency domain of when two Gabor generators yield dual frames. Moreover, we prove the Walnut and Janssen representation of the Gabor frame operator and consider the Wexler-Raz biorthogonality relations for dual generators. Finally, we prove the duality principle for Gabor frames. Unlike most duality results on Gabor systems, we do not rely on the fact that the translation and modulation groups are discrete and co-compact subgroups. Our results only rely on the assumption that either one of the translation and modulation group (in some cases both) are co-compact subgroups of the time and frequency domain. This presentation offers a unified approach to the study of continuous and the discrete Gabor frames.", "field": "math", "label": 1}
{"text": "Title: Classification of algebras of level two in the variety of nilpotent algebras and Leibniz algebras\nAbstract: This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the variety of Leibniz algebras. It is shown that, up to isomorphism, there exist three Leibniz algebras of level two, one of which is solvable, and two of which are nilpotent. Moreover we describe all algebras of level two in the variety of nilpotent algebras.", "field": "math", "label": 1}
{"text": "Title: Leader Election Problem Versus Pattern Formation Problem\nAbstract: Leader election and arbitrary pattern formation are funda- mental tasks for a set of autonomous mobile robots. The former consists in distinguishing a unique robot, called the leader. The latter aims in arranging the robots in the plane to form any given pattern. The solv- ability of both these tasks turns out to be necessary in order to achieve more complex tasks. In this paper, we study the relationship between these two tasks in a model, called CORDA, wherein the robots are weak in several aspects. In particular, they are fully asynchronous and they have no direct means of communication. They cannot remember any previous observation nor computation performed in any previous step. Such robots are said to be oblivious. The robots are also uniform and anonymous, i.e, they all have the same program using no global parameter (such as an identity) allowing to differentiate any of them. Moreover, we assume that none of them share any kind of common coordinate mechanism or common sense of direction and we discuss the influence of a common handedness (i.e., chirality). In such a system, Flochini et al. proved in [11] that it is possible to elect a leader for n \\geq 3 robots if it is possible to form any pattern for n \\geq 3. In this paper, we show that the converse is true for n \\geq 4 when the robots share a common handedness and for n \\geq 5 when they do not. Thus, we deduce that with chirality (resp. without chirality) both problems are equivalent for n \\geq 4 (resp. n \\geq 5) in CORDA.", "field": "cs", "label": 1}
{"text": "Title: Supersonic flow past an airfoil\nAbstract: We consider a supersonic flow past an airfoil in the context of the steady, isentropic and irrotational compressible Euler equations. We show that for appropriate data, either a shock forms, in which case certain derivatives of the solution blow up, or a sonic line forms, which translates to the fact that the hyperbolic character of the equations degenerates.", "field": "math", "label": 0}
{"text": "Title: Emerging Language Spaces Learned From Massively Multilingual Corpora\nAbstract: Translations capture important information about languages that can be used as implicit supervision in learning linguistic properties and semantic representations. In an information-centric view, translated texts may be considered as semantic mirrors of the original text and the significant variations that we can observe across various languages can be used to disambiguate a given expression using the linguistic signal that is grounded in translation. Parallel corpora consisting of massive amounts of human translations with a large linguistic variation can be applied to increase abstractions and we propose the use of highly multilingual machine translation models to find language-independent meaning representations. Our initial experiments show that neural machine translation models can indeed learn in such a setup and we can show that the learning algorithm picks up information about the relation between languages in order to optimize transfer leaning with shared parameters. The model creates a continuous language space that represents relationships in terms of geometric distances, which we can visualize to illustrate how languages cluster according to language families and groups. Does this open the door for new ideas of data-driven language typology with promising models and techniques in empirical cross-linguistic research?", "field": "cs", "label": 1}
{"text": "Title: Signal Detection for Ultra-Massive MIMO: An Information Geometry Approach\nAbstract: In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori probability distribution of the transmitted symbol vector. Then, a maximization of the a posteriori marginals (MPM) for signal detection can be performed. With the information geometry theory, we calculate the approximations of the a posteriori marginals. It is formulated as an iterative m-projection process between submanifolds with different constraints. We then apply the central-limit-theorem (CLT) to simplify the calculation of the m-projection since the direct calculation of the m-projection is of exponential-complexity. With the CLT, we obtain an approximate solution of the m-projection, which is asymptotically accurate. Simulation results demonstrate that the proposed IGA-SD emerges as a promising and efficient method to implement the signal detector in ultra-massive MIMO systems.", "field": "cs", "label": 0}
{"text": "Title: QoE-oriented Dependent Task Scheduling under Multi-dimensional QoS Constraints over Distributed Networks\nAbstract: Task scheduling as an effective strategy can improve application performance on computing resource-limited devices over distributed networks. However, existing evaluation mechanisms fail to depict the complexity of diverse applications, which involve dependencies among tasks, computing resource requirements, and multi-dimensional quality of service (QoS) constraints. Furthermore, traditional QoS-oriented task scheduling strategies struggle to meet the performance requirements without considering differences in satisfaction and acceptance of application, leading application failures and resource wastage. To tackle these issues, a quality of experience (QoE) cost model is designed to evaluate application completion, depicting the relationship among application satisfaction, communications, and computing resources in the distributed networks. Specifically, considering the sensitivity and preference of QoS, we model the different dimensional QoS degradation cost functions for dependent tasks, which are then integrated into the QoE cost model. Based on the QoE model, the dependent task scheduling problem is formulated as the minimization of overall QoE cost, aiming to improve the application performance in the distributed networks, which is proven Np-hard. Moreover, a heuristic Hierarchical Multi-queue Task Scheduling Algorithm (HMTSA) is proposed to address the QoE-oriented task scheduling problem among multiple dependent tasks, which utilizes hierarchical multiple queues to determine the optimal task execution order and location according to different dimensional QoS priorities. Finally, extensive experiments demonstrate that the proposed algorithm can significantly improve the satisfaction of applications.", "field": "cs", "label": 0}
{"text": "Title: Identification of the Heat Transfer Coefficient Using an Inverse Heat Conduction Model\nAbstract: Inverse problems of recovering heat transfer coefficient from integral measurements are considered. The heat transfer coefficient occurs in the transmission conditions of imperfect contact type or the Robin type boundary conditions. It is representable as a finite part of the Fourier series with time dependent coefficients. The additional measurements are integrals of a solution multiplied by some weights. Existence and uniqueness of solutions in Sobolev classes are proven and the conditions on the data are sharp. These conditions include smoothness and consistency conditions on the data and additional conditions on the kernels of the integral operators used in additional measurements. The proof relies on a priori bounds and the contraction mapping principle. The existence and uniqueness theorems are local in time.", "field": "math", "label": 0}
{"text": "Title: A Non-Holonomic Systems Approach to Special Function Identities\nAbstract: We extend Zeilberger's approach to special function identities to cases that are not holonomic. The method of creative telescoping is thus applied to definite sums or integrals involving Stirling or Bernoulli numbers, incomplete Gamma function or polylogarithms, which are not covered by the holonomic framework. The basic idea is to take into account the dimension of appropriate ideals in Ore algebras. This unifies several earlier extensions and provides algorithms for summation and integration in classes that had not been accessible to computer algebra before.", "field": "cs", "label": 1}
{"text": "Title: Rigid Components of Random Graphs\nAbstract: The planar rigidity problem asks, given a set of m pairwise distances among a set P of n unknown points, whether it is possible to reconstruct P, up to a finite set of possibilities (modulo rigid motions of the plane). The celebrated Maxwell-Laman Theorem from Rigidity Theory says that, generically, the rigidity problem has a combinatorial answer: the underlying combinatorial structure must contain a spanning minimally-rigid graph (Laman graph). In the case where the system is not rigid, its inclusion-wise maximal rigid substructures (rigid components) are also combinatorially characterized via the Maxwell-Laman theorem, and may be found efficiently. Physicists have used planar combinatorial rigidity has been used to study the phase transition between liquid and solid in network glasses. The approach has been to generate a graph via a stochastic process and then experimentally analyze its rigidity properties. Of particular interest is the size of the largest rigid components. In this paper, we study the emergence of rigid components in an Erdos-Renyi random graph G(n,p), using the parameterization p=c/n for a fixed constant c>0. Our first result is that for all c>0, almost surely all rigid components have size 2, 3 or Omega(n). We also show that for c>4, almost surely the largest rigid components have size at least n/10. While the G(n,p) model is simpler than those appearing in the physics literature, these results are the first of this type where the distribution is over all graphs on n vertices and the expected number of edges is O(n).", "field": "math", "label": 1}
{"text": "Title: Open Gromov-Witten invariants from the Fukaya category\nAbstract: This paper proposes a framework to show that the Fukaya category of a symplectic manifold $X$ determines the open Gromov-Witten invariants of Lagrangians $L \\subset X$. We associate to an object in an $A_\\infty$-category an extension of the negative cyclic homology, called \\emph{relative cyclic homology}. We extend the Getzler-Gauss-Manin connection to relative cyclic homology. Then, we construct (under simplifying technical assumptions) a relative cyclic open-closed map, which maps the relative cyclic homology of a Lagrangian $L$ in the Fukaya category of a symplectic manifold $X$ to the $S^1$-equivariant relative quantum homology of $(X,L)$. Relative quantum homology is the dual to the relative quantum cohomology constructed by Solomon-Tukachinsky. This is an extension of quantum cohomology, and comes equipped with a connection extending the quantum connection. We prove that the relative open-closed map respects connections. As an application of this framework, we show, assuming a construction of the relative cyclic open-closed map in a broader technical setup, that the Fukaya category of a Calabi-Yau variety determines the open Gromov-Witten invariants with one interior marked point for any null-homologous Lagrangian brane.", "field": "math", "label": 1}
{"text": "Title: Advanced Determinant Calculus: A Complement\nAbstract: This is a complement to my previous article \"Advanced Determinant Calculus\" (S\\'eminaire Lotharingien Combin. 42 (1999), Article B42q, 67 pp.). In the present article, I share with the reader my experience of applying the methods described in the previous article in order to solve a particular problem from number theory (G. Almkvist, J. Petersson and the author, Experiment. Math. 12 (2003), 441-456). Moreover, I add a list of determinant evaluations which I consider as interesting, which have been found since the appearance of the previous article, or which I failed to mention there, including several conjectures and open problems.", "field": "math", "label": 1}
{"text": "Title: Cellular Automata to More Efficiently Compute the Collatz Map\nAbstract: The Collatz, or 3x+1, Conjecture claims that for every positive integer n, there exists some k such that T^k(n)=1, where T is the Collatz map. We present three cellular automata (CA) that transform the global problem of mimicking the Collatz map in bases 2, 3, and 4 into a local one of transforming the digits of iterates. The CAs streamline computation first by bypassing calculation of certain parts of trajectories: the binary CA bypasses division by two altogether. In addition, they allow for multiple trajectories to be calculated simultaneously, representing both a significant improvement upon existing sequential methods of computing the Collatz map and a demonstration of the efficacy of using a massively parallel approach with cellular automata to tackle iterative problems like the Collatz Conjecture.", "field": "math", "label": 1}
{"text": "Title: Sasakian structure associated with a second order ODE and Hamiltonian dynamical systems\nAbstract: We define a contact metric structure on the manifold corresponding to a second order ordinary differential equation $d^2y/dx^2=f(x,y,y')$ and show that the contact metric structure is Sasakian if and only if the 1-form $\\frac{1}{2}(dp-fdx)$ defines a Poisson structure. We consider a Hamiltonian dynamical system defined by this Poisson structure and show that the Hamiltonian vector field, which is a multiple of the Reeb vector field, admits a compatible bi-Hamiltonian structure for which $f$ can be regarded as a Hamiltonian function. As a particular case, we give a compatible bi-Hamiltonian structure of the Reeb vector field such that the structure equations correspond to the Maurer-Cartan equations of an invariant coframe on the Heisenberg group and the independent variable plays the role of a Hamiltonian function. We also show that the first Chern class of the normal bundle of an integral curve of a multiple of the Reeb vector field vanishes iff $f_x+ff_p = \\Psi (x)$ for some $\\Psi$.", "field": "math", "label": 1}
{"text": "Title: Energy balance and damage for brittle fracture: nonlocal formulation\nAbstract: A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Here inelasticity corresponds to material failure. Existence and uniqueness of the elastic displacement-failure set pair follow from the initial value problem. The displacement-failure pair satisfies energy balance. The length scale of nonlocality $\\epsilon$ is taken to be small relative to the domain in $\\mathbb{R}^d$, $d=2,3$. The new nonlocal model delivers a two point strain dynamics on a subset of $\\mathbb{R}^d\\times\\mathbb{R}^d$. This dynamics provides an energy that interpolates between volume energy corresponding to recoverable strain and surface energy corresponding to non recoverable strain. The deformation energy resulting in material failure over a region $R$ is given by a $d-1$ dimensional integral that is uniformly bounded as $\\epsilon\\rightarrow 0$. For fixed $\\epsilon$, this energy is nonzero for $d-1$ dimensional regions $R$ associated with flat crack surfaces. The failure energy is the Griffith fracture energy for a given crack $R$ in terms of its area for $d=3$ (or length for $d=2$). This energy follows directly from the nonlocal model without sending $\\epsilon$ to zero. Simulations illustrate fracture evolution through generation of an internal traction free boundary as a wake left behind a moving strain concentration. Crack paths are seen to follow a maximal strain energy density criterion.", "field": "math", "label": 0}
{"text": "Title: Mixed Poisson process with Min-U-Exp mixing variable\nAbstract: This work continues the research done in Jordanova and Veleva (2023) where the history of the problem could be found. In order to obtain the structure distribution of the newly-defined Mixed Poisson process, here the operation \"max\" is replaced with \"min\". We start with the definition of Min-U-Exp distribution. Then, we compute its numerical characteristics and investigate some of its properties. The joint distribution of the inter-arrival times (which are dependent) is the Multivariate Exp-Min-U-Exp distribution of $II^{-nd}$ kind. Its univariate and multivariate versions are described, and the formulae for their numerical characteristics are obtained. The distribution of the moments of arrival of different events is called Erlang-Min-U-Exp. Different properties of these distributions are obtained, and their numerical characteristics are computed. Multivariate ordered Mixed Poisson-Min-U-Exp distribution describes the joint distribution of the time-intersection of a Mixed Poisson process with Min-U-Exp mixing variable. The corresponding distribution of the additive increments (which are also dependent) is the Mixed Poisson-Min-U-Exp one. The considered relations between these distributions simplify their understanding.", "field": "math", "label": 0}
{"text": "Title: Xorbits: Automating Operator Tiling for Distributed Data Science\nAbstract: Data science pipelines commonly utilize dataframe and array operations for tasks such as data preprocessing, analysis, and machine learning. The most popular tools for these tasks are pandas and NumPy. However, these tools are limited to executing on a single node, making them unsuitable for processing large-scale data. Several systems have attempted to distribute data science applications to clusters while maintaining interfaces similar to single-node libraries, enabling data scientists to scale their workloads without significant effort. However, existing systems often struggle with processing large datasets due to Out-of-Memory (OOM) problems caused by poor data partitioning. To overcome these challenges, we develop Xorbits, a high-performance, scalable data science framework specifically designed to distribute data science workloads across clusters while retaining familiar APIs. The key differentiator of Xorbits is its ability to dynamically switch between graph construction and graph execution. Xorbits has been successfully deployed in production environments with up to 5k CPU cores. Its applications span various domains, including user behavior analysis and recommendation systems in the e-commerce sector, as well as credit assessment and risk management in the finance industry. Users can easily scale their data science workloads by simply changing the import line of their pandas and NumPy code. Our experiments demonstrate that Xorbits can effectively process very large datasets without encountering OOM or data-skewing problems. Over the fastest state-of-the-art solutions, Xorbits achieves an impressive 2.66* speedup on average. In terms of API coverage, Xorbits attains a compatibility rate of 96.7%, surpassing the fastest framework by an impressive margin of 60 percentage points. Xorbits is available at https: //github.com/xorbitsai/xorbits.", "field": "cs", "label": 0}
{"text": "Title: Energy-optimal Timetable Design for Sustainable Metro Railway Networks\nAbstract: We present our collaboration with Thales Canada Inc, the largest provider of communication-based train control (CBTC) systems worldwide. We study the problem of designing energy-optimal timetables in metro railway networks to minimize the effective energy consumption of the network, which corresponds to simultaneously minimizing total energy consumed by all the trains and maximizing the transfer of regenerative braking energy from suitable braking trains to accelerating trains. We propose a novel data-driven linear programming model that minimizes the total effective energy consumption in a metro railway network, capable of computing the optimal timetable in real-time, even for some of the largest CBTC systems in the world. In contrast with existing works, which are either NP-hard or involve multiple stages requiring extensive simulation, our model is a single linear programming model capable of computing the energy-optimal timetable subject to the constraints present in the railway network. Furthermore, our model can predict the total energy consumption of the network without requiring time-consuming simulations, making it suitable for widespread use in managerial settings. We apply our model to Shanghai Railway Network's Metro Line 8 -- one of the largest and busiest railway services in the world -- and empirically demonstrate that our model computes energy-optimal timetables for thousands of active trains spanning an entire service period of one day in real-time (solution time less than one second on a standard desktop), achieving energy savings between approximately 20.93% and 28.68%. Given the compelling advantages, our model is in the process of being integrated into Thales Canada Inc's industrial timetable compiler.", "field": "math", "label": 0}
{"text": "Title: Mapping and Validating a Point Neuron Model on Intel's Neuromorphic Hardware Loihi\nAbstract: Neuromorphic hardware is based on emulating the natural biological structure of the brain. Since its computational model is similar to standard neural models, it could serve as a computational acceleration for research projects in the field of neuroscience and artificial intelligence, including biomedical applications. However, in order to exploit this new generation of computer chips, rigorous simulation and consequent validation of brain-based experimental data is imperative. In this work, we investigate the potential of Intel's fifth generation neuromorphic chip - `Loihi', which is based on the novel idea of Spiking Neural Networks (SNNs) emulating the neurons in the brain. The work is implemented in context of simulating the Leaky Integrate and Fire (LIF) models based on the mouse primary visual cortex matched to a rich data set of anatomical, physiological and behavioral constraints. Simulations on the classical hardware serve as the validation platform for the neuromorphic implementation. We find that Loihi replicates classical simulations very efficiently and scales notably well in terms of both time and energy performance as the networks get larger.", "field": "cs", "label": 1}
{"text": "Title: From Function to Distribution Modeling: A PAC-Generative Approach to Offline Optimization\nAbstract: This paper considers the problem of offline optimization, where the objective function is unknown except for a collection of ``offline\" data examples. While recent years have seen a flurry of work on applying various machine learning techniques to the offline optimization problem, the majority of these work focused on learning a surrogate of the unknown objective function and then applying existing optimization algorithms. While the idea of modeling the unknown objective function is intuitive and appealing, from the learning point of view it also makes it very difficult to tune the objective of the learner according to the objective of optimization. Instead of learning and then optimizing the unknown objective function, in this paper we take on a less intuitive but more direct view that optimization can be thought of as a process of sampling from a generative model. To learn an effective generative model from the offline data examples, we consider the standard technique of ``re-weighting\", and our main technical contribution is a probably approximately correct (PAC) lower bound on the natural optimization objective, which allows us to jointly learn a weight function and a score-based generative model. The robustly competitive performance of the proposed approach is demonstrated via empirical studies using the standard offline optimization benchmarks.", "field": "cs", "label": 0}
{"text": "Title: Dorfman connections and Courant algebroids\nAbstract: We define Dorfman connections, which are to Courant algebroids what connections are to Lie algebroids. Several examples illustrate this analogy. A linear connection $\\nabla\\colon \\mathfrak{X}(M)\\times\\Gamma(E)\\to\\Gamma(E)$ on a vector bundle $E$ over a smooth manifold $M$ is tantamount to a linear splitting $TE\\simeq T^{q_E}E\\oplus H_\\nabla$, where $T^{q_E}E$ is the set of vectors tangent to the fibres of $E$. Furthermore, the curvature of the connection measures the failure of the horizontal space $H_\\nabla$ to be integrable. We show that linear horizontal complements to $T^{q_E}E\\oplus (T^{q_E}E)^\\circ$ in the Pontryagin bundle over the vector bundle $E$ can be described in the same manner via a certain class of Dorfman connections $\\Delta\\colon \\Gamma(TM\\oplus E^*)\\times\\Gamma(E\\oplus T^*M)\\to\\Gamma(E\\oplus T^*M)$. Similarly to the tangent bundle case, we find that, after the choice of a linear splitting, the standard Courant algebroid structure of $TE\\oplus T^*E\\to E$ can be completely described by properties of the Dorfman connection. As an application, we study splittings of $TA\\oplus T^*A$ over a Lie algebroid $A$ and, following Gracia-Saz and Mehta, we compute the representations up to homotopy defined by any linear splitting of $TA\\oplus T^*A$ and the linear Lie algebroid $TA\\oplus T^*A\\to TM\\oplus A^*$. Further, we characterise VB- and LA-Dirac structures in $TA\\oplus T^*A$ via Dorfman connections.", "field": "math", "label": 1}
{"text": "Title: Can AI Be as Creative as Humans?\nAbstract: Creativity serves as a cornerstone for societal progress and innovation, but its assessment remains a complex and often subjective endeavor. With the rise of advanced generative AI models capable of tasks once reserved for human creativity, the study of AI's creative potential becomes imperative for its responsible development and application. This paper addresses the complexities in defining and evaluating creativity by introducing a new concept called Relative Creativity. Instead of trying to define creativity universally, we shift the focus to whether AI can match the creative abilities of a hypothetical human. This perspective draws inspiration from the Turing Test, expanding upon it to address the challenges and subjectivities inherent in evaluating creativity. This methodological shift facilitates a statistically quantifiable evaluation of AI's creativity, which we term Statistical Creativity. This approach allows for direct comparisons of AI's creative abilities with those of specific human groups. Building on this foundation, we discuss the application of statistical creativity in contemporary prompt-conditioned autoregressive models. In addition to defining and analyzing a measure of creativity, we introduce an actionable training guideline, effectively bridging the gap between theoretical quantification of creativity and practical model training. Through these multifaceted contributions, the paper establishes a cohesive, continuously evolving, and transformative framework for assessing and fostering statistical creativity in AI models.", "field": "cs", "label": 0}
{"text": "Title: Nonconforming virtual element method for an incompressible miscible displacement problem in porous media\nAbstract: This article presents a priori error estimates of the miscible displacement of one incompressible fluid by another through a porous medium characterized by a coupled system of nonlinear elliptic and parabolic equations. The study utilizes the $H(\\rm{div})$ conforming virtual element method (VEM) for the approximation of the velocity, while a non-conforming virtual element approach is employed for the concentration. The pressure is discretised using the standard piecewise discontinuous polynomial functions. These spatial discretization techniques are combined with a backward Euler difference scheme for time discretization. The article also includes numerical results that validate the theoretical estimates presented.", "field": "math", "label": 0}
{"text": "Title: Relative Fourier transforms and expectations on coideal subalgebras\nAbstract: For an algebraic compact quantum group $H$ we establish a bijection between the set of right coideal $*$-subalgebras $A\\to H$ and that of left module quotient $*$-coalgebras $H\\to C$. It turns out that the inclusion $A\\to H$ always splits as a map of right $A$-modules and right $H$-comodules, and the resulting expectation $E:H\\to A$ is positive (and lifts to a positive map on the full $C^*$ completion on $H$) if and only if $A$ is invariant under the squared antipode of $H$. The proof proceeds by Tannaka-reconstructing the coalgebra $C$ corresponding to $A\\to H$ by means of a fiber functor from $H$-equivariant $A$-modules to Hilbert spaces, while the characterization of those $A\\to H$ which admit positive expectations makes use of a Fourier transform turning elements of $H$ into functions on $C$.", "field": "math", "label": 1}
{"text": "Title: Stochastic Broadcast Control of Multi-Agent Swarms\nAbstract: We present a model for controlling swarms of mobile agents via broadcast control, assumed to be detected by a random set of agents in the swarm. The agents that detect the control signal become ad-hoc leaders of the swarm. The agents are assumed to be velocity controlled, identical, anonymous, memory-less units with limited capabilities of sensing their neighborhood. Each agent is programmed to behave according to a linear local gathering process, based on the relative position of all its neighbors. The detected exogenous control, which is a desired velocity vector, is added by the leaders to the local gathering control. The graph induced by the agents adjacency is referred to as the visibility graph. We show that for piece-wise constant system parameters and a connected visibility graph, the swarm asymptotically aligns in each time-interval on a line in the direction of the exogenous control signal, and all the agents move with identical speed. These results hold for two models of pairwise influence in the gathering process, uniform and scaled. The impact of the influence model is mostly evident when the visibility graph is incomplete. These results are conditioned by the preservation of the connectedness of the visibility graph. In the second part of the report we analyze sufficient conditions for preserving the connectedness of the visibility graph. We show that if the visibility graph is complete then certain bounds on the control signal suffice to preserve the completeness of the graph. However, when the graph is incomplete, general conditions, independent of the leaders topology, could not be found.", "field": "cs", "label": 1}
{"text": "Title: Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions\nAbstract: We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We systematically investigate all the possible quadratic null form type quasilinear strong coupling nonlinearities, and provide a new, robust approach for the proof. In a second paper we will complete the present results to full global well-posedness.", "field": "math", "label": 1}
{"text": "Title: Asymptotics for the Taylor coefficients of certain infinite products\nAbstract: Let $(m_1,\\ldots,m_J)$ and $(r_1,\\ldots,r_J)$ be two sequences of $J$ positive integers satisfying $1\\le r_j< m_j$ for all $j=1,\\ldots,J$. Let $(\\delta_1,\\ldots,\\delta_J)$ be a sequence of $J$ nonzero integers. In this paper, we study the asymptotic behavior of the Taylor coefficients of the infinite product $$\\prod_{j=1}^J\\Bigg(\\prod_{k\\ge 1}\\big(1-q^{r_j+m_j(k-1)}\\big)\\big(1-q^{-r_j+m_jk}\\big)\\Bigg)^{\\delta_j}.$$", "field": "math", "label": 1}
{"text": "Title: Task and Explanation Network\nAbstract: Explainability in deep networks has gained increased importance in recent years. We argue herein that an AI must be tasked not just with a task but also with an explanation of why said task was accomplished as such. We present a basic framework -- Task and Explanation Network (TENet) -- which fully integrates task completion and its explanation. We believe that the field of AI as a whole should insist -- quite emphatically -- on explainability.", "field": "cs", "label": 0}
{"text": "Title: Braid variety cluster structures, II: general type\nAbstract: We show that braid varieties for any complex simple algebraic group $G$ are cluster varieties. This includes open Richardson varieties inside the flag variety $G/B$.", "field": "math", "label": 1}
{"text": "Title: Orlov spectra: bounds and gaps\nAbstract: The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D. Orlov building on work of A. Bondal-M. van den Bergh and R. Rouquier. The supremum of the Orlov spectrum of a triangulated category is called the ultimate dimension. In this work, we study Orlov spectra of triangulated categories arising in mirror symmetry. We introduce the notion of gaps and outline their geometric significance. We provide the first large class of examples where the ultimate dimension is finite: categories of singularities associated to isolated hypersurface singularities. Similarly, given any nonzero object in the bounded derived category of coherent sheaves on a smooth Calabi-Yau hypersurface, we produce a new generator by closing the object under a certain monodromy action and uniformly bound this new generator's generation time. In addition, we provide new upper bounds on the generation times of exceptional collections and connect generation time to braid group actions to provide a lower bound on the ultimate dimension of the derived Fukaya category of a symplectic surface of genus greater than one.", "field": "math", "label": 1}
{"text": "Title: Characterization of circular D0L systems\nAbstract: We prove that every non-circular D0L system contains arbitrarily long repetitions. This result was already published in 1993 by Mignosi and S\\'e\\'ebold, however their proof is only a sketch. We give here a complete proof. Further, employing our previous result, we give a simple algorithm to test circularity of an injective D0L system.", "field": "math", "label": 1}
{"text": "Title: Polynomial-time Approximation Scheme for Equilibriums of Games\nAbstract: Whether a PTAS (polynomial-time approximation scheme) exists for equilibriums of games has been an open question, which relates to the practicality of methods in algorithmic game theory and the problem of non-stationarity in training and curse of dimensionality in multi-agent reinforcement learning. This paper introduces our theory that implies a method that is sufficient and necessary to be the PTAS for perfect equilibriums of dynamic games. The theory consists of cone interior dynamic programming and primal-dual unbiased regret minimization. The former enables the dynamic programming operator to iteratively converge to a perfect equilibrium based on a concept called policy cone. The latter enables the line search method to approximate a Nash equilibrium based on two concepts called primal-dual bias and unbiased central path, solving a subproblem of the former. Validity of our discovery is cross-corroborated by a combination of theorem proofs, graphs of the three core concepts, and experimental results.", "field": "cs", "label": 0}
{"text": "Title: Time Protection: the Missing OS Abstraction\nAbstract: Timing channels enable data leakage that threatens the security of computer systems, from cloud platforms to smartphones and browsers executing untrusted third-party code. Preventing unauthorised information flow is a core duty of the operating system, however, present OSes are unable to prevent timing channels. We argue that OSes must provide time protection in addition to the established memory protection. We examine the requirements of time protection, present a design and its implementation in the seL4 microkernel, and evaluate its efficacy as well as performance overhead on Arm and x86 processors.", "field": "cs", "label": 1}
{"text": "Title: Beyond Information Exchange: An Approach to Deploy Network Properties for Information Diffusion\nAbstract: Information diffusion in Online Social Networks is a new and crucial problem in social network analysis field and requires significant research attention. Efficient diffusion of information are of critical importance in diverse situations such as; pandemic prevention, advertising, marketing etc. Although several mathematical models have been developed till date, but previous works lacked systematic analysis and exploration of the influence of neighborhood for information diffusion. In this paper, we have proposed Common Neighborhood Strategy (CNS) algorithm for information diffusion that demonstrates the role of common neighborhood in information propagation throughout the network. The performance of CNS algorithm is evaluated on several real-world datasets in terms of diffusion speed and diffusion outspread and compared with several widely used information diffusion models. Empirical results show CNS algorithm enables better information diffusion both in terms of diffusion speed and diffusion outspread.", "field": "cs", "label": 1}
{"text": "Title: Big Ramsey Degrees in Ultraproducts of Finite Structures\nAbstract: We develop a transfer principle of structural Ramsey theory from finite structures to ultraproducts. We show that under certain mild conditions, when a class of finite structures has finite small Ramsey degrees, under the (Generalized) Continuum Hypothesis the ultraproduct has finite big Ramsey degrees for internal colorings. The necessity of restricting to internal colorings is demonstrated by the example of the ultraproduct of finite linear orders. Under CH, this ultraproduct $\\fLL^*$ has, as a spine, $\\eta_1$, an uncountable analogue of the order type of rationals $\\eta$. Finite big Ramsey degrees for $\\eta$ were exactly calculated by Devlin in \\cite{Devlin}. It is immediate from \\cite{Tod87} that $\\eta_1$ fails to have finite big Ramsey degrees. Moreover, we extend Devlin's coloring to $\\eta_1$ to show that it witnesses big Ramsey degrees of finite tuples in $\\eta$ on every copy of $\\eta$ in $\\eta_1,$ and consequently in $\\fLL^*$. This work gives additional confirmation that ultraproducts are a suitable environment for studying Ramsey properties of finite and infinite structures.", "field": "math", "label": 1}
{"text": "Title: Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients\nAbstract: We prove heat kernel bounds for the operator (1 + |x|^{\\alpha})\\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.", "field": "math", "label": 1}
{"text": "Title: Symbolic Dynamics of Magnetic Bumps\nAbstract: For n convex magnetic bumps in the plane, whose boundary has a curvature somewhat smaller than the absolute value of the constant magnetic field inside the bump, we construct a complete symbolic dynamics of a classical particle moving with speed one.", "field": "math", "label": 1}
{"text": "Title: LLaMA Pro: Progressive LLaMA with Block Expansion\nAbstract: Humans generally acquire new skills without compromising the old; however, the opposite holds for Large Language Models (LLMs), e.g., from LLaMA to CodeLLaMA. To this end, we propose a new post-pretraining method for LLMs with an expansion of Transformer blocks. We tune the expanded blocks using only new corpus, efficiently and effectively improving the model's knowledge without catastrophic forgetting. In this paper, we experiment on the corpus of code and math, yielding LLaMA Pro-8.3B, a versatile foundation model initialized from LLaMA2-7B, excelling in general tasks, programming, and mathematics. LLaMA Pro and its instruction-following counterpart (LLaMA Pro-Instruct) achieve advanced performance among various benchmarks, demonstrating superiority over existing open models in the LLaMA family and the immense potential of reasoning and addressing diverse tasks as an intelligent agent. Our findings provide valuable insights into integrating natural and programming languages, laying a solid foundation for developing advanced language agents that operate effectively in various environments.", "field": "cs", "label": 0}
{"text": "Title: Lambda Module structure on higher $K$-groups\nAbstract: In this article, we show that for a quasicompact scheme $X$ and $n>0,$ the $n$-th $K$-group $K_{n}(X)$ is a $\\lambda$-module over a $\\lambda$-ring $K_{0}(X)$ in the sense of Hesselholt.", "field": "math", "label": 0}
{"text": "Title: An analysis of the logic of Riesz Spaces with strong unit\nAbstract: We study \\L ukasiewicz logic enriched with a scalar multiplication with scalars taken in $[0,1]$. Its algebraic models, called {\\em Riesz MV-algebras}, are, up to isomorphism, unit intervals of Riesz spaces with a strong unit endowed with an appropriate structure. When only rational scalars are considered, one gets the class of {\\em DMV-algebras} and a corresponding logical system. Our research follows two objectives. The first one is to deepen the connections between functional analysis and the logic of Riesz MV-algebras. The second one is to study the finitely presented MV-algebras, DMV-algebras and Riesz MV-algebras, connecting them from logical, algebraic and geometric perspective.", "field": "math", "label": 1}
{"text": "Title: Hochschild cohomology of the second kind: Koszul duality and Morita invariance\nAbstract: We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in a compactly generated derived category of the second kind, and show that it is invariant under Morita equivalence of the second kind. A bimodule version of Koszul duality is constructed and used to show that Hochschild cohomology of the second kind is preserved under (nonconilpotent) Koszul duality. Hochschild cohomology of the second kind of an algebra often computes the ordinary Hochschild cohomology of geometrically meaningful dg categories. Examples include the category of infinity local systems on a topological space, the bounded derived category of a complex algebraic manifold and the category of matrix factorizations.", "field": "math", "label": 0}
{"text": "Title: Recursive Monte Carlo and Variational Inference with Auxiliary Variables\nAbstract: A key design constraint when implementing Monte Carlo and variational inference algorithms is that it must be possible to cheaply and exactly evaluate the marginal densities of proposal distributions and variational families. This takes many interesting proposals off the table, such as those based on involved simulations or stochastic optimization. This paper broadens the design space, by presenting a framework for applying Monte Carlo and variational inference algorithms when proposal densities cannot be exactly evaluated. Our framework, recursive auxiliary-variable inference (RAVI), instead approximates the necessary densities using meta-inference: an additional layer of Monte Carlo or variational inference, that targets the proposal, rather than the model. RAVI generalizes and unifies several existing methods for inference with expressive approximating families, which we show correspond to specific choices of meta-inference algorithm, and provides new theory for analyzing their bias and variance. We illustrate RAVI's design framework and theorems by using them to analyze and improve upon Salimans et al.'s Markov Chain Variational Inference, and to design a novel sampler for Dirichlet process mixtures, achieving state-of-the-art results on a standard benchmark dataset from astronomy and on a challenging datacleaning task with Medicare hospital data.", "field": "cs", "label": 1}
{"text": "Title: Non-local games and quantum symmetries of quantum metric spaces\nAbstract: We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries between two quantum metric spaces, and we show that if a pair of quantum metric spaces are algebraically quantum isometric, then their quantum isometry groups are monoidally equivalent. Motivated by the recent work on the graph isomorphism game, we introduce a new two-player non-local game called the metric isometry game, where players can win classically if and only if the metric spaces are isometric. Winning quantum strategies of this game align with quantum isometries of the metric spaces.", "field": "math", "label": 1}
{"text": "Title: Various Covering Spectra for Complete Metric Spaces\nAbstract: We study various covering spectra for complete noncompact length spaces with universal covers (including Riemannian manifolds and the pointed Gromov Hausdorff limits of Riemannian manifolds with lower bounds on their Ricci curvature). We relate the covering spectrum to the (marked) shift spectrum of such a space. We define the slipping group generated by elements of the fundamental group whose translative lengths are 0. We introduce a rescaled length, the rescaled covering spectrum and the rescaled slipping group. Applying these notions we prove that certain complete noncompact Riemannian manifolds with nonnegative or positive Ricci curvature have finite fundamental groups. Throughout we suggest further problems both for those interested in Riemannian geometry and those interested in metric space theory.", "field": "math", "label": 1}
{"text": "Title: Understanding the Effects of RLHF on LLM Generalisation and Diversity\nAbstract: Large language models (LLMs) fine-tuned with reinforcement learning from human feedback (RLHF) have been used in some of the most widely deployed AI models to date, such as OpenAI's ChatGPT or Anthropic's Claude. % , or Meta's LLaMA-2. While there has been significant work developing these methods, our understanding of the benefits and downsides of each stage in RLHF is still limited. To fill this gap, we present an extensive analysis of how each stage of the process (i.e.~supervised fine-tuning (SFT), reward modelling, and RLHF) affects two key properties: out-of-distribution (OOD) generalisation and output diversity. OOD generalisation is crucial given the wide range of real-world scenarios in which these models are being used, while output diversity refers to the model's ability to generate varied outputs and is important for a variety of use cases. We perform our analysis across two base models on both summarisation and instruction following tasks, the latter being highly relevant for current LLM use cases. We find that RLHF generalises better than SFT to new inputs, particularly as the distribution shift between train and test becomes larger. However, RLHF significantly reduces output diversity compared to SFT across a variety of measures, implying a tradeoff in current LLM fine-tuning methods between generalisation and diversity. Our results provide guidance on which fine-tuning method should be used depending on the application, and show that more research is needed to improve the tradeoff between generalisation and diversity.", "field": "cs", "label": 0}
{"text": "Title: Domination structure for number three\nAbstract: From a research of several recent papers, in the first part, we are concerned with domination number in cubic graphs and give a sufficient condition of Reed's conjecture. In the second part, from a perspective, we study the structure of a minimum dominating set in 3-connected graphs. It is derived from a collection of cycles with length 0 mod 3.", "field": "math", "label": 1}
{"text": "Title: Functional Dimensionality of Koopman Eigenfunction Space\nAbstract: This work presents the general form solution of Koopman Partial Differential Equation and shows that its functional dimensionality is finite. The dimensionality is as the dimensionality of the dynamics. Thus, the representation of nonlinear dynamics as a linear one with a finite set of Koopman eigenfunctions without error is possible. This formulation justifies the flowbox statement and provides a simple numerical method to find such representation.", "field": "math", "label": 0}
{"text": "Title: Assistive Tele-op: Leveraging Transformers to Collect Robotic Task Demonstrations\nAbstract: Sharing autonomy between robots and human operators could facilitate data collection of robotic task demonstrations to continuously improve learned models. Yet, the means to communicate intent and reason about the future are disparate between humans and robots. We present Assistive Tele-op, a virtual reality (VR) system for collecting robot task demonstrations that displays an autonomous trajectory forecast to communicate the robot's intent. As the robot moves, the user can switch between autonomous and manual control when desired. This allows users to collect task demonstrations with both a high success rate and with greater ease than manual teleoperation systems. Our system is powered by transformers, which can provide a window of potential states and actions far into the future -- with almost no added computation time. A key insight is that human intent can be injected at any location within the transformer sequence if the user decides that the model-predicted actions are inappropriate. At every time step, the user can (1) do nothing and allow autonomous operation to continue while observing the robot's future plan sequence, or (2) take over and momentarily prescribe a different set of actions to nudge the model back on track. We host the videos and other supplementary material at https://sites.google.com/view/assistive-teleop.", "field": "cs", "label": 1}
{"text": "Title: Federated Class-Incremental Learning with Prototype Guided Transformer\nAbstract: Existing federated learning methods have effectively addressed decentralized learning in scenarios involving data privacy and non-IID data. However, in real-world situations, each client dynamically learns new classes, requiring the global model to maintain discriminative capabilities for both new and old classes. To effectively mitigate the effects of catastrophic forgetting and data heterogeneity under low communication costs, we designed a simple and effective method named PLoRA. On the one hand, we adopt prototype learning to learn better feature representations and leverage the heuristic information between prototypes and class features to design a prototype re-weight module to solve the classifier bias caused by data heterogeneity without retraining the classification layer. On the other hand, our approach utilizes a pre-trained model as the backbone and utilizes LoRA to fine-tune with a tiny amount of parameters when learning new classes. Moreover, PLoRA does not rely on similarity-based module selection strategies, thereby further reducing communication overhead. Experimental results on standard datasets indicate that our method outperforms the state-of-the-art approaches significantly. More importantly, our method exhibits strong robustness and superiority in various scenarios and degrees of data heterogeneity. Our code will be publicly available.", "field": "cs", "label": 0}
{"text": "Title: Ahlfors' contribution to the theory of meromorphic functions\nAbstract: This is an expanded version of one of the Lectures in memory of Lars Ahlfors in Haifa in 1996. Some mistakes are corrected and references added. It contains a survey of his work on meromorphic functions and related topics written in 1929-1941.", "field": "math", "label": 1}
{"text": "Title: The Principal Ideal Theorem in Spectral Synthesis\nAbstract: In an earlier paper we solved a long-standing problem which goes back to Laurent Schwartz's work on mean-periodic functions. Namely, we completely characterised those locally compact Abelian groups having spectral synthesis. The method is based on the localisation concept. In this paper we show that localisation can be used to prove another basic result in spectral synthesis: the principal ideal theorem.", "field": "math", "label": 0}
{"text": "Title: Towards Open Set Deep Networks\nAbstract: Deep networks have produced significant gains for various visual recognition problems, leading to high impact academic and commercial applications. Recent work in deep networks highlighted that it is easy to generate images that humans would never classify as a particular object class, yet networks classify such images high confidence as that given class - deep network are easily fooled with images humans do not consider meaningful. The closed set nature of deep networks forces them to choose from one of the known classes leading to such artifacts. Recognition in the real world is open set, i.e. the recognition system should reject unknown/unseen classes at test time. We present a methodology to adapt deep networks for open set recognition, by introducing a new model layer, OpenMax, which estimates the probability of an input being from an unknown class. A key element of estimating the unknown probability is adapting Meta-Recognition concepts to the activation patterns in the penultimate layer of the network. OpenMax allows rejection of \"fooling\" and unrelated open set images presented to the system; OpenMax greatly reduces the number of obvious errors made by a deep network. We prove that the OpenMax concept provides bounded open space risk, thereby formally providing an open set recognition solution. We evaluate the resulting open set deep networks using pre-trained networks from the Caffe Model-zoo on ImageNet 2012 validation data, and thousands of fooling and open set images. The proposed OpenMax model significantly outperforms open set recognition accuracy of basic deep networks as well as deep networks with thresholding of SoftMax probabilities.", "field": "cs", "label": 1}
{"text": "Title: Weight functions on Berkovich curves\nAbstract: Let $C$ be a curve over a complete discretely valued field $K$. We give tropical descriptions of the weight function attached to a pluricanonical form on $C$ and the essential skeleton of $C$. We show that the Laplacian of the weight function equals the pluricanonical divisor on Berkovich skeleta, and we describe the essential skeleton of $C$ as a combinatorial skeleton of the Berkovich skeleton of the minimal $snc$-model. In particular, if $C$ has semi-stable reduction, then the essential skeleton coincides with the minimal skeleton. As an intermediate step, we describe the base loci of logarithmic pluricanonical line bundles on minimal $snc$-models.", "field": "math", "label": 1}
{"text": "Title: Absence of Lavrentiev's gap for anisotropic functionals\nAbstract: We establish the absence of the Lavrentiev gap between Sobolev and smooth maps for a non-autonomous variational problem of a general structure, where the integrand is assumed to be controlled by a function which is convex and anisotropic with respect to the last variable. This fact results from new results on good approximation properties of the natural underlying unconventional function space. Scalar and vector-valued problems are studied.", "field": "math", "label": 1}
{"text": "Title: Efficient Second Order Online Learning by Sketching\nAbstract: We propose Sketched Online Newton (SON), an online second order learning algorithm that enjoys substantially improved regret guarantees for ill-conditioned data. SON is an enhanced version of the Online Newton Step, which, via sketching techniques enjoys a running time linear in the dimension and sketch size. We further develop sparse forms of the sketching methods (such as Oja's rule), making the computation linear in the sparsity of features. Together, the algorithm eliminates all computational obstacles in previous second order online learning approaches.", "field": "cs", "label": 1}
{"text": "Title: New multivariate Gini's indices\nAbstract: The Gini's mean difference was defined as the expected absolute difference between a random variable and its independent copy. The corresponding normalized version, namely Gini's index, denotes two times the area between the egalitarian line and the Lorenz curve. Both are dispersion indices because they quantify how far a random variable and its independent copy are. Aiming to measure dispersion in the multivariate case, we define and study new Gini's indices. For the bivariate case we provide several results and we point out that they are \"dependence-dispersion\" indices. Covariance representations are exhibited, with an interpretation also in terms of conditional distributions. Further results, bounds and illustrative examples are discussed too. Multivariate extensions are defined, aiming to apply both indices in more general settings. Then, we define efficiency Gini's indices for any semi-coherent system and we discuss about their interpretation. Empirical versions are considered in order as well to apply multivariate Gini's indices to data.", "field": "math", "label": 0}
{"text": "Title: A Stochastic Alternating Direction Method of Multipliers for Non-smooth and Non-convex Optimization\nAbstract: Alternating direction method of multipliers (ADMM) is a popular first-order method owing to its simplicity and efficiency. However, similar to other proximal splitting methods, the performance of ADMM degrades significantly when the scale of the optimization problems to solve becomes large. In this paper, we consider combining ADMM with a class of stochastic gradient with variance reduction for solving large-scale non-convex and non-smooth optimization problems. Global convergence of the generated sequence is established under the extra additional assumption that the object function satisfies Kurdyka-Lojasiewicz (KL) property. Numerical experiments on graph-guided fused Lasso and computed tomography are presented to demonstrate the performance of the proposed methods.", "field": "math", "label": 1}
{"text": "Title: Blow up of solutions for a Parabolic-Elliptic Chemotaxis System with gradient dependent chemotactic coefficient\nAbstract: We consider a Parabolic-Elliptic system of PDE's with a chemotactic term in a $N$-dimensional unit ball describing the behavior of the density of a biological species \"$u$\" and a chemical stimulus \"$v$\". The system includes a nonlinear chemotactic coefficient depending of ``$\\nabla v$\", i.e. the chemotactic term is given in the form $$- div (\\chi u |\\nabla v|^{p-2} \\nabla v), \\qquad \\mbox{ for } \\ p \\in ( \\frac{N}{N-1},2), \\qquad N >2 $$ for a positive constant $\\chi$ when $v$ satisfies the poisson equation $$- \\Delta v = u - \\frac{1}{|\\Omega|} \\int_{\\Omega} u_0dx.$$ We study the radially symmetric solutions under the assumption in the initial mass $$ \\frac{1}{|\\Omega|} \\int_{\\Omega} u_0dx>6.$$ For $\\chi$ large enough, we present conditions in the initial data, such that any regular solution of the problem blows up at finite time.", "field": "math", "label": 1}
{"text": "Title: Hierarchical Aligned Multimodal Learning for NER on Tweet Posts\nAbstract: Mining structured knowledge from tweets using named entity recognition (NER) can be beneficial for many down stream applications such as recommendation and intention understanding. With tweet posts tending to be multimodal, multimodal named entity recognition (MNER) has attracted more attention. In this paper, we propose a novel approach, which can dynamically align the image and text sequence and achieve the multi-level cross-modal learning to augment textual word representation for MNER improvement. To be specific, our framework can be split into three main stages: the first stage focuses on intra-modality representation learning to derive the implicit global and local knowledge of each modality, the second evaluates the relevance between the text and its accompanying image and integrates different grained visual information based on the relevance, the third enforces semantic refinement via iterative cross-modal interactions and co-attention. We conduct experiments on two open datasets, and the results and detailed analysis demonstrate the advantage of our model.", "field": "cs", "label": 0}
{"text": "Title: Prescribed graphon symmetries and flavors of rigidity\nAbstract: We prove that an arbitrary compact metrizable group can be realized as the automorphism group of a graphing; this is a continuous analogue to Frucht's theorem recovering arbitrary finite groups are automorphism groups of finite graphs. The paper also contains a number of results the persistence of transitivity of a compact-group action upon passing to a limit of graphons. Call a compact group $\\mathbb{G}$ graphon-rigid if, whenever it acts transitively on each member $\\Gamma_n$ of a convergent sequence of graphons, it also acts transitively on the limit $\\lim_n \\Gamma$. We show that for a compact Lie group $\\mathbb{G}$ graphon rigidity is equivalent to the identity component $\\mathbb{G}_0$ being semisimple; as a partial converse to a result of Lov\\'{a}sz and Szegedy, this is also equivalent to weak randomness: the property that the group have only finitely many irreducible representations in each dimension. Similarly, call a compact group $\\mathbb{G}$ image-rigid if for every compact Lie group $\\mathbb{H}$ the images of morphisms $\\mathbb{G}\\to \\mathbb{H}$ form a closed set (of closed subgroups, in the natural topology). We prove that graphon rigidity implies image rigidity for compact groups that are either connected or profinite, and the two conditions are equivalent (and also equivalent to being torsion) for profinite abelian groups.", "field": "math", "label": 1}
{"text": "Title: Indecomposable motivic cycles on K3 surfaces of degree 2\nAbstract: In this paper we construct new indecomposable motivic cycles in the group $H^3_{\\mathcal M}(X,{\\mathds Q}(2))$ where X is a degree 2 K3 surface. This generalizes our construction in [Sre22] for Kummer surfaces of Abelian surfaces as well as the recent work of Ma and Sato [MS23] on degree 2 K3 surfaces.", "field": "math", "label": 0}
{"text": "Title: Poisson catenarity in Poisson nilpotent algebras\nAbstract: We prove that for the iterated Poisson polynomial rings known as Poisson nilpotent algebras (or Poisson-CGL extensions), the Poisson prime spectrum is catenary, i.e., all saturated chains of inclusions of Poisson prime ideals between any two given Poisson prime ideals have the same length.", "field": "math", "label": 1}
{"text": "Title: Limit trees for free group automorphisms: universality\nAbstract: To any free group automorphism, we associate a universal (cone of) limit tree(s) with three defining properties: first, the tree has a minimal isometric action of the free group with trivial arc stabilizers; second, there is a unique expanding dilation of the tree that represents the free group automorphism; and finally, the loxodromic elements are exactly the elements that weakly limit to dominating attracting laminations under forward iteration by the automorphism. So the action on the tree detects the automorphism's dominating exponential dynamics. As a corollary, our previously constructed limit pretree that detects the exponential dynamics is canonical. We also characterize all very small trees that admit an expanding homothety representing a given automorphism. In the appendix, we prove a variation of Feighn--Handel's recognition theorem for atoroidal outer automorphisms.", "field": "math", "label": 1}
{"text": "Title: Analytic Linear Lie rack Structures on Leibniz Algebras\nAbstract: A linear Lie rack structure on a finite dimensional vector space $V$ is a Lie rack operation $(x,y)\\mapsto x\\rhd y$ pointed at the origin and such that for any $x$, the left translation $\\mathrm{L}_x:y\\mapsto \\mathrm{L}_x(y)= x\\rhd y$ is linear. A linear Lie rack operation $\\rhd$ is called analytic if for any $x,y\\in V$, \\[ x\\rhd y=y+\\sum_{n=1}^\\infty A_{n,1}(x,\\ldots,x,y), \\]where $A_{n,1}:V\\times\\ldots\\times V\\Leftarrow V$ is an $n+1$-multilinear map symmetric in the $n$ first arguments. In this case, $A_{1,1}$ is exactly the left Leibniz product associated to $\\rhd$. Any left Leibniz algebra $(\\mathfrak{h},[\\;,\\;])$ has a canonical analytic linear Lie rack structure given by $x\\stackrel{c}{\\rhd} y=\\exp(\\mathrm{ad}_x)(y)$, where $\\mathrm{ad}_x(y)=[x,y]$. In this paper, we show that a sequence $(A_{n,1})_{n\\geq1}$ of $n+1$-multilinear maps on a vector space $V$ defines an analytic linear Lie rack structure if and only if $[\\;,\\;]:=A_{1,1}$ is a left Leibniz bracket, the $A_{n,1}$ are invariant for $(V,[\\;,\\;]:)$ and satisfy a sequence of multilinear equations. Some of these equations have a cohomological interpretation and can be solved when the zero and the 1-cohomology of the left Leibniz algebra $(V,[\\;,\\;])$ are trivial. On the other hand, given a left Leibniz algebra $(\\mathfrak{h},[\\;,\\;])$, we show that there is a large class of (analytic) linear Lie rack structures on $(\\mathfrak{h},[\\;,\\;])$ which can be built from the canonical one and invariant multilinear symmetric maps on $\\mathfrak{h}$. A left Leibniz algebra on which all the analytic linear Lie rack structures are build in this way will be called rigid. We use our characterizations of analytic linear Lie rack structures to show that $\\mathfrak{sl}_2(\\mathbb{R})$ and $\\mathfrak{so}(3)$ are rigid. We conjecture that any simple Lie algebra is rigid as a left Leibniz algebra.", "field": "math", "label": 1}
{"text": "Title: Counting double cosets with application to generic 3-manifolds\nAbstract: We study the growth of double cosets in the class of groups with contracting elements, including relatively hyperbolic groups, CAT(0) groups and mapping class groups among others. Generalizing a recent work of Gitik and Rips about hyperbolic groups, we prove that the double coset growth of two Morse subgroups of infinite index is comparable with the orbital growth function. The same result is further obtained for a more general class of subgroups whose limit sets are proper subsets in the entire limit set of the ambient group. As an application, we confirm a conjecture of Maher that hyperbolic 3-manifolds are exponentially generic in the set of 3-manifolds built from Heegaard splitting using complexity in Teichm\\\"{u}ller metric.", "field": "math", "label": 0}
{"text": "Title: StROL: Stabilized and Robust Online Learning from Humans\nAbstract: Robots often need to learn the human's reward function online, during the current interaction. This real-time learning requires fast but approximate learning rules: when the human's behavior is noisy or suboptimal, current approximations can result in unstable robot learning. Accordingly, in this paper we seek to enhance the robustness and convergence properties of gradient descent learning rules when inferring the human's reward parameters. We model the robot's learning algorithm as a dynamical system over the human preference parameters, where the human's true (but unknown) preferences are the equilibrium point. This enables us to perform Lyapunov stability analysis to derive the conditions under which the robot's learning dynamics converge. Our proposed algorithm (StROL) uses these conditions to learn robust-by-design learning rules: given the original learning dynamics, StROL outputs a modified learning rule that now converges to the human's true parameters under a larger set of human inputs. In practice, these autonomously generated learning rules can correctly infer what the human is trying to convey, even when the human is noisy, biased, and suboptimal. Across simulations and a user study we find that StROL results in a more accurate estimate and less regret than state-of-the-art approaches for online reward learning. See videos and code here: https://github.com/VT-Collab/StROL_RAL", "field": "cs", "label": 0}
{"text": "Title: The stochastic fractional Strichartz estimate and blow-up for Schrödinger equation\nAbstract: We establish the stochastic Strichartz estimate for the fractional Schr\\\"odinger equation with multiplicative noise. With the help of the deterministic Strichartz estimates, we prove the existence and uniqueness of a global solution to the stochastic fractional nonlinear Schr\\\"odinger equation in $L^2(\\mathbb{R}^n)$. In addition, we also prove a general blow up result by deriving a localized virial estimate and the generalized Strauss inequality with a restricted class of initial data.", "field": "math", "label": 0}
{"text": "Title: Asymptotic characterizations of strong pseudoconvexity on pseudoconvex domains of finite type in $\\mathbb{C}^2$\nAbstract: In this paper, we provide some characterizations of strong pseudoconvexity by the boundary behavior of intrinsic invariants for smoothly bounded pseudoconvex domains of finite type in $\\mathbb{C}^2$. As a consequence, if such domain is biholomorphically equivalent to a quotient of the unit ball, then it is strongly pseudoconvex.", "field": "math", "label": 0}
{"text": "Title: Weak Solutions of SPDEs in the space of Tempered distributions\nAbstract: In this article, we construct weak solutions for a class of Stochastic PDEs in the space of tempered distributions via Girsanov's theorem. It is to be noted that our drift and diffusion coefficients $(L,A)$ of the considered Stochastic PDE satisfy a Monotonicity type inequality, rather than Lipschitz conditions. As such, we can not follow the usual infinite dimensional analysis as described in \\cite[sections 10.2 and 10.3]{MR3236753}. Instead, we exploit related SDEs to obtain our desired result, and we point out an important observation that the same Novikov condition is used in changing the Brownian motion in both the SDEs and the Stochastic PDEs.", "field": "math", "label": 0}
{"text": "Title: Smoothing Methods for Automatic Differentiation Across Conditional Branches\nAbstract: Programs involving discontinuities introduced by control flow constructs such as conditional branches pose challenges to mathematical optimization methods that assume a degree of smoothness in the objective function's response surface. Smooth interpretation (SI) is a form of abstract interpretation that approximates the convolution of a program's output with a Gaussian kernel, thus smoothing its output in a principled manner. Here, we combine SI with automatic differentiation (AD) to efficiently compute gradients of smoothed programs. In contrast to AD across a regular program execution, these gradients also capture the effects of alternative control flow paths. The combination of SI with AD enables the direct gradient-based parameter synthesis for branching programs, allowing for instance the calibration of simulation models or their combination with neural network models in machine learning pipelines. We detail the effects of the approximations made for tractability in SI and propose a novel Monte Carlo estimator that avoids the underlying assumptions by estimating the smoothed programs' gradients through a combination of AD and sampling. Using DiscoGrad, our tool for automatically translating simple C++ programs to a smooth differentiable form, we perform an extensive evaluation. We compare the combination of SI with AD and our Monte Carlo estimator to existing gradient-free and stochastic methods on four non-trivial and originally discontinuous problems ranging from classical simulation-based optimization to neural network-driven control. While the optimization progress with the SI-based estimator depends on the complexity of the program's control flow, our Monte Carlo estimator is competitive in all problems, exhibiting the fastest convergence by a substantial margin in our highest-dimensional problem.", "field": "cs", "label": 0}
{"text": "Title: Shayona@SMM4H23: COVID-19 Self diagnosis classification using BERT and LightGBM models\nAbstract: This paper describes approaches and results for shared Task 1 and 4 of SMMH4-23 by Team Shayona. Shared Task-1 was binary classification of english tweets self-reporting a COVID-19 diagnosis, and Shared Task-4 was Binary classification of English Reddit posts self-reporting a social anxiety disorder diagnosis. Our team has achieved the highest f1-score 0.94 in Task-1 among all participants. We have leveraged the Transformer model (BERT) in combination with the LightGBM model for both tasks.", "field": "cs", "label": 0}
{"text": "Title: Perfect precise colorings of plane semiregular tilings\nAbstract: A coloring of a planar semiregular tiling $\\mathcal{T}$ is an assignment of a unique color to each tile of $\\mathcal{T}$. If $G$ is the symmetry group of $\\mathcal{T}$, we say that the coloring is perfect if every element of $G$ induces a permutation on the finite set of colors. If $\\mathcal{T}$ is $k$-valent, then a coloring of $\\mathcal{T}$ with $k$ colors is said to be precise if no two tiles of $\\mathcal{T}$ sharing the same vertex have the same color. In this work, we obtain perfect precise colorings of some families of $k$-valent semiregular tilings in the plane, where $k\\leq 6$.", "field": "math", "label": 0}
{"text": "Title: Pointwise estimates for rough operators with applications to Sobolev inequalities\nAbstract: We investigate Sobolev inequalities for several rough operators. We prove that several operators satisfy a pointwise bound by the Riesz potential applied to the gradient. From this inequality, we derive several new Sobolev-type inequalities with an operator on the left-hand side.", "field": "math", "label": 0}
{"text": "Title: Minimal surfaces with symmetries\nAbstract: Let $G$ be a finite group acting on a connected open Riemann surface $X$ by holomorphic automorphisms and acting on a Euclidean space $\\mathbb R^n$ $(n\\ge 3)$ by orthogonal transformations. We identify a necessary and sufficient condition for the existence of a $G$-equivariant conformal minimal immersion $F:X\\to\\mathbb R^n$. We show in particular that such a map $F$ always exists if $G$ acts without fixed points on $X$. Furthermore, every finite group $G$ arises in this way for some open Riemann surface $X$ and $n=2|G|$. We obtain an analogous result for minimal surfaces having complete ends with finite total Gaussian curvature, and for discrete infinite groups acting on $X$ properly discontinuously and acting on $\\mathbb R^n$ by rigid transformations.", "field": "math", "label": 0}
{"text": "Title: The impact of the limit $q$-Durrmeyer operator on continuous functions\nAbstract: The limit $q$-Durrmeyer operator, $D_{\\infty,q},$ was introduced and its approximation properties were investigated by V. Gupta in 2008 during a study of $q$-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of $D_{\\infty,q}$. The interrelation between the analytic properties of a function $f$ and the rate of growth for $D_{\\infty,q}f$ are established, and the sharpness of the obtained results are demonstrated.", "field": "math", "label": 0}
{"text": "Title: On the modulus of continuity of solutions to nonlocal parabolic equations\nAbstract: A general modulus of continuity is quantified for locally bounded, local, weak solutions to nonlocal parabolic equations, under a minimal tail condition. H\\\"older modulus of continuity is then deduced under a slightly stronger tail condition. These regularity estimates are demonstrated under the framework of nonlocal $p$-Laplacian with measurable kernels.", "field": "math", "label": 0}
{"text": "Title: Raphtory: The temporal graph engine for Rust and Python\nAbstract: Raphtory is a platform for building and analysing temporal networks. The library includes methods for creating networks from a variety of data sources; algorithms to explore their structure and evolution; and an extensible GraphQL server for deployment of applications built on top. Raphtory's core engine is built in Rust, for efficiency, with Python interfaces, for ease of use. Raphtory is developed by network scientists, with a background in Physics, Applied Mathematics, Engineering and Computer Science, for use across academia and industry.", "field": "cs", "label": 0}
{"text": "Title: Answers to Two Questions on the DP Color Function\nAbstract: DP-coloring is a generalization of list coloring that was introduced in 2015 by Dvo\\v{r}\\'{a}k and Postle. The chromatic polynomial of a graph is a notion that has been extensively studied since the early 20th century. The chromatic polynomial of graph $G$ is denoted $P(G,m)$, and it is equal to the number of proper $m$-colorings of $G$. In 2019, Kaul and Mudrock introduced an analogue of the chromatic polynomial for DP-coloring; specifically, the DP color function of graph $G$ is denoted $P_{DP}(G,m)$. Two fundamental questions posed by Kaul and Mudrock are: (1) For any graph $G$ with $n$ vertices, is it the case that $P(G,m)-P_{DP}(G,m) = O(m^{n-3})$ as $m \\rightarrow \\infty$? and (2) For every graph $G$, does there exist $p,N \\in \\mathbb{N}$ such that $P_{DP}(K_p \\vee G, m) = P(K_p \\vee G, m)$ whenever $m \\geq N$? We show that the answer to both these questions is yes. In fact, we show the answer to (2) is yes even if we require $p=1$.", "field": "math", "label": 1}
{"text": "Title: Provably Powerful Graph Neural Networks for Directed Multigraphs\nAbstract: This paper analyses a set of simple adaptations that transform standard message-passing Graph Neural Networks (GNN) into provably powerful directed multigraph neural networks. The adaptations include multigraph port numbering, ego IDs, and reverse message passing. We prove that the combination of these theoretically enables the detection of any directed subgraph pattern. To validate the effectiveness of our proposed adaptations in practice, we conduct experiments on synthetic subgraph detection tasks, which demonstrate outstanding performance with almost perfect results. Moreover, we apply our proposed adaptations to two financial crime analysis tasks. We observe dramatic improvements in detecting money laundering transactions, improving the minority-class F1 score of a standard message-passing GNN by up to 30%, and closely matching or outperforming tree-based and GNN baselines. Similarly impressive results are observed on a real-world phishing detection dataset, boosting three standard GNNs' F1 scores by around 15% and outperforming all baselines.", "field": "cs", "label": 0}
{"text": "Title: Self-Stabilizing Indulgent Zero-degrading Binary Consensus\nAbstract: Guerraoui proposed an indulgent solution for the binary consensus problem. Namely, he showed that an arbitrary behavior of the failure detector never violates safety requirements even if it compromises liveness. Consensus implementations are often used in a repeated manner. Dutta and Guerraoui proposed a zero-degrading solution, \\ie during system runs in which the failure detector behaves perfectly, a node failure during one consensus instance has no impact on the performance of future instances. Our study, which focuses on indulgent zero-degrading binary consensus, aims at the design of an even more robust communication abstraction. We do so through the lenses of self-stabilization - a very strong notion of fault-tolerance. In addition to node and communication failures, self-stabilizing algorithms can recover after the occurrence of arbitrary transient faults; these faults represent any violation of the assumptions according to which the system was designed to operate (as long as the algorithm code stays intact). This work proposes the first, to the best of our knowledge, self-stabilizing algorithm for indulgent zero-degrading binary consensus for time-free message-passing systems prone to detectable process failures. The proposed algorithm has an O(1) stabilization time (in terms of asynchronous cycles) from arbitrary transient faults. Since the proposed solution uses an {\\Omega} failure detector, we also present the first, to the best of our knowledge, self-stabilizing asynchronous {\\Omega} failure detector, which is a variation on the one by Most\\'efaoui, Mourgaya, and Raynal.", "field": "cs", "label": 1}
{"text": "Title: Near Optimal Bounds for Collision in Pollard Rho for Discrete Log\nAbstract: We analyze a fairly standard idealization of Pollard's Rho algorithm for finding the discrete logarithm in a cyclic group G. It is found that, with high probability, a collision occurs in $O(\\sqrt{|G|\\log |G| \\log \\log |G|})$ steps, not far from the widely conjectured value of $\\Theta(\\sqrt{|G|})$. This improves upon a recent result of Miller--Venkatesan which showed an upper bound of $O(\\sqrt{|G|}\\log^3 |G|)$. Our proof is based on analyzing an appropriate nonreversible, non-lazy random walk on a discrete cycle of (odd) length |G|, and showing that the mixing time of the corresponding walk is $O(\\log |G| \\log \\log |G|)$.", "field": "math", "label": 1}
{"text": "Title: A Bregman Proximal Stochastic Gradient Method with Extrapolation for Nonconvex Nonsmooth Problems\nAbstract: In this paper, we explore a specific optimization problem that involves the combination of a differentiable nonconvex function and a nondifferentiable function. The differentiable component lacks a global Lipschitz continuous gradient, posing challenges for optimization. To address this issue and accelerate the convergence, we propose a Bregman proximal stochastic gradient method with extrapolation (BPSGE), which only requires smooth adaptivity of the differentiable part. Under the variance reduction framework, we not only analyze the subsequential and global convergence of the proposed algorithm under certain conditions, but also analyze the sublinear convergence rate of the subsequence, and the complexity of the algorithm, revealing that the BPSGE algorithm requires at most O(epsilon\\^\\,(-2)) iterations in expectation to attain an epsilon-stationary point. To validate the effectiveness of our proposed algorithm, we conduct numerical experiments on three real-world applications: graph regularized nonnegative matrix factorization (NMF), matrix factorization with weakly-convex regularization, and NMF with nonconvex sparsity constraints. These experiments demonstrate that BPSGE is faster than the baselines without extrapolation.", "field": "math", "label": 0}
{"text": "Title: Estimating Categorical Counterfactuals via Deep Twin Networks\nAbstract: Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, one requires knowledge of the underlying causal mechanisms. However, causal mechanisms cannot be uniquely determined from observations and interventions alone. This raises the question of how to choose the causal mechanisms so that resulting counterfactual inference is trustworthy in a given domain. This question has been addressed in causal models with binary variables, but the case of categorical variables remains unanswered. We address this challenge by introducing for causal models with categorical variables the notion of counterfactual ordering, a principle that posits desirable properties causal mechanisms should posses, and prove that it is equivalent to specific functional constraints on the causal mechanisms. To learn causal mechanisms satisfying these constraints, and perform counterfactual inference with them, we introduce deep twin networks. These are deep neural networks that, when trained, are capable of twin network counterfactual inference -- an alternative to the abduction, action, & prediction method. We empirically test our approach on diverse real-world and semi-synthetic data from medicine, epidemiology, and finance, reporting accurate estimation of counterfactual probabilities while demonstrating the issues that arise with counterfactual reasoning when counterfactual ordering is not enforced.", "field": "cs", "label": 1}
{"text": "Title: On the real zeros of depth 1 quasimodular forms\nAbstract: We discuss the critical points of modular forms, or more generally the zeros of quasimodular forms of depth $1$ for $\\mathrm{PSL}_2(\\mathbb Z)$. In particular, we consider the derivatives of the unique weight $k$ modular forms $f_k$ with the maximal number of consecutive zero Fourier coefficients following the constant $1$. Our main results state that (1) every zero of a depth $1$ quasimodular form near the derivative of the Eisenstein series in the standard fundamental domain lies on the geodesic segment $\\{z \\in \\mathbb H: \\Re(z)=1/2\\}$, and (2) more than half of zeros of $f_k$ in the standard fundamental domain lie on the geodesic segment $\\{z \\in \\mathbb H: \\Re(z)=1/2\\}$ for large enough $k$ with $k\\equiv 0 \\pmod{12}$.", "field": "math", "label": 0}
{"text": "Title: A new metric on the contactomorphism group of orderable contact manifolds\nAbstract: We introduce a pseudo-metric on the contactomorphism group of any contact manifold $(M,\\xi)$ with a cooriented contact structure $\\xi$. It is the contact analogue of a corresponding semi-norm in Hofer's geometry, and on certain classes of contact manifolds, its lift to the universal cover can be viewed as a continuous version of the integer valued bi-invariant metric introduced by Fraser, Polterovich, and Rosen. We show that it is non-degenerate if and only if $(M,\\xi)$ is strongly orderable and that its metric topology agrees with the interval topology introduced by Chernov and Nemirovski. In particular, the interval topology is Hausdorff whenever it is non-trivial, which answers a question of Chernov and Nemirovski. We discuss analogous results for isotopy classes of Legendrians and universal covers.", "field": "math", "label": 0}
{"text": "Title: Searching for (sharp) thresholds in random structures: where are we now?\nAbstract: We survey the current state of affairs in the study of thresholds and sharp thresholds in random structures on the occasion of the recent proof of the Kahn--Kalai Conjecture by Park and Pham and the fairly recent proof of the satisfiability conjecture for large $k$ by Ding, Sly, and Sun. Random discrete structures appear as fundamental objects of study in many scientific and mathematical fields including statistical physics, combinatorics, algorithms and complexity, social choice theory, coding theory, and statistics. While the models and properties of interest in these fields vary widely, much progress has been made through the development of general tools applicable to large families of models and properties all at once. Historically these tools originated to solve or make progress on specific, difficult conjectures in the areas mentioned above. We will survey recent progress on some of these hard problems and describe some challenges for the future.", "field": "math", "label": 0}
{"text": "Title: On Zeros of q-Entire Functions\nAbstract: In this work we first give a upper bound for the modulus of q-transcendental entire functions, then prove certain sums associated with their zeros are convergent, and derive the asymptotic behaviors of their associated heat kernels.", "field": "math", "label": 0}
{"text": "Title: A Multi-Criteria Metaheuristic Algorithm for Distributed Optimization of Electric Energy Storage\nAbstract: The distributed schedule optimization of energy storage constitutes a challenge. Such algorithms often expect an input set containing all feasible schedules or respectively require to efficiently search the schedule space. It is hardly possible to accomplish this with energy storage due to its high flexibility. In this paper, the problem is introduced in detail and addressed by a metaheuristic algorithm, which generates a preselection of schedules. Three contributions are presented to achieve this goal: First, an extension for a distributed schedule optimization allowing a simultaneous optimization is developed. Second, an evolutionary algorithm is designed to generate optimized schedules. Third, the algorithm is extended to include an arbitrary local criterion. It is shown that the presented approach is suitable to schedule electric energy storage in real households and industries with different generator and storage types.", "field": "cs", "label": 1}
{"text": "Title: Re-evaluating the Memory-balanced Pipeline Parallelism: BPipe\nAbstract: Pipeline parallelism is an essential technique in the training of large-scale Transformer models. However, it suffers from imbalanced memory consumption, leading to insufficient memory utilization. The BPipe technique was proposed to address this issue and has proven effective in the GPT-3 model. Nevertheless, our experiments have not yielded similar benefits for LLaMA training. Additionally, BPipe only yields negligible benefits for GPT-3 training when applying flash attention. We analyze the underlying causes of the divergent performance of BPipe on GPT-3 and LLaMA. Furthermore, we introduce a novel method to estimate the performance of BPipe.", "field": "cs", "label": 0}
{"text": "Title: Unsupervised learning from videos using temporal coherency deep networks\nAbstract: In this work we address the challenging problem of unsupervised learning from videos. Existing methods utilize the spatio-temporal continuity in contiguous video frames as regularization for the learning process. Typically, this temporal coherence of close frames is used as a free form of annotation, encouraging the learned representations to exhibit small differences between these frames. But this type of approach fails to capture the dissimilarity between videos with different content, hence learning less discriminative features. We here propose two Siamese architectures for Convolutional Neural Networks, and their corresponding novel loss functions, to learn from unlabeled videos, which jointly exploit the local temporal coherence between contiguous frames, and a global discriminative margin used to separate representations of different videos. An extensive experimental evaluation is presented, where we validate the proposed models on various tasks. First, we show how the learned features can be used to discover actions and scenes in video collections. Second, we show the benefits of such an unsupervised learning from just unlabeled videos, which can be directly used as a prior for the supervised recognition tasks of actions and objects in images, where our results further show that our features can even surpass a traditional and heavily supervised pre-training plus fine-tunning strategy.", "field": "cs", "label": 1}
{"text": "Title: Discriminants of stable rank two sheaves on some general type surfaces\nAbstract: We prove sharp bounds on the discriminants of stable rank two sheaves on surfaces in three-dimensional projective space. The key technical ingredient is to study them as torsion sheaves in projective space via tilt stability in the derived category. We then proceed to describe the surface itself as a moduli space of rank two vector bundles on it. Lastly, we give a proof of the Bogomolov inequality for semistable rank two sheaves on integral surfaces in three-dimensional projective space in all characteristics.", "field": "math", "label": 1}
{"text": "Title: Infinite-Time Singularities of the Lagrangian Mean Curvature Flow\nAbstract: In this paper, we exhibit examples of Lagrangian mean curvature flow which exist and are embedded for all time, but form an infinite-time singularity and converge to an immersed special Lagrangian as $t\\to\\infty$. This result shows that infinite-time singularities can form in the Thomas--Yau `semi-stable' situation. Our work is a parabolic analogue of the results of Dominic Joyce and Yng-Ing Lee regarding desingularisation of special Lagrangians with conical singularities. The gluing construction that we employ is inspired by the work of Simon Brendle and Nikolaos Kapouleas regarding ancient solutions of the Ricci flow.", "field": "math", "label": 0}
{"text": "Title: Sparsity and spectral properties of dual frames\nAbstract: We study sparsity and spectral properties of dual frames of a given finite frame. We show that any finite frame has a dual with no more than $n^2$ non-vanishing entries, where $n$ denotes the ambient dimension, and that for most frames no sparser dual is possible. Moreover, we derive an expression for the exact sparsity level of the sparsest dual for any given finite frame using a generalized notion of spark. We then study the spectral properties of dual frames in terms of singular values of the synthesis operator. We provide a complete characterization for which spectral patterns of dual frames are possible for a fixed frame. For many cases, we provide simple explicit constructions for dual frames with a given spectrum, in particular, if the constraint on the dual is that it be tight.", "field": "math", "label": 1}
{"text": "Title: Uncertainty in Minimum Cost Multicuts for Image and Motion Segmentation\nAbstract: The minimum cost lifted multicut approach has proven practically good performance in a wide range of applications such as image decomposition, mesh segmentation, multiple object tracking, and motion segmentation. It addresses such problems in a graph-based model, where real-valued costs are assigned to the edges between entities such that the minimum cut decomposes the graph into an optimal number of segments. Driven by a probabilistic formulation of minimum cost multicuts, we provide a measure for the uncertainties of the decisions made during the optimization. We argue that access to such uncertainties is crucial for many practical applications and conduct an evaluation by means of sparsifications on three different, widely used datasets in the context of image decomposition (BSDS-500) and motion segmentation (DAVIS2016 and FBMS59) in terms of variation of information (VI) and Rand index (RI).", "field": "cs", "label": 1}
{"text": "Title: Entropy-based Discovery of Summary Causal Graphs in Time Series\nAbstract: This study addresses the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new causal temporal mutual information measure for time series. We then show how this measure relates to an entropy reduction principle that can be seen as a special case of the probability raising principle. We finally combine these two ingredients in PC-like and FCI-like algorithms to construct the summary causal graph. There algorithm are evaluated on several datasets, which shows both their efficacy and efficiency.", "field": "cs", "label": 1}
{"text": "Title: Counting symmetric and non-symmetric peaks in a set partition\nAbstract: The aim of this paper is to derive explicit formulas for two distinct values. The first is the total number of symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks, and the second one is the total number of non-symmetric peaks in a set partition of $[n]$ with exactly $k$ blocks. We represent these results in two ways. First by using the theory of generating functions, and the second by using combinatorial tools.", "field": "math", "label": 0}
{"text": "Title: A Bayesian Model for Discovering Typological Implications\nAbstract: A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such implications are typically discovered by painstaking hand analysis over a small sample of languages. We propose a computational model for assisting at this process. Our model is able to discover both well-known implications as well as some novel implications that deserve further study. Moreover, through a careful application of hierarchical analysis, we are able to cope with the well-known sampling problem: languages are not independent.", "field": "cs", "label": 1}
{"text": "Title: On Dyck Path Expansion Formulas for Rank 2 Cluster Variables\nAbstract: In this paper, we simplify and generalize formulas for the expansion of rank 2 cluster variables. In particular, we prove an equivalent, but simpler, description of the colored Dyck subpaths framework introduced by Lee and Schiffler. We then prove the conjectured bijectivity of a map constructed by Feiyang Lin between collections of colored Dyck subpaths and compatible pairs, objects introduced by Lee, Li, and Zelevinsky to study the greedy basis. We use this bijection along with Rupel's expansion formula for quantum greedy basis elements, which sums over compatible pairs, to provide a quantum generalization of Lee and Schiffler's colored Dyck subpaths formula.", "field": "math", "label": 1}
{"text": "Title: Towards understanding the Pierce-Birkhoff conjecture via MV-algebras\nAbstract: Our main issue was to understand the connection between \\L ukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we define the class of \\textit{f}MV-algebras, which are MV-algebras endowed with both an internal binary product and a scalar product with scalars from $[0,1]$. The proper quasi-variety generated by $[0,1]$, with both products interpreted as the real product, provides the desired framework: the normal form theorem of its corresponding logical system can be seen as a local version of the Pierce-Birkhoff conjecture.", "field": "math", "label": 1}
{"text": "Title: Allison-Benkart-Gao functor and the free non-unital alternative algebras\nAbstract: Let $k$ be a field of characteristic $0$. We introduce a pair of adjoint functors, Allison-Benkart-Gao functor $\\mathcal{ABG}$ and Berman-Moody functor $\\mathcal{BM}$, between the category of non-unital alternative algebras over $k$ and the category ${\\text{\\bf Lie}_{\\text{R}}}$ of Lie algebras with appropriate $sl_3(k)$-module structures. Surprisingly, when $A$ is a non-unital alternative algebra, the Allison-Gao Lie algebra $\\mathcal{ABG}(A)$ is different from the more well-known Steinberg Lie algebra $st_3(A)$. Next, let $A(D)$ be the free (non-unit) alternative algebra generated by $D$ elements and $\\text{Inner} A(D)$ the inner derivation algebra of $A(D)$. A conjecture on the homology of $H_r(\\mathcal{ABG}(A(D)))$ is proposed. Let $A(D)_n$(resp. $\\text{Inner} A(D)_n$) be the degree $n$ component of $A(D)_n$(resp. $\\text{Inner} A(D)_n$). The previous conjecture implies another conjecture on the dimensions on $A(D)_n$ and $\\text{Inner} A(D)_n$. We also give some evidences to support the these conjectures.", "field": "math", "label": 0}
{"text": "Title: A characterisation of elementary fibrations\nAbstract: Grothendieck fibrations provide a unifying algebraic framework that underlies the treatment of various form of logics, such as first order logic, higher order logics and dependent type theories. In the categorical approach to logic proposed by Lawvere, which systematically uses adjoints to describe the logical operations, equality is presented in the form of a left adjoint to reindexing along a diagonal arrows in the base. Taking advantage of the modular perspective provided by category theory, one can look at those Grothendieck fibrations which sustain just the structure of equality, the so-called elementary fibrations, aka fibrations with equality. The present paper provides a characterisation of elementary fibrations based on particular structures in the fibres, called transporters. The characterisation is a substantial generalisation of the one already available for faithful fibrations. There is a close resemblance between transporters and the structures used in the semantics of the identity type of Martin-L\\\"of type theory. We close the paper by comparing the two.", "field": "math", "label": 1}
{"text": "Title: Stability over a predicate and prime closure\nAbstract: We prove that in a theory $T$ stable over a predicate $P$, for any $\\lambda > |T|$, there is a $\\lambda$-prime model over any complete set A with a $\\lambda$-saturated $P$-part.", "field": "math", "label": 0}
{"text": "Title: An Effective Baseline for Robustness to Distributional Shift\nAbstract: Refraining from confidently predicting when faced with categories of inputs different from those seen during training is an important requirement for the safe deployment of deep learning systems. While simple to state, this has been a particularly challenging problem in deep learning, where models often end up making overconfident predictions in such situations. In this work we present a simple, but highly effective approach to deal with out-of-distribution detection that uses the principle of abstention: when encountering a sample from an unseen class, the desired behavior is to abstain from predicting. Our approach uses a network with an extra abstention class and is trained on a dataset that is augmented with an uncurated set that consists of a large number of out-of-distribution (OoD) samples that are assigned the label of the abstention class; the model is then trained to learn an effective discriminator between in and out-of-distribution samples. We compare this relatively simple approach against a wide variety of more complex methods that have been proposed both for out-of-distribution detection as well as uncertainty modeling in deep learning, and empirically demonstrate its effectiveness on a wide variety of of benchmarks and deep architectures for image recognition and text classification, often outperforming existing approaches by significant margins. Given the simplicity and effectiveness of this method, we propose that this approach be used as a new additional baseline for future work in this domain.", "field": "cs", "label": 1}
{"text": "Title: Big pictures of motivic and classical homotopy theories\nAbstract: Motivic homotopy theory is meant to play the role of algebraic topology, in particular homotopy theory, in the context of algebraic geometry. As proved by Oliver Rondigs and Paul Arne Ostvaer, this theory is closely connected to Voevodsky's triangulated category of motives. A connection that is the motivic analogue of the connection between algebraic topology and homological algebra. In this paper, we try to understand the big picture of motivic homotopy theory and its connection to Voevodsky's motives by comparison to the classical counterpart.", "field": "math", "label": 0}
{"text": "Title: An almost linear time algorithm testing whether the Markoff graph modulo $p$ is connected\nAbstract: The Markoff graph modulo $p$ is known to be connected for all but finitely many primes $p$ (see Eddy, Fuchs, Litman, Martin, Tripeny, and Vanyo [arxiv:2308.07579]), and it is conjectured that these graphs are connected for all primes. In this paper, we provide an algorithmic realization of the process introduced by Bourgain, Gamburd, and Sarnak [arxiv:1607.01530] to test whether a Markoff graph modulo $p$ is connected for arbitrary primes. Our algorithm runs in $o(p^{1 + \\epsilon})$ time for every $\\epsilon > 0$. We demonstrate this algorithm by confirming that the Markoff graph modulo $p$ is connected for all primes less than one million.", "field": "math", "label": 0}
{"text": "Title: Sorting by Reversals and the Theory of 4-Regular Graphs\nAbstract: We show that the theory of sorting by reversals fits into the well-established theory of circuit partitions of 4-regular multigraphs (which also involves the combinatorial structures of circle graphs and delta-matroids). In this way, we expose strong connections between the two theories that have not been fully appreciated before. We also discuss a generalization of sorting by reversals involving the double-cut-and-join (DCJ) operation. Finally, we also show that the theory of sorting by reversals is closely related to that of gene assembly in ciliates.", "field": "cs", "label": 1}
{"text": "Title: Harmonic curvature in dimension four\nAbstract: We provide a step towards classifying Riemannian four-manifolds in which the curvature tensor has zero divergence, or -- equivalently -- the Ricci tensor Ric satisfies the Codazzi equation. Every known compact manifold of this type belongs to one of five otherwise-familiar classes of examples. The main result consists in showing that, if such a manifold (not necessarily compact or even complete) lies outside of the five classes -- a non-vacuous assumption -- then, at all points of a dense open subset, Ric has four distinct eigenvalues, while suitable local coordinates simultaneously diagonalize Ric, the metric and, in a natural sense, also the curvature tensor. Furthermore, in a local orthonormal frame formed by Ricci eigenvectors, the connection form (or, curvature tensor) has just twelve (or, respectively, six) possibly-nonzero components, which together satisfy a specific system, not depending on the point, of homogeneous polynomial equations. A part of the classification problem is thus reduced to a question in real algebraic geometry.", "field": "math", "label": 0}
{"text": "Title: A Bag of Visual Words Approach for Symbols-Based Coarse-Grained Ancient Coin Classification\nAbstract: The field of Numismatics provides the names and descriptions of the symbols minted on the ancient coins. Classification of the ancient coins aims at assigning a given coin to its issuer. Various issuers used various symbols for their coins. We propose to use these symbols for a framework that will coarsely classify the ancient coins. Bag of visual words (BoVWs) is a well established visual recognition technique applied to various problems in computer vision like object and scene recognition. Improvements have been made by incorporating the spatial information to this technique. We apply the BoVWs technique to our problem and use three symbols for coarse-grained classification. We use rectangular tiling, log-polar tiling and circular tiling to incorporate spatial information to BoVWs. Experimental results show that the circular tiling proves superior to the rest of the methods for our problem.", "field": "cs", "label": 1}
{"text": "Title: The Hochschild Cohomology of Uniform Roe Algebras\nAbstract: In Rufus Willett's and the authors paper \"Bounded Derivations on Uniform Roe Algebras\" we showed that all bounded derivations on a uniform Roe algebra $C^*_u(X)$ associated to a bounded geometry metric space $X$ are inner. This naturally leads to the question of whether or not the higher dimensional Hochschild cohomology groups of the uniform Roe algebra vanish also. While we cannot answer this question completely, we are able to give necessary and sufficient conditions for the vanishing of $H^n_c(C_u^*(X),C_u^*(X))$. Lastly, we show that if the norm continuous Hochschild cohomology of a uniform Roe algebra vanishes in all dimensions then the ultraweak-weak* continuous Hochschild cohomology of that uniform Roe algebra vanishes also.", "field": "math", "label": 1}
{"text": "Title: Isometric Dilations for Representations of Product Systems\nAbstract: We discuss representations of product systems (of $W^*$-correspondences) over the semigroup $\\mathbb{Z}^n_+$ and show that, under certain pureness and Szego positivity conditions, a completely contractive representation can be dilated to an isometric representation. For $n=1,2$ this is known to hold in general (without assuming the conditions) but, for $n\\geq 3$, it does not hold in general (as is known for the special case of isometric dilations of a tuple of commuting contractions). Restricting to the case of tuples of commuting contractions, our result reduces to a result of Barik, Das, Haria and Sarkar. Our dilation is explicitly constructed and we present some applications.", "field": "math", "label": 0}
{"text": "Title: The Knothe-Rosenblatt distance and its induced topology\nAbstract: A basic and natural coupling between two probabilities on $\\mathbb R^N$ is given by the Knothe-Rosenblatt coupling. It represents a multiperiod extension of the quantile coupling and is simple to calculate numerically. We consider the distance on $\\mathcal P (\\mathbb R^N)$ that is induced by considering the transport costs associated to the Knothe-Rosenblatt coupling. We show that this Knothe-Rosenblatt distance metrizes the adapted weak topology which is a stochastic process version of the usual weak topology and plays an important role, e.g. concerning questions on stability of stochastic control and probabilistic operations. We also establish that the Knothe-Rosenblatt distance is a geodesic distance, give a Skorokhod representation theorem for the adapted weak topology, and provide multi-dimensional versions of our results.", "field": "math", "label": 0}
{"text": "Title: Green functions for GJMS operators on spheres, Gegenbauer polynomials and rigidity theorems\nAbstract: We derive explicit representation formulae of Green functions for GJMS operators on $n$-spheres, including the fractional ones. These formulae not only have natural geometric interpretations concerning the extrinsic geometry of the round sphere, but also reflect the spherical rigidity among closed embedded hypersurfaces in $\\mathbb{R}^{n+1}$.", "field": "math", "label": 0}
{"text": "Title: Asymptotic expansion of 2-dimensional gradient graph with vanishing mean curvature at infinity\nAbstract: In this paper, we establish the asymptotic expansion at infinity of gradient graph in dimension 2 with vanishing mean curvature at infinity. This corresponds to our previous results in higher dimensions and generalizes the results for minimal gradient graph on exterior domain in dimension 2. Different from the strategies for higher dimensions, instead of the equivalence of Green's function on unbounded domains, we apply a version of iteration methods from Bao--Li--Zhang [Calc.Var PDE, 52(2015), pp. 39-63] that is refined by spherical harmonic expansions to provide a more explicit asymptotic behavior than known results.", "field": "math", "label": 1}
{"text": "Title: Stability of Rellich-Sobolev type inequality involving Hardy term for bi-Laplacian\nAbstract: For $N\\geq 5$ and $0<\\mu<N-4$, we first show a non-degenerate result of the extremal for the following Rellich-Sobolev type inequality \\begin{align*} & \\int_{\\mathbb{R}^N}|\\Delta u|^2 \\mathrm{d}x -C_{\\mu,1}\\int_{\\mathbb{R}^N}\\frac{|\\nabla u|^2}{|x|^2} \\mathrm{d}x +C_{\\mu,2}\\int_{\\mathbb{R}^N}\\frac{u^2}{|x|^4} \\mathrm{d}x \\geq \\mathcal{S}_\\mu\\left(\\int_{\\mathbb{R}^N}|u|^{\\frac{2N}{N-4}} \\mathrm{d}x\\right)^\\frac{N-4}{N},\\quad u\\in C^\\infty_0(\\mathbb{R}^N), \\end{align*} where $C_{\\mu,1}$, $C_{\\mu,1}$ and $\\mathcal{S}_\\mu$ are constants depending on $\\mu$, furthermore equality only holds for some radial functions, which is a key ingredient in analyzing the blow-up phenomena of solutions to various elliptic equations on bounded or unbounded domain. Moreover, by using spectral estimate combined with a compactness argument, we give the remainder term of above inequality.", "field": "math", "label": 0}
{"text": "Title: Jacobi-Jordan conformal algebras: Basics, Constructions and related structures\nAbstract: The main purpose of this paper is to introduce and investigate the notion of Jacobi-Jordan conformal algebra. They are a generalization of Jacobi-Jordan algebras which correspond to the case in which the formal parameter lambda equals 0. We consider some related structures such as conformal modules, corresponding representations and O-operators. Therefore, conformal derivations from Jacobi-Jordan conformal algebras to their conformal modules are used to describe conformal derivations of Jacobi-Jordan conformal algebras of semidirect product type. Moreover, we study a class of Jacobi-Jordan conformal algebras called quadratic Jacobi-Jordan conformal algebras, which are characterized by mock-Gel'fand Dorfman bialgebras. Finally, the C[delta]-split extending structures problem for Jacobi-Jordan conformal algebras is studied. Furthermore, we introduce an unified product of a given Jacobi-Jordan conformal algebra $J$ and a given C[delta]-module K. This product includes some other interesting products of Jacobi-Jordan conformal algebras such as twisted product or crossed product. Using this product, a cohomological type object is constructed to provide a theoretical answer to the C[delta]-split extending structures problem.", "field": "math", "label": 0}
{"text": "Title: Uncertainty-Aware Deep Attention Recurrent Neural Network for Heterogeneous Time Series Imputation\nAbstract: Missingness is ubiquitous in multivariate time series and poses an obstacle to reliable downstream analysis. Although recurrent network imputation achieved the SOTA, existing models do not scale to deep architectures that can potentially alleviate issues arising in complex data. Moreover, imputation carries the risk of biased estimations of the ground truth. Yet, confidence in the imputed values is always unmeasured or computed post hoc from model output. We propose DEep Attention Recurrent Imputation (DEARI), which jointly estimates missing values and their associated uncertainty in heterogeneous multivariate time series. By jointly representing feature-wise correlations and temporal dynamics, we adopt a self attention mechanism, along with an effective residual component, to achieve a deep recurrent neural network with good imputation performance and stable convergence. We also leverage self-supervised metric learning to boost performance by optimizing sample similarity. Finally, we transform DEARI into a Bayesian neural network through a novel Bayesian marginalization strategy to produce stochastic DEARI, which outperforms its deterministic equivalent. Experiments show that DEARI surpasses the SOTA in diverse imputation tasks using real-world datasets, namely air quality control, healthcare and traffic.", "field": "cs", "label": 0}
{"text": "Title: LLM4TS: Aligning Pre-Trained LLMs as Data-Efficient Time-Series Forecasters\nAbstract: Multivariate time-series forecasting is vital in various domains, e.g., economic planning and weather prediction. Deep train-from-scratch models have exhibited effective performance yet require large amounts of data, which limits real-world applicability. Recently, researchers have explored pre-trained Large Language Models (LLMs) for limited non-linguistic datasets. However, incorporating LLMs with time-series data presents challenges of limited adaptation due to different compositions between time-series and linguistic data, and the inability to process multi-scale temporal information. To tackle these challenges, we propose LLM4TS, a framework for time-series forecasting with pre-trained LLMs. LLM4TS consists of a two-stage fine-tuning strategy: the time-series alignment stage to align LLMs with the nuances of time-series data, and the forecasting fine-tuning stage, which is specifically designed for time-series forecasting tasks. Furthermore, our framework features a novel two-level aggregation method that integrates multi-scale temporal data within pre-trained LLMs, enhancing their ability to interpret time-specific information. In experiments across 7 time-series forecasting datasets, LLM4TS is superior to existing state-of-the-art methods, including those trained from scratch, in full-shot scenarios, and also achieves an average improvement of 6.84% in MSE in few-shot scenarios. In addition, evaluations compared with different self-supervised learning approaches highlight LLM4TS's effectiveness with representation learning in forecasting scenarios.", "field": "cs", "label": 0}
{"text": "Title: An optimization-based reformulation of the classical displacement approach for state update of non-linear material models\nAbstract: In this paper, we build on recent work using a mathematical programming approach for incremental state update in analysis of non-linear mechanics models. In particular, we consider quasi-static analysis of continuum problems in the linearized kinematics regime, with non-linear material models described using convex energy functions. We find in this case that the classical displacement-based nested approach for incremental state update can be reformulated as solving a reduced dual optimization problem. This reformulation provides insights into the working of the algorithm, and eliminates the need for some heuristics. An important purpose of this paper is to further illustrate the unifying nature of the mathematical programming approach. We therefore present relationships with several of these types of algorithms recently presented in the literature for incremental state update.", "field": "math", "label": 1}
{"text": "Title: A class of finite $p$-groups and the normalized unit groups of group algebras\nAbstract: Let $p$ be a prime and $\\mathbb{F}_p$ be a finite field of $p$ elements. Let $\\mathbb{F}_pG$ denote the group algebra of the finite $p$-group $G$ over the field $\\mathbb{F}_p$ and $V(\\mathbb{F}_pG)$ denote the group of normalized units in $\\mathbb{F}_pG$. Suppose that $G$ is a finite $p$-group given by a central extension of the form $$1\\longrightarrow \\mathbb{Z}_{p^n}\\times \\mathbb{Z}_{p^m} \\longrightarrow G \\longrightarrow \\mathbb{Z}_p\\times \\cdots\\times \\mathbb{Z}_p \\longrightarrow 1$$ and $G'\\cong \\mathbb{Z}_p$, $n, m\\geq 1$ and $p$ is odd. In this paper, the structure of $G$ is determined. And the relations of $V(\\mathbb{F}_pG)^{p^l}$ and $G^{p^l}$, $\\Omega_l(V(\\mathbb{F}_pG))$ and $\\Omega_l(G)$ are given. Furthermore, there is a direct proof for $V(\\mathbb{F}_pG)^p\\bigcap G=G^p$.", "field": "math", "label": 0}
{"text": "Title: Perceptual Musical Features for Interpretable Audio Tagging\nAbstract: In the age of music streaming platforms, the task of automatically tagging music audio has garnered significant attention, driving researchers to devise methods aimed at enhancing performance metrics on standard datasets. Most recent approaches rely on deep neural networks, which, despite their impressive performance, possess opacity, making it challenging to elucidate their output for a given input. While the issue of interpretability has been emphasized in other fields like medicine, it has not received attention in music-related tasks. In this study, we explored the relevance of interpretability in the context of automatic music tagging. We constructed a workflow that incorporates three different information extraction techniques: a) leveraging symbolic knowledge, b) utilizing auxiliary deep neural networks, and c) employing signal processing to extract perceptual features from audio files. These features were subsequently used to train an interpretable machine-learning model for tag prediction. We conducted experiments on two datasets, namely the MTG-Jamendo dataset and the GTZAN dataset. Our method surpassed the performance of baseline models in both tasks and, in certain instances, demonstrated competitiveness with the current state-of-the-art. We conclude that there are use cases where the deterioration in performance is outweighed by the value of interpretability.", "field": "cs", "label": 0}
{"text": "Title: On the hardness of learning under symmetries\nAbstract: We study the problem of learning equivariant neural networks via gradient descent. The incorporation of known symmetries (\"equivariance\") into neural nets has empirically improved the performance of learning pipelines, in domains ranging from biology to computer vision. However, a rich yet separate line of learning theoretic research has demonstrated that actually learning shallow, fully-connected (i.e. non-symmetric) networks has exponential complexity in the correlational statistical query (CSQ) model, a framework encompassing gradient descent. In this work, we ask: are known problem symmetries sufficient to alleviate the fundamental hardness of learning neural nets with gradient descent? We answer this question in the negative. In particular, we give lower bounds for shallow graph neural networks, convolutional networks, invariant polynomials, and frame-averaged networks for permutation subgroups, which all scale either superpolynomially or exponentially in the relevant input dimension. Therefore, in spite of the significant inductive bias imparted via symmetry, actually learning the complete classes of functions represented by equivariant neural networks via gradient descent remains hard.", "field": "cs", "label": 0}
{"text": "Title: Topological aspects of Boolean functions\nAbstract: We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.", "field": "math", "label": 1}
{"text": "Title: On the unicity of types in special linear groups\nAbstract: Let $F$ be a non-archimedean local field. We show that any representation of a maximal compact subgroup of $\\mathbf{SL}_N(F)$ which is typical for an essentially tame supercuspidal representation must be induced from a Bushnell--Kutzko maximal simple type. From this, we explicitly count and describe the conjugacy classes of such typical representations, and give an explicit description of an inertial Langlands correspondence for essentially tame irreducible $N$-dimensional projective representations of the Weil group of $F$.", "field": "math", "label": 1}
{"text": "Title: Verifiable Computation with Massively Parallel Interactive Proofs\nAbstract: As the cloud computing paradigm has gained prominence, the need for verifiable computation has grown increasingly urgent. The concept of verifiable computation enables a weak client to outsource difficult computations to a powerful, but untrusted, server. Protocols for verifiable computation aim to provide the client with a guarantee that the server performed the requested computations correctly, without requiring the client to perform the computations herself. By design, these protocols impose a minimal computational burden on the client. However, existing protocols require the server to perform a large amount of extra bookkeeping in order to enable a client to easily verify the results. Verifiable computation has thus remained a theoretical curiosity, and protocols for it have not been implemented in real cloud computing systems. Our goal is to leverage GPUs to reduce the server-side slowdown for verifiable computation. To this end, we identify abundant data parallelism in a state-of-the-art general-purpose protocol for verifiable computation, originally due to Goldwasser, Kalai, and Rothblum, and recently extended by Cormode, Mitzenmacher, and Thaler. We implement this protocol on the GPU, obtaining 40-120x server-side speedups relative to a state-of-the-art sequential implementation. For benchmark problems, our implementation reduces the slowdown of the server to factors of 100-500x relative to the original computations requested by the client. Furthermore, we reduce the already small runtime of the client by 100x. Similarly, we obtain 20-50x server-side and client-side speedups for related protocols targeted at specific streaming problems. We believe our results demonstrate the immediate practicality of using GPUs for verifiable computation, and more generally that protocols for verifiable computation have become sufficiently mature to deploy in real cloud computing systems.", "field": "cs", "label": 1}
{"text": "Title: Hilbert Poincaré series and kernels for products of $L$-functions\nAbstract: We study Hilbert Poincar\\'e series associated to general seed functions and construct Cohen's kernels and double Eisenstein series as series of Hilbert Poincar\\'e series. Then we calculate the Rankin-Cohen brackets of Hilbert Poincar\\'e series and Hilbert modular forms and extend Zagier's kernel formula to totally real number fields. Finally, we show that the Rankin-Cohen brackets of two different types of Eisenstein series are special values of double Eisenstein series up to a constant.", "field": "math", "label": 0}
{"text": "Title: Computationally Assisted Quality Control for Public Health Data Streams\nAbstract: Irregularities in public health data streams (like COVID-19 Cases) hamper data-driven decision-making for public health stakeholders. A real-time, computer-generated list of the most important, outlying data points from thousands of daily-updated public health data streams could assist an expert reviewer in identifying these irregularities. However, existing outlier detection frameworks perform poorly on this task because they do not account for the data volume or for the statistical properties of public health streams. Accordingly, we developed FlaSH (Flagging Streams in public Health), a practical outlier detection framework for public health data users that uses simple, scalable models to capture these statistical properties explicitly. In an experiment where human experts evaluate FlaSH and existing methods (including deep learning approaches), FlaSH scales to the data volume of this task, matches or exceeds these other methods in mean accuracy, and identifies the outlier points that users empirically rate as more helpful. Based on these results, FlaSH has been deployed on data streams used by public health stakeholders.", "field": "cs", "label": 0}
{"text": "Title: An example for Kuznetsov-Shinder conjecture\nAbstract: We give an example for the Kuznetsov-Shinder conjecture, with infinitely many non-isomorphic D-equivalent and L-equivalent varieties.", "field": "math", "label": 0}
{"text": "Title: A new characterization of $E_8 (p)$ via its vanishing elements\nAbstract: Let $G$ be a finite group, and $g \\in G$. Then $g$ is said to be a vanishing element of $G$, if there exists an irreducible character $\\chi$ of $G$ such that $\\chi (g)=0$. Denote by ${\\rm Vo} (G)$ the set of the orders of vanishing elements of $G$. We say a non-abelian group $G$ is V-recognizable, if any group $N$ with ${\\rm Vo} (N) = {\\rm Vo} (G)$ is isomorphic to $G$. In this paper, we investigate the V-recognizability of $E_8 (p)$, where $p$ is a prime number. As an application, among the 610 primes $p$ with $p<10000$ and $p \\equiv 0,1,4\\,(\\!\\!\\!\\mod 5)$, we obtain that the method is always valid for confirming the V-recognizability of $E_8 (p)$ for all such $p$ but $ 919,1289,1931,3911,4691,5381$ and $7589 $.", "field": "math", "label": 0}
{"text": "Title: Representing topological full groups in Steinberg algebras and C*-algebras\nAbstract: We study the natural representation of the topological full group of an ample Hausdorff groupoid in the groupoid's complex Steinberg algebra and in its full and reduced C*-algebras. We characterise precisely when this representation is injective and show that it is rarely surjective. We then restrict our attention to discrete groupoids, which provide unexpected insight into the behaviour of the representation of the topological full group in the full and reduced groupoid C*-algebras. We show that the image of the representation is not dense in the full groupoid C*-algebra unless the groupoid is a group, and we provide an example showing that the image of the representation may still be dense in the reduced groupoid C*-algebra even when the groupoid is not a group.", "field": "math", "label": 0}
{"text": "Title: LLM-SAP: Large Language Model Situational Awareness Based Planning\nAbstract: This work pioneers evaluating emergent planning capabilities based on situational awareness in large language models. We contribute (i) novel benchmarks and metrics for standardized assessment; (ii) a unique dataset to spur progress; and (iii) demonstrations that prompting and multi-agent schemes significantly enhance planning performance in context-sensitive planning tasks. Positioning this within a situated agent and automated planning research, we highlight inherent reliability challenges--efficiently mapping world states to actions without environmental guidance remains open despite simulated domain advances. Although out-of-scope, limitations around validation methodology and data availability indicate exciting directions, including fine-tuning on expanded planning corpora and optimizations for triggering fast latent planning. By conclusively demonstrating current methods' promise and limitations via rigorous comparison, we catalyze investigating reliable goal-directed reasoning for situated agents.", "field": "cs", "label": 0}
{"text": "Title: 2-Dimensional Combinatorial Calabi Flow in Hyperbolic Background Geometry\nAbstract: For triangulated surfaces locally embedded in the standard hyperbolic space, we introduce combinatorial Calabi flow as the negative gradient flow of combinatorial Calabi energy. We prove that the flow produces solutions which converge to ZCCP-metric (zero curvature circle packing metric) if the initial energy is small enough. Assuming the curvature has a uniform upper bound less than $2\\pi$, we prove that combinatorial Calabi flow exists for all time. Moreover, it converges to ZCCP-metric if and only if ZCCP-metric exists.", "field": "math", "label": 1}
{"text": "Title: Graph Neural Network Based Access Point Selection for Cell-Free Massive MIMO Systems\nAbstract: A graph neural network (GNN) based access point (AP) selection algorithm for cell-free massive multiple-input multiple-output (MIMO) systems is proposed. Two graphs, a homogeneous graph which includes only AP nodes representing the structure of the APs in the network, and a heterogeneous graph which includes both AP nodes and user equipment (UE) nodes are constructed to represent a cell-free massive MIMO network. A GNN based on the inductive graph learning framework GraphSAGE is used to obtain the embeddings which are then used to predict the links between the nodes. The numerical results show that compared to the proximity-based AP selection algorithms, the proposed GNN based algorithm predicts the potential APs with more accuracy. Compared to the large scale fading coefficient based AP selection algorithms, the proposed algorithm does not require measured and sorted signal strengths of all the neighbouring APs. Furthermore, the proposed algorithm is scalable in terms of the number of users in the cell-free system.", "field": "cs", "label": 1}
{"text": "Title: Novikov homology and noncommutative Alexander polynomials\nAbstract: In the early 2000's Cochran and Harvey introduced non-commutative Alexander polynomials for 3-manifolds. Their degrees give strong lower bounds on the Thurston norm. In this paper we make the case that the vanishing of a certain Novikov-Sikorav homology module is the correct notion of a monic non-commutative Alexander polynomial. Furthermore we will use the opportunity to give new proofs of several statements about Novikov-Sikorav homology in the three-dimensional context.", "field": "math", "label": 1}
{"text": "Title: Singular metrics and a conjecture by Campana and Peternell\nAbstract: A conjecture by Campana and Peternell says that if a positive multiple of $K_X$ is linearly equivalent to an effective divisor $D$ plus a pseudo-effective divisor, then the Kodaira dimension of $X$ should be at least as big as the Iitaka dimension of $D$. This is a very useful generalization of the non-vanishing conjecture (which is the case $D = 0$). We use recent work about singular metrics on pluri-adjoint bundles to show that the Campana-Peternell conjecture is almost equivalent to the non-vanishing conjecture.", "field": "math", "label": 1}
{"text": "Title: On the expected L2-discrepancy of stratified samples from parallel lines\nAbstract: We study the expected $\\mathcal{L}_2$-discrepancy of stratified samples generated from special equi-volume partitions of the unit square. The partitions are defined via parallel lines that are all orthogonal to the diagonal of the square. It is shown that the expected discrepancy of stratified samples derived from these partitions is a factor 2 smaller than the expected discrepancy of the same number of i.i.d uniformly distributed random points in the unit square. We conjecture that this is best possible among all partitions generated from parallel lines.", "field": "math", "label": 0}
{"text": "Title: The Alexander module of a trigonal curve\nAbstract: We describe the Alexander modules and Alexander polynomials (both over $\\Q$ and over finite fields $\\FF{p}$) of generalized trigonal curves. The rational case is closed completely; in the case of characteristic $p>0$, a few points remain open.", "field": "math", "label": 1}
{"text": "Title: Deep AUC Maximization for Medical Image Classification: Challenges and Opportunities\nAbstract: In this extended abstract, we will present and discuss opportunities and challenges brought about by a new deep learning method by AUC maximization (aka \\underline{\\bf D}eep \\underline{\\bf A}UC \\underline{\\bf M}aximization or {\\bf DAM}) for medical image classification. Since AUC (aka area under ROC curve) is a standard performance measure for medical image classification, hence directly optimizing AUC could achieve a better performance for learning a deep neural network than minimizing a traditional loss function (e.g., cross-entropy loss). Recently, there emerges a trend of using deep AUC maximization for large-scale medical image classification. In this paper, we will discuss these recent results by highlighting (i) the advancements brought by stochastic non-convex optimization algorithms for DAM; (ii) the promising results on various medical image classification problems. Then, we will discuss challenges and opportunities of DAM for medical image classification from three perspectives, feature learning, large-scale optimization, and learning trustworthy AI models.", "field": "cs", "label": 1}
{"text": "Title: Construction of spherical cubature formulas using lattices\nAbstract: We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on the sphere of dimension n-1 for n=4, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming.", "field": "math", "label": 1}
{"text": "Title: CardiGraphormer: Unveiling the Power of Self-Supervised Learning in Revolutionizing Drug Discovery\nAbstract: In the expansive realm of drug discovery, with approximately 15,000 known drugs and only around 4,200 approved, the combinatorial nature of the chemical space presents a formidable challenge. While Artificial Intelligence (AI) has emerged as a powerful ally, traditional AI frameworks face significant hurdles. This manuscript introduces CardiGraphormer, a groundbreaking approach that synergizes self-supervised learning (SSL), Graph Neural Networks (GNNs), and Cardinality Preserving Attention to revolutionize drug discovery. CardiGraphormer, a novel combination of Graphormer and Cardinality Preserving Attention, leverages SSL to learn potent molecular representations and employs GNNs to extract molecular fingerprints, enhancing predictive performance and interpretability while reducing computation time. It excels in handling complex data like molecular structures and performs tasks associated with nodes, pairs of nodes, subgraphs, or entire graph structures. CardiGraphormer's potential applications in drug discovery and drug interactions are vast, from identifying new drug targets to predicting drug-to-drug interactions and enabling novel drug discovery. This innovative approach provides an AI-enhanced methodology in drug development, utilizing SSL combined with GNNs to overcome existing limitations and pave the way for a richer exploration of the vast combinatorial chemical space in drug discovery.", "field": "cs", "label": 0}
{"text": "Title: Introduction to twisted commutative algebras\nAbstract: This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate rings of determinantal varieties, Segre-Veronese embeddings, and Grassmannians. The article is meant to serve as a gentle introduction to the papers of the two authors on the subject, and also to point out some literature in which these algebras appear. The first part reviews the representation theory of the symmetric groups and general linear groups. The second part introduces a related category and develops its basic properties. The third part develops some basic properties of twisted commutative algebras from the perspective of classical commutative algebra and summarizes some of the results of the authors. We have tried to keep the prerequisites to this article at a minimum. The article is aimed at graduate students interested in commutative algebra, algebraic combinatorics, or representation theory, and the interactions between these subjects.", "field": "math", "label": 1}
{"text": "Title: How Descriptive are GMRES Convergence Bounds?\nAbstract: GMRES is a popular Krylov subspace method for solving linear systems of equations involving a general non-Hermitian coefficient matrix. The conventional bounds on GMRES convergence involve polynomial approximation problems in the complex plane. Three popular approaches pose this approximation problem on the spectrum, the field of values, or pseudospectra of the coefficient matrix. We analyze and compare these bounds, illustrating with six examples the success and failure of each. When the matrix departs from normality due only to a low-dimensional invariant subspace, we discuss how these bounds can be adapted to exploit this structure. Since the Arnoldi process that underpins GMRES provides approximations to the pseudospectra, one can estimate the GMRES convergence bounds as an iteration proceeds.", "field": "math", "label": 1}
{"text": "Title: Discovery of Causal Additive Models in the Presence of Unobserved Variables\nAbstract: Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than in linear cases. In this study, we focus on causal additive models in the presence of unobserved variables. Causal additive models exhibit structural equations that are additive in the variables and error terms. We take into account the presence of not only unobserved common causes but also unobserved intermediate variables. Our theoretical results show that, when the causal relationships are nonlinear and there are unobserved variables, it is not possible to identify all the causal relationships between observed variables through regression and independence tests. However, our theoretical results also show that it is possible to avoid incorrect inferences. We propose a method to identify all the causal relationships that are theoretically possible to identify without being biased by unobserved variables. The empirical results using artificial data and simulated functional magnetic resonance imaging (fMRI) data show that our method effectively infers causal structures in the presence of unobserved variables.", "field": "cs", "label": 1}
{"text": "Title: Semi-supervised Contrastive Outlier removal for Pseudo Expectation Maximization (SCOPE)\nAbstract: Semi-supervised learning is the problem of training an accurate predictive model by combining a small labeled dataset with a presumably much larger unlabeled dataset. Many methods for semi-supervised deep learning have been developed, including pseudolabeling, consistency regularization, and contrastive learning techniques. Pseudolabeling methods however are highly susceptible to confounding, in which erroneous pseudolabels are assumed to be true labels in early iterations, thereby causing the model to reinforce its prior biases and thereby fail to generalize to strong predictive performance. We present a new approach to suppress confounding errors through a method we describe as Semi-supervised Contrastive Outlier removal for Pseudo Expectation Maximization (SCOPE). Like basic pseudolabeling, SCOPE is related to Expectation Maximization (EM), a latent variable framework which can be extended toward understanding cluster-assumption deep semi-supervised algorithms. However, unlike basic pseudolabeling which fails to adequately take into account the probability of the unlabeled samples given the model, SCOPE introduces an outlier suppression term designed to improve the behavior of EM iteration given a discrimination DNN backbone in the presence of outliers. Our results show that SCOPE greatly improves semi-supervised classification accuracy over a baseline, and furthermore when combined with consistency regularization achieves the highest reported accuracy for the semi-supervised CIFAR-10 classification task using 250 and 4000 labeled samples. Moreover, we show that SCOPE reduces the prevalence of confounding errors during pseudolabeling iterations by pruning erroneous high-confidence pseudolabeled samples that would otherwise contaminate the labeled set in subsequent retraining iterations.", "field": "cs", "label": 1}
{"text": "Title: State Space Decomposition and Subgoal Creation for Transfer in Deep Reinforcement Learning\nAbstract: Typical reinforcement learning (RL) agents learn to complete tasks specified by reward functions tailored to their domain. As such, the policies they learn do not generalize even to similar domains. To address this issue, we develop a framework through which a deep RL agent learns to generalize policies from smaller, simpler domains to more complex ones using a recurrent attention mechanism. The task is presented to the agent as an image and an instruction specifying the goal. This meta-controller guides the agent towards its goal by designing a sequence of smaller subtasks on the part of the state space within the attention, effectively decomposing it. As a baseline, we consider a setup without attention as well. Our experiments show that the meta-controller learns to create subgoals within the attention.", "field": "cs", "label": 1}
{"text": "Title: Adversarial Data Poisoning for Fake News Detection: How to Make a Model Misclassify a Target News without Modifying It\nAbstract: Fake news detection models are critical to countering disinformation but can be manipulated through adversarial attacks. In this position paper, we analyze how an attacker can compromise the performance of an online learning detector on specific news content without being able to manipulate the original target news. In some contexts, such as social networks, where the attacker cannot exert complete control over all the information, this scenario can indeed be quite plausible. Therefore, we show how an attacker could potentially introduce poisoning data into the training data to manipulate the behavior of an online learning method. Our initial findings reveal varying susceptibility of logistic regression models based on complexity and attack type.", "field": "cs", "label": 0}
{"text": "Title: Biologically Plausible Learning of Text Representation with Spiking Neural Networks\nAbstract: This study proposes a novel biologically plausible mechanism for generating low-dimensional spike-based text representation. First, we demonstrate how to transform documents into series of spikes spike trains which are subsequently used as input in the training process of a spiking neural network (SNN). The network is composed of biologically plausible elements, and trained according to the unsupervised Hebbian learning rule, Spike-Timing-Dependent Plasticity (STDP). After training, the SNN can be used to generate low-dimensional spike-based text representation suitable for text/document classification. Empirical results demonstrate that the generated text representation may be effectively used in text classification leading to an accuracy of $80.19\\%$ on the bydate version of the 20 newsgroups data set, which is a leading result amongst approaches that rely on low-dimensional text representations.", "field": "cs", "label": 1}
{"text": "Title: Error Forward-Propagation: Reusing Feedforward Connections to Propagate Errors in Deep Learning\nAbstract: We introduce Error Forward-Propagation, a biologically plausible mechanism to propagate error feedback forward through the network. Architectural constraints on connectivity are virtually eliminated for error feedback in the brain; systematic backward connectivity is not used or needed to deliver error feedback. Feedback as a means of assigning credit to neurons earlier in the forward pathway for their contribution to the final output is thought to be used in learning in the brain. How the brain solves the credit assignment problem is unclear. In machine learning, error backpropagation is a highly successful mechanism for credit assignment in deep multilayered networks. Backpropagation requires symmetric reciprocal connectivity for every neuron. From a biological perspective, there is no evidence of such an architectural constraint, which makes backpropagation implausible for learning in the brain. This architectural constraint is reduced with the use of random feedback weights. Models using random feedback weights require backward connectivity patterns for every neuron, but avoid symmetric weights and reciprocal connections. In this paper, we practically remove this architectural constraint, requiring only a backward loop connection for effective error feedback. We propose reusing the forward connections to deliver the error feedback by feeding the outputs into the input receiving layer. This mechanism, Error Forward-Propagation, is a plausible basis for how error feedback occurs deep in the brain independent of and yet in support of the functionality underlying intricate network architectures. We show experimentally that recurrent neural networks with two and three hidden layers can be trained using Error Forward-Propagation on the MNIST and Fashion MNIST datasets, achieving $1.90\\%$ and $11\\%$ generalization errors respectively.", "field": "cs", "label": 1}
{"text": "Title: Hereditary $n$-exangulated categories\nAbstract: Herschend-Liu-Nakaoka introduced the concept of $n$-exangulated categories as higher-dimensional analogues of extriangulated categories defined by Nakaoka-Palu. The class of $n$-exangulated categories contains $n$-exact categories and $(n+2)$-angulated categories as specific examples. In this article, we introduce the notion of hereditary $n$-exangulated categories, which generalize hereditary extriangulated categories. We provide two classes of hereditary $n$-exangulated categories through closed subfunctors. Additionally, we define the concept of $0$-Auslander $n$-exangulated categories and discuss the circumstances under which these two classes of hereditary $n$-exangulated categories become $0$-Auslander.", "field": "math", "label": 0}
{"text": "Title: Algebraic boundary of matrices of nonnegative rank at most three\nAbstract: The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component. In fact, this generating set is a Grobner basis with respect to the graded reverse lexicographic order. This solves a conjecture by Robeva, Sturmfels and the last author.", "field": "math", "label": 1}
{"text": "Title: Irreducibility and periodicity in $\\mathbb{Z}^{2}$ symbolic systems\nAbstract: We show that there exist $\\mathbb{Z}^{2}$ symbolic systems that are strongly irreducible and have no (fully) periodic points", "field": "math", "label": 0}
{"text": "Title: Measurable functions on charge spaces\nAbstract: The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are proposed. Conditions under which the various forms of measurability are logically equivalent are identified. Applying these concepts to real-valued functions, some recent characterisations of measurable functions on a bounded charge space are generalised to the unbounded case.", "field": "math", "label": 0}
{"text": "Title: Maximum principal ratio of the signless Laplacian of graphs\nAbstract: Let $G$ be a connected graph and $Q(G)$ be the signless Laplacian of $G$. The principal ratio $\\gamma(G)$ of $Q(G)$ is the ratio of the maximum and minimum entries of the Perron vector of $Q(G)$. In this paper, we consider the maximum principal ratio $\\gamma(G)$ among all connected graphs of order $n$, and show that for sufficiently large $n$ the extremal graph is a kite graph obtained by identifying an end vertex of a path to any vertex of a complete graph.", "field": "math", "label": 1}
{"text": "Title: Efficiency, Fairness, and Stability in Non-Commercial Peer-to-Peer Ridesharing\nAbstract: Unlike commercial ridesharing, non-commercial peer-to-peer (P2P) ridesharing has been subject to limited research -- although it can promote viable solutions in non-urban communities. This paper focuses on the core problem in P2P ridesharing: the matching of riders and drivers. We elevate users' preferences as a first-order concern and introduce novel notions of fairness and stability in P2P ridesharing. We propose algorithms for efficient matching while considering user-centric factors, including users' preferred departure time, fairness, and stability. Results suggest that fair and stable solutions can be obtained in reasonable computational times and can improve baseline outcomes based on system-wide efficiency exclusively.", "field": "cs", "label": 1}
{"text": "Title: Principled network extraction from images\nAbstract: Images of natural systems may represent patterns of network-like structure, which could reveal important information about the topological properties of the underlying subject. However, the image itself does not automatically provide a formal definition of a network in terms of sets of nodes and edges. Instead, this information should be suitably extracted from the raw image data. Motivated by this, we present a principled model to extract network topologies from images that is scalable and efficient. We map this goal into solving a routing optimization problem where the solution is a network that minimizes an energy function which can be interpreted in terms of an operational and infrastructural cost. Our method relies on recent results from optimal transport theory and is a principled alternative to standard image-processing techniques that are based on heuristics. We test our model on real images of the retinal vascular system, slime mold and river networks and compare with routines combining image-processing techniques. Results are tested in terms of a similarity measure related to the amount of information preserved in the extraction. We find that our model finds networks from retina vascular network images that are more similar to hand-labeled ones, while also giving high performance in extracting networks from images of rivers and slime mold for which there is no ground truth available. While there is no unique method that fits all the images the best, our approach performs consistently across datasets, its algorithmic implementation is efficient and can be fully automatized to be run on several datasets with little supervision.", "field": "cs", "label": 1}
{"text": "Title: Splitting Methods for differential equations\nAbstract: This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class of integrators are composition methods, in which one or several low-order schemes are composed to construct higher-order numerical approximations to the exact solution. We analyze in detail the order conditions that have to be satisfied by these classes of methods to achieve a given order, and provide some insight about their qualitative properties in connection with geometric numerical integration and the treatment of highly oscillatory problems. Since splitting methods have received considerable attention in the realm of partial differential equations, we also cover this subject in the present survey, with special attention to parabolic equations and their problems. An exhaustive list of methods of different orders is collected and tested on simple examples. Finally, some applications of splitting methods in different areas, ranging from celestial mechanics to statistics, are also provided.", "field": "math", "label": 0}
{"text": "Title: Toda brackets in n-angulated categories\nAbstract: We introduce Toda brackets for n-angulated categories and show that the various definitions of Toda brackets coincide. We prove juggling formulas for these Toda brackets generalizing the triangulated case. Following that, we generalize a theorem due to Heller in the triangulated setting to the setting of n-angulated categories. We also provide several examples of computing Toda brackets for n-angulated categories. Finally, for an n-angulated category sitting in a triangulated category as in the setup of Geiss, Keller and Oppermann, we show that Toda brackets in the n-angulated sense coincide with n-fold Toda brackets in the triangulated sense up to an explicit sign.", "field": "math", "label": 0}
{"text": "Title: Discover and Mitigate Unknown Biases with Debiasing Alternate Networks\nAbstract: Deep image classifiers have been found to learn biases from datasets. To mitigate the biases, most previous methods require labels of protected attributes (e.g., age, skin tone) as full-supervision, which has two limitations: 1) it is infeasible when the labels are unavailable; 2) they are incapable of mitigating unknown biases -- biases that humans do not preconceive. To resolve those problems, we propose Debiasing Alternate Networks (DebiAN), which comprises two networks -- a Discoverer and a Classifier. By training in an alternate manner, the discoverer tries to find multiple unknown biases of the classifier without any annotations of biases, and the classifier aims at unlearning the biases identified by the discoverer. While previous works evaluate debiasing results in terms of a single bias, we create Multi-Color MNIST dataset to better benchmark mitigation of multiple biases in a multi-bias setting, which not only reveals the problems in previous methods but also demonstrates the advantage of DebiAN in identifying and mitigating multiple biases simultaneously. We further conduct extensive experiments on real-world datasets, showing that the discoverer in DebiAN can identify unknown biases that may be hard to be found by humans. Regarding debiasing, DebiAN achieves strong bias mitigation performance.", "field": "cs", "label": 1}
{"text": "Title: Phase field modelling of fracture and fatigue in Shape Memory Alloys\nAbstract: We present a new phase field framework for modelling fracture and fatigue in Shape Memory Alloys (SMAs). The constitutive model captures the superelastic behaviour of SMAs and damage is driven by the elastic and transformation strain energy densities. We consider both the assumption of a constant fracture energy and the case of a fracture energy dependent on the martensitic volume fraction. The framework is implemented in an implicit time integration scheme, with both monolithic and staggered solution strategies. The potential of this formulation is showcased by modelling a number of paradigmatic problems. First, a boundary layer model is used to examine crack tip fields and compute crack growth resistance curves (R-curves). We show that the model is able to capture the main fracture features associated with SMAs, including the toughening effect associated with stress-induced phase transformation. Insight is gained into the role of temperature, material strength, crack density function and fracture energy homogenisation. Secondly, several 2D and 3D boundary value problems are addressed, demonstrating the capabilities of the model in capturing complex cracking phenomena in SMAs, such as unstable crack growth, mixed-mode fracture or the interaction between several cracks. Finally, the model is extended to fatigue and used to capture crack nucleation and propagation in biomedical stents, a paradigmatic application of nitinol SMAs.", "field": "cs", "label": 1}
{"text": "Title: Learning the 3D Fauna of the Web\nAbstract: Learning 3D models of all animals on the Earth requires massively scaling up existing solutions. With this ultimate goal in mind, we develop 3D-Fauna, an approach that learns a pan-category deformable 3D animal model for more than 100 animal species jointly. One crucial bottleneck of modeling animals is the limited availability of training data, which we overcome by simply learning from 2D Internet images. We show that prior category-specific attempts fail to generalize to rare species with limited training images. We address this challenge by introducing the Semantic Bank of Skinned Models (SBSM), which automatically discovers a small set of base animal shapes by combining geometric inductive priors with semantic knowledge implicitly captured by an off-the-shelf self-supervised feature extractor. To train such a model, we also contribute a new large-scale dataset of diverse animal species. At inference time, given a single image of any quadruped animal, our model reconstructs an articulated 3D mesh in a feed-forward fashion within seconds.", "field": "cs", "label": 0}
{"text": "Title: Unconditional stability of equilibria in thermally driven compressible fluids\nAbstract: We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by thermal convection converges to an equilibrium as time goes to infinity. The main difficulty to overcome is the fact the problem does not admit any obvious Lyapunov function. The result applies, in particular, to the Rayleigh--B\\' enard convection problem.", "field": "math", "label": 0}
{"text": "Title: Discrete Time Markovian Agents Interacting Through a Potential\nAbstract: A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the 'gradient' of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport in response to external stimulus such as a chemical gradient. One of the basic mathematical challenges is to develop a general theory of stability for such interacting Markovian systems and for the corresponding nonlinear Markov processes that arise in the large agent limit. Such a theory would be key to a mathematical understanding of the interactive structure formation that results from the complex feedback between the agents and the potential field. It will also be a crucial ingredient in developing simulation schemes that are faithful to the underlying model over long periods of time. The goal of this work is to study qualitative properties of the above stochastic system as the number of particles (N) and the time parameter (n) approach infinity. In this regard asymptotic properties of a deterministic nonlinear dynamical system, that arises in the propagation of chaos limit of the stochastic model, play a key role. We show that under suitable conditions this dynamical system has a unique fixed point. This result allows us to study stability properties of the underlying stochastic model. We show that as N \\rightarrow \\infty, the stochastic system is well approximated by the dynamical system, uniformly over time. As a consequence, for an arbitrarily initialized system, as N\\rightarrow \\infty and n \\rightarrow \\infty, the potential field and the empirical measure of the interacting particles are shown to converge to the unique fixed point of the dynamical system. In general, simulation of such interacting Markovian systems is a computationally daunting task. We propose a particle based approximation for the dynamic potential field which allows for a numerically tractable simulation scheme. It is shown that this simulation scheme well approximates the true physical system, uniformly over an infinite time horizon.", "field": "math", "label": 1}
{"text": "Title: Moduli spaces of arrangements of 12 projective lines with a sextic point\nAbstract: In this paper, we try to classify moduli spaces of arrangements of $12$ lines with sextic points. We show that moduli spaces of arrangements of $12$ lines with sextic points can consist of more than two connected components. We also present defining equations of the arrangements whose moduli spaces are not irreducible taking quotients by the complex conjugation by supply some potential Zariski pairs. Through complex conjugation we take quotients and supply some potential Zariski pairs.", "field": "math", "label": 0}
{"text": "Title: The limit theorem for maximum of partial sums of exchangeable random variables\nAbstract: We obtain the analogue of the classical result by Erd\\\"os and Kac on the limiting distribution of the maximum of partial sums for exchangeable random variables with zero mean and variance one. We show that, if the conditions of the central limit theorem of Blum et al. hold, the limit coincides with the classical one. Under more general assumptions, the probability of the random variables having conditional negative drift appears in the limiting distribution.", "field": "math", "label": 1}
{"text": "Title: Periodic and quasi-motivic pencils of flat connections\nAbstract: We introduce a new notion of a periodic pencil of flat connections on a smooth algebraic variety $X$. This is a family $\\nabla(s_1,...,s_n)$ of flat connections on a trivial vector bundle on $X$ depending linearly on parameters $s_1,...,s_n$ and generically invariant, up to isomorphism, under the shifts $s_i\\mapsto s_i+1$ for all $i$. If in addition $\\nabla$ has regular singularities, we call it a quasi-motivic pencil. We use tools from complex analysis to establish various remarkable properties of such pencils over $\\mathbb C$. For example, we show that the monodromy of a quasi-motivic pencil is defined over the field of algebraic functions in $e^{2\\pi is_j}$, and that its singularities are constrained to an arrangement of hyperplanes with integer normal vectors. Then we show that many important examples of families of flat connections, such as Knizhnik-Zamolodchikov, Dunkl, and Casimir connections, are quasi-motivic and thus periodic pencils. Besides being interesting in its own right, the periodic property of a pencil of flat connections turns out to be very useful in computing the eigenvalues of the $p$-curvature of its reduction to positive characteristic. This will be done in our forthcoming paper.", "field": "math", "label": 0}
{"text": "Title: Local behavior for solutions to anisotropic weighted quasilinear degenerate parabolic equations\nAbstract: This paper aims to study the local behavior of solutions to a class of anisotropic weighted quasilinear degenerate parabolic equations with the weights comprising two power-type weights of different dimensions. We first capture the asymptotic behavior of the solution near the singular or degenerate point of the weights. In particular, we find an explicit upper bound on the decay rate exponent determined by the structures of the equations and weights, which can be achieved under certain condition and meanwhile reflects the damage effect of the weights on the regularity of the solution. Furthermore, we prove the local H\\\"{o}lder regularity of solutions to non-homogeneous parabolic $p$-Laplace equations with single power-type weights.", "field": "math", "label": 0}
{"text": "Title: Some Grönwall inequalities for a class of discretizations of time fractional equations on nonuniform meshes\nAbstract: We consider the completely positive discretizations of fractional ordinary differential equations (FODEs) on nonuniform meshes. Making use of the resolvents for nonuniform meshes, we first establish comparison principles for the discretizations. Then we prove some discrete Gr\\\"onwall inequalities using the comparison principles and careful analysis of the solutions to the time continuous FODEs. Our results do not have any restrictions on the step size ratio. The Gr\\\"onwall inequalities for dissipative equations can be used to obtain the uniform-in-time error control and decay estimates of the numerical solutions. The Gr\\\"onwall inequalities are then applied to subdiffusion problems and the time fractional Allen-Cahn equations for illustration.", "field": "math", "label": 0}
{"text": "Title: A novel iterative time integration scheme for linear poroelasticity\nAbstract: Within this paper, we introduce and analyze a novel time stepping scheme for linear poroelasticity. In each time frame, we iteratively solve the flow and mechanics equations with an additional damping step for the pressure variable. Depending on the coupling strength of the two equations, we explicitly quantify the needed number of inner iteration steps to guarantee first-order convergence. Within a number of numerical experiments, we confirm the theoretical results and study the dependence of inner iteration steps in terms of the coupling strength. Moreover, we compare our method to the well-known fixed-stress scheme.", "field": "math", "label": 0}
{"text": "Title: Vanishing theorems on covering manifolds\nAbstract: Let $M$ be an oriented even-dimensional Riemannian manifold on which a discrete group $\\Gamma$ of orientation-preserving isometries acts freely, so that the quotient $X=M/\\Gamma$ is compact. We prove a vanishing theorem for a half-kernel of a $\\Gamma$-invariant Dirac operator on a $\\Gamma$-equivariant Clifford module over $M$, twisted by a sufficiently large power of a $\\Gamma$-equivariant line bundle, whose curvature is non-degenerate at any point of $M$. This generalizes our previous vanishing theorems for Dirac operators on a compact manifold. In particular, if $M$ is an almost complex manifold we prove a vanishing theorem for the half-kernel of a $\\spin^c$ Dirac operator, twisted by a line bundle with curvature of a mixed sign. In this case we also relax the assumption of non-degeneracy of the curvature. When $M$ is a complex manifold our results imply analogues of Kodaira and Andreotti-Grauert vanishing theorems for covering manifolds. As another application, we show that semiclassically the $\\spin^c$ quantization of an almost complex covering manifold gives an \"honest\" Hilbert space. This generalizes a result of Borthwick and Uribe, who considered quantization of compact manifolds. Application of our results to homogeneous manifolds of a real semisimple Lie group leads to new proofs of Griffiths-Schmidt and Atiyah-Schmidt vanishing theorems.", "field": "math", "label": 1}
{"text": "Title: Further results on orbits and incidence matrices for the class $\\mathcal{O}_6$ of lines external to the twisted cubic in $\\mathrm{PG}(3,q)$\nAbstract: In the literature, lines of the projective space $\\mathrm{PG}(3,q)$ are partitioned into classes, each of which is a union of line orbits under the stabilizer group of the twisted cubic. The least studied class is named $\\mathcal{O}_6$. This class contains lines external to the twisted cubic which are not its chords or axes and do not lie in any of its osculating planes. For even and odd $q$, we propose a new family of orbits of $\\mathcal{O}_6$ and investigate in detail their stabilizer groups and the corresponding submatrices of the point-line and plane-line incidence matrices. To obtain these submatrices, we explored the number of solutions of cubic and quartic equations connected with intersections of lines (including the tangents to the twisted cubic), points, and planes in $\\mathrm{PG}(3,q)$.", "field": "math", "label": 0}
{"text": "Title: Leveraging ParsBERT and Pretrained mT5 for Persian Abstractive Text Summarization\nAbstract: Text summarization is one of the most critical Natural Language Processing (NLP) tasks. More and more researches are conducted in this field every day. Pre-trained transformer-based encoder-decoder models have begun to gain popularity for these tasks. This paper proposes two methods to address this task and introduces a novel dataset named pn-summary for Persian abstractive text summarization. The models employed in this paper are mT5 and an encoder-decoder version of the ParsBERT model (i.e., a monolingual BERT model for Persian). These models are fine-tuned on the pn-summary dataset. The current work is the first of its kind and, by achieving promising results, can serve as a baseline for any future work.", "field": "cs", "label": 1}
{"text": "Title: Historical Review of Fluid Antenna and Movable Antenna\nAbstract: Recently, significant attention has been drawn to the development of two antenna technologies known as \"Fluid Antenna\" and \"Movable Antenna\" in wireless communication research community, owing to their flexibility and reconfigurability for improving the wireless system performance in various applications. However, some confusions/concerns have also ensued on their nomenclature. In fact, both \"Fluid Antenna\" and \"Movable Antenna\" are not newly-made terms, while they have a longstanding presence in the field of antenna technology. This article thus aims to review the historical evolution of these technologies for fostering a clear understanding of their origins and recent development in the realm of wireless communication. It is hoped that this article will help dispel any confusion, concern or even dispute on the appropriate use of their names in the literature and motivate more research endeavors to focus on resolving their technical issues in the future.", "field": "cs", "label": 0}
{"text": "Title: CLAPP: Contrastive Language-Audio Pre-training in Passive Underwater Vessel Classification\nAbstract: Existing research on audio classification faces challenges in recognizing attributes of passive underwater vessel scenarios and lacks well-annotated datasets due to data privacy concerns. In this study, we introduce CLAPP (Contrastive Language-Audio Pre-training in Passive Underwater Vessel Classification), a novel model. Our aim is to train a neural network using a wide range of vessel audio and vessel state text pairs obtained from an oceanship dataset. CLAPP is capable of directly learning from raw vessel audio data and, when available, from carefully curated labels, enabling improved recognition of vessel attributes in passive underwater vessel scenarios. Model's zero-shot capability allows predicting the most relevant vessel state description for a given vessel audio, without directly optimizing for the task. Our approach aims to solve 2 challenges: vessel audio-text classification and passive underwater vessel audio attribute recognition. The proposed method achieves new state-of-the-art results on both Deepship and Shipsear public datasets, with a notable margin of about 7%-13% for accuracy compared to prior methods on zero-shot task.", "field": "cs", "label": 0}
{"text": "Title: Markov modulated fluid network process: Tail asymptotics of the stationary distribution\nAbstract: We consider a Markov modulated fluid network with a finite number of stations. We are interested in the tail asymptotics behavior of the stationary distribution of its buffer content process. Using two different approaches, we derive upper and lower bounds for the stationary tail decay rate in various directions. Both approaches are based on a well-known time-evolution formula of a Markov process, so-called Dynkin's formula, where a key ingredient is a suitable choice of test functions. Those results show how multidimensional tail asymptotics can be studied for the more than two-dimensional case, which is known as a hard problem.", "field": "math", "label": 1}
{"text": "Title: Smoothness Estimation for Whittle-Matérn Processes on Closed Riemannian Manifolds\nAbstract: The family of Mat\\'ern kernels are often used in spatial statistics, function approximation and Gaussian process methods in machine learning. One reason for their popularity is the presence of a smoothness parameter that controls, for example, optimal error bounds for kriging and posterior contraction rates in Gaussian process regression. On closed Riemannian manifolds, we show that the smoothness parameter can be consistently estimated from the maximizer(s) of the Gaussian likelihood when the underlying data are from point evaluations of a Gaussian process and, perhaps surprisingly, even when the data comprise evaluations of a non-Gaussian process. The points at which the process is observed need not have any particular spatial structure beyond quasi-uniformity. Our methods are based on results from approximation theory for the Sobolev scale of Hilbert spaces. Moreover, we generalize a well-known equivalence of measures phenomenon related to Mat\\'ern kernels to the non-Gaussian case by using Kakutani's theorem.", "field": "math", "label": 0}
{"text": "Title: DiffAttack: Evasion Attacks Against Diffusion-Based Adversarial Purification\nAbstract: Diffusion-based purification defenses leverage diffusion models to remove crafted perturbations of adversarial examples and achieve state-of-the-art robustness. Recent studies show that even advanced attacks cannot break such defenses effectively, since the purification process induces an extremely deep computational graph which poses the potential problem of gradient obfuscation, high memory cost, and unbounded randomness. In this paper, we propose a unified framework DiffAttack to perform effective and efficient attacks against diffusion-based purification defenses, including both DDPM and score-based approaches. In particular, we propose a deviated-reconstruction loss at intermediate diffusion steps to induce inaccurate density gradient estimation to tackle the problem of vanishing/exploding gradients. We also provide a segment-wise forwarding-backwarding algorithm, which leads to memory-efficient gradient backpropagation. We validate the attack effectiveness of DiffAttack compared with existing adaptive attacks on CIFAR-10 and ImageNet. We show that DiffAttack decreases the robust accuracy of models compared with SOTA attacks by over 20% on CIFAR-10 under $\\ell_\\infty$ attack $(\\epsilon=8/255)$, and over 10% on ImageNet under $\\ell_\\infty$ attack $(\\epsilon=4/255)$. We conduct a series of ablations studies, and we find 1) DiffAttack with the deviated-reconstruction loss added over uniformly sampled time steps is more effective than that added over only initial/final steps, and 2) diffusion-based purification with a moderate diffusion length is more robust under DiffAttack.", "field": "cs", "label": 0}
{"text": "Title: Learning Concept Embeddings with Combined Human-Machine Expertise\nAbstract: This paper presents our work on \"SNaCK,\" a low-dimensional concept embedding algorithm that combines human expertise with automatic machine similarity kernels. Both parts are complimentary: human insight can capture relationships that are not apparent from the object's visual similarity and the machine can help relieve the human from having to exhaustively specify many constraints. We show that our SNaCK embeddings are useful in several tasks: distinguishing prime and nonprime numbers on MNIST, discovering labeling mistakes in the Caltech UCSD Birds (CUB) dataset with the help of deep-learned features, creating training datasets for bird classifiers, capturing subjective human taste on a new dataset of 10,000 foods, and qualitatively exploring an unstructured set of pictographic characters. Comparisons with the state-of-the-art in these tasks show that SNaCK produces better concept embeddings that require less human supervision than the leading methods.", "field": "cs", "label": 1}
{"text": "Title: Natural Language Adversarial Defense through Synonym Encoding\nAbstract: In the area of natural language processing, deep learning models are recently known to be vulnerable to various types of adversarial perturbations, but relatively few works are done on the defense side. Especially, there exists few effective defense method against the successful synonym substitution based attacks that preserve the syntactic structure and semantic information of the original text while fooling the deep learning models. We contribute in this direction and propose a novel adversarial defense method called Synonym Encoding Method (SEM). Specifically, SEM inserts an encoder before the input layer of the target model to map each cluster of synonyms to a unique encoding and trains the model to eliminate possible adversarial perturbations without modifying the network architecture or adding extra data. Extensive experiments demonstrate that SEM can effectively defend the current synonym substitution based attacks and block the transferability of adversarial examples. SEM is also easy and efficient to scale to large models and big datasets.", "field": "cs", "label": 1}
{"text": "Title: Sub-Riemannian curvature of Carnot groups with rank-two distributions\nAbstract: The notion of curvature discussed in this paper is a far going generalization of the Riemannian sectional curvature. It was first introduced by Agrachev, Barilari and Rizzi in arXiv:1306.5318, and it is defined for a wide class of optimal control problems: a unified framework including geometric structures such as Riemannian, sub-Riemannian, Finsler, and sub-Finsler structures. In this work we study the generalized sectional curvature of Carnot groups with rank-two distributions. In particular, we consider the Cartan group and Carnot groups with horizontal distribution of Goursat-type. In these Carnot groups we characterize ample and equiregular geodesics. For Carnot groups with horizontal Goursat distribution we show that their generalized sectional curvatures depend only on the Engel part of the distribution. This family of Carnot groups contains naturally the three-dimensional Heisenberg group, as well as the Engel group. Moreover, we also show that in the Engel and Cartan groups there exist initial covectors for which there is an infinite discrete set of times at which the corresponding ample geodesics are not equiregular.", "field": "math", "label": 1}
{"text": "Title: Simplification of inclusion-exclusion on intersections of unions with application to network systems reliability\nAbstract: Reliability of safety-critical systems is an important issue in system engineering and in most practical situations the reliability of a non series-parallel network system has to be calculated. Some methods for calculating reliability use the probability principle of inclusion-exclusion. When dealing with complex networks, this leads to very long mathematical expressions which are usually computationally very expensive to calculate. In this paper, we provide a new expression to simplify the probability principle of inclusion-exclusion's formula for intersections of unions, which appear when calculating reliability on non series parallel network systems. This new expression has much less terms, which reduces enormously the computational cost. We also show that the general form of the probability principle of inclusion-exclusion's formula has double exponential complexity whereas the simplified form has only exponential complexity with a linear exponent. Finally, we illustrate how to use this result when calculating the reliability of a door management system in aircraft engineering.", "field": "math", "label": 1}
{"text": "Title: On the measurability of a numerical function with respect to a family of sets\nAbstract: The following document is a translation (from French to English) of: Gabriele H. Greco, Sur la mesurabilit\\'e d'une fonction num\\'erique par rapport \\`a une famille d'ensembles, Rendiconti del Seminario Matematico della Universit\\`a di Padova}, tome 65 (1981), pp. 163--176. Translated by: Jonathan M. Keith, School of Mathematics, Monash University, jonathan.keith@monash.edu. With thanks to: Prof. Andrea D'Agnolo, Editor-in-Chief of the above journal, for permission to publish this translation.", "field": "math", "label": 0}
{"text": "Title: Learning with Noisy Labels by Adaptive Gradient-Based Outlier Removal\nAbstract: An accurate and substantial dataset is essential for training a reliable and well-performing model. However, even manually annotated datasets contain label errors, not to mention automatically labeled ones. Previous methods for label denoising have primarily focused on detecting outliers and their permanent removal - a process that is likely to over- or underfilter the dataset. In this work, we propose AGRA: a new method for learning with noisy labels by using Adaptive GRAdient-based outlier removal. Instead of cleaning the dataset prior to model training, the dataset is dynamically adjusted during the training process. By comparing the aggregated gradient of a batch of samples and an individual example gradient, our method dynamically decides whether a corresponding example is helpful for the model at this point or is counter-productive and should be left out for the current update. Extensive evaluation on several datasets demonstrates AGRA's effectiveness, while a comprehensive results analysis supports our initial hypothesis: permanent hard outlier removal is not always what model benefits the most from.", "field": "cs", "label": 0}
{"text": "Title: An improved spectral inequality for sums of eigenfunctions\nAbstract: We establish a new spectral inequality for the quantified estimation of the $H^s$-norm, $s\\ge 0$ of a finite linear combination of eigenfunctions in a domain in terms of its $H^s$-norm in a strictly open subset of the whole domain. The corresponding upper bound depends exponentially on the square root of the frequency number associated to the linear combination.", "field": "math", "label": 0}
{"text": "Title: Testing popularity in linear time via maximum matching\nAbstract: Popularity is an approach in mechanism design to find fair structures in a graph, based on the votes of the nodes. Popular matchings are the relaxation of stable matchings: given a graph G=(V,E) with strict preferences on the neighbors of the nodes, a matching M is popular if there is no other matching M' such that the number of nodes preferring M' is more than those preferring M. This paper considers the popularity testing problem, when the task is to decide whether a given matching is popular or not. Previous algorithms applied reductions to maximum weight matchings. We give a new algorithm for testing popularity by reducing the problem to maximum matching testing, thus attaining a linear running time O(|E|). Linear programming-based characterization of popularity is often applied for proving the popularity of a certain matching. As a consequence of our algorithm we derive a more structured dual witness than previous ones. Based on this result we give a combinatorial characterization of fractional popular matchings, which are a special class of popular matchings.", "field": "cs", "label": 0}
{"text": "Title: A Note on the Two Approaches to Stringy Functors for Orbifolds\nAbstract: In this note, we reconcile two approaches that have been used to construct stringy multiplications. The pushing forward after pulling back that has been used to give a global stringy extension of the functors K_0,K^{top},A^*,H^* [CR, FG, AGV, JKK2], and the pulling back after having pushed forward, which we have previously used in our (re)-construction program for G-Frobenius algebras, notably in considerations of singularities with symmetries and for symmetric products. A similar approach was also used by [CH] in their considerations of the Chen-Ruan product in a deRham setting for Abelian orbifolds. We show that the pull-push formalism has a solution by the push-pull equations in two situations. The first is a deRham formalism with Thom push-forward maps and the second is the setting of cyclic twisted sectors, which was at the heart of the (re)-construction program. We go on to do formal calculations using fractional Euler classes which allows us to formally treat all the stringy multiplications mentioned above in the general setting. The upshot is the formal trivialization of the co-cycles of the reconstruction program using the presentation of the obstruction bundle of [JKK2].", "field": "math", "label": 1}
{"text": "Title: Asymptotically Optimal Proper Conflict-Free Colouring\nAbstract: A proper conflict-free colouring of a graph is a colouring of the vertices such that any two adjacent vertices receive different colours, and for every non-isolated vertex $v$, some colour appears exactly once on the neighbourhood of $v$. Caro, Petru\\v{s}evski and \\v{S}krekovski conjectured that every connected graph with maximum degree $\\Delta \\geq 3$ has a proper conflict-free colouring with at most $\\Delta+1$ colours. This conjecture holds for $\\Delta=3$ and remains open for $\\Delta \\geq 4$. In this paper we prove that this conjecture holds asymptotically; namely, every graph with maximum degree $\\Delta$ has a proper conflict-free colouring with $(1+o(1))\\Delta$ colours.", "field": "math", "label": 0}
{"text": "Title: Additive Correlation and the Inverse Problem for the Large Sieve\nAbstract: Let $A\\subset [1,N]$ be a set of positive integers with $|A|\\gg \\sqrt N$. We show that if avoids about $p/2$ residue classes modulo $p$ for each prime $p$, the $A$ must correlate additively with the squares $S=\\{n^2:1\\leq n\\leq \\sqrt N\\}$, in the sense that we have the additive energy estimate $E(A,S)\\gg N\\log N$. This is, in a sense, optimal.", "field": "math", "label": 1}
{"text": "Title: Existence of weak solutions to borderline double-phase problems with logarithmic convection term\nAbstract: In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data. The proof is based on the surjectivity theorem for the pseudo-monotone operators and modular function spaces and embedding theorems in generalized Orlicz spaces. Our approach in this paper can be extended naturally to a larger class of unbalanced double-phase problems with logarithmic perturbation and gradient dependence on the right-hand sides.", "field": "math", "label": 0}
{"text": "Title: Some remarks on combinatorial wall-crossing\nAbstract: We establish a new simple explicit description of combinatorial wall-crossing for the rational Cherednik algebra applied to the trivial representation. In this way we recover a theorem of P. Dimakis and G. Yue. We also present two conjectures on combinatorial wall-crossing which were found using computer experiments.", "field": "math", "label": 1}
{"text": "Title: ALOHA Receivers: a Network Calculus Approach for Analyzing Coded Multiple Access with SIC\nAbstract: Motivated by the need to hide the complexity of the physical layer from performance analysis in a layer 2 protocol, a class of abstract receivers, called Poisson receivers, was recently proposed in [1] as a probabilistic framework for providing differentiated services in uplink transmissions in 5G networks. In this paper, we further propose a deterministic framework of ALOHA receivers that can be incorporated into the probabilistic framework of Poisson receivers for analyzing coded multiple access with successive interference cancellation. An ALOHA receiver is characterized by a success function of the number of packets that can be successfully received. Inspired by the theory of network calculus, we derive various algebraic properties for several operations on success functions and use them to prove various closure properties of ALOHA receivers, including (i) ALOHA receivers in tandem, (ii) cooperative ALOHA receivers, (iii) ALOHA receivers with traffic multiplexing, and (iv) ALOHA receivers with packet coding. By conducting extensive simulations, we show that our theoretical results match extremely well with the simulation results.", "field": "cs", "label": 1}
{"text": "Title: Towards High Fidelity Face Relighting with Realistic Shadows\nAbstract: Existing face relighting methods often struggle with two problems: maintaining the local facial details of the subject and accurately removing and synthesizing shadows in the relit image, especially hard shadows. We propose a novel deep face relighting method that addresses both problems. Our method learns to predict the ratio (quotient) image between a source image and the target image with the desired lighting, allowing us to relight the image while maintaining the local facial details. During training, our model also learns to accurately modify shadows by using estimated shadow masks to emphasize on the high-contrast shadow borders. Furthermore, we introduce a method to use the shadow mask to estimate the ambient light intensity in an image, and are thus able to leverage multiple datasets during training with different global lighting intensities. With quantitative and qualitative evaluations on the Multi-PIE and FFHQ datasets, we demonstrate that our proposed method faithfully maintains the local facial details of the subject and can accurately handle hard shadows while achieving state-of-the-art face relighting performance.", "field": "cs", "label": 1}
{"text": "Title: Fast and Smooth Interpolation on Wasserstein Space\nAbstract: We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox of spline interpolation. Unlike previous approaches to measure-valued splines, our interpolated curves (i) have a clear interpretation as governing particle flows, which is natural for applications, and (ii) come with the first approximation guarantees on Wasserstein space. Finally, we demonstrate the broad applicability of our interpolation methodology by fitting surfaces of measures using thin-plate splines.", "field": "math", "label": 1}
{"text": "Title: Schur Multipliers of Nilpotent Lie Algebras\nAbstract: We consider the Schur multipliers of finite dimensional nilpotent Lie algebras. If the algebra has dimension greater than one, then the Schur multiplier is non-zero. We give a direct proof of an upper bound for the dimension of the Schur multiplier as a function of class and the minimum number of generators of the algebra. We then compare this bound with another known bound.", "field": "math", "label": 1}
{"text": "Title: Towards Palmprint Verification On Smartphones\nAbstract: With the rapid development of mobile devices, smartphones have gradually become an indispensable part of people's lives. Meanwhile, biometric authentication has been corroborated to be an effective method for establishing a person's identity with high confidence. Hence, recently, biometric technologies for smartphones have also become increasingly sophisticated and popular. But it is noteworthy that the application potential of palmprints for smartphones is seriously underestimated. Studies in the past two decades have shown that palmprints have outstanding merits in uniqueness and permanence, and have high user acceptance. However, currently, studies specializing in palmprint verification for smartphones are still quite sporadic, especially when compared to face- or fingerprint-oriented ones. In this paper, aiming to fill the aforementioned research gap, we conducted a thorough study of palmprint verification on smartphones and our contributions are twofold. First, to facilitate the study of palmprint verification on smartphones, we established an annotated palmprint dataset named MPD, which was collected by multi-brand smartphones in two separate sessions with various backgrounds and illumination conditions. As the largest dataset in this field, MPD contains 16,000 palm images collected from 200 subjects. Second, we built a DCNN-based palmprint verification system named DeepMPV+ for smartphones. In DeepMPV+, two key steps, ROI extraction and ROI matching, are both formulated as learning problems and then solved naturally by modern DCNN models. The efficiency and efficacy of DeepMPV+ have been corroborated by extensive experiments. To make our results fully reproducible, the labeled dataset and the relevant source codes have been made publicly available at https://cslinzhang.github.io/MobilePalmPrint/.", "field": "cs", "label": 1}
{"text": "Title: Quasi-streamwise vortices and enhanced dissipation for the incompressible 3D Navier-Stokes equations\nAbstract: We consider the 3D incompressible Navier-Stokes equations under the following $2+\\frac{1}{2}$-dimensional situation: vertical vortex blob (quasi-streamwise vortices) being stretched by two-dimensional shear flow. We prove enhanced dissipation induced by such quasi-streamwise vortices.", "field": "math", "label": 1}
{"text": "Title: Uniform mixing and completely positive sofic entropy\nAbstract: Let $G$ be a countable discrete sofic group. We define a concept of uniform mixing for measure-preserving $G$-actions and show that it implies completely positive sofic entropy. When $G$ contains an element of infinite order, we use this to produce an uncountable family of pairwise nonisomorphic $G$-actions with completely positive sofic entropy. None of our examples is a factor of a Bernoulli shift.", "field": "math", "label": 1}
{"text": "Title: A Decentralized Multiagent-Based Task Scheduling Framework for Handling Uncertain Events in Fog Computing\nAbstract: Fog computing has become an attractive research topic in recent years. As an extension of the cloud, fog computing provides computing resources for Internet of Things (IoT) applications through communicative fog nodes located at the network edge. Fog nodes assist cloud services in handling real-time and mobile applications by bringing the processing capability to where the data is generated. However, the introduction of fog nodes can increase scheduling openness and uncertainty. The scheduling issues in fog computing need to consider the geography, load balancing, and network latency between IoT devices, fog nodes, as well as the parent cloud. Besides, the scheduling methods also need to deal with the occurrence of uncertain events in real-time so as to ensure service reliability. This paper proposes an agent-based framework with a decentralized structure to construct the architecture of fog computing, while three agent-based algorithms are proposed to implement the scheduling, load balance, and rescheduling processes. The proposed framework is implemented by JADE and evaluated on the iFogSim toolkit. Experimental results show that the proposed scheduling framework can adaptively schedule tasks and resources for different service requests in fog computing and can also improve the task success rate when uncertain events occur.", "field": "cs", "label": 0}
{"text": "Title: Centers of categorified endomorphism rings\nAbstract: We prove that for a large class of well-behaved cocomplete categories $\\mathcal C$ the weak and strong Drinfeld centers of the monoidal category $\\mathcal{E}$ of cocontinuous endofunctors of $\\mathcal{C}$ coincide. This generalizes similar results in the literature, where $\\mathcal{C}$ is the category of modules over a ring $A$ and hence $\\mathcal{E}$ is the category of $A$-bimodules.", "field": "math", "label": 1}
{"text": "Title: Search Games with Predictions\nAbstract: We study search games between a mobile Searcher and an immobile Hider in which the Searcher aims to minimize some payoff, which is either the time to find the Hider (the search time), or a normalized search time. We consider a new setting in which the Searcher has some potentially erroneous information, or prediction on the Hider's position. Specifically, we study tradeoffs between the consistency of a search strategy (i.e., its worst case expected payoff assuming the prediction is correct) and the robustness (i.e., the worst case expected payoff assuming that the prediction is adversarially generated). We show how to apply this framework in search games over both discrete and continuous, as well as bounded and unbounded spaces. Specifically, we prove optimal consistency/robustness tradeoffs for three fundamental search games, namely searching in a number of discrete locations, expanding search in a tree network, and searching in the infinite line. Our study is the first to address the full power of mixed (randomized) strategies; previous work focused only on deterministic strategies, or relied on stochastic assumptions that do not guarantee worst-case robustness in adversarial situations.", "field": "cs", "label": 0}
{"text": "Title: Improved uncertainty quantification for neural networks with Bayesian last layer\nAbstract: Uncertainty quantification is an important task in machine learning - a task in which standardneural networks (NNs) have traditionally not excelled. This can be a limitation for safety-critical applications, where uncertainty-aware methods like Gaussian processes or Bayesian linear regression are often preferred. Bayesian neural networks are an approach to address this limitation. They assume probability distributions for all parameters and yield distributed predictions. However, training and inference are typically intractable and approximations must be employed. A promising approximation is NNs with Bayesian last layer (BLL). They assume distributed weights only in the linear output layer and yield a normally distributed prediction. To approximate the intractable Bayesian neural network, point estimates of the distributed weights in all but the last layer should be obtained by maximizing the marginal likelihood. This has previously been challenging, as the marginal likelihood is expensive to evaluate in this setting. We present a reformulation of the log-marginal likelihood of a NN with BLL which allows for efficient training using backpropagation. Furthermore, we address the challenge of uncertainty quantification for extrapolation points. We provide a metric to quantify the degree of extrapolation and derive a method to improve the uncertainty quantification for these points. Our methods are derived for the multivariate case and demonstrated in a simulation study. In comparison to Bayesian linear regression with fixed features, and a Bayesian neural network trained with variational inference, our proposed method achieves the highest log-predictive density on test data.", "field": "cs", "label": 0}
{"text": "Title: Non-singular actions of infinite-dimensional groups and polymorphisms\nAbstract: Let $Z$ be a probabilistic measure space with a measure $\\zeta$, $\\mathbb{R}^\\times$ be the multiplicative group of positive reals, let $t$ be the coordinate on $\\mathbb{R}^\\times$. A polymorphism of $Z$ is a measure $\\pi$ on $Z\\times Z\\times \\mathbb{R}^\\times$ such that for any measurable $A$, $B\\subset Z$ we have $\\pi(A\\times Z\\times \\mathbb{R}^\\times)=\\zeta(A)$ and the integral $\\int t\\,d\\pi(z,u,t)$ over $Z\\times B\\times \\mathbb{R}^\\times$ is $\\zeta(B)$. The set of all polymorphisms has a natural semigroup structure, the group of all nonsingular transformations is dense in this semigroup. We discuss a problem of closure in polymorphisms for certain types of infinite dimensional ('large') groups and show that a non-singular action of an infinite-dimensional group generates a representation of its train (category of double cosets) by polymorphisms.", "field": "math", "label": 0}
{"text": "Title: Face Relighting with Geometrically Consistent Shadows\nAbstract: Most face relighting methods are able to handle diffuse shadows, but struggle to handle hard shadows, such as those cast by the nose. Methods that propose techniques for handling hard shadows often do not produce geometrically consistent shadows since they do not directly leverage the estimated face geometry while synthesizing them. We propose a novel differentiable algorithm for synthesizing hard shadows based on ray tracing, which we incorporate into training our face relighting model. Our proposed algorithm directly utilizes the estimated face geometry to synthesize geometrically consistent hard shadows. We demonstrate through quantitative and qualitative experiments on Multi-PIE and FFHQ that our method produces more geometrically consistent shadows than previous face relighting methods while also achieving state-of-the-art face relighting performance under directional lighting. In addition, we demonstrate that our differentiable hard shadow modeling improves the quality of the estimated face geometry over diffuse shading models.", "field": "cs", "label": 1}
{"text": "Title: Algorithmically Effective Differentially Private Synthetic Data\nAbstract: We present a highly effective algorithmic approach for generating $\\varepsilon$-differentially private synthetic data in a bounded metric space with near-optimal utility guarantees under the 1-Wasserstein distance. In particular, for a dataset $X$ in the hypercube $[0,1]^d$, our algorithm generates synthetic dataset $Y$ such that the expected 1-Wasserstein distance between the empirical measure of $X$ and $Y$ is $O((\\varepsilon n)^{-1/d})$ for $d\\geq 2$, and is $O(\\log^2(\\varepsilon n)(\\varepsilon n)^{-1})$ for $d=1$. The accuracy guarantee is optimal up to a constant factor for $d\\geq 2$, and up to a logarithmic factor for $d=1$. Our algorithm has a fast running time of $O(\\varepsilon dn)$ for all $d\\geq 1$ and demonstrates improved accuracy compared to the method in (Boedihardjo et al., 2022) for $d\\geq 2$.", "field": "cs", "label": 1}
{"text": "Title: A Novel Paradigm for Neural Computation: X-Net with Learnable Neurons and Adaptable Structure\nAbstract: Artificial neural networks (ANNs) have permeated various disciplinary domains, ranging from bioinformatics to financial analytics, where their application has become an indispensable facet of contemporary scientific research endeavors. However, the inherent limitations of traditional neural networks arise due to their relatively fixed network structures and activation functions. 1, The type of activation function is single and relatively fixed, which leads to poor \"unit representation ability\" of the network, and it is often used to solve simple problems with very complex networks; 2, the network structure is not adaptive, it is easy to cause network structure redundant or insufficient. To address the aforementioned issues, this study proposes a novel neural network called X-Net. By utilizing our designed Alternating Backpropagation mechanism, X-Net dynamically selects appropriate activation functions based on derivative information during training to enhance the network's representation capability for specific tasks. Simultaneously, it accurately adjusts the network structure at the neuron level to accommodate tasks of varying complexities and reduce computational costs. Through a series of experiments, we demonstrate the dual advantages of X-Net in terms of reducing model size and improving representation power. Specifically, in terms of the number of parameters, X-Net is only 3$\\%$ of baselines on average, and only 1.4$\\%$ under some tasks. In terms of representation ability, X-Net can achieve an average $R^2$=0.985 on the fitting task by only optimizing the activation function without introducing any parameters. Finally, we also tested the ability of X-Net to help scientific discovery on data from multiple disciplines such as society, energy, environment, and aerospace, and achieved concise and good results.", "field": "cs", "label": 0}
{"text": "Title: A Kernel Framework to Quantify a Model's Local Predictive Uncertainty under Data Distributional Shifts\nAbstract: Traditional Bayesian approaches for model uncertainty quantification rely on notoriously difficult processes of marginalization over each network parameter to estimate its probability density function (PDF). Our hypothesis is that internal layer outputs of a trained neural network contain all of the information related to both its mapping function (quantified by its weights) as well as the input data distribution. We therefore propose a framework for predictive uncertainty quantification of a trained neural network that explicitly estimates the PDF of its raw prediction space (before activation), p(y'|x,w), which we refer to as the model PDF, in a Gaussian reproducing kernel Hilbert space (RKHS). The Gaussian RKHS provides a localized density estimate of p(y'|x,w), which further enables us to utilize gradient based formulations of quantum physics to decompose the model PDF in terms of multiple local uncertainty moments that provide much greater resolution of the PDF than the central moments characterized by Bayesian methods. This provides the framework with a better ability to detect distributional shifts in test data away from the training data PDF learned by the model. We evaluate the framework against existing uncertainty quantification methods on benchmark datasets that have been corrupted using common perturbation techniques. The kernel framework is observed to provide model uncertainty estimates with much greater precision based on the ability to detect model prediction errors.", "field": "cs", "label": 1}
{"text": "Title: All terms in a complete exceptional sequence are relatively projective or relatively injective\nAbstract: We prove the statement in the title, define the terms and give one application.", "field": "math", "label": 0}
{"text": "Title: Contractibility of the orbit space of a saturated fusion system after Steinberg\nAbstract: Recently, Steinberg used discrete Morse theory to give a new proof of a theorem of Symonds that the orbit space of the poset of nontrivial $p$-subgroups of a finite group is contractible. We extend Steinberg's argument in two ways, covering more general versions of the theorem that were already known. In particular, following a strategy of Libman, we give a discrete Morse theoretic argument for the contractibility of the orbit space of a saturated fusion system.", "field": "math", "label": 0}
{"text": "Title: Continual Learning: Forget-free Winning Subnetworks for Video Representations\nAbstract: Inspired by the Lottery Ticket Hypothesis (LTH), which highlights the existence of efficient subnetworks within larger, dense networks, a high-performing Winning Subnetwork (WSN) in terms of task performance under appropriate sparsity conditions is considered for various continual learning tasks. It leverages pre-existing weights from dense networks to achieve efficient learning in Task Incremental Learning (TIL) scenarios. In Few-Shot Class Incremental Learning (FSCIL), a variation of WSN referred to as the Soft subnetwork (SoftNet) is designed to prevent overfitting when the data samples are scarce. Furthermore, the sparse reuse of WSN weights is considered for Video Incremental Learning (VIL). The use of Fourier Subneural Operator (FSO) within WSN is considered. It enables compact encoding of videos and identifies reusable subnetworks across varying bandwidths. We have integrated FSO into different architectural frameworks for continual learning, including VIL, TIL, and FSCIL. Our comprehensive experiments demonstrate FSO's effectiveness, significantly improving task performance at various convolutional representational levels. Specifically, FSO enhances higher-layer performance in TIL and FSCIL and lower-layer performance in VIL", "field": "cs", "label": 0}
{"text": "Title: Ramsey and Turán numbers of sparse hypergraphs\nAbstract: Degeneracy plays an important role in understanding Tur\\'an- and Ramsey-type properties of graphs. Unfortunately, the usual hypergraphical generalization of degeneracy fails to capture these properties. We define the skeletal degeneracy of a $k$-uniform hypergraph as the degeneracy of its $1$-skeleton (i.e., the graph formed by replacing every $k$-edge by a $k$-clique). We prove that skeletal degeneracy controls hypergraph Tur\\'an and Ramsey numbers in a similar manner to (graphical) degeneracy. Specifically, we show that $k$-uniform hypergraphs with bounded skeletal degeneracy have linear Ramsey number. This is the hypergraph analogue of the Burr-Erd\\H{o}s conjecture (proved by Lee). In addition, we give upper and lower bounds of the same shape for the Tur\\'an number of a $k$-uniform $k$-partite hypergraph in terms of its skeletal degeneracy. The proofs of both results use the technique of dependent random choice. In addition, the proof of our Ramsey result uses the `random greedy process' introduced by Lee in his resolution of the Burr-Erd\\H{o}s conjecture.", "field": "math", "label": 0}
{"text": "Title: Matching of Users and Creators in Two-Sided Markets with Departures\nAbstract: Many online platforms of today, including social media sites, are two-sided markets bridging content creators and users. Most of the existing literature on platform recommendation algorithms largely focuses on user preferences and decisions, and does not simultaneously address creator incentives. We propose a model of content recommendation that explicitly focuses on the dynamics of user-content matching, with the novel property that both users and creators may leave the platform permanently if they do not experience sufficient engagement. In our model, each player decides to participate at each time step based on utilities derived from the current match: users based on alignment of the recommended content with their preferences, and creators based on their audience size. We show that a user-centric greedy algorithm that does not consider creator departures can result in arbitrarily poor total engagement, relative to an algorithm that maximizes total engagement while accounting for two-sided departures. Moreover, in stark contrast to the case where only users or only creators leave the platform, we prove that with two-sided departures, approximating maximum total engagement within any constant factor is NP-hard. We present two practical algorithms, one with performance guarantees under mild assumptions on user preferences, and another that tends to outperform algorithms that ignore two-sided departures in practice.", "field": "cs", "label": 0}
{"text": "Title: Determinants of Circulant Matrices with Some Certain Sequences\nAbstract: Let $\\{a_k\\}$ be a sequence of real numbers defined by an $m$th order linear homogenous recurrence relation. In this paper we obtain a determinant formula for the circulant matrix $A=circ(a_1, a_2, \\cdots, a_n)$, providing a generalization of determinantal results in papers of Bozkurt \\cite{Bozkurt}, Bozkurt and Tam \\cite{BozkurtTam}, and Shen, et al. \\cite{ShenCenHao}.", "field": "math", "label": 1}
{"text": "Title: Probability-graphons: Limits of large dense weighted graphs\nAbstract: We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of subgraph sampling converge. The edge-weights are taken from a general Polish space, which also covers the case of decorated graphs. Here, graphs can be either directed or undirected. Starting from a distance $d_m$ inducing the weak topology on measures, we define a cut distance on probability-graphons, making it a Polish space, and study the properties of this cut distance. In particular, we exhibit a tightness criterion for probability-graphons related to relative compactness in the cut distance. We also prove that under some conditions on the distance $d_m$, which are satisfied for some well-know distances like the Prohorov distance, and the Fortet-Mourier and Kantorovitch-Rubinstein norms, the topology induced by the cut distance on the spaceof probability-graphons is independent from the choice of $d_m$. Eventually, we prove that this topology coincides with the topology induced by the convergence in distribution of the sampled subgraphs.", "field": "cs", "label": 0}
{"text": "Title: Fit-NGP: Fitting Object Models to Neural Graphics Primitives\nAbstract: Accurate 3D object pose estimation is key to enabling many robotic applications that involve challenging object interactions. In this work, we show that the density field created by a state-of-the-art efficient radiance field reconstruction method is suitable for highly accurate and robust pose estimation for objects with known 3D models, even when they are very small and with challenging reflective surfaces. We present a fully automatic object pose estimation system based on a robot arm with a single wrist-mounted camera, which can scan a scene from scratch, detect and estimate the 6-Degrees of Freedom (DoF) poses of multiple objects within a couple of minutes of operation. Small objects such as bolts and nuts are estimated with accuracy on order of 1mm.", "field": "cs", "label": 0}
{"text": "Title: Bounded Derivations on Uniform Roe Algebras\nAbstract: We show that if $C_u^*(X)$ is a uniform Roe algebra associated to a bounded geometry metric space X, then all bounded derivations on $C^*_u(X)$ are inner.", "field": "math", "label": 1}
{"text": "Title: A Geometry-Sensitive Approach for Photographic Style Classification\nAbstract: Photographs are characterized by different compositional attributes like the Rule of Thirds, depth of field, vanishing-lines etc. The presence or absence of one or more of these attributes contributes to the overall artistic value of an image. In this work, we analyze the ability of deep learning based methods to learn such photographic style attributes. We observe that although a standard CNN learns the texture and appearance based features reasonably well, its understanding of global and geometric features is limited by two factors. First, the data-augmentation strategies (cropping, warping, etc.) distort the composition of a photograph and affect the performance. Secondly, the CNN features, in principle, are translation-invariant and appearance-dependent. But some geometric properties important for aesthetics, e.g. the Rule of Thirds (RoT), are position-dependent and appearance-invariant. Therefore, we propose a novel input representation which is geometry-sensitive, position-cognizant and appearance-invariant. We further introduce a two-column CNN architecture that performs better than the state-of-the-art (SoA) in photographic style classification. From our results, we observe that the proposed network learns both the geometric and appearance-based attributes better than the SoA.", "field": "cs", "label": 1}
{"text": "Title: Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition\nAbstract: We consider a non-local Shr\\\"odinger problem driven by the fractional Orlicz g-Laplace operator as follows \\begin{equation}\\label{PP} (-\\triangle_{g})^{\\alpha}u+g(u)=K(x)f(x,u),\\ \\ \\text{in}\\ \\mathbb{R}^{d},\\tag{P} \\end{equation} where $d\\geq 3,\\ (-\\triangle_{g})^{\\alpha}$ is the fractional Orlicz g-Laplace operator, $f:\\mathbb{R}^d\\times\\mathbb{R}\\rightarrow \\mathbb{R}$ is a measurable function and $K$ is a positive continuous function. Employing the Nehari manifold method and without assuming the well-known Ambrosetti-Rabinowitz and differentiability conditions on the non-linear term $f$, we prove that the problem \\eqref{PP} has a ground state of fixed sign and a nodal (or sign-changing) solutions.", "field": "math", "label": 1}
{"text": "Title: Recourse under Model Multiplicity via Argumentative Ensembling (Technical Report)\nAbstract: Model Multiplicity (MM) arises when multiple, equally performing machine learning models can be trained to solve the same prediction task. Recent studies show that models obtained under MM may produce inconsistent predictions for the same input. When this occurs, it becomes challenging to provide counterfactual explanations (CEs), a common means for offering recourse recommendations to individuals negatively affected by models' predictions. In this paper, we formalise this problem, which we name recourse-aware ensembling, and identify several desirable properties which methods for solving it should satisfy. We show that existing ensembling methods, naturally extended in different ways to provide CEs, fail to satisfy these properties. We then introduce argumentative ensembling, deploying computational argumentation to guarantee robustness of CEs to MM, while also accommodating customisable user preferences. We show theoretically and experimentally that argumentative ensembling satisfies properties which the existing methods lack, and that the trade-offs are minimal wrt accuracy.", "field": "cs", "label": 0}
{"text": "Title: Quadratic relations of the deformed $W$-algebra\nAbstract: The deformed $W$-algebra is a quantum deformation of the $W$-algebra ${\\cal W}_\\beta(\\mathfrak{g})$ in conformal field theory. Using the free field construction, we obtain a closed set of quadratic relations of the $W$-currents of the deformed $W$-algebra. This allows us to define the deformed $W$-algebra by generators and relations. In this review, we study two types of deformed $W$-algebra. One is the deformed $W$-algebra ${\\cal W}_{x,r}\\big(A_{2N}^{(2)}\\big)$, and the other is the $q$-deformed corner vertex algebra $q$-$Y_{L_1, L_2, L_3}$ that is a generalization of the deformed $W$-algebra ${\\cal W}_{x,r}\\big(A(M,N)^{(1)}\\big)$ via the quantum toroidal algebra.", "field": "math", "label": 0}
{"text": "Title: An upper bound on the size of avoidance couplings\nAbstract: We show that a coupling of non-colliding simple random walkers on the complete graph on $n$ vertices can include at most $n - \\log n$ walkers. This improves the only previously known upper bound of $n-2$ due to Angel, Holroyd, Martin, Wilson, and Winkler ({\\it Electron.~Commun.~Probab.~18}, 2013). The proof considers couplings of i.i.d.~sequences of Bernoulli random variables satisfying a similar avoidance property, for which there is separate interest. Our bound in this setting should be closer to optimal.", "field": "math", "label": 1}
{"text": "Title: Derivatives of symplectic eigenvalues and a Lidskii type theorem\nAbstract: Associated with every $2n\\times 2n$ real positive definite matrix $A,$ there exist $n$ positive numbers called the symplectic eigenvalues of $A,$ and a basis of $\\mathbb{R}^{2n}$ called the symplectic eigenbasis of $A$ corresponding to these numbers. In this paper, we discuss the differentiability (analyticity) of the symplectic eigenvalues and corresponding symplectic eigenbasis for differentiable (analytic) map $t\\mapsto A(t),$ and compute their derivatives. We then derive an analogue of Lidskii's theorem for symplectic eigenvalues as an application.", "field": "math", "label": 1}
{"text": "Title: Online Learning for Network Constrained Demand Response Pricing in Distribution Systems\nAbstract: Flexible demand response (DR) resources can be leveraged to accommodate the stochasticity of some distributed energy resources. This paper develops an online learning approach that continuously estimates price sensitivities of residential DR participants and produces such price signals to the DR participants that ensure a desired level of DR capacity. The proposed learning approach incorporates the dispatch decisions on DR resources into the distributionally robust chance-constrained optimal power flow (OPF) framework. This integration is shown to adequately remunerate DR resources and co-optimize the dispatch of DR and conventional generation resources. The distributionally robust chance-constrained formulation only relies on empirical data acquired over time and makes no restrictive assumptions on the underlying distribution of the demand uncertainty. The distributional robustness also allows for robustifying the optimal solution against systematically misestimating empirically learned parameters. The effectiveness of the proposed learning approach is shown via numerical experiments. The paper is accompanied by the code and data supplement released for public use, see [27].", "field": "cs", "label": 1}
{"text": "Title: High-Fidelity Diffusion-based Image Editing\nAbstract: Diffusion models have attained remarkable success in the domains of image generation and editing. It is widely recognized that employing larger inversion and denoising steps in diffusion model leads to improved image reconstruction quality. However, the editing performance of diffusion models tends to be no more satisfactory even with increasing denoising steps. The deficiency in editing could be attributed to the conditional Markovian property of the editing process, where errors accumulate throughout denoising steps. To tackle this challenge, we first propose an innovative framework where a rectifier module is incorporated to modulate diffusion model weights with residual features, thereby providing compensatory information to bridge the fidelity gap. Furthermore, we introduce a novel learning paradigm aimed at minimizing error propagation during the editing process, which trains the editing procedure in a manner similar to denoising score-matching. Extensive experiments demonstrate that our proposed framework and training strategy achieve high-fidelity reconstruction and editing results across various levels of denoising steps, meanwhile exhibits exceptional performance in terms of both quantitative metric and qualitative assessments. Moreover, we explore our model's generalization through several applications like image-to-image translation and out-of-domain image editing.", "field": "cs", "label": 0}
{"text": "Title: Aggregation-diffusion phenomena: from microscopic models to free boundary problems\nAbstract: This paper reviews (and expands) some recent results on the modeling of aggregation-diffusion phenomena at various scales, focusing on the emergence of collective dynamics as a result of the competition between attractive and repulsive phenomena - especially (but not exclusively) in the context of attractive chemotaxis phenomena. At microscopic scales, particles (or other agents) are represented by spheres of radius $\\delta>0$ and we discuss both soft-sphere models (with a pressure term penalizing the overlap of the particles) and hard-sphere models (in which overlap is prohibited). The first case leads to so-called ``blob models\" which have received some attention recently as a tool to approximate non-linear diffusion by particle systems. The hard-sphere model is similar to a classical model for congested crowd motion. We review well-posedness results for these models and discuss their relationship to classical continuum description of aggregation-diffusion phenomena in the limit $\\delta\\to0$: the classical nonlinear drift diffusion equation and its incompressible counterpart. In the second part of the paper, we discuss recent results on the emergence and evolution of sharp interfaces when a large population of particles is considered at appropriate space and time scales: At some intermediate time scale, phase separation occurs and a sharp interface appears which evolves according to a Stefan free boundary problem (and the density function eventually relaxes to a characteristic function - metastable steady state for the original problem). At a larger time scale the attractive forces lead to surface tension phenomena and the evolution of the sharp interface can be described by a Hele-Shaw free boundary problem with surface tension. At that same time scale, we will also discuss the emergence of contact angle conditions for problems set in bounded domains.", "field": "math", "label": 0}
{"text": "Title: Van der Corput and metric theorems for geometric progressions for self-similar measures\nAbstract: We prove a van der Corput lemma for non-atomic self-similar measures $\\mu$. As an application, we show that the correlations of all finite orders of $( x^n \\mod 1 )_{n\\geq 1}$ converge to the Poissonian model for $\\mu$-a.e. $x$, assuming $x>1$. We also complete a recent result of Algom, Rodriguez Hertz, and Wang (obtained simultaneously by Baker and Banaji), showing that any self-conformal measure with respect to a non-affine real analytic IFS has polynomial Fourier decay.", "field": "math", "label": 0}
{"text": "Title: Notes on limits of accessible categories\nAbstract: Let $\\kappa$ be a regular cardinal, $\\lambda<\\kappa$ be a smaller infinite cardinal, and $\\mathsf K$ be a $\\kappa$-accessible category where colimits of $\\lambda$-indexed chains exist. We show that various category-theoretic constructions applied to $\\mathsf K$, such as the inserter and the equifier, produce $\\kappa$-accessible categories $\\mathsf E$ again, and the most obvious expected description of the full subcategory of $\\kappa$-presentable objects in $\\mathsf E$ in terms of $\\kappa$-presentable objects in $\\mathsf K$ holds true. In particular, if $\\mathsf C$ is a $\\kappa$-small category, then the category of functors $\\mathsf C\\rightarrow\\mathsf K$ is $\\kappa$-accessible, and its $\\kappa$-presentable objects are precisely all the functors from $\\mathsf C$ to the $\\kappa$-presentable objects of $\\mathsf K$. We proceed to discuss the preservation of $\\kappa$-accessibility by conical pseudolimits, lax and oplax limits, and weighted pseudolimits. The results of this paper go back to an unpublished 1977 preprint of Ulmer. Our motivation comes from the theory of flat modules and flat quasi-coherent sheaves.", "field": "math", "label": 0}
{"text": "Title: Learning nonlinear level sets for dimensionality reduction in function approximation\nAbstract: We developed a Nonlinear Level-set Learning (NLL) method for dimensionality reduction in high-dimensional function approximation with small data. This work is motivated by a variety of design tasks in real-world engineering applications, where practitioners would replace their computationally intensive physical models (e.g., high-resolution fluid simulators) with fast-to-evaluate predictive machine learning models, so as to accelerate the engineering design processes. There are two major challenges in constructing such predictive models: (a) high-dimensional inputs (e.g., many independent design parameters) and (b) small training data, generated by running extremely time-consuming simulations. Thus, reducing the input dimension is critical to alleviate the over-fitting issue caused by data insufficiency. Existing methods, including sliced inverse regression and active subspace approaches, reduce the input dimension by learning a linear coordinate transformation; our main contribution is to extend the transformation approach to a nonlinear regime. Specifically, we exploit reversible networks (RevNets) to learn nonlinear level sets of a high-dimensional function and parameterize its level sets in low-dimensional spaces. A new loss function was designed to utilize samples of the target functions' gradient to encourage the transformed function to be sensitive to only a few transformed coordinates. The NLL approach is demonstrated by applying it to three 2D functions and two 20D functions for showing the improved approximation accuracy with the use of nonlinear transformation, as well as to an 8D composite material design problem for optimizing the buckling-resistance performance of composite shells of rocket inter-stages.", "field": "math", "label": 1}
{"text": "Title: Posets, Tensor Products and Schur positivity\nAbstract: Let g be a complex finite-dimensional simple Lie algebra. Given a positive integer k and a dominant weight \\lambda, we define a preorder on the set $P(\\lambda, k)$ of k-tuples of dominant weights which add up to \\lambda. Let $P(\\lambda, k)/\\sim$ be the corresponding poset of equivalence classes defined by the preorder. We show that if \\lambda is a multiple of a fundamental weight (and k is general) or if k=2 (and \\lambda is general), then $P(\\lambda, k)/\\sim$ coincides with the set of S_k-orbits in $P(\\lambda,k)$, where S_k acts on $P(\\lambda, k)$ as the permutations of components. If g is of type A_n and k=2, we show that the S_2-orbit of the row shuffle defined by Fomin et al is the unique maximal element in the poset. Given an element of $P(\\lambda, k)$, consider the tensor product of the corresponding simple finite-dimensional g-modules. We show that (for general g, \\lambda, and k) the dimension of this tensor product increases along with the partial order. We also show that in the case when \\lambda is a multiple of a fundamental minuscule weight (g and k are general) or if g is of type A_2 and k=2 (\\lambda is general), there exists an inclusion of tensor products of g-modules along with the partial order. In particular, if g is of type A_n, this means that the difference of the characters is Schur positive.", "field": "math", "label": 1}
{"text": "Title: Packing graphs of bounded codegree\nAbstract: Two graphs $G_1$ and $G_2$ on $n$ vertices are said to pack if there exist injective mappings of their vertex sets into $[n]$ such that the images of their edge sets are disjoint. A longstanding conjecture due to Bollob\\'as and Eldridge and, independently, Catlin, asserts that, if $(\\Delta_1(G)+1) (\\Delta_2(G)+1) \\le n+1$, then $G_1$ and $G_2$ pack. We consider the validity of this assertion under the additional assumption that $G_1$ or $G_2$ has bounded codegree. In particular, we prove for all $t \\ge 2$ that, if $G_1$ contains no copy of the complete bipartite graph $K_{2,t}$ and $\\Delta_1 > 17 t \\cdot \\Delta_2$, then $(\\Delta_1(G)+1) (\\Delta_2(G)+1) \\le n+1$ implies that $G_1$ and $G_2$ pack. We also provide a mild improvement if moreover $G_2$ contains no copy of the complete tripartite graph $K_{1,1,s}$, $s\\ge 1$.", "field": "math", "label": 1}
{"text": "Title: A PDE approach for solving the characteristic function of the generalised signature process\nAbstract: The signature of a path, as a fundamental object in Rough path theory, serves as a generating function for non-communicative monomials on path space. It transforms the path into a grouplike element in the tensor algebra space, summarising the path faithfully up to a generalised form of re-parameterisation (a negligible equivalence class in this context). Our paper concerns stochastic processes and studies the characteristic function of the path signature of the stochastic process. In contrast to the expected signature, it determines the law on the random signatures without any regularity condition. The computation of the characteristic function of the random signature offers potential applications in stochastic analysis and machine learning, where the expected signature plays an important role. In this paper, we focus on a time-homogeneous It\\^o diffusion process, and adopt a PDE approach to derive the characteristic function of its signature defined at any fixed time horizon. A key ingredient of our approach is the introduction of the generalised-signature process. This lifting enables us to establish the Feynman-Kac-type theorem for the characteristic function of the generalised-signature process by following the martingale approach. Moreover, as an application of our results, we present a novel derivation of the joint characteristic function of Brownian motion coupled with the L\\'evy area, leveraging the structure theorem of anti-symmetric matrices.", "field": "math", "label": 0}
{"text": "Title: Normal subgroups and relative centers of linearly reductive quantum groups\nAbstract: We prove a number of structural and representation-theoretic results on linearly reductive quantum groups, i.e. objects dual to that of cosemisimple Hopf algebras: (a) a closed normal quantum subgroup is automatically linearly reductive if its squared antipode leaves invariant each simple subcoalgebra of the underlying Hopf algebra; (b) for a normal embedding $\\mathbb{H}\\trianglelefteq \\mathbb{G}$ there is a Clifford-style correspondence between two equivalence relations on irreducible $\\mathbb{G}$- and, respectively, $\\mathbb{H}$-representations; and (c) given an embedding $\\mathbb{H}\\le \\mathbb{G}$ of linearly reductive quantum groups the Pontryagin dual of the relative center $Z(\\mathbb{G})\\cap \\mathbb{H}$ can be described by generators and relations, with one generator $g_V$ for each irreducible $\\mathbb{G}$-representation $V$ and one relation $g_U=g_Vg_W$ whenever $U$ and $V\\otimes W$ are not disjoint over $\\mathbb{H}$. This latter center-reconstruction result generalizes and recovers M\\\"uger's compact-group analogue and the author's quantum-group version of that earlier result by setting $\\mathbb{H}=\\mathbb{G}$.", "field": "math", "label": 1}
{"text": "Title: On the complexity of the generalized Q2R automaton\nAbstract: We study the dynamic and complexity of the generalized Q2R automaton. We show the existence of non-polynomial cycles as well as its capability to simulate with the synchronous update the classical version of the automaton updated under a block sequential update scheme. Furthermore, we show that the decision problem consisting in determine if a given node in the network changes its state is \\textbf{P}-Hard.", "field": "cs", "label": 1}
{"text": "Title: Gaussian Process based Stochastic Model Predictive Control for Cooperative Adaptive Cruise Control\nAbstract: Cooperative driving relies on communication among vehicles to create situational awareness. One application of cooperative driving is Cooperative Adaptive Cruise Control (CACC) that aims at enhancing highway transportation safety and capacity. Model-based communication (MBC) is a new paradigm with a flexible content structure for broadcasting joint vehicle-driver predictive behavioral models. The vehicle's complex dynamics and diverse driving behaviors add complexity to the modeling process. Gaussian process (GP) is a fully data-driven and non-parametric Bayesian modeling approach which can be used as a modeling component of MBC. The knowledge about the uncertainty is propagated through predictions by generating local GPs for vehicles and broadcasting their hyper-parameters as a model to the neighboring vehicles. In this research study, GP is used to model each vehicle's speed trajectory, which allows vehicles to access the future behavior of their preceding vehicle during communication loss and/or low-rate communication. Besides, to overcome the safety issues in a vehicle platoon, two operating modes for each vehicle are considered; free following and emergency braking. This paper presents a discrete hybrid stochastic model predictive control, which incorporates system modes as well as uncertainties captured by GP models. The proposed control design approach finds the optimal vehicle speed trajectory with the goal of achieving a safe and efficient platoon of vehicles with small inter-vehicle gap while reducing the reliance of the vehicles on a frequent communication. Simulation studies demonstrate the efficacy of the proposed controller considering the aforementioned communication paradigm with low-rate intermittent communication.", "field": "cs", "label": 1}
{"text": "Title: Definability of continuous isomorphisms of groups definable in o-minimal expansions of the real field\nAbstract: In this paper, we study the relation between the category of real Lie groups and that of groups definable in o-minimal expansions of the real field (which we will refer to as \"definable groups\"). It is known (\\cite{Pi88}) that any group definable in an o-minimal expansion of the real field is a Lie group, and in \\cite{COP} a complete characterization of when a Lie group has a \"definable group\" which is \\emph{Lie isomorphic} to it was given. We continue the analysis by explaining when a Lie homomorphism between definable groups is a definable isomorphism. Among other things, we prove that in any o-minimal expansion $\\mathcal R$ of the real field we can add a function symbol for any Lie isomorphism between definable groups to the language of $\\mathcal R$ preserving o-minimality, and that any definable group $G$ can be endowed with an analytic manifold structure definable in $\\mathcal R_{\\text{Pfaff}}$ that makes it an analytic group.", "field": "math", "label": 0}
{"text": "Title: Fiber criteria for flatness and homomorphisms of flat affine group schemes\nAbstract: A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finiteness'' assumptions. Motivated by a Tannakian viewpoint (where the category of representations comes to the front), we derive applications to the theory of affine and flat group schemes.", "field": "math", "label": 0}
{"text": "Title: Decomposable and atomic projection maps\nAbstract: It is shown that a trace invariant projection map, i.e. a positive unital idempotent map, of a finite dimensional C*-algebra into itself is non-decomposable if and only if it is atomic, or equivalently not the sum of a 2-positive and a 2-copositive map. In particular projections onto spin factors of dimension greater than 6 are atomic.", "field": "math", "label": 1}
{"text": "Title: Absolute continuity of the limiting eigenvalue distribution of the random Toeplitz matrix\nAbstract: We show that the limiting eigenvalue distribution of random symmetric Toeplitz matrices is absolutely continuous with density bounded by 8, partially answering a question of Bryc, Dembo and Jiang (2006). The main tool used in the proof is a spectral averaging technique from the theory of random Schr\\\"{o}dinger operators. The similar question for Hankel matrices remains open.", "field": "math", "label": 1}
{"text": "Title: Speeding Up Distributed Machine Learning Using Codes\nAbstract: Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes, system failures, or communication bottlenecks -- but there has been little interaction cutting across codes, machine learning, and distributed systems. In this work, we provide theoretical insights on how coded solutions can achieve significant gains compared to uncoded ones. We focus on two of the most basic building blocks of distributed learning algorithms: matrix multiplication and data shuffling. For matrix multiplication, we use codes to alleviate the effect of stragglers, and show that if the number of homogeneous workers is $n$, and the runtime of each subtask has an exponential tail, coded computation can speed up distributed matrix multiplication by a factor of $\\log n$. For data shuffling, we use codes to reduce communication bottlenecks, exploiting the excess in storage. We show that when a constant fraction $\\alpha$ of the data matrix can be cached at each worker, and $n$ is the number of workers, \\emph{coded shuffling} reduces the communication cost by a factor of $(\\alpha + \\frac{1}{n})\\gamma(n)$ compared to uncoded shuffling, where $\\gamma(n)$ is the ratio of the cost of unicasting $n$ messages to $n$ users to multicasting a common message (of the same size) to $n$ users. For instance, $\\gamma(n) \\simeq n$ if multicasting a message to $n$ users is as cheap as unicasting a message to one user. We also provide experiment results, corroborating our theoretical gains of the coded algorithms.", "field": "cs", "label": 1}
{"text": "Title: One-sided reflected Brownian motions and the KPZ fixed point\nAbstract: We consider the system of one-sided reflected Brownian motions which is in variational duality with Brownian last passage percolation. We show that it has integrable transition probabilities, expressed in terms of Hermite polynomials and hitting times of exponential random walks, and that it converges in the 1:2:3 scaling limit to the KPZ fixed point, the scaling invariant Markov process defined in [MQR17] and believed to govern the long time large scale fluctuations for all models in the KPZ universality class. Brownian last passage percolation was shown recently in [DOV18] to converge to the Airy sheet (or directed landscape), defined there as a strong limit of a functional of the Airy line ensemble. This establishes the variational formula for the KPZ fixed point in terms of the Airy sheet.", "field": "math", "label": 1}
{"text": "Title: Spectral conditions for factor-criticality of graphs\nAbstract: A graph $G$ is $k$-factor-critical if $G-S$ has a perfect matching for any $k$-subset $S$ of the vertex set of $G$. In this paper, we investigate the factor-criticality of graphs with fixed minimum degree and provide sufficient conditions for such graphs to be $k$-factor-critical in terms of spectral radius and signless Laplacian spectral radius.", "field": "math", "label": 0}
{"text": "Title: DGDNN: Decoupled Graph Diffusion Neural Network for Stock Movement Prediction\nAbstract: Forecasting future stock trends remains challenging for academia and industry due to stochastic inter-stock dynamics and hierarchical intra-stock dynamics influencing stock prices. In recent years, graph neural networks have achieved remarkable performance in this problem by formulating multiple stocks as graph-structured data. However, most of these approaches rely on artificially defined factors to construct static stock graphs, which fail to capture the intrinsic interdependencies between stocks that rapidly evolve. In addition, these methods often ignore the hierarchical features of the stocks and lose distinctive information within. In this work, we propose a novel graph learning approach implemented without expert knowledge to address these issues. First, our approach automatically constructs dynamic stock graphs by entropy-driven edge generation from a signal processing perspective. Then, we further learn task-optimal dependencies between stocks via a generalized graph diffusion process on constructed stock graphs. Last, a decoupled representation learning scheme is adopted to capture distinctive hierarchical intra-stock features. Experimental results demonstrate substantial improvements over state-of-the-art baselines on real-world datasets. Moreover, the ablation study and sensitivity study further illustrate the effectiveness of the proposed method in modeling the time-evolving inter-stock and intra-stock dynamics.", "field": "cs", "label": 0}
{"text": "Title: Robust Physics Informed Neural Networks\nAbstract: We introduce a Robust version of the Physics-Informed Neural Networks (RPINNs) to approximate the Partial Differential Equations (PDEs) solution. Standard Physics Informed Neural Networks (PINN) takes into account the governing physical laws described by PDE during the learning process. The network is trained on a data set that consists of randomly selected points in the physical domain and its boundary. PINNs have been successfully applied to solve various problems described by PDEs with boundary conditions. The loss function in traditional PINNs is based on the strong residuals of the PDEs. This loss function in PINNs is generally not robust with respect to the true error. The loss function in PINNs can be far from the true error, which makes the training process more difficult. In particular, we do not know if the training process has already converged to the solution with the required accuracy. This is especially true if we do not know the exact solution, so we cannot estimate the true error during the training. This paper introduces a different way of defining the loss function. It incorporates the residual and the inverse of the Gram matrix, computed using the energy norm. We test our RPINN algorithm on two Laplace problems and one advection-diffusion problem in two spatial dimensions. We conclude that RPINN is a robust method. The proposed loss coincides well with the true error of the solution, as measured in the energy norm. Thus, we know if our training process goes well, and we know when to stop the training to obtain the neural network approximation of the solution of the PDE with the true error of required accuracy.", "field": "cs", "label": 0}
{"text": "Title: Controllability of evolution equations with memory\nAbstract: This article is devoted to studying the null controllability of evolution equations with memory terms. The problem is challenging not only because the state equation contains memory terms but also because the classical controllability requirement at the final time has to be reinforced, involving the contribution of the memory term, to ensure that the solution reaches the equilibrium. Using duality arguments, the problem is reduced to the obtention of suitable observability estimates for the adjoint system. We first consider finite-dimensional dynamical systems involving memory terms and derive rank conditions for controllability. Then the null controllability property is established for some parabolic equations with memory terms, by means of Carleman estimates.", "field": "math", "label": 1}
{"text": "Title: Index concepts for linear differential-algebraic equations in finite and infinite dimensions\nAbstract: Different index concepts for linear differential-algebraic equations are defined in the general Banach space setting, and compared. For regular finite-dimensional linear differential-algebraic equations, all these indices exist and are equivalent. For infinite-dimensional systems, the situation is more complex. It is proven that although some indices imply others, in general they are not equivalent. The situation is illustrated with a number of examples.", "field": "math", "label": 0}
{"text": "Title: A rewriting-logic-with-SMT-based formal analysis and parameter synthesis framework for parametric time Petri nets\nAbstract: This paper presents a concrete and a symbolic rewriting logic semantics for parametric time Petri nets with inhibitor arcs (PITPNs), a flexible model of timed systems where parameters are allowed in firing bounds. We prove that our semantics is bisimilar to the \"standard\" semantics of PITPNs. This allows us to use the rewriting logic tool Maude, combined with SMT solving, to provide sound and complete formal analyses for PITPNs. We develop and implement a new general folding approach for symbolic reachability, so that Maude-with-SMT reachability analysis terminates whenever the parametric state-class graph of the PITPN is finite. Our work opens up the possibility of using the many formal analysis capabilities of Maude -- including full LTL model checking, analysis with user-defined analysis strategies, and even statistical model checking -- for such nets. We illustrate this by explaining how almost all formal analysis and parameter synthesis methods supported by the state-of-the-art PITPN tool Romeo can be performed using Maude with SMT. In addition, we also support analysis and parameter synthesis from parametric initial markings, as well as full LTL model checking and analysis with user-defined execution strategies. Experiments show that our methods outperform Romeo in many cases.", "field": "cs", "label": 0}
{"text": "Title: The spectrality of self-affine measure under the similarity transformation of $GL_n(p)$\nAbstract: Let $\\mu_{M,D}$ be the self-affine measure generated by an expanding integer matrix $M\\in M_n(\\mathbb{Z})$ and a finite digit set $D\\subset\\mathbb{Z}^n$. It is well known that the two measures $\\mu_{M,D}$ and $\\mu_{\\tilde{M},\\tilde{D}}$ have the same spectrality if $\\tilde{M}=B^{-1}MB$ and $\\tilde{D}=B^{-1}D$, where $B\\in M_n(\\mathbb{R})$ is a nonsingular matrix. This fact is usually used to simplify the digit set $D$ or the expanding matrix $M$. However, it often transforms integer digit set $D$ or expanding matrix $M$ into real, which brings many difficulties to study the spectrality of $\\mu_{\\tilde{M},\\tilde{D}}$. In this paper, we introduce a similarity transformation of general linear group $GL_n(p)$ for some self-affine measures, and discuss their spectrality. This kind of similarity transformation can keep the integer properties of $D$ and $M$ simultaneously, which leads to many advantages in discussing the spectrality of self-affine measures. As an application, we extend some well-known spectral self-affine measures to more general forms.", "field": "math", "label": 1}
{"text": "Title: Two point concentration of maximum degree in sparse random planar graphs\nAbstract: Let $P(n,m)$ be a graph chosen uniformly at random from the class of all planar graphs on vertex set $\\left\\{1, \\ldots, n\\right\\}$ with $m=m(n)$ edges. We show that in the sparse regime, when $\\limsup_{n \\to \\infty} m/n<1$, with high probability the maximum degree of $P(n,m)$ takes at most two different values.", "field": "math", "label": 1}
{"text": "Title: Polynomial Fourier decay for fractal measures and their pushforwards\nAbstract: We prove that the pushforwards of a very general class of fractal measures $\\mu$ on $\\mathbb{R}^d$ under a large family of non-linear maps $F \\colon \\mathbb{R}^d \\to \\mathbb{R}$ exhibit polynomial Fourier decay: there exist $C,\\eta>0$ such that $|\\widehat{F\\mu}(\\xi)|\\leq C|\\xi|^{-\\eta}$ for all $\\xi\\neq 0$. Using this, we prove that if $\\Phi = \\{ \\varphi_a \\colon [0,1] \\to [0,1] \\}_{a \\in \\mathcal{A}}$ is an iterated function system consisting of analytic contractions, and there exists $a \\in \\mathcal{A}$ such that $\\varphi_a$ is not an affine map, then every non-atomic self-conformal measure for $\\Phi$ has polynomial Fourier decay; this result was obtained simultaneously by Algom, Rodriguez Hertz, and Wang. We prove applications related to the Fourier uniqueness problem, Fractal Uncertainty Principles, and normal numbers in fractal sets.", "field": "math", "label": 0}
{"text": "Title: Higher Order Model Checking in Isabelle for Human Centric Infrastructure Security\nAbstract: In this paper we present an efficient approach to implementing model checking in the Higher Order Logic (HOL) of Isabelle. This is a non-trivial task since model checking is restricted to finite state sets. By restricting our scope to considering security attacks, we achieve an efficient executable specification of a model checking algorithm for attack trees. We provide the existing background, the necessary theory and illustrate its application. Theory and application are fully formalized in Isabelle thus providing an executable model checking algorithm.", "field": "cs", "label": 0}
{"text": "Title: Improved Adversarial Systems for 3D Object Generation and Reconstruction\nAbstract: This paper describes a new approach for training generative adversarial networks (GAN) to understand the detailed 3D shape of objects. While GANs have been used in this domain previously, they are notoriously hard to train, especially for the complex joint data distribution over 3D objects of many categories and orientations. Our method extends previous work by employing the Wasserstein distance normalized with gradient penalization as a training objective. This enables improved generation from the joint object shape distribution. Our system can also reconstruct 3D shape from 2D images and perform shape completion from occluded 2.5D range scans. We achieve notable quantitative improvements in comparison to existing baselines", "field": "cs", "label": 1}
{"text": "Title: Comultiplication for shifted Yangians and quantum open Toda lattice\nAbstract: We study a coproduct in type A quantum open Toda lattice in terms of a coproduct in the shifted Yangian of sl_2. At the classical level this corresponds to the multiplication of scattering matrices of euclidean SU(2) monopoles. We also study coproducts for shifted Yangians for any simply-laced Lie algebra.", "field": "math", "label": 1}
{"text": "Title: A phase field formulation for hydrogen assisted cracking\nAbstract: We present a phase field modeling framework for hydrogen assisted cracking. The model builds upon a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, and a hydrogen-dependent fracture energy degradation law grounded on first principles calculations. The coupled problem is solved in an implicit time integration scheme, where displacements, phase field order parameter and hydrogen concentration are the primary variables. We show that phase field formulations for fracture are particularly suitable to capture material degradation due to hydrogen. Specifically, we model (i) unstable crack growth in the presence of hydrogen, (ii) failure stress sensitivity to hydrogen content in notched specimens, (iii) cracking thresholds under constant load, (iv) internal hydrogen assisted fracture in cracked specimens, and (v) complex crack paths arising from corrosion pits. Computations reveal a good agreement with experiments, highlighting the predictive capabilities of the present scheme. The work could have important implications for the prediction and prevention of catastrophic failures in corrosive environments. The finite element code developed can be downloaded from www.empaneda.com/codes", "field": "math", "label": 1}
{"text": "Title: On the first two eigenvalues of regular graphs\nAbstract: Let $G$ be a regular graph with $m$ edges, and let $\\mu_1, \\mu_2$ denote the two largest eigenvalues of $A_G$, the adjacency matrix of $G$. We show that, if $G$ is not complete, then $$\\mu_1^2 + \\mu_2^2 \\leq \\frac{2(\\omega - 1)}{\\omega} m$$ where $\\omega$ is the clique number of $G$. This confirms a conjecture of Bollob\\'{a}s and Nikiforov for regular graphs. We also show that equality holds if and only if $G$ is either a balanced Tur\\'{a}n graph or the disjoint union of two balanced Tur\\'{a}n graphs of the same size.", "field": "math", "label": 0}
{"text": "Title: Implementation Notes for the Soft Cosine Measure\nAbstract: The standard bag-of-words vector space model (VSM) is efficient, and ubiquitous in information retrieval, but it underestimates the similarity of documents with the same meaning, but different terminology. To overcome this limitation, Sidorov et al. proposed the Soft Cosine Measure (SCM) that incorporates term similarity relations. Charlet and Damnati showed that the SCM is highly effective in question answering (QA) systems. However, the orthonormalization algorithm proposed by Sidorov et al. has an impractical time complexity of $\\mathcal O(n^4)$, where n is the size of the vocabulary. In this paper, we prove a tighter lower worst-case time complexity bound of $\\mathcal O(n^3)$. We also present an algorithm for computing the similarity between documents and we show that its worst-case time complexity is $\\mathcal O(1)$ given realistic conditions. Lastly, we describe implementation in general-purpose vector databases such as Annoy, and Faiss and in the inverted indices of text search engines such as Apache Lucene, and ElasticSearch. Our results enable the deployment of the SCM in real-world information retrieval systems.", "field": "cs", "label": 1}
{"text": "Title: On the total disconnectedness of the quotient Aubry set\nAbstract: In this paper we show that the quotient Aubry set associated to certain Lagrangians is totally disconnected (i.e., every connected component consists of a single point). Moreover, we discuss the relation between this problem and a Morse-Sard type property for (difference of) critical subsolutions of Hamilton-Jacobi equations.", "field": "math", "label": 1}
{"text": "Title: CARAT: Contrastive Feature Reconstruction and Aggregation for Multi-modal Multi-label Emotion Recognition\nAbstract: Multi-modal multi-label emotion recognition (MMER) aims to identify relevant emotions from multiple modalities. The challenge of MMER is how to effectively capture discriminative features for multiple labels from heterogeneous data. Recent studies are mainly devoted to exploring various fusion strategies to integrate multi-modal information into a unified representation for all labels. However, such a learning scheme not only overlooks the specificity of each modality but also fails to capture individual discriminative features for different labels. Moreover, dependencies of labels and modalities cannot be effectively modeled. To address these issues, this paper presents ContrAstive feature Reconstruction and AggregaTion (CARAT) for the MMER task. Specifically, we devise a reconstruction-based fusion mechanism to better model fine-grained modality-to-label dependencies by contrastively learning modal-separated and label-specific features. To further exploit the modality complementarity, we introduce a shuffle-based aggregation strategy to enrich co-occurrence collaboration among labels. Experiments on two benchmark datasets CMU-MOSEI and M3ED demonstrate the effectiveness of CARAT over state-of-the-art methods. Code is available at https://github.com/chengzju/CARAT.", "field": "cs", "label": 0}
{"text": "Title: Deutsch paths and their enumeration\nAbstract: A variation of Dyck paths allows for down-steps of arbitrary length, not just one. Credits for this invention are given to Emeric Deutsch. Surprisingly, the enumeration of them is somewhat akin to the analysis of Motzkin-paths; the last section contains a bijection.", "field": "math", "label": 1}
{"text": "Title: Learning to Generalize towards Unseen Domains via a Content-Aware Style Invariant Model for Disease Detection from Chest X-rays\nAbstract: Performance degradation due to distribution discrepancy is a longstanding challenge in intelligent imaging, particularly for chest X-rays (CXRs). Recent studies have demonstrated that CNNs are biased toward styles (e.g., uninformative textures) rather than content (e.g., shape), in stark contrast to the human vision system. Radiologists tend to learn visual cues from CXRs and thus perform well across multiple domains. Motivated by this, we employ the novel on-the-fly style randomization modules at both image (SRM-IL) and feature (SRM-FL) levels to create rich style perturbed features while keeping the content intact for robust cross-domain performance. Previous methods simulate unseen domains by constructing new styles via interpolation or swapping styles from existing data, limiting them to available source domains during training. However, SRM-IL samples the style statistics from the possible value range of a CXR image instead of the training data to achieve more diversified augmentations. Moreover, we utilize pixel-wise learnable parameters in the SRM-FL compared to pre-defined channel-wise mean and standard deviations as style embeddings for capturing more representative style features. Additionally, we leverage consistency regularizations on global semantic features and predictive distributions from with and without style-perturbed versions of the same CXR to tweak the model's sensitivity toward content markers for accurate predictions. Our proposed method, trained on CheXpert and MIMIC-CXR datasets, achieves 77.32$\\pm$0.35, 88.38$\\pm$0.19, 82.63$\\pm$0.13 AUCs(%) on the unseen domain test datasets, i.e., BRAX, VinDr-CXR, and NIH chest X-ray14, respectively, compared to 75.56$\\pm$0.80, 87.57$\\pm$0.46, 82.07$\\pm$0.19 from state-of-the-art models on five-fold cross-validation with statistically significant results in thoracic disease classification.", "field": "cs", "label": 0}
{"text": "Title: GUESS:GradUally Enriching SyntheSis for Text-Driven Human Motion Generation\nAbstract: In this paper, we propose a novel cascaded diffusion-based generative framework for text-driven human motion synthesis, which exploits a strategy named GradUally Enriching SyntheSis (GUESS as its abbreviation). The strategy sets up generation objectives by grouping body joints of detailed skeletons in close semantic proximity together and then replacing each of such joint group with a single body-part node. Such an operation recursively abstracts a human pose to coarser and coarser skeletons at multiple granularity levels. With gradually increasing the abstraction level, human motion becomes more and more concise and stable, significantly benefiting the cross-modal motion synthesis task. The whole text-driven human motion synthesis problem is then divided into multiple abstraction levels and solved with a multi-stage generation framework with a cascaded latent diffusion model: an initial generator first generates the coarsest human motion guess from a given text description; then, a series of successive generators gradually enrich the motion details based on the textual description and the previous synthesized results. Notably, we further integrate GUESS with the proposed dynamic multi-condition fusion mechanism to dynamically balance the cooperative effects of the given textual condition and synthesized coarse motion prompt in different generation stages. Extensive experiments on large-scale datasets verify that GUESS outperforms existing state-of-the-art methods by large margins in terms of accuracy, realisticness, and diversity. Code is available at https://github.com/Xuehao-Gao/GUESS.", "field": "cs", "label": 0}
{"text": "Title: On broadcast channels with binary inputs and symmetric outputs\nAbstract: We study the capacity regions of broadcast channels with binary inputs and symmetric outputs. We study the partial order induced by the more capable ordering of broadcast channels for channels belonging to this class. This study leads to some surprising connections regarding various notions of dominance of receivers. The results here also help us isolate some classes of symmetric channels where the best known inner and outer bounds differ.", "field": "cs", "label": 1}
{"text": "Title: On the $k$-measure of partitions and distinct partitions\nAbstract: The $k$-measure of an integer partition was recently introduced by Andrews, Bhattacharjee and Dastidar. In this paper, we establish trivariate generating function identities counting both the length and the $k$-measure for partitions and distinct partitions, respectively. The $2$-measure case for partitions extends a result of Andrews, Bhattacharjee and Dastidar.", "field": "math", "label": 1}
{"text": "Title: Identifying contact graphs of sphere packings with generic radii\nAbstract: Ozkan et al. conjectured that any packing of $n$ spheres with generic radii will be stress-free, and hence will have at most $3n-6$ contacts. In this paper we prove that this conjecture is true for any sphere packing with contact graph of the form $G \\oplus K_2$, i.e., the graph formed by connecting every vertex in a graph $G$ to every vertex in the complete graph with two vertices. We also prove the converse of the conjecture holds in this special case: specifically, a graph $G \\oplus K_2$ is the contact graph of a generic radii sphere packing if and only if $G$ is a penny graph with no cycles.", "field": "math", "label": 0}
{"text": "Title: Iyama-Solberg correspondence for exact dg categories\nAbstract: We generalize the notions of $d$-cluster tilting pair and $d$-Auslander exact dg category to $d$-precluster tilting triple and $d$-minimal Auslander--Gorenstein exact dg category. We give a bijection between equivalence classes of $d$-precluster tilting triples and equivalence classes of $d$-minimal Auslander--Gorenstein exact dg categories. Our bijection generalizes Iyama--Solberg correspondence for module categories.", "field": "math", "label": 0}
{"text": "Title: Reversible Joint Hilbert and Linear Canonical Transform Without Distortion\nAbstract: Generalized analytic signal associated with the linear canonical transform (LCT) was proposed recently by Fu and Li [\"Generalized Analytic Signal Associated With Linear Canonical Transform,\" Opt. Commun., vol. 281, pp. 1468-1472, 2008]. However, most real signals, especially for baseband real signals, cannot be perfectly recovered from their generalized analytic signals. Therefore, in this paper, the conventional Hilbert transform (HT) and analytic signal associated with the LCT are concerned. To transform a real signal into the LCT of its HT, two integral transforms (i.e., the HT and LCT) are required. The goal of this paper is to simplify cascades of multiple integral transforms, which may be the HT, analytic signal, LCT or inverse LCT. The proposed transforms can reduce the complexity when realizing the relationships among the following six kinds of signals: a real signal, its HT and analytic signal, and the LCT of these three signals. Most importantly, all the proposed transforms are reversible and undistorted. Using the proposed transforms, several signal processing applications are discussed and show the advantages and flexibility over simply using the analytic signal or the LCT.", "field": "cs", "label": 1}
{"text": "Title: A Quasi Curtis-Tits-Phan theorem for the symplectic group\nAbstract: We obtain the symplectic group as an amalgam of low rank subgroups akin to Levi components. We do this by having the group act flag-transitively on a new type of geometry and applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups. The geometry consists of all subspaces of maximal rank in a vector space of maximal rank with respect to a symplectic form. The main result holds for fields of size at least 3. We analyze the geometry over the field of size 2 and describe its simply connected cover if different from the geometry.", "field": "math", "label": 1}
{"text": "Title: Non-holomorphic Kaehler submanifolds of Euclidean space\nAbstract: This paper is about non-holomorphic isometric immersions of Kaehler manifolds into Euclidean space $f\\colon M^{2n}\\to\\R^{2n+p}$, $p\\leq n-1$, with low codimension $p\\leq 11$. In particular, it addresses a conjecture proposed by J. Yan and F. Zheng. The claim that if the index of complex relative nullity of the submanifold satisfies $\\nu_f^c<2n-2p$ at any point, then $f(M)$ can be realized as a holomorphic submanifold of a non-holomorphic Kaehler submanifold of $\\R^{2n+p}$ of larger dimension and some large index of complex relative nullity. This conjecture had previously been confirmed by Dajczer-Gromoll for codimension $p=3$, and then by Yan-Zheng for $p=4$. For codimension $p\\leq 11$, we already showed that the pointwise structure of the second fundamental form of the submanifold aligns with the anticipated characteristics, assuming the validity of the conjecture. In this paper, we confirm the conjecture until codimension $p=6$, whereas for codimensions $7\\leq p\\leq 9$ it is also possible that the submanifold exhibits a complex ruled structure with rulings of a specific dimension. Moreover, we prove that the claim of the conjecture holds for codimensions $7\\leq p\\leq 11$ albeit subject to an additional assumption.", "field": "math", "label": 0}
{"text": "Title: Pattern avoidance in ascent sequences\nAbstract: Ascent sequences are sequences of nonnegative integers with restrictions on the size of each letter, depending on the number of ascents preceding it in the sequence. Ascent sequences have recently been related to (2+2)-free posets and various other combinatorial structures. We study pattern avoidance in ascent sequences, giving several results for patterns of lengths up to 4, for Wilf equivalence and for growth rates. We establish bijective connections between pattern avoiding ascent sequences and various other combinatorial objects, in particular with set partitions. We also make a number of conjectures related to all of these aspects.", "field": "math", "label": 1}
{"text": "Title: Compensating trajectory bias for unsupervised patient stratification using adversarial recurrent neural networks\nAbstract: Electronic healthcare records are an important source of information which can be used in patient stratification to discover novel disease phenotypes. However, they can be challenging to work with as data is often sparse and irregularly sampled. One approach to solve these limitations is learning dense embeddings that represent individual patient trajectories using a recurrent neural network autoencoder (RNN-AE). This process can be susceptible to unwanted data biases. We show that patient embeddings and clusters using previously proposed RNN-AE models might be impacted by a trajectory bias, meaning that results are dominated by the amount of data contained in each patients trajectory, instead of clinically relevant details. We investigate this bias on 2 datasets (from different hospitals) and 2 disease areas as well as using different parts of the patient trajectory. Our results using 2 previously published baseline methods indicate a particularly strong bias in case of an event-to-end trajectory. We present a method that can overcome this issue using an adversarial training scheme on top of a RNN-AE. Our results show that our approach can reduce the trajectory bias in all cases.", "field": "cs", "label": 1}
{"text": "Title: Parallel Integer Sort: Theory and Practice\nAbstract: Integer sorting is a fundamental problem in computer science. This paper studies parallel integer sort both in theory and in practice. In theory, we show tighter bounds for a class of existing practical integer sort algorithms, which provides a solid theoretical foundation for their widespread usage in practice and strong performance. In practice, we design a new integer sorting algorithm, \\textsf{DovetailSort}, that is theoretically-efficient and has good practical performance. In particular, \\textsf{DovetailSort} overcomes a common challenge in existing parallel integer sorting algorithms, which is the difficulty of detecting and taking advantage of duplicate keys. The key insight in \\textsf{DovetailSort} is to combine algorithmic ideas from both integer- and comparison-sorting algorithms. In our experiments, \\textsf{DovetailSort} achieves competitive or better performance than existing state-of-the-art parallel integer and comparison sorting algorithms on various synthetic and real-world datasets.", "field": "cs", "label": 0}
{"text": "Title: On the displacement of generators of free Fuchsian groups\nAbstract: We prove an inequality that must be satisfied by displacement of generators of free Fuchsian groups, which is the two-dimensional version of the $\\log (2k-1)$ Theorem for Kleinian groups due to Anderson-Canary-Culler-Shalen. As applications, we obtain quantitative results on the geometry of hyperbolic surfaces such as the two-dimensional Margulis constant and lengths of closed curves, which improves a result of Buser's.", "field": "math", "label": 1}
{"text": "Title: Legendrians with vanishing Shelukhin-Chekanov-Hofer metric\nAbstract: We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin-Chekanov-Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.", "field": "math", "label": 0}
{"text": "Title: Answering Queries with Negation over Existential Rules\nAbstract: Ontology-based query answering with existential rules is well understood and implemented for positive queries, in particular conjunctive queries. The situation changes drastically for queries with negation, where there is no agreed-upon semantics or standard implementation. Stratification, as used for Datalog, is not enough for existential rules, since the latter still admit multiple universal models that can differ on negative queries. We therefore propose universal core models as a basis for a meaningful (non-monotonic) semantics for queries with negation. Since cores are hard to compute, we identify syntactic descriptions of queries that can equivalently be answered over other types of models. This leads to fragments of queries with negation that can safely be evaluated by current chase implementations. We establish new techniques to estimate how the core model differs from other universal models, and we incorporate our findings into a new reasoning approach for existential rules with negation.", "field": "cs", "label": 1}
{"text": "Title: How does Observational Learning Impact Crowdfunding Outcomes for Backers, Project Creators and Platforms?\nAbstract: Reward-based crowdfunding platforms are becoming increasingly popular to finance projects proposing innovative products, e.g., Kickstarter. One important challenge of this form of financing is the uncertainty in the quality of projects. To mitigate the negative effects of this uncertainty for backers, platforms share information regarding the decisions of earlier backers visiting the project campaign pages. This allows backers not only to rely on their expertise to identify project qualities but also to learn from the decisions of their fellow backers who might be more informed. Current studies on observational learning (OL) in crowdfunding mainly focus on predicting the success chances of projects, and there is a lack of understanding of how OL affects crowdfunding dynamics for backers, project creators and platforms. This paper aims to fill this gap by using a theoretical OL model involving two projects competing for funding from backers who may have differentiated expertness in identifying project quality. By introducing various performance measures for backers, creators and platforms and comparing these measures under OL to the case without learning, we provide a thorough analysis of how OL impacts crowdfunding outcomes. We find that information sharing and OL always benefit backers, especially when the early backers are experts. Regarding the impact of OL on creators and platforms, our analysis reveals two understudied but important aspects: the tightness of the competition for projects according to the availability of funding, and the quality difference among the proposed projects. Additionally, we investigate how OL affects the quality decisions of creators and show that OL increases the incentive for high-quality products, especially in situations where funding is scarce.", "field": "math", "label": 0}
{"text": "Title: A Truthful Referral Auction Over Networks\nAbstract: This paper studies a mechanism design problem over a network, where agents can only participate by referrals. The Bulow-Klemberer theorem proposes that expanding the number of participants is a more effective approach to increase revenue than modifying the auction format. However, agents lack the motivation to invite others because doing so intensifies competition among them. On the other hand, misreporting social networks is also a common problem that can reduce revenue. Examples of misreporting include Sybil attacks (an agent pretending to be multiple bidders) and coalition groups (multiple agents pretending to be an agent). To address these challenges, we introduce a novel mechanism called the Truthful Referral Diffusion Mechanism (TRDM). TRDM incentivizes agents to report their social networks truthfully, and some of them are rewarded by the seller for improving revenue. In spite of the fact that some agents overbid in TRDM, the revenue is fixed, and it is higher than the revenue of any mechanism without referrals. TRDM is budget-balanced (non-negative revenue) and generates an efficient outcome (maximized social welfare), making it attractive for both the seller and the buyers as it improves revenue and reward.", "field": "cs", "label": 1}
{"text": "Title: On infinitesimal generators of sublinear Markov semigroups\nAbstract: We establish a Dynkin formula and a Courr\\`ege-von Waldenfels theorem for sublinear Markov semigroups. In particular, we show that any sublinear operator $A$ on $C_c^{\\infty}(\\mathbb{R}^d)$ satisfying the positive maximum principle can be represented as supremum of a family of pseudo-differential operators: $$Af(x) = \\sup_{\\alpha \\in I} (-q_{\\alpha}(x,D) f)(x).$$ As an immediate consequence, we obtain a representation formula for infinitesimal generators of sublinear Markov semigroups with a sufficiently rich domain. We give applications in the theory of non-linear Hamilton--Jacobi--Bellman equations and L\\'evy processes for sublinear expectations.", "field": "math", "label": 1}
{"text": "Title: Stochastic Coalitional Games for Cooperative Random Access in M2M Communications\nAbstract: In this paper, the problem of random access contention between machine type devices (MTDs) in the uplink of a wireless cellular network is studied. In particular, the possibility of forming cooperative groups to coordinate the MTDs' requests for the random access channel (RACH) is analyzed. The problem is formulated as a stochastic coalition formation game in which the MTDs are the players that seek to form cooperative coalitions to optimize a utility function that captures each MTD's energy consumption and time-varying queue length. Within each coalition, an MTD acts as a coalition head that sends the access requests of the coalition members over the RACH. One key feature of this game is its ability to cope with stochastic environments in which the arrival requests of MTDs and the packet success rate over RACH are dynamically time-varying. The proposed stochastic coalitional is composed of multiple stages, each of which corresponds to a coalitional game in stochastic characteristic form that is played by the MTDs at each time step. To solve this game, a novel distributed coalition formation algorithm is proposed and shown to converge to a stable MTD partition. Simulation results show that, on the average, the proposed stochastic coalition formation algorithm can reduce the average fail ratio and energy consumption of up to 36% and 31% for a cluster-based distribution of MTDs, respectively, compared with a noncooperative case. Moreover, when the MTDs are more sensitive to the energy consumption (queue length), the coalitions' size will increase (decrease).", "field": "cs", "label": 1}
{"text": "Title: Popularity of patterns over $d$-equivalence classes of words and permutations\nAbstract: Two same length words are $d$-equivalent if they have same descent set and same underlying alphabet. In particular, two same length permutations are $d$-equivalent if they have same descent set. The popularity of a pattern in a set of words is the overall number of copies of the pattern within the words of the set. We show the far-from-trivial fact that two patterns are $d$-equivalent if and only if they are equipopular over any $d$-equivalence class, and this equipopularity does not follow obviously from a trivial equidistribution.", "field": "cs", "label": 1}
{"text": "Title: Second homotopy classes associated with non-cancellative monoids\nAbstract: We construct second homotopy classes associated with twins of non-cancellative tuples of a monoid, where the monoid is defined by the semi-positive fundamental relations of the fundamental group of a CW-complex. As an application, we reconstruct the second homotopy classes for the complement of generic lines arrangement studied by Akio Hattori.", "field": "math", "label": 0}
{"text": "Title: A note on the growth of regularity with respect to Frobenius\nAbstract: Let $R=k[x_1,\\dots,x_n]/I$ be a standard graded $k$-algebra where $k$ is a field of prime characteristic and let $J$ be a homogeneous ideal in $R$. Denote $(x_1,\\dots,x_n)$ by $\\mathfrak{m}$. We prove that there is a constant $C$ (independent of $e$) such that the regularity of $H^s_{\\mathfrak{m}}(R/J^{[p^e]})$ is bounded above by $Cp^e$ for all $e\\geq 1$ and all integers $s$ such that $s+1$ is at least the dimension of the locus where $R/J$ doesn't have finite projective dimension.", "field": "math", "label": 1}
{"text": "Title: Microlocal Morse theory of wrapped Fukaya categories\nAbstract: The Nadler--Zaslow correspondence famously identifies the finite-dimensional Floer homology groups between Lagrangians in cotangent bundles with the finite-dimensional Hom spaces between corresponding constructible sheaves. We generalize this correspondence to incorporate the infinite-dimensional spaces of morphisms 'at infinity', given on the Floer side by Reeb trajectories (also known as \"wrapping\") and on the sheaf side by allowing unbounded infinite rank sheaves which are categorically compact. When combined with existing sheaf theoretic computations, our results confirm many new instances of homological mirror symmetry. More precisely, given a real analytic manifold $M$ and a subanalytic isotropic subset $\\Lambda$ of its co-sphere bundle $S^*M$, we show that the partially wrapped Fukaya category of $T^*M$ stopped at $\\Lambda$ is equivalent to the category of compact objects in the unbounded derived category of sheaves on $M$ with microsupport inside $\\Lambda$. By an embedding trick, we also deduce a sheaf theoretic description of the wrapped Fukaya category of any Weinstein sector admitting a stable polarization.", "field": "math", "label": 1}
{"text": "Title: Elementary SFT Spectral Gaps And The Strong Closing Property\nAbstract: We formulate elementary SFT spectral invariants of a large class of symplectic cobordisms and stable Hamiltonian manifolds, in any dimension. We give criteria for the strong closing property using these invariants, and verify these criteria for Hofer near periodic systems. This extends the class of symplectic dynamical systems in any dimension that satisfy the strong closing property.", "field": "math", "label": 0}
{"text": "Title: P-TimeSync: A Precise Time Synchronization Simulation with Network Propagation Delays\nAbstract: Time serves as the foundation of modern society and will continue to grow in value in the future world. Unlike previous research papers, authors delve into various time sources, ranging from atomic time and GPS time to quartz time. Specifically, we explore the time uncertainty associated with the four major Global Navigation Satellite Systems. Additionally, we provide a summary of eight metrics used to evaluate time accuracy. In existing time synchronization simulations provide partial usages. However, our research introduces a comprehensive and precise time synchronization simulation named P-TimeSync, leading to a better understanding of time synchronization in distributed environments. It is a state-of-the-art simulation tool for time because (1) it can simulate atomic clocks and quartz clocks with user-defined software clock algorithms, (2) the simulation provides nanosecond-level precision time across different network propagation paths and distances, (3) the tool offers a visualization platform with classic algorithms for distributed time synchronization, such as Cristian's algorithm and Berkeley algorithm, and (4) the simulation includes three time-sync attack functions, including distributed denial-of-service (DDoS) attack, IP spoofer, and router hijacker. The simulation easily allows for the redefinition of configurations and functions, supporting advanced research and development. The simulation tool could be downloaded via the website: https://github.com/rui5097/purdue_timesync", "field": "cs", "label": 0}
{"text": "Title: Density bounds for unit ball packings relative to their outer parallel domains\nAbstract: We prove that the highest density of non-overlapping translates of a given centrally symmetric convex domain relative to its outer parallel domain of given outer radius is attained by a lattice packing in the Euclidean plane. This generalizes some earlier (classical) results. Sharp upper bounds are proved for the analogue problem on congruent circular disks in the spherical (resp., hyperbolic) plane and on congruent balls in Euclidean $3$-space.", "field": "math", "label": 0}
{"text": "Title: Homology spheres and property R\nAbstract: We present infinitely many homology spheres which contain two distinct knots whose 0-surgeries are $S^1 \\times S^2$. This resolves a question posed by Kirby and Melvin in 1978.", "field": "math", "label": 1}
{"text": "Title: InternVid: A Large-scale Video-Text Dataset for Multimodal Understanding and Generation\nAbstract: This paper introduces InternVid, a large-scale video-centric multimodal dataset that enables learning powerful and transferable video-text representations for multimodal understanding and generation. The InternVid dataset contains over 7 million videos lasting nearly 760K hours, yielding 234M video clips accompanied by detailed descriptions of total 4.1B words. Our core contribution is to develop a scalable approach to autonomously build a high-quality video-text dataset with large language models (LLM), thereby showcasing its efficacy in learning video-language representation at scale. Specifically, we utilize a multi-scale approach to generate video-related descriptions. Furthermore, we introduce ViCLIP, a video-text representation learning model based on ViT-L. Learned on InternVid via contrastive learning, this model demonstrates leading zero-shot action recognition and competitive video retrieval performance. Beyond basic video understanding tasks like recognition and retrieval, our dataset and model have broad applications. They are particularly beneficial for generating interleaved video-text data for learning a video-centric dialogue system, advancing video-to-text and text-to-video generation research. These proposed resources provide a tool for researchers and practitioners interested in multimodal video understanding and generation.", "field": "cs", "label": 0}
{"text": "Title: SGFormer: Simplifying and Empowering Transformers for Large-Graph Representations\nAbstract: Learning representations on large-sized graphs is a long-standing challenge due to the inter-dependence nature involved in massive data points. Transformers, as an emerging class of foundation encoders for graph-structured data, have shown promising performance on small graphs due to its global attention capable of capturing all-pair influence beyond neighboring nodes. Even so, existing approaches tend to inherit the spirit of Transformers in language and vision tasks, and embrace complicated models by stacking deep multi-head attentions. In this paper, we critically demonstrate that even using a one-layer attention can bring up surprisingly competitive performance across node property prediction benchmarks where node numbers range from thousand-level to billion-level. This encourages us to rethink the design philosophy for Transformers on large graphs, where the global attention is a computation overhead hindering the scalability. We frame the proposed scheme as Simplified Graph Transformers (SGFormer), which is empowered by a simple attention model that can efficiently propagate information among arbitrary nodes in one layer. SGFormer requires none of positional encodings, feature/graph pre-processing or augmented loss. Empirically, SGFormer successfully scales to the web-scale graph ogbn-papers100M and yields up to 141x inference acceleration over SOTA Transformers on medium-sized graphs. Beyond current results, we believe the proposed methodology alone enlightens a new technical path of independent interest for building Transformers on large graphs.", "field": "cs", "label": 0}
{"text": "Title: Exponential sums, twisted multiplicativity and moments\nAbstract: We study averages over squarefree moduli of the size of exponential sums with polynomial phases. We prove upper bounds on various moments of such sums, and obtain evidence of un-correlation of exponential sums associated to different suitably unrelated and generic polynomials. The proofs combine analytic arguments with the algebraic interpretation of exponential sums and their monodromy groups.", "field": "math", "label": 1}
{"text": "Title: Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables\nAbstract: The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic estimation variance and derived an optimal set for the case without hidden variables. For the case with hidden variables there can be settings where no optimal set exists and currently only a sufficient graphical optimality criterion of limited applicability has been derived. In the present work optimality is characterized as maximizing a certain adjustment information which allows to derive a necessary and sufficient graphical criterion for the existence of an optimal adjustment set and a definition and algorithm to construct it. Further, the optimal set is valid if and only if a valid adjustment set exists and has higher (or equal) adjustment information than the Adjust-set proposed in Perkovi{\\'c} et al. [Journal of Machine Learning Research, 18: 1--62, 2018] for any graph. The results translate to minimal asymptotic estimation variance for a class of estimators whose asymptotic variance follows a certain information-theoretic relation. Numerical experiments indicate that the asymptotic results also hold for relatively small sample sizes and that the optimal adjustment set or minimized variants thereof often yield better variance also beyond that estimator class. Surprisingly, among the randomly created setups more than 90\\% fulfill the optimality conditions indicating that also in many real-world scenarios graphical optimality may hold. Code is available as part of the python package \\url{https://github.com/jakobrunge/tigramite}.", "field": "cs", "label": 1}
{"text": "Title: Explicit characterisation of the fractional power spaces of the Dirichlet Laplacian and Stokes operators\nAbstract: We identify explicitly the fractional power spaces for the $L^2$ Dirichlet Laplacian and Dirichlet Stokes operators using the theory of real interpolation. The results are not new, but we hope that our arguments are relatively accessible.", "field": "math", "label": 1}
{"text": "Title: Frechet differentiability of the metric projection operator in Banach spaces\nAbstract: In this paper, we prove Frechet differentiability of the metric projection operator onto closed balls, closed and convex cylinders and positives cones in uniformly convex and uniformly smooth Banach spaces. With respect to these closed and convex subsets, we find the exact expressions for Frechet derivatives and Gateaux directional derivatives of the metric projection operator.", "field": "math", "label": 0}
{"text": "Title: On Rank-Monotone Graph Operations and Minimal Obstruction Graphs for the Lovász--Schrijver SDP Hierarchy\nAbstract: We study the lift-and-project rank of the stable set polytopes of graphs with respect to the Lov\\'{a}sz--Schrijver SDP operator $\\text{LS}_+$, with a particular focus on finding and characterizing the smallest graphs with a given $\\text{LS}_+$-rank (the least number of iterations of the $\\text{LS}_+$ operator on the fractional stable set polytope to compute the stable set polytope). We introduce a generalized vertex-stretching operation that appears to be promising in generating $\\text{LS}_+$-minimal graphs and study its properties. We also provide several new $\\text{LS}_+$-minimal graphs, most notably the first known instances of $12$-vertex graphs with $\\text{LS}_+$-rank $4$, which provides the first advance in this direction since Escalante, Montelar, and Nasini's discovery of a $9$-vertex graph with $\\text{LS}_+$-rank $3$ in 2006.", "field": "cs", "label": 0}
{"text": "Title: Schwartz $κ$-densities for the moduli stack of rank $2$ bundles on a curve over a local field\nAbstract: Let $\\rm{Bun}$ be the moduli stack of rank $2$ bundles with fixed determinant on a smooth proper curve $C$ over a local field $F$. We show how to associate with a Schwartz $\\kappa$-density, for $\\rm{Re}(\\kappa)\\ge 1/2$, a smooth function on the corresponding coarse moduli space of very stable bundles. In the non-archimedean case we also prove that the stack $\\rm{Bun}$ is $\\kappa$-bounded in the sense of Definition 2.10 of [arXiv:2112.08139] for any $\\kappa\\in\\mathbb{C}$.", "field": "math", "label": 0}
{"text": "Title: Basmajian-type identities and Hausdorff dimension of limit sets\nAbstract: In this paper, we study Basmajian-type series identities on holomorphic families of Cantor sets associated to one-dimensional complex dynamical systems. We show that the series is absolutely summable if and only if the Hausdorff dimension of the Cantor set is strictly less than one. Throughout the domain of convergence, these identities can be analytically continued and they exhibit nontrivial monodromy.", "field": "math", "label": 1}
{"text": "Title: Quotients of Special Classes of Positroids\nAbstract: In this paper, we give a complete characterization of rank $k-1$ positroids that are quotients of the uniform matroid $U_{k,n}$, completing a partial result by Bendetti-Chavez-Jim\\'enez. Furthermore, we show that any pair of concordant positroids with adjacent ranks are related by a cyclic shift on their decorated permutations. We also use the concept of conecklaces to give a full characterization of concordant lattice path matroids (LPMs).", "field": "math", "label": 0}
{"text": "Title: Quasitriangular structure and twisting of the 2+1 bicrossproduct model\nAbstract: We show that the bicrossproduct model $C[SU_2^*]{\\blacktriangleright\\!\\!\\triangleleft} U(su_2)$ quantum Poincare group in 2+1 dimensions acting on the quantum spacetime $[x_i,t]=\\imath\\lambda x_i$ is related by a Drinfeld and module-algebra twist to the quantum double $U(su_2)\\ltimes C[SU_2]$ acting on the quantum spacetime $[x_\\mu,x_\\nu]=\\imath\\lambda\\epsilon_{\\mu\\nu\\rho}x_\\rho$. We obtain this twist by taking a scaling limit as $q\\to 1$ of the $q$-deformed version of the above where it corresponds to a previous theory of $q$-deformed Wick rotation from $q$-Euclidean to $q$-Minkowski space. We also recover the twist result at the Lie bialgebra level.", "field": "math", "label": 1}
{"text": "Title: Transfer Regression via Pairwise Similarity Regularization\nAbstract: Transfer learning methods address the situation where little labeled training data from the \"target\" problem exists, but much training data from a related \"source\" domain is available. However, the overwhelming majority of transfer learning methods are designed for simple settings where the source and target predictive functions are almost identical, limiting the applicability of transfer learning methods to real world data. We propose a novel, weaker, property of the source domain that can be transferred even when the source and target predictive functions diverge. Our method assumes the source and target functions share a Pairwise Similarity property, where if the source function makes similar predictions on a pair of instances, then so will the target function. We propose Pairwise Similarity Regularization Transfer, a flexible graph-based regularization framework which can incorporate this modeling assumption into standard supervised learning algorithms. We show how users can encode domain knowledge into our regularizer in the form of spatial continuity, pairwise \"similarity constraints\" and how our method can be scaled to large data sets using the Nystrom approximation. Finally, we present positive and negative results on real and synthetic data sets and discuss when our Pairwise Similarity transfer assumption seems to hold in practice.", "field": "cs", "label": 1}
{"text": "Title: On the associativity of the addition on elliptic curves\nAbstract: In this short note we give a simple elementary proof of the associativity of the addition on elliptic curves. We do this by providing an explicit formula for the sum of three points, using the explicit definition of the group structure.", "field": "math", "label": 0}
{"text": "Title: A Three-Valued Semantics for Typed Logic Programming\nAbstract: Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we define a new semantics for logic programming, where programs evaluate to true, false, and to a new semantic value called wrong, corresponding to a run-time type error. We then have a type language with a separated semantics of types. Finally, we define a type system for logic programming and prove that it is semantically sound with respect to a semantic relation between programs and types where, if a program has a type, then its semantics is not wrong. Our work follows Milner's approach for typed functional languages where the semantics of programs is independent from the semantic of types, and the type system is proved to be sound with respect to a relation between both semantics.", "field": "cs", "label": 1}
{"text": "Title: Positive Semidefinite Metric Learning with Boosting\nAbstract: The learning of appropriate distance metrics is a critical problem in image classification and retrieval. In this work, we propose a boosting-based technique, termed \\BoostMetric, for learning a Mahalanobis distance metric. One of the primary difficulties in learning such a metric is to ensure that the Mahalanobis matrix remains positive semidefinite. Semidefinite programming is sometimes used to enforce this constraint, but does not scale well. \\BoostMetric is instead based on a key observation that any positive semidefinite matrix can be decomposed into a linear positive combination of trace-one rank-one matrices. \\BoostMetric thus uses rank-one positive semidefinite matrices as weak learners within an efficient and scalable boosting-based learning process. The resulting method is easy to implement, does not require tuning, and can accommodate various types of constraints. Experiments on various datasets show that the proposed algorithm compares favorably to those state-of-the-art methods in terms of classification accuracy and running time.", "field": "cs", "label": 1}
{"text": "Title: 3D Open-Vocabulary Panoptic Segmentation with 2D-3D Vision-Language Distillation\nAbstract: 3D panoptic segmentation is a challenging perception task, which aims to predict both semantic and instance annotations for 3D points in a scene. Although prior 3D panoptic segmentation approaches have achieved great performance on closed-set benchmarks, generalizing to novel categories remains an open problem. For unseen object categories, 2D open-vocabulary segmentation has achieved promising results that solely rely on frozen CLIP backbones and ensembling multiple classification outputs. However, we find that simply extending these 2D models to 3D does not achieve good performance due to poor per-mask classification quality on novel categories. In this paper, we propose the first method to tackle 3D open-vocabulary panoptic segmentation. Our model takes advantage of the fusion between learnable LiDAR features and dense frozen vision CLIP features, using a single classification head to make predictions for both base and novel classes. To further improve the classification performance on novel classes and leverage the CLIP model, we propose two novel loss functions: object-level distillation loss and voxel-level distillation loss. Our experiments on the nuScenes and SemanticKITTI datasets show that our method outperforms strong baselines by a large margin.", "field": "cs", "label": 0}
{"text": "Title: Relations Between $p$-Means of Convex Bodies and a New Suggestion for the Definition of the Geometric Mean\nAbstract: In light of the log-Brunn-Minkowski conjecture, various attempts have been made to define the geometric mean of convex bodies. Many of these constructions are fairly complex and/or fail to satisfy some natural properties one would expect of such a mean. We remedy this by providing a new geometric mean that is both technically simple and inherits all the natural properties expected. To improve our understanding of potential geometric mean definitions, we first study general $p$-means of convex bodies, with the usual definition extended to two series ranging over all $p \\in [-\\infty,\\infty]$. We characterize their equality cases and obtain (in almost all instances tight) inequalities that quantify how well these means approximate each other. As a corollary, we establish that every Minkowski centered body is equidistant from all its $p$-symmetrizations with respect to the Banach-Mazur distance. Finally, we show that our geometric mean satisfies all the properties considered in recent literature and extend this list with some properties regarding symmetrization and asymmetry.", "field": "math", "label": 0}
{"text": "Title: The Effect of Learning Strategy versus Inherent Architecture Properties on the Ability of Convolutional Neural Networks to Develop Transformation Invariance\nAbstract: As object recognition becomes an increasingly common ML task, and recent research demonstrating CNNs vulnerability to attacks and small image perturbations necessitate fully understanding the foundations of object recognition. We focus on understanding the mechanisms behind how neural networks generalize to spatial transformations of complex objects. While humans excel at discriminating between objects shown at new positions, orientations, and scales, past results demonstrate that this may be limited to familiar objects - humans demonstrate low tolerance of spatial-variances for purposefully constructed novel objects. Because training artificial neural networks from scratch is similar to showing novel objects to humans, we seek to understand the factors influencing the tolerance of CNNs to spatial transformations. We conduct a thorough empirical examination of seven Convolutional Neural Network (CNN) architectures. By training on a controlled face image dataset, we measure model accuracy across different degrees of 5 transformations: position, size, rotation, Gaussian blur, and resolution transformation due to resampling. We also examine how learning strategy affects generalizability by examining how different amounts of pre-training have on model robustness. Overall, we find that the most significant contributor to transformation invariance is pre-training on a large, diverse image dataset. Moreover, while AlexNet tends to be the least robust network, VGG and ResNet architectures demonstrate higher robustness for different transformations. Along with kernel visualizations and qualitative analyses, we examine differences between learning strategy and inherent architectural properties in contributing to invariance of transformations, providing valuable information towards understanding how to achieve greater robustness to transformations in CNNs.", "field": "cs", "label": 1}
{"text": "Title: Directed Homology and Persistence Modules\nAbstract: In this note, we give a self-contained account on a construction for a directed homology theory based on modules over algebras, linking it to both persistence homology and natural homology. We study its first properties, among which some exact sequences.", "field": "math", "label": 0}
{"text": "Title: A Comprehensive Survey on Graph Summarization with Graph Neural Networks\nAbstract: As large-scale graphs become more widespread, more and more computational challenges with extracting, processing, and interpreting large graph data are being exposed. It is therefore natural to search for ways to summarize these expansive graphs while preserving their key characteristics. In the past, most graph summarization techniques sought to capture the most important part of a graph statistically. However, today, the high dimensionality and complexity of modern graph data are making deep learning techniques more popular. Hence, this paper presents a comprehensive survey of progress in deep learning summarization techniques that rely on graph neural networks (GNNs). Our investigation includes a review of the current state-of-the-art approaches, including recurrent GNNs, convolutional GNNs, graph autoencoders, and graph attention networks. A new burgeoning line of research is also discussed where graph reinforcement learning is being used to evaluate and improve the quality of graph summaries. Additionally, the survey provides details of benchmark datasets, evaluation metrics, and open-source tools that are often employed in experimentation settings, along with a detailed comparison, discussion, and takeaways for the research community focused on graph summarization. Finally, the survey concludes with a number of open research challenges to motivate further study in this area.", "field": "cs", "label": 0}
{"text": "Title: Efficient computation of the cumulative distribution function of a linear mixture of independent random variables\nAbstract: For a variant of the algorithm in [Pit19] (arXiv:1903.10816) to compute the approximate density or distribution function of a linear mixture of independent random variables known by a finite sample, it is presented a proof of the functional correctness, i.e. the convergence of the computed distribution function towards the true distribution function (given the observations) as the algorithm resolution is increased to infinity. The algorithm (like its predecessor version) bears elements which are closely related to early known methods for numerical inversion of the characteristic function of a probability distribution, however here efficiently computes the complete distribution function. Possible applications are in computing the distribution of the bootstrap estimate in any linear bootstrap method (e.g. in the block bootstrap for the mean as parameter of interest, or residual bootstrap in linear regression with fixed design), or in elementary analysis-of-variance hypothesis testing.", "field": "math", "label": 1}
{"text": "Title: Efficient Detection of Botnet Traffic by features selection and Decision Trees\nAbstract: Botnets are one of the online threats with the biggest presence, causing billionaire losses to global economies. Nowadays, the increasing number of devices connected to the Internet makes it necessary to analyze large amounts of network traffic data. In this work, we focus on increasing the performance on botnet traffic classification by selecting those features that further increase the detection rate. For this purpose we use two feature selection techniques, Information Gain and Gini Importance, which led to three pre-selected subsets of five, six and seven features. Then, we evaluate the three feature subsets along with three models, Decision Tree, Random Forest and k-Nearest Neighbors. To test the performance of the three feature vectors and the three models we generate two datasets based on the CTU-13 dataset, namely QB-CTU13 and EQB-CTU13. We measure the performance as the macro averaged F1 score over the computational time required to classify a sample. The results show that the highest performance is achieved by Decision Trees using a five feature set which obtained a mean F1 score of 85% classifying each sample in an average time of 0.78 microseconds.", "field": "cs", "label": 1}
{"text": "Title: A dilation theoretic approach to approximation by inner functions\nAbstract: Using results from theory of operators on a Hilbert space, we prove approximation results for matrix-valued holomorphic functions on the unit disc and the unit bidisc. The essential tools are the theory of unitary dilation of a contraction and the realization formula for functions in the unit ball of $H^\\infty$. We first prove a generalization of a result of Carath\\'eodory. This generalization has many applications. A uniform approximation result for matrix-valued holomorphic functions which extend continuously to the unit circle is proved using the Potapov factorization. This generalizes a theorem due to Fisher. Approximation results are proved for matrix-valued functions for whom a naturally associated kernel has finitely many negative squares. This uses the Krein-Langer factorization. Approximation results for $J$-contractive meromorphic functions where $J$ induces an indefinite metric on $\\mathbb C^N$ are proved using the Potapov-Ginzburg Theorem. Moreover, approximation results for holomorphic functions on the unit disc with values in certain other domains of interest are also proved.", "field": "math", "label": 1}
{"text": "Title: The automatic solution of partial differential equations using a global spectral method\nAbstract: A spectral method for solving linear partial differential equations (PDEs) with variable coefficients and general boundary conditions defined on rectangular domains is described, based on separable representations of partial differential operators and the one-dimensional ultraspherical spectral method. If a partial differential operator is of splitting rank $2$, such as the operator associated with Poisson or Helmholtz, the corresponding PDE is solved via a generalized Sylvester matrix equation, and a bivariate polynomial approximation of the solution of degree $(n_x,n_y)$ is computed in $\\mathcal{O}((n_x n_y)^{3/2})$ operations. Partial differential operators of splitting rank $\\geq 3$ are solved via a linear system involving a block-banded matrix in $\\mathcal{O}(\\min(n_x^{3} n_y,n_x n_y^{3}))$ operations. Numerical examples demonstrate the applicability of our 2D spectral method to a broad class of PDEs, which includes elliptic and dispersive time-evolution equations. The resulting PDE solver is written in MATLAB and is publicly available as part of CHEBFUN. It can resolve solutions requiring over a million degrees of freedom in under $60$ seconds. An experimental implementation in the Julia language can currently perform the same solve in $10$ seconds.", "field": "math", "label": 1}
{"text": "Title: Theta divisors whose Gauss map has a fiber of positive dimension\nAbstract: We construct families of principally polarized abelian varieties whose theta divisor is irreducible and contains an abelian subvariety. These families are used to construct examples when the Gauss map of the theta divisor is only generically finite and not finite. That is, the Gauss map in these cases has at least one positive-dimensional fiber. We also obtain lower-bounds on the dimension of Andreotti-Mayer loci.", "field": "math", "label": 1}
{"text": "Title: On knots that divide ribbon knotted surfaces\nAbstract: We define a knot to be half ribbon if it is the cross-section of a ribbon 2-knot, and observe that ribbon implies half ribbon implies slice. We introduce the half ribbon genus of a knot K, the minimum genus of a ribbon knotted surface of which K is a cross-section. We compute this genus for all prime knots up to 12 crossings, and many 13-crossing knots. The same approach yields new computations of the doubly slice genus. We also introduce the half fusion number of a knot K, that measures the complexity of ribbon 2-knots of which K is a cross-section. We show that it is bounded from below by the Levine-Tristram signatures, and differs from the standard fusion number by an arbitrarily large amount.", "field": "math", "label": 1}
{"text": "Title: Stanley--Elder--Fine theorems for colored partitions\nAbstract: We give a new proof of a partition theorem popularly known as Elder's theorem, but which is also credited to Stanley and Fine. We extend the theorem to the context of colored partitions (or prefabs). More specifically, we give analogous results for $b$-colored partitions, where each part occurs in $b$ colors; for $b$-colored partitions with odd parts (or distinct parts); for partitions where the part $k$ comes in $k$ colors; and, overpartitions.", "field": "math", "label": 1}
{"text": "Title: View-based Explanations for Graph Neural Networks\nAbstract: Generating explanations for graph neural networks (GNNs) has been studied to understand their behavior in analytical tasks such as graph classification. Existing approaches aim to understand the overall results of GNNs rather than providing explanations for specific class labels of interest, and may return explanation structures that are hard to access, nor directly queryable. We propose GVEX, a novel paradigm that generates Graph Views for EXplanation. (1) We design a two-tier explanation structure called explanation views. An explanation view consists of a set of graph patterns and a set of induced explanation subgraphs. Given a database G of multiple graphs and a specific class label l assigned by a GNN-based classifier M, it concisely describes the fraction of G that best explains why l is assigned by M. (2) We propose quality measures and formulate an optimization problem to compute optimal explanation views for GNN explanation. We show that the problem is $\\Sigma^2_P$-hard. (3) We present two algorithms. The first one follows an explain-and-summarize strategy that first generates high-quality explanation subgraphs which best explain GNNs in terms of feature influence maximization, and then performs a summarization step to generate patterns. We show that this strategy provides an approximation ratio of 1/2. Our second algorithm performs a single-pass to an input node stream in batches to incrementally maintain explanation views, having an anytime quality guarantee of 1/4 approximation. Using real-world benchmark data, we experimentally demonstrate the effectiveness, efficiency, and scalability of GVEX. Through case studies, we showcase the practical applications of GVEX.", "field": "cs", "label": 0}
{"text": "Title: Constrained quantization for a uniform distribution\nAbstract: Constrained quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with a finite number of supporting points lying on a specific set. The specific set is known as the constraint of the constrained quantization. A quantization without a constraint is known as an unconstrained quantization, which traditionally in the literature is known as quantization. Constrained quantization has recently been introduced by Pandey and Roychowdhury. In this paper, for a uniform distribution with support lying on a side of an equilateral triangle, and the constraint as the union of the other two sides, we obtain the optimal sets of $n$-points and the $n$th constrained quantization errors for all positive integers $n$. We also calculate the constrained quantization dimension and the constrained quantization coefficient.", "field": "math", "label": 0}
{"text": "Title: On Augmenting Scenario-Based Modeling with Generative AI\nAbstract: The manual modeling of complex systems is a daunting task; and although a plethora of methods exist that mitigate this issue, the problem remains very difficult. Recent advances in generative AI have allowed the creation of general-purpose chatbots, capable of assisting software engineers in various modeling tasks. However, these chatbots are often inaccurate, and an unstructured use thereof could result in erroneous system models. In this paper, we outline a method for the safer and more structured use of chatbots as part of the modeling process. To streamline this integration, we propose leveraging scenario-based modeling techniques, which are known to facilitate the automated analysis of models. We argue that through iterative invocations of the chatbot and the manual and automatic inspection of the resulting models, a more accurate system model can eventually be obtained. We describe favorable preliminary results, which highlight the potential of this approach.", "field": "cs", "label": 0}
{"text": "Title: Image classification and retrieval with random depthwise signed convolutional neural networks\nAbstract: We propose a random convolutional neural network to generate a feature space in which we study image classification and retrieval performance. Put briefly we apply random convolutional blocks followed by global average pooling to generate a new feature, and we repeat this k times to produce a k-dimensional feature space. This can be interpreted as partitioning the space of image patches with random hyperplanes which we formalize as a random depthwise convolutional neural network. In the network's final layer we perform image classification and retrieval with the linear support vector machine and k-nearest neighbor classifiers and study other empirical properties. We show that the ratio of image pixel distribution similarity across classes to within classes is higher in our network's final layer compared to the input space. When we apply the linear support vector machine for image classification we see that the accuracy is higher than if we were to train just the final layer of VGG16, ResNet18, and DenseNet40 with random weights. In the same setting we compare it to an unsupervised feature learning method and find our accuracy to be comparable on CIFAR10 but higher on CIFAR100 and STL10. We see that the accuracy is not far behind that of trained networks, particularly in the top-k setting. For example the top-2 accuracy of our network is near 90% on both CIFAR10 and a 10-class mini ImageNet, and 85% on STL10. We find that k-nearest neighbor gives a comparable precision on the Corel Princeton Image Similarity Benchmark than if we were to use the final layer of trained networks. As with other networks we find that our network fails to a black box attack even though we lack a gradient and use the sign activation. We highlight sensitivity of our network to background as a potential pitfall and an advantage. Overall our work pushes the boundary of what can be achieved with random weights.", "field": "cs", "label": 1}
{"text": "Title: Some remarks on Grothendieck pairs\nAbstract: We revisit the paper of Alexander Grothendiek where he introduced Grothendieck pairs and discuss the relation between profinite rigidity and left/right Grothendieck rigidity. We also show that various groups are left and/or right Grothendieck rigid and, in particular, all ascending HNN extensiona of finitely generated free groups are right Grothendieck rigid. Along the way we present a number of questions and suggestions for further research.", "field": "math", "label": 0}
{"text": "Title: Concentration-compactness at the mountain pass level in semilinear elliptic problems\nAbstract: The concentration compactness framework for semilinear elliptic equations without compactness, set originally by P.-L.Lions for constrained minimization in the case of homogeneous nonlinearity, is extended here to the case of general nonlinearities in the standard mountain pass setting of Ambrosetti-Rabinowitz. In these setting, existence of solutions at the mountain pass level is verified under a single penalty condition analogous to that in the Lions' case. Problems on the whole space and problems with critical nonlinearity are considered. Particular attention is given to nonhomogeneous critical nonlinearities that oscillate about the \"critical stem\".", "field": "math", "label": 1}
{"text": "Title: Solving a Random Asymmetric TSP Exactly in Quasi-Polynomial Time w.h.p\nAbstract: Let the costs $A(i,j)$ for an instance of the Asymmetric Traveling Salesperson Problem (ATSP) be independent exponential mean one random variables. We describe an enumerative algorithm that solves ATSP exactly in time $e^{\\log^{3+o(1)}n}$.", "field": "cs", "label": 0}
{"text": "Title: Supremum norm A Posteriori Error control of Quadratic Finite Element Method for the Signorini problem\nAbstract: In this paper, we develop a new residual-based pointwise a posteriori error estimator of the quadratic finite element method for the Signorini problem. The supremum norm a posteriori error estimates enable us to locate the singularities locally to control the pointwise errors. In the analysis the discrete counterpart of contact force density is constructed suitably to exhibit the desired sign property. We employ a priori estimates for the standard Green's matrix for the divergence type operator and introduce the upper and lower barriers functions by appropriately modifying the discrete solution. Finally, we present numerical experiments that illustrate the excellent performance of the proposed error estimator.", "field": "math", "label": 0}
{"text": "Title: Algebraic trace functions over the primes\nAbstract: We study sums over primes of trace functions of $\\ell$-adic sheaves. Using an extension of our earlier results on algebraic twist of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of the Riemann Hypothesis over finite fields, we prove general estimates with power-saving for such sums. We then derive various concrete applications.", "field": "math", "label": 1}
{"text": "Title: Particle systems and kinetic equations modeling interacting agents in high dimension\nAbstract: In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain dynamical systems modeling complex interactions. In such systems, one has to deal with a large number of agents (typically millions) in spaces of parameters describing each agent of high dimension (thousands or more). Even with today's powerful computers, numerical simulations of such systems are prohibitively expensive. We propose an approach for the simulation of dynamical systems governed by functions of adjacency matrices in high dimension, by random projections via Johnson-Lindenstrauss embeddings, and recovery by compressed sensing techniques. We show how these concepts can be generalized to work for associated kinetic equations, by addressing the phenomenon of the delayed curse of dimension, known in information-based complexity for optimal numerical integration problems in high dimensions.", "field": "math", "label": 1}
{"text": "Title: Matchings and loose cycles in the semirandom hypergraph model\nAbstract: We study the 2-offer semirandom 3-uniform hypergraph model on $n$ vertices. At each step, we are presented with 2 uniformly random vertices. We choose any other vertex, thus creating a hyperedge of size 3. We show a strategy that constructs a perfect matching, and another that constructs a loose Hamilton cycle, both succeeding asymptotically almost surely within $\\Theta(n)$ steps. Both results extend to $s$-uniform hypergraphs. Much of the analysis is done on an auxiliary graph that is a uniform $k$-out subgraph of a random bipartite graph, and this tool may be useful in other contexts.", "field": "math", "label": 0}
{"text": "Title: On volumes of hyperbolic right-angled polyhedra\nAbstract: In this paper we obtain new upper bounds on volumes of right-angled polyhedra in hyperbolic space $\\mathbb{H}^3$ in three different cases: for ideal polyhedra with all vertices on the ideal hyperbolic boundary, for compact polytopes with only finite (or usual) vertices, and for finite volume polyhedra with vertices of both types.", "field": "math", "label": 1}
{"text": "Title: Legendre-Moment Transform for Linear Ensemble Control and Computation\nAbstract: Ensemble systems, pervasive in diverse scientific and engineering domains, pose challenges to existing control methods due to their massive scale and underactuated nature. This paper presents a dynamic moment approach to addressing theoretical and computational challenges in systems-theoretic analysis and control design for linear ensemble systems. We introduce the Legendre-moments and Legendre-moment transform, which maps an ensemble system defined on the $L^2$-space to a Legendre-moment system defined on the $\\ell^2$-space. We show that this pair of systems is of one-to-one correspondence and shares the same controllability property. This equivalence admits the control of an ensemble system through the control of the corresponding Legendre-moment system and inspires a unified control design scheme for linear ensemble systems using structured truncated moment systems. In particular, we develop a sampling-free ensemble control design algorithm, then conduct error analysis for control design using truncated moment systems and derive error bounds with respect to the truncation orders, which are illustrated with numerical examples.", "field": "math", "label": 0}
{"text": "Title: Offline Policy Optimization with Eligible Actions\nAbstract: Offline policy optimization could have a large impact on many real-world decision-making problems, as online learning may be infeasible in many applications. Importance sampling and its variants are a commonly used type of estimator in offline policy evaluation, and such estimators typically do not require assumptions on the properties and representational capabilities of value function or decision process model function classes. In this paper, we identify an important overfitting phenomenon in optimizing the importance weighted return, in which it may be possible for the learned policy to essentially avoid making aligned decisions for part of the initial state space. We propose an algorithm to avoid this overfitting through a new per-state-neighborhood normalization constraint, and provide a theoretical justification of the proposed algorithm. We also show the limitations of previous attempts to this approach. We test our algorithm in a healthcare-inspired simulator, a logged dataset collected from real hospitals and continuous control tasks. These experiments show the proposed method yields less overfitting and better test performance compared to state-of-the-art batch reinforcement learning algorithms.", "field": "cs", "label": 1}
{"text": "Title: An entropy bound due to symmetries\nAbstract: Let $H$ be a local net of real Hilbert subspaces of a complex Hilbert space on the family of double cones of the spacetime $\\mathbb{R}^{d+1}$, covariant with respect to a positive energy, unitary representation $U$ of the Poincar\\'e group, with the Bisognano-Wichmann property for the wedge modular group. We set an upper bound on the local entropy $S_H(\\phi|\\! | C)$ of a vector in a region $C$ that depends only on $U$ and the PCT anti-unitary canonically associated with $H$. A similar result holds for local, M\\\"obius covariant nets of standard subspaces on the circle. We compute the entropy increase and illustrate this bound for the nets associated with the $U(1)$-current derivatives.", "field": "math", "label": 0}
{"text": "Title: Symbolic dynamics and rotation symmetric Boolean functions\nAbstract: We identify the weights $wt(f_n)$ of a family $\\{f_n\\}$ of rotation symmetric Boolean functions with the cardinalities of the sets of $n$-periodic points of a finite-type shift, recovering the second author's result that said weights satisfy a linear recurrence. Similarly, the weights of idempotent functions $f_n$ defined on finite fields can be recovered as the cardinalities of curves over those fields and hence satisfy a linear recurrence as a consequence of the rationality of curves' zeta functions. Weil's Riemann hypothesis for curves then provides additional information about $wt(f_n)$. We apply our results to the case of quadratic functions and considerably extend the results in an earlier paper of ours.", "field": "cs", "label": 1}
{"text": "Title: Efficient UAVs Deployment and Resource Allocation in UAV-Relay Assisted Public Safety Networks for Video Transmission\nAbstract: Wireless communication highly depends on the cellular ground base station (GBS). A failure of the cellular GBS, fully or partially, during natural or man-made disasters creates a communication gap in the disaster-affected areas. In such situations, public safety communication (PSC) can significantly save the national infrastructure, property, and lives. Throughout emergencies, the PSC can provide mission-critical communication and video transmission services in the affected area. Unmanned aerial vehicles (UAVs) as flying base stations (UAV-BSs) are particularly suitable for PSC services as they are flexible, mobile, and easily deployable. This manuscript considers a multi-UAV-assisted PSC network with an observational UAV receiving videos from the affected area's ground users (AGUs) and transmitting them to the nearby GBS via a relay UAV. The objective of the proposed study is to maximize the average utility of the video streams generated by the AGUs upon reaching the GBS. This is achieved by optimizing the positions of the observational and relay UAVs, as well as the distribution of communication resources, such as bandwidth, and transmit power, while satisfying the system-designed constraints, such as transmission rate, rate outage probability, transmit power budget, and available bandwidth. To this end, a joint UAVs placement and resource allocation problem is mathematically formulated. The proposed problem poses a significant challenge for a solution. Considering the block coordinate descent and successive convex approximation techniques, an efficient iterative algorithm is proposed. Finally, simulation results are provided which show that our proposed approach outperforms the existing methods.", "field": "cs", "label": 0}
{"text": "Title: Unicron: Economizing Self-Healing LLM Training at Scale\nAbstract: Training large-scale language models is increasingly critical in various domains, but it is hindered by frequent failures, leading to significant time and economic costs. Current failure recovery methods in cloud-based settings inadequately address the diverse and complex scenarios that arise, focusing narrowly on erasing downtime for individual tasks without considering the overall cost impact on a cluster. We introduce Unicron, a workload manager designed for efficient self-healing in large-scale language model training. Unicron optimizes the training process by minimizing failure-related costs across multiple concurrent tasks within a cluster. Its key features include in-band error detection for real-time error identification without extra overhead, a dynamic cost-aware plan generation mechanism for optimal reconfiguration, and an efficient transition strategy to reduce downtime during state changes. Deployed on a 128-GPU distributed cluster, Unicron demonstrates up to a 1.9x improvement in training efficiency over state-of-the-art methods, significantly reducing failure recovery costs and enhancing the reliability of large-scale language model training.", "field": "cs", "label": 0}
{"text": "Title: Byzantine-Resilient Gradient Coding through Local Gradient Computations\nAbstract: We consider gradient coding in the presence of an adversary controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the responses from malicious workers as errors and correct them using the error-correction properties of the code. This comes at the expense of increasing the replication, i.e., the number of workers each partial gradient is computed by. In this work, we propose a way to reduce the replication to $s+1$ instead of $2s+1$ in the presence of $s$ malicious workers. Our method detects erroneous inputs from the malicious workers, transforming them into erasures. This comes at the expense of $s$ additional local computations at the main node and additional rounds of light communication between the main node and the workers. We define a general framework and give fundamental limits for fractional repetition data allocations. Our scheme is optimal in terms of replication and local computation and incurs a communication cost that is asymptotically, in the size of the dataset, a multiplicative factor away from the derived bound. We furthermore show how additional redundancy can be exploited to reduce the number of local computations and communication cost, or, alternatively, tolerate straggling workers.", "field": "cs", "label": 0}
{"text": "Title: Sampling Acquisition Functions for Batch Bayesian Optimization\nAbstract: We present Acquisition Thompson Sampling (ATS), a novel technique for batch Bayesian Optimization (BO) based on the idea of sampling multiple acquisition functions from a stochastic process. We define this process through the dependency of the acquisition functions on a set of model hyper-parameters. ATS is conceptually simple, straightforward to implement and, unlike other batch BO methods, it can be employed to parallelize any sequential acquisition function or to make existing parallel methods scale further. We present experiments on a variety of benchmark functions and on the hyper-parameter optimization of a popular gradient boosting tree algorithm. These demonstrate the advantages of ATS with respect to classical parallel Thompson Sampling for BO, its competitiveness with two state-of-the-art batch BO methods, and its effectiveness if applied to existing parallel BO algorithms.", "field": "cs", "label": 1}
{"text": "Title: SyCoCa: Symmetrizing Contrastive Captioners with Attentive Masking for Multimodal Alignment\nAbstract: Multimodal alignment between language and vision is the fundamental topic in current vision-language model research. Contrastive Captioners (CoCa), as a representative method, integrates Contrastive Language-Image Pretraining (CLIP) and Image Caption (IC) into a unified framework, resulting in impressive results. CLIP imposes a bidirectional constraints on global representation of entire images and sentences. Although IC conducts an unidirectional image-to-text generation on local representation, it lacks any constraint on local text-to-image reconstruction, which limits the ability to understand images at a fine-grained level when aligned with texts. To achieve multimodal alignment from both global and local perspectives, this paper proposes Symmetrizing Contrastive Captioners (SyCoCa), which introduces bidirectional interactions on images and texts across the global and local representation levels. Specifically, we expand a Text-Guided Masked Image Modeling (TG-MIM) head based on ITC and IC heads. The improved SyCoCa can further leverage textual cues to reconstruct contextual images and visual cues to predict textual contents. When implementing bidirectional local interactions, the local contents of images tend to be cluttered or unrelated to their textual descriptions. Thus, we employ an attentive masking strategy to select effective image patches for interaction. Extensive experiments on five vision-language tasks, including image-text retrieval, image-captioning, visual question answering, and zero-shot/finetuned image classification, validate the effectiveness of our proposed method.", "field": "cs", "label": 0}
{"text": "Title: A spectral theorem for compact representations and non-unitary cusp forms\nAbstract: We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms.", "field": "math", "label": 0}
{"text": "Title: Returns to the origin of the Pólya walk with stochastic resetting\nAbstract: We consider the simple random walk (or P\\'olya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability $r$ at each time step. The focus is on the joint statistics of the numbers ${\\mathcal{N}}_t^{\\times}$ of spontaneous returns of the walker to the origin and ${\\mathcal{N}}_t^{\\bullet}$ of resetting events up to some observation time $t$. These numbers are extensive in time in a strong sense: all their joint cumulants grow linearly in $t$, with explicitly computable amplitudes, and their fluctuations are described by a smooth bivariate large deviation function. A non-trivial crossover phenomenon takes place in the regime of weak resetting and late times. Remarkably, the time intervals between spontaneous returns to the origin of the reset random walk form a renewal process described in terms of a single `dressed' probability distribution. These time intervals are probabilistic copies of the first one, the `dressed' first-passage time. The present work follows a broader study, covered in a companion paper, on general nested renewal processes.", "field": "math", "label": 0}
{"text": "Title: On the support of the Kloosterman paths\nAbstract: We obtain statistical results on the possible distribution of all partial sums of a Kloosterman sum modulo a prime, by computing explicitly the support of the limiting random Fourier series of our earlier functional limit theorem for Kloosterman paths.", "field": "math", "label": 1}
{"text": "Title: Universal Approximation Theorem for Vector- and Hypercomplex-Valued Neural Networks\nAbstract: The universal approximation theorem states that a neural network with one hidden layer can approximate continuous functions on compact sets with any desired precision. This theorem supports using neural networks for various applications, including regression and classification tasks. Furthermore, it is valid for real-valued neural networks and some hypercomplex-valued neural networks such as complex-, quaternion-, tessarine-, and Clifford-valued neural networks. However, hypercomplex-valued neural networks are a type of vector-valued neural network defined on an algebra with additional algebraic or geometric properties. This paper extends the universal approximation theorem for a wide range of vector-valued neural networks, including hypercomplex-valued models as particular instances. Precisely, we introduce the concept of non-degenerate algebra and state the universal approximation theorem for neural networks defined on such algebras.", "field": "cs", "label": 0}
{"text": "Title: Potentially crystalline deformation rings in the ordinary case\nAbstract: We study potentially crystalline deformation rings for a residual, ordinary Galois representation $\\overline{\\rho}: G_{\\mathbb{Q}_p}\\rightarrow \\mathrm{GL}_3(\\mathbb{F}_p)$. We consider deformations with Hodge-Tate weights $(0,1,2)$ and inertial type chosen to contain exactly one Fontaine-Laffaille modular weight for $\\overline{\\rho}$. We show that, in this setting, the potentially crystalline deformation space is formally smooth over $\\mathbb{Z}_p$ and any potentially crystalline lift is ordinary. The proof requires an understanding of the condition imposed by the monodromy operator on Breuil modules with descent datum, in particular, that this locus mod p is formally smooth.", "field": "math", "label": 1}
{"text": "Title: UstanceBR: a multimodal language resource for stance prediction\nAbstract: This work introduces UstanceBR, a multimodal corpus in the Brazilian Portuguese Twitter domain for target-based stance prediction. The corpus comprises 86.8 k labelled stances towards selected target topics, and extensive network information about the users who published these stances on social media. In this article we describe the corpus multimodal data, and a number of usage examples in both in-domain and zero-shot stance prediction based on text- and network-related information, which are intended to provide initial baseline results for future studies in the field.", "field": "cs", "label": 0}
{"text": "Title: Linear inverse problems for Markov processes and their regularisation\nAbstract: We study the solutions of the inverse problem \\[ g(z)=\\int f(y) P_T(z,dy) \\] for a given $g$, where $(P_t(\\cdot,\\cdot))_{t \\geq 0}$ is the transition function of a given Markov process, $X$, and $T$ is a fixed deterministic time, which is linked to the solutions of the ill-posed Cauchy problem \\[ u_t + A u=0, \\qquad u(0,\\cdot)=g, \\] where $A$ is the generator of $X$. A necessary and sufficient condition ensuring square integrable solutions is given. Moreover, a family of regularisations for the above problems is suggested. We show in particular that these inverse problems have a solution when $X$ is replaced by $\\xi X + (1-\\xi)J$, where $\\xi$ is a Bernoulli random variable, whose probability of success can be chosen arbitrarily close to $1$, and $J$ is a suitably constructed jump process.", "field": "math", "label": 1}
{"text": "Title: Are LLMs Robust for Spoken Dialogues?\nAbstract: Large Pre-Trained Language Models have demonstrated state-of-the-art performance in different downstream tasks, including dialogue state tracking and end-to-end response generation. Nevertheless, most of the publicly available datasets and benchmarks on task-oriented dialogues focus on written conversations. Consequently, the robustness of the developed models to spoken interactions is unknown. In this work, we have evaluated the performance of LLMs for spoken task-oriented dialogues on the DSTC11 test sets. Due to the lack of proper spoken dialogue datasets, we have automatically transcribed a development set of spoken dialogues with a state-of-the-art ASR engine. We have characterized the ASR-error types and their distributions and simulated these errors in a large dataset of dialogues. We report the intrinsic (perplexity) and extrinsic (human evaluation) performance of fine-tuned GPT-2 and T5 models in two subtasks of response generation and dialogue state tracking, respectively. The results show that LLMs are not robust to spoken noise by default, however, fine-tuning/training such models on a proper dataset of spoken TODs can result in a more robust performance.", "field": "cs", "label": 0}
{"text": "Title: Littlewood's problem for sets with multidimensional structure\nAbstract: We give $L^1$-norm estimates for exponential sums of a finite sets $A$ consisting of integers or lattice points. Under the assumption that $A$ possesses sufficient multidimensional structure, our estimates are stronger than those of McGehee-Pigno-Smith and Konyagin. These theorems improve upon past work of Petridis.", "field": "math", "label": 1}
{"text": "Title: Some Inequalities Related to the Seysen Measure of a Lattice\nAbstract: Given a lattice $L$, a basis $B$ of $L$ together with its dual $B^*$, the orthogonality measure $S(B)=\\sum_i ||b_i||^2 ||b_i^*||^2$ of $B$ was introduced by M. Seysen in 1993. This measure is at the heart of the Seysen lattice reduction algorithm and is linked with different geometrical properties of the basis. In this paper, we explicit different expressions for this measure as well as new inequalities.", "field": "math", "label": 1}
{"text": "Title: On the minimal set for counterexamples to the local-global principle\nAbstract: We prove that only for powers of 2 and 3 could occur counterexamples to the local-global divisibility principle for elliptic curves defined over the rationals. For we refine our previous criterion for the validity of the principle. We also give an example that shows that the assumptions of our criterion are necessary.", "field": "math", "label": 1}
{"text": "Title: Dataset Difficulty and the Role of Inductive Bias\nAbstract: Motivated by the goals of dataset pruning and defect identification, a growing body of methods have been developed to score individual examples within a dataset. These methods, which we call \"example difficulty scores\", are typically used to rank or categorize examples, but the consistency of rankings between different training runs, scoring methods, and model architectures is generally unknown. To determine how example rankings vary due to these random and controlled effects, we systematically compare different formulations of scores over a range of runs and model architectures. We find that scores largely share the following traits: they are noisy over individual runs of a model, strongly correlated with a single notion of difficulty, and reveal examples that range from being highly sensitive to insensitive to the inductive biases of certain model architectures. Drawing from statistical genetics, we develop a simple method for fingerprinting model architectures using a few sensitive examples. These findings guide practitioners in maximizing the consistency of their scores (e.g. by choosing appropriate scoring methods, number of runs, and subsets of examples), and establishes comprehensive baselines for evaluating scores in the future.", "field": "cs", "label": 0}
{"text": "Title: Efficient Algorithms for Learning from Coarse Labels\nAbstract: For many learning problems one may not have access to fine grained label information; e.g., an image can be labeled as husky, dog, or even animal depending on the expertise of the annotator. In this work, we formalize these settings and study the problem of learning from such coarse data. Instead of observing the actual labels from a set $\\mathcal{Z}$, we observe coarse labels corresponding to a partition of $\\mathcal{Z}$ (or a mixture of partitions). Our main algorithmic result is that essentially any problem learnable from fine grained labels can also be learned efficiently when the coarse data are sufficiently informative. We obtain our result through a generic reduction for answering Statistical Queries (SQ) over fine grained labels given only coarse labels. The number of coarse labels required depends polynomially on the information distortion due to coarsening and the number of fine labels $|\\mathcal{Z}|$. We also investigate the case of (infinitely many) real valued labels focusing on a central problem in censored and truncated statistics: Gaussian mean estimation from coarse data. We provide an efficient algorithm when the sets in the partition are convex and establish that the problem is NP-hard even for very simple non-convex sets.", "field": "cs", "label": 1}
{"text": "Title: 2-Rainbow domination number of circulant graphs C(n; {1,4})\nAbstract: Let $k$ be a positive integer. A $k$-rainbow domination function (kRDF) of a graph $G$ is a function $f$ from $V(G)$ to the set of all subsets of $\\{1,2,\\dots,k\\}$ such that every vertex $v \\in V(G)$ with $f(v) = \\emptyset$ satisfies $\\bigcup_{u \\in N(v)} f(u) = \\{1,2,\\dots,k\\}$. The weight of a $k$RDF is defined as $w(f)= \\sum_{v \\in V(G)} |f(v)|$. The $k$-rainbow domination number of $G$, denoted by $\\gamma_{rk}(G)$, is the minimum weight of all kRDFs of $G$. In this paper, we determine the exact value of the 2-rainbow domination number of circulant graphs $C(n; \\{1,4\\})$, which is $\\gamma_{r2}(C(n; \\{1,4\\})) = \\lceil n/3 \\rceil + \\alpha$, where $\\alpha = 0$ for $n \\equiv 0 \\pmod{6}$, $\\alpha = 1$ for $n \\equiv 1,2,3,5 \\pmod{6}$, and $\\alpha = 2$ for $n \\equiv 4 \\pmod{6}$.", "field": "math", "label": 0}
{"text": "Title: ChartAssisstant: A Universal Chart Multimodal Language Model via Chart-to-Table Pre-training and Multitask Instruction Tuning\nAbstract: Charts play a vital role in data visualization, understanding data patterns, and informed decision-making. However, their unique combination of graphical elements (e.g., bars, lines) and textual components (e.g., labels, legends) poses challenges for general-purpose multimodal models. While vision-language models trained on chart data excel in comprehension, they struggle with generalization and require task-specific fine-tuning. To address these challenges, we propose ChartAssistant, a chart-based vision-language model for universal chart comprehension and reasoning. ChartAssistant leverages ChartSFT, a comprehensive dataset covering diverse chart-related tasks with basic and specialized chart types. It undergoes a two-stage training process, starting with pre-training on chart-to-table parsing to align chart and text, followed by multitask instruction-following fine-tuning. This approach enables ChartAssistant to achieve competitive performance across various chart tasks without task-specific fine-tuning. Experimental results demonstrate significant performance gains over the state-of-the-art UniChart method, outperforming OpenAI's GPT-4V(ision) on real-world chart data. The code and data are available at https://github.com/OpenGVLab/ChartAst.", "field": "cs", "label": 0}
{"text": "Title: Approximation in Hölder Spaces\nAbstract: For a modulus of continuity $\\omega$ and Banach spaces $X,Y$ we introduce and study the subspaces $\\dot{\\operatorname{VC}}^{0,\\omega}_{\\Upsilon}(X,Y)$ of vanishing scales $\\Upsilon\\in \\{\\operatorname{small},\\operatorname{large},\\operatorname{far}\\}$ of the homogeneous H\\\"{o}lder space $\\dot{C}^{0,\\omega}(X,Y).$ For a wide class of couples $X$ and $Y$, we characterize the subspaces of functions approximable by smooth and Lipschitz and boundedly supported functions in terms of these three vanishing scales. In the particular case $X=\\mathbb{R}^n,$ we identify the spaces $\\dot{\\operatorname{VC}}^{0,\\omega}_{\\Upsilon}(\\mathbb{R}^n,Y)$ with the corresponding vanishing mean oscillation spaces $\\operatorname{VMO}^{\\omega}_{\\Upsilon}(\\mathbb{R}^n,Y)$, thus providing a proof for the density of test functions also on these spaces.", "field": "math", "label": 0}
{"text": "Title: Anisotropy of quadratic forms over a global field of odd characteristic is diophantine\nAbstract: We prove that the anisotropy of quadratic forms over any global field of characteristic not equal to 2 is diophantine, by using a generalization of the method of Koenigsmann and some known results in diophantine sets and quadratic forms.", "field": "math", "label": 0}
{"text": "Title: On Codes for the Noisy Substring Channel\nAbstract: We consider the problem of coding for the substring channel, in which information strings are observed only through their (multisets of) substrings. Due to existing DNA sequencing techniques and applications in DNA-based storage systems, interest in this channel has renewed in recent years. In contrast to existing literature, we consider a noisy channel model where information is subject to noise before its substrings are sampled, motivated by in-vivo storage. We study two separate noise models, substitutions or deletions. In both cases, we examine families of codes which may be utilized for error-correction and present combinatorial bounds on their sizes. Through a generalization of the concept of repeat-free strings, we show that the added required redundancy due to this imperfect observation assumption is sublinear, either when the fraction of errors in the observed substring length is sufficiently small, or when that length is sufficiently long. This suggests that no asymptotic cost in rate is incurred by this channel model in these cases. Moreover, we develop an efficient encoder for such constrained strings in some cases. Finally, we show how a similar encoder can be used to avoid formation of secondary-structures in coded DNA strands, even when accounting for imperfect structures.", "field": "cs", "label": 1}
{"text": "Title: On the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs without AC\nAbstract: In set theory without the Axiom of Choice, we study the set-theoretic strength of a generalized version of the Rainbow Ramsey theorem and the Canonical Ramsey Theorem for pairs introduced by Erd\\H{o}s and Rado, concerning their interrelation with several weak choice forms.", "field": "math", "label": 0}
{"text": "Title: Towards Computing an Optimal Abstraction for Structural Causal Models\nAbstract: Working with causal models at different levels of abstraction is an important feature of science. Existing work has already considered the problem of expressing formally the relation of abstraction between causal models. In this paper, we focus on the problem of learning abstractions. We start by defining the learning problem formally in terms of the optimization of a standard measure of consistency. We then point out the limitation of this approach, and we suggest extending the objective function with a term accounting for information loss. We suggest a concrete measure of information loss, and we illustrate its contribution to learning new abstractions.", "field": "cs", "label": 1}
{"text": "Title: Understanding Softmax Confidence and Uncertainty\nAbstract: It is often remarked that neural networks fail to increase their uncertainty when predicting on data far from the training distribution. Yet naively using softmax confidence as a proxy for uncertainty achieves modest success in tasks exclusively testing for this, e.g., out-of-distribution (OOD) detection. This paper investigates this contradiction, identifying two implicit biases that do encourage softmax confidence to correlate with epistemic uncertainty: 1) Approximately optimal decision boundary structure, and 2) Filtering effects of deep networks. It describes why low-dimensional intuitions about softmax confidence are misleading. Diagnostic experiments quantify reasons softmax confidence can fail, finding that extrapolations are less to blame than overlap between training and OOD data in final-layer representations. Pre-trained/fine-tuned networks reduce this overlap.", "field": "cs", "label": 1}
{"text": "Title: A collection of integrals, products and series\nAbstract: This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental constants.", "field": "math", "label": 0}
{"text": "Title: Approximate innerness and central triviality of endomorphisms\nAbstract: We introduce the notions of approximate innerness and central triviality for endomorphisms on separable von Neumann factors, and we characterize them for hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular endomorphisms which are introduced by Izumi. Our result is a generalization of the corresponding result obtained by Kawahigashi-Sutherland-Takesaki in automorphism case.", "field": "math", "label": 1}
{"text": "Title: The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture\nAbstract: We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurface called {\\em the jet transcendence degree}. Using this invariant, we solve in the negative the Conjecture of Huang, Ji and Yau on the algabraizability of real hypersurfaces with algebraic syzygies.", "field": "math", "label": 0}
{"text": "Title: An equivariant generalisation of McDuff-Segal's group-completion theorem\nAbstract: In this short note, we prove a G-equivariant generalisation of McDuff-Segal's group-completion theorem for finite groups G. A new complication regarding genuine equivariant localisations arises and we resolve this by isolating a simple condition on the homotopy groups of E-infinity-rings in G-spectra. We check that this condition is satisfied when our inputs are a suitable variant of E-infinity-monoids in G-spaces via the existence of multiplicative norm structures, thus giving a localisation formula for their associated G-spherical group rings.", "field": "math", "label": 0}
{"text": "Title: Micro-macro Parareal, from ODEs to SDEs and back again\nAbstract: In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver is applied as a corrector in parallel over smaller chunks of the time interval. Moreover, the coarse solver acts on a reduced state variable, which is coupled to the fine state variable through appropriate coupling operators. We first provide a contribution to the convergence analysis of the micro-macro Parareal method for multiscale linear ordinary differential equations (ODEs). Then, we extend a variant of the micro-macro Parareal algorithm for scalar stochastic differential equations (SDEs) to higher-dimensional SDEs.", "field": "math", "label": 0}
{"text": "Title: Transversal and Paving Positroids\nAbstract: In this paper, we study positroids and its overlap with two classes of matroids: transversal and paving matroids. We exhibit a new class of fundamental transversal matroids and classify the Le-diagram for rank two transversal positroids. We also establish a combinatorial description for paving positroids in terms of Le-diagrams.", "field": "math", "label": 0}
{"text": "Title: Sharp density discrepancy for cut and project sets: An approach via lattice point counting\nAbstract: Cut and project sets are obtained by taking an irrational slice of a lattice and projecting it to a lower dimensional subspace, and are fully characterised by the shape of the slice (window) and the choice of the lattice. In this context we seek to quantify fluctuations from the asymptotics for point counts. We obtain uniform upper bounds on the discrepancy depending on the diophantine properties of the lattice as well as universal lower bounds on the average of the discrepancy. In an appendix, Michael Bj\\\"orklund and Tobias Hartnick obtain lower bounds on the $L^2$-norm of the discrepancy also depending on the diophantine class; these lower bounds match our uniform upper bounds and both are therefore sharp. Using the sufficient criteria of Burago--Kleiner and Aliste-Prieto--Coronel--Gambaudo we find an explicit full-measure class of cut and project sets that are biLipschitz equivalent to lattices; the lower bounds on the variance indicate that this is the largest class of cut and project sets for which those sufficient criteria can apply.", "field": "math", "label": 0}
{"text": "Title: On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure\nAbstract: We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure.", "field": "math", "label": 1}
{"text": "Title: Nonassociative $\\mathrm{L}^p$-spaces and embeddings in noncommutative $\\mathrm{L}^p$-spaces\nAbstract: We define a notion of nonassociative $\\mathrm{L}^p$-space associated to a $\\mathrm{JBW}^*$-algebra (Jordan von Neumann algebra) equipped with a normal faithful state $\\varphi$. In the particular case of $\\mathrm{JW}^*$-algebras underlying von Neumann algebras, we connect these spaces to a complex interpolation theorem of Ricard and Xu on noncommutative $\\mathrm{L}^p$-spaces. We also make the link with the nonassociative $\\mathrm{L}^p$-spaces of Iochum associated to $\\mathrm{JBW}$-algebras and the investigation of contractively complemented subspaces of noncommutative $\\mathrm{L}^p$-spaces. More precisely, we show that our nonassociative $\\mathrm{L}^p$-spaces contain isometrically the $\\mathrm{L}^p$-spaces of Iochum and that all tracial nonassociative $\\mathrm{L}^p$-spaces from $\\mathrm{JW}^*$-factors arise as positively contractively complemented subspaces of noncommutative $\\mathrm{L}^p$-spaces.", "field": "math", "label": 0}
{"text": "Title: Three results on representations of Mackey Lie algebras\nAbstract: I. Penkov and V. Serganova have recently introduced, for any non-degenerate pairing $W\\otimes V\\to\\mathbb C$ of vector spaces, the Lie algebra $\\mathfrak{gl}^M=\\mathfrak{gl}^M(V,W)$ consisting of endomorphisms of $V$ whose duals preserve $W\\subseteq V^*$. In their work, the category $\\mathbb{T}_{\\mathfrak{gl}^M}$ of $\\mathfrak{gl}^M$-modules which are finite length subquotients of the tensor algebra $T(W\\otimes V)$ is singled out and studied. In this note we solve three problems posed by these authors concerning the categories $\\mathbb{T}_{\\mathfrak{gl}^M}$. Denoting by $\\mathbb{T}_{V\\otimes W}$ the category with the same objects as $\\mathbb{T}_{\\mathfrak{gl}^M}$ but regarded as $V\\otimes W$-modules, we first show that when $W$ and $V$ are paired by dual bases, the functor $\\mathbb{T}_{\\mathfrak{gl}^M}\\to \\mathbb{T}_{V\\otimes W}$ taking a module to its largest weight submodule with respect to a sufficiently nice Cartan subalgebra of $V\\otimes W$ is a tensor equivalence. Secondly, we prove that when $W$ and $V$ are countable-dimensional, the objects of $\\mathbb{T}_{\\mathrm{End}(V)}$ have finite length as $\\mathfrak{gl}^M$-modules. Finally, under the same hypotheses, we compute the socle filtration of a simple object in $\\mathbb{T}_{\\mathrm{End}(V)}$ as a $\\mathfrak{gl}^M$-module.", "field": "math", "label": 1}
{"text": "Title: Combinatorial spectra using polynomials\nAbstract: In this paper we would like to introduce some new methods for studying magic type-colorings of graphs or domination of graphs, based on combinatorial spectrum on polynomial rings. We hope that this concept will be potentially useful for the graph theorists.", "field": "math", "label": 0}
{"text": "Title: Heisenberg uncertainty principle and its analogues in higher dimension: via Wigdersons' method\nAbstract: The following question was proposed by Avi Wigderson and Yuval Wigderson: Is it possible to use the method in their paper(The uncertainty principle: variations on a theme) to prove Heisenberg uncertainty principle in higher dimension R^d, and get the correct dependence of the constant on d? We answer this question affirmatively, and also prove some generalizations of Heisenberg uncertainty principle in R^d via Wigdersons' method.", "field": "math", "label": 0}
{"text": "Title: Height functions on Whitney umbrellas\nAbstract: We study the singularities of the members of the family of height functions on Whitney umbrellas, which is also known as cross-caps, and show that the family of the height functions is a versal unfolding. Moreover, we study local intersections of a Whitney umbrella with a hyperplane through its singular point.", "field": "math", "label": 1}
{"text": "Title: Depth-Regularized Optimization for 3D Gaussian Splatting in Few-Shot Images\nAbstract: In this paper, we present a method to optimize Gaussian splatting with a limited number of images while avoiding overfitting. Representing a 3D scene by combining numerous Gaussian splats has yielded outstanding visual quality. However, it tends to overfit the training views when only a small number of images are available. To address this issue, we introduce a dense depth map as a geometry guide to mitigate overfitting. We obtained the depth map using a pre-trained monocular depth estimation model and aligning the scale and offset using sparse COLMAP feature points. The adjusted depth aids in the color-based optimization of 3D Gaussian splatting, mitigating floating artifacts, and ensuring adherence to geometric constraints. We verify the proposed method on the NeRF-LLFF dataset with varying numbers of few images. Our approach demonstrates robust geometry compared to the original method that relies solely on images. Project page: robot0321.github.io/DepthRegGS", "field": "cs", "label": 0}
{"text": "Title: Resonances for homoclinic trapped sets\nAbstract: We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of results is proved for homoclinic sets of maximal dimension. Next, we generalize to the case of homoclinic/heteroclinic trajectories and we study the three bump case. In all these settings, the resonances may either accumulate on curves or form clouds. We also describe the corresponding resonant states.", "field": "math", "label": 1}
{"text": "Title: The Total Matching Polytope of Complete Bipartite Graphs\nAbstract: The total matching polytope generalizes the stable set polytope and the matching polytope. In this paper, we first propose new facet-defining inequalities for the total matching polytope. We then give an exponential-sized, non-redundant description in the original space and a compact description in an extended space of the total matching polytope of complete bipartite graphs.", "field": "cs", "label": 0}
{"text": "Title: SPEER: Sentence-Level Planning of Long Clinical Summaries via Embedded Entity Retrieval\nAbstract: Clinician must write a lengthy summary each time a patient is discharged from the hospital. This task is time-consuming due to the sheer number of unique clinical concepts covered in the admission. Identifying and covering salient entities is vital for the summary to be clinically useful. We fine-tune open-source LLMs (Mistral-7B-Instruct and Zephyr-7B-\\b{eta}) on the task and find that they generate incomplete and unfaithful summaries. To increase entity coverage, we train a smaller, encoder-only model to predict salient entities, which are treated as content-plans to guide the LLM. To encourage the LLM to focus on specific mentions in the source notes, we propose SPEER: Sentence-level Planning via Embedded Entity Retrieval. Specifically, we mark each salient entity span with special \"{{ }}\" boundary tags and instruct the LLM to retrieve marked spans before generating each sentence. Sentence-level planning acts as a form of state tracking in that the model is explicitly recording the entities it uses. We fine-tune Mistral and Zephyr variants on a large-scale, diverse dataset of ~167k in-patient hospital admissions and evaluate on 3 datasets. SPEER shows gains in both coverage and faithfulness metrics over non-guided and guided baselines.", "field": "cs", "label": 0}
{"text": "Title: Non-existence of three non-coalescing infinite geodesics with the same direction in the directed landscape\nAbstract: It is believed that for metric-like models in the KPZ class the following property holds: with probability one, starting from any point, there are at most two semi-infinite geodesics with the same direction that do not coalesce. Until now, such a result was only proved for one model - exponential LPP (Coupier 11') using its inherent connection to the totally asymmetric exclusion process. We prove that the above property holds for the directed landscape, the universal scaling limit of models in the KPZ class. Our proof reduces the problem to one on line ensembles and therefore paves the way to show similar results for other metric-like models in the KPZ class. Finally, combining our result with the ones in (Busani, Seppalainen,Sorensen 22', Bhatia 23') we obtain the full qualitative geometric description of infinite geodesics in the directed landscape.", "field": "math", "label": 0}
{"text": "Title: Minimum Coverage Sets for Training Robust Ad Hoc Teamwork Agents\nAbstract: Robustly cooperating with unseen agents and human partners presents significant challenges due to the diverse cooperative conventions these partners may adopt. Existing Ad Hoc Teamwork (AHT) methods address this challenge by training an agent with a population of diverse teammate policies obtained through maximizing specific diversity metrics. However, prior heuristic-based diversity metrics do not always maximize the agent's robustness in all cooperative problems. In this work, we first propose that maximizing an AHT agent's robustness requires it to emulate policies in the minimum coverage set (MCS), the set of best-response policies to any partner policies in the environment. We then introduce the L-BRDiv algorithm that generates a set of teammate policies that, when used for AHT training, encourage agents to emulate policies from the MCS. L-BRDiv works by solving a constrained optimization problem to jointly train teammate policies for AHT training and approximating AHT agent policies that are members of the MCS. We empirically demonstrate that L-BRDiv produces more robust AHT agents than state-of-the-art methods in a broader range of two-player cooperative problems without the need for extensive hyperparameter tuning for its objectives. Our study shows that L-BRDiv outperforms the baseline methods by prioritizing discovering distinct members of the MCS instead of repeatedly finding redundant policies.", "field": "cs", "label": 0}
{"text": "Title: Structural characterization of Cayley graphs\nAbstract: We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle language, or just the same elementary cycle language. Under the assumption of the axiom of choice, we characterize the Cayley graphs for all group subsets as the deterministic, co-deterministic, vertex-transitive simple graphs.", "field": "cs", "label": 1}
{"text": "Title: Preserving Image Properties Through Initializations in Diffusion Models\nAbstract: Retail photography imposes specific requirements on images. For instance, images may need uniform background colors, consistent model poses, centered products, and consistent lighting. Minor deviations from these standards impact a site's aesthetic appeal, making the images unsuitable for use. We show that Stable Diffusion methods, as currently applied, do not respect these requirements. The usual practice of training the denoiser with a very noisy image and starting inference with a sample of pure noise leads to inconsistent generated images during inference. This inconsistency occurs because it is easy to tell the difference between samples of the training and inference distributions. As a result, a network trained with centered retail product images with uniform backgrounds generates images with erratic backgrounds. The problem is easily fixed by initializing inference with samples from an approximation of noisy images. However, in using such an approximation, the joint distribution of text and noisy image at inference time still slightly differs from that at training time. This discrepancy is corrected by training the network with samples from the approximate noisy image distribution. Extensive experiments on real application data show significant qualitative and quantitative improvements in performance from adopting these procedures. Finally, our procedure can interact well with other control-based methods to further enhance the controllability of diffusion-based methods.", "field": "cs", "label": 0}
{"text": "Title: Actions, quotients and lattices of locally compact quantum groups\nAbstract: We prove a number of property (T) permanence results for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of invariant weights on quantum homogeneous spaces of quotient type, and relate invariant states for LCQG actions on von Neumann algebras to invariant vectors in canonical unitary implementations, providing an application to amenability. Finally, we introduce a notion of lattice in a locally compact quantum group, noting examples provided by Drinfeld doubles of compact quantum groups. We show that property (T) lifts from a lattice to the ambient LCQG, just as it does classically, thus obtaining new examples of non-classical, non-compact, non-discrete LCQGs with property (T).", "field": "math", "label": 1}
{"text": "Title: Bayesian optimization for backpropagation in Monte-Carlo tree search\nAbstract: In large domains, Monte-Carlo tree search (MCTS) is required to estimate the values of the states as efficiently and accurately as possible. However, the standard update rule in backpropagation assumes a stationary distribution for the returns, and particularly in min-max trees, convergence to the true value can be slow because of averaging. We present two methods, Softmax MCTS and Monotone MCTS, which generalize previous attempts to improve upon the backpropagation strategy. We demonstrate that both methods reduce to finding optimal monotone functions, which we do so by performing Bayesian optimization with a Gaussian process (GP) prior. We conduct experiments on computer Go, where the returns are given by a deep value neural network, and show that our proposed framework outperforms previous methods.", "field": "cs", "label": 1}
{"text": "Title: Proportional 2-Choosability with a Bounded Palette\nAbstract: Proportional choosability is a list coloring analogue of equitable coloring. Specifically, a $k$-assignment $L$ for a graph $G$ specifies a list $L(v)$ of $k$ available colors to each $v \\in V(G)$. An $L$-coloring assigns a color to each vertex $v$ from its list $L(v)$. A proportional $L$-coloring of $G$ is a proper $L$-coloring in which each color $c \\in \\bigcup_{v \\in V(G)} L(v)$ is used $\\lfloor \\eta(c)/k \\rfloor$ or $\\lceil \\eta(c)/k \\rceil$ times where $\\eta(c)=\\left\\lvert{\\{v \\in V(G) : c \\in L(v) \\}}\\right\\rvert$. A graph $G$ is proportionally $k$-choosable if a proportional $L$-coloring of $G$ exists whenever $L$ is a $k$-assignment for $G$. Motivated by earlier work, we initiate the study of proportional choosability with a bounded palette by studying proportional 2-choosability with a bounded palette. In particular, when $\\ell \\geq 2$, a graph $G$ is said to be proportionally $(2, \\ell)$-choosable if a proportional $L$-coloring of $G$ exists whenever $L$ is a $2$-assignment for $G$ satisfying $|\\bigcup_{v \\in V(G)} L(v)| \\leq \\ell$. We observe that a graph is proportionally $(2,2)$-choosable if and only if it is equitably 2-colorable. As $\\ell$ gets larger, the set of proportionally $(2, \\ell)$-choosable graphs gets smaller. We show that whenever $\\ell \\geq 5$ a graph is proportionally $(2, \\ell)$-choosable if and only if it is proportionally 2-choosable. We also completely characterize the connected proportionally $(2, \\ell)$-choosable graphs when $\\ell = 3,4$.", "field": "math", "label": 1}
{"text": "Title: Arithmetic progression in a finite field with prescribed norms\nAbstract: Given a prime power $q$ and a positive integer $n$, let $\\mathbb{F}_{q^{n}}$ represents a finite extension of degree $n$ of the finite field ${\\mathbb{F}_{q}}$. In this article, we investigate the existence of $m$ elements in arithmetic progression, where every element is primitive and at least one is normal with prescribed norms. Moreover, for $n\\geq6,q=3^k,m=2$ we establish that there are only $10$ possible exceptions.", "field": "math", "label": 0}
{"text": "Title: Learning Pixel Trajectories with Multiscale Contrastive Random Walks\nAbstract: A range of video modeling tasks, from optical flow to multiple object tracking, share the same fundamental challenge: establishing space-time correspondence. Yet, approaches that dominate each space differ. We take a step towards bridging this gap by extending the recent contrastive random walk formulation to much denser, pixel-level space-time graphs. The main contribution is introducing hierarchy into the search problem by computing the transition matrix between two frames in a coarse-to-fine manner, forming a multiscale contrastive random walk when extended in time. This establishes a unified technique for self-supervised learning of optical flow, keypoint tracking, and video object segmentation. Experiments demonstrate that, for each of these tasks, the unified model achieves performance competitive with strong self-supervised approaches specific to that task. Project webpage: https://jasonbian97.github.io/flowwalk", "field": "cs", "label": 1}
{"text": "Title: Improved bounds for the bracketing number of orthants or revisiting an algorithm of Thiémard to compute bounds for the star discrepancy\nAbstract: We improve the best known upper bound for the bracketing number of $d$-dimensional axis-parallel boxes anchored in $0$ (or, put differently, of lower left orthants intersected with the $d$-dimensional unit cube $[0,1]^d$). More precisely, we provide a better upper bound for the cardinality of an algorithmic bracketing cover construction due to Eric Thi\\'emard, which forms the core of his algorithm to approximate the star discrepancy of arbitrary point sets from [E. Thi\\'emard, An algorithm to compute bounds for the star discrepancy, J.~Complexity 17 (2001), 850 -- 880]. Moreover, the new upper bound for the bracketing number of anchored axis-parallel boxes yields an improved upper bound for the bracketing number of arbitrary axis-parallel boxes in $[0,1]^d$. In our upper bounds all constants are fully explicit.", "field": "math", "label": 0}
{"text": "Title: Generalized Divide and Color models\nAbstract: In this paper, we initiate the study of \"Generalized Divide and Color Models\". A very special interesting case of this is the \"Divide and Color Model\" (which motivates the name we use) introduced and studied by Olle H\\\"aggstr\\\"om. In this generalized model, one starts with a finite or countable set $V$, a random partition of $V$ and a parameter $p\\in [0,1]$. The corresponding Generalized Divide and Color Model is the $\\{0,1\\}$-valued process indexed by $V$ obtained by independently, for each partition element in the random partition chosen, with probability $p$, assigning all the elements of the partition element the value 1, and with probability $1-p$, assigning all the elements of the partition element the value 0. Some of the questions which we study here are the following. Under what situations can different random partitions give rise to the same color process? What can one say concerning exchangeable random partitions? What is the set of product measures that a color process stochastically dominates? For random partitions which are translation invariant, what ergodic properties do the resulting color processes have? The motivation for studying these processes is twofold; on the one hand, we believe that this is a very natural and interesting class of processes that deserves investigation and on the other hand, a number of quite varied well-studied processes actually fall into this class such as (1) the Ising model, (2) the fuzzy Potts model, (3) the stationary distributions for the Voter Model, (4) random walk in random scenery and of course (5) the original Divide and Color Model.", "field": "math", "label": 1}
{"text": "Title: Providing Self-Aware Systems with Reflexivity\nAbstract: We propose a new type of self-aware systems inspired by ideas from higher-order theories of consciousness. First, we discussed the crucial distinction between introspection and reflexion. Then, we focus on computational reflexion as a mechanism by which a computer program can inspect its own code at every stage of the computation. Finally, we provide a formal definition and a proof-of-concept implementation of computational reflexion, viewed as an enriched form of program interpretation and a way to dynamically \"augment\" a computational process.", "field": "cs", "label": 1}
{"text": "Title: Staircase symmetries in Hirzebruch surfaces\nAbstract: This paper continues the investigation of staircases in the family of Hirzebruch surfaces formed by blowing up the projective plane with weight b, that was started in Bertozzi, Holm et al. in arXiv:2010.08567. We explain the symmetries underlying the structure of the set of b that admit staircases, and show how the properties of these symmetries arise from a governing Diophantine equation. We also greatly simplify the techniques needed to show that a family of steps does form a staircase by using arithmetic properties of the accumulation function. There should be analogous results about both staircases and mutations for the other rational toric domains considered, for example, by Cristofaro-Gardiner et al. in arXiv:2004.07829 and by Casals--Vianna in arXiv:2004.13232.", "field": "math", "label": 1}
{"text": "Title: Orthogonal matroids over tracts\nAbstract: We generalize Baker-Bowler's theory of matroids over tracts to orthogonal matroids, define orthogonal matroids with coefficients in tracts in terms of Wick functions, orthogonal signatures, circuit sets, and orthogonal vector sets, and establish basic properties on functoriality, duality, and minors. Our cryptomorphic definitions of orthogonal matroids over tracts provide proofs of several representation theorems for orthogonal matroids. In particular, we give a new proof that an orthogonal matroid is regular if and only if it is representable over $\\mathbb{F}_2$ and $\\mathbb{F}_3$, which was originally shown by Geelen, and we prove that an orthogonal matroid is representable over the sixth-root-of-unity partial field if and only if it is representable over $\\mathbb{F}_3$ and $\\mathbb{F}_4$.", "field": "math", "label": 0}
{"text": "Title: Few-shot Adaptation of Multi-modal Foundation Models: A Survey\nAbstract: Multi-modal (vision-language) models, such as CLIP, are replacing traditional supervised pre-training models (e.g., ImageNet-based pre-training) as the new generation of visual foundation models. These models with robust and aligned semantic representations learned from billions of internet image-text pairs and can be applied to various downstream tasks in a zero-shot manner. However, in some fine-grained domains like medical imaging and remote sensing, the performance of multi-modal foundation models often leaves much to be desired. Consequently, many researchers have begun to explore few-shot adaptation methods for these models, gradually deriving three main technical approaches: 1) prompt-based methods, 2) adapter-based methods, and 3) external knowledge-based methods. Nevertheless, this rapidly developing field has produced numerous results without a comprehensive survey to systematically organize the research progress. Therefore, in this survey, we introduce and analyze the research advancements in few-shot adaptation methods for multi-modal models, summarizing commonly used datasets and experimental setups, and comparing the results of different methods. In addition, due to the lack of reliable theoretical support for existing methods, we derive the few-shot adaptation generalization error bound for multi-modal models. The theorem reveals that the generalization error of multi-modal foundation models is constrained by three factors: domain gap, model capacity, and sample size. Based on this, we propose three possible solutions from the following aspects: 1) adaptive domain generalization, 2) adaptive model selection, and 3) adaptive knowledge utilization.", "field": "cs", "label": 0}
{"text": "Title: Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating\nAbstract: In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using the energy method together with a fixed point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is short enough.", "field": "math", "label": 0}
{"text": "Title: Nonlocal problems with critical Hardy nonlinearity\nAbstract: By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical growth.", "field": "math", "label": 1}
{"text": "Title: Covid19 Vaccine Acceptance and Deprivation in US Counties\nAbstract: This report explores the central question of how socioeconomic status affects Covid19 vaccination rates in the United States, using existing open-source data. In general, a negative correlation exists between Area Deprivation Index (ADI) of a county and first dose, primary series and booster vaccination rates. Higher area deprivation correlated with polled vaccine hesitancy and lower search interest in vaccine interest, intention to vaccinate or concern about safety of vaccination. Positive correlations between ADI and certain mental health search trends were noted. No clear correlation between deprivation index and accessibility to vaccination sites were observed. In a small data sample, county level housing assistance policies and public information campaigns were noted to positively influence vaccine follow through rates. Finally, random forest, linear regression and KNN models were explored to validate the use of the above features for vaccine acceptance prediction.", "field": "cs", "label": 0}
{"text": "Title: Representation Learning of Multivariate Time Series using Attention and Adversarial Training\nAbstract: A critical factor in trustworthy machine learning is to develop robust representations of the training data. Only under this guarantee methods are legitimate to artificially generate data, for example, to counteract imbalanced datasets or provide counterfactual explanations for blackbox decision-making systems. In recent years, Generative Adversarial Networks (GANs) have shown considerable results in forming stable representations and generating realistic data. While many applications focus on generating image data, less effort has been made in generating time series data, especially multivariate signals. In this work, a Transformer-based autoencoder is proposed that is regularized using an adversarial training scheme to generate artificial multivariate time series signals. The representation is evaluated using t-SNE visualizations, Dynamic Time Warping (DTW) and Entropy scores. Our results indicate that the generated signals exhibit higher similarity to an exemplary dataset than using a convolutional network approach.", "field": "cs", "label": 0}
{"text": "Title: C*-Algebras of one-sided subshifts over arbitrary alphabets\nAbstract: We associate a C*-algebra $\\widetilde{\\mathcal{O}}_{\\textsf{X}}$ with a subshift over an arbitrary, possibly infinite, alphabet. We show that $\\widetilde{\\mathcal{O}}_{\\textsf{X}}$ is a full invariant for topological conjugacy of the subshifts of Ott, Tomforde, and Willis. When the alphabet is countable, we show that $\\widetilde{\\mathcal{O}}_{\\textsf{X}}$ is an invariant for isometric conjugacy of subshifts with the product metric. For a suitable partial action associated with a subshift over a countable alphabet, we show that $\\widetilde{\\mathcal{O}}_{\\textsf{X}}$ is also an invariant for continuous orbit equivalence. Additionally, we give a concrete way to compute the K-theory of $\\widetilde{\\mathcal{O}}_{\\textsf{X}}$ and illustrate it with two examples.", "field": "math", "label": 0}
{"text": "Title: Statistical Mechanical Analysis of Neural Network Pruning\nAbstract: Deep learning architectures with a huge number of parameters are often compressed using pruning techniques to ensure computational efficiency of inference during deployment. Despite multitude of empirical advances, there is a lack of theoretical understanding of the effectiveness of different pruning methods. We inspect different pruning techniques under the statistical mechanics formulation of a teacher-student framework and derive their generalization error (GE) bounds. It has been shown that Determinantal Point Process (DPP) based node pruning method is notably superior to competing approaches when tested on real datasets. Using GE bounds in the aforementioned setup we provide theoretical guarantees for their empirical observations. Another consistent finding in literature is that sparse neural networks (edge pruned) generalize better than dense neural networks (node pruned) for a fixed number of parameters. We use our theoretical setup to prove this finding and show that even the baseline random edge pruning method performs better than the DPP node pruning method. We also validate this empirically on real datasets.", "field": "cs", "label": 1}
{"text": "Title: Branch Prediction in Hardcaml for a RISC-V 32im CPU\nAbstract: Accurate branch prediction is a critical part of high performance instruction stream processing. In this paper, I present a hardware implementation of branch prediction for a RV32IM CPU, starting with static decode stage predictions and culminating in the use of BATAGE. In addition, I detail my experience writing the RTL in Hardcaml, a hardware description library for the functional programming language OCaml.", "field": "cs", "label": 0}
{"text": "Title: Synergizing Beyond Diagonal Reconfigurable Intelligent Surface and Rate-Splitting Multiple Access\nAbstract: This work focuses on the synergy of rate-splitting multiple access (RSMA) and beyond diagonal reconfigurable intelligent surface (BD-RIS) to enlarge the coverage, improve the performance, and save on antennas. Specifically, we employ a multi-sector BD-RIS modeled as a prism, which can achieve highly directional full-space coverage, in a multiuser multiple input single output communication system. With the multi-sector BD-RIS aided RSMA model, we jointly design the transmit precoder and BD-RIS matrix under the imperfect channel state information (CSI) conditions. The robust design is performed by solving a stochastic average sum-rate maximization problem. With sample average approximation and weighted minimum mean square error-rate relationship, the stochastic problem is transformed into a deterministic one with multiple blocks, each of which is iteratively designed. Simulation results show that multi-sector BD-RIS aided RSMA outperforms space division multiple access schemes. More importantly, synergizing multi-sector BD-RIS with RSMA is an efficient strategy to reduce the number of active antennas at the transmitter and the number of passive antennas in BD-RIS.", "field": "cs", "label": 0}
{"text": "Title: Moduli spaces of orthogonal bundles over an algebraic curve\nAbstract: We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the invariants on the representation space of a quiver under the action of a product of classical groups.", "field": "math", "label": 1}
{"text": "Title: Text mining arXiv: a look through quantitative finance papers\nAbstract: This paper explores articles hosted on the arXiv preprint server with the aim to uncover valuable insights hidden in this vast collection of research. Employing text mining techniques and through the application of natural language processing methods, we examine the contents of quantitative finance papers posted in arXiv from 1997 to 2022. We extract and analyze crucial information from the entire documents, including the references, to understand the topics trends over time and to find out the most cited researchers and journals on this domain. Additionally, we compare numerous algorithms to perform topic modeling, including state-of-the-art approaches.", "field": "cs", "label": 0}
{"text": "Title: MedSumm: A Multimodal Approach to Summarizing Code-Mixed Hindi-English Clinical Queries\nAbstract: In the healthcare domain, summarizing medical questions posed by patients is critical for improving doctor-patient interactions and medical decision-making. Although medical data has grown in complexity and quantity, the current body of research in this domain has primarily concentrated on text-based methods, overlooking the integration of visual cues. Also prior works in the area of medical question summarisation have been limited to the English language. This work introduces the task of multimodal medical question summarization for codemixed input in a low-resource setting. To address this gap, we introduce the Multimodal Medical Codemixed Question Summarization MMCQS dataset, which combines Hindi-English codemixed medical queries with visual aids. This integration enriches the representation of a patient's medical condition, providing a more comprehensive perspective. We also propose a framework named MedSumm that leverages the power of LLMs and VLMs for this task. By utilizing our MMCQS dataset, we demonstrate the value of integrating visual information from images to improve the creation of medically detailed summaries. This multimodal strategy not only improves healthcare decision-making but also promotes a deeper comprehension of patient queries, paving the way for future exploration in personalized and responsive medical care. Our dataset, code, and pre-trained models will be made publicly available.", "field": "cs", "label": 0}
{"text": "Title: Evaluating Trustworthiness of Online News Publishers via Article Classification\nAbstract: The proliferation of low-quality online information in today's era has underscored the need for robust and automatic mechanisms to evaluate the trustworthiness of online news publishers. In this paper, we analyse the trustworthiness of online news media outlets by leveraging a dataset of 4033 news stories from 40 different sources. We aim to infer the trustworthiness level of the source based on the classification of individual articles' content. The trust labels are obtained from NewsGuard, a journalistic organization that evaluates news sources using well-established editorial and publishing criteria. The results indicate that the classification model is highly effective in classifying the trustworthiness levels of the news articles. This research has practical applications in alerting readers to potentially untrustworthy news sources, assisting journalistic organizations in evaluating new or unfamiliar media outlets and supporting the selection of articles for their trustworthiness assessment.", "field": "cs", "label": 0}
{"text": "Title: Ergodicity of skew products over linearly recurrent IETs\nAbstract: We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic functions of intervals is ergodic with respect to Lebesgue measure.", "field": "math", "label": 1}
{"text": "Title: Algebraic twists of modular forms and Hecke orbits\nAbstract: We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistribution property for twisted Hecke orbits. This is done by exploiting the amplification method and the Riemann Hypothesis over finite fields, relying in particular on the ell-adic Fourier transform introduced by Deligne and studied by Katz and Laumon.", "field": "math", "label": 1}
{"text": "Title: The Case for Bayesian Deep Learning\nAbstract: The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically underspecified by the data, and can represent many different but high performing models corresponding to different settings of parameters, which is exactly when marginalization will make the biggest difference for both calibration and accuracy. (2) Deep ensembles have been mistaken as competing approaches to Bayesian methods, but can be seen as approximate Bayesian marginalization. (3) The structure of neural networks gives rise to a structured prior in function space, which reflects the inductive biases of neural networks that help them generalize. (4) The observed correlation between parameters in flat regions of the loss and a diversity of solutions that provide good generalization is further conducive to Bayesian marginalization, as flat regions occupy a large volume in a high dimensional space, and each different solution will make a good contribution to a Bayesian model average. (5) Recent practical advances for Bayesian deep learning provide improvements in accuracy and calibration compared to standard training, while retaining scalability.", "field": "cs", "label": 1}
{"text": "Title: Performance Trade-off and Joint Waveform Design for MIMO-OFDM DFRC Systems\nAbstract: Dual-functional radar-communication (DFRC) has attracted considerable attention. This paper considers the frequency-selective multipath fading environment and proposes DFRC waveform design strategies based on multiple-input and multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) techniques. In the proposed waveform design strategies, the Cramer-Rao bound (CRB) of the radar system, the inter-stream interference (ISI) and the achievable rate of the communication system, are respectively considered as the performance metrics. In this paper, we focus on the performance trade-off between the radar system and the communication system, and the optimization problems are formulated. In the ISI minimization based waveform design strategy, the optimization problem is convex and can be easily solved. In the achievable rate maximization based waveform design strategy, we propose a water-filling (WF) and sequential quadratic programming (SQP) based algorithm to derive the covariance matrix and the precoding matrix. Simulation results validate the proposed DFRC waveform designs and show that the achievable rate maximization based strategy has a better performance than the ISI minimization based strategy.", "field": "cs", "label": 0}
{"text": "Title: Extension of the Topological Abel-Jacobi Map for Cubic Threefolds\nAbstract: The difference $[L_1]-[L_2]$ of a pair of skew lines on a cubic threefold defines a vanishing cycle on the cubic surface as the hyperplane section spanned by the two lines. By deforming the hyperplane, the flat translation of such vanishing cycle forms a 72-to-1 covering space $T_v$ of a Zariski open subspace of $(\\mathbb P^4)^*$. Based on a lemma of Stein on the compactification of finite analytic covers, we found a compactification of $T_v$ to which the topological Abel-Jacobi map extends. Moreover, the boundary points of the compactification can be interpreted in terms of local monodromy and the singularities on cubic surfaces. We prove the associated map on fundamental groups of topological Abel-Jacobi map is surjective.", "field": "math", "label": 0}
{"text": "Title: Predictive Multiplicity in Probabilistic Classification\nAbstract: Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely.", "field": "cs", "label": 1}
{"text": "Title: Mesoscopic averaging of the two-dimensional KPZ equation\nAbstract: We study the limit of a local average of the KPZ equation in dimension $d=2$ with general initial data in the subcritical regime. Our result shows that a proper spatial averaging of the KPZ equation converges in distribution to the sum of the solution to a deterministic KPZ equation and a Gaussian random variable that depends solely on the scale of averaging. This shows a unique mesoscopic averaging phenomenon that is only present in dimension two. Our work is inspired by the recent findings by Chatterjee \\cite{chatterjee2021weak}.", "field": "math", "label": 0}
{"text": "Title: Do DL models and training environments have an impact on energy consumption?\nAbstract: Current research in the computer vision field mainly focuses on improving Deep Learning (DL) correctness and inference time performance. However, there is still little work on the huge carbon footprint that has training DL models. This study aims to analyze the impact of the model architecture and training environment when training greener computer vision models. We divide this goal into two research questions. First, we analyze the effects of model architecture on achieving greener models while keeping correctness at optimal levels. Second, we study the influence of the training environment on producing greener models. To investigate these relationships, we collect multiple metrics related to energy efficiency and model correctness during the models' training. Then, we outline the trade-offs between the measured energy efficiency and the models' correctness regarding model architecture, and their relationship with the training environment. We conduct this research in the context of a computer vision system for image classification. In conclusion, we show that selecting the proper model architecture and training environment can reduce energy consumption dramatically (up to 81.38%) at the cost of negligible decreases in correctness. Also, we find evidence that GPUs should scale with the models' computational complexity for better energy efficiency.", "field": "cs", "label": 0}
{"text": "Title: Functional central limit theorems for stick-breaking priors\nAbstract: We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general stick-breaking weights, the Poisson-Dirichlet process, the normalized inverse Gaussian process, the normalized generalized gamma process, and the generalized Dirichlet process. For the Dirichlet process with general stick-breaking weights, we introduce two general conditions such that the central limit theorem and functional central limit theorem hold. Except in the case of the generalized Dirichlet process, since the finite dimensional distributions of these processes are either hard to obtain or are complicated to use even they are available, we use the method of moments to obtain the convergence results. For the generalized Dirichlet process we use its finite dimensional marginal distributions to obtain the asymptotics although the computations are highly technical.", "field": "math", "label": 1}
{"text": "Title: Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations\nAbstract: We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase contrast. Similar equations manifest in diverse applications like chemical diffusion, electrostatics, and Darcy flow. The neural network aims to establish the link between the complex thermal conductivity profiles and temperature distributions, as well as heat flux components within the microstructure, under fixed boundary conditions. A distinctive aspect is our independence from classical solvers like finite element methods for data. A noteworthy contribution lies in our novel approach to defining the loss function, based on the discretized weak form of the governing equation. This not only reduces the required order of derivatives but also eliminates the need for automatic differentiation in the construction of loss terms, accepting potential numerical errors from the chosen discretization method. As a result, the loss function in this work is an algebraic equation that significantly enhances training efficiency. We benchmark our methodology against the standard finite element method, demonstrating accurate yet faster predictions using the trained neural network for temperature and flux profiles. We also show higher accuracy by using the proposed method compared to purely data-driven approaches for unforeseen scenarios.", "field": "cs", "label": 0}
{"text": "Title: Sums, products and dilates on sparse graphs\nAbstract: Let $A \\subset \\mathbb R$ and $G \\subset A \\times A$. We prove that, for any $\\lambda \\in \\mathbb R \\setminus \\{-1,0,1\\}$, \\[ \\max \\{|A+_G A|, |A+_G \\lambda A|, |A\\cdot_G A|\\} \\gg |G|^{6/11}. \\]", "field": "math", "label": 1}
{"text": "Title: Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries\nAbstract: A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of functionals of solution to the SDE and a reconstruction theorem for general stochastic symmetries is proved. Moreover, the notable case of reduction under the closed subclass of quasi Doob transformations is presented. The theoretical results are applied to stochastic models relevant in the applications.", "field": "math", "label": 1}
{"text": "Title: An anisotropic partial regularity criterion for the Navier-Stokes equations\nAbstract: In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier--Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if $(u,p)$ is a suitable weak solution and a certain scale-invariant quantity involving only $u_3$ is small on a space-time cylinder $Q_r(x_0,t_0)$, then $u$ is regular at $(x_0,t_0)$.", "field": "math", "label": 1}
{"text": "Title: A coordinate free characterization of certain quasidiagonal operators\nAbstract: We obtain (i) a new, coordinate free, characterization of quasidiagonal operators with essential spectra contained in the unit circle by adapting the proof of a classical result in the theory of Banach spaces, (ii) an affirmative answer to some questions of Hadwin, and (iii) an alternative proof of Hadwin's characterization of the SOT, WOT and $*$-SOT closure of the unitary orbit of a given operator on a separable, infinite dimensional, complex Hilbert space.", "field": "math", "label": 1}
{"text": "Title: Exact Computation of LTI Reach Set from Integrator Reach Set with Bounded Input\nAbstract: We present a semi-analytical method for exact computation of the boundary of the reach set of a single-input controllable linear time invariant (LTI) system with given bounds on its input range. In doing so, we deduce a parametric formula for the boundary of the reach set of an integrator linear system with time-varying bounded input. This formula generalizes recent results on the geometry of an integrator reach set with time-invariant bounded input. We show that the same ideas allow for computing the volume of the LTI reach set.", "field": "math", "label": 0}
{"text": "Title: Estimation of statistics of transitions and Hill relation for Langevin dynamics\nAbstract: In molecular dynamics, statistics of transitions, such as the mean transition time, are macroscopic observables which provide important dynamical information on the underlying microscopic stochastic process. A direct estimation using simulations of microscopic trajectories over long time scales is typically computationally intractable in metastable situations. To overcome this issue, several numerical methods rely on a potential-theoretic identity, sometimes attributed to Hill in the computational statistical physics litterature, which expresses statistics of transitions in terms of the invariant measure of the sequence of configurations by which the underlying process enters metastable sets. The use of this identity then allows to replace the long time simulation problem with a rare event sampling problem, for which efficient algorithms are available. In this article, we rigorously analyse such a method for molecular systems modelled by the Langevin dynamics. Our main contributions are twofold. First, we prove the Hill relation in the fairly general context of positive Harris recurrent chains, and show that this formula applies to the Langevin dynamics. Second, we provide an explicit expression of the invariant measure involved in the Hill relation, and describe an elementary exact simulation procedure. Overall, this yields a simple and complete numerical method to estimate statistics of transitions.", "field": "math", "label": 1}
{"text": "Title: Families of costs with zero and nonnegative MTW tensor in optimal transport\nAbstract: We compute explicitly the MTW tensor (or cross curvature) for the optimal transport problem on $\\mathbb{R}^n$ with a cost function of form $\\mathsf{c}(x, y) = \\mathsf{u}(x^{\\mathfrak{t}}y)$, where $\\mathsf{u}$ is a scalar function with inverse $\\mathsf{s}$, $x^{\\ft}y$ is a nondegenerate bilinear pairing of vectors $x, y$ belonging to an open subset of $\\mathbb{R}^n$. The condition that the MTW-tensor vanishes on null vectors under the Kim-McCann metric is a fourth-order nonlinear ODE, which could be reduced to a linear ODE of the form $\\mathsf{s}^{(2)} - S\\mathsf{s}^{(1)} + P\\mathsf{s} = 0$ with constant coefficients $P$ and $S$. The resulting inverse functions include {\\it Lambert} and {\\it generalized inverse hyperbolic\\slash trigonometric} functions. The square Euclidean metric and $\\log$-type costs are equivalent to instances of these solutions. The optimal map for the family is also explicit. For cost functions of a similar form on a hyperboloid model of the hyperbolic space and unit sphere, we also express this tensor in terms of algebraic expressions in derivatives of $\\mathsf{s}$ using the Gauss-Codazzi equation, obtaining new families of strictly regular costs for these manifolds, including new families of {\\it power function costs}. We analyze the $\\sinh$-type hyperbolic cost, providing examples of $\\mathsf{c}$-convex functions and divergence.", "field": "math", "label": 0}
{"text": "Title: A novel efficient Multi-view traffic-related object detection framework\nAbstract: With the rapid development of intelligent transportation system applications, a tremendous amount of multi-view video data has emerged to enhance vehicle perception. However, performing video analytics efficiently by exploiting the spatial-temporal redundancy from video data remains challenging. Accordingly, we propose a novel traffic-related framework named CEVAS to achieve efficient object detection using multi-view video data. Briefly, a fine-grained input filtering policy is introduced to produce a reasonable region of interest from the captured images. Also, we design a sharing object manager to manage the information of objects with spatial redundancy and share their results with other vehicles. We further derive a content-aware model selection policy to select detection methods adaptively. Experimental results show that our framework significantly reduces response latency while achieving the same detection accuracy as the state-of-the-art methods.", "field": "cs", "label": 1}
{"text": "Title: On components of the tensor square of a Weyl module\nAbstract: For a simple Lie algebra $\\mathfrak{g}$ of type $A_n,B_n,C_n$ or $D_n$, we give a characterization of the set of dominant integral weights $\\lambda$ such that for any rational point $\\mu$ in the fundamental Weyl chamber, $2\\lambda-\\mu$ is a non-negative rational combination of the simple roots if and only if $V_{m\\mu}\\subseteq V_{m\\lambda}\\otimes V_{m\\lambda}$ for some positive integer $m$.", "field": "math", "label": 0}
{"text": "Title: Two-Stage Surrogate Modeling for Data-Driven Design Optimization with Application to Composite Microstructure Generation\nAbstract: This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the \"learner\" identifies a limited set of candidates within the input design space whose predicted outputs closely align with desired outcomes. Subsequently, in the second stage, a separate surrogate model, functioning as an \"evaluator,\" is employed to assess the reduced candidate space generated in the first stage. This evaluation process eliminates inaccurate and uncertain solutions, guided by a user-defined coverage level. The framework's distinctive contribution is the integration of conformal inference, providing a versatile and efficient approach that can be widely applicable. To demonstrate the effectiveness of the proposed framework compared to conventional single-stage inverse problems, we conduct several benchmark tests and investigate an engineering application focused on the micromechanical modeling of fiber-reinforced composites. The results affirm the superiority of our proposed framework, as it consistently produces more reliable solutions. Therefore, the introduced framework offers a unique perspective on fostering interactions between machine learning-based surrogate models in real-world applications.", "field": "cs", "label": 0}
{"text": "Title: The relation between Granger causality and directed information theory: a review\nAbstract: This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We present the definitions based on conditional independence. The notion of instantaneous coupling is included in the definitions. The concept of Granger causality graphs is discussed. We present directed information theory from the perspective of studies of causal influences between stochastic processes. Causal conditioning appears to be the cornerstone for the relation between information theory and Granger causality. In the bivariate case, the fundamental measure is the directed information, which decomposes as the sum of the transfer entropies and a term quantifying instantaneous coupling. We show the decomposition of the mutual information into the sums of the transfer entropies and the instantaneous coupling measure, a relation known for the linear Gaussian case. We study the multivariate case, showing that the useful decomposition is blurred by instantaneous coupling. The links are further developed by studying how measures based on directed information theory naturally emerge from Granger causality inference frameworks as hypothesis testing.", "field": "cs", "label": 1}
{"text": "Title: Location Aware Modular Biencoder for Tourism Question Answering\nAbstract: Answering real-world tourism questions that seek Point-of-Interest (POI) recommendations is challenging, as it requires both spatial and non-spatial reasoning, over a large candidate pool. The traditional method of encoding each pair of question and POI becomes inefficient when the number of candidates increases, making it infeasible for real-world applications. To overcome this, we propose treating the QA task as a dense vector retrieval problem, where we encode questions and POIs separately and retrieve the most relevant POIs for a question by utilizing embedding space similarity. We use pretrained language models (PLMs) to encode textual information, and train a location encoder to capture spatial information of POIs. Experiments on a real-world tourism QA dataset demonstrate that our approach is effective, efficient, and outperforms previous methods across all metrics. Enabled by the dense retrieval architecture, we further build a global evaluation baseline, expanding the search space by 20 times compared to previous work. We also explore several factors that impact on the model's performance through follow-up experiments. Our code and model are publicly available at https://github.com/haonan-li/LAMB.", "field": "cs", "label": 0}
{"text": "Title: Brain-Conditional Multimodal Synthesis: A Survey and Taxonomy\nAbstract: In the era of Artificial Intelligence Generated Content (AIGC), conditional multimodal synthesis technologies (e.g., text-to-image, text-to-video, text-to-audio, etc) are gradually reshaping the natural content in the real world. The key to multimodal synthesis technology is to establish the mapping relationship between different modalities. Brain signals, serving as potential reflections of how the brain interprets external information, exhibit a distinctive One-to-Many correspondence with various external modalities. This correspondence makes brain signals emerge as a promising guiding condition for multimodal content synthesis. Brian-conditional multimodal synthesis refers to decoding brain signals back to perceptual experience, which is crucial for developing practical brain-computer interface systems and unraveling complex mechanisms underlying how the brain perceives and comprehends external stimuli. This survey comprehensively examines the emerging field of AIGC-based Brain-conditional Multimodal Synthesis, termed AIGC-Brain, to delineate the current landscape and future directions. To begin, related brain neuroimaging datasets, functional brain regions, and mainstream generative models are introduced as the foundation of AIGC-Brain decoding and analysis. Next, we provide a comprehensive taxonomy for AIGC-Brain decoding models and present task-specific representative work and detailed implementation strategies to facilitate comparison and in-depth analysis. Quality assessments are then introduced for both qualitative and quantitative evaluation. Finally, this survey explores insights gained, providing current challenges and outlining prospects of AIGC-Brain. Being the inaugural survey in this domain, this paper paves the way for the progress of AIGC-Brain research, offering a foundational overview to guide future work.", "field": "cs", "label": 0}
{"text": "Title: Regularity for multi-phase problems at nearly linear growth\nAbstract: Minima of the log-multiphase variational integral $$ w \\mapsto \\int_{\\Omega} \\left[|Dw|\\log(1+|Dw|) + a(x)|Dw|^q + b(x)|Dw|^s\\right] \\, {\\rm d}x\\,, $$ have locally H\\\"older continuous gradient under sharp quantitative bounds linking the growth powers $(q,s)$ to the H\\\"older exponents of the modulating coefficients $a(\\cdot)$ and $b(\\cdot)$ respectively.", "field": "math", "label": 0}
{"text": "Title: Existence and uniqueness of solutions to rate independent systems with history variable of integral type\nAbstract: This paper investigates rate independent systems (RIS), where the dissipation functional depends not only on the rate but also on the history of the state. The latter is expressed in terms of a Volterra integral operator. We establish an existence result for the original problem and for the control thereof, without resorting to smallness assumptions. Under a smoothness condition, we prove the uniqueness of solutions to a certain class of history dependent RIS with unbounded dissipation potentials. In this context, we derive an essential estimate that opens the door to future research on the topic of optimization.", "field": "math", "label": 0}
{"text": "Title: Wavenumber-explicit analysis for the Helmholtz $h$-BEM: error estimates and iteration counts for the Dirichlet problem\nAbstract: We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the number of GMRES iterations must grow with the wavenumber $k$ to have the error in the iterative solution bounded independently of $k$ as $k\\rightarrow \\infty$ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the first-ever sharp bound on how the number of GMRES iterations depends on the wavenumber for an integral equation used to solve a scattering problem. We also prove new bounds on how $h$ must decrease with $k$ to maintain $k$-independent quasi-optimality of the Galerkin solutions as $k \\rightarrow \\infty$ when the obstacle is nontrapping.", "field": "math", "label": 1}
{"text": "Title: Multidimensional Sticky Brownian Motions: Tail Behaviour of the Joint Stationary Distribution\nAbstract: Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary distributions of a multidimensional sticky Brownian motion, provided it is stable. We will study the large deviations principle for stationary distribution and the tail behaviour of the joint stationary distribution.", "field": "math", "label": 1}
{"text": "Title: Distributed Multi-Object Tracking Under Limited Field of View Heterogeneous Sensors with Density Clustering\nAbstract: We consider the problem of tracking multiple, unknown, and time-varying numbers of objects using a distributed network of heterogeneous sensors. In an effort to derive a formulation for practical settings, we consider limited and unknown sensor field-of-views (FoVs), sensors with limited local computational resources and communication channel capacity. The resulting distributed multi-object tracking algorithm involves solving an NP-hard multidimensional assignment problem either optimally for small-size problems or sub-optimally for general practical problems. For general problems, we propose an efficient distributed multi-object tracking algorithm that performs track-to-track fusion using a clustering-based analysis of the state space transformed into a density space to mitigate the complexity of the assignment problem. The proposed algorithm can more efficiently group local track estimates for fusion than existing approaches. To ensure we achieve globally consistent identities for tracks across a network of nodes as objects move between FoVs, we develop a graph-based algorithm to achieve label consensus and minimise track segmentation. Numerical experiments with a synthetic and a real-world trajectory dataset demonstrate that our proposed method is significantly more computationally efficient than state-of-the-art solutions, achieving similar tracking accuracy and bandwidth requirements but with improved label consistency.", "field": "cs", "label": 0}
{"text": "Title: Towards the Atiyah-Sutcliffe conjectures for coplanar hyperbolic points\nAbstract: The Atiyah-Sutcliffe normalized determinant function $D$ is a smooth complex-valued function on $C_n(H^3)$, where $C_n(H^3)$ denotes the configuration space of $n$ distinct points in hyperbolic $3$-space $H^3$. The hyperbolic version of the Atiyah-Sutcliffe conjecture $1$ (AS conjecture $1$) states that $D$ is nowhere vanishing. AS conjecture $2$ (hyperbolic version) is the stronger statement that $|D(\\mathbf{x})| \\geq 1$ for any $\\mathbf{x} \\in C_n(H^3)$. In this short article, we prove AS conjecture $2$ for hyperbolic convex coplanar quadrilaterals, that is for configurations of $4$ points in $H^2$ with none of the points in the configuration lying in the convex hull of the other three. We also obtain Y. Zhang and J. Ma's result, namely AS conjecture $1$ for non-convex quadrilaterals in $H^2$. Finally, we find an explicit lower bound for $|D|$ depending on $n$ only for the natural ``star-based'' variant of the AS problem, for convex coplanar hyperbolic configurations. The latter result holds for any $n \\geq 2$. The proofs for $n=4$ make use of the symbolic library of Python. The proof of the general result follows from a general formula for the determinant. In all these cases, $D$ can be expanded as a linear combination of non-negative rational functions with positive coefficients.", "field": "math", "label": 1}
{"text": "Title: A Distributed SDN Control Plane for Consistent Policy Updates\nAbstract: Software-defined networking (SDN) is a novel paradigm that out-sources the control of packet-forwarding switches to a set of software controllers. The most fundamental task of these controllers is the correct implementation of the \\emph{network policy}, i.e., the intended network behavior. In essence, such a policy specifies the rules by which packets must be forwarded across the network. This paper studies a distributed SDN control plane that enables \\emph{concurrent} and \\emph{robust} policy implementation. We introduce a formal model describing the interaction between the data plane and a distributed control plane (consisting of a collection of fault-prone controllers). Then we formulate the problem of \\emph{consistent} composition of concurrent network policy updates (short: the \\emph{CPC Problem}). To anticipate scenarios in which some conflicting policy updates must be rejected, we enable the composition via a natural \\emph{transactional} interface with all-or-nothing semantics. We show that the ability of an $f$-resilient distributed control plane to process concurrent policy updates depends on the tag complexity, i. e., the number of policy labels (a.k.a. \\emph{tags}) available to the controllers, and describe a CPC protocol with optimal tag complexity $f+2$.", "field": "cs", "label": 1}
{"text": "Title: Certifying the novelty of equichordal tight fusion frames\nAbstract: An equichordal tight fusion frame (ECTFF) is a finite sequence of equi-dimensional subspaces of a finite-dimensional Hilbert space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ECTFF is a type of optimal Grassmannian code, being a way to arrange a given number of members of a Grassmannian so that the minimal chordal distance between any pair of them is as large as possible. Any nontrivial ECTFF has both a Naimark complement and spatial complement which themselves are ECTFFs. It turns out that whenever the number of subspaces is at least five, taking iterated alternating Naimark and spatial complements of one ECTFF yields an infinite family of them with distinct parameters. This makes it challenging to certify the novelty of any recently discovered ECTFF: how can one guarantee that it does not arise from any previously known construction in such a Naimark-spatial way? In this paper, we propose a solution to this problem, showing that any ECTFF is a member of a Naimark-spatial family originating from either a trivial ECTFF or one with unique \"minimal\" parameters. In the latter case, if its minimal parameters do not match those of any previously known ECTFF, it is certifiably new. As a proof of concept, we then use these ideas to certify the novelty of some ECTFFs arising from a new method for constructing them from difference families for finite abelian groups. This method properly generalizes King's construction of ECTFFs from semiregular divisible difference sets.", "field": "math", "label": 1}
{"text": "Title: On hypergraphs without loose cycles\nAbstract: Recently, Mubayi and Wang showed that for $r\\ge 4$ and $\\ell \\ge 3$, the number of $n$-vertex $r$-graphs that do not contain any loose cycle of length $\\ell$ is at most $2^{O( n^{r-1} (\\log n)^{(r-3)/(r-2)})}$. We improve this bound to $2^{O( n^{r-1} \\log \\log n) }$.", "field": "math", "label": 1}
{"text": "Title: The relationship between the negative inertia index of graph $G$ and its girth $g$ and diameter $d$\nAbstract: Let $G$ be a simple connected graph. We use $n(G)$, $p(G)$, and $\\eta(G)$ to denote the number of negative eigenvalues, positive eigenvalues, and zero eigenvalues of the adjacency matrix $A(G)$ of $G$, respectively. In this paper, we prove that $2n(G)\\geq d(G) + 1$ when $d(G)$ is odd, and $n(G) \\geq \\lceil \\frac{g}{2}\\rceil - 1$ for a graph containing cycles, where $d(G)$ and $g$ are the diameter and girth of the graph $G$, respectively. Furthermore, we characterize the extremal graphs for the cases of $2n(G) = d(G) + 1$, $n(G) = \\lceil \\frac{g}{2}\\rceil$, and $n(G) = \\lceil \\frac{g}{2}\\rceil - 1$.", "field": "math", "label": 0}
{"text": "Title: Dynamic Packet Scheduler Optimization in Wireless Relay Networks\nAbstract: In this work, we investigate the optimal dynamic packet scheduling policy in a wireless relay network (WRN). We model this network by two sets of parallel queues, that represent the subscriber stations (SS) and the relay stations (RS), with random link connectivity. An optimal policy minimizes, in stochastic ordering sense, the process of cost function of the SS and RS queue sizes. We prove that, in a system with symmetrical connectivity and arrival distributions, a policy that tries to balance the lengths of all the system queues, at every time slot, is optimal. We use stochastic dominance and coupling arguments in our proof. We also provide a low-overhead algorithm for optimal policy implementation.", "field": "cs", "label": 1}
{"text": "Title: High order Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation\nAbstract: We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward Differentiation Formulas up to order $q=5$. The development and analysis of the methods are performed in the framework of time evolving finite elements presented in C. M. Elliot and T. Ranner, IMA Journal of Numerical Analysis \\textbf{41}, 1696-1845 (2021). The error estimates show through their dependence on the parameters of the equation the existence of different regimes in the behavior of the numerical solution; namely, in the diffusive regime, that is, when the diffusion parameter $\\mu$ is large, the error is $O(h^{k+1}+\\Delta t^{q})$, whereas in the advective regime, $\\mu \\ll 1$, the convergence is $O(\\min (h^{k},\\frac{h^{k+1} }{\\Delta t})+\\Delta t^{q})$. It is worth remarking that the error constant does not have exponential $\\mu ^{-1}$ dependence.", "field": "math", "label": 0}
{"text": "Title: Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions\nAbstract: In this paper we consider quasilinear Keller-Segel type systems of two kinds in higher dimensions. In the case of a nonlinear diffusion system we prove an optimal (with respect to possible nonlinear diffusions generating explosion in finite time of solutions) finite-time blowup result. In the case of a cross-diffusion system we give results which are optimal provided one assumes some proper non-decay of a nonlinear chemical sensitivity. Moreover, we show that once we do not assume the above mentioned non-decay, our result cannot be as strong as in the case of nonlinear diffusion without nonlinear cross-diffusion terms. To this end we provide an example, interesting by itself, of global-in-time unbounded solutions to the nonlinear cross-diffusion Keller-Segel system with chemical sensitivity decaying fast enough, in a range of parameters in which there is a finite-time blowup result in a corresponding case without nonlinear cross-diffusion.", "field": "math", "label": 1}
{"text": "Title: Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion\nAbstract: Several earlier studies have shown impressive control performance in complex robotic systems by designing the controller using a neural network and training it with model-free reinforcement learning. However, these outstanding controllers with natural motion style and high task performance are developed through extensive reward engineering, which is a highly laborious and time-consuming process of designing numerous reward terms and determining suitable reward coefficients. In this work, we propose a novel reinforcement learning framework for training neural network controllers for complex robotic systems consisting of both rewards and constraints. To let the engineers appropriately reflect their intent to constraints and handle them with minimal computation overhead, two constraint types and an efficient policy optimization algorithm are suggested. The learning framework is applied to train locomotion controllers for several legged robots with different morphology and physical attributes to traverse challenging terrains. Extensive simulation and real-world experiments demonstrate that performant controllers can be trained with significantly less reward engineering, by tuning only a single reward coefficient. Furthermore, a more straightforward and intuitive engineering process can be utilized, thanks to the interpretability and generalizability of constraints. The summary video is available at https://youtu.be/KAlm3yskhvM.", "field": "cs", "label": 0}
{"text": "Title: The abstract cotangent complex and Quillen cohomology of enriched categories\nAbstract: In his fundamental work, Quillen developed the theory of the cotangent complex as a universal abelian derived invariant, and used it to define and study a canonical form of cohomology, encompassing many known cohomology theories. Additional cohomology theories, such as generalized cohomology of spaces and topological Andr\\'e-Quillen cohomology, can be accommodated by considering a spectral version of the cotangent complex. Recent work of Lurie established a comprehensive $\\infty$-categorical analogue of the cotangent complex formalism using stabilization of $\\infty$-categories. In this paper we study the spectral cotangent complex while working in Quillen's model categorical setting. Our main result gives new and explicit computations of the cotangent complex and Quillen cohomology of enriched categories. For this we make essential use of previous work, which identifies the tangent categories of operadic algebras in unstable model categories. In particular, we present the cotangent complex of an $\\infty$-category as a spectrum valued functor on its twisted arrow category, and consider the associated obstruction theory in some examples of interest.", "field": "math", "label": 1}
{"text": "Title: Distributed Hardware Accelerated Secure Joint Computation on the COPA Framework\nAbstract: Performance of distributed data center applications can be improved through use of FPGA-based SmartNICs, which provide additional functionality and enable higher bandwidth communication. Until lately, however, the lack of a simple approach for customizing SmartNICs to application requirements has limited the potential benefits. Intel's Configurable Network Protocol Accelerator (COPA) provides a customizable FPGA framework that integrates both hardware and software development to improve computation and communication performance. In this first case study, we demonstrate the capabilities of the COPA framework with an application from cryptography -- secure Multi-Party Computation (MPC) -- that utilizes hardware accelerators connected directly to host memory and the COPA network. We find that using the COPA framework gives significant improvements to both computation and communication as compared to traditional implementations of MPC that use CPUs and NICs. A single MPC accelerator running on COPA enables more than 17Gbps of communication bandwidth while using only 1% of Stratix 10 resources. We show that utilizing the COPA framework enables multiple MPC accelerators running in parallel to fully saturate a 100Gbps link enabling higher performance compared to traditional NICs.", "field": "cs", "label": 1}
{"text": "Title: Completing the Asymptotic Classification of Mostly Symmetric Short Step Walks in an Orthant\nAbstract: In recent years, the techniques of analytic combinatorics in several variables (ACSV) have been applied to determine asymptotics for several families of lattice path models restricted to the orthant $\\mathbb{N}^d$ and defined by step sets $\\mathcal{S}\\subset\\{-1,0,1\\}^d\\setminus\\{\\mathbf{0}\\}$. Using the theory of ACSV for smooth singular sets, Melczer and Mishna determined asymptotics for the number of walks in any model whose set of steps $\\mathcal{S}$ is \"highly symmetric\" (symmetric over every axis). Building on this work, Melczer and Wilson determined asymptotics for all models where $\\mathcal{S}$ is \"mostly symmetric\" (symmetric over all but one axis) *except* for models whose set of steps have a vector sum of zero but are not highly symmetric. In this paper we complete the asymptotic classification of the mostly symmetric case by analyzing a family of saddle-point-like integrals whose amplitudes are singular near their saddle points.", "field": "math", "label": 0}
{"text": "Title: Failures and Fixes: A Study of Software System Incident Response\nAbstract: This paper presents the results of a research study related to software system failures, with the goal of understanding how we might better evolve, maintain and support software systems in production. We have qualitatively analyzed thirty incidents: fifteen collected through in depth interviews with engineers, and fifteen sampled from publicly published incident reports (generally produced as part of postmortem reviews). Our analysis focused on understanding and categorizing how failures occurred, and how they were detected, investigated and mitigated. We also captured analytic insights related to the current state of the practice and associated challenges in the form of 11 key observations. For example, we observed that failures can cascade through a system leading to major outages; and that often engineers do not understand the scaling limits of systems they are supporting until those limits are exceeded. We argue that the challenges we have identified can lead to improvements to how systems are engineered and supported.", "field": "cs", "label": 1}
{"text": "Title: Inverse questions for the large sieve\nAbstract: Suppose that an infinite set $A$ occupies at most $\\frac{1}{2}(p+1)$ residue classes modulo $p$, for every sufficiently large prime $p$. The squares, or more generally the integer values of any quadratic, are an example of such a set. By the large sieve inequality the number of elements of $A$ that are at most $X$ is $O(X^{1/2})$, and the quadratic examples show that this is sharp. The simplest form of the inverse large sieve problem asks whether they are the only examples. We prove a variety of results and formulate various conjectures in connection with this problem, including several improvements of the large sieve bound when the residue classes occupied by $A$ have some additive structure. Unfortunately we cannot solve the problem itself.", "field": "math", "label": 1}
{"text": "Title: The \"exponential\" torsion of superelliptic Jacobians\nAbstract: Let $J$ be the Jacobian of a superelliptic curve defined by the equation $y^{\\ell} = f(x)$, where $f$ is a separable polynomial of degree non-divisible by $\\ell$. In this article we study the \"exponential\" (i.e. $\\ell$-power) torsion of $J$. In particular, under some mild conditions on the polynomial $f$, we determine the image of the associated $\\ell$-adic representation up to the determinant. We show also that the image of the determinant is contained in an explicit $\\mathbb Z_{\\ell}$-lattice with a finite index. As an application, we prove the Mumford-Tate conjecture for a generic superelliptic Jacobian of the above type.", "field": "math", "label": 0}
{"text": "Title: Regular polygraphs and the Simpson conjecture\nAbstract: We prove Carlos Simpson's \"semi-strictification\" (or \"weak unit\") conjecture in the case of infinity-groupoids. More precisely, we introduce two precise versions of the conjecture, the \"general\" and the \"regular\" conjecture, involving two different notions of \"non-unital categories\". The \"general\" version involve infinity-categories where absolutely all composition operations (horizontal, vertical and whiskering) are defined and compatible, the \"regular\" version involve infinity-categories where all the composition operations corresponding to \"regular\" pasting diagram are defined and compatible. In both case we construct (weak) model structures on these categories such that fibrant objects have weak units and weak inverse. We prove the regular version of the conjecture using the original strategy of Kapranov and Voevodsky, together with our previous work on polygraphs. The general version cannot be proved by these methods and is still open. In order to do this we also study some subtle property of the combinatorics of polygraphs, and we construct a new counting function for polygraphs, inspired by previous work of Makkai.", "field": "math", "label": 1}
{"text": "Title: Sharp phase transition for random loop models on trees\nAbstract: We investigate the random loop model on the $d$-ary tree. For $d \\geq 3$, we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive rigorous bounds that in principle allow to determine the value of the critical parameter with arbitrary precision. Additionally, we prove the existence of an asymptotic expansion for the critical parameter in terms of $d^{-1}$. The corresponding coefficients can be determined in a schematic way and we calculated them up to order $6$.", "field": "math", "label": 1}
{"text": "Title: Hörmander properties of discrete time Markov processes\nAbstract: We present an abstract framework for establishing smoothing properties within a specific class of inhomogeneous discrete-time Markov processes. These properties, in turn, serve as a basis for demonstrating the existence of a density function for our process or more precisely for a regularized version of it. They can also be exploited to show its total variation convergence towards the solution of a Stochastic Differential Equation as the time step between two observations of our discrete time Markov process tends to zero. The distinctive feature of our methodology lies in the exploration of smoothing properties under a local weak H\\\"ormander type condition satisfied by the discrete-time Markov process. Our H\\\"ormander property is demonstrated to align with the standard local weak H\\\"ormander associated to the Stochastic Differential Equation which is the total variation limit of our discrete time Markov process.", "field": "math", "label": 0}
{"text": "Title: Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators\nAbstract: Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature.", "field": "math", "label": 0}
{"text": "Title: Learning to Prompt with Text Only Supervision for Vision-Language Models\nAbstract: Foundational vision-language models such as CLIP are becoming a new paradigm in vision, due to their excellent generalization abilities. However, adapting these models for downstream tasks while maintaining their generalization remains a challenge. In literature, one branch of methods adapts CLIP by learning prompts using visual information. While effective, most of these works require labeled data which is not practical, and often struggle to generalize towards new datasets due to over-fitting on the source data. An alternative approach resorts to training-free methods by generating class descriptions from large language models (LLMs) and perform prompt ensembling. However, these methods often generate class specific prompts that cannot be transferred to other classes, which incur higher costs by generating LLM descriptions for each class separately. In this work, we propose to combine the strengths of these both streams of methods by learning prompts using only text data derived from LLMs. As supervised training of prompts is not trivial due to absence of images, we develop a training approach that allows prompts to extract rich contextual knowledge from LLM data. Moreover, with LLM contextual data mapped within the learned prompts, it enables zero-shot transfer of prompts to new classes and datasets potentially cutting the LLM prompt engineering cost. To the best of our knowledge, this is the first work that learns generalized prompts using text only data. We perform extensive evaluations on 4 benchmarks where our method improves over prior ensembling works while being competitive to those utilizing labeled images. Our code and pre-trained models are available at https://github.com/muzairkhattak/ProText.", "field": "cs", "label": 0}
{"text": "Title: Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ Fail Statistical Tests for Linearity\nAbstract: L'Ecuyer & Simard's Big Crush statistical test suite has revealed statistical flaws in many popular random number generators including Marsaglia's Xorshift generators. Vigna recently proposed some 64-bit variations on the Xorshift scheme that are further scrambled (i.e., Xorshift1024*, Xorshift1024+, Xorshift128+, Xoroshiro128+). Unlike their unscrambled counterparts, they pass Big Crush when interleaving blocks of 32 bits for each 64-bit word (most significant, least significant, most significant, least significant, etc.). We report that these scrambled generators systematically fail Big Crush---specifically the linear-complexity and matrix-rank tests that detect linearity---when taking the 32 lowest-order bits in reverse order from each 64-bit word.", "field": "cs", "label": 1}
{"text": "Title: Logic of temporal attribute implications\nAbstract: We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and prove that the entailment problem is NP-hard and belongs to EXPSPACE. We show that by restricting to predictive formulas, the entailment problem is decidable in pseudo-linear time.", "field": "cs", "label": 1}
{"text": "Title: The Art of Deception: Robust Backdoor Attack using Dynamic Stacking of Triggers\nAbstract: The area of Machine Learning as a Service (MLaaS) is experiencing increased implementation due to recent advancements in the AI (Artificial Intelligence) industry. However, this spike has prompted concerns regarding AI defense mechanisms, specifically regarding potential covert attacks from third-party providers that cannot be entirely trusted. Recent research has uncovered that auditory backdoors may use certain modifications as their initiating mechanism. DynamicTrigger is introduced as a methodology for carrying out dynamic backdoor attacks that use cleverly designed tweaks to ensure that corrupted samples are indistinguishable from clean. By utilizing fluctuating signal sampling rates and masking speaker identities through dynamic sound triggers (such as the clapping of hands), it is possible to deceive speech recognition systems (ASR). Our empirical testing demonstrates that DynamicTrigger is both potent and stealthy, achieving impressive success rates during covert attacks while maintaining exceptional accuracy with non-poisoned datasets.", "field": "cs", "label": 0}
{"text": "Title: Nuclei instance segmentation and classification in histopathology images with StarDist\nAbstract: Instance segmentation and classification of nuclei is an important task in computational pathology. We show that StarDist, a deep learning nuclei segmentation method originally developed for fluorescence microscopy, can be extended and successfully applied to histopathology images. This is substantiated by conducting experiments on the Lizard dataset, and through entering the Colon Nuclei Identification and Counting (CoNIC) challenge 2022, where our approach achieved the first spot on the leaderboard for the segmentation and classification task for both the preliminary and final test phase.", "field": "cs", "label": 1}
{"text": "Title: Twisted Rokhlin property for mapping class groups\nAbstract: In this paper, generalising the idea of the Rokhlin property, we explore the concept of the twisted Rokhlin property of topological groups. A topological group is said to exhibit the twisted Rokhlin property if, for each automorphism $\\phi$ of the group, there exists a $\\phi$-twisted conjugacy class that is dense in the group. We provide a complete classification of connected orientable infinite-type surfaces without boundaries whose mapping class groups possess the twisted Rokhlin property. Additionally, we prove that the mapping class groups of the remaining surfaces do not admit any dense $\\phi$-twisted conjugacy class for any automorphism $\\phi$. This supplements the recent work of Lanier and Vlamis on the Rokhlin property of big mapping class groups. We also prove that the mapping class group of each connected orientable infinite-type surface without boundary possesses the $R_\\infty$-property.", "field": "math", "label": 0}
{"text": "Title: Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption\nAbstract: This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \\begin{eqnarray*} \\begin{array}{llc} u_t=\\Delta u-\\chi\\nabla\\cdot (u\\nabla v)+\\kappa u-\\mu u^2,\\\\ v_t=\\Delta v-uv, \\end{array} \\end{eqnarray*} in $N$-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large $\\mu$ and prove that for any $\\mu>0$ there exists a weak solution. Moreover, in the case of $\\kappa>0$ convergence to the constant equilibrium $(\\frac{\\kappa}{\\mu},0)$ is shown.", "field": "math", "label": 1}
{"text": "Title: Design and Implementation Considerations for a Virtual File System Using an Inode Data Structure\nAbstract: Virtual file systems are a tool to centralize and mobilize a file system that could otherwise be complex and consist of multiple hierarchies, hard disks, and more. In this paper, we discuss the design of Unix-based file systems and how this type of file system layout using inode data structures and a disk emulator can be implemented as a single-file virtual file system in Linux. We explore the ways that virtual file systems are vulnerable to security attacks and introduce straightforward solutions that can be implemented to help prevent or mitigate the consequences of such attacks.", "field": "cs", "label": 0}
{"text": "Title: The Rank of the Odd Normal Out\nAbstract: Say we have a collection of independent random variables $X_0, ... , X_n$, where $X_0 \\sim \\mathcal{N}(\\mu_0, \\sigma_0^2)$, but $X_i \\sim \\mathcal{N}(\\mu, \\sigma^2)$, for $1 \\leq i \\leq n$. We characterize the distribution of $R_0 := 1 + \\sum_{i=1}^{n} \\mathbf{1}\\{X_i \\leq X_0\\}$, the rank of the random variable whose distribution potentially differs from that of the others -- the odd normal out. We show that $R_0 - 1$ is approximately beta-binomial, an approximation that becomes equality as $\\sigma/\\sigma_0$ or $(\\mu-\\mu_0)/\\sigma_0$ become large or small. The intra-class correlation of the approximating beta-binomial depends on $\\Pr(X_1 \\leq X_0)$ and $\\Pr(X_1 \\leq X_0, X_2 \\leq X_0)$. Our approach relies on the conjugacy of the beta distribution for the binomial: $\\Phi((X_0-\\mu)/\\sigma)$ is approximately $\\mathrm{Beta}(\\alpha(\\sigma/\\sigma_0, (\\mu-\\mu_0)/\\sigma_0), \\beta(\\sigma/\\sigma_0, (\\mu-\\mu_0)/\\sigma_0))$ for functions $\\alpha, \\beta > 0$. We study the distributions of the in-normal ranks. Throughout, simulations corroborate the formulae we derive.", "field": "math", "label": 0}
{"text": "Title: Stochastic PDEs involving a bilaplacian operator\nAbstract: In this article, we study the existence and uniqueness problem for linear Stochastic PDEs involving a bilaplacian operator. Our results on the existence and uniqueness are obtained through an application of a Monotonicity inequality, which we also prove here. As an application of these results, we also obtain a probabilistic representation of the solution for a linear PDE involving the bilaplacian operator.", "field": "math", "label": 0}
{"text": "Title: On Probabilistic Completeness of Probabilistic Cell Decomposition\nAbstract: Probabilistic Cell Decomposition (PCD) is a probabilistic path planning method combining the concepts of approximate cell decomposition with probabilistic sampling. It has been shown that the use of lazy evaluation techniques and supervised sampling in important areas result in a high performance path planning method. Even if it was postulated before that PCD is probabilistically complete, we present a detailed proof of probabilistic completeness here for the first time.", "field": "cs", "label": 1}
{"text": "Title: Fully Automated Image De-fencing using Conditional Generative Adversarial Networks\nAbstract: Image de-fencing is one of the important aspects of recreational photography in which the objective is to remove the fence texture present in an image and generate an aesthetically pleasing version of the same image without the fence texture. In this paper, we aim to develop an automated and effective technique for fence removal and image reconstruction using conditional Generative Adversarial Networks (cGANs). These networks have been successfully applied in several domains of Computer Vision focusing on image generation and rendering. Our initial approach is based on a two-stage architecture involving two cGANs that generate the fence mask and the inpainted image, respectively. Training of these networks is carried out independently and, during evaluation, the input image is passed through the two generators in succession to obtain the de-fenced image. The results obtained from this approach are satisfactory, but the response time is long since the image has to pass through two sets of convolution layers. To reduce the response time, we propose a second approach involving only a single cGAN architecture that is trained using the ground-truth of fenced de-fenced image pairs along with the edge map of the fenced image produced by the Canny Filter. Incorporation of the edge map helps the network to precisely detect the edges present in the input image, and also imparts it an ability to carry out high quality de-fencing in an efficient manner, even in the presence of a fewer number of layers as compared to the two-stage network. Qualitative and quantitative experimental results reported in the manuscript reveal that the de-fenced images generated by the single-stage de-fencing network have similar visual quality to those produced by the two-stage network. Comparative performance analysis also emphasizes the effectiveness of our approach over state-of-the-art image de-fencing techniques.", "field": "cs", "label": 1}
{"text": "Title: Stanley decompositions of modules of covariants\nAbstract: For a complex reductive group $H$ with finite-dimensional representations $W$ and $U$, the module of covariants for $W$ of type $U$ is the space of all $H$-equivariant polynomial functions $W \\longrightarrow U$. In this paper, we take $H$ to be one of the classical groups $\\operatorname{GL}(V)$, $\\operatorname{Sp}(V)$, or $\\operatorname{O}(V)$ arising in Howe's dual pair setting, where $W$ is a direct sum of copies of $V$ and $V^*$. Our main result is a uniform combinatorial model for Stanley decompositions of the modules of covariants, using visualizations that we call jellyfish. Our decompositions allow us to interpret the Hilbert series as a positive combination of rational expressions which have concrete combinatorial interpretations in terms of lattice paths; significantly, this interpretation does not depend on the Cohen-Macaulay property. As a corollary, we recover a major result of Nishiyama-Ochiai-Taniguchi (2001) regarding the Bernstein degree of unitary highest weight $(\\mathfrak{g},K)$-modules. We also extend our methods to compute the Hilbert series of the invariant rings for the groups $\\operatorname{SL}(V)$ and $\\operatorname{SO}(V)$, as well as the Wallach representations of type ADE.", "field": "math", "label": 0}
{"text": "Title: Optimal Placement of Dynamic Var Sources by Using Empirical Controllability Covariance\nAbstract: In this paper, the empirical controllability covariance (ECC), which is calculated around the considered operating condition of a power system, is applied to quantify the degree of controllability of system voltages under specific dynamic var source locations. An optimal dynamic var source placement method addressing fault-induced delayed voltage recovery (FIDVR) issues is further formulated as an optimization problem that maximizes the determinant of ECC. The optimization problem is effectively solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search algorithm. The proposed method is tested on an NPCC 140-bus system and the results show that the proposed method with fault specified ECC can solve the FIDVR issue caused by the most severe contingency with fewer dynamic var sources than the Voltage Sensitivity Index (VSI) based method. The proposed method with fault unspecified ECC does not depend on the settings of the contingency and can address more FIDVR issues than VSI method when placing the same number of SVCs under different fault durations. It is also shown that the proposed method can help mitigate voltage collapse.", "field": "math", "label": 1}
{"text": "Title: DEM: A Method for Certifying Deep Neural Network Classifier Outputs in Aerospace\nAbstract: Software development in the aerospace domain requires adhering to strict, high-quality standards. While there exist regulatory guidelines for commercial software in this domain (e.g., ARP-4754 and DO-178), these do not apply to software with deep neural network (DNN) components. Consequently, it is unclear how to allow aerospace systems to benefit from the deep learning revolution. Our work here seeks to address this challenge with a novel, output-centric approach for DNN certification. Our method employs statistical verification techniques, and has the key advantage of being able to flag specific inputs for which the DNN's output may be unreliable - so that they may be later inspected by a human expert. To achieve this, our method conducts a statistical analysis of the DNN's predictions for other, nearby inputs, in order to detect inconsistencies. This is in contrast to existing techniques, which typically attempt to certify the entire DNN, as opposed to individual outputs. Our method uses the DNN as a black-box, and makes no assumptions about its topology. We hope that this work constitutes another step towards integrating DNNs in safety-critical applications - especially in the aerospace domain, where high standards of quality and reliability are crucial.", "field": "cs", "label": 0}
{"text": "Title: Towards a Formal Modelling, Analysis, and Verification of a Clone Node Attack Detection Scheme in the Internet of Things\nAbstract: In a clone node attack, an attacker attempted to physically capture the devices to gather sensitive information to conduct various insider attacks. Several solutions for detecting clone node attacks on IoT networks have been presented in the viewpoints above. These solutions are focused on specific system designs, processes, and feature sets and act as a high-level abstraction of underlying system architectures based on a few performance requirements. However, critical features like formal analysis, modelling, and verification are frequently overlooked in existing proposed solutions aimed at verifying the correctness and robustness of systems in order to ensure that no problematic scenarios or anomalies exist. This paper presents a formal analysis, modelling, and verification of our existing proposed clone node attack detection scheme in IoT. Firstly, we modelled the architectural components of the proposed scheme using High-Level Petri Nets (HLPNs) and then mapped them using their specified functionalities. Secondly, we defined and analysed the behavioural properties of the proposed scheme using Z specification language. Furthermore, we used the Satisfiability Modulo Theories Library (SMT-Lib) and the Z3 Solver to validate and demonstrate the overall functionality of the proposed scheme. Finally, in addition to modelling and analysis, this work employs Coloured Petri Nets (CPNs), which combine Petri Nets with a high-level programming language, making them more suitable for large-scale system modelling. To perform the simulations in CPN, we used both timed and untimed models, where timed models are used to evaluate performance, and untimed models are used to validate logical validity.", "field": "cs", "label": 1}
{"text": "Title: Stable determination of the initial data in an IBVP for the wave equation outside a non-trapping obstacle\nAbstract: We establish a double logarithmic stability inequality for the problem of determining the initial data in an IBVP for the wave equation outside a non-trapping obstacle from two localized measurements.", "field": "math", "label": 0}
{"text": "Title: Hopf algebras with enough quotients\nAbstract: A family of algebra maps $H\\to A_i$ whose common domain is a Hopf algebra is said to be jointly inner faithful if it does not factor simultaneously through a proper Hopf quotient of $H$. We show that tensor and free products of jointly inner faithful maps of Hopf algebras are again jointly inner faithful, generalizing a number of results in the literature on torus generation of compact quantum groups.", "field": "math", "label": 1}
{"text": "Title: On two open questions for extension bundles\nAbstract: In this paper we give positive answers for two open questions on extension bundles over weighted projective lines, raised by Kussin, Lenzing and Meltzer in the paper ``Triangle singularities, ADE-chains and weighted projective lines''.", "field": "math", "label": 0}
{"text": "Title: CLASS-M: Adaptive stain separation-based contrastive learning with pseudo-labeling for histopathological image classification\nAbstract: Histopathological image classification is an important task in medical image analysis. Recent approaches generally rely on weakly supervised learning due to the ease of acquiring case-level labels from pathology reports. However, patch-level classification is preferable in applications where only a limited number of cases are available or when local prediction accuracy is critical. On the other hand, acquiring extensive datasets with localized labels for training is not feasible. In this paper, we propose a semi-supervised patch-level histopathological image classification model, named CLASS-M, that does not require extensively labeled datasets. CLASS-M is formed by two main parts: a contrastive learning module that uses separated Hematoxylin and Eosin images generated through an adaptive stain separation process, and a module with pseudo-labels using MixUp. We compare our model with other state-of-the-art models on two clear cell renal cell carcinoma datasets. We demonstrate that our CLASS-M model has the best performance on both datasets. Our code is available at github.com/BzhangURU/Paper_CLASS-M/tree/main", "field": "cs", "label": 0}
{"text": "Title: A noncommutative Davis' decomposition for martingales\nAbstract: We prove an analogue of the classical Davis' decomposition for martingales in noncommutative L_p-spaces, involving the square functions. We also determine the dual space of the noncommutative conditioned Hardy space \\h_1. We further extend this latter result to the case 1<p<2.", "field": "math", "label": 1}
{"text": "Title: A two-stage stochastic programming model for electric substation flood mitigation prior to an imminent hurricane\nAbstract: We present a stochastic programming model for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation.", "field": "math", "label": 0}
{"text": "Title: Improving the Deployment of Recycling Classification through Efficient Hyper-Parameter Analysis\nAbstract: The paradigm of automated waste classification has recently seen a shift in the domain of interest from conventional image processing techniques to powerful computer vision algorithms known as convolutional neural networks (CNN). Historically, CNNs have demonstrated a strong dependency on powerful hardware for real-time classification, yet the need for deployment on weaker embedded devices is greater than ever. The work in this paper proposes a methodology for reconstructing and tuning conventional image classification models, using EfficientNets, to decrease their parameterisation with no trade-off in model accuracy and develops a pipeline through TensorRT for accelerating such models to run at real-time on an NVIDIA Jetson Nano embedded device. The train-deployment discrepancy, relating how poor data augmentation leads to a discrepancy in model accuracy between training and deployment, is often neglected in many papers and thus the work is extended by analysing and evaluating the impact real world perturbations had on model accuracy once deployed. The scope of the work concerns developing a more efficient variant of WasteNet, a collaborative recycling classification model. The newly developed model scores a test-set accuracy of 95.8% with a real world accuracy of 95%, a 14% increase over the original. Our acceleration pipeline boosted model throughput by 750% to 24 inferences per second on the Jetson Nano and real-time latency of the system was verified through servomotor latency analysis.", "field": "cs", "label": 1}
{"text": "Title: Normal operators for momentum ray transforms, I: The inversion formula\nAbstract: The momentum ray transform $I_m^k$ integrates a rank $m$ symmetric tensor field $f$ on $\\mathbb R^n$ over lines with the weight $t^k$, $I_m^kf(x,\\xi)=\\int_{-\\infty}^\\infty t^k\\langle f(x+t\\xi),\\xi^m\\rangle\\,\\mathrm{d}t$. We compute the normal operator $N_m^k=(I_m^k){}^*I_m^k$ and present an inversion formula recovering a rank $m$ tensor field $f$ from the data $(N_m^0f,\\dots,N_m^mf)$.", "field": "math", "label": 0}
{"text": "Title: On Classes of Fredholm Type Operators\nAbstract: Given an idempotent $p$ in a Banach algebra and following the study in \\cite{P50} of p-invertibility, we consider here left p-invertibility, right p-invertibility and p-invertibility in the Calkin Algebra $\\mathcal{C}(X),$ where $X$ is a Banach space. Then we define and study left and right generalized Drazin invertibility and we characterize left and right Drazin invertible elements in the Calkin algebra. Globally, this leads to define and characterize the classes of P-Fredholm, pseudo B-Fredholm and weak B-Fredholm operators.", "field": "math", "label": 0}
{"text": "Title: Strategic Bidding Wars in On-chain Auctions\nAbstract: The Ethereum block-building process has changed significantly since the emergence of Proposer-Builder Separation. Validators access blocks through a marketplace, where block builders bid for the right to construct the block and earn MEV (Maximal Extractable Value) rewards in an on-chain competition, known as the MEV-boost auction. While more than 90% of blocks are currently built via MEV-Boost, trade-offs between builders' strategic behaviors and auction design remain poorly understood. In this paper we address this gap. We introduce a game-theoretic model for MEV-Boost auctions and use simulations to study different builders' bidding strategies observed in practice. We study various strategic interactions and auction setups and evaluate how the interplay between critical elements such as access to MEV opportunities and improved connectivity to relays impact bidding performance. Our results demonstrate the importance of latency on the effectiveness of builders' strategies and the overall auction outcome from the proposer's perspective.", "field": "cs", "label": 0}
{"text": "Title: The Weyl law for algebraic tori\nAbstract: We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus $T$ with bounded analytic conductor. The analytic conductor which we use is defined via the local Langlands correspondence for tori by choosing a finite dimensional complex algebraic representation of the $L$-group of $T$. Our results therefore fit into a general framework of counting automorphic representations on reductive groups by analytic conductor.", "field": "math", "label": 1}
{"text": "Title: Space reduction techniques for the $3$-wise Kemeny problem\nAbstract: Kemeny's rule is one of the most studied and well-known voting schemes with various important applications in computational social choice and biology. Recently, Kemeny's rule was generalized via a set-wise approach by Gilbert et. al. This paradigm presents interesting advantages in comparison with Kemeny's rule since not only pairwise comparisons but also the discordance between the winners of subsets of three alternatives are also taken into account in the definition of the $3$-wise Kendall-tau distance between two rankings. In spite of the NP-hardness of the 3-wise Kemeny problem which consists of computing the set of $3$-wise consensus rankings, namely rankings whose total $3$-wise Kendall-tau distance to a given voting profile is minimized, we establish in this paper several generalizations of the Major Order Theorems, as obtained by Milosz and Hamel for Kemeny's rule, for the $3$-wise Kemeny voting schemes to achieve a substantial search space reduction by efficiently determining in polynomial time the relative orders of pairs of alternatives. Essentially, our theorems quantify precisely the nontrivial property that if the preference for an alternative over another one in an election is strong enough, not only in the head-to-head competition but even when taking into account one or two more alternatives, then the relative order of these two alternatives in all $3$-wise consensus rankings must be as expected. As an application, we also obtain an improvement of the Major Order Theorems for Kememy's rule. Moreover, we show that the well-known $3/4$-majority rule of Betzler et al. for Kemeny's rule is only valid in general for elections with no more than $5$ alternatives with respect to the $3$-wise Kemeny scheme. Several simulations and tests of our algorithms on real-world and uniform data are provided.", "field": "cs", "label": 0}
{"text": "Title: A Deep Dive on the Impact of COVID-19 in Software Development\nAbstract: Context: COVID-19 pandemic has impacted different business sectors around the world. Objective. This study investigates the impact of COVID-19 on software projects and software development professionals. Method: We conducted a mining software repository study based on 100 GitHub projects developed in Java using ten different metrics. Next, we surveyed 279 software development professionals for better understanding the impact of COVID-19 on daily activities and wellbeing. Results: We identified 12 observations related to productivity, code quality, and wellbeing. Conclusions: Our findings highlight that the impact of COVID-19 is not binary (reduce productivity vs. increase productivity) but rather a spectrum. For many of our observations, substantial proportions of respondents have differing opinions from each other. We believe that more research is needed to uncover specific conditions that cause certain outcomes to be more prevalent.", "field": "cs", "label": 1}
{"text": "Title: Scalable network reconstruction in subquadratic time\nAbstract: Network reconstruction consists in determining the unobserved pairwise couplings between $N$ nodes given only observational data on the resulting behavior that is conditioned on those couplings -- typically a time-series or independent samples from a graphical model. A major obstacle to the scalability of algorithms proposed for this problem is a seemingly unavoidable quadratic complexity of $O(N^2)$, corresponding to the requirement of each possible pairwise coupling being contemplated at least once, despite the fact that most networks of interest are sparse, with a number of non-zero couplings that is only $O(N)$. Here we present a general algorithm applicable to a broad range of reconstruction problems that achieves its result in subquadratic time, with a data-dependent complexity loosely upper bounded by $O(N^{3/2}\\log N)$, but with a more typical log-linear complexity of $O(N\\log^2N)$. Our algorithm relies on a stochastic second neighbor search that produces the best edge candidates with high probability, thus bypassing an exhaustive quadratic search. In practice, our algorithm achieves a performance that is many orders of magnitude faster than the quadratic baseline, allows for easy parallelization, and thus enables the reconstruction of networks with hundreds of thousands and even millions of nodes and edges.", "field": "cs", "label": 0}
{"text": "Title: Second-order Approximation of Exponential Random Graph Models\nAbstract: Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\\\"os-R\\'enyi random graphs, where edges are independent. In this paper, to distinguish ERGMs from Erd\\\"os-R\\'enyi random graphs, we consider second-order approximations of ERGMs using two-stars and triangles. We prove that the second-order approximation indeed achieves second-order accuracy in the triangle-free case. The new approximation is formally obtained by Hoeffding decomposition and rigorously justified using Stein's method.", "field": "math", "label": 0}
{"text": "Title: An analysis of training and generalization errors in shallow and deep networks\nAbstract: This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in the case of regression problems when each unit evaluates a periodic activation function. We argue that the minimal expected value of the square loss is inappropriate to measure the generalization error in approximation of compositional functions in order to take full advantage of the compositional structure. Instead, we measure the generalization error in the sense of maximum loss, and sometimes, as a pointwise error. We give estimates on exactly how many parameters ensure both zero training error as well as a good generalization error. We prove that a solution of a regularization problem is guaranteed to yield a good training error as well as a good generalization error and estimate how much error to expect at which test data.", "field": "cs", "label": 1}
{"text": "Title: Edge-Linear First-Order Dependency Parsing with Undirected Minimum Spanning Tree Inference\nAbstract: The run time complexity of state-of-the-art inference algorithms in graph-based dependency parsing is super-linear in the number of input words (n). Recently, pruning algorithms for these models have shown to cut a large portion of the graph edges, with minimal damage to the resulting parse trees. Solving the inference problem in run time complexity determined solely by the number of edges (m) is hence of obvious importance. We propose such an inference algorithm for first-order models, which encodes the problem as a minimum spanning tree (MST) problem in an undirected graph. This allows us to utilize state-of-the-art undirected MST algorithms whose run time is O(m) at expectation and with a very high probability. A directed parse tree is then inferred from the undirected MST and is subsequently improved with respect to the directed parsing model through local greedy updates, both steps running in O(n) time. In experiments with 18 languages, a variant of the first-order MSTParser (McDonald et al., 2005b) that employs our algorithm performs very similarly to the original parser that runs an O(n^2) directed MST inference.", "field": "cs", "label": 1}
{"text": "Title: Symmetry and asymmetry between positive and negative square energies of graphs\nAbstract: The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. We answer some questions previously asked about $s^{+}$ and $s^{-}$ and suggest several further avenues of research.", "field": "math", "label": 0}
{"text": "Title: Generalized domination structure in cubic graphs\nAbstract: In this paper, we consider generalized domination structure in graphs, which stipulates the structure of a minimum dominating set. Two cycles of length 0 mod 3 intersecting with one path are the constituents of the domination structure and by taking every three vertices on the cycles we can obtain a minimum dominating set. For a cubic graph, we construct generalized domination structure by adding edges in a certain way. We prove that the minimum dominating set of a cubic graph is determined in polynomial time.", "field": "math", "label": 1}
{"text": "Title: Adaptive Belief Discretization for POMDP Planning\nAbstract: Partially Observable Markov Decision Processes (POMDP) is a widely used model to represent the interaction of an environment and an agent, under state uncertainty. Since the agent does not observe the environment state, its uncertainty is typically represented through a probabilistic belief. While the set of possible beliefs is infinite, making exact planning intractable, the belief space's complexity (and hence planning complexity) is characterized by its covering number. Many POMDP solvers uniformly discretize the belief space and give the planning error in terms of the (typically unknown) covering number. We instead propose an adaptive belief discretization scheme, and give its associated planning error. We furthermore characterize the covering number with respect to the POMDP parameters. This allows us to specify the exact memory requirements on the planner, needed to bound the value function error. We then propose a novel, computationally efficient solver using this scheme. We demonstrate that our algorithm is highly competitive with the state of the art in a variety of scenarios.", "field": "cs", "label": 1}
{"text": "Title: On perturbations of singular complex analytic curves\nAbstract: Suppose $V$ is a singular complex analytic curve inside $\\mathbb{C}^{2}$. We investigate when a singular or non-singular complex analytic curve $W$ inside $\\mathbb{C}^{2}$ with sufficiently small Hausdorff distance $d_{H}(V, W)$ from $V$ must intersect $V$. We obtain a sufficient condition on $W$ which when satisfied gives an affirmative answer to our question. More precisely, we show the intersection is non-empty for any such $W$ that admits at most one non-normal crossing type discriminant point associated with some proper projection. As an application, we prove a special case of the higher-dimensional analog, and also a holomorphic multifunction analog of a result by Lyubich-Peters.", "field": "math", "label": 0}
{"text": "Title: On the maximum of the weighted binomial sum $(1+a)^{-r}\\sum_{i=0}^{r}\\binom{m}{i}a^{i}$\nAbstract: Recently, Glasby and Paseman considered the following sequence of binomial sums $\\{2^{-r}\\sum_{i=0}^{r}\\binom{m}{i}\\}_{r=0}^{m}$ and showed that this sequence is unimodal and attains its maximum value at $r=\\lfloor\\frac{m}{3}\\rfloor+1$ for $m\\in\\mathbb{Z}_{\\geq0}\\setminus\\{0,3,6,9,12\\}$. They also analyzed the asymptotic behavior of the maximum value of the sequence as $m$ approaches infinity. In the present work, we generalize their results by considering the sequence $\\{(1+a)^{-r}\\sum_{i=0}^{r}\\binom{m}{i}a^{i}\\}_{r=0}^{m}$ for integers $a \\geq 1$. We also consider a family of discrete probability distributions that naturally arises from this sequence.", "field": "math", "label": 0}
{"text": "Title: Short Squeeze in DeFi Lending Market: Decentralization in Jeopardy?\nAbstract: Anxiety levels in the Aave community spiked in November 2022 as Avi Eisenberg performed an attack on Aave. Eisenberg attempted to short the CRV token by using funds borrowed on the protocol to artificially deflate the value of CRV. While the attack was ultimately unsuccessful, it left the Aave community scared and even raised question marks regarding the feasibility of large lending platforms under decentralized governance. In this work, we analyze Avi Eisenberg's actions and show how he was able to artificially lower the price of CRV by selling large quantities of borrowed CRV for stablecoins on both decentralized and centralized exchanges. Despite the failure of his attack, it still led to irretrievable debt worth more than 1.5 Mio USD at the time and, thereby, quadrupled the protocol's irretrievable debt. Furthermore, we highlight that his attack was enabled by the vast proportion of CRV available to borrow as well as Aave's lending protocol design hindering rapid intervention. We stress Eisenberg's attack exposes a predicament of large DeFi lending protocols: limit the scope or compromise on 'decentralization'.", "field": "cs", "label": 1}
{"text": "Title: Normalized solutions to the Chern-Simons-Schrödinger system: the supercritical case\nAbstract: We are concerned with the existence of normalized solutions for a class of generalized Chern-Simons-Schr\\\"{o}dinger type problems with supercritical exponential growth $$ -\\Delta u +\\lambda u+A_0 u+\\sum\\limits_{j=1}^2A_j^2 u=f(u),\\quad \\partial_1A_2-\\partial_2A_1=-\\frac{1}{2}|u|^2,\\quad \\partial_1A_1+\\partial_2A_2=0,\\quad \\partial_1A_0=A_2|u|^2,\\quad \\partial_2A_0=-A_1|u|^2,\\quad \\int_{\\mathbb{R}^2}|u|^2dx=a^2, $$ where $a\\neq0$, $\\lambda\\in \\mathbb{R}$ is known as the Lagrange multiplier and $f\\in C^1(\\mathbb{R})$ denotes the nonlinearity that fulfills the supercritical exponential growth in the Trudinger-Moser sense at infinity. Under suitable assumptions, combining the constrained minimization approach together with the homotopy stable family and elliptic regularity theory, we obtain that the problem has at least a ground state solution.", "field": "math", "label": 0}
{"text": "Title: Image of Lie polynomial of degree $2$ evaluated on Nilpotent Lie algebra\nAbstract: We delineate the image of multilinear Lie polynomial of degree $2$ evaluated on $L$ where $L$ is a finite-dimensional nilpotent Lie algebra over field $k$ with $\\dim L' \\leq 4$.", "field": "math", "label": 1}
{"text": "Title: Synchrony and Anti-synchrony in Weighted Networks\nAbstract: We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a dynamical systems perspective by associating to each network a set of continuous dynamical systems, the ones that respect the graph structure of the network. For weighted networks it is natural for the admissible coupled cell systems to have an additive input structure. We present a characterization of the synchrony subspaces and the anti-synchrony subspaces for a weighted network depending on the restrictions that are imposed to their admissible input-additive coupled cell systems. These subspaces are flow-invariant by those systems and are generalized polydiagonal subspaces, that is, are characterized by conditions on the cell coordinates of the types $x_i = x_j$ and/or $x_k = -x_l$ and/or $x_m=0$. The existence and identification of the synchrony and anti-synchony subspaces for a weighted network are deeply relevant from the applications and dynamics point of view. Our characterization of the synchrony and anti-synchrony subspaces of a weighted network follows from our results where we give necessary and sufficient conditions for a generalized polydiagonal to be left invariant by the adjacency matrix and/or the Laplacian matrix of the network.", "field": "math", "label": 1}
{"text": "Title: In Lieu of Privacy: Anonymous Contact Tracing\nAbstract: We present Tracer Tokens, a hardware token of privacy-preserving contact tracing utilizing Exposure Notification \\cite{GAEN} protocol. Through subnetworks, we show that any disease spread by proximity can be traced such as seasonal flu, cold, regional strains of COVID-19, or Tuberculosis. Further, we show this protocol to notify $n^n$ users in parallel, providing a speed of information unmatched by current contact tracing methods.", "field": "cs", "label": 1}
{"text": "Title: Channel Estimation for FAS-assisted Multiuser mmWave Systems\nAbstract: This letter investigates the challenge of channel estimation in a multiuser millimeter-wave (mmWave) time-division duplexing (TDD) system. In this system, the base station (BS) employs a multi-antenna uniform linear array (ULA), while each mobile user is equipped with a fluid antenna system (FAS). Accurate channel state information (CSI) plays a crucial role in the precise placement of antennas in FAS. Traditional channel estimation methods designed for fixed-antenna systems are inadequate due to the high dimensionality of FAS. To address this issue, we propose a low-sample-size sparse channel reconstruction (L3SCR) method, capitalizing on the sparse propagation paths characteristic of mmWave channels. In this approach, each fluid antenna only needs to switch and measure the channel at a few specific locations. By observing this reduced-dimensional data, we can effectively extract angular and gain information related to the sparse channel, enabling us to reconstruct the full CSI. Simulation results demonstrate that our proposed method allows us to obtain precise CSI with minimal hardware switching and pilot overhead. As a result, the system sum-rate approaches the upper bound achievable with perfect CSI.", "field": "cs", "label": 0}
{"text": "Title: Modulus representation of the Riemann xi-function and equivalent inequalities for the Riemann hypothesis\nAbstract: We derive a representation of the modulus of the Riemann xi-function and present purely analytical inequalities which are equivalent to the Riemann hypothesis. We also discuss polynomial approximations of the inequalities.", "field": "math", "label": 0}
{"text": "Title: IoT in the Era of Generative AI: Vision and Challenges\nAbstract: Equipped with sensing, networking, and computing capabilities, Internet of Things (IoT) such as smartphones, wearables, smart speakers, and household robots have been seamlessly weaved into our daily lives. Recent advancements in Generative AI exemplified by GPT, LLaMA, DALL-E, and Stable Difussion hold immense promise to push IoT to the next level. In this article, we share our vision and views on the benefits that Generative AI brings to IoT, and discuss some of the most important applications of Generative AI in IoT-related domains. Fully harnessing Generative AI in IoT is a complex challenge. We identify some of the most critical challenges including high resource demands of the Generative AI models, prompt engineering, on-device inference, offloading, on-device fine-tuning, federated learning, security, as well as development tools and benchmarks, and discuss current gaps as well as promising opportunities on enabling Generative AI for IoT. We hope this article can inspire new research on IoT in the era of Generative AI.", "field": "cs", "label": 0}
{"text": "Title: On Model Compression for Neural Networks: Framework, Algorithm, and Convergence Guarantee\nAbstract: Model compression is a crucial part of deploying neural networks (NNs), especially when the memory and storage of computing devices are limited in many applications. This paper focuses on two model compression techniques: low-rank approximation and weight pruning in neural networks, which are very popular nowadays. However, training NN with low-rank approximation and weight pruning always suffers significant accuracy loss and convergence issues. In this paper, a holistic framework is proposed for model compression from a novel perspective of nonconvex optimization by designing an appropriate objective function. Then, we introduce NN-BCD, a block coordinate descent (BCD) algorithm to solve the nonconvex optimization. One advantage of our algorithm is that an efficient iteration scheme can be derived with closed-form, which is gradient-free. Therefore, our algorithm will not suffer from vanishing/exploding gradient problems. Furthermore, with the Kurdyka-{\\L}ojasiewicz (K{\\L}) property of our objective function, we show that our algorithm globally converges to a critical point at the rate of O(1/k), where k denotes the number of iterations. Lastly, extensive experiments with tensor train decomposition and weight pruning demonstrate the efficiency and superior performance of the proposed framework. Our code implementation is available at https://github.com/ChenyangLi-97/NN-BCD", "field": "cs", "label": 0}
{"text": "Title: The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps\nAbstract: We consider MRL maps (Markov-Renyi-L\\\"uroth), a class of interval maps with infinitely many branches that can have parabolic fixed points. We prove that for every MRL map $T$, the Lyapunov spectrum can be expressed in terms of the Legendre transform of the topological pressure of $-t\\log|T'|$, generalizing previous results in the area. We also show that the Lyapunov spectrum coincides with a function directly related to the Newton-Raphson method applied to the topological pressure of $-t\\log|T'|$.", "field": "math", "label": 0}
{"text": "Title: Entropy and the Kullback-Leibler Divergence for Bayesian Networks: Computational Complexity and Efficient Implementation\nAbstract: Bayesian networks (BNs) are a foundational model in machine learning and causal inference. Their graphical structure can handle high-dimensional problems, divide them into a sparse collection of smaller ones, underlies Judea Pearl's causality, and determines their explainability and interpretability. Despite their popularity, there are almost no resources in the literature on how to compute Shannon's entropy and the Kullback-Leibler (KL) divergence for BNs under their most common distributional assumptions. In this paper, we provide computationally efficient algorithms for both by leveraging BNs' graphical structure, and we illustrate them with a complete set of numerical examples. In the process, we show it is possible to reduce the computational complexity of KL from cubic to quadratic for Gaussian BNs.", "field": "cs", "label": 0}
{"text": "Title: Zero-one law for directional transience of one dimensional excited random walks\nAbstract: The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner [8].", "field": "math", "label": 1}
{"text": "Title: Better and Simpler Lower Bounds for Differentially Private Statistical Estimation\nAbstract: We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\\alpha \\le O(1)$, estimating the covariance of a Gaussian up to spectral error $\\alpha$ requires $\\tilde{\\Omega}\\left(\\frac{d^{3/2}}{\\alpha \\varepsilon} + \\frac{d}{\\alpha^2}\\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\\alpha \\le O\\left(\\frac{1}{\\sqrt{d}}\\right)$, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded $k$th moments requires $\\tilde{\\Omega}\\left(\\frac{d}{\\alpha^{k/(k-1)} \\varepsilon} + \\frac{d}{\\alpha^2}\\right)$ samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of $k = 2$. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples.", "field": "math", "label": 0}
{"text": "Title: Limit Theorems for the Fractional Non-homogeneous Poisson Process\nAbstract: The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse $\\alpha$-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional non-homogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation.", "field": "math", "label": 1}
{"text": "Title: Euler's Theorem for Regular CW-Complexes\nAbstract: For strongly connected, pure $n$-dimensional regular CW-complexes, we show that {\\it evenness} (each $(n{-}1)$-cell is contained in an even number of $n$-cells) is equivalent to generalizations of both cycle decomposition and traversability.", "field": "math", "label": 0}
{"text": "Title: On the Law of Large Numbers and Convergence Rates for the Discrete Fourier Transform of Random Fields\nAbstract: We study the Marcinkiewicz-Zygmund strong law of large numbers for the cubic partial sums of the discrete Fourier transform of random fields. We establish Marcinkiewicz-Zygmund types rate of convergence for the discrete Fourier transform of random fields under weaker conditions than identical distribution.", "field": "math", "label": 0}
{"text": "Title: Strong universality, recurrence, and analytic P-ideals in dynamical systems\nAbstract: Given a dynamical system $(X,T)$ and a family $\\mathsf{I}\\subseteq \\mathcal{P}(\\omega)$ of \"small\" sets of nonnegative integers, a point $x \\in X$ is said to be $\\mathsf{I}$-strong universal if for each $y \\in X$ there exists a subsequence $(T^nx: n \\in A)$ of its orbit which is convergent to $y$ and, in addition, the set of indexes $A$ is \"not small,\" that is, $A\\notin \\mathsf{I}$. An analoguous definition is given for $\\mathsf{I}$-strong recurrence. In this work, we provide several structural properties and relationships between $\\mathsf{I}$-strong universality, $\\mathsf{I}$-strong recurrence, and the corresponding ordinary notions of $\\mathsf{I}$-universality and $\\mathsf{I}$-recurrence. As applications, we provide sufficient conditions which ensure the equivalence between the above notions and the property that each nonempty open set contains some cluster point of some orbit. In addition, we show that if $T$ is a homomorphism on a Fr\\'{e}chet space $X$ and there exists a dense set of vectors with null orbit, then for each $y \\in X$ the set of all vectors $x \\in X$ such that $\\lim_{n \\in A}T^nx=y$ for some $A\\subseteq \\omega$ with nonzero upper asymptotic density is either empty or comeager. In the special case of linear dynamical systems on Banach spaces with a dense set of uniformly recurrent vectors, we obtain that $T$ is upper frequently hypercyclic if and only if there exists a hypercyclic vector $x \\in X$ for which $\\lim_{n \\in A}T^nx=0$ for some $A\\subseteq \\omega$ with nonzero upper asymptotic density.", "field": "math", "label": 0}
{"text": "Title: Phase transitions of McKean-Vlasov SDEs in Multi-well Landscapes\nAbstract: Phase transitions and critical behaviour of a class of MV-SDEs, whose concomitant non-local Fokker-Planck equation includes the Granular Media equation with quadratic interaction potential as a special case, is studied. By careful analysis of an implicit auxiliary integral equation, it is shown for a wide class of potentials that below a certain `critical threshold' there are exactly as many stationary measures as extrema of the potential, while above another the stationary measure is unique, and consequently phase transition(s) between. For symmetric bistable potentials, these critical thresholds are proven to be equal and a strictly increasing function of the aggregation parameter. Additionally, a simple condition is provided for symmetric multi-well potentials with an arbitrary number of extrema to demonstrate analogous behaviour. This answers, with considerably more generality, a conjecture of Tugaut [Stochastics, 86:2, 257-284]. To the best of our knowledge many of these results are novel. Others simplify the proofs of known results whilst greatly increasing their applicability.", "field": "math", "label": 0}
{"text": "Title: On the Ramsey number of the double star\nAbstract: The double star $S(m_1,m_2)$ is obtained from joining the centres of a star with $m_1$ leaves and a star with $m_2$ leaves. We give a short proof of a new upper bound on the two-colour Ramsey number of $S(m_1,m_2)$, for positive $m_1,m_2$ fulfilling $(\\sqrt 5+1)m_2/2 < m_1 < 3m_2$. Our result implies that for all positive $m$, the Ramsey number of the double star $S(2m,m)$ is at most $4.275m$.", "field": "math", "label": 0}
{"text": "Title: Asynchronous Downlink Massive MIMO Networks: A Stochastic Geometry Approach\nAbstract: Massive multiple-input multiple-output (MIMO) is recognized as a promising technology for the next generation of wireless networks because of its potential to increase the spectral efficiency. In initial studies of massive MIMO, the system has been considered to be perfectly synchronized throughout the entire cells. However, perfect synchronization may be hard to attain in practice. Therefore, we study a massive MIMO system whose cells are not synchronous to each other, while transmissions in a cell are still synchronous. We analyze an asynchronous downlink massive MIMO system in terms of the coverage probability and the ergodic rate by means of the stochastic geometry tool. For comparison, we also obtain the results for the synchronous systems. In addition, we investigate the effect of the uplink power control and the number of pilot symbols on the downlink ergodic rate, and we observe that there is an optimal value for the number of pilot symbols maximizing the downlink ergodic rate of a cell. Our results also indicate that, compared to the cases with synchronous transmission, the downlink ergodic rate is more sensitive to the uplink power control in the asynchronous mode.", "field": "cs", "label": 1}
{"text": "Title: Constructing Thick $B_h$-sets\nAbstract: A subset $A$ of a commutative semigroup $X$ is called a $B_h$ set in $X$ if the only solutions to $a_1+\\dots+a_h = b_1 + \\cdots +b_h$ (with $a_i,b_i \\in A$) are the trivial solutions $\\{a_1,\\dots,a_h\\} = \\{b_1,\\dots,b_h\\}$ (as multisets). With $h=2$ and $X={\\mathbb Z}$, these sets are also known as Sidon sets, Golomb Rulers, and Babcock sets. In this work, we generalize constructions of Bose-Chowla and Singer and give the resultant bounds on the diameter of a $k$ element $B_h$ set in $\\mathbb Z$ for small $k$. We conclude with a list of open problems.", "field": "math", "label": 0}
{"text": "Title: MindOpt Adapter for CPLEX Benchmarking Performance Analysis\nAbstract: This report provides a comprehensive analysis of the performance of MindOpt Adapter for CPLEX 12.9 in benchmark testing. CPLEX, recognized as a robust Mixed Integer Programming (MIP) solver, has faced some scrutiny regarding its performance on MIPLIB 2017 when configured to default settings. MindOpt Adapter aims to enhance CPLEX's performance by automatically applying improved configurations for solving optimization problems. Our testing demonstrates that MindOpt Adapter for CPLEX yields successfully solved 230 of the 240 problems in the MIPLIB 2017 benchmark set. This performance surpasses all the other solvers in terms of the number of problems solved and the geometric mean of running times. The report provides a comparison of the benchmark results against the outcomes achieved by CPLEX under its default configuration.", "field": "cs", "label": 0}
{"text": "Title: Detecting Unseen Falls from Wearable Devices using Channel-wise Ensemble of Autoencoders\nAbstract: A fall is an abnormal activity that occurs rarely, so it is hard to collect real data for falls. It is, therefore, difficult to use supervised learning methods to automatically detect falls. Another challenge in using machine learning methods to automatically detect falls is the choice of engineered features. In this paper, we propose to use an ensemble of autoencoders to extract features from different channels of wearable sensor data trained only on normal activities. We show that the traditional approach of choosing a threshold as the maximum of the reconstruction error on the training normal data is not the right way to identify unseen falls. We propose two methods for automatic tightening of reconstruction error from only the normal activities for better identification of unseen falls. We present our results on two activity recognition datasets and show the efficacy of our proposed method against traditional autoencoder models and two standard one-class classification methods.", "field": "cs", "label": 1}
{"text": "Title: Learning Traffic Speed Dynamics from Visualizations\nAbstract: Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the macroscopic traffic speed dynamics from these space-time visualizations, and demonstrate its application in the framework of traffic state estimation. Compared to existing estimation approaches, our approach allows a finer estimation resolution, eliminates the dependence on the initial conditions, and is agnostic to external factors such as traffic demand, road inhomogeneities and driving behaviors. Our model respects causality in traffic dynamics, which improves the robustness of estimation. We present the high-resolution traffic speed fields estimated for several freeway sections using the data obtained from the Next Generation Simulation Program (NGSIM) and German Highway (HighD) datasets. We further demonstrate the quality and utility of the estimation by inferring vehicle trajectories from the estimated speed fields, and discuss the benefits of deep neural network models in approximating the traffic dynamics.", "field": "cs", "label": 1}
{"text": "Title: A localization-delocalization transition for nonhomogeneous random matrices\nAbstract: We consider $N\\times N$ self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with $d$ nonzero entries per row. We show that such random matrices exhibit a canonical localization-delocalization transition near the edge of the spectrum: when $d\\gg\\log N$ the random matrix possesses a delocalized approximate top eigenvector, while when $d\\ll\\log N$ any approximate top eigenvector is localized. The key feature of this phenomenon is that it is universal with respect to the sparsity pattern, in contrast to the delocalization properties of exact eigenvectors which are sensitive to the specific sparsity pattern of the random matrix.", "field": "math", "label": 0}
{"text": "Title: Full instability of boundary layers with the Navier boundary condition\nAbstract: We consider the problem of the stability of the Navier-Stokes equations in $\\mathbb{T}\\times \\mathbb{R}_+$ near shear flows which are linearly unstable for the Euler equation. In \\cite{greniernguyen}, the authors prove an $L^{\\infty}$ instability result for the no-slip boundary condition which also denies the validity of the Prandtl boundary layer expansion. In this paper, we generalise this result to a Navier slip boundary condition with viscosity dependent slip length: $\\partial_y u =\\nu^{-\\gamma}u$ at $y=0$, where $\\gamma >1/2$. This range includes the physical slip rate $\\gamma=1$.", "field": "math", "label": 0}
{"text": "Title: Spectral-based Graph Neutral Networks for Complementary Item Recommendation\nAbstract: Modeling complementary relationships greatly helps recommender systems to accurately and promptly recommend the subsequent items when one item is purchased. Unlike traditional similar relationships, items with complementary relationships may be purchased successively (such as iPhone and Airpods Pro), and they not only share relevance but also exhibit dissimilarity. Since the two attributes are opposites, modeling complementary relationships is challenging. Previous attempts to exploit these relationships have either ignored or oversimplified the dissimilarity attribute, resulting in ineffective modeling and an inability to balance the two attributes. Since Graph Neural Networks (GNNs) can capture the relevance and dissimilarity between nodes in the spectral domain, we can leverage spectral-based GNNs to effectively understand and model complementary relationships. In this study, we present a novel approach called Spectral-based Complementary Graph Neural Networks (SComGNN) that utilizes the spectral properties of complementary item graphs. We make the first observation that complementary relationships consist of low-frequency and mid-frequency components, corresponding to the relevance and dissimilarity attributes, respectively. Based on this spectral observation, we design spectral graph convolutional networks with low-pass and mid-pass filters to capture the low-frequency and mid-frequency components. Additionally, we propose a two-stage attention mechanism to adaptively integrate and balance the two attributes. Experimental results on four e-commerce datasets demonstrate the effectiveness of our model, with SComGNN significantly outperforming existing baseline models.", "field": "cs", "label": 0}
{"text": "Title: Attackers reveal their arsenal: An investigation of adversarial techniques in CTI reports\nAbstract: Context: Cybersecurity vendors often publish cyber threat intelligence (CTI) reports, referring to the written artifacts on technical and forensic analysis of the techniques used by the malware in APT attacks. Objective: The goal of this research is to inform cybersecurity practitioners about how adversaries form cyberattacks through an analysis of adversarial techniques documented in cyberthreat intelligence reports. Dataset: We use 594 adversarial techniques cataloged in MITRE ATT\\&CK. We systematically construct a set of 667 CTI reports that MITRE ATT\\&CK used as citations in the descriptions of the cataloged adversarial techniques. Methodology: We analyze the frequency and trend of adversarial techniques, followed by a qualitative analysis of the implementation of techniques. Next, we perform association rule mining to identify pairs of techniques recurring in APT attacks. We then perform qualitative analysis to identify the underlying relations among the techniques in the recurring pairs. Findings: The set of 667 CTI reports documents 10,370 techniques in total, and we identify 19 prevalent techniques accounting for 37.3\\% of documented techniques. We also identify 425 statistically significant recurring pairs and seven types of relations among the techniques in these pairs. The top three among the seven relationships suggest that techniques used by the malware inter-relate with one another in terms of (a) abusing or affecting the same system assets, (b) executing in sequences, and (c) overlapping in their implementations. Overall, the study quantifies how adversaries leverage techniques through malware in APT attacks based on publicly reported documents. We advocate organizations prioritize their defense against the identified prevalent techniques and actively hunt for potential malicious intrusion based on the identified pairs of techniques.", "field": "cs", "label": 0}
{"text": "Title: Efficient Scenario Generation for Chance-constrained Economic Dispatch Considering Ambient Wind Conditions\nAbstract: Scenario generation is an effective data-driven method for solving chance-constrained optimization while ensuring desired risk guarantees with a finite number of samples. Crucial challenges in deploying this technique in the real world arise due to the absence of appropriate risk-tuning models tailored for the desired application. In this paper, we focus on designing efficient scenario generation schemes for economic dispatch in power systems. We propose a novel scenario generation method based on filtering scenarios using ambient wind conditions. These filtered scenarios are deployed incrementally in order to meet desired risk levels while using minimum resources. In order to study the performance of the proposed scheme, we illustrate the procedure on case studies performed for both 24-bus and 118-bus systems with real-world wind power forecasting data. Numerical results suggest that the proposed filter-and-increment scenario generation model leads to a precise and efficient solution for the chance-constrained economic dispatch problem.", "field": "math", "label": 0}
{"text": "Title: Simplicial $*$-modules and mild actions\nAbstract: We develop an analogue of the theory of $*$-modules in the world of simplicial sets, based on actions of a certain simplicial monoid $E\\mathcal M$ originally appearing in the construction of global algebraic $K$-theory. As our main results, we show that strictly commutative monoids with respect to a certain box product on these simplicial $*$-modules yield models of equivariantly and globally coherently commutative monoids, and we give a characterization of simplicial $*$-modules in terms of a certain mildness condition on the $E\\mathcal M$-action, relaxing the notion of tameness previously investigated by Sagave-Schwede and the first author.", "field": "math", "label": 0}
{"text": "Title: Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable\nAbstract: This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg. Comm. Comput. 11 (2001), 417-436], wherein Olver uses a moving frames approach to examine the action of a group on a curve within a generalization of jet space known as multispace. Here we seek to further study group actions on the multispace of curves by computing the infinitesimals for a given action. For the most part, we proceed formally, and produce in the multispace a recursion relation that closely mimics the previously known prolongation recursion relations for infinitesimals of a group action on jet space.", "field": "math", "label": 0}
{"text": "Title: Fractional non-homogeneous counting process\nAbstract: A new fractional non-homogeneous counting process has been introduced and developed using the Kilbas and Saigo three-parameter generalization of the Mittag-Leffler function. The probability distribution function of this process reproduces for certain set of the fractality parameters the famous Poisson and fractional Poisson probability distributions as well as the probability distribution function of a counting process displaying stretched exponential interarrival times distribution. Applications of the developed fractional non-homogeneous counting process cover fractional compound process, the generalization of combinatorial polynomials and numbers, statistics of the fractional non-homogeneous counting process and a new representation of the Kilbas and Saigo function.", "field": "math", "label": 0}
{"text": "Title: Maximum Likelihood With a Time Varying Parameter\nAbstract: We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in which the log-likelihood of the observations acts as time varying gain function. We prove convergence in mean-square error in a suitable neighbourhood of the unknown time varying parameter and illustrate the details of our findings in the case where data are generated from distributions belonging to the exponential family.", "field": "math", "label": 1}
{"text": "Title: On dual quaternions, dual split quaternions and Cartan-Schouten metrics on perfect Lie groups\nAbstract: We discuss Cartan-Schouten metrics (Riemannian or pseudo-Riemannian metrics that are parallel with respect to the Cartan-Schouten canonical connection) on perfect Lie groups. Applications are foreseen in Information Geometry. Throughout this work, the tangent bundle TG and the cotangent bundle T*G of a Lie group G, are always endowed with their Lie group structures induced by the right trivialization. We show that TG and T*G are isomorphic if G possesses a biinvariant Riemannian or pseudo-Riemannian metric. We also show that, if on a perfect Lie group, there exists a Cartan-Schouten metric, then it must be biinvariant. We compute all such metrics on the cotangent bundles of simple Lie groups. We further show the following. Endowed with their canonical Lie group structures, the set of unit dual quaternions is isomorphic to TSU(2), the set of unit dual split quaternions is isomorphic to T*SL(2,R). The group SE(3) of special rigid displacements of the Euclidean 3-space is isomorphic to T*SO(3). The group SE(2,1) of special rigid displacements of the Minkowski 3-space is isomorphic to T*SO(2,1). Some results on SE(3) by N. Miolane and X. Pennec, and M. Zefran, V. Kumar and C. Croke, are generalized to SE(2,1) and to T*G, for any simple Lie group G.", "field": "math", "label": 0}
{"text": "Title: The Zassenhaus variety of a reductive Lie algebra in positive characteristic\nAbstract: Let g be the Lie algebra of a connected reductive group G over an algebraically closed field k of characteristic p>0. Let $Z$ be the centre of the universal enveloping algebra U=U(g) of g. Its maximal spectrum is called the Zassenhaus variety of g. We show that, under certain mild assumptions on G, the field of fractions Frac(Z) of Z is G-equivariantly isomorphic to the function field of the dual space g* with twisted G-action. In particular Frac(Z) is rational. This confirms a conjecture J. Alev. Furthermore we show that Z is a unique factorisation domain, confirming a conjecture of A. Braun and C. Hajarnavis. Recently, A. Premet used the above result about Frac(Z), a result of Colliot-Thelene, Kunyavskii, Popov and Reichstein and reduction mod p arguments to show that the Gelfand-Kirillov conjecture cannot hold for simple complex Lie algebras that are not of type A, C or G_2.", "field": "math", "label": 1}
{"text": "Title: Optimal Hardy-weights for the $(p,A)$-Laplacian with a potential term\nAbstract: We construct new optimal $L^p$ Hardy-type inequalities for elliptic Schr\\\"odinger-type operators", "field": "math", "label": 1}
{"text": "Title: LMBot: Distilling Graph Knowledge into Language Model for Graph-less Deployment in Twitter Bot Detection\nAbstract: As malicious actors employ increasingly advanced and widespread bots to disseminate misinformation and manipulate public opinion, the detection of Twitter bots has become a crucial task. Though graph-based Twitter bot detection methods achieve state-of-the-art performance, we find that their inference depends on the neighbor users multi-hop away from the targets, and fetching neighbors is time-consuming and may introduce bias. At the same time, we find that after finetuning on Twitter bot detection, pretrained language models achieve competitive performance and do not require a graph structure during deployment. Inspired by this finding, we propose a novel bot detection framework LMBot that distills the knowledge of graph neural networks (GNNs) into language models (LMs) for graph-less deployment in Twitter bot detection to combat the challenge of data dependency. Moreover, LMBot is compatible with graph-based and graph-less datasets. Specifically, we first represent each user as a textual sequence and feed them into the LM for domain adaptation. For graph-based datasets, the output of LMs provides input features for the GNN, enabling it to optimize for bot detection and distill knowledge back to the LM in an iterative, mutually enhancing process. Armed with the LM, we can perform graph-less inference, which resolves the graph data dependency and sampling bias issues. For datasets without graph structure, we simply replace the GNN with an MLP, which has also shown strong performance. Our experiments demonstrate that LMBot achieves state-of-the-art performance on four Twitter bot detection benchmarks. Extensive studies also show that LMBot is more robust, versatile, and efficient compared to graph-based Twitter bot detection methods.", "field": "cs", "label": 0}
{"text": "Title: GIT-Mol: A Multi-modal Large Language Model for Molecular Science with Graph, Image, and Text\nAbstract: Large language models have made significant strides in natural language processing, enabling innovative applications in molecular science by processing textual representations of molecules. However, most existing language models cannot capture the rich information with complex molecular structures or images. In this paper, we introduce GIT-Mol, a multi-modal large language model that integrates the Graph, Image, and Text information. To facilitate the integration of multi-modal molecular data, we propose GIT-Former, a novel architecture that is capable of aligning all modalities into a unified latent space. We achieve a 5%-10% accuracy increase in properties prediction and a 20.2% boost in molecule generation validity compared to the baselines. With the any-to-language molecular translation strategy, our model has the potential to perform more downstream tasks, such as compound name recognition and chemical reaction prediction.", "field": "cs", "label": 0}
{"text": "Title: A note on Laguerre truncated polynomials and quadrature formula\nAbstract: In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in order to test the accuracy in the computation of the coefficients of the three-term recurrence relation, the zeros and weights, as well as the dependence on the parameter $z.$", "field": "math", "label": 0}
{"text": "Title: Optimal Decomposition and Recombination of Isostatic Geometric Constraint Systems for Designing Layered Materials\nAbstract: Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint systems, we describe an O(n^3) algorithm for a broad class of constraint systems that are isostatic or underconstrained. The algorithm achieves optimality by using the new notion of a canonical DR-plan that also meets various desirable, previously studied criteria. In addition, we leverage recent results on Cayley configuration spaces to show that the indecomposable systems---that are solved at the nodes of the optimal DR-plan by recombining solutions to child systems---can be minimally modified to become decomposable and have a small DR-plan, leading to efficient realization algorithms. We show formal connections to well-known problems such as completion of underconstrained systems. Well suited to these methods are classes of constraint systems that can be used to efficiently model, design and analyze quasi-uniform (aperiodic) and self-similar, layered material structures. We formally illustrate by modeling silica bilayers as body-hyperpin systems and cross-linking microfibrils as pinned line-incidence systems. A software implementation of our algorithms and videos demonstrating the software are publicly available online (visit http://cise.ufl.edu/~tbaker/drp/index.html.)", "field": "cs", "label": 1}
{"text": "Title: The bridge number of satellite knots, links, and spatial graphs in the 3-sphere and lens spaces\nAbstract: Let $T$ be a satellite knot, link, or spatial graph in a 3-manifold $M$ that is either $S^3$ or a lens space. Let $b_0$ and $b_1$ denote genus 0 and genus 1 bridge number, respectively. Suppose that $T$ has a companion knot $K$ and wrapping number $\\omega$ with respect to $K$. When $K$ is not a torus knot, we show that $b_1(T)\\geq \\omega b_1(K)$. There are previously known counter-examples if $K$ is a torus knot. Along the way, we generalize and give a new proof of Schubert's result that $b_0(T) \\geq \\omega b_0(K)$. We also prove versions of the theorem applicable to when $T$ is a ``lensed satellite'' or when there is a torus separating components of $T$.", "field": "math", "label": 0}
{"text": "Title: Towards Seamless Serverless Computing Across an Edge-Cloud Continuum\nAbstract: Serverless computing has emerged as an attractive paradigm due to the efficiency of development and the ease of deployment without managing any underlying infrastructure. Nevertheless, serverless computing approaches face numerous challenges to unlock their full potential in hybrid environments. To gain a deeper understanding and firsthand knowledge of serverless computing in edge-cloud deployments, we review the current state of open-source serverless platforms and compare them based on predefined requirements. We then design and implement a serverless computing platform with a novel edge orchestration technique that seamlessly deploys serverless functions across the edge and cloud environments on top of the Knative serverless platform. Moreover, we propose an offloading strategy for edge environments and four different functions for experimentation and showcase the performance benefits of our solution. Our results demonstrate that such an approach can efficiently utilize both cloud and edge resources by dynamically offloading functions from the edge to the cloud during high activity, while reducing the overall application latency and increasing request throughput compared to an edge-only deployment.", "field": "cs", "label": 0}
{"text": "Title: An Adaptive Incremental Gradient Method With Support for Non-Euclidean Norms\nAbstract: Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some large-scale optimization tasks. To overcome the problem, we propose and analyze several novel adaptive variants of the popular SAGA algorithm. Eventually, we design a variant of Barzilai-Borwein step-size which is tailored for the incremental gradient method to ensure memory efficiency and fast convergence. We establish its convergence guarantees under general settings that allow non-Euclidean norms in the definition of smoothness and the composite objectives, which cover a broad range of applications in machine learning. We improve the analysis of SAGA to support non-Euclidean norms, which fills the void of existing work. Numerical experiments on standard datasets demonstrate a competitive performance of the proposed algorithm compared with existing variance-reduced methods and their adaptive variants.", "field": "math", "label": 1}
{"text": "Title: Comparison of Syntactic Parsers on Biomedical Texts\nAbstract: Syntactic parsing is an important step in the automated text analysis which aims at information extraction. Quality of the syntactic parsing determines to a large extent the recall and precision of the text mining results. In this paper we evaluate the performance of several popular syntactic parsers in application to the biomedical text mining.", "field": "cs", "label": 1}
{"text": "Title: Sorting Can Exponentially Speed Up Pure Dynamic Programming\nAbstract: Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are \"pure\" in that they only perform basic operations, as min, max, +, but no conditional branchings via if-then-else in their recursion equations. It is known that any pure (min,+) DP algorithm solving the minimum weight spanning tree problem on undirected n-vertex graphs must perform at least $2^{\\Omega(\\sqrt{n})}$ operations. We show that this problem can be solved by a pure (min,max,+) DP algorithm performing only $O(n^3)$ operations. The algorithm is essentially a (min,max) algorithm: addition operations are only used to output the final values. The presence of both min and max operations means that now DP algorithms can sort: this explains the title of the paper.", "field": "cs", "label": 1}
{"text": "Title: Manipulating Trajectory Prediction with Backdoors\nAbstract: Autonomous vehicles ought to predict the surrounding agents' trajectories to allow safe maneuvers in uncertain and complex traffic situations. As companies increasingly apply trajectory prediction in the real world, security becomes a relevant concern. In this paper, we focus on backdoors - a security threat acknowledged in other fields but so far overlooked for trajectory prediction. To this end, we describe and investigate four triggers that could affect trajectory prediction. We then show that these triggers (for example, a braking vehicle), when correlated with a desired output (for example, a curve) during training, cause the desired output of a state-of-the-art trajectory prediction model. In other words, the model has good benign performance but is vulnerable to backdoors. This is the case even if the trigger maneuver is performed by a non-casual agent behind the target vehicle. As a side-effect, our analysis reveals interesting limitations within trajectory prediction models. Finally, we evaluate a range of defenses against backdoors. While some, like simple offroad checks, do not enable detection for all triggers, clustering is a promising candidate to support manual inspection to find backdoors.", "field": "cs", "label": 0}
{"text": "Title: Some results and a conjecture on certain subclasses of graphs according to the relations among certain energies, degrees and conjugate degrees of graphs\nAbstract: Let $G$ be a simple graph of order $n$ with degree sequence $(d)=(d_1,d_2,\\ldots,d_n)$ and conjugate degree sequence $(d^*)=(d_1^*,d_2^*,\\ldots,d_n^*)$. In \\cite{AkbariGhorbaniKoolenObudi2010,DasMojallalGutman2017} it was proven that $\\mathcal{E}(G)\\leq \\sum_{i=1}^{n} \\sqrt{d_i}$ and $\\sum_{i=1}^{n} \\sqrt{d_i^*} \\leq LEL(G) \\leq IE(G) \\leq \\sum_{i=1}^{n} \\sqrt{d_i}$, where $\\mathcal{E}(G)$, $LEL(G)$ and $IE(G)$ are the energy, the Laplacian-energy-like invariant and the incidence energy of $G$, respectively, and in \\cite{DasMojallalGutman2017} it was concluded that the class of all connected simple graphs of order $n$ can be dividend into four subclasses according to the position of $\\mathcal{E}(G)$ in the order relations above. Then, they proposed a problem about characterizing all graphs in each subclass. In this paper, we attack this problem. First, we count the number of graphs of order $n$ in each of four subclasses for every $1\\leq n \\leq 8$ using a Sage code. Second, we present a conjecture on the ratio of the number of graphs in each subclass to the number of all graphs of order $n$ as $n$ approaches the infinity. Finally, as a first partial solution to the problem, we determine subclasses to which a path, a complete graph and a cycle graph of order $n\\geq 1$ belong.", "field": "math", "label": 1}
{"text": "Title: Local-in-time strong solutions of the homogeneous Landau-Coulomb equation with $L^p$ initial datum\nAbstract: We consider the homogeneous Landau equation with Coulomb potential and general initial data $f_{in} \\in L^p$, where $p$ is arbitrarily close to $3/2$. We show the local-in-time existence and uniqueness of smooth solutions for such initial data. The constraint $p > 3/2$ has appeared in several related works and appears to be the minimal integrability assumption achievable with current techniques. We adapt recent ODE methods and conditional regularity results appearing in [arXiv:2303.02281] to deduce new short time $L^p \\to L^\\infty$ smoothing estimates. These estimates enable us to construct local-in-time smooth solutions for large $L^p$ initial data, and allow us to show directly conditional regularity results for solutions verifying \\emph{unweighted} Prodi-Serrin type conditions. As a consequence, we obtain additional stability and uniqueness results for the solutions we construct.", "field": "math", "label": 0}
{"text": "Title: Electromechanical phase-field fracture modelling of piezoresistive CNT-based composites\nAbstract: We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic tensor, fracture energy, electrical conductivity, and linear piezoresistive coefficients. These properties are inputted into a coupled electro-structural finite element model, which simulates the evolution of cracks based upon phase-field fracture. The coupled physical problem is solved in a monolithic manner, exploiting the robustness and efficiency of a quasi-Newton algorithm. 2D and 3D boundary value problems are simulated to illustrate the potential of the modelling framework in assessing the influence of defects on the electromechanical response of meso- and macro-scale smart structures. Case studies aim at shedding light into the interplay between fracture and the electromechanical material response and include parametric analyses, validation against experiments and the simulation of complex cracking conditions (multiple defects, crack merging). The presented numerical results showcase the efficiency and robustness of the computational framework, as well as its ability to model a large variety of structural configurations and damage patterns. The deformation-electrical-fracture finite element code developed is made freely available to download.", "field": "cs", "label": 1}
{"text": "Title: On upper bounds on expectations of gOSs based on DFR and DFRA distributions\nAbstract: We focus on the problem of establishing the optimal upper bounds on generalized order statistics which are based on the underlying cdf belonging to the family of distributions with decreasing failure rate and decreasing failure rate on the average. This issue has been previously considered by Bieniek [Projection bounds on expectations of generalized order statistics from DFR and DFRA families, Statistics, 2006; 40: 339--351], who established upper nonnegative mean-variance bounds with use of the projections of the compositions of density functions of the uniform generalized order statistic and the exponential distribution function onto the properly chosen convex cones. In this paper we obtain possibly negative upper bounds, by improving the zero bounds obtained by Bieniek for some particular cases of gOSs. We express the bounds in the scale units generated by the central absolute moments of arbitrary orders. We also describe the attainability conditions.", "field": "math", "label": 1}
{"text": "Title: Phase transition and diffusion among socially interacting self-propelled agents\nAbstract: We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large self-propulsion force limit, we provide evidence of a phase transition from disordered to ordered motion which manifests itself as a change of type of the limit model (from hyperbolic to diffusive) at the crossing of a critical noise intensity. In the hyperbolic regime, the resulting model, referred to as the `Self-Organized Hydrodynamics (SOH)', consists of a system of compressible Euler equations with a speed constraint. We show that the range of SOH models obtained by this limit is restricted. To waive this restriction, we compute the Navier-Stokes diffusive corrections to the hydrodynamic model. Adding these diffusive corrections, the limit of a large propulsion force yields unrestricted SOH models and offers an alternative to the derivation of the SOH using kinetic models with speed constraints.", "field": "math", "label": 1}
{"text": "Title: Universality for bounded degree spanning trees in randomly perturbed graphs\nAbstract: We solve a problem of Krivelevich, Kwan and Sudakov [SIAM Journal on Discrete Mathematics 31 (2017), 155-171] concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph $G_\\alpha$ on $n$ vertices with $\\delta(G_\\alpha)\\ge \\alpha n$ for $\\alpha>0$ and we add to it the binomial random graph $G(n,C/n)$, then with high probability the graph $G_\\alpha\\cup G(n,C/n)$ contains copies of all spanning trees with maximum degree at most $\\Delta$ simultaneously, where $C$ depends only on $\\alpha$ and $\\Delta$.", "field": "math", "label": 1}
{"text": "Title: On wormholes in the moduli space of surfaces\nAbstract: We study a certain wormholing phenomenon that takes place in the Koll\\'ar--Shepherd-Barron--Alexeev (KSBA) compactification of the moduli space of surfaces of general type. It occurs because of the appearance of particular extremal P-resolutions in surfaces on the KSBA boundary. We state a general wormhole conjecture, and we prove it for a wide range of cases. At the end, we discuss some topological properties and open questions.", "field": "math", "label": 1}
{"text": "Title: Model order reduction and sensitivity analysis for complex heat transfer simulations inside the human eyeball\nAbstract: Heat transfer in the human eyeball, a complex organ, is significantly influenced by various pathophysiological and external parameters. Particularly, heat transfer critically affects fluid behavior within the eye and ocular drug delivery processes. Overcoming the challenges of experimental analysis, this study introduces a comprehensive three-dimensional mathematical and computational model to simulate the heat transfer in a realistic geometry. Our work includes an extensive sensitivity analysis to address uncertainties and delineate the impact of different variables on heat distribution in ocular tissues. To manage the model's complexity, we employed a very fast model reduction technique with certified sharp error bounds, ensuring computational efficiency without compromising accuracy. Our results demonstrate remarkable consistency with experimental observations and align closely with existing numerical findings in the literature. Crucially, our findings underscore the significant role of blood flowand environmental conditions, particularly in the eye's internal tissues. Clinically, this model offers a promising tool for examining the temperature-related effects of various therapeutic interventions on the eye. Such insights are invaluable for optimizing treatment strategies in ophthalmology.", "field": "math", "label": 0}
{"text": "Title: Normal operators with highly incompatible off-diagonal corners\nAbstract: Let $\\mathcal{H}$ be a complex, separable Hilbert space, and $\\mathcal{B}(\\mathcal{H})$ denote the set of all bounded linear operators on $\\mathcal{H}$. Given an orthogonal projection $P \\in \\mathcal{B}(\\mathcal{H})$ and an operator $D \\in \\mathcal{B}(\\mathcal{H})$, we may write $D=\\begin{bmatrix} D_1& D_2 D_3 & D_4 \\end{bmatrix}$ relative to the decomposition $\\mathcal{H} = \\mathrm{ran}\\, P \\oplus \\mathrm{ran}\\, (I-P)$. In this paper we study the question: for which non-negative integers $j, k$ can we find a normal operator $D$ and an orthogonal projection $P$ such that $\\mathrm{rank}\\, D_2 = j$ and $\\mathrm{rank}\\, D_3 = k$? Complete results are obtained in the case where $\\mathrm{dim}\\, \\mathcal{H} < \\infty$, and partial results are obtained in the infinite-dimensional setting.", "field": "math", "label": 1}
{"text": "Title: Architectural Design for Secure Smart Contract Development\nAbstract: As time progresses, the need for more secure applications grows exponentially. The different types of sensitive information that is being transferred virtually has sparked a rise in systems that leverage blockchain. Different sectors are beginning to use this disruptive technology to evaluate the risks and benefits. Sectors like finance, medicine, higher education, and wireless communication have research regarding blockchain. Futhermore, the need for security standards in this area of research is pivotal. In recent past, several attacks on blockchain infrastructures have resulted in hundreds of millions dollars lost and sensitive information compromised. Some of these attacks include DAO attacks, bZx attacks, and Parity Multisignature Wallet Double Attacks which targeted vulnerabilities within smart contracts on the Ethereum network. These attacks exposed the weaknesses of current smart contract development practices which has led to the increase in distrust and adoption of systems that leverage blockchain for its functionality. In this paper, I identify common software vulnerabilities and attacks on blockchain infrastructures, thoroughly detail the smart contract development process and propose a model for ensuring a stronger security standard for future systems leveraging smart contracts. The purpose for proposing a model is to promote trust among end users in the system which is a foundational element for blockchain adoption in the future.", "field": "cs", "label": 0}
{"text": "Title: A multipartite analogue of Dilworth's Theorem\nAbstract: We prove that every partially ordered set on $n$ elements contains $k$ subsets $A_{1},A_{2},\\dots,A_{k}$ such that either each of these subsets has size $\\Omega(n/k^{5})$ and, for every $i<j$, every element in $A_{i}$ is less than or equal to every element in $A_{j}$, or each of these subsets has size $\\Omega(n/(k^{2}\\log n))$ and, for every $i \\not = j$, every element in $A_{i}$ is incomparable with every element in $A_{j}$ for $i\\ne j$. This answers a question of the first author from 2006. As a corollary, we prove for each positive integer $h$ there is $C_h$ such that for any $h$ partial orders $<_{1},<_{2},\\dots,<_{h}$ on a set of $n$ elements, there exists $k$ subsets $A_{1},A_{2},\\dots,A_{k}$ each of size at least $n/(k\\log n)^{C_{h}}$ such that for each partial order $<_{\\ell}$, either $a_{1}<_{\\ell}a_{2}<_{\\ell}\\dots<_{\\ell}a_{k}$ for any tuple of elements $(a_1,a_2,\\dots,a_k) \\in A_1\\times A_2\\times \\dots \\times A_k$, or $a_{1}>_{\\ell}a_{2}>_{\\ell}\\dots>_{\\ell}a_{k}$ for any $(a_1,a_2,\\dots,a_k) \\in A_1\\times A_2\\times \\dots \\times A_k$, or $a_i$ is incomparable with $a_j$ for any $i\\ne j$, $a_i\\in A_i$ and $a_j\\in A_j$. This improves on a 2009 result of Pach and the first author motivated by problems in discrete geometry.", "field": "math", "label": 0}
{"text": "Title: A complete characterization of spectra of the Randic matrix of level-wise regular trees\nAbstract: Let $G$ be a simple finite connected graph with vertex set $V(G) = \\{v_1,v_2,\\ldots,v_n\\}$. Denote the degree of vertex $v_i$ by $d_i$ for all $1 \\leq i \\leq n$. The Randi\\'c matrix of $G$, denoted by $R(G) = [r_{i,j}]$, is the $n \\times n$ matrix whose $(i,j)$-entry $r_{i,j}$ is $r_{i,j} = 1/\\sqrt{d_id_j}$ if $v_i$ and $v_j$ are adjacent in $G$ and 0 otherwise. A tree is a connected acyclic graph. A level-wise regular tree is a tree rooted at one vertex $r$ or two (adjacent) vertices $r$ and $r'$ in which all vertices with the minimum distance $i$ from $r$ or $r'$ have the same degree $m_i$ for $0 \\leq i \\leq h$, where $h$ is the height of $T$. In this paper, we give a complete characterization of the eigenvalues with their multiplicity of the Randi\\'c matrix of level-wise regular trees. We prove that the eigenvalues of the Randi\\'c matrix of a level-wise regular tree are the eigenvalues of the particular tridiagonal matrices, which are formed using the degree sequence $(m_0,m_1,\\ldots,m_{h-1})$ of level-wise regular trees.", "field": "math", "label": 0}
{"text": "Title: Grassroots Social Networking: Where Members Own and Control their Personal Information and Social Graph\nAbstract: Offering an architecture for social networking in which the members are in control of their personal information and social graph is an open challenge. Here we present a grassroots architecture for serverless, permissionless, peer-to-peer social networks termed Grassroots Social Networking that aims to address this challenge. The architecture is geared for roaming (address-changing) agents communicating over an unreliable network, e.g., smartphones communicating via UDP. The architecture incorporates (i) a decentralized social graph, where each member controls, maintains and stores only their local neighborhood in the graph; (ii) member-created feeds, with authors and followers who create and store the feeds; and (iii) a grassroots dissemination protocol, in which communication among members occurs only along the edges of the social graph. The architecture realizes these components using the blocklace data structure -- a distributed partially-ordered counterpart of the replicated totally-ordered blockchain. We provide two example Grassroots Social Networking protocols -- Twitter-like and WhatsApp-like -- and address their security (safety, liveness and privacy), spam/bot/deep-fake resistance, and implementation, demonstrating how server-based social networks could be supplanted by a grassroots architecture.", "field": "cs", "label": 0}
{"text": "Title: The homology of the partition algebras\nAbstract: We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with the number of nodes. Furthermore, we show that when the defining parameter $\\delta$ of the partition algebra is invertible, the homology of the partition algebra is in fact isomorphic to the homology of the symmetric group in all degrees. These results parallel those obtained for the Brauer algebras in the authors' earlier work, but with significant differences and difficulties in the inductive resolution and high acyclicity arguments required to prove them. Our results join the growing literature on homological stability for algebras, which now encompasses the Temperley-Lieb, Brauer and partition algebras, as well as the Iwahori-Hecke algebras of types A and B.", "field": "math", "label": 0}
{"text": "Title: Minimum Sobolev norm interpolation of derivative data\nAbstract: We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree $\\le n$ given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable and of high-order.", "field": "math", "label": 1}
{"text": "Title: Evaluating LLMs on Document-Based QA: Exact Answer Selection and Numerical Extraction using Cogtale dataset\nAbstract: Document-based Question-Answering (QA) tasks are crucial for precise information retrieval. While some existing work focus on evaluating large language models performance on retrieving and answering questions from documents, assessing the LLMs performance on QA types that require exact answer selection from predefined options and numerical extraction is yet to be fully assessed. In this paper, we specifically focus on this underexplored context and conduct empirical analysis of LLMs (GPT-4 and GPT-3.5) on question types, including single-choice, yes-no, multiple-choice, and number extraction questions from documents in zero-shot setting. We use the CogTale dataset for evaluation, which provide human expert-tagged responses, offering a robust benchmark for precision and factual grounding. We found that LLMs, particularly GPT-4, can precisely answer many single-choice and yes-no questions given relevant context, demonstrating their efficacy in information retrieval tasks. However, their performance diminishes when confronted with multiple-choice and number extraction formats, lowering the overall performance of the model on this task, indicating that these models may not yet be sufficiently reliable for the task. This limits the applications of LLMs on applications demanding precise information extraction from documents, such as meta-analysis tasks. These findings hinge on the assumption that the retrievers furnish pertinent context necessary for accurate responses, emphasizing the need for further research. Our work offers a framework for ongoing dataset evaluation, ensuring that LLM applications for information retrieval and document analysis continue to meet evolving standards.", "field": "cs", "label": 0}
{"text": "Title: Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation\nAbstract: We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the universal function approximation capability of ESN, it is shown that the reconstruction problem can be formulated as a fixed-point problem, in which the trajectory of the dynamical system is a fixed point of the ESN. An under-relaxed fixed-point iteration is proposed to reconstruct the nonlinear dynamics from a sparse observation. The proposed fixed-point ESN is tested against both univariate and multivariate chaotic dynamical systems by randomly removing up to 95% of the data. It is shown that the fixed-point ESN is able to reconstruct the complex dynamics from only 5 ~ 10% of the data. For a relatively simple non-chaotic dynamical system, the numerical experiments on a forced van der Pol oscillator show that it is possible to reconstruct the nonlinear dynamics from only 1~2% of the data.", "field": "cs", "label": 1}
{"text": "Title: Embedding 1-Planar Graphs in Ten Pages\nAbstract: Every planar graph has a 4-page book embedding and this bound is tight. We show that every 1-planar graph, which is a graph that admits a drawing with at most one crossing per edge, has a 10-page book embedding. In addition, four pages are sometimes necessary and always sufficient if the planar skeleton, obtained from a 1-planar drawing by removing all crossed edges, has a Hamiltonian cycle.", "field": "cs", "label": 0}
{"text": "Title: Efficient Communication in Federated Learning Using Floating-Point Lossy Compression\nAbstract: In the expanding realm of machine learning (ML) within edge computing, the efficient exchange of information in federated learning (FL) environments is paramount. FL's decentralized nature often leads to significant communication bottlenecks, particularly in settings where resources are limited. Traditional data compression techniques, such as quantization and pruning, provide partial solutions but can compromise model performance or necessitate costly retraining. Our paper addresses this issue through \\textit{FedSZ}, a novel lossy compression-based FL framework. \\textit{FedSZ} is designed to minimize the size of local model updates without impacting model performance. Our framework features a compression pipeline integrating data partitioning, lossy and lossless model parameters, metadata compression, and efficient serialization. We conduct a thorough evaluation of \\textit{FedSZ} utilizing a variety of lossy compressors, among which SZ2 emerged as the most effective, consistently performing well across diverse neural network architectures, including AlexNet, MobileNetV2, and ResNet50, and datasets such as CIFAR-10, Caltech101, and FMNIST. A relative error bound of 1E-2 balances compression and data integrity, achieving compression ratios ranging from $5.55\\mbox{--}12.61\\times$. Furthermore, we observed that the runtime overhead introduced by \\textit{FedSZ} is minimal, at less than $4.7\\%$, compared to a significant reduction in network transfer times, which we noted to exceed $13.3\\times$ reduction or saving of over $100$s in edge networks operating at 10Mbps. Our findings firmly establish the efficacy of \\textit{FedSZ}, offering valuable insights for achieving an optimal balance between communication efficiency and model performance in FL settings, particularly in edge computing environments.", "field": "cs", "label": 0}
{"text": "Title: Robustness Evaluation of Regression Tasks with Skewed Domain Preferences\nAbstract: In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common outcome. In many scientific contexts it is exactly these tail events that researchers are most interested in anticipating, so that adequate measures can be taken to prevent or attenuate a major impact on society. Despite such efforts, we have yet to provide definite answers to crucial issues in evaluating predictive solutions in domains such as weather, pollution, health. In this paper, we deal with two encapsulated problems simultaneously. First, assessing the performance of regression models when non-uniform preferences apply - not all values are equally relevant concerning the accuracy of their prediction, and there's a particular interest in the most extreme values. Second, assessing the robustness of models when dealing with uncertainty regarding the actual underlying distribution of values relevant for such problems. We show how different levels of relevance associated with target values may impact experimental conclusions, and demonstrate the practical utility of the proposed methods.", "field": "cs", "label": 1}
{"text": "Title: Synthetic Data in AI: Challenges, Applications, and Ethical Implications\nAbstract: In the rapidly evolving field of artificial intelligence, the creation and utilization of synthetic datasets have become increasingly significant. This report delves into the multifaceted aspects of synthetic data, particularly emphasizing the challenges and potential biases these datasets may harbor. It explores the methodologies behind synthetic data generation, spanning traditional statistical models to advanced deep learning techniques, and examines their applications across diverse domains. The report also critically addresses the ethical considerations and legal implications associated with synthetic datasets, highlighting the urgent need for mechanisms to ensure fairness, mitigate biases, and uphold ethical standards in AI development.", "field": "cs", "label": 0}
{"text": "Title: On the Uniqueness of Bayesian Coarse Correlated Equilibria in Standard First-Price and All-Pay Auctions\nAbstract: In first-price and all-pay auctions under the standard symmetric independent private-values model, we show that the unique Bayesian Coarse Correlated Equilibrium with symmetric, differentiable and strictly increasing bidding strategies is the unique strict Bayesian Nash Equilibrium. Interestingly, this result does not require assumptions on the prior distribution. The proof is based on a dual bound of the infinite-dimensional linear program. Numerical experiments without restrictions on bidding strategies show that for first-price auctions and discretisations up to 21 of the type and bid space, increasing discretisation sizes actually increase the concentration of Bayesian Coarse Correlated Equilibrium over the Bayesian Nash Equilibrium, so long as the prior c.d.f. is concave. Such a concentration is also observed for all-pay auctions, independent of the prior distribution. Overall, our results imply that the equilibria of these important class of auctions are indeed learnable.", "field": "cs", "label": 0}
{"text": "Title: Inductive Synthesis of Finite-State Controllers for POMDPs\nAbstract: We present a novel learning framework to obtain finite-state controllers (FSCs) for partially observable Markov decision processes and illustrate its applicability for indefinite-horizon specifications. Our framework builds on oracle-guided inductive synthesis to explore a design space compactly representing available FSCs. The inductive synthesis approach consists of two stages: The outer stage determines the design space, i.e., the set of FSC candidates, while the inner stage efficiently explores the design space. This framework is easily generalisable and shows promising results when compared to existing approaches. Experiments indicate that our technique is (i) competitive to state-of-the-art belief-based approaches for indefinite-horizon properties, (ii) yields smaller FSCs than existing methods for several models, and (iii) naturally treats multi-objective specifications.", "field": "cs", "label": 1}
{"text": "Title: Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels\nAbstract: We show the existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation for homogeneous kernels satisfying $C_1 \\left(x^{-a}y^{b}+x^{b}y^{-a}\\right)\\leq K\\left(x,y\\right)\\leq C_2\\left(x^{-a}y^{b}+x^{b}y^{-a}\\right)$ with $a>0$ and $b<1$. This covers especially the case of Smoluchowski's classical kernel $K(x,y)=(x^{1/3} + y^{1/3})(x^{-1/3} + y^{-1/3})$. For the proof of existence we first consider some regularized kernel $K_{\\epsilon}$ for which we construct a sequence of solutions $h_{\\epsilon}$. In a second step we pass to the limit $\\epsilon\\to 0$ to obtain a solution for the original kernel $K$. The main difficulty is to establish a uniform lower bound on $h_{\\epsilon}$. The basic idea for this is to consider the time-dependent problem and choosing a special test function that solves the dual problem.", "field": "math", "label": 1}
{"text": "Title: Inequalities about the area bounded by three cevian lines of a triangle\nAbstract: In the paper we prove generalization of Schl\\\"omilch's and Zetel's theorems about concurrent lines in a triangle. This generalization is obtained as a corollary of sharp geometric inequality about the ratio of triangular areas which is proved using discrete variant of H\\\"older's inequality. Also a new sharp refinement of J.F. Rigby's inequality, which itself generalized M\\\"obius theorem about the areas of triangles formed by cevians of a triangle, is proved.", "field": "math", "label": 0}
{"text": "Title: b-articulation points and b-bridges in strongly biconnected directed graphs\nAbstract: A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. This class of directed graphs was first introduced by Wu and Grumbach. Let $G=(V,E)$ be a strongly biconnected directed graph. An edge $e\\in E$ is a b-bridge if the subgraph $G\\setminus \\left\\lbrace e\\right\\rbrace =(V,E\\setminus \\left\\lbrace e\\right\\rbrace) $ is not strongly biconnected. A vertex $w\\in V$ is a b-articulation point if $G\\setminus \\left\\lbrace w\\right\\rbrace$ is not strongly biconnected, where $G\\setminus \\left\\lbrace w\\right\\rbrace$ is the subgraph obtained from $G$ by removing $w$. In this paper we study b-articulation points and b-bridges.", "field": "cs", "label": 1}
{"text": "Title: Gradient Methods Never Overfit On Separable Data\nAbstract: A line of recent works established that when training linear predictors over separable data, using gradient methods and exponentially-tailed losses, the predictors asymptotically converge in direction to the max-margin predictor. As a consequence, the predictors asymptotically do not overfit. However, this does not address the question of whether overfitting might occur non-asymptotically, after some bounded number of iterations. In this paper, we formally show that standard gradient methods (in particular, gradient flow, gradient descent and stochastic gradient descent) never overfit on separable data: If we run these methods for $T$ iterations on a dataset of size $m$, both the empirical risk and the generalization error decrease at an essentially optimal rate of $\\tilde{\\mathcal{O}}(1/\\gamma^2 T)$ up till $T\\approx m$, at which point the generalization error remains fixed at an essentially optimal level of $\\tilde{\\mathcal{O}}(1/\\gamma^2 m)$ regardless of how large $T$ is. Along the way, we present non-asymptotic bounds on the number of margin violations over the dataset, and prove their tightness.", "field": "cs", "label": 1}
{"text": "Title: SCALA: Sparsification-based Contrastive Learning for Anomaly Detection on Attributed Networks\nAbstract: Anomaly detection on attributed networks aims to find the nodes whose behaviors are significantly different from other majority nodes. Generally, network data contains information about relationships between entities, and the anomaly is usually embodied in these relationships. Therefore, how to comprehensively model complex interaction patterns in networks is still a major focus. It can be observed that anomalies in networks violate the homophily assumption. However, most existing studies only considered this phenomenon obliquely rather than explicitly. Besides, the node representation of normal entities can be perturbed easily by the noise relationships introduced by anomalous nodes. To address the above issues, we present a novel contrastive learning framework for anomaly detection on attributed networks, \\textbf{SCALA}, aiming to improve the embedding quality of the network and provide a new measurement of qualifying the anomaly score for each node by introducing sparsification into the conventional method. Extensive experiments are conducted on five benchmark real-world datasets and the results show that SCALA consistently outperforms all baseline methods significantly.", "field": "cs", "label": 0}
{"text": "Title: Asymptotic behavior of positive solutions of some nonlinear elliptic equations on cylinders\nAbstract: We establish quantitative asymptotic behavior of positive solutions of a family of nonlinear elliptic equations on the half cylinder near the end. This unifies the study of isolated singularities of some semilinear elliptic equations, such as the Yamabe equation, Hardy-H\\'enon equation etc.", "field": "math", "label": 1}
{"text": "Title: Twisted Yang-Baxter sets, cohomology theory, and application to knots\nAbstract: In this article, we introduce a notion of twisted set-theoretic Yang-Baxter solution, which is a triplet $(X,f,R)$, where $(X,R)$ is a Yang-Baxter set and $f:X \\to X$ is an automorphism of $(X,R)$. We present a cohomology theory for it, and use cocycles of twisted biquandles in amalgamation with Alexander numbering to construct state-sum invariant of knots and knotted surfaces. Additionally, we introduce a twisted version of cohomology theory for Yang-Baxter sets and give applications to knot theory.", "field": "math", "label": 0}
{"text": "Title: Bounds on the minimum distance of locally recoverable codes\nAbstract: We consider locally recoverable codes (LRCs) and aim to determine the smallest possible length $n=n_q(k,d,r)$ of a linear $[n,k,d]_q$-code with locality $r$. For $k\\le 7$ we exactly determine all values of $n_2(k,d,2)$ and for $k\\le 6$ we exactly determine all values of $n_2(k,d,1)$. For the ternary field we also state a few numerical results. As a general result we prove that $n_q(k,d,r)$ equals the Griesmer bound if the minimum Hamming distance $d$ is sufficiently large and all other parameters are fixed.", "field": "math", "label": 0}
{"text": "Title: Best Practices for Scientific Computing\nAbstract: Scientists spend an increasing amount of time building and using software. However, most scientists are never taught how to do this efficiently. As a result, many are unaware of tools and practices that would allow them to write more reliable and maintainable code with less effort. We describe a set of best practices for scientific software development that have solid foundations in research and experience, and that improve scientists' productivity and the reliability of their software.", "field": "cs", "label": 1}
{"text": "Title: GEqO: ML-Accelerated Semantic Equivalence Detection\nAbstract: Large scale analytics engines have become a core dependency for modern data-driven enterprises to derive business insights and drive actions. These engines support a large number of analytic jobs processing huge volumes of data on a daily basis, and workloads are often inundated with overlapping computations across multiple jobs. Reusing common computation is crucial for efficient cluster resource utilization and reducing job execution time. Detecting common computation is the first and key step for reducing this computational redundancy. However, detecting equivalence on large-scale analytics engines requires efficient and scalable solutions that are fully automated. In addition, to maximize computation reuse, equivalence needs to be detected at the semantic level instead of just the syntactic level (i.e., the ability to detect semantic equivalence of seemingly different-looking queries). Unfortunately, existing solutions fall short of satisfying these requirements. In this paper, we take a major step towards filling this gap by proposing GEqO, a portable and lightweight machine-learning-based framework for efficiently identifying semantically equivalent computations at scale. GEqO introduces two machine-learning-based filters that quickly prune out nonequivalent subexpressions and employs a semi-supervised learning feedback loop to iteratively improve its model with an intelligent sampling mechanism. Further, with its novel database-agnostic featurization method, GEqO can transfer the learning from one workload and database to another. Our extensive empirical evaluation shows that, on TPC-DS-like queries, GEqO yields significant performance gains-up to 200x faster than automated verifiers-and finds up to 2x more equivalences than optimizer and signature-based equivalence detection approaches.", "field": "cs", "label": 0}
{"text": "Title: Function approximation by deep networks\nAbstract: We show that deep networks are better than shallow networks at approximating functions that can be expressed as a composition of functions described by a directed acyclic graph, because the deep networks can be designed to have the same compositional structure, while a shallow network cannot exploit this knowledge. Thus, the blessing of compositionality mitigates the curse of dimensionality. On the other hand, a theorem called good propagation of errors allows to `lift' theorems about shallow networks to those about deep networks with an appropriate choice of norms, smoothness, etc. We illustrate this in three contexts where each channel in the deep network calculates a spherical polynomial, a non-smooth ReLU network, or another zonal function network related closely with the ReLU network.", "field": "cs", "label": 1}
{"text": "Title: Pre-foliations of co-degree one on $\\mathbb{P}^{2}_{\\mathbb{C}}$ with a flat Legendre transform\nAbstract: A holomorphic pre-foliation $\\mathscr{F}=\\ell\\boxtimes\\mathcal{F}$ of co-degree $1$ and degree $d$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$ is the data of a line $\\ell$ of $\\mathbb{P}^{2}_{\\mathbb{C}}$ and a holomorphic foliation $\\mathcal{F}$ on $\\mathbb{P }^{2}_{\\mathbb{C}}$ of degree $d-1.$ We study pre-foliations of co-degree $1$ on $\\mathbb{P}^{2}_{\\mathbb{ C}}$ with a flat Legendre transform (dual web). After having established some general results on the flatness of the dual $d$-web of a homogeneous pre-foliation of co-degree $1$ and degree $d$, we describe some explicit examples and we show that up to automorphism of $\\mathbb{P}^{2}_{\\mathbb{C}}$ there are two families and six examples of homogeneous pre-foliations of co-degree $1$ and degree $3$ on $\\mathbb {P}^{2}_{\\mathbb{C}}$ with a flat dual web. This allows us to prove an analogue for pre-foliations of co-degree $1$ and degree~$3$ of a result, obtained in collaboration with D. Mar\\'{\\i}n, on foliations of degree $3$ with non-degenerate singularities and a flat Legendre transform. We also show that the dual web of a reduced convex pre-foliation of co-degree $1$ on $\\mathbb{P}^{2}_{\\mathbb{C}}$ is flat. This is an analogue of a result on foliations of $\\mathbb{P}^{2}_{\\mathbb{C}}$ due to D. Mar\\'{\\i}n and J. V. Pereira.", "field": "math", "label": 0}
{"text": "Title: A minimum semi-degree sufficient condition for one-to-many disjoint path covers in semicomplete digraphs\nAbstract: Let $D$ be a digraph. We define the minimum semi-degree of $D$ as $\\delta^{0}(D) := \\min \\{\\delta^{+}(D), \\delta^{-}(D)\\}$. Let $k$ be a positive integer, and let $S = \\{s\\}$ and $T = \\{t_{1}, \\dots ,t_{k}\\}$ be any two disjoint subsets of $V(D)$. A set of $k$ internally disjoint paths joining source set $S$ and sink set $T$ that cover all vertices $D$ are called a one-to-many $k$-disjoint directed path cover ($k$-DDPC for short) of $D$. A digraph $D$ is semicomplete if for every pair $x,y$ of vertices of it, there is at least one arc between $x$ and $y$. In this paper, we prove that every semicomplete digraph $D$ of sufficiently large order $n$ with $\\delta^{0}(D) \\geq \\lceil (n+k-1)/2\\rceil$ has a one-to-many $k$-DDPC joining any disjoint source set $S$ and sink set $T$, where $S = \\{s\\}, T = \\{t_{1}, \\dots, t_{k}\\}$.", "field": "math", "label": 1}
{"text": "Title: Infinite transition solutions for an Allen-Cahn equation\nAbstract: We give another proof of a theorem of Rabinowitz and Stredulinsky obtaining infinite transition solutions for an Allen--Cahn equation. Rabinowitz and Stredulinsky have constructed infinite transition solutions as locally minimal solutions, but it is still an interesting question to establish these solutions by other method. Our result may attract the interest of constructing solutions with the shape of locally minimal solutions of Rabinowitz and Stredulinsky for problems defined on descrete group.", "field": "math", "label": 0}
{"text": "Title: A Markov Process Approach to Ensemble Control of Smart Buildings\nAbstract: This paper describes a step-by-step procedure that converts a physical model of a building into a Markov Process that characterizes energy consumption of this and other similar buildings. Relative to existing thermo-physics-based building models, the proposed procedure reduces model complexity and depends on fewer parameters, while also maintaining accuracy and feasibility sufficient for system-level analyses. Furthermore, the proposed Markov Process approach makes it possible to leverage real-time data streams available from intelligent data acquisition systems, which are readily available in smart buildings, and merge it with physics-based and statistical models. Construction of the Markov Process naturally leads to a Markov Decision Process formulation, which describes optimal probabilistic control of a collection of similar buildings. The approach is illustrated using validated building data from Belgium.", "field": "cs", "label": 1}
{"text": "Title: Dynamical processes on metric networks\nAbstract: The structure of a network has a major effect on dynamical processes on that network. Many studies of the interplay between network structure and dynamics have focused on models of phenomena such as disease spread, opinion formation and changes, coupled oscillators, and random walks. In parallel to these developments, there have been many studies of wave propagation and other spatially extended processes on networks. These latter studies consider metric networks, in which the edges are associated with real intervals. Metric networks give a mathematical framework to describe dynamical processes that include both temporal and spatial evolution of some quantity of interest -- such as the concentration of a diffusing substance or the amplitude of a wave -- by using edge-specific intervals that quantify distance information between nodes. Dynamical processes on metric networks often take the form of partial differential equations (PDEs). In this paper, we present a collection of techniques and paradigmatic linear PDEs that are useful to investigate the interplay between structure and dynamics in metric networks. We start by considering a time-independent Schr\\\"odinger equation. We then use both finite-difference and spectral approaches to study the Poisson, heat, and wave equations as paradigmatic examples of elliptic, parabolic, and hyperbolic PDE problems on metric networks. Our spectral approach is able to account for degenerate eigenmodes. In our numerical experiments, we consider metric networks with up to about $10^4$ nodes and about $10^4$ edges. A key contribution of our paper is to increase the accessibility of studying PDEs on metric networks. Software that implements our numerical approaches is available at https://gitlab.com/ComputationalScience/metric-networks.", "field": "math", "label": 0}
{"text": "Title: Domination Polynomial of the Rook Graph\nAbstract: A placement of chess pieces on a chessboard is called dominating, if each free square of the chessboard is under attack by at least one piece. In this contribution we compute the number of dominating arrangements of $k$ rooks on an $n\\times m$ chessboard. To this end we derive an expression for the corresponding generating function, the domination polynomial of the $n\\times m$ rook graph.", "field": "math", "label": 0}
{"text": "Title: Estimates for Character Sums with Various Convolutions\nAbstract: We provide estimates for sums of the form \\[\\left|\\sum_{a\\in A}\\sum_{b\\in B}\\sum_{c\\in C}\\chi(a+b+c)\\right|\\] and \\[\\left|\\sum_{a\\in A}\\sum_{b\\in B}\\sum_{c\\in C}\\sum_{d\\in D}\\chi(a+b+cd)\\right|\\] when $A,B,C,D\\subset \\mathbb F_p$, the field with $p$ elements and $\\chi$ is a non-trivial multiplicative character modulo $p$.", "field": "math", "label": 1}
{"text": "Title: Cuckoo Trie: Exploiting Memory-Level Parallelism for Efficient DRAM Indexing\nAbstract: We present the Cuckoo Trie, a fast, memory-efficient ordered index structure. The Cuckoo Trie is designed to have memory-level parallelism -- which a modern out-of-order processor can exploit to execute DRAM accesses in parallel -- without sacrificing memory efficiency. The Cuckoo Trie thus breaks a fundamental performance barrier faced by current indexes, whose bottleneck is a series of dependent pointer-chasing DRAM accesses -- e.g., traversing a search tree path -- which the processor cannot parallelize. Our evaluation shows that the Cuckoo Trie outperforms state-of-the-art-indexes by up to 20%--360% on a variety of datasets and workloads, typically with a smaller or comparable memory footprint.", "field": "cs", "label": 1}
{"text": "Title: Existence and concentration of solutions for a class of biharmonic equations\nAbstract: Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of nontrivial solutions are related to a suitable truncated equation.", "field": "math", "label": 1}
{"text": "Title: Purposeful and Operation-based Cognitive System for AGI\nAbstract: This paper proposes a new cognitive model, acting as the main component of an AGI agent. The model is introduced in its mature state, and as an extension of previous models, DENN, and especially AKREM, by including operational models (frames/classes) and will. In addition, it is mainly based on the duality principle in every known intelligent aspect, such as exhibiting both top-down and bottom-up model learning, generalization verse specialization, and more. Furthermore, a holistic approach is advocated for AGI designing and cognition under constraints or efficiency is proposed, in the form of reusability and simplicity. Finally, reaching this mature state is described via a cognitive evolution from infancy to adulthood, utilizing a consolidation principle. The final product of this cognitive model is a dynamic operational memory of models and instances.", "field": "cs", "label": 1}
{"text": "Title: Nonterminal complexity of some families of infinite regular languages\nAbstract: Nonterminal complexity of a context-free language is the smallest possible number of nonterminals in its generating grammar. While in general case nonterminal complexity computation problem is unsolvable, it can be computed for different families of regular languages. In this paper we study nonterminal complexity of some families of infinite regular languages.", "field": "cs", "label": 1}
{"text": "Title: Obvious Manipulability of Voting Rules\nAbstract: The Gibbard-Satterthwaite theorem states that no unanimous and non-dictatorial voting rule is strategyproof. We revisit voting rules and consider a weaker notion of strategyproofness called not obvious manipulability that was proposed by Troyan and Morrill (2020). We identify several classes of voting rules that satisfy this notion. We also show that several voting rules including k-approval fail to satisfy this property. We characterize conditions under which voting rules are obviously manipulable. One of our insights is that certain rules are obviously manipulable when the number of alternatives is relatively large compared to the number of voters. In contrast to the Gibbard-Satterthwaite theorem, many of the rules we examined are not obviously manipulable. This reflects the relatively easier satisfiability of the notion and the zero information assumption of not obvious manipulability, as opposed to the perfect information assumption of strategyproofness. We also present algorithmic results for computing obvious manipulations and report on experiments.", "field": "cs", "label": 1}
{"text": "Title: Diametral notions for elements of the unit ball of a Banach space\nAbstract: We introduce extensions of $\\Delta$-points and Daugavet points in which slices are replaced by relative weakly open subsets (super $\\Delta$-points and super Daugavet points) or by convex combinations of slices (ccs $\\Delta$-points and ccs Daugavet points). We first give a general overview on these new concepts and provide some isometric consequences on the spaces. As examples: if a Banach space contains a super $\\Delta$-point, then it does not admit an unconditional FDD with suppression constant smaller than two; if a real Banach space contains a ccs $\\Delta$-point, then it does not admit a one-unconditional basis; if a Banach space contains a ccs Daugavet point, then every convex combination of slices of its unit ball has diameter two. We next characterize the notions in some classes of Banach spaces showing, for instance, that all the notions coincide in $L_1$-predual spaces and that all the notions but ccs Daugavet points coincide in $L_1$-spaces. We next remark on some examples which have previously appeared in the literature and provide some new intriguing examples: examples of super $\\Delta$-points which are as closed as desired to strongly exposed points (hence failing to be Daugavet points in an extreme way); an example of a super $\\Delta$-point which is strongly regular (hence failing to be a ccs $\\Delta$-point in the strongest way); a super Daugavet point which fails to be a ccs $\\Delta$-point. The extensions of the diametral notions to point in the open unit ball and the consequences on the spaces are also studied. Last, we investigate the Kuratowski measure of relative weakly open subsets and of convex combinations of slices in the presence of super $\\Delta$-points or ccs $\\Delta$-points, as well as for spaces enjoying diameter 2 properties. We conclude the paper with a section on open problems.", "field": "math", "label": 1}
{"text": "Title: Zero-shot Active Learning Using Self Supervised Learning\nAbstract: Deep learning algorithms are often said to be data hungry. The performance of such algorithms generally improve as more and more annotated data is fed into the model. While collecting unlabelled data is easier (as they can be scraped easily from the internet), annotating them is a tedious and expensive task. Given a fixed budget available for data annotation, Active Learning helps selecting the best subset of data for annotation, such that the deep learning model when trained over that subset will have maximum generalization performance under this budget. In this work, we aim to propose a new Active Learning approach which is model agnostic as well as one doesn't require an iterative process. We aim to leverage self-supervised learnt features for the task of Active Learning. The benefit of self-supervised learning, is that one can get useful feature representation of the input data, without having any annotation.", "field": "cs", "label": 0}
{"text": "Title: Semistability of pairs for projective toric varieties\nAbstract: Let $X \\to \\mathbb P^N$ be a smooth linearly normal projective variety. It was proved by Paul that the $K$-energy of $(X,\\omega_{FS}|_{X})$ restricted to the Bergman metrics is bounded from below if and only if the pair of (rescaled) Chow/Hurwitz forms of $X$ is semistable. In this paper, we provide a necessary and sufficient condition for a given smooth toric variety $X_P$ to be semistable of pairs with respect to $\\mathcal O_{X_P}(i)$ for a positive integer $i$. Applying this result to a smooth polarized toric variety $(X_P, L_P)$, we prove that $(X_P, L_P)$ is asymptotically semistable of pairs if and only if it is K-semistable for toric degenerations.", "field": "math", "label": 0}
{"text": "Title: A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds\nAbstract: We present a comprehensive survey and benchmark of both traditional and learning-based methods for surface reconstruction from point clouds. This task is particularly challenging for real-world acquisitions due to factors like noise, outliers, non-uniform sampling, and missing data. Traditional approaches often simplify the problem by imposing handcrafted priors on either the input point clouds or the resulting surface, a process that can necessitate tedious hyperparameter tuning. Conversely, deep learning models have the capability to directly learn the properties of input point clouds and desired surfaces from data. We study the influence of these handcrafted and learned priors on the precision and robustness of surface reconstruction techniques. We evaluate various time-tested and contemporary methods in a standardized manner. When both trained and evaluated on point clouds with identical characteristics, the learning-based models consistently produce superior surfaces compared to their traditional counterparts$\\unicode{x2013}$even in scenarios involving novel shape categories. However, traditional methods demonstrate greater resilience to the diverse array of point cloud anomalies commonly found in real-world 3D acquisitions. For the benefit of the research community, we make our code and datasets available, inviting further enhancements to learning-based surface reconstruction. This can be accessed at https://github.com/raphaelsulzer/dsr-benchmark .", "field": "cs", "label": 0}
{"text": "Title: On groups with BFC-covered word values\nAbstract: For a group G and a positive integer n write B_n(G) = {x \\in G : |x^G | \\le n}. If s is a positive integer and w is a group word, say that G satisfies the (n,s)-covering condition with respect to the word w if there exists a subset S of G such that |S| \\le s and all w-values of G are contained in B_n(G)S. In a natural way, this condition emerged in the study of probabilistically nilpotent groups of class two. In this paper we obtain the following results. Let w be a multilinear commutator word on k variables and let G be a group satisfying the (n,s)-covering condition with respect to the word w. Then G has a soluble subgroup T such that the index [G : T] and the derived length of T are both (k,n,s)-bounded. Let G be a group satisfying the (n,s)-covering condition with respect to the word \\gamma_k. Then (1) \\gamma_{2k-1}(G) has a subgroup $T$ such that the index [\\gamma_{2k-1}(G) : T] and |T'| are both (k,n,s)-bounded; and (2) G has a nilpotent subgroup U such that the index [G : U] and the nilpotency class of U are both (k,n,s)-bounded.", "field": "math", "label": 0}
{"text": "Title: Unsupervised Body Part Regression via Spatially Self-ordering Convolutional Neural Networks\nAbstract: Automatic body part recognition for CT slices can benefit various medical image applications. Recent deep learning methods demonstrate promising performance, with the requirement of large amounts of labeled images for training. The intrinsic structural or superior-inferior slice ordering information in CT volumes is not fully exploited. In this paper, we propose a convolutional neural network (CNN) based Unsupervised Body part Regression (UBR) algorithm to address this problem. A novel unsupervised learning method and two inter-sample CNN loss functions are presented. Distinct from previous work, UBR builds a coordinate system for the human body and outputs a continuous score for each axial slice, representing the normalized position of the body part in the slice. The training process of UBR resembles a self-organization process: slice scores are learned from inter-slice relationships. The training samples are unlabeled CT volumes that are abundant, thus no extra annotation effort is needed. UBR is simple, fast, and accurate. Quantitative and qualitative experiments validate its effectiveness. In addition, we show two applications of UBR in network initialization and anomaly detection.", "field": "cs", "label": 1}
{"text": "Title: Augmenting Supervised Learning by Meta-learning Unsupervised Local Rules\nAbstract: The brain performs unsupervised learning and (perhaps) simultaneous supervised learning. This raises the question as to whether a hybrid of supervised and unsupervised methods will produce better learning. Inspired by the rich space of Hebbian learning rules, we set out to directly learn the unsupervised learning rule on local information that best augments a supervised signal. We present the Hebbian-augmented training algorithm (HAT) for combining gradient-based learning with an unsupervised rule on pre-synpatic activity, post-synaptic activities, and current weights. We test HAT's effect on a simple problem (Fashion-MNIST) and find consistently higher performance than supervised learning alone. This finding provides empirical evidence that unsupervised learning on synaptic activities provides a strong signal that can be used to augment gradient-based methods. We further find that the meta-learned update rule is a time-varying function; thus, it is difficult to pinpoint an interpretable Hebbian update rule that aids in training. We do find that the meta-learner eventually degenerates into a non-Hebbian rule that preserves important weights so as not to disturb the learner's convergence.", "field": "cs", "label": 1}
{"text": "Title: Damped Arrow-Hurwicz algorithm for sphere packing\nAbstract: We consider algorithms that, from an arbitrarily sampling of $N$ spheres (possibly overlapping), find a close packed configuration without overlapping. These problems can be formulated as minimization problems with non-convex constraints. For such packing problems, we observe that the classical iterative Arrow-Hurwicz algorithm does not converge. We derive a novel algorithm from a multi-step variant of the Arrow-Hurwicz scheme with damping. We compare this algorithm with classical algorithms belonging to the class of linearly constrained Lagrangian methods and show that it performs better. We provide an analysis of the convergence of these algorithms in the simple case of two spheres in one spatial dimension. Finally, we investigate the behaviour of our algorithm when the number of spheres is large.", "field": "math", "label": 1}
{"text": "Title: Duality for convex infinite optimization on linear spaces\nAbstract: This note establishes a limiting formula for the conic Lagrangian dual of a convex infinite optimization problem, correcting the classical version of Karney [Math. Programming 27 (1983) 75-82] for convex semi-infinite programs. A reformulation of the convex infinite optimization problem with a single constraint leads to a limiting formula for the corresponding Lagrangian dual, called sup-dual, and also for the primal problem in the case when strong Slater condition holds, which also entails strong sup-duality.", "field": "math", "label": 1}
{"text": "Title: Theory of Solutions for An Inextensible Cantilever\nAbstract: Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending; for an inextensible cantilever, the enforcement of arc-length preservation leads to quasilinear stiffness effects and inertial effects that are both nonlinear and nonlocal. For this model, smooth solutions are constructed via a spectral Galerkin approach. Additional compactness is needed to pass to the limit, and this is obtained through a complex procession of higher energy estimates. Uniqueness is obtained through a non-trivial decomposition of the nonlinearity. The confounding effects of nonlinear inertia are overcome via the addition of structural (Kelvin-Voigt) damping to the equations of motion. Local well-posedness of smooth solutions is shown first in the absence of nonlinear inertial effects, and then shown with these inertial effects present, taking into account structural damping. With damping in force, global-in-time, strong well-posedness result is obtained by achieving exponential decay for small data.", "field": "math", "label": 1}
{"text": "Title: Existence of Classic Solution of the Boussinesq Equation\nAbstract: We generalize intermediate value Theorem to metric space,and make use of it to discuss existence of classic solution of the Boussinesq equation.", "field": "math", "label": 0}
{"text": "Title: Chaos expansion of 2D parabolic Anderson model\nAbstract: We prove a chaos expansion for the 2D parabolic Anderson Model in small time, with the expansion coefficients expressed in terms of the annealed density function of the polymer in a white noise environment.", "field": "math", "label": 1}
{"text": "Title: Sensing Aided Covert Communications: Turning Interference into Allies\nAbstract: In this paper, we investigate the realization of covert communication in a general radar-communication cooperation system, which includes integrated sensing and communications as a special example. We explore the possibility of utilizing the sensing ability of radar to track and jam the aerial adversary target attempting to detect the transmission. Based on the echoes from the target, the extended Kalman filtering technique is employed to predict its trajectory as well as the corresponding channels. Depending on the maneuvering altitude of adversary target, two channel state information (CSI) models are considered, with the aim of maximizing the covert transmission rate by jointly designing the radar waveform and communication transmit beamforming vector based on the constructed channels. For perfect CSI under the free-space propagation model, by decoupling the joint design, we propose an efficient algorithm to guarantee that the target cannot detect the transmission. For imperfect CSI due to the multi-path components, a robust joint transmission scheme is proposed based on the property of the Kullback-Leibler divergence. The convergence behaviour, tracking MSE, false alarm and missed detection probabilities, and covert transmission rate are evaluated. Simulation results show that the proposed algorithms achieve accurate tracking. For both channel models, the proposed sensing-assisted covert transmission design is able to guarantee the covertness, and significantly outperforms the conventional schemes.", "field": "cs", "label": 0}
{"text": "Title: Transformers in Action Recognition: A Review on Temporal Modeling\nAbstract: In vision-based action recognition, spatio-temporal features from different modalities are used for recognizing activities. Temporal modeling is a long challenge of action recognition. However, there are limited methods such as pre-computed motion features, three-dimensional (3D) filters, and recurrent neural networks (RNN) for modeling motion information in deep-based approaches. Recently, transformers success in modeling long-range dependencies in natural language processing (NLP) tasks has gotten great attention from other domains; including speech, image, and video, to rely entirely on self-attention without using sequence-aligned RNNs or convolutions. Although the application of transformers to action recognition is relatively new, the amount of research proposed on this topic within the last few years is astounding. This paper especially reviews recent progress in deep learning methods for modeling temporal variations. It focuses on action recognition methods that use transformers for temporal modeling, discussing their main features, used modalities, and identifying opportunities and challenges for future research.", "field": "cs", "label": 1}
{"text": "Title: Fundamental groups, coregularity, and low dimensional klt Calabi-Yau pairs\nAbstract: In this article, we study how the absolute coregularity of a projective log pair reflects on its fundamental group. More precisely, we conjecture that for a projective klt log pair $(X,D)$ of absolute coregularity $c$ (and arbitrary dimension) the fundamental group $\\pi_1^{\\rm reg}(X,D)$ admits a normal abelian subgroup of finite index and rank at most $2c$. We prove this conjecture in the cases $c\\in \\{0,1,2\\}$, building on the almost abelianity of the fundamental groups of klt Calabi-Yau pairs of dimension $\\leq 2$. In the cases $c \\in \\{0,1,2\\}$ and fixed dimension, we can furthermore bound the index of a solvable normal subgroup. In dimension three, we are able to prove almost abelianity for projective varieties with klt singularities and $\\mathbb{Q}$-trivial canonical divisor.", "field": "math", "label": 0}
{"text": "Title: Accelerating Text-to-Image Editing via Cache-Enabled Sparse Diffusion Inference\nAbstract: Due to the recent success of diffusion models, text-to-image generation is becoming increasingly popular and achieves a wide range of applications. Among them, text-to-image editing, or continuous text-to-image generation, attracts lots of attention and can potentially improve the quality of generated images. It's common to see that users may want to slightly edit the generated image by making minor modifications to their input textual descriptions for several rounds of diffusion inference. However, such an image editing process suffers from the low inference efficiency of many existing diffusion models even using GPU accelerators. To solve this problem, we introduce Fast Image Semantically Edit (FISEdit), a cached-enabled sparse diffusion model inference engine for efficient text-to-image editing. The key intuition behind our approach is to utilize the semantic mapping between the minor modifications on the input text and the affected regions on the output image. For each text editing step, FISEdit can automatically identify the affected image regions and utilize the cached unchanged regions' feature map to accelerate the inference process. Extensive empirical results show that FISEdit can be $3.4\\times$ and $4.4\\times$ faster than existing methods on NVIDIA TITAN RTX and A100 GPUs respectively, and even generates more satisfactory images.", "field": "cs", "label": 0}
{"text": "Title: Approximation to multifractional Riemann-Liouville Brownian sheet\nAbstract: In this paper, we first introduce multifrational Riemann-Liouville Brownian sheets. Then, we show a result of approximation in law of the multifractional Riemann-Liouville Brownian sheet. The construction of these approximations is based on a sequence of I.I.D random variables.", "field": "math", "label": 1}
{"text": "Title: In Quest of Significance: Identifying Types of Twitter Sentiment Events that Predict Spikes in Sales\nAbstract: We study the power of Twitter events to predict consumer sales events by analysing sales for 75 companies from the retail sector and over 150 million tweets mentioning those companies along with their sentiment. We suggest an approach for events identification on Twitter extending existing methodologies of event study. We also propose a robust method for clustering Twitter events into different types based on their shape, which captures the varying dynamics of information propagation through the social network. We provide empirical evidence that through events differentiation based on their shape we can clearly identify types of Twitter events that have a more significant power to predict spikes in sales than the aggregated Twitter signal.", "field": "cs", "label": 1}
{"text": "Title: Context-Free TextSpotter for Real-Time and Mobile End-to-End Text Detection and Recognition\nAbstract: In the deployment of scene-text spotting systems on mobile platforms, lightweight models with low computation are preferable. In concept, end-to-end (E2E) text spotting is suitable for such purposes because it performs text detection and recognition in a single model. However, current state-of-the-art E2E methods rely on heavy feature extractors, recurrent sequence modellings, and complex shape aligners to pursue accuracy, which means their computations are still heavy. We explore the opposite direction: How far can we go without bells and whistles in E2E text spotting? To this end, we propose a text-spotting method that consists of simple convolutions and a few post-processes, named Context-Free TextSpotter. Experiments using standard benchmarks show that Context-Free TextSpotter achieves real-time text spotting on a GPU with only three million parameters, which is the smallest and fastest among existing deep text spotters, with an acceptable transcription quality degradation compared to heavier ones. Further, we demonstrate that our text spotter can run on a smartphone with affordable latency, which is valuable for building stand-alone OCR applications.", "field": "cs", "label": 1}
{"text": "Title: On the $δ$-chromatic numbers of the Cartesian products of graphs\nAbstract: In this work, we study the $\\delta$-chromatic number of a graph which is the chromatic number of the $\\delta$-complement of a graph. We give a structure of the $\\delta$-complements and sharp bounds on the $\\delta$-chromatic numbers of the Cartesian products of graphs. Furthermore, we compute the $\\delta$-chromatic numbers of various classes of Cartesian product graphs, including the Cartesian products between cycles, paths, and stars.", "field": "math", "label": 0}
{"text": "Title: Divides with cusps and symmetric links\nAbstract: A Divide with cusps is the image of a proper generic immersion from finite intervals and circles into a $2$-disk which allows to have cusps. A divide with cusps is the generalization of the notion of the divide which is introduced by A'Campo. From a divide with cusps, we can define the associated link in $S^3$. In this paper, we give the characterization of the link in $S^3$ which can be described as the associated link of a divide with cusps. In particular, we prove that every strongly invertible link and $2$-periodic link can be described as the link of a divide with cusps.", "field": "math", "label": 0}
{"text": "Title: Non-smoothable $\\mathbb{Z}/p$-actions on nuclei\nAbstract: In this article we construct examples of non-smoothable $\\mathbb{Z}/p$-actions on indefinite spin 4-manifolds with boundary for all primes $p\\geq 5$. For example, we show that for each prime $p\\geq 5$ and each $n\\geq 1$ there exists a locally linear $\\mathbb{Z}/p$-action on the Gompf nucleus $N(2pn)$ which is not smoothable with respect to any smooth structure on $N(2pn)$. Furthermore we investigate the behavior of these actions under two different types of equivariant stabilizations with $S^{2}\\times S^{2}$, namely \\emph{free} and \\emph{homologically trivial} stabilizations -- in particular we show that our non-smoothable $\\mathbb{Z}/p$-action on $N(2pn)$ remains non-smoothable after $2n-2$ free stabilizations, and after arbitrarily many homologically trivial stabilizations. We also show that free stabilizations satisfy a Wall stabilization principle in the sense that any non-smoothable $\\mathbb{Z}/p$-action becomes smoothable after some finite number free stabilizations (under certain assumptions), whereas our aforementioned result implies that homologically trivial stabilizations do not satisfy this property. The proofs of these results use equivariant $\\kappa$-invariants defined by the author in \\cite{Mon22}, calculations of equivariant $\\eta$-invariants for the odd signature and Dirac operators on Seifert-fibered spaces, as well as an analysis of the geometric $S^{1}$-action on the Seiberg-Witten moduli spaces of Seifert-fibered spaces induced by rotation in the fibers, which may be of independent interest.", "field": "math", "label": 0}
{"text": "Title: Associators in mould theory\nAbstract: By developing various techniques of mould theory, we introduce $\\mathsf{GARI}(\\mathscr{F})_{\\mathsf{as}+\\mathsf{bal}}$, a mould theoretic formulation of Drinfeld's associator set. We give a mould-theoretical generalization of the result that associator relations imply double shuffle relations, namely, we explain that $\\mathsf{GARI}(\\mathscr{F})_{\\mathsf{as}+\\mathsf{bal}}$ is embedded to Ecalle's set $\\mathsf{GARI}(\\mathscr{F})_{\\mathsf{as}\\ast\\mathsf{is}}$ which is a mould theoretic version of Racinet's double shuffle set.", "field": "math", "label": 0}
{"text": "Title: A Tiny CNN Architecture for Medical Face Mask Detection for Resource-Constrained Endpoints\nAbstract: The world is going through one of the most dangerous pandemics of all time with the rapid spread of the novel coronavirus (COVID-19). According to the World Health Organisation, the most effective way to thwart the transmission of coronavirus is to wear medical face masks. Monitoring the use of face masks in public places has been a challenge because manual monitoring could be unsafe. This paper proposes an architecture for detecting medical face masks for deployment on resource-constrained endpoints having extremely low memory footprints. A small development board with an ARM Cortex-M7 microcontroller clocked at 480 Mhz and having just 496 KB of framebuffer RAM, has been used for the deployment of the model. Using the TensorFlow Lite framework, the model is quantized to further reduce its size. The proposed model is 138 KB post quantization and runs at the inference speed of 30 FPS.", "field": "cs", "label": 1}
{"text": "Title: $q$-de Rham complexes of higher level\nAbstract: In this article, we construct two kinds of de Rham-like complexes which compute the cohomology of complete crystals on higher-level $q$-crystalline site, which was introduced in the previous article of the author. One complex is the $q$-analog of the higher de Rham complex constructed by Miyatani, and another complex is the $q$-analog of the jet complex constructed by Le Stum-Quir\\'os. The complexes we constructed can also be regarded as the higher-level analogs of the $q$-de Rham complex.", "field": "math", "label": 0}
{"text": "Title: Unsupervised Program Synthesis for Images By Sampling Without Replacement\nAbstract: Program synthesis has emerged as a successful approach to the image parsing task. Most prior works rely on a two-step scheme involving supervised pretraining of a Seq2Seq model with synthetic programs followed by reinforcement learning (RL) for fine-tuning with real reference images. Fully unsupervised approaches promise to train the model directly on the target images without requiring curated pretraining datasets. However, they struggle with the inherent sparsity of meaningful programs in the search space. In this paper, we present the first unsupervised algorithm capable of parsing constructive solid geometry (CSG) images into context-free grammar (CFG) without pretraining via non-differentiable renderer. To tackle the \\emph{non-Markovian} sparse reward problem, we combine three key ingredients -- (i) a grammar-encoded tree LSTM ensuring program validity (ii) entropy regularization and (iii) sampling without replacement from the CFG syntax tree. Empirically, our algorithm recovers meaningful programs in large search spaces (up to $3.8 \\times 10^{28}$). Further, even though our approach is fully unsupervised, it generalizes better than supervised methods on the synthetic 2D CSG dataset. On the 2D computer aided design (CAD) dataset, our approach significantly outperforms the supervised pretrained model and is competitive to the refined model.", "field": "cs", "label": 1}
{"text": "Title: On embeddings of certain spherical homogeneous spaces in prime characteristic\nAbstract: Let $\\mc G$ be a reductive group over an algebraically closed field of characteristic $p>0$. We study homogeneous $\\mc G$-spaces that are induced from the $G\\times G$-space $G$, $G$ a suitable reductive group, along a parabolic subgroup of $\\mc G$. We show that, under certain mild assumptions, any (normal) equivariant embedding of such a homogeneous space is canonically Frobenius split compatible with certain subvarieties and has an equivariant rational resolution by a toroidal embedding. In particular, all these embeddings are Cohen-Macaulay. Examples are the $G\\times G$-orbits in normal reductive monoids with unit group $G$. Our class of homogeneous spaces also includes the open orbits of the well-known determinantal varieties and the varieties of (circular) complexes. We also show that all $G$-orbit closures in a spherical variety which is canonically Frobenius split are normal. Finally we study the Gorenstein property for the varieties of circular complexes and for a related reductive monoid.", "field": "math", "label": 1}
{"text": "Title: Integrability of moduli and regularity of Denjoy counterexamples\nAbstract: We study the regularity of exceptional actions of groups by $C^{1,\\alpha}$ diffeomorphisms on the circle, i.e. ones which admit exceptional minimal sets, and whose elements have first derivatives that are continuous with concave modulus of continuity $\\alpha$. Let $G$ be a finitely generated group admitting a $C^{1,\\alpha}$ action $\\rho$ with a free orbit on the circle, and such that the logarithms of derivatives of group elements are uniformly bounded at some point of the circle. We prove that if $G$ has spherical growth bounded by $c n^{d-1}$ and if the function $1/\\alpha^d$ is integrable near zero, then under some mild technical assumptions on $\\alpha$, there is a sequence of exceptional $C^{1,\\alpha}$ actions of $G$ which converge to $\\rho$ in the $C^1$ topology. As a consequence for a single diffeomorphism, we obtain that if the function $1/\\alpha$ is integrable near zero, then there exists a $C^{1,\\alpha}$ exceptional diffeomorphism of the circle. This corollary accounts for all previously known moduli of continuity for derivatives of exceptional diffeomorphisms. We also obtain a partial converse to our main result. For finitely generated free abelian groups, the existence of an exceptional action, together with some natural hypotheses on the derivatives of group elements, puts integrability restrictions on the modulus $\\alpha$. These results are related to a long-standing question of D. McDuff concerning the length spectrum of exceptional $C^1$ diffeomorphisms of the circle.", "field": "math", "label": 1}
{"text": "Title: Representative Families: A Unified Tradeoff-Based Approach\nAbstract: Let $M=(E,{\\cal I})$ be a matroid, and let $\\cal S$ be a family of subsets of size $p$ of $E$. A subfamily $\\widehat{\\cal S}\\subseteq{\\cal S}$ represents ${\\cal S}$ if for every pair of sets $X\\in{\\cal S}$ and $Y\\subseteq E\\setminus X$ such that $X\\cup Y\\in{\\cal I}$, there is a set $\\widehat{X}\\in\\widehat{\\cal S}$ disjoint from $Y$ such that $\\widehat{X}\\cup Y\\in{\\cal I}$. Fomin et al. (Proc. ACM-SIAM Symposium on Discrete Algorithms, 2014) introduced a powerful technique for fast computation of representative families for uniform matroids. In this paper, we show that this technique leads to a unified approach for substantially improving the running times of parameterized algorithms for some classic problems. This includes, among others, $k$-Partial Cover, $k$-Internal Out-Branching, and Long Directed Cycle. Our approach exploits an interesting tradeoff between running time and the size of the representative families.", "field": "cs", "label": 1}
{"text": "Title: An algebra structure for reproducing kernel Hilbert spaces\nAbstract: Reproducing kernel Hilbert spaces (RKHSs) are Hilbert spaces of functions where pointwise evaluation is continuous. There are known examples of RKHSs that are Banach algebras under pointwise multiplication. These examples are built from weights on the dual of a locally compact abelian group. In this paper we define an algebra structure on an RKHS that is equivalent to subconvolutivity of the weight for known examples (referred to as reproducing kernel Hilbert algebras, or RKHAs). We show that the class of RKHAs is closed under the Hilbert space tensor product and the pullback construction on the category of RKHSs. The subcategory of RKHAs becomes a monoidal category with the spectrum as a monoidal functor to the category of topological spaces. The image of this functor is shown to contain all compact subspaces of $\\mathbb R^n$ for $n>0$.", "field": "math", "label": 0}
{"text": "Title: Liouville formulas for quantum affine algebras and eigenvalues of quantum Gelfand invariants\nAbstract: We construct new central elements in the quantum affine algebras of type $A$ and prove Liouville-type formulas relating them to the quantum determinants. We apply these formulas to calculate the eigenvalues of the quantum Gelfand invariants as introduced by Reshetikhin, Takhtadzhyan and Faddeev (1989) acting in irreducible highest weight representations of the quantized enveloping algebra for ${\\mathfrak {gl}}_n$.", "field": "math", "label": 0}
{"text": "Title: Tarski's Least Fixed Point Theorem: A Type Theoretic Formulation\nAbstract: We translate Giovanni Curi's predicative least fixed point theorem into type theory. There are multiple benefits of having a type theoretic formulation apart from the potential for routine formalization. By taking advantage of (higher) inductive types, we have skirted the painstaking set theoretic constructions and as a result believe our presentation is conceptually clearer. Additionally, due the predicative admissibility of (higher) inductive types we take a step towards the \\say{system independent} derivation that Curi calls for in his conclusion. We also explore restrictions on monotone maps that guarantee they are \\say{generated} in a sense we make precise. This allows for an alternative statement of the least fixed point theorem which goes beyond the version found in Curi's work.", "field": "math", "label": 0}
{"text": "Title: The effect of approximate coarsest-level solves on the convergence of multigrid V-cycle methods\nAbstract: The multigrid V-cycle method is a popular method for solving systems of linear equations. It computes an approximate solution by using smoothing on fine levels and solving a system of linear equations on the coarsest level. Solving on the coarsest level depends on the size and difficulty of the problem. If the size permits, it is typical to use a direct method based on LU or Cholesky decomposition. In settings with large coarsest-level problems, approximate solvers such as iterative Krylov subspace methods, or direct methods based on low-rank approximation, are often used. The accuracy of the coarsest-level solver is typically determined based on the experience of the users with the concrete problems and methods. In this paper we present an approach to analyzing the effects of approximate coarsest-level solves on the convergence of the V-cycle method for symmetric positive definite problems. Using these results, we derive coarsest-level stopping criterion through which we may control the difference between the approximation computed by a V-cycle method with approximate coarsest-level solver and the approximation which would be computed if the coarsest-level problems were solved exactly. The coarsest-level stopping criterion may thus be set up such that the V-cycle method converges to a chosen finest-level accuracy in (nearly) the same number of V-cycle iterations as the V-cycle method with exact coarsest-level solver. We also utilize the theoretical results to discuss how the convergence of the V-cycle method may be affected by the choice of a tolerance in a coarsest-level stopping criterion based on the relative residual norm.", "field": "math", "label": 0}
{"text": "Title: On almost sure convergence of random variables with finite chaos decomposition\nAbstract: Under mild conditions on a family of independent random variables $(X_n)$ we prove that almost sure convergence of a sequence of tetrahedral polynomial chaoses of uniformly bounded degrees in the variables $(X_n)$ implies the almost sure convergence of their homogeneous parts. This generalizes a recent result due to Poly and Zheng obtained under stronger integrability conditions. In particular for i.i.d. sequences we provide a simple necessary and sufficient condition for this property to hold. We also discuss similar phenomena for sums of multiple stochastic integrals with respect to Poisson processes, answering a question by Poly and Zheng.", "field": "math", "label": 1}
{"text": "Title: Bagchi's Theorem for families of automorphic forms\nAbstract: We prove a version of Bagchi's Theorem and of Voronin's Universality Theorem for family of primitive cusp forms of weight $2$ and prime level, and discuss under which conditions the argument will apply to general reasonable family of automorphic $L$-functions.", "field": "math", "label": 1}
{"text": "Title: Connections between K-stability and Vojta's conjecture\nAbstract: In this note, we use recent advances concerning the K-stability of $\\mathbb{Q}$-Fano varieties to provide settings for which Vojta's conjecture holds.", "field": "math", "label": 0}
{"text": "Title: Quasi-invariant theorem on the Gaussian path space\nAbstract: In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the case of the fractional Brownian motion. As applications, we will establish the integration by parts formula and Bismut-Elworthy-Li formula on the Gaussian path space, and by which some logarithmic Sobolev inequalities will be presented. Moreover, we will also provides some applications in the field of financial mathematics.", "field": "math", "label": 0}
{"text": "Title: Data Assimilation in Chaotic Systems Using Deep Reinforcement Learning\nAbstract: Data assimilation (DA) plays a pivotal role in diverse applications, ranging from climate predictions and weather forecasts to trajectory planning for autonomous vehicles. A prime example is the widely used ensemble Kalman filter (EnKF), which relies on linear updates to minimize variance among the ensemble of forecast states. Recent advancements have seen the emergence of deep learning approaches in this domain, primarily within a supervised learning framework. However, the adaptability of such models to untrained scenarios remains a challenge. In this study, we introduce a novel DA strategy that utilizes reinforcement learning (RL) to apply state corrections using full or partial observations of the state variables. Our investigation focuses on demonstrating this approach to the chaotic Lorenz '63 system, where the agent's objective is to minimize the root-mean-squared error between the observations and corresponding forecast states. Consequently, the agent develops a correction strategy, enhancing model forecasts based on available system state observations. Our strategy employs a stochastic action policy, enabling a Monte Carlo-based DA framework that relies on randomly sampling the policy to generate an ensemble of assimilated realizations. Results demonstrate that the developed RL algorithm performs favorably when compared to the EnKF. Additionally, we illustrate the agent's capability to assimilate non-Gaussian data, addressing a significant limitation of the EnKF.", "field": "math", "label": 0}
{"text": "Title: The primitive curve complex for a handlebody\nAbstract: A simple closed curve in the boundary surface of a handlebody is called primitive if there exists an essential disk in the handlebody whose boundary circle intersects the curve transversely in a single point. The primitive curve complex is then defined to be the full subcomplex of the curve complex for the boundary surface, spanned by the vertices of primitive curves. Given any two primitive curves, we construct a sequence of primitive curves from one to the other one satisfying a certain property. As a consequence, we prove that the primitive curve complex for the handlebody is connected.", "field": "math", "label": 0}
{"text": "Title: A minimal Gröbner basis for simple $\\mathfrak{sl}_n$- or $\\mathfrak{sp}_n$-modules\nAbstract: We explicitly provide minimal Gr\\\"obner bases for simple, finite-dimensional modules of complex Lie algebras of types A and C, using a weighted ordering that is compatible with the PBW filtration on the universal enveloping algebras.", "field": "math", "label": 0}
{"text": "Title: The Cytnx Library for Tensor Networks\nAbstract: We introduce a tensor network library designed for classical and quantum physics simulations called Cytnx (pronounced as sci-tens). This library provides almost an identical interface and syntax for both C++ and Python, allowing users to effortlessly switch between two languages. Aiming at a quick learning process for new users of tensor network algorithms, the interfaces resemble the popular Python scientific libraries like NumPy, Scipy, and PyTorch. Not only multiple global Abelian symmetries can be easily defined and implemented, Cytnx also provides a new tool called Network that allows users to store large tensor networks and perform tensor network contractions in an optimal order automatically. With the integration of cuQuantum, tensor calculations can also be executed efficiently on GPUs. We present benchmark results for tensor operations on both devices, CPU and GPU. We also discuss features and higher-level interfaces to be added in the future.", "field": "cs", "label": 0}
{"text": "Title: A direct approach for function approximation on data defined manifolds\nAbstract: In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere. In practice, the data might not be dense on these domains, and therefore, the approximation theory results are observed to be too conservative. In manifold learning, one assumes instead that the data is sampled from an unknown manifold; i.e., the manifold is defined by the data itself. Function approximation on this unknown manifold is then a two stage procedure: first, one approximates the Laplace-Beltrami operator (and its eigen-decomposition) on this manifold using a graph Laplacian, and next, approximates the target function using the eigen-functions. Alternatively, one estimates first some atlas on the manifold and then uses local approximation techniques based on the local coordinate charts. In this paper, we propose a more direct approach to function approximation on \\emph{unknown}, data defined manifolds without computing the eigen-decomposition of some operator or an atlas for the manifold, and without any kind of training in the classical sense. Our constructions are universal; i.e., do not require the knowledge of any prior on the target function other than continuity on the manifold. We estimate the degree of approximation. For smooth functions, the estimates do not suffer from the so-called saturation phenomenon. We demonstrate via a property called good propagation of errors how the results can be lifted for function approximation using deep networks where each channel evaluates a Gaussian network on a possibly unknown manifold.", "field": "cs", "label": 1}
{"text": "Title: The Security and Privacy of Mobile Edge Computing: An Artificial Intelligence Perspective\nAbstract: Mobile Edge Computing (MEC) is a new computing paradigm that enables cloud computing and information technology (IT) services to be delivered at the network's edge. By shifting the load of cloud computing to individual local servers, MEC helps meet the requirements of ultralow latency, localized data processing, and extends the potential of Internet of Things (IoT) for end-users. However, the crosscutting nature of MEC and the multidisciplinary components necessary for its deployment have presented additional security and privacy concerns. Fortunately, Artificial Intelligence (AI) algorithms can cope with excessively unpredictable and complex data, which offers a distinct advantage in dealing with sophisticated and developing adversaries in the security industry. Hence, in this paper we comprehensively provide a survey of security and privacy in MEC from the perspective of AI. On the one hand, we use European Telecommunications Standards Institute (ETSI) MEC reference architecture as our based framework while merging the Software Defined Network (SDN) and Network Function Virtualization (NFV) to better illustrate a serviceable platform of MEC. On the other hand, we focus on new security and privacy issues, as well as potential solutions from the viewpoints of AI. Finally, we comprehensively discuss the opportunities and challenges associated with applying AI to MEC security and privacy as possible future research directions.", "field": "cs", "label": 0}
{"text": "Title: The covariant functoriality of graph algebras\nAbstract: In the standard category of directed graphs, graph morphisms map edges to edges. By allowing graph morphisms to map edges to finite paths (path homomorphisms of graphs), we obtain an ambient category in which we determine subcategories enjoying covariant functors to categories of algebras given by constructions of path algebras, Cohn path algebras, and Leavitt path algebras, respectively. Thus we obtain new tools to unravel homomorphisms between Leavitt path algebras and graph C*-algebras. In particular, a graph-algebraic presentation of the inclusion of the C*-algebra of a quantum real projective plane into the Toeplitz algebra allows us to determine a quantum CW-complex structure of the former. It comes as a mixed-pullback theorem where two $*$-homomorphisms are covariantly induced from path homomorphisms of graphs and the remaining two are contravariantly induced by admissible inclusions of graphs. As a main result and an application of new covariant-induction tools, we prove such a mixed-pullback theorem for arbitrary graphs whose all vertex-simple loops have exits, which substantially enlarges the scope of examples coming from noncommutative topology.", "field": "math", "label": 0}
{"text": "Title: ODIN: A Single Model for 2D and 3D Perception\nAbstract: State-of-the-art models on contemporary 3D perception benchmarks like ScanNet consume and label dataset-provided 3D point clouds, obtained through post processing of sensed multiview RGB-D images. They are typically trained in-domain, forego large-scale 2D pre-training and outperform alternatives that featurize the posed RGB-D multiview images instead. The gap in performance between methods that consume posed images versus post-processed 3D point clouds has fueled the belief that 2D and 3D perception require distinct model architectures. In this paper, we challenge this view and propose ODIN (Omni-Dimensional INstance segmentation), a model that can segment and label both 2D RGB images and 3D point clouds, using a transformer architecture that alternates between 2D within-view and 3D cross-view information fusion. Our model differentiates 2D and 3D feature operations through the positional encodings of the tokens involved, which capture pixel coordinates for 2D patch tokens and 3D coordinates for 3D feature tokens. ODIN achieves state-of-the-art performance on ScanNet200, Matterport3D and AI2THOR 3D instance segmentation benchmarks, and competitive performance on ScanNet, S3DIS and COCO. It outperforms all previous works by a wide margin when the sensed 3D point cloud is used in place of the point cloud sampled from 3D mesh. When used as the 3D perception engine in an instructable embodied agent architecture, it sets a new state-of-the-art on the TEACh action-from-dialogue benchmark. Our code and checkpoints can be found at the project website: https://odin-seg.github.io.", "field": "cs", "label": 0}
{"text": "Title: Characterization and Prediction of Deep Learning Workloads in Large-Scale GPU Datacenters\nAbstract: Modern GPU datacenters are critical for delivering Deep Learning (DL) models and services in both the research community and industry. When operating a datacenter, optimization of resource scheduling and management can bring significant financial benefits. Achieving this goal requires a deep understanding of the job features and user behaviors. We present a comprehensive study about the characteristics of DL jobs and resource management. First, we perform a large-scale analysis of real-world job traces from SenseTime. We uncover some interesting conclusions from the perspectives of clusters, jobs and users, which can facilitate the cluster system designs. Second, we introduce a general-purpose framework, which manages resources based on historical data. As case studies, we design: a Quasi-Shortest-Service-First scheduling service, which can minimize the cluster-wide average job completion time by up to 6.5x; and a Cluster Energy Saving service, which improves overall cluster utilization by up to 13%.", "field": "cs", "label": 1}
{"text": "Title: Autonomous Driving Implementation in an Experimental Environment\nAbstract: Autonomous systems require identifying the environment and it has a long way to go before putting it safely into practice. In autonomous driving systems, the detection of obstacles and traffic lights are of importance as well as lane tracking. In this study, an autonomous driving system is developed and tested in the experimental environment designed for this purpose. In this system, a model vehicle having a camera is used to trace the lanes and avoid obstacles to experimentally study autonomous driving behavior. Convolutional Neural Network models were trained for Lane tracking. For the vehicle to avoid obstacles, corner detection, optical flow, focus of expansion, time to collision, balance calculation, and decision mechanism were created, respectively.", "field": "cs", "label": 1}
{"text": "Title: Canonical and $n$-canonical modules on a Noetherian algebra\nAbstract: We define canonical and $n$-canonical modules on a module-finite algebra over a Noether commutative ring and study their basic properties. Using $n$-canonical modules, we generalize a theorem on $(n,C)$-syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a non-commutative version of Aoyama's theorem which states that a canonical module descends with respect to a flat local homomorphism. We also prove the codimension two-argument for modules over a coherent sheaf of algebras with a $2$-canonical module, generalizing a result of the author.", "field": "math", "label": 1}
{"text": "Title: EcoFed: Efficient Communication for DNN Partitioning-based Federated Learning\nAbstract: Efficiently running federated learning (FL) on resource-constrained devices is challenging since they are required to train computationally intensive deep neural networks (DNN) independently. DNN partitioning-based FL (DPFL) has been proposed as one mechanism to accelerate training where the layers of a DNN (or computation) are offloaded from the device to the server. However, this creates significant communication overheads since the intermediate activation and gradient need to be transferred between the device and the server during training. While current research reduces the communication introduced by DNN partitioning using local loss-based methods, we demonstrate that these methods are ineffective in improving the overall efficiency (communication overhead and training speed) of a DPFL system. This is because they suffer from accuracy degradation and ignore the communication costs incurred when transferring the activation from the device to the server. This article proposes EcoFed - a communication efficient framework for DPFL systems. EcoFed eliminates the transmission of the gradient by developing pre-trained initialization of the DNN model on the device for the first time. This reduces the accuracy degradation seen in local loss-based methods. In addition, EcoFed proposes a novel replay buffer mechanism and implements a quantization-based compression technique to reduce the transmission of the activation. It is experimentally demonstrated that EcoFed can reduce the communication cost by up to 133x and accelerate training by up to 21x when compared to classic FL. Compared to vanilla DPFL, EcoFed achieves a 16x communication reduction and 2.86x training time speed-up. EcoFed is available from https://github.com/blessonvar/EcoFed.", "field": "cs", "label": 0}
{"text": "Title: Bounds for traces of Hecke operators and applications to modular and elliptic curves over a finite field\nAbstract: We give an upper bound for the trace of a Hecke operator acting on the space of holomorphic cusp forms with respect to certain congruence subgroups. Such an estimate has applications to the analytic theory of elliptic curves over a finite field, going beyond the Riemann hypothesis over finite fields. As the main tool to prove our bound on traces of Hecke operators, we develop a Petersson formula for newforms for general nebentype characters.", "field": "math", "label": 1}
{"text": "Title: Towards dense object tracking in a 2D honeybee hive\nAbstract: From human crowds to cells in tissue, the detection and efficient tracking of multiple objects in dense configurations is an important and unsolved problem. In the past, limitations of image analysis have restricted studies of dense groups to tracking a single or subset of marked individuals, or to coarse-grained group-level dynamics, all of which yield incomplete information. Here, we combine convolutional neural networks (CNNs) with the model environment of a honeybee hive to automatically recognize all individuals in a dense group from raw image data. We create new, adapted individual labeling and use the segmentation architecture U-Net with a loss function dependent on both object identity and orientation. We additionally exploit temporal regularities of the video recording in a recurrent manner and achieve near human-level performance while reducing the network size by 94% compared to the original U-Net architecture. Given our novel application of CNNs, we generate extensive problem-specific image data in which labeled examples are produced through a custom interface with Amazon Mechanical Turk. This dataset contains over 375,000 labeled bee instances across 720 video frames at 2 FPS, representing an extensive resource for the development and testing of tracking methods. We correctly detect 96% of individuals with a location error of ~7% of a typical body dimension, and orientation error of 12 degrees, approximating the variability of human raters. Our results provide an important step towards efficient image-based dense object tracking by allowing for the accurate determination of object location and orientation across time-series image data efficiently within one network architecture.", "field": "cs", "label": 1}
{"text": "Title: A Concrete View of Rule 110 Computation\nAbstract: Rule 110 is a cellular automaton that performs repeated simultaneous updates of an infinite row of binary values. The values are updated in the following way: 0s are changed to 1s at all positions where the value to the right is a 1, while 1s are changed to 0s at all positions where the values to the left and right are both 1. Though trivial to define, the behavior exhibited by Rule 110 is surprisingly intricate, and in (Cook, 2004) we showed that it is capable of emulating the activity of a Turing machine by encoding the Turing machine and its tape into a repeating left pattern, a central pattern, and a repeating right pattern, which Rule 110 then acts on. In this paper we provide an explicit compiler for converting a Turing machine into a Rule 110 initial state, and we present a general approach for proving that such constructions will work as intended. The simulation was originally assumed to require exponential time, but surprising results of Neary and Woods (2006) have shown that in fact, only polynomial time is required. We use the methods of Neary and Woods to exhibit a direct simulation of a Turing machine by a tag system in polynomial time.", "field": "cs", "label": 1}
{"text": "Title: Near-Field Velocity Sensing and Predictive Beamforming\nAbstract: The novel concept of near-field velocity sensing is proposed. In contrast to far-field velocity sensing, near-field velocity sensing enables the simultaneous estimation of both radial and transverse velocities of a moving target. A maximum-likelihood-based method is proposed for jointly estimating the radial and transverse velocities from the echo signals. Assisted by near-field velocity sensing, a predictive beamforming framework is proposed for a moving communication user, which requires no channel estimation but achieves seamless data transmission. Finally, numerical examples validate the proposed approaches.", "field": "cs", "label": 0}
{"text": "Title: Towards a quality metric for dense light fields\nAbstract: Light fields become a popular representation of three dimensional scenes, and there is interest in their processing, resampling, and compression. As those operations often result in loss of quality, there is a need to quantify it. In this work, we collect a new dataset of dense reference and distorted light fields as well as the corresponding quality scores which are scaled in perceptual units. The scores were acquired in a subjective experiment using an interactive light-field viewing setup. The dataset contains typical artifacts that occur in light-field processing chain due to light-field reconstruction, multi-view compression, and limitations of automultiscopic displays. We test a number of existing objective quality metrics to determine how well they can predict the quality of light fields. We find that the existing image quality metrics provide good measures of light-field quality, but require dense reference light- fields for optimal performance. For more complex tasks of comparing two distorted light fields, their performance drops significantly, which reveals the need for new, light-field-specific metrics.", "field": "cs", "label": 1}
{"text": "Title: Tensorial structure of the lifting doctrine in constructive domain theory\nAbstract: We present a survey of the two-dimensional and tensorial structure of the lifting doctrine in constructive domain theory. We establish the universal property of lifting of directed-complete partial orders (dcpos) as the Sierpi\\'nski cone, from which we deduce (1) that lifting forms a Kock-Z\\\"oberlein doctrine, (2) that lifting algebras, pointed dcpos, and inductive partial orders form canonically equivalent locally posetal 2-categories, and (3) that the category of lifting algebras is cocomplete, with connected colimits created by the forgetful functor to dcpos. Finally we deduce the symmetric monoidal closure of the Eilenberg-Moore resolution of the lifting 2-monad by means of smash products; these are shown to classify both bilinear maps and strict maps, which we prove to coincide in the constructive setting. We provide several concrete computations of the smash product as dcpo coequalisers and lifting algebra coequalisers, and compare these with the more abstract results of Seal. Although all these results are well-known classically, the existing proofs do not apply in a constructive setting; indeed, the classical analysis of the Eilenberg-Moore category of the lifting monad relies on the fact that all lifting algebras are free, a condition that is not known to hold constructively.", "field": "math", "label": 0}
{"text": "Title: BA-SAM: Scalable Bias-Mode Attention Mask for Segment Anything Model\nAbstract: In this paper, we address the challenge of image resolution variation for the Segment Anything Model (SAM). SAM, known for its zero-shot generalizability, exhibits a performance degradation when faced with datasets with varying image sizes. Previous approaches tend to resize the image to a fixed size or adopt structure modifications, hindering the preservation of SAM's rich prior knowledge. Besides, such task-specific tuning necessitates a complete retraining of the model, which is cost-expensive and unacceptable for deployment in the downstream tasks. In this paper, we reformulate this issue as a length extrapolation problem, where token sequence length varies while maintaining a consistent patch size for images of different sizes. To this end, we propose Scalable Bias-Mode Attention Mask (BA-SAM) to enhance SAM's adaptability to varying image resolutions while eliminating the need for structure modifications. Firstly, we introduce a new scaling factor to ensure consistent magnitude in the attention layer's dot product values when the token sequence length changes. Secondly, we present a bias-mode attention mask that allows each token to prioritize neighboring information, mitigating the impact of untrained distant information. Our BA-SAM demonstrates efficacy in two scenarios: zero-shot and fine-tuning. Extensive evaluation on diverse datasets, including DIS5K, DUTS, ISIC, COD10K, and COCO, reveals its ability to significantly mitigate performance degradation in the zero-shot setting and achieve state-of-the-art performance with minimal fine-tuning. Furthermore, we propose a generalized model and benchmark, showcasing BA-SAM's generalizability across all four datasets simultaneously.", "field": "cs", "label": 0}
{"text": "Title: Infinite Eulerian trails are computable on graphs with vertices of infinite degree\nAbstract: The Erd\\H{o}s, Gr\\\"unwald and Weiszfeld theorem provides a characterization of infinite graphs which are Eulerian. That is, infinite graphs which admit infinite Eulerian trails. In this article we complement this theorem with a characterization of those finite trails that can be extended to infinite Eulerian trails. This allows us to prove an effective version of the Erd\\H{o}s, Gr\\\"unwald and Weiszfeld theorem for a class of graphs that includes non locally finite ones, generalizing a theorem of D.Bean.", "field": "math", "label": 0}
{"text": "Title: Evolution of Retweet Rates in Twitter User Careers: Analysis and Model\nAbstract: We study the evolution of the number of retweets received by Twitter users over the course of their \"careers\" on the platform. We find that on average the number of retweets received by users tends to increase over time. This is partly expected because users tend to gradually accumulate followers. Normalizing by the number of followers, however, reveals that the relative, per-follower retweet rate tends to be non-monotonic, maximized at a \"peak age\" after which it does not increase, or even decreases. We develop a simple mathematical model of the process behind this phenomenon, which assumes a constantly growing number of followers, each of whom loses interest over time. We show that this model is sufficient to explain the non-monotonic nature of per-follower retweet rates, without any assumptions about the quality of content posted at different times.", "field": "cs", "label": 1}
{"text": "Title: TSGAN: An Optical-to-SAR Dual Conditional GAN for Optical based SAR Temporal Shifting\nAbstract: In contrast to the well-investigated field of SAR-to-Optical translation, this study explores the lesser-investigated domain of Optical-to-SAR translation, a challenging field due to the ill-posed nature of this translation. The complexity arises as a single optical data can have multiple SAR representations based on the SAR viewing geometry. We propose a novel approach, termed SAR Temporal Shifting, which inputs an optical data from the desired timestamp along with a SAR data from a different temporal point but with a consistent viewing geometry as the expected SAR data, both complemented with a change map of optical data during the intervening period. This model modifies the SAR data based on the changes observed in optical data to generate the SAR data for the desired timestamp. Our model, a dual conditional Generative Adversarial Network (GAN), named Temporal Shifting GAN (TSGAN), incorporates a siamese encoder in both the Generator and the Discriminator. To prevent the model from overfitting on the input SAR data, we employed a change weighted loss function. Our approach surpasses traditional translation methods by eliminating the GAN's fiction phenomenon, particularly in unchanged regions, resulting in higher SSIM and PSNR in these areas. Additionally, modifications to the Pix2Pix architecture and the inclusion of attention mechanisms have enhanced the model's performance on all regions of the data. This research paves the way for leveraging legacy optical datasets, the most abundant and longstanding source of Earth imagery data, extending their use to SAR domains and temporal analyses. To foster further research, we provide the code, datasets used in our study, and a framework for generating paired SAR-Optical datasets for new regions of interest. These resources are available on github.com/moienr/TemporalGAN", "field": "cs", "label": 0}
{"text": "Title: Limits of subcritical random graphs and random graphs with excluded minors\nAbstract: We prove local convergence results for the uniformly random, labelled or unlabelled, graphs from subcritical families. As an example special case, we prove Benjamini-Schramm convergence for the uniform random unlabelled tree. We introduce a compactification of the space of countable (connected) rooted graphs, and use it to generalise the notion of Benjamini-Schramm convergence in order to allow for vertices of infinite degree in the limit object.", "field": "math", "label": 1}
{"text": "Title: One Shot Learning as Instruction Data Prospector for Large Language Models\nAbstract: Aligning large language models(LLMs) with human is a critical step in effectively utilizing their pre-trained capabilities across a wide array of language tasks. Current instruction tuning practices often rely on expanding dataset size without a clear strategy for ensuring data quality, which can inadvertently introduce noise and degrade model performance. To address this challenge, we introduce Nuggets, a novel and efficient methodology that employs one shot learning to select high-quality instruction data from expansive datasets. Nuggets assesses the potential of individual instruction examples to act as effective one shot examples, thereby identifying those that can significantly enhance diverse task performance. Nuggets utilizes a scoring system based on the impact of candidate examples on the perplexity of a diverse anchor set, facilitating the selection of the most beneficial data for instruction tuning. Through rigorous testing on two benchmarks, including MT-Bench and Alpaca-Eval, we demonstrate that instruction tuning with the top 1% of Nuggets-curated examples substantially outperforms conventional methods that use the full dataset. These findings advocate for a data selection paradigm that prioritizes quality, offering a more efficient pathway to align LLMs with humans.", "field": "cs", "label": 0}
{"text": "Title: A Note on Matching Variables to Equations\nAbstract: We showed with J. P. Gollin that if a (possibly infinite) homogeneous linear equation system has only the trivial solution, then there exists an injective function from the variables to the equations such that each variable has non-zero coefficient in its image. Shortly after a more elementary proof was found by Aharoni and Guo. In this note we present a very short matroid-theoretic proof which we believe is the simplest possible proof of this theorem.", "field": "math", "label": 0}
{"text": "Title: A Dataset for Statutory Reasoning in Tax Law Entailment and Question Answering\nAbstract: Legislation can be viewed as a body of prescriptive rules expressed in natural language. The application of legislation to facts of a case we refer to as statutory reasoning, where those facts are also expressed in natural language. Computational statutory reasoning is distinct from most existing work in machine reading, in that much of the information needed for deciding a case is declared exactly once (a law), while the information needed in much of machine reading tends to be learned through distributional language statistics. To investigate the performance of natural language understanding approaches on statutory reasoning, we introduce a dataset, together with a legal-domain text corpus. Straightforward application of machine reading models exhibits low out-of-the-box performance on our questions, whether or not they have been fine-tuned to the legal domain. We contrast this with a hand-constructed Prolog-based system, designed to fully solve the task. These experiments support a discussion of the challenges facing statutory reasoning moving forward, which we argue is an interesting real-world task that can motivate the development of models able to utilize prescriptive rules specified in natural language.", "field": "cs", "label": 1}
{"text": "Title: Full quantum crossed products, invariant measures, and type-I lifting\nAbstract: We show that for a closed embedding $\\mathbb{H}\\le \\mathbb{G}$ of locally compact quantum groups (LCQGs) with $\\mathbb{G}/\\mathbb{H}$ admitting an invariant probability measure, a unitary $\\mathbb{G}$-representation is type-I if its restriction to $\\mathbb{H}$ is. On a related note, we also prove that if an action $\\mathbb{G}\\circlearrowright A$ of an LCQG on a unital $C^*$-algebra admits an invariant state then the full group algebra of $\\mathbb{G}$ embeds into the resulting full crossed product (and into the multiplier algebra of that crossed product if the original algebra is not unital). We also prove a few other results on crossed products of LCQG actions, some of which seem to be folklore; among them are (a) the fact that two mutually dual quantum-group morphisms produce isomorphic full crossed products, and (b) the fact that full and reduced crossed products by dual-coamenable LCQGs are isomorphic.", "field": "math", "label": 1}
{"text": "Title: Deep Demosaicing for Edge Implementation\nAbstract: Most digital cameras use sensors coated with a Color Filter Array (CFA) to capture channel components at every pixel location, resulting in a mosaic image that does not contain pixel values in all channels. Current research on reconstructing these missing channels, also known as demosaicing, introduces many artifacts, such as zipper effect and false color. Many deep learning demosaicing techniques outperform other classical techniques in reducing the impact of artifacts. However, most of these models tend to be over-parametrized. Consequently, edge implementation of the state-of-the-art deep learning-based demosaicing algorithms on low-end edge devices is a major challenge. We provide an exhaustive search of deep neural network architectures and obtain a pareto front of Color Peak Signal to Noise Ratio (CPSNR) as the performance criterion versus the number of parameters as the model complexity that beats the state-of-the-art. Architectures on the pareto front can then be used to choose the best architecture for a variety of resource constraints. Simple architecture search methods such as exhaustive search and grid search require some conditions of the loss function to converge to the optimum. We clarify these conditions in a brief theoretical study.", "field": "cs", "label": 1}
{"text": "Title: Accurate Leukocyte Detection Based on Deformable-DETR and Multi-Level Feature Fusion for Aiding Diagnosis of Blood Diseases\nAbstract: In standard hospital blood tests, the traditional process requires doctors to manually isolate leukocytes from microscopic images of patients' blood using microscopes. These isolated leukocytes are then categorized via automatic leukocyte classifiers to determine the proportion and volume of different types of leukocytes present in the blood samples, aiding disease diagnosis. This methodology is not only time-consuming and labor-intensive, but it also has a high propensity for errors due to factors such as image quality and environmental conditions, which could potentially lead to incorrect subsequent classifications and misdiagnosis. To address these issues, this paper proposes an innovative method of leukocyte detection: the Multi-level Feature Fusion and Deformable Self-attention DETR (MFDS-DETR). To tackle the issue of leukocyte scale disparity, we designed the High-level Screening-feature Fusion Pyramid (HS-FPN), enabling multi-level fusion. This model uses high-level features as weights to filter low-level feature information via a channel attention module and then merges the screened information with the high-level features, thus enhancing the model's feature expression capability. Further, we address the issue of leukocyte feature scarcity by incorporating a multi-scale deformable self-attention module in the encoder and using the self-attention and cross-deformable attention mechanisms in the decoder, which aids in the extraction of the global features of the leukocyte feature maps. The effectiveness, superiority, and generalizability of the proposed MFDS-DETR method are confirmed through comparisons with other cutting-edge leukocyte detection models using the private WBCDD, public LISC and BCCD datasets. Our source code and private WBCCD dataset are available at https://github.com/JustlfC03/MFDS-DETR.", "field": "cs", "label": 0}
{"text": "Title: Multifunctions determined by integrable functions\nAbstract: Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.", "field": "math", "label": 1}
{"text": "Title: Weighted extremal metrics on blowups\nAbstract: We show that if a compact K\\\"ahler manifold admits a weighted extremal metric for the action of a torus, so too does its blowup at a relatively stable point that is fixed by both the torus action and the extremal field. This generalises previous results on extremal metrics by Arezzo--Pacard--Singer and Sz\\'ekelyhidi to many other canonical metrics, including extremal Sasaki metrics, deformations of K\\\"ahler--Ricci solitons and $\\mu$-cscK metrics. In a sequel to this paper, we use this result to study the weighted K-stability of weighted extremal manifolds.", "field": "math", "label": 0}
{"text": "Title: Cross-modal Prototype Driven Network for Radiology Report Generation\nAbstract: Radiology report generation (RRG) aims to describe automatically a radiology image with human-like language and could potentially support the work of radiologists, reducing the burden of manual reporting. Previous approaches often adopt an encoder-decoder architecture and focus on single-modal feature learning, while few studies explore cross-modal feature interaction. Here we propose a Cross-modal PROtotype driven NETwork (XPRONET) to promote cross-modal pattern learning and exploit it to improve the task of radiology report generation. This is achieved by three well-designed, fully differentiable and complementary modules: a shared cross-modal prototype matrix to record the cross-modal prototypes; a cross-modal prototype network to learn the cross-modal prototypes and embed the cross-modal information into the visual and textual features; and an improved multi-label contrastive loss to enable and enhance multi-label prototype learning. XPRONET obtains substantial improvements on the IU-Xray and MIMIC-CXR benchmarks, where its performance exceeds recent state-of-the-art approaches by a large margin on IU-Xray and comparable performance on MIMIC-CXR.", "field": "cs", "label": 1}
{"text": "Title: Tensor Ranks and the Fine-Grained Complexity of Dynamic Programming\nAbstract: Generalizing work of K\\\"unnemann, Paturi, and Schneider [ICALP 2017], we study a wide class of high-dimensional dynamic programming (DP) problems in which one must find the shortest path between two points in a high-dimensional grid given a tensor of transition costs between nodes in the grid. This captures many classical problems which are solved using DP such as the knapsack problem, the airplane refueling problem, and the minimal-weight polygon triangulation problem. We observe that for many of these problems, the tensor naturally has low tensor rank or low slice rank. We then give new algorithms and a web of fine-grained reductions to tightly determine the complexity of these problems. For instance, we show that a polynomial speedup over the DP algorithm is possible when the tensor rank is a constant or the slice rank is 1, but that such a speedup is impossible if the tensor rank is slightly super-constant (assuming SETH) or the slice rank is at least 3 (assuming the APSP conjecture). We find that this characterizes the known complexities for many of these problems, and in some cases leads to new faster algorithms.", "field": "cs", "label": 0}
{"text": "Title: On the joint distributions of succession and Eulerian statistics\nAbstract: The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. As an generalization a result of Diaconis-Evans-Graham (Adv. in Appl. Math., 61 (2014), 102--124), we show that two triple set-valued statistics of permutations are equidistributed on symmetric groups. We then introduce the definition of proper left-to-right minimum. We discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc (p,q)-Eulerian polynomials and the joint distribution of succession and several Eulerian-type statistics.", "field": "math", "label": 0}
{"text": "Title: Adaptive Signal Variances: CNN Initialization Through Modern Architectures\nAbstract: Deep convolutional neural networks (CNN) have achieved the unwavering confidence in its performance on image processing tasks. The CNN architecture constitutes a variety of different types of layers including the convolution layer and the max-pooling layer. CNN practitioners widely understand the fact that the stability of learning depends on how to initialize the model parameters in each layer. Nowadays, no one doubts that the de facto standard scheme for initialization is the so-called Kaiming initialization that has been developed by He et al. The Kaiming scheme was derived from a much simpler model than the currently used CNN structure having evolved since the emergence of the Kaiming scheme. The Kaiming model consists only of the convolution and fully connected layers, ignoring the max-pooling layer and the global average pooling layer. In this study, we derived the initialization scheme again not from the simplified Kaiming model, but precisely from the modern CNN architectures, and empirically investigated how the new initialization method performs compared to the de facto standard ones that are widely used today.", "field": "cs", "label": 1}
{"text": "Title: Configuration space, moduli space and 3-fold covering space\nAbstract: A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid groups and mapping class groups of surface, respectively. This map $\\phi: B_k \\rightarrow \\Gamma_{g,b}$ is induced by 3-fold branched covering over a disk with some branch points. In this thesis we give a concrete description of this map and show that it is injective by Birman-Hilden theory. This gives us a new interesting non-geometric embedding of braid group into mapping class group. On the other hand, we show that the map on the level of classifying spaces of groups is compatible with the action of little 2-cube operad so that it induces a trivial homomorphim between stable homology group of braid groups and that of mapping class groups(Harer conjecture). We also show how the lift $\\tilde{\\beta_i}$ acts on the fundamental group of the surface and through this we prove that $\\tilde{\\beta_i}$ equals the product of two inverse Dehn twists.", "field": "math", "label": 1}
{"text": "Title: A-infinity algebras, modules and functor categories\nAbstract: In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis. Finally, starting from an idea of V. Lyubashenko's, we give a conceptual construction of A-infinity functor categories using a suitable closed monoidal category of cocategories. In particular, this yields a natural construction of the bialgebra structure on the bar construction of the Hochschild complex of an associative algebra.", "field": "math", "label": 1}
{"text": "Title: Global Well-posedness for 2D non-resistive MHD equations in half-space\nAbstract: This paper focuses on the initial boundary value problem of two-dimensional non-resistive MHD equations in a half space. We prove that the MHD equations have a unique global strong solution around the equilibrium state $(0,\\bf{e_1})$ for Dirichlet boundary condition of velocity and modified Neumann boundary condition of magnetic.", "field": "math", "label": 0}
{"text": "Title: Liberating dimension and spectral norm: A universal approach to spectral properties of sample covariance matrices\nAbstract: In this paper, our objective is to present a constraining principle governing the spectral properties of the sample covariance matrix. This principle exhibits harmonious behavior across diverse limiting frameworks, eliminating the need for constraints on the rates of dimension $p$ and sample size $n$, as long as they both tend to infinity. We accomplish this by employing a suitable normalization technique on the original sample covariance matrix. Following this, we establish a harmonic central limit theorem for linear spectral statistics within this expansive framework. This achievement effectively eliminates the necessity for a bounded spectral norm on the population covariance matrix and relaxes constraints on the rates of dimension $p$ and sample size $n$, thereby significantly broadening the applicability of these results in the field of high-dimensional statistics. We illustrate the power of the established results by considering the test for covariance structure under high dimensionality, freeing both $p$ and $n$.", "field": "math", "label": 0}
{"text": "Title: Child Face Age-Progression via Deep Feature Aging\nAbstract: Given a gallery of face images of missing children, state-of-the-art face recognition systems fall short in identifying a child (probe) recovered at a later age. We propose a feature aging module that can age-progress deep face features output by a face matcher. In addition, the feature aging module guides age-progression in the image space such that synthesized aged faces can be utilized to enhance longitudinal face recognition performance of any face matcher without requiring any explicit training. For time lapses larger than 10 years (the missing child is found after 10 or more years), the proposed age-progression module improves the closed-set identification accuracy of FaceNet from 16.53% to 21.44% and CosFace from 60.72% to 66.12% on a child celebrity dataset, namely ITWCC. The proposed method also outperforms state-of-the-art approaches with a rank-1 identification rate of 95.91%, compared to 94.91%, on a public aging dataset, FG-NET, and 99.58%, compared to 99.50%, on CACD-VS. These results suggest that aging face features enhances the ability to identify young children who are possible victims of child trafficking or abduction.", "field": "cs", "label": 1}
{"text": "Title: Long range order for three-dimensional random field Ising model throughout the entire low temperature regime\nAbstract: For $d\\geq 3$, we study the Ising model on $\\mathbb Z^d$ with random field given by $\\{\\epsilon h_v: v\\in \\mathbb Z^d\\}$ where $h_v$'s are independent normal variables with mean 0 and variance 1. We show that for any $T < T_c$ (here $T_c$ is the critical temperature without disorder), long range order exists as long as $\\epsilon$ is sufficiently small depending on $T$. Our work extends previous results of Imbrie (1985) and Bricmont--Kupiainen (1988) from the very low temperature regime to the entire low temperature regime.", "field": "math", "label": 1}
{"text": "Title: Craig's Interpolation Theorem formalised and mechanised in Isabelle/HOL\nAbstract: We formalise and mechanise a construtive, proof theoretic proof of Craig's Interpolation Theorem in Isabelle/HOL. We give all the definitions and lemma statements both formally and informally. We also transcribe informally the formal proofs. We detail the main features of our mechanisation, such as the formalisation of binding for first order formulae. We also give some applications of Craig's Interpolation Theorem.", "field": "cs", "label": 1}
{"text": "Title: A stochastic representation theorem for sublinear semigroups with non-local generators\nAbstract: In this paper we investigate sublinear semigroups whose pointwise generators are given by non-local Hamilton-Jacobi-Bellman operators. Our main result provides a stochastic representation in terms of a family of sublinear (conditional) expectations that can be understood as a nonlinear Markov family with uncertain local characteristics. The proofs are based on viscosity methods.", "field": "math", "label": 0}
{"text": "Title: An Artificial Neural Network Functionalized by Evolution\nAbstract: The topology of artificial neural networks has a significant effect on their performance. Characterizing efficient topology is a field of promising research in Artificial Intelligence. However, it is not a trivial task and it is mainly experimented on through convolutional neural networks. We propose a hybrid model which combines the tensor calculus of feed-forward neural networks with Pseudo-Darwinian mechanisms. This allows for finding topologies that are well adapted for elaboration of strategies, control problems or pattern recognition tasks. In particular, the model can provide adapted topologies at early evolutionary stages, and 'structural convergence', which can found applications in robotics, big-data and artificial life.", "field": "cs", "label": 1}
{"text": "Title: Properties from Mechanisms: An Equivariance Perspective on Identifiable Representation Learning\nAbstract: A key goal of unsupervised representation learning is \"inverting\" a data generating process to recover its latent properties. Existing work that provably achieves this goal relies on strong assumptions on relationships between the latent variables (e.g., independence conditional on auxiliary information). In this paper, we take a very different perspective on the problem and ask, \"Can we instead identify latent properties by leveraging knowledge of the mechanisms that govern their evolution?\" We provide a complete characterization of the sources of non-identifiability as we vary knowledge about a set of possible mechanisms. In particular, we prove that if we know the exact mechanisms under which the latent properties evolve, then identification can be achieved up to any equivariances that are shared by the underlying mechanisms. We generalize this characterization to settings where we only know some hypothesis class over possible mechanisms, as well as settings where the mechanisms are stochastic. We demonstrate the power of this mechanism-based perspective by showing that we can leverage our results to generalize existing identifiable representation learning results. These results suggest that by exploiting inductive biases on mechanisms, it is possible to design a range of new identifiable representation learning approaches.", "field": "cs", "label": 1}
{"text": "Title: A Robust Quantile Huber Loss With Interpretable Parameter Adjustment In Distributional Reinforcement Learning\nAbstract: Distributional Reinforcement Learning (RL) estimates return distribution mainly by learning quantile values via minimizing the quantile Huber loss function, entailing a threshold parameter often selected heuristically or via hyperparameter search, which may not generalize well and can be suboptimal. This paper introduces a generalized quantile Huber loss function derived from Wasserstein distance (WD) calculation between Gaussian distributions, capturing noise in predicted (current) and target (Bellman-updated) quantile values. Compared to the classical quantile Huber loss, this innovative loss function enhances robustness against outliers. Notably, the classical Huber loss function can be seen as an approximation of our proposed loss, enabling parameter adjustment by approximating the amount of noise in the data during the learning process. Empirical tests on Atari games, a common application in distributional RL, and a recent hedging strategy using distributional RL, validate the effectiveness of our proposed loss function and its potential for parameter adjustments in distributional RL.", "field": "cs", "label": 0}
{"text": "Title: Theta-Induced Diffusion on Tate Elliptic Curves over Non-Archimedean Local Fields\nAbstract: A diffusion operator on the $K$-rational points of a Tate elliptic curve $E_q$ is constructed, where $K$ is a non-archimedean local field, as well as an operator on the Berkovich-analytification $E_q^{an}$ of $E_q$. These are integral operators for measures coming from a regular $1$-form, and kernel functions constructed via theta functions. The second operator can be described via certain non-archimedan curvature forms on $E_q^{an}$. The spectra of these self-adjoint bounded operators on the Hilbert spaces of $L^2$-functions are identical and found to consist of finitely many eigenvalues. A study of the corresponding heat equations yields a positive answer to the Cauchy problem, and induced Markov processes on the curve. Finally, some geometric information about the $K$-rational points of $E_q$ is retrieved from the spectrum.", "field": "math", "label": 0}
{"text": "Title: A Galton-Watson tree approach to local limits of permutations avoiding a pattern of length three\nAbstract: We use local limits of Galton-Watson trees to establish local limit theorems for permutations conditioned to avoid a pattern of length three. In the case of 321-avoiding permutations our results resolve an open problem of Pinsky. In the other cases our results give new descriptions of the limiting objects in terms of size-biased Galton-Watson trees.", "field": "math", "label": 0}
{"text": "Title: An Equivariant Tensor Product on Mackey Functors\nAbstract: For all subgroups $H$ of a cyclic $p$-group $G$ we define norm functors that build a $G$-Mackey functor from an $H$-Mackey functor. We give an explicit construction of these functors in terms of generators and relations based solely on the intrinsic, algebraic properties of Mackey functors and Tambara functors. We use these norm functors to define a monoidal structure on the category of Mackey functors where Tambara functors are the commutative ring objects.", "field": "math", "label": 1}
{"text": "Title: Causal Stream Inclusions\nAbstract: We study solutions to systems of stream inclusions 'f in T(f)', where T is assumed to be causal in the sense that elements in output streams are determined by a finite history of inputs. For solving these inclusions we develop a correspondence of causality and contraction with respect to the prefix distance on streams. Now, based on this causality-contraction correspondence, we apply fixpoint principles for the spherically complete ultrametric space of streams to obtain solutions for causal stream inclusions. The underlying fixpoint iterations induce fixpoint induction principles for reasoning about solutions of causal stream inclusions. In addition, these fixpoint approximations induce anytime algorithms for computing finite stream prefixes of solutions. We illustrate the use of these developments for some central concepts of system design.", "field": "cs", "label": 0}
{"text": "Title: Crafting, Communality, and Computing: Building on Existing Strengths To Support a Vulnerable Population\nAbstract: In Nepal, sex-trafficking survivors and the organizations that support them have limited resources to assist the survivors in their on-going journey towards reintegration. We take an asset-based approach wherein we identify and build on the strengths possessed by such groups. In this work, we present reflections from introducing a voice-annotated web application to a group of survivors. The web application tapped into and built upon two elements of pre-existing strengths possessed by the survivors -- the social bond between them and knowledge of crafting as taught to them by the organization. Our findings provide insight into the array of factors influencing how the survivors act in relation to one another as they created novel use practices and adapted the technology. Experience with the application seemed to open knowledge of computing as a potential source of strength. Finally, we articulate three design desiderata that could help promote communal spaces: make activity perceptible to the group, create appropriable steps, and build in fun choices.", "field": "cs", "label": 1}
{"text": "Title: Balancing Adaptability and Non-exploitability in Repeated Games\nAbstract: We study the problem of guaranteeing low regret in repeated games against an opponent with unknown membership in one of several classes. We add the constraint that our algorithm is non-exploitable, in that the opponent lacks an incentive to use an algorithm against which we cannot achieve rewards exceeding some \"fair\" value. Our solution is an expert algorithm (LAFF) that searches within a set of sub-algorithms that are optimal for each opponent class and uses a punishment policy upon detecting evidence of exploitation by the opponent. With benchmarks that depend on the opponent class, we show that LAFF has sublinear regret uniformly over the possible opponents, except exploitative ones, for which we guarantee that the opponent has linear regret. To our knowledge, this work is the first to provide guarantees for both regret and non-exploitability in multi-agent learning.", "field": "cs", "label": 1}
{"text": "Title: Dynamics of point-vortex systems near thermal equilibrium: relaxation or not?\nAbstract: This article is devoted to the long-time dynamics of point-vortex systems near thermal equilibrium and to the possible emergence of collisional relaxation. More precisely, we consider a tagged particle coupled to a large number of background particles that are initially at equilibrium, and we analyze its resulting slow dynamics. On the one hand, in the spirit of the Lenard-Balescu relaxation for plasmas, we establish in a generic setting the outset of the slow thermalization of the tagged particle. On the other hand, we show that a completely different phenomenology is also possible in some degenerate regime: the slow dynamics of the tagged particle then remains conservative and the thermalization no longer holds in a strict sense. We provide the first detailed description of this degenerate regime and of its mixing properties. Note that it is particularly delicate to handle due to statistical closure problems, which manifest themselves as a lack of self-adjointness of the effective Hamiltonian.", "field": "math", "label": 0}
{"text": "Title: Thue-Morse constant is not badly approximable\nAbstract: We prove that Thue-Morse constant $\\tau_{TM}=0.01101001..._2$ is not a badly approximable number. Moreover, we prove that $\\tau_{TM}(a)=0.01101001..._a$ is not badly approximable for every integer base $a\\geq 2$ such that $a$ is not divisible by 15. At the same time we provide a precise formula for convergents of the Laurent series $\\tilde{f}_{TM}(z) = z^{-1}\\prod_{n=1}^\\infty (1-z^{-2^n})$, thus developing further the research initiated by Alf van der Poorten and others.", "field": "math", "label": 1}
{"text": "Title: The Influence of Biomedical Research on Future Business Funding: Analyzing Scientific Impact and Content in Industrial Investments\nAbstract: This paper investigates the relationship between scientific innovation in biomedical sciences and its impact on industrial activities, focusing on how the historical impact and content of scientific papers influenced future funding and innovation grant application content for small businesses. The research incorporates bibliometric analyses along with SBIR (Small Business Innovation Research) data to yield a holistic view of the science-industry interface. By evaluating the influence of scientific innovation on industry across 10,873 biomedical topics and taking into account their taxonomic relationships, we present an in-depth exploration of science-industry interactions where we quantify the temporal effects and impact latency of scientific advancements on industrial activities, spanning from 2010 to 2021. Our findings indicate that scientific progress substantially influenced industrial innovation funding and the direction of industrial innovation activities. Approximately 76% and 73% of topics showed a correlation and Granger-causality between scientific interest in papers and future funding allocations to relevant small businesses. Moreover, around 74% of topics demonstrated an association between the semantic content of scientific abstracts and future grant applications. Overall, the work contributes to a more nuanced and comprehensive understanding of the science-industry interface, opening avenues for more strategic resource allocation and policy developments aimed at fostering innovation.", "field": "cs", "label": 0}
{"text": "Title: The tensor product in the theory of Frobenius manifolds\nAbstract: We introduce the operation of forming the tensor product in the theory of analytic Frobenius manifolds. Building on the results for formal Frobenius manifolds which we extend to the additional structures of Euler fields and flat identities, we prove that the tensor product of pointed germs of Frobenius manifolds exists. Furthermore, we define the notion of a tensor product diagram of Frobenius manifolds with factorizable flat identity and prove the existence such a diagram and hence a tensor product Frobenius manifold. These diagrams and manifolds are unique up to equivalence. Finally, we derive the special initial conditions for a tensor product of semi--simple Frobenius manifolds in terms of the special initial conditions of the factors.", "field": "math", "label": 1}
{"text": "Title: Poisson summation for Hankel transforms\nAbstract: In this article we study the Poisson summation for Hankel transform in the sense of Braverman-Kazhdan-Ngo in the special case of $L$-embedding $\\rho: GL_1\\rightarrow GL_2$. We view such a summation formula as the generalization of the classical Voronoi summation formula.", "field": "math", "label": 1}
{"text": "Title: Interface spaces based on physics for multiscale mixed methods applied to flows in fractured-like porous media\nAbstract: It is well known that domain-decomposition-based multiscale mixed methods rely on interface spaces, defined on the skeleton of the decomposition, to connect the solution among the non-overlapping subdomains. Usual spaces, such as polynomial-based ones, cannot properly represent high-contrast channelized features such as fractures (high permeability) and barriers (low permeability) for flows in heterogeneous porous media. We propose here new interface spaces, which are based on physics, to deal with permeability fields in the simultaneous presence of fractures and barriers, accommodated respectively, by the pressure and flux spaces. Existing multiscale methods based on mixed formulations can take advantage of the proposed interface spaces, however, in order to present and test our results, we use the newly developed Multiscale Robin Coupled Method (MRCM) [Guiraldello, et al., J. Comput. Phys., 355 (2018) pp. 1-21], which generalizes most well-known multiscale mixed methods, and allows for the independent choice of the pressure and flux interface spaces. An adaptive version of the MRCM [Rocha, et al., J. Comput. Phys., 409 (2020), 109316] is considered that automatically selects the physics-based pressure space for fractured structures and the physics-based flux space for regions with barriers, resulting in a procedure with unprecedented accuracy. The features of the proposed approach are investigated through several numerical simulations of single-phase and two-phase flows, in different heterogeneous porous media. The adaptive MRCM combined with the interface spaces based on physics provides promising results for challenging problems with the simultaneous presence of fractures and barriers.", "field": "math", "label": 1}
{"text": "Title: On the first restricted cohomology of a reductive Lie algebra and its Borel subalgebras\nAbstract: Let k be an algebraically closed field of characteristic p>0 and let G be a connected reductive group over k. Let B be a Borel subgroup of G and let g and b be the Lie algebras of G and B. Denote the first Frobenius kernels of G and B by G_1 and B_1. Furthermore, denote the algebras of polynomial functions on G and g by k[G] and k[g], and similar for B and b. The group G acts on k[G] via the conjugation action and on k[g] via the adjoint action. Similarly, B acts on k[B] via the conjugation action and on k[b] via the adjoint action. We show that, under certain mild assumptions, the cohomology groups H^1(G_1,k[g]), H^1(B_1,k[b]), H^1(G_1,k[G]) and H^1(B_1,k[B]) are zero. We also extend all our results to the cohomology for the higher Frobenius kernels.", "field": "math", "label": 1}
{"text": "Title: On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation\nAbstract: We consider the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability exponent, but the exact values of the constants are unknown in many cases. We describe a new approach to the Gamma-convergence result that leads in some special cases to the exact value of the constants, and to the existence of smooth recovery families.", "field": "math", "label": 1}
{"text": "Title: Rethinking Response Evaluation from Interlocutor's Eye for Open-Domain Dialogue Systems\nAbstract: Open-domain dialogue systems have started to engage in continuous conversations with humans. Those dialogue systems are required to be adjusted to the human interlocutor and evaluated in terms of their perspective. However, it is questionable whether the current automatic evaluation methods can approximate the interlocutor's judgments. In this study, we analyzed and examined what features are needed in an automatic response evaluator from the interlocutor's perspective. The first experiment on the Hazumi dataset revealed that interlocutor awareness plays a critical role in making automatic response evaluation correlate with the interlocutor's judgments. The second experiment using massive conversations on X (formerly Twitter) confirmed that dialogue continuity prediction can train an interlocutor-aware response evaluator without human feedback while revealing the difficulty in evaluating generated responses compared to human responses.", "field": "cs", "label": 0}
{"text": "Title: PBW bases and KLR algebras\nAbstract: We generalize Lusztig's geometric construction of the PBW bases of finite quantum groups of type $\\mathsf{ADE}$ under the framework of [Varagnolo-Vasserot, J. reine angew. Math. 659 (2011)]. In particular, every PBW basis of such quantum groups is proven to yield a semi-orthogonal collection in the module category of the KLR-algebras. This enables us to prove Lusztig's conjecture on the positivity of the canonical (lower global) bases in terms of the (lower) PBW bases in the $\\mathsf{ADE}$ case. In addition, we verify Kashiwara's problem on the finiteness of the global dimensions of the KLR-algebras of type $\\mathsf{ADE}$.", "field": "math", "label": 1}
{"text": "Title: A Deep Reinforcement Learning Approach to Efficient Distributed Optimization\nAbstract: In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a given specific problem. In this paper, we propose a learning-based method to achieve efficient distributed optimization over networked systems. Specifically, a deep reinforcement learning (DRL) framework is developed for adaptive configuration within a parameterized unifying algorithmic form, which incorporates an abundance of decentralized first-order and second-order optimization algorithms. We exploit the local consensus and objective information to represent the regularities of problem instances and trace the solving progress, which constitute the states observed by a DRL agent. The framework is trained using Proximal Policy Optimization (PPO) on a number of practical problem instances of similar structures yet different problem data. Experiments on various smooth and non-smooth classes of objective functions demonstrate that our proposed learning-based method outperforms several state-of-the-art distributed optimization algorithms in terms of convergence speed and solution accuracy.", "field": "math", "label": 0}
{"text": "Title: Two kinds of partial Motzkin paths with air pockets\nAbstract: Motzkin paths with air pockets (MAP) are defined as a generalization of Dyck paths with air pockets by adding some horizontal steps with certain conditions. In this paper, we introduce two generalizations. The first one consists of lattice paths in $\\Bbb{N}^2$ starting at the origin made of steps $U=(1,1)$, $D_k=(1,-k)$, $k\\geq 1$ and $H=(1,0)$, where two down steps cannot be consecutive, while the second one are lattice paths in $\\Bbb{N}^2$ starting at the origin, made of steps $U$, $D_k$ and $H$, where each step $D_k$ and $H$ is necessarily followed by an up step, except for the last step of the path. We provide enumerative results for these paths according to the length, the type of the last step, and the height of its end-point. A similar study is made for these paths read from right to left. As a byproduct, we obtain new classes of paths counted by the Motzkin numbers. Finally, we express our results using Riordan arrays.", "field": "math", "label": 1}
{"text": "Title: Ramsey properties of random graphs and Folkman numbers\nAbstract: For two graphs, $G$ and $F$, and an integer $r\\ge2$ we write $G\\rightarrow (F)_r$ if every $r$-coloring of the edges of $G$ results in a monochromatic copy of $F$. In 1995, the first two authors established a threshold edge probability for the Ramsey property $G(n,p)\\to (F)_r$, where $G(n,p)$ is a random graph obtained by including each edge of the complete graph on $n$ vertices, independently, with probability $p$. The original proof was based on the regularity lemma of Szemer\\'edi and this led to tower-type dependencies between the involved parameters. Here, for $r=2$, we provide a self-contained proof of a quantitative version of the Ramsey threshold theorem with only double exponential dependencies between the constants. As a corollary we obtain a double exponential upper bound on the 2-color Folkman numbers. By a different proof technique, a similar result was obtained independently by Conlon and Gowers.", "field": "math", "label": 1}
{"text": "Title: Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation\nAbstract: In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilatation, then back-substitute dilatation, and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. We then apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lam\\'{e} parameters satisfy $\\lambda \\geq \\mu$ to avoid adding extra constraints on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.", "field": "math", "label": 1}
{"text": "Title: On Newton polytopes of Lagrangian augmentations\nAbstract: This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many distinct Lagrangian fillings, both for Legendrian links and higher-dimensional Legendrian spheres. The computations we perform work in finite characteristic, which significantly simplifies arguments and also allows us to show that there exist Legendrian links with infinitely many non-orientable exact Lagrangian fillings.", "field": "math", "label": 0}
{"text": "Title: Entropy-minimizing dynamical transport on Riemannian manifolds\nAbstract: Given a smooth Riemannian manifold $(M,g)$, compact and without boundary, we analyze the dynamical optimal mass transport problem where the cost is given by the sum of the kinetic energy and the relative entropy with respect to a reference volume measure $e^{-V}dx$. Under the only assumption that the prescribed marginals lie in $L^1(M)$, and a lower bound on the Ricci curvature, we characterize the minimal curves as unique weak solutions of the optimality system coupling the continuity equation with a backward Hamilton-Jacobi equation (with source given by $\\log (m)$). We give evidence that the entropic cost enhances diffusive effects in the evolution of the optimal densities, proving $L^1\\to L^\\infty$ regularization in time for any initial-terminal data, and smoothness of the solutions whenever the marginals are positive and smooth. We use displacement convexity arguments (in the Eulerian approach) and gradient bounds from quasilinear elliptic equations. We also prove the convergence of optimal curves towards the classical Wasserstein geodesics, as the entropic term is multiplied by a vanishing parameter, showing that this kind of functionals can be used to build a smoothing approximation of the standard optimal transport problem.", "field": "math", "label": 0}
{"text": "Title: Joint Beamforming and Offloading Design for Integrated Sensing, Communication and Computation System\nAbstract: Mobile edge computing (MEC) is powerful to alleviate the heavy computing tasks in integrated sensing and communication (ISAC) systems. In this paper, we investigate joint beamforming and offloading design in a three-tier integrated sensing, communication and computation (ISCC) framework comprising one cloud server, multiple mobile edge servers, and multiple terminals. While executing sensing tasks, the user terminals can optionally offload sensing data to either MEC server or cloud servers. To minimize the execution latency, we jointly optimize the transmit beamforming matrices and offloading decision variables under the constraint of sensing performance. An alternating optimization algorithm based on multidimensional fractional programming is proposed to tackle the non-convex problem. Simulation results demonstrates the superiority of the proposed mechanism in terms of convergence and task execution latency reduction, compared with the state-of-the-art two-tier ISCC framework.", "field": "cs", "label": 0}
{"text": "Title: Rationality of holomorphic vertex operator algebras\nAbstract: We prove that if V is a unitary simple holomorphic vertex operator algebra of CFT type, then V is rational, that is, all N-gradable V-modules are direct sums of copies of V.", "field": "math", "label": 0}
{"text": "Title: Integer Forcing-and-Forward Transceiver Design for MIMO Multi-Pair Two-Way Relaying\nAbstract: In this paper, we propose a new transmission scheme, named as Integer Forcing-and-Forward (IFF), for communications among multi-pair multiple-antenna users in which each pair exchanges their messages with the help of a single multi antennas relay in the multiple-access and broadcast phases. The proposed scheme utilizes Integer Forcing Linear Receiver (IFLR) at relay, which uses equations, i.e., linear integer-combinations of messages, to harness the intra-pair interference. Accordingly, we propose the design of mean squared error (MSE) based transceiver, including precoder and projection matrices for the relay and users, assuming that the perfect channel state information (CSI) is available. In this regards, in the multiple-access phase, we introduce two new MSE criteria for the related precoding and filter designs, i.e., the sum of the equations MSE (Sum-Equation MSE) and the maximum of the equations MSE (Max-Equation MSE), to exploit the equations in the relay. In addition, the convergence of the proposed criteria is proven as well. Moreover, in the broadcast phase, we use the two traditional MSE criteria, i.e. the sum of the users' mean squred errors (Sum MSE) and the maximum of the users' mean squared errors (Max MSE), to design the related precoding and filters for recovering relay's equations by the users. Then, we consider a more practical scenario with imperfect CSI. For this case, IFLR receiver is modified, and another transceiver design is proposed, which take into account the effect of channels estimation error. We evaluate the performance of our proposed strategy and compare the results with the conventional amplify-and-forward (AF) and denoise-and-forward (DF) strategies for the same scenario. The results indicate the substantial superiority of the proposed strategy in terms of the outage probability and the sum rate.", "field": "cs", "label": 1}
{"text": "Title: Neural Collapse for Cross-entropy Class-Imbalanced Learning with Unconstrained ReLU Feature Model\nAbstract: The current paradigm of training deep neural networks for classification tasks includes minimizing the empirical risk that pushes the training loss value towards zero, even after the training error has been vanished. In this terminal phase of training, it has been observed that the last-layer features collapse to their class-means and these class-means converge to the vertices of a simplex Equiangular Tight Frame (ETF). This phenomenon is termed as Neural Collapse (NC). To theoretically understand this phenomenon, recent works employ a simplified unconstrained feature model to prove that NC emerges at the global solutions of the training problem. However, when the training dataset is class-imbalanced, some NC properties will no longer be true. For example, the class-means geometry will skew away from the simplex ETF when the loss converges. In this paper, we generalize NC to imbalanced regime for cross-entropy loss under the unconstrained ReLU feature model. We prove that, while the within-class features collapse property still holds in this setting, the class-means will converge to a structure consisting of orthogonal vectors with different lengths. Furthermore, we find that the classifier weights are aligned to the scaled and centered class-means with scaling factors depend on the number of training samples of each class, which generalizes NC in the class-balanced setting. We empirically prove our results through experiments on practical architectures and dataset.", "field": "cs", "label": 0}
{"text": "Title: Estimating continuous data of wrist joint angles using ultrasound images\nAbstract: Ultrasound imaging has recently been introduced as a sensing interface for joint motion estimation. The use of ultrasound images as an estimation method is expected to improve the control performance of assistive devices and human--machine interfaces. This study aimed to estimate continuous wrist joint angles using ultrasound images. Specifically, in an experiment, joint angle information was obtained during extension--flexion movements, and ultrasound images of the associated muscles were acquired. Using the features obtained from ultrasound images, a multivariate linear regression model was used to estimate the joint angles. The coordinates of the feature points obtained using optical flow from the ultrasound images were used as explanatory variables of the multivariate linear regression model. The model was trained and tested for each trial by each participant to verify the estimation accuracy. The results show that the mean and standard deviation of the estimation accuracy for all trials were root mean square error (RMSE)=1.82 $\\pm$ 0.54 deg and coefficient of determination (R2)=0.985 $\\pm$ 0.009. Our method achieves a highly accurate estimation of joint angles compared with previous studies using other signals, such as surface electromyography, while the multivariate linear regression model is simple and both computational and model training costs are low.", "field": "cs", "label": 0}
{"text": "Title: Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation on cylindrical spaces\nAbstract: We prove that the Zakharov-Kuznetsov equation on cylindrical spaces is globally well-posed below the energy norm. As is known, local well-posedness below energy space was obtained by the first author. We adapt I-method to extend the solutions globally in time. Using modified energies, we obtain the polynomial bounds on the $H^s$ growth for the global solutions.", "field": "math", "label": 0}
{"text": "Title: Hessian estimates for special Lagrangian equation by doubling\nAbstract: New, doubling proofs are given for the interior Hessian estimates of the special Lagrangian equation. These estimates were originally shown by Chen-Warren-Yuan in CPAM 2009 and Wang-Yuan in AJM 2014. This yields a higher codimension analogue of Korevaar's 1987 pointwise proof of the gradient estimate for minimal hypersurfaces, without using the Michael-Simon mean value inequality.", "field": "math", "label": 0}
{"text": "Title: Towards Fully Decoupled End-to-End Person Search\nAbstract: End-to-end person search aims to jointly detect and re-identify a target person in raw scene images with a unified model. The detection task unifies all persons while the re-id task discriminates different identities, resulting in conflict optimal objectives. Existing works proposed to decouple end-to-end person search to alleviate such conflict. Yet these methods are still sub-optimal on one or two of the sub-tasks due to their partially decoupled models, which limits the overall person search performance. In this paper, we propose to fully decouple person search towards optimal person search. A task-incremental person search network is proposed to incrementally construct an end-to-end model for the detection and re-id sub-task, which decouples the model architecture for the two sub-tasks. The proposed task-incremental network allows task-incremental training for the two conflicting tasks. This enables independent learning for different objectives thus fully decoupled the model for persons earch. Comprehensive experimental evaluations demonstrate the effectiveness of the proposed fully decoupled models for end-to-end person search.", "field": "cs", "label": 0}
{"text": "Title: FairGridSearch: A Framework to Compare Fairness-Enhancing Models\nAbstract: Machine learning models are increasingly used in critical decision-making applications. However, these models are susceptible to replicating or even amplifying bias present in real-world data. While there are various bias mitigation methods and base estimators in the literature, selecting the optimal model for a specific application remains challenging. This paper focuses on binary classification and proposes FairGridSearch, a novel framework for comparing fairness-enhancing models. FairGridSearch enables experimentation with different model parameter combinations and recommends the best one. The study applies FairGridSearch to three popular datasets (Adult, COMPAS, and German Credit) and analyzes the impacts of metric selection, base estimator choice, and classification threshold on model fairness. The results highlight the significance of selecting appropriate accuracy and fairness metrics for model evaluation. Additionally, different base estimators and classification threshold values affect the effectiveness of bias mitigation methods and fairness stability respectively, but the effects are not consistent across all datasets. Based on these findings, future research on fairness in machine learning should consider a broader range of factors when building fair models, going beyond bias mitigation methods alone.", "field": "cs", "label": 0}
{"text": "Title: Chromatic symmetric function of graphs from Borcherds algebras\nAbstract: Let $\\mathfrak g$ be a Borcherds algebra with the associated graph $G$. We prove that the chromatic symmetric function of $G$ can be recovered from the Weyl denominator identity of $\\mathfrak g$ and this gives a Lie theoretic proof of Stanley's expression for chromatic symmetric function in terms of power sum symmetric function. Also, this gives an expression for chromatic symmetric function of $G$ in terms of root multiplicities of $\\lie g$. The absolute value of the linear coefficient of the chromatic polynomial of $G$ is known as the chromatic discriminant of $G$. As an application of our main theorem, we prove that graphs with different chromatic discriminants are distinguished by their chromatic symmetric functions. Also, we find a connection between the Weyl denominators and the $G$-elementary symmetric functions. Using this connection, we give a Lie theoretic proof of non-negativity of coefficients of $G$-power sum symmetric functions.", "field": "math", "label": 1}
{"text": "Title: Isometric immersions of Riemannian manifolds in $k$-codimensional Euclidean space\nAbstract: We use a new method to give conditions for the existence of a local isometric immersion of a Riemannian $n$-manifold $M$ in $\\mathbb{R}^{n+k}$, for a given $n$ and $k$. These equate to the (local) existence of a $k$-tuple of scalar fields on the manifold, satisfying a certain non-linear equation involving the Riemannian curvature tensor of $M$. Setting $k=1$, we proceed to recover the fundamental theorem of hypersurfaces. In the case of manifolds of positive sectional curvature and $n\\geq 3$, we reduce the solvability of the Gauss and Codazzi equations to the cancelation of a set of obstructions involving the logarithm of the Riemann curvature operator. The resulting theorem has a structural similarity to the Weyl-Schouten theorem, suggesting a parallelism between conformally flat $n$-manifolds and those that admit an isometric immersion in $\\mathbb{R}^{n+1}$.", "field": "math", "label": 1}
{"text": "Title: The crystalline measure that is not a Fourier Quasicrystal\nAbstract: We construct a crystalline measure on the real line, which is not a Fourier Quasicrystal.", "field": "math", "label": 0}
{"text": "Title: Efficient iterative methods for hyperparameter estimation in large-scale linear inverse problems\nAbstract: We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for small problems with very few hyperparameters but are not computationally feasible for problems with a very large number of unknown parameters. In this work, we describe an empirical Bayesian (EB) method to estimate hyperparameters that maximize the marginal posterior, i.e., the probability density of the hyperparameters conditioned on the data, and then we use the estimated values to compute the posterior of the inverse parameters. For problems where the computation of the square root and inverse of prior covariance matrices are not feasible, we describe an approach based on the generalized Golub-Kahan bidiagonalization to approximate the marginal posterior and seek hyperparameters that minimize the approximate marginal posterior. Numerical results from seismic and atmospheric tomography demonstrate the accuracy, robustness, and potential benefits of the proposed approach.", "field": "math", "label": 0}
{"text": "Title: Deep Recurrent Level Set for Segmenting Brain Tumors\nAbstract: Variational Level Set (VLS) has been a widely used method in medical segmentation. However, segmentation accuracy in the VLS method dramatically decreases when dealing with intervening factors such as lighting, shadows, colors, etc. Additionally, results are quite sensitive to initial settings and are highly dependent on the number of iterations. In order to address these limitations, the proposed method incorporates VLS into deep learning by defining a novel end-to-end trainable model called as Deep Recurrent Level Set (DRLS). The proposed DRLS consists of three layers, i.e, Convolutional layers, Deconvolutional layers with skip connections and LevelSet layers. Brain tumor segmentation is taken as an instant to illustrate the performance of the proposed DRLS. Convolutional layer learns visual representation of brain tumor at different scales. Since brain tumors occupy a small portion of the image, deconvolutional layers are designed with skip connections to obtain a high quality feature map. Level-Set Layer drives the contour towards the brain tumor. In each step, the Convolutional Layer is fed with the LevelSet map to obtain a brain tumor feature map. This in turn serves as input for the LevelSet layer in the next step. The experimental results have been obtained on BRATS2013, BRATS2015 and BRATS2017 datasets. The proposed DRLS model improves both computational time and segmentation accuracy when compared to the the classic VLS-based method. Additionally, a fully end-to-end system DRLS achieves state-of-the-art segmentation on brain tumors.", "field": "cs", "label": 1}
{"text": "Title: Debiased Cross-modal Matching for Content-based Micro-video Background Music Recommendation\nAbstract: Micro-video background music recommendation is a complicated task where the matching degree between videos and uploader-selected background music is a major issue. However, the selection of the user-generated content (UGC) is biased caused by knowledge limitations and historical preferences among music of each uploader. In this paper, we propose a Debiased Cross-Modal (DebCM) matching model to alleviate the influence of such selection bias. Specifically, we design a teacher-student network to utilize the matching of segments of music videos, which is professional-generated content (PGC) with specialized music-matching techniques, to better alleviate the bias caused by insufficient knowledge of users. The PGC data is captured by a teacher network to guide the matching of uploader-selected UGC data of the student network by KL-based knowledge transfer. In addition, uploaders' personal preferences of music genres are identified as confounders that spuriously correlate music embeddings and background music selections, resulting in the learned recommender system to over-recommend music from the majority groups. To resolve such confounders in the UGC data of the student network, backdoor adjustment is utilized to deconfound the spurious correlation between music embeddings and prediction scores. We further utilize Monte Carlo (MC) estimator with batch-level average as the approximations to avoid integrating the entire confounder space calculated by the adjustment. Extensive experiments on the TT-150k-genre dataset demonstrate the effectiveness of the proposed method towards the selection bias. The code is publicly available on: \\url{https://github.com/jing-1/DebCM}.", "field": "cs", "label": 1}
{"text": "Title: Separable homology of graphs and the Whitehead complex\nAbstract: We introduce the Whitehead complex, a one-complex associated to a finite regular cover of the rose and show that it is connected if and only if the fundamental group of the associated cover is generated by its intersection with the set of elements in proper free factors of $\\mathbf{F}_n$. The Whitehead complex admits an action of $\\mathrm{Out}(\\mathbf{F}_n)$ by isometries if the associated cover corresponds to a characteristic subgroup of $\\mathbf{F}_n$. We prove that the Whitehead complex of the rose has infinite diameter and is nonhyperbolic, implying it is not quasi-isometric to the free splitting complex or the free factor complex.", "field": "math", "label": 0}
{"text": "Title: Compatibility of Hodge Theory on Alexander Modules\nAbstract: Let $U$ be a smooth connected complex algebraic variety, and let $f\\colon U\\to \\mathbb C^*$ be an algebraic map. To the pair $(U,f)$ one can associate an infinite cyclic cover $U^f$, and (homology) Alexander modules are defined as the homology groups of this cover. In two recent works, the first of which is joint with Geske, Maxim and Wang, we developed two different ways to put a mixed Hodge structure on Alexander modules. Since they are not finite dimensional in general, each approach replaces the Alexander module by a different finite dimensional module: one of them takes the torsion submodule, the other takes finite dimensional quotients, and the constructions are not directly comparable. In this note, we show that both constructions are compatible, in the sense that the map from the torsion to the quotients is a mixed Hodge structure morphism.", "field": "math", "label": 0}
{"text": "Title: Cartan calculus for $C^\\infty$-ringed spaces\nAbstract: In an earlier paper (arXiv:2212.11163) I constructed a complex of differential forms on a local $C^\\infty$-ringed space. In this paper I define a sheaf of vector fields (``the tangent sheaf'') on a local $C^\\infty$-ringed space, define contractions of vector fields and forms, Lie derivatives of forms with respect to vector fields, and show that the standard equations of Cartan calculus hold for vector fields and differential forms on local $C^\\infty$-ringed spaces.", "field": "math", "label": 0}
{"text": "Title: ETTR Bounds and Approximation Solutions of Blind Rendezvous Policies in Cognitive Radio Networks with Random Channel States\nAbstract: In this paper, we consider the multichannel rendezvous problem in cognitive radio networks (CRNs) where the probability that two users hopping on the same channel have a successful rendezvous is a function of channel states. The channel states are modeled by stochastic processes with joint distributions known to users. However, the exact state of a channel at any time is not observable. We first consider two channel models: (i) the fast time-varying channel model (where the channel states are assumed to be independent and identically distributed in each time slot), and (ii) the slow time-varying channel model (where the channel states remain unchanged over time). Among the classes of the blind rendezvous policies that randomly hop on channels according to certain channel selection probabilities, we show the optimal channel selection policy that minimizes the expected time-to-rendezvous (ETTR) is the single selection policy that hops on the ``best'' channel all the time in the fast time-varying channel model. However, for the slow time-varying channel model, it is much more difficult to find the optimal channel selection policy. By using the majorization ordering, we derive a lower bound and an upper bound for the ETTR under the assumption that the channel states are exchangeable random variables. Bases on these bounds, we then prove various approximation solutions. We then extend our results to general channel models where the joint distribution of the channel states is only assumed to be stationary in time.", "field": "cs", "label": 1}
{"text": "Title: Simple Combinatorial Algorithms for Combinatorial Bandits: Corruptions and Approximations\nAbstract: We consider the stochastic combinatorial semi-bandit problem with adversarial corruptions. We provide a simple combinatorial algorithm that can achieve a regret of $\\tilde{O}\\left(C+d^2K/\\Delta_{min}\\right)$ where $C$ is the total amount of corruptions, $d$ is the maximal number of arms one can play in each round, $K$ is the number of arms. If one selects only one arm in each round, we achieves a regret of $\\tilde{O}\\left(C+\\sum_{\\Delta_i>0}(1/\\Delta_i)\\right)$. Our algorithm is combinatorial and improves on the previous combinatorial algorithm by [Gupta et al., COLT2019] (their bound is $\\tilde{O}\\left(KC+\\sum_{\\Delta_i>0}(1/\\Delta_i)\\right)$), and almost matches the best known bounds obtained by [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] (up to logarithmic factor). Note that the algorithms in [Zimmert et al., ICML2019] and [Zimmert and Seldin, AISTATS2019] require one to solve complex convex programs while our algorithm is combinatorial, very easy to implement, requires weaker assumptions and has very low oracle complexity and running time. We also study the setting where we only get access to an approximation oracle for the stochastic combinatorial semi-bandit problem. Our algorithm achieves an (approximation) regret bound of $\\tilde{O}\\left(d\\sqrt{KT}\\right)$. Our algorithm is very simple, only worse than the best known regret bound by $\\sqrt{d}$, and has much lower oracle complexity than previous work.", "field": "cs", "label": 1}
{"text": "Title: Interacting stochastic processes on sparse random graphs\nAbstract: Large ensembles of stochastically evolving interacting particles describe phenomena in diverse fields including statistical physics, neuroscience, biology, and engineering. In such systems, the infinitesimal evolution of each particle depends only on its own state (or history) and the states (or histories) of neighboring particles with respect to an underlying, possibly random, interaction graph. While these high-dimensional processes are typically too complex to be amenable to exact analysis, their dynamics are quite well understood when the interaction graph is the complete graph. In this case, classical theorems show that in the limit as the number of particles goes to infinity, the dynamics of the empirical measure and the law of a typical particle coincide and can be characterized in terms of a much more tractable dynamical system of reduced dimension called the mean-field limit. In contrast, until recently not much was known about corresponding convergence results in the complementary case when the interaction graph is sparse (i.e., with uniformly bounded average degree). This article provides a brief survey of classical work and then describes recent progress on the sparse regime that relies on a combination of techniques from random graph theory, Markov random fields, and stochastic analysis. The article concludes by discussing ramifications for applications and posing several open problems.", "field": "math", "label": 0}
{"text": "Title: Box complexes: at the crossroad of graph theory and topology\nAbstract: Various simplicial complexes can be associated with a graph. Box complexes form an important families of such simplicial complexes and are especially useful for providing lower bounds on the chromatic number of the graph via some of their topological properties. They provide thus a fascinating topic mixing topology and discrete mathematics. This paper is intended to provide an up-do-date survey on box complexes. It is based on classical results and recent findings from the literature, but also establishes new results improving our current understanding of the topic, and identifies several challenging open questions.", "field": "math", "label": 0}
{"text": "Title: Large and moderate deviations for Gaussian neural networks\nAbstract: We prove large and moderate deviations for the output of Gaussian fully connected neural networks. The main achievements concern deep neural networks (i.e., when the model has more than one hidden layer) and hold for bounded and continuous pre-activation functions. However, for deep neural networks fed by a single input, we have results even if the pre-activation is ReLU. When the network is shallow (i.e., there is exactly one hidden layer) the large and moderate principles hold for quite general pre-activations and in an infinite-dimensional setting.", "field": "math", "label": 0}
{"text": "Title: On transfer maps in the algebraic $K$-theory of spaces\nAbstract: We show that the Waldhausen trace map $\\mathrm{Tr}_X \\colon A(X) \\to QX_+$, which defines a natural splitting map from the algebraic $K$-theory of spaces to stable homotopy, is natural up to \\emph{weak} homotopy with respect to transfer maps in algebraic $K$-theory and Becker-Gottlieb transfer maps respectively.", "field": "math", "label": 1}
{"text": "Title: Query Based Access Control for Linked Data\nAbstract: In recent years we have seen significant advances in the technology used to both publish and consume Linked Data. However, in order to support the next generation of ebusiness applications on top of interlinked machine readable data suitable forms of access control need to be put in place. Although a number of access control models and frameworks have been put forward, very little research has been conducted into the security implications associated with granting access to partial data or the correctness of the proposed access control mechanisms. Therefore the contributions of this paper are two fold: we propose a query rewriting algorithm which can be used to partially restrict access to SPARQL 1.1 queries and updates; and we demonstrate how a set of criteria, which was originally used to verify that an access control policy holds over different database states, can be adapted to verify the correctness of access control via query rewriting.", "field": "cs", "label": 1}
{"text": "Title: EPA: Neural Collapse Inspired Robust Out-of-Distribution Detector\nAbstract: Out-of-distribution (OOD) detection plays a crucial role in ensuring the security of neural networks. Existing works have leveraged the fact that In-distribution (ID) samples form a subspace in the feature space, achieving state-of-the-art (SOTA) performance. However, the comprehensive characteristics of the ID subspace still leave under-explored. Recently, the discovery of Neural Collapse ($\\mathcal{NC}$) sheds light on novel properties of the ID subspace. Leveraging insight from $\\mathcal{NC}$, we observe that the Principal Angle between the features and the ID feature subspace forms a superior representation for measuring the likelihood of OOD. Building upon this observation, we propose a novel $\\mathcal{NC}$-inspired OOD scoring function, named Entropy-enhanced Principal Angle (EPA), which integrates both the global characteristic of the ID subspace and its inner property. We experimentally compare EPA with various SOTA approaches, validating its superior performance and robustness across different network architectures and OOD datasets.", "field": "cs", "label": 0}
{"text": "Title: Extremal results for odd cycles in sparse pseudorandom graphs\nAbstract: We consider extremal problems for subgraphs of pseudorandom graphs. For graphs $F$ and $\\Gamma$ the generalized Tur\\'an density $\\pi_F(\\Gamma)$ denotes the density of a maximum subgraph of $\\Gamma$, which contains no copy of~$F$. Extending classical Tur\\'an type results for odd cycles, we show that $\\pi_{F}(\\Gamma)=1/2$ provided $F$ is an odd cycle and $\\Gamma$ is a sufficiently pseudorandom graph. In particular, for $(n,d,\\lambda)$-graphs $\\Gamma$, i.e., $n$-vertex, $d$-regular graphs with all non-trivial eigenvalues in the interval $[-\\lambda,\\lambda]$, our result holds for odd cycles of length $\\ell$, provided \\[ \\lambda^{\\ell-2}\\ll \\frac{d^{\\ell-1}}n\\log(n)^{-(\\ell-2)(\\ell-3)}\\,. \\] Up to the polylog-factor this verifies a conjecture of Krivelevich, Lee, and Sudakov. For triangles the condition is best possible and was proven previously by Sudakov, Szab\\'o, and Vu, who addressed the case when $F$ is a complete graph. A construction of Alon and Kahale (based on an earlier construction of Alon for triangle-free $(n,d,\\lambda)$-graphs) shows that our assumption on $\\Gamma$ is best possible up to the polylog-factor for every odd $\\ell\\geq 5$.", "field": "math", "label": 1}
{"text": "Title: A proximal point algorithm for sequential feature extraction applications\nAbstract: We propose a proximal point algorithm to solve LAROS problem, that is the problem of finding a \"large approximately rank-one submatrix\". This LAROS problem is used to sequentially extract features in data. We also develop a new stopping criterion for the proximal point algorithm, which is based on the duality conditions of \\eps-optimal solutions of the LAROS problem, with a theoretical guarantee. We test our algorithm with two image databases and show that we can use the LAROS problem to extract appropriate common features from these images.", "field": "math", "label": 1}
{"text": "Title: Tramp Ship Scheduling Problem with Berth Allocation Considerations and Time-dependent Constraints\nAbstract: This work presents a model for the Tramp Ship Scheduling problem including berth allocation considerations, motivated by a real case of a shipping company. The aim is to determine the travel schedule for each vessel considering multiple docking and multiple time windows at the berths. This work is innovative due to the consideration of both spatial and temporal attributes during the scheduling process. The resulting model is formulated as a mixed-integer linear programming problem, and a heuristic method to deal with multiple vessel schedules is also presented. Numerical experimentation is performed to highlight the benefits of the proposed approach and the applicability of the heuristic. Conclusions and recommendations for further research are provided.", "field": "cs", "label": 1}
{"text": "Title: On Error and Compression Rates for Prototype Rules\nAbstract: We study the close interplay between error and compression in the non-parametric multiclass classification setting in terms of prototype learning rules. We focus in particular on a recently proposed compression-based learning rule termed OptiNet (Kontorovich, Sabato, and Urner 2016; Kontorovich, Sabato, and Weiss 2017; Hanneke et al. 2021). Beyond its computational merits, this rule has been recently shown to be universally consistent in any metric instance space that admits a universally consistent rule--the first learning algorithm known to enjoy this property. However, its error and compression rates have been left open. Here we derive such rates in the case where instances reside in Euclidean space under commonly posed smoothness and tail conditions on the data distribution. We first show that OptiNet achieves non-trivial compression rates while enjoying near minimax-optimal error rates. We then proceed to study a novel general compression scheme for further compressing prototype rules that locally adapts to the noise level without sacrificing accuracy. Applying it to OptiNet, we show that under a geometric margin condition, further gain in the compression rate is achieved. Experimental results comparing the performance of the various methods are presented.", "field": "cs", "label": 1}
{"text": "Title: Impact of RIS on Outage Probability and Ergodic Rate in Wireless Powered Communication\nAbstract: Wireless powered communication (WPC) combines information and energy transmission for energy-constrained nodes. Reconfigurable intelligent surfaces (RISs) are capable of controlling radio signals in a dynamic and goal-oriented manner. This paper investigates the combination of RIS and WPC to enhance the performance of an energy-constrained user. Using an RIS, a base station, and a wireless user transmit energy and information signals, respectively. We derive closed-form expressions for outage probability and secrecy rate to analyze the performance of the proposed framework. Based on the theoretical analysis and simulation results, valuable insights are revealed and parameter selection is demonstrated.", "field": "cs", "label": 0}
{"text": "Title: Compositing with 2D Vector Fields by using Shape Maps that can represent Inconsistent, Impossible, and Incoherent Shapes\nAbstract: In this paper, we present a new compositing approach to obtain stylized reflections and refractions with a simple control. Our approach does not require any mask or separate 3D rendering. Moreover, only one additional image is sufficient to obtain a composited image with convincing qualitative reflection and refraction effects. We have also developed linearized methods that are easy to compute. Although these methods do not directly correspond to the underlying physical phenomena of reflection and refraction, they can provide results that are visually similar to realistic 3D rendering. The main advantage of this approach is the ability to treat images as ``mock-3D'' shapes that can be inserted into any digital paint system without any significant structural change. The core of our approach is the shape map, which encodes 2D shape and thickness information for all visible points of an image of a shape. This information does not have to be complete or consistent to obtain interesting composites. In particular, the shape maps allow us to represent impossible and incoherent shapes with 2D non-conservative vector fields.", "field": "cs", "label": 0}
{"text": "Title: Fast Discrete Linear Canonical Transform Based on CM-CC-CM Decomposition and FFT\nAbstract: In this paper, a discrete LCT (DLCT) irrelevant to the sampling periods and without oversampling operation is developed. This DLCT is based on the well-known CM-CC-CM decomposition, that is, implemented by two discrete chirp multiplications (CMs) and one discrete chirp convolution (CC). This decomposition doesn't use any scaling operation which will change the sampling period or cause the interpolation error. Compared with previous works, DLCT calculated by direct summation and DLCT based on center discrete dilated Hermite functions (CDDHFs), the proposed method implemented by FFTs has much lower computational complexity. The relation between the proposed DLCT and the continuous LCT is also derived to approximate the samples of the continuous LCT. Simulation results show that the proposed method somewhat outperforms the CDDHFs-based method in the approximation accuracy. Besides, the proposed method has approximate additivity property with error as small as the CDDHFs-based method. Most importantly, the proposed method has perfect reversibility, which doesn't hold in many existing DLCTs. With this property, it is unnecessary to develop the inverse DLCT additionally because it can be replaced by the forward DLCT.", "field": "cs", "label": 1}
{"text": "Title: Rigorous uniaxial limit of the Qian--Sheng inertial Q-tensor hydrodynamics for liquid crystals\nAbstract: This article is concerned with the rigorous connections between the inertial Qian--Sheng model and the Ericksen--Leslie model for the liquid crystal flow, under a more general condition of coefficients. More specifically, in the framework of Hilbert expansions, we show that: (i) when the elastic coefficients tend to zero (also called the uniaxial limit), the smooth solution to the inertial Qian--Sheng model converges to that to the full inertial Ericksen--Leslie model; (ii) when the elastic coefficients and the inertial coefficient tend to zero simultaneously, the smooth solution to the inertial Qian--Sheng model converges to that to the noninertial Ericksen--Leslie model.", "field": "math", "label": 0}
{"text": "Title: Using Malliavin calculus to solve a chemical diffusion master equation\nAbstract: We propose a novel method to solve a chemical diffusion master equation of birth and death type. This is an infinite system of Fokker-Planck equations where the different components are coupled by reaction dynamics similar in form to a chemical master equation. This system was proposed in [3] for modelling the probabilistic evolution of chemical reaction kinetics associated with spatial diffusion of individual particles. Using some basic tools and ideas from infinite dimensional Gaussian analysis we are able to reformulate the aforementioned infinite system of Fokker-Planck equations as a single evolution equation solved by a generalized stochastic process and written in terms of Malliavin derivatives and differential second quantization operators. Via this alternative representation we link certain finite dimensional projections of the solution of the original problem to the solution of a single partial differential equations of Ornstein-Uhlenbeck type containing as many variables as the dimension of the aforementioned projection space.", "field": "math", "label": 1}
{"text": "Title: Lightweight Fish Classification Model for Sustainable Marine Management: Indonesian Case\nAbstract: The enormous demand for seafood products has led to exploitation of marine resources and near-extinction of some species. In particular, overfishing is one the main issues in sustainable marine development. In alignment with the protection of marine resources and sustainable fishing, this study proposes to advance fish classification techniques that support identifying protected fish species using state-of-the-art machine learning. We use a custom modification of the MobileNet model to design a lightweight classifier called M-MobileNet that is capable of running on limited hardware. As part of the study, we compiled a labeled dataset of 37,462 images of fish found in the waters of the Indonesian archipelago. The proposed model is trained on the dataset to classify images of the captured fish into their species and give recommendations on whether they are consumable or not. Our modified MobileNet model uses only 50\\% of the top layer parameters with about 42% GTX 860M utility and achieves up to 97% accuracy in fish classification and determining its consumability. Given the limited computing capacity available on many fishing vessels, the proposed model provides a practical solution to on-site fish classification. In addition, synchronized implementation of the proposed model on multiple vessels can supply valuable information about the movement and location of different species of fish.", "field": "cs", "label": 0}
{"text": "Title: On-the-fly Adaptation of Patrolling Strategies in Changing Environments\nAbstract: We consider the problem of efficient patrolling strategy adaptation in a changing environment where the topology of Defender's moves and the importance of guarded targets change unpredictably. The Defender must instantly switch to a new strategy optimized for the new environment, not disrupting the ongoing patrolling task, and the new strategy must be computed promptly under all circumstances. Since strategy switching may cause unintended security risks compromising the achieved protection, our solution includes mechanisms for detecting and mitigating this problem. The efficiency of our framework is evaluated experimentally.", "field": "cs", "label": 1}
{"text": "Title: Evaluating Fairness in Self-supervised and Supervised Models for Sequential Data\nAbstract: Self-supervised learning (SSL) has become the de facto training paradigm of large models where pre-training is followed by supervised fine-tuning using domain-specific data and labels. Hypothesizing that SSL models would learn more generic, hence less biased, representations, this study explores the impact of pre-training and fine-tuning strategies on fairness (i.e., performing equally on different demographic breakdowns). Motivated by human-centric applications on real-world timeseries data, we interpret inductive biases on the model, layer, and metric levels by systematically comparing SSL models to their supervised counterparts. Our findings demonstrate that SSL has the capacity to achieve performance on par with supervised methods while significantly enhancing fairness--exhibiting up to a 27% increase in fairness with a mere 1% loss in performance through self-supervision. Ultimately, this work underscores SSL's potential in human-centric computing, particularly high-stakes, data-scarce application domains like healthcare.", "field": "cs", "label": 0}
{"text": "Title: Invariance of Abel universality under composition and applications\nAbstract: A holomorphic function $f$ on the unit disc $\\mathbb{D}$ belongs to the class $\\mathcal{U}_A (\\mathbb{D})$ of Abel universal functions if the family $\\{f_r: 0\\leq r<1\\}$ of its dilates $f_r(z):=f(rz)$ is dense in the Banach space of all continuous functions on $K$, endowed with the supremum norm, for any proper compact subset $K$ of the unit circle. We prove that this property is invariant under composition from the left with any non-constant entire function. As an application, we show that $\\mathcal{U}_A (\\mathbb{D})$ is strongly-algebrable. Furthermore, we prove that Abel universality is invariant under composition from the right with an automorphism $\\Phi$ of $\\mathbb{D}$ if and only if $\\Phi$ a rotation. On the other hand, we establish the existence of a subset of $\\mathcal{U}_A (\\mathbb{D})$ which is residual in the space of holomorphic functions on $\\mathbb{D}$ and is invariant under composition from the right with any automorphism of $\\mathbb{D}$.", "field": "math", "label": 0}
{"text": "Title: An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems\nAbstract: We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving large-scale CMOT problems. The experiments on the discrete tomography problem also highlight the potential modeling power of our model.", "field": "math", "label": 1}
{"text": "Title: Heavy Ball Neural Ordinary Differential Equations\nAbstract: We propose heavy ball neural ordinary differential equations (HBNODEs), leveraging the continuous limit of the classical momentum accelerated gradient descent, to improve neural ODEs (NODEs) training and inference. HBNODEs have two properties that imply practical advantages over NODEs: (i) The adjoint state of an HBNODE also satisfies an HBNODE, accelerating both forward and backward ODE solvers, thus significantly reducing the number of function evaluations (NFEs) and improving the utility of the trained models. (ii) The spectrum of HBNODEs is well structured, enabling effective learning of long-term dependencies from complex sequential data. We verify the advantages of HBNODEs over NODEs on benchmark tasks, including image classification, learning complex dynamics, and sequential modeling. Our method requires remarkably fewer forward and backward NFEs, is more accurate, and learns long-term dependencies more effectively than the other ODE-based neural network models. Code is available at \\url{https://github.com/hedixia/HeavyBallNODE}.", "field": "cs", "label": 1}
{"text": "Title: Lie Algebroids and generalized projective structures on Riemann surfaces\nAbstract: The space of generalized projective structures on a Riemann surface $\\Sigma$ of genus g with n marked points is the affine space over the cotangent bundle to the space of SL(N)-opers. It is a phase space of $W_N$-gravity on $\\Sigma\\times\\mathbb{R}$. This space is a generalization of the space of projective structures on the Riemann surface. We define the moduli space of $W_N$-gravity as a symplectic quotient with respect to the canonical action of a special class of Lie algebroids. This moduli space describes in particular the moduli space of deformations of complex structures on the Riemann surface by differential operators of finite order, or equivalently, by a quotient space of Volterra operators. We call these algebroids the Adler-Gelfand-Dikii (AGD) algebroids, because they are constructed by means of AGD bivector on the space of opers restricted on a circle. The AGD-algebroids are particular case of Lie algebroids related to a Poisson sigma-model. The moduli space of the generalized projective structure can be described by cohomology of a BRST-complex.", "field": "math", "label": 1}
{"text": "Title: Finite subgraphs of an extension graph\nAbstract: Let $\\Gamma$ be a finite graph and let $\\Gamma^{\\mathrm{e}}$ be its extension graph. We inductively define a sequence $\\{\\Gamma_i\\}$ of finite induced subgraphs of $\\Gamma^{\\mathrm{e}}$ through successive applications of an operation called \"doubling along a star\". Then we show that every finite induced subgraph of $\\Gamma^{\\mathrm{e}}$ is isomorphic to an induced subgraph of some $\\Gamma_i$.", "field": "math", "label": 1}
{"text": "Title: Noncommutative Hamiltonian structures and quantizations on preprojective algebras\nAbstract: Given a noncommutative Hamiltonian space $A$, we show that the conjecture ``{\\it quantization commutes with reduction}'' holds on $A$. We also construct a semi-product algebra $A \\rtimes \\mG^A$, equivariant sheaves on the representation space are related to left $A \\rtimes \\mG^A$-modules. In the quiver setting, via the quantum and classical trace maps, we establish the explicit correspondence between quantizations on a preprojective algebra and those on a quiver variety.", "field": "math", "label": 0}
{"text": "Title: Higher depth quantum modular forms and plumbed $3$-manifolds\nAbstract: In this paper we study new invariants $\\widehat{Z}_{\\boldsymbol{a}}(q)$ attached to plumbed $3$-manifolds that were introduced by Gukov, Pei, Putrov, and Vafa. These remarkable $q$-series at radial limits conjecturally compute WRT invariants of the corresponding plumbed $3$-manifold. Here we investigate the series $\\widehat{Z}_{0}(q)$ for unimodular plumbing ${\\tt H}$-graphs with six vertices. We prove that for every positive definite unimodular plumbing matrix, $\\widehat{Z}_{0}(q)$ is a depth two quantum modular form on $\\mathbb{Q}$.", "field": "math", "label": 1}
{"text": "Title: Persistent components in Canny's resultant\nAbstract: When using resultants for elimination, one standard issue is that the resultant vanishes if the variety contains components of dimension larger than the expected dimension. J. Canny proposed an elegant construction, generalized characteristic polynomial, to address this issue by symbolically perturbing the system before the resultant computation. Such perturbed resultant would typically involve artefact components only loosely related to the geometry of the variety of interest. For removing these components, J.M. Rojas proposed to take the greatest common divisor of the results of two different perturbations. In this paper, we investigate this construction, and show that the extra components persistent under taking different perturbations must come either from singularities or from positive-dimensional fibers.", "field": "cs", "label": 0}
{"text": "Title: Knowledge-based XAI through CBR: There is more to explanations than models can tell\nAbstract: The underlying hypothesis of knowledge-based explainable artificial intelligence is the data required for data-centric artificial intelligence agents (e.g., neural networks) are less diverse in contents than the data required to explain the decisions of such agents to humans. The idea is that a classifier can attain high accuracy using data that express a phenomenon from one perspective whereas the audience of explanations can entail multiple stakeholders and span diverse perspectives. We hence propose to use domain knowledge to complement the data used by agents. We formulate knowledge-based explainable artificial intelligence as a supervised data classification problem aligned with the CBR methodology. In this formulation, the inputs are case problems composed of both the inputs and outputs of the data-centric agent and case solutions, the outputs, are explanation categories obtained from domain knowledge and subject matter experts. This formulation does not typically lead to an accurate classification, preventing the selection of the correct explanation category. Knowledge-based explainable artificial intelligence extends the data in this formulation by adding features aligned with domain knowledge that can increase accuracy when selecting explanation categories.", "field": "cs", "label": 1}
{"text": "Title: On the maximal and minimal degree components of the cocenter of the cyclotomic KLR algebras\nAbstract: Let $\\mathscr{R}_\\alpha^\\Lambda$ be the cyclotomic KLR algebra associated to a symmetrizable Kac-Moody Lie algebra $\\mathfrak{g}$ and polynomials $\\{Q_{ij}(u,v)\\}_{i,j\\in I}$. Shan, Varagnolo and Vasserot show that, when the ground field $K$ has characteristic $0$, the degree $d$ component of the cocenter $Tr(\\mathscr{R}_\\alpha^\\Lambda)$ is nonzero only if $0\\leq d\\leq d_{\\Lambda,\\alpha}$. In this paper we show that this holds true for arbitrary ground field $K$, arbitrary $\\mathfrak{g}$ and arbitrary polynomials $\\{Q_{ij}(u,v)\\}_{i,j\\in I}$. We generalize our earlier results on the $K$-linear generators of $Tr(\\mathscr{R}_\\alpha^\\Lambda), Tr(\\mathscr{R}_\\alpha^\\Lambda)_0, Tr(\\mathscr{R}_\\alpha^\\Lambda)_{d_{\\Lambda,\\alpha}}$ to arbitrary ground field $K$. Moreover, we show that the dimension of the degree $0$ component $Tr(\\mathscr{R}_\\alpha^\\Lambda)_0$ is always equal to $\\dim V(\\Lambda)_{\\Lambda-\\alpha}$, where $V(\\Lambda)$ is the integrable highest weight $U(\\mathfrak{g})$-module with highest weight $\\Lambda$, and we obtain a basis for $Tr(\\mathscr{R}_\\alpha^\\Lambda)_0$.", "field": "math", "label": 0}
{"text": "Title: A network-level transport model of tau progression in the Alzheimer's brain\nAbstract: One of the hallmarks of Alzheimer's disease (AD) is the accumulation and spread of toxic aggregates of tau protein. The progression of AD tau pathology is thought to be highly stereotyped, which is in part due to the fact that tau can spread between regions via the white matter tracts that connect them. Mathematically, this phenomenon has been described using models of \"network diffusion\", where the rate of spread of tau between brain regions is proportional to its concentration gradient and the amount of white matter between them. Although these models can robustly predict the progression of pathology in a wide variety of neurodegenerative diseases, including AD, an under explored aspect of tau spreading is that it is governed not simply by diffusion but also active transport along axonal microtubules. Spread can therefore take on a directional bias, resulting in distinct patterns of deposition, but current models struggle to capture this phenomenon. Recently, we have developed a mathematical model of the axonal transport of toxic tau proteins that takes into account the effects tau exerts on the molecular motors. Here we describe and implement a macroscopic version of this model, which we call the Network Transport Model (NTM). A key feature of this model is that, while it predicts tau dynamics at a regional level, it is parameterized in terms of only microscopic processes such as aggregation and transport rates; that is, differences in brain-wide tau progression can be explained by its microscopic properties. We provide numerical evidence that, as with the two-neuron model that the NTM extends, there are distinct and rich dynamics with respect to the overall rate of spread and the staging of pathology when we simulated the NTM on the hippocampal subnetwork. The theoretical insights provided by the NTM have broad implications for understanding AD pathophysiology more generally.", "field": "math", "label": 0}
{"text": "Title: Equivariant $K$-theory of Springer Varieties\nAbstract: The aim of this paper is to describe the topological equivariant $K$-ring, in terms of generators and relations, of a Springer variety $\\mathcal{F}_{\\lambda}$ of type $A$ associated to a nilpotent operator having Jordan canonical form whose block sizes form a weakly decreasing sequence $\\lambda=(\\lambda_1,\\ldots, \\lambda_l)$. This parallels the description of the equivariant cohomology ring of $\\mathcal{F}_{\\lambda}$ due to Abe and Horiguchi and generalizes the description of ordinary topological $K$-ring of $\\mathcal{F}_{\\lambda}$ due to Sankaran and Uma \\cite{su}.", "field": "math", "label": 0}
{"text": "Title: Variational Autoencoders Without the Variation\nAbstract: Variational autoencdoers (VAE) are a popular approach to generative modelling. However, exploiting the capabilities of VAEs in practice can be difficult. Recent work on regularised and entropic autoencoders have begun to explore the potential, for generative modelling, of removing the variational approach and returning to the classic deterministic autoencoder (DAE) with additional novel regularisation methods. In this paper we empirically explore the capability of DAEs for image generation without additional novel methods and the effect of the implicit regularisation and smoothness of large networks. We find that DAEs can be used successfully for image generation without additional loss terms, and that many of the useful properties of VAEs can arise implicitly from sufficiently large convolutional encoders and decoders when trained on CIFAR-10 and CelebA.", "field": "cs", "label": 1}
{"text": "Title: Partial classification of the large-time behavior of solutions to cubic nonlinear Schrödinger systems\nAbstract: In this paper, we study the large-time behavior of small solutions to the standard form of the systems of 1D cubic nonlinear Schr\\\"odinger equations consisting of two components and possessing a coercive mass-like conserved quantity. The cubic nonlinearity is known to be critical in one space dimension in view of the large-time behavior. By employing the result by Katayama and Sakoda, one can obtain the large-time behavior of the solution if we can integrate the corresponding ODE system. We introduce an integration scheme suited to the system. The key idea is to rewrite the ODE system, which is cubic, as a quadratic system of quadratic quantities of the original unknown. By using this technique, we described the large-time behavior of solutions in terms of elementary functions and the Jacobi elliptic functions for several examples of standard systems.", "field": "math", "label": 0}
{"text": "Title: Semiring Provenance for First-Order Model Checking\nAbstract: Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the data items that describe the model. Previous work on provenance was, to a large extent, restricted to the negation-free fragment of first-order logic and showed how provenance abstractions can be usefully described as elements of commutative semirings --- most generally as multivariate polynomials with positive integer coefficients. In this paper we introduce a novel approach to dealing with negation and a corresponding commutative semiring of polynomials with dual indeterminates. These polynomials are used to perform reverse provenance analysis, i.e., finding models that satisfy various properties under given provenance tracking assumptions.", "field": "cs", "label": 1}
{"text": "Title: On the connected (sub)partition polytope\nAbstract: Let $k$ be a positive integer and let $G$ be a graph with $n$ vertices. A connected $k$-subpartition of $G$ is a collection of $k$ pairwise disjoint sets (a.k.a. classes) of vertices in $G$ such that each set induces a connected subgraph. The connected $k$-partition polytope of $G$, denoted by $P(G,k)$, is defined as the convex hull of the incidence vectors of all connected $k$-subpartitions of $G$. Many applications arising in off-shore oil-drilling, forest planning, image processing, cluster analysis, political districting, police patrolling, and biology are modeled in terms of finding connected (sub)partitions of a graph. This study focus on the facial structure of $P(G,k)$ and the computational complexity of the corresponding separation problems. We first propose a set of valid inequalities having non-null coefficients associated with a single class that extends and generalizes the ones in the literature of related problems, show sufficient conditions for these inequalities to be facet-defining, and design a polynomial-time separation algorithm for them. We also devise two sets of inequalities that consider multiple classes, prove when they define facets, and study the computational complexity of associated separation problems.", "field": "math", "label": 0}
{"text": "Title: Non-Atomic Arbitrage in Decentralized Finance\nAbstract: The prevalence of maximal extractable value (MEV) in the Ethereum ecosystem has led to a characterization of the latter as a dark forest. Studies of MEV have thus far largely been restricted to purely on-chain MEV, i.e., sandwich attacks, cyclic arbitrage, and liquidations. In this work, we shed light on the prevalence of non-atomic arbitrage on decentralized exchanges (DEXes) on the Ethereum blockchain. Importantly, non-atomic arbitrage exploits price differences between DEXes on the Ethereum blockchain as well as exchanges outside the Ethereum blockchain (i.e., centralized exchanges or DEXes on other blockchains). Thus, non-atomic arbitrage is a type of MEV that involves actions on and off the Ethereum blockchain. In our study of non-atomic arbitrage, we uncover that more than a fourth of the volume on Ethereum's biggest five DEXes from the merge until 31 October 2023 can likely be attributed to this type of MEV. We further highlight that only eleven searchers are responsible for more than 80% of the identified non-atomic arbitrage volume sitting at a staggering 137 billion US$ and draw a connection between the centralization of the block construction market and non-atomic arbitrage. Finally, we discuss the security implications of these high-value transactions that account for more than 10% of Ethereum's total block value and outline possible mitigations.", "field": "cs", "label": 0}
{"text": "Title: Proven Distributed Memory Parallelization of Particle Methods\nAbstract: We provide a mathematically proven parallelization scheme for particle methods on distributed-memory computer systems. Particle methods are a versatile and widely used class of algorithms for computer simulations and numerical predictions in various applications, ranging from continuum fluid dynamics and granular flows, using methods such as Smoothed Particle Hydrodynamics (SPH) and Discrete Element Methods (DEM) to Molecular Dynamics (MD) simulations in molecular modeling. Particle methods naturally lend themselves to implementation on parallel-computing hardware. So far, however, a mathematical proof of correctness and equivalence to sequential implementations was only available for shared-memory parallelism. Here, we leverage a formal definition of the algorithmic class of particle methods to provide a proven parallelization scheme for distributed-memory computers. We prove that these parallelized particle methods on distributed memory computers are formally equivalent to their sequential counterpart for a well-defined class of particle methods. Notably, the here analyzed parallelization scheme is well-known and commonly used. Our analysis is, therefore, of immediate practical relevance to existing and new parallel software implementations of particle methods and places them on solid theoretical grounds.", "field": "cs", "label": 0}
{"text": "Title: Sequential choice functions and stability problems\nAbstract: The concept of sequential choice functions is introduced and studied. This concept applies to the reduction of the problem of stable matchings with sequential workers to a situation where the workers are linear.", "field": "math", "label": 0}
{"text": "Title: Physics-informed neural network for modeling dynamic linear elasticity\nAbstract: In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently for material identification in a dynamic setting. In this work, we assume linear continuum elasticity. We show results for two-dimensional (2D) plane strain problem and then we proceed to apply the same techniques for a three-dimensional (3D) problem. As for the training data we use the solution based on the finite element method. We rigorously show that PINN models are accurate, robust and computationally efficient, especially as a surrogate model for material identification problems. Also, we employ state-of-the-art techniques from the PINN literature which are an improvement to the vanilla implementation of PINN. Based on our results, we believe that the framework we have developed can be readily adapted to computational platforms for solving multiple dynamic problems in solid mechanics.", "field": "cs", "label": 0}
{"text": "Title: Speed Partitioning for Indexing Moving Objects\nAbstract: Indexing moving objects has been extensively studied in the past decades. Moving objects, such as vehicles and mobile device users, usually exhibit some patterns on their velocities, which can be utilized for velocity-based partitioning to improve performance of the indexes. Existing velocity-based partitioning techniques rely on some kinds of heuristics rather than analytically calculate the optimal solution. In this paper, we propose a novel speed partitioning technique based on a formal analysis over speed values of the moving objects. We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on query performance of the indexes. Next we formulate the optimal speed partitioning problem based on search space expansion analysis and then compute the optimal solution using dynamic programming. We then build the partitioned indexing system where queries are duplicated and processed in each index partition. Extensive experiments demonstrate that our method dramatically improves the performance of indexes for moving objects and outperforms other state-of-the-art velocity-based partitioning approaches.", "field": "cs", "label": 1}
{"text": "Title: Ricci flows which terminate in cones\nAbstract: We prove that a complete solution to the Ricci flow on $M\\times [-T, 0)$ which has quadratic curvature decay on some end of $M$ and converges locally smoothly to the end of a cone on that neighborhood as $t\\nearrow 0$ must be a gradient shrinking soliton.", "field": "math", "label": 0}
{"text": "Title: Termination of Rewriting on Reversible Boolean Circuits as a Free 3-Category Problem\nAbstract: Reversible Boolean Circuits are an interesting computational model under many aspects and in different fields, ranging from Reversible Computing to Quantum Computing. Our contribution is to describe a specific class of Reversible Boolean Circuits - which is as expressive as classical circuits - as a bi-dimensional diagrammatic programming language. We uniformly represent the Reversible Boolean Circuits we focus on as a free 3-category Toff. This formalism allows us to incorporate the representation of circuits and of rewriting rules on them, and to prove termination of rewriting. Termination follows from defining a non-identities-preserving functor from our free 3-category Toff into a suitable 3-category Move that traces the \"moves\" applied to wires inside circuits.", "field": "cs", "label": 0}
{"text": "Title: Hierarchical Over-the-Air Federated Learning with Awareness of Interference and Data Heterogeneity\nAbstract: When implementing hierarchical federated learning over wireless networks, scalability assurance and the ability to handle both interference and device data heterogeneity are crucial. This work introduces a learning method designed to address these challenges, along with a scalable transmission scheme that efficiently uses a single wireless resource through over-the-air computation. To provide resistance against data heterogeneity, we employ gradient aggregations. Meanwhile, the impact of interference is minimized through optimized receiver normalizing factors. For this, we model a multi-cluster wireless network using stochastic geometry, and characterize the mean squared error of the aggregation estimations as a function of the network parameters. We show that despite the interference and the data heterogeneity, the proposed scheme achieves high learning accuracy and can significantly outperform the conventional hierarchical algorithm.", "field": "cs", "label": 0}
{"text": "Title: Multimodal Sampling via Approximate Symmetries\nAbstract: Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the distributions from most applications do not have exact symmetries. This paper considers the distributions with approximate symmetries. We first construct an exactly symmetric reference distribution from the target one by averaging over the group orbit associated with the approximate symmetry. Next, we can apply the multilevel Monte Carlo methods by constructing a continuation path between the reference and target distributions. We discuss how to implement these steps with annealed importance sampling and tempered transitions. Compared with traditional multilevel methods, the proposed approach can be more effective since the reference and target distributions are much closer. Numerical results of the Ising models are presented to illustrate the efficiency of the proposed method.", "field": "math", "label": 0}
{"text": "Title: Mechanizing the Metatheory of LF\nAbstract: LF is a dependent type theory in which many other formal systems can be conveniently embedded. However, correct use of LF relies on nontrivial metatheoretic developments such as proofs of correctness of decision procedures for LF's judgments. Although detailed informal proofs of these properties have been published, they have not been formally verified in a theorem prover. We have formalized these properties within Isabelle/HOL using the Nominal Datatype Package, closely following a recent article by Harper and Pfenning. In the process, we identified and resolved a gap in one of the proofs and a small number of minor lacunae in others. We also formally derive a version of the type checking algorithm from which Isabelle/HOL can generate executable code. Besides its intrinsic interest, our formalization provides a foundation for studying the adequacy of LF encodings, the correctness of Twelf-style metatheoretic reasoning, and the metatheory of extensions to LF.", "field": "cs", "label": 1}
{"text": "Title: Limitless HTTP in an HTTPS World: Inferring the Semantics of the HTTPS Protocol without Decryption\nAbstract: We present new analytic techniques for inferring HTTP semantics from passive observations of HTTPS that can infer the value of important fields including the status-code, Content-Type, and Server, and the presence or absence of several additional HTTP header fields, e.g., Cookie and Referer. Our goals are twofold: to better understand the limitations of the confidentiality of HTTPS, and to explore benign uses of traffic analysis such as application troubleshooting and malware detection that could replace HTTPS interception and static private keys in some scenarios. We found that our techniques improve the efficacy of malware detection, but they do not enable more powerful website fingerprinting attacks against Tor. Our broader set of results raises concerns about the confidentiality goals of TLS relative to a user's expectation of privacy, warranting future research. We apply our methods to the semantics of both HTTP/1.1 and HTTP/2 on data collected from automated runs of Firefox 58.0, Chrome 63.0, and Tor Browser 7.0.11 in a lab setting, and from applications running in a malware sandbox. We obtain ground truth plaintext for a diverse set of applications from the malware sandbox by extracting the key material needed for decryption from RAM post-execution. We developed an iterative approach to simultaneously solve several multi-class (field values) and binary (field presence) classification problems, and we show that our inference algorithm achieves an unweighted $F_1$ score greater than 0.900 for most HTTP fields examined.", "field": "cs", "label": 1}
{"text": "Title: 5-Engel Lie algebras\nAbstract: We prove that 5-Engel Lie algebras over a field of characteristic zero, or over a field of prime characteristic $p>7$, are nilpotent of class at most 11. We also prove that if $G$ is a finite 5-Engel $p$-group for $p>7$ then $G$ is nilpotent of class at most 10.", "field": "math", "label": 0}
{"text": "Title: Equidistribution from the Chinese Remainder Theorem\nAbstract: We prove the equidistribution of subsets of $(\\Rr/\\Zz)^n$ defined by fractional parts of subsets of~$(\\Zz/q\\Zz)^n$ that are constructed using the Chinese Remainder Theorem.", "field": "math", "label": 1}
{"text": "Title: A New Foundation for Finitary Corecursion\nAbstract: This paper contributes to a theory of the behaviour of \"finite-state\" systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to a new fixpoint of the coalgebraic type functor called locally finite fixpoint (LFF). We prove that if the given endofunctor preserves monomorphisms then the LFF always exists and is a subcoalgebra of the final coalgebra (unlike the rational fixpoint previously studied by Ad\\'amek, Milius and Velebil). Moreover, we show that the LFF is characterized by two universal properties: 1. as the final locally finitely generated coalgebra, and 2. as the initial fg-iterative algebra. As instances of the LFF we first obtain the known instances of the rational fixpoint, e.g. regular languages, rational streams and formal power-series, regular trees etc. And we obtain a number of new examples, e.g. (realtime deterministic resp. non-deterministic) context-free languages, constructively S-algebraic formal power-series (and any other instance of the generalized powerset construction by Silva, Bonchi, Bonsangue, and Rutten) and the monad of Courcelle's algebraic trees.", "field": "math", "label": 1}
{"text": "Title: On the completeness of root function system of the $2\\times 2$ Dirac operators with non-regular boundary conditions\nAbstract: The paper is concerned with the completeness property of root functions of the $2\\times 2$ Dirac operator with summable complex-valued potential and non-regular boundary conditions. Sufficient conditions for the completeness of the root function system of the operator under consideration are established.", "field": "math", "label": 0}
{"text": "Title: Evolutionary Alternating Direction Method of Multipliers for Constrained Multi-Objective Optimization with Unknown Constraints\nAbstract: Constrained multi-objective optimization problems (CMOPs) pervade real-world applications in science, engineering, and design. Constraint violation has been a building block in designing evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, in certain scenarios, constraint functions might be unknown or inadequately defined, making constraint violation unattainable and potentially misleading for conventional constrained evolutionary multi-objective optimization algorithms. To address this issue, we present the first of its kind evolutionary optimization framework, inspired by the principles of the alternating direction method of multipliers that decouples objective and constraint functions. This framework tackles CMOPs with unknown constraints by reformulating the original problem into an additive form of two subproblems, each of which is allotted a dedicated evolutionary population. Notably, these two populations operate towards complementary evolutionary directions during their optimization processes. In order to minimize discrepancy, their evolutionary directions alternate, aiding the discovery of feasible solutions. Comparative experiments conducted against five state-of-the-art constrained evolutionary multi-objective optimization algorithms, on 120 benchmark test problem instances with varying properties, as well as two real-world engineering optimization problems, demonstrate the effectiveness and superiority of our proposed framework. Its salient features include faster convergence and enhanced resilience to various Pareto front shapes.", "field": "cs", "label": 0}
{"text": "Title: Asymptotic approximations of the continuous Hahn polynomials and their zeros\nAbstract: Asymptotic approximations for the continuous Hahn polynomials and their zeros as the degree grows to infinity are established via their three-term recurrence relation. The methods are based on the uniform asymptotic expansions for difference equations developed by Wang and Wong (\\textit{Numer. Math.}, 2003) and the matching technique in the complex plane developed by Wang (\\textit{J. Approx. Theory}, 2014).", "field": "math", "label": 1}
{"text": "Title: Unique equilibrium states for some intermediate beta transformations\nAbstract: We prove uniqueness of equilibrium states for subshifts corresponding to intermediate beta transformations with $\\beta > 2$ having the property that the orbit of 0 is bounded away from 1.", "field": "math", "label": 1}
{"text": "Title: A quick probability-oriented introduction to operator splitting methods\nAbstract: This paper is an extended and reworked version of a short course given by the author at ''Uzbekistan-Ukrainian readings in stochastic processes'', Tashkent-Kyiv, 2022, and was prepared for a special issue of ''Theory of stochastic processes'', devoted to publishing lecture notes from the aforementioned workshop. The survey is devoted to operator splitting methods in the abstract formulation and their applications in probability. While the survey is focused on multiplicative methods, the BCH formula is used to discuss exponential splitting methods and a short informal introduction to additive splitting is presented. We introduce frameworks and available deterministic and probabilistic results and concentrate on constructing a wide picture of the field of operator splitting methods, providing a rigorous description in the setting of abstract Cauchy problems and an informal discussion for further and parallel advances. Some limitations and common difficulties are listed, as well as examples of works that provide solutions or hints. No new results are given. The bibliography contains illustrative deterministic examples and a selection of probability-related works.", "field": "math", "label": 0}
{"text": "Title: On Higher-Order Extensions of the Weighted Projection Body Operator\nAbstract: For a convex body $K$ in $\\mathbb{R}^n$, the inequalities of Rogers-Shephard and Zhang, written succinctly, are $\\text{vol}_n(DK)\\leq \\binom{2n}{n} \\text{vol}_n(K) \\leq \\text{vol}_n(n\\text{vol}_n(K)\\Pi^\\circ K).$ Here, $DK=\\{x\\in\\mathbb{R}^n:K\\cap(K+x)\\neq \\emptyset\\}$ is the difference body of $K$, and $\\Pi^\\circ K$ is the polar projection body of $K$. There is equality in either if, and only if, $K$ is a $n$-dimensional simplex. In fact, there exists a collection of convex bodies, the so-called radial mean bodies $R_p K$ introduced by Gardner and Zhang, which continuously interpolates between $DK$ and $\\Pi^\\circ K$. Schneider defined the higher-order difference body as, for $m\\in\\mathbb{N}$, $$D^m(K)=\\{(x_1,\\dots,x_m)\\in\\mathbb{R}^{nm}:K\\cap_{i=1}^m(K+x_i)\\neq \\emptyset\\}\\subset \\mathbb{R}^{nm}$$ and proved a higher-order version of the Rogers-Shephard inequality. In a prequel to this work, the authors, working with Haddad, extended the higher-order concept to the radial mean bodies and the polar projection body, establishing the associated Zhang-type inequality. In this work, we introduce weighted versions of the above-mentioned operators by replacing the Lebesgue measure with measures that have density. The weighted version of these operators in the $m=1$ case was first done by Roysdon (difference body), Langharst-Roysdon-Zvavitch (polar projection body) and Langharst-Putterman (radial mean bodies). This work can be seen as a sequel to all those works, generalizing them to the higher-order setting. In the last section, we extend many of these ideas to the setting of generalized volume, first introduced by Gardner-Hug-Weil-Xing-Ye.", "field": "math", "label": 0}
{"text": "Title: Sheaves of Probability\nAbstract: What does it mean for multiple agents' credence functions to be consistent with each other, if the agents have distinct but overlapping sets of evidence? Mathematical philosopher Michael Titelbaum's rule, called Generalized Conditionalization (GC), sensibly requires each pair of agents to acquire identical credences if they updated on each other's evidence. However, GC allows for paradoxical arrangements of agent credences that we would not like to call consistent. We interpret GC as a gluing condition in the context of sheaf theory, and show that if we further assume that the agents' evidence is logically consistent then the sheaf condition is satisfied and the paradoxes are resolved.", "field": "math", "label": 0}
{"text": "Title: Casson towers and slice links\nAbstract: We prove that a Casson tower of height 4 contains a flat embedded disc bounded by the attaching circle, and we prove disc embedding results for height 2 and 3 Casson towers which are embedded into a 4-manifold, with some additional fundamental group assumptions. In the proofs we create a capped grope from a Casson tower and use a refined height raising argument to establish the existence of a symmetric grope which has two layers of caps, data which is sufficient for a topological disc to exist, with the desired boundary. As applications, we present new slice knots and links by giving direct geometric constructions of slicing discs. In particular we construct a family of slice knots which are potential counterexamples to the homotopy ribbon slice conjecture.", "field": "math", "label": 1}
{"text": "Title: A Preliminary Exploration of Floating Point Grammatical Evolution\nAbstract: Current GP frameworks are highly effective on a range of real and simulated benchmarks. However, due to the high dimensionality of the genotypes for GP, the task of visualising the fitness landscape for GP search can be difficult. This paper describes a new framework: Floating Point Grammatical Evolution (FP-GE) which uses a single floating point genotype to encode an individual program. This encoding permits easier visualisation of the fitness landscape arbitrary problems by providing a way to map fitness against a single dimension. The new framework also makes it trivially easy to apply continuous search algorithms, such as Differential Evolution, to the search problem. In this work, the FP-GE framework is tested against several regression problems, visualising the search landscape for these and comparing different search meta-heuristics.", "field": "cs", "label": 1}
{"text": "Title: Emotionally Numb or Empathetic? Evaluating How LLMs Feel Using EmotionBench\nAbstract: Evaluating Large Language Models' (LLMs) anthropomorphic capabilities has become increasingly important in contemporary discourse. Utilizing the emotion appraisal theory from psychology, we propose to evaluate the empathy ability of LLMs, i.e., how their feelings change when presented with specific situations. After a careful and comprehensive survey, we collect a dataset containing over 400 situations that have proven effective in eliciting the eight emotions central to our study. Categorizing the situations into 36 factors, we conduct a human evaluation involving more than 1,200 subjects worldwide. With the human evaluation results as references, our evaluation includes five LLMs, covering both commercial and open-source models, including variations in model sizes, featuring the latest iterations, such as GPT-4 and LLaMA-2. We find that, despite several misalignments, LLMs can generally respond appropriately to certain situations. Nevertheless, they fall short in alignment with the emotional behaviors of human beings and cannot establish connections between similar situations. Our collected dataset of situations, the human evaluation results, and the code of our testing framework, dubbed EmotionBench, is made openly accessible via https://github.com/CUHK-ARISE/EmotionBench. We aspire to contribute to the advancement of LLMs regarding better alignment with the emotional behaviors of human beings, thereby enhancing their utility and applicability as intelligent assistants.", "field": "cs", "label": 0}
{"text": "Title: On a Navier-Stokes-Fourier-like system capturing transitions between viscous and inviscid fluid regimes and between no-slip and perfect-slip boundary conditions\nAbstract: We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is continuously parametrized by the temperature. As such, the considered fluid may go through transitions between three of the following regimes: it can flow as a Bingham fluid for a specific value of the temperature, while it can behave as the Navier-Stokes fluid for another value of the temperature or, for yet another temperature, it can respond as the Euler fluid until a certain activation initiates the response of the Navier-Stokes fluid. At the same time, we regard a generalized threshold slip on the boundary that also may go through various regimes continuously with the temperature. All material coefficients like the dynamic viscosity, friction or activation coefficients are assumed to be temperature-dependent. We establish the large-data and long-time existence of weak solutions, applying the $L^{\\infty}$-truncation technique to approximate the velocity field.", "field": "math", "label": 1}
{"text": "Title: Can poachers find animals from public camera trap images?\nAbstract: To protect the location of camera trap data containing sensitive, high-target species, many ecologists randomly obfuscate the latitude and longitude of the camera when publishing their data. For example, they may publish a random location within a 1km radius of the true camera location for each camera in their network. In this paper, we investigate the robustness of geo-obfuscation for maintaining camera trap location privacy, and show via a case study that a few simple, intuitive heuristics and publicly available satellite rasters can be used to reduce the area likely to contain the camera by 87% (assuming random obfuscation within 1km), demonstrating that geo-obfuscation may be less effective than previously believed.", "field": "cs", "label": 1}
{"text": "Title: Incentivizing Massive Unknown Workers for Budget-Limited Crowdsensing: From Off-Line and On-Line Perspectives\nAbstract: How to incentivize strategic workers using limited budget is a very fundamental problem for crowdsensing systems; nevertheless, since the sensing abilities of the workers may not always be known as prior knowledge due to the diversities of their sensor devices and behaviors, it is difficult to properly select and pay the unknown workers. Although the uncertainties of the workers can be addressed by the standard Combinatorial Multi-Armed Bandit (CMAB) framework in existing proposals through a trade-off between exploration and exploitation, we may not have sufficient budget to enable the trade-off among the individual workers, especially when the number of the workers is huge while the budget is limited. Moreover, the standard CMAB usually assumes the workers always stay in the system, whereas the workers may join in or depart from the system over time, such that what we have learnt for an individual worker cannot be applied after the worker leaves. To address the above challenging issues, in this paper, we first propose an off-line Context-Aware CMAB-based Incentive (CACI) mechanism. We innovate in leveraging the exploration-exploitation trade-off in an elaborately partitioned context space instead of the individual workers, to effectively incentivize the massive unknown workers with a very limited budget. We also extend the above basic idea to the on-line setting where unknown workers may join in or depart from the systems dynamically, and propose an on-line version of the CACI mechanism. We perform rigorous theoretical analysis to reveal the upper bounds on the regrets of our CACI mechanisms and to prove their truthfulness and individual rationality, respectively. Extensive experiments on both synthetic and real datasets are also conducted to verify the efficacy of our mechanisms.", "field": "cs", "label": 0}
{"text": "Title: A characteristic-index inequality for closed embeddings of locally compact groups\nAbstract: The characteristic index of a locally compact connected group $G$ is the non-negative integer $d$ for which we have a homeomorphism $G\\cong K\\times \\mathbb{R}^d$ with $K\\le G$ maximal compact. We prove that the characteristic indices of closed connected subgroups are dominated by those of the ambient groups.", "field": "math", "label": 1}
{"text": "Title: Chiplet Cloud: Building AI Supercomputers for Serving Large Generative Language Models\nAbstract: Large language models (LLMs) such as ChatGPT have demonstrated unprecedented capabilities in multiple AI tasks. However, hardware inefficiencies have become a significant factor limiting the democratization of LLMs. We propose Chiplet Cloud, an ASIC supercomputer architecture that optimizes total cost of ownership (TCO) per token for serving generative LLMs. Chiplet Cloud fits all model parameters inside the on-chip SRAMs to eliminate bandwidth limitations while moderating the die size to improve system costs while leveraging software mappings to overcome data communication overhead. We propose a comprehensive design methodology that accurately explores a spectrum of major design trade-offs in the joint space of hardware-software and generates a detailed performance-cost analysis on all valid design points. We evaluate Chiplet Cloud on four popular LLMs. Compared to GPU and TPU, our architecture can achieve up to 94x and 15x improvement in TCO/Token respectively, significantly reducing the cost for realistically serving modern LLMs.", "field": "cs", "label": 0}
{"text": "Title: New obstructions to symplectic embeddings\nAbstract: In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.", "field": "math", "label": 1}
{"text": "Title: Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold\nAbstract: For a Fano manifold, We consider the geometric quantization of the K\\\"ahler-Ricci flow and the associated entropy functional. Convergence to the original flow and entropy is established. It is also possible to formulate the finite-dimensional analogue of the optimal degeneration for the anti-canonical polarization.", "field": "math", "label": 0}
{"text": "Title: Numerical Analysis for Dirichlet Optimal Control Problems on Convex Polyhedral Domains\nAbstract: In this paper error analysis for finite element discretizations of Dirichlet boundary control problems is developed. For the first time, optimal discretization error estimates are established in the case of three dimensional polyhedral and convex domains. The convergence rates solely depend on the size of largest interior edge angle. These results are comparable to those for the two dimensional case. However, the approaches from the two dimensional setting are not directly extendable such that new techniques have to be used. The theoretical results are confirmed by numerical experiments.", "field": "math", "label": 0}
{"text": "Title: Ravnest: Decentralized Asynchronous Training on Heterogeneous Devices\nAbstract: Modern deep learning models, growing larger and more complex, have demonstrated exceptional generalization and accuracy due to training on huge datasets. This trend is expected to continue. However, the increasing size of these models poses challenges in training, as traditional centralized methods are limited by memory constraints at such scales. This paper proposes an asynchronous decentralized training paradigm for large modern deep learning models that harnesses the compute power of regular heterogeneous PCs with limited resources connected across the internet to achieve favourable performance metrics. Ravnest facilitates decentralized training by efficiently organizing compute nodes into clusters with similar data transfer rates and compute capabilities, without necessitating that each node hosts the entire model. These clusters engage in $\\textit{Zero-Bubble Asynchronous Model Parallel}$ training, and a $\\textit{Parallel Multi-Ring All-Reduce}$ method is employed to effectively execute global parameter averaging across all clusters. We have framed our asynchronous SGD loss function as a block structured optimization problem with delayed updates and derived an optimal convergence rate of $O\\left(\\frac{1}{\\sqrt{K}}\\right)$. We further discuss linear speedup with respect to the number of participating clusters and the bound on the staleness parameter.", "field": "cs", "label": 0}
{"text": "Title: On the Constructor-Blocker Game\nAbstract: In the Constructor-Blocker game, two players, Constructor and Blocker, alternatively claim unclaimed edges of the complete graph $K_n$. For given graphs $F$ and $H$, Constructor can only claim edges that leave her graph $F$-free, while Blocker has no restrictions. Constructor's goal is to build as many copies of $H$ as she can, while Blocker attempts to stop this. The game ends once there are no more edges that Constructor can claim. The score $g(n,H,F)$ of the game is the number of copies of $H$ in Constructor's graph at the end of the game, when both players play optimally and Constructor plays first. In this paper, we extend results of Patk\\'os, Stojakovi\\'c and Vizer on $g(n, H, F)$ to many pairs of $H$ and $F$: We determine $g(n, H, F)$ when $H=K_r$ and $\\chi(F)>r$, also when both $H$ and $F$ are odd cycles, using Szemer\\'edi's Regularity Lemma. We also obtain bounds of $g(n, H, F)$ when $H=K_3$ and $F=K_{2,2}$.", "field": "math", "label": 0}
{"text": "Title: Estimation of the incubation time distribution in the singly and doubly interval censored model\nAbstract: We analyze nonparametric estimators for the distribution function of the incubation time in the singly and doubly interval censoring model. The classical approach is to use parametric families like Weibull, log-normal or gamma distributions in the estimation procedure. We propose nonparametric estimates which stay closer to the data than the classical parametric methods. We also give explicit limit distributions for discrete versions of the models and apply this to compute confidence intervals. The methods complement the analysis of the continuous model. R scripts for computation of the estimates are provided on https://github.com/pietg/incubationtime.", "field": "math", "label": 0}
{"text": "Title: Generalized Modularity Embedding: a General Framework for Network Embedding\nAbstract: The network embedding problem aims to map nodes that are similar to each other to vectors in a Euclidean space that are close to each other. Like centrality analysis (ranking) and community detection, network embedding is in general considered as an ill-posed problem, and its solution may depend on a person's view on this problem. In this book chapter, we adopt the framework of sampled graphs that treat a person's view as a sampling method for a network. The modularity for a sampled graph, called the generalized modularity in the book chapter, is a similarity matrix that has a specific probabilistic interpretation. One of the main contributions of this book chapter is to propose using the generalized modularity matrix for network embedding and show that the network embedding problem can be treated as a trace maximization problem like the community detection problem. Our generalized modularity embedding approach is very general and flexible. In particular, we show that the Laplacian eigenmaps is a special case of our generalized modularity embedding approach. Also, we show that dimensionality reduction can be done by using a particular sampled graph. Various experiments are conducted on real datasets to illustrate the effectiveness of our approach.", "field": "cs", "label": 1}
{"text": "Title: Large deviation principle for a two-time-scale McKean-Vlasov model with jumps\nAbstract: This work focus on the large deviation principle for a two-time scale McKean-Vlasov system with jumps. Based on the variational framework of the McKean-Vlasov system with jumps, it is turned into weak convergence for the controlled system. Unlike general two-time scale system, the controlled McKean-Vlasov system is related to the law of the original system, which causes difficulties in qualitative analysis. In solving this problem, employing asymptotics of the original system and a Khasminskii-type averaging principle together is efficient. Finally, it is shown that the limit is related to the Dirac measure of the solution to the ordinary differential equation.", "field": "math", "label": 0}
{"text": "Title: On an open problem about a class of optimal ternary cyclic codes\nAbstract: Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, we settle an open problem about a class of optimal ternary cyclic codes which was proposed by Ding and Helleseth. Let $C_{(1,e)}$ be a cyclic code of length $3^m-1$ over GF(3) with two nonzeros $\\alpha$ and $\\alpha^e$, where $\\alpha$ is a generator of $GF(3^m)^*$ and e is a given integer. It is shown that $C_{(1,e)}$ is optimal with parameters $[3^m-1,3^m-1-2m,4]$ if one of the following conditions is met. 1) $m\\equiv0(\\mathrm{mod}~ 4)$, $m\\geq 4$, and $e=3^\\frac{m}{2}+5$. 2) $m\\equiv2(\\mathrm{mod}~ 4)$, $m\\geq 6$, and $e=3^\\frac{m+2}{2}+5$.", "field": "math", "label": 1}
{"text": "Title: Suppression of blow-up in 3-D Keller-Segel model via Couette flow in whole space\nAbstract: In this paper, we study the 3-D parabolic-parabolic and parabolic-elliptic Keller-Segel models with Couette flow in $\\mathbb{R}^3$. We prove that the blow-up phenomenon of solution can be suppressed by enhanced dissipation of large Couette flows. Here we develop Green's function method to describe the enhanced dissipation via a more precise space-time structure and obtain the global existence together with pointwise estimates of the solutions. The result of this paper shows that the enhanced dissipation exists for all frequencies in the case of whole space and it is reason that we obtain global existence for 3-D Keller-Segel models here. It is totally different from the case with the periodic spatial variable $x$ in [2,10]. This paper provides a new methodology to capture dissipation enhancement and also a surprising result which shows a totally new mechanism.", "field": "math", "label": 0}
{"text": "Title: Efficient tensor tomography in fan-beam coordinates\nAbstract: We propose a thorough analysis of the tensor tomography problem on the Euclidean unit disk parameterized in fan-beam coordinates. This includes, for the inversion of the Radon transform over functions, using another range characterization first appearing in [Pestov-Uhlmann, IMRN 2004] to enforce in a fast way classical moment conditions at all orders. When considering direction-dependent integrands (e.g., tensors), a problem where injectivity no longer holds, we propose a suitable representative (other than the traditionally sought-after solenoidal candidate) to be reconstructed, as well as an efficient procedure to do so. Numerical examples illustrating the method are provided at the end.", "field": "math", "label": 1}
{"text": "Title: Geometries arising from trilinear forms on low-dimensional vector spaces\nAbstract: Let ${\\mathcal G}_k(V)$ be the $k$-Grassmannian of a vector space $V$ with $\\dim V=n$. Given a hyperplane $H$ of ${\\mathcal G}_k(V)$, we define in [I. Cardinali, L. Giuzzi, A. Pasini, A geometric approach to alternating $k$-linear forms, J. Algebraic Combin. doi:10.1007/s10801-016-0730-6] a point-line subgeometry of ${\\mathrm{PG}}(V)$ called the {\\it geometry of poles of $H$}. In the present paper, exploiting the classification of alternating trilinear forms in low dimension, we characterize the possible geometries of poles arising for $k=3$ and $n\\leq 7$ and propose some new constructions. We also extend a result of [J.Draisma, R. Shaw, Singular lines of trilinear forms, Linear Algebra Appl. doi:10.1016/j.laa.2010.03.040] regarding the existence of line spreads of ${\\mathrm{PG}}(5,{\\mathbb K})$ arising from hyperplanes of ${\\mathcal G}_3(V).$", "field": "math", "label": 1}
{"text": "Title: k-Winners-Take-All Ensemble Neural Network\nAbstract: Ensembling is one approach that improves the performance of a neural network by combining a number of independent neural networks, usually by either averaging or summing up their individual outputs. We modify this ensembling approach by training the sub-networks concurrently instead of independently. This concurrent training of sub-networks leads them to cooperate with each other, and we refer to them as \"cooperative ensemble\". Meanwhile, the mixture-of-experts approach improves a neural network performance by dividing up a given dataset to its sub-networks. It then uses a gating network that assigns a specialization to each of its sub-networks called \"experts\". We improve on these aforementioned ways for combining a group of neural networks by using a k-Winners-Take-All (kWTA) activation function, that acts as the combination method for the outputs of each sub-network in the ensemble. We refer to this proposed model as \"kWTA ensemble neural networks\" (kWTA-ENN). With the kWTA activation function, the losing neurons of the sub-networks are inhibited while the winning neurons are retained. This results in sub-networks having some form of specialization but also sharing knowledge with one another. We compare our approach with the cooperative ensemble and mixture-of-experts, where we used a feed-forward neural network with one hidden layer having 100 neurons as the sub-network architecture. Our approach yields a better performance compared to the baseline models, reaching the following test accuracies on benchmark datasets: 98.34% on MNIST, 88.06% on Fashion-MNIST, 91.56% on KMNIST, and 95.97% on WDBC.", "field": "cs", "label": 0}
{"text": "Title: A spectral result for Hardy inequalities\nAbstract: Let P be a linear, second order, elliptic operator satisfying a Hardy inequality with potential W (i.e. $P-W\\geq0$) and best constant $\\alpha$. We give conditions so that the spectrum of $W^{-1}P$ is $[\\alpha,\\infty)$. We apply this to several well-known Hardy inequalities: (improved) Hardy inequalities on a bounded convex domain with potential involving the distance to the boundary, and Hardy inequalities for minimal submanifolds of the Euclidean space.", "field": "math", "label": 1}
{"text": "Title: Perfect matchings and Hamilton cycles in uniform attachment graphs\nAbstract: We study Hamilton cycles and perfect matchings in a uniform attachment graph. In this random graph, vertices are added sequentially, and when a vertex $t$ is created, it makes $k$ independent and uniform choices from $\\{1,\\dots,t-1\\}$ and attaches itself to these vertices. Improving the results of Frieze, P\\'erez-Gim\\'enez, Pra\\l{}at and Reiniger (2019), we show that, with probability approaching 1 as $n$ tends to infinity, a uniform attachment graph on $n$ vertices has a perfect matching for $k \\ge 5$ and a Hamilton cycle for $k\\ge 13$. One of the ingredients in our proofs is the identification of a subset of vertices that is least likely to expand, which provides us with better expansion rates than the existing ones.", "field": "math", "label": 1}
{"text": "Title: Influence Maximization in Ising Models\nAbstract: Given a complex high-dimensional distribution over $\\{\\pm 1\\}^n$, what is the best way to increase the expected number of $+1$'s by controlling the values of only a small number of variables? Such a problem is known as influence maximization and has been widely studied in social networks, biology, and computer science. In this paper, we consider influence maximization on the Ising model which is a prototypical example of undirected graphical models and has wide applications in many real-world problems. We establish a sharp computational phase transition for influence maximization on sparse Ising models under a bounded budget: In the high-temperature regime, we give a linear-time algorithm for finding a small subset of variables and their values which achieve nearly optimal influence; In the low-temperature regime, we show that the influence maximization problem cannot be solved in polynomial time under commonly-believed complexity assumption. The critical temperature coincides with the tree uniqueness/non-uniqueness threshold for Ising models which is also a critical point for other computational problems including approximate sampling and counting.", "field": "cs", "label": 0}
{"text": "Title: Characterizations and Constructions of Linear Intersection Pairs of Cyclic Codes over Finite Fields\nAbstract: Linear intersection pairs of linear codes have become of interest due to their nice algebraic properties and wide applications. In this paper, we focus on linear intersection pairs of cyclic codes over finite fields. Some properties of cyclotomic cosets in cyclic groups are presented as key tools in the study of such linear intersection pairs. Characterization and constructions of two cyclic codes of a fixed intersecting dimension are given in terms of their generator polynomials and cyclotomic cosets. In some cases, constructions of two cyclic codes of a fixed intersecting subcode are presented as well. Based on the theoretical characterization, some numerical examples of linear intersection pairs of cyclic codes with good parameters are illustrated.", "field": "cs", "label": 0}
{"text": "Title: The ZFC analogue of the Halpern-Levy theorem\nAbstract: Here we present ZFC theorems yielding the Halpern-L\\a\"uchli theorem and avoiding metamathematical notions in their formulations.", "field": "math", "label": 0}
{"text": "Title: A determinantal formula for orthosymplectic Schur functions\nAbstract: We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J. Algebraic Combin., 2003) for general linear Lie superalgebras. Our proof uses the Jacobi--Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent. Math., 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J. Combin. Theory Ser. A, 2016).", "field": "math", "label": 0}
{"text": "Title: Non-conforming FEM for the quasi-static contact problem\nAbstract: In this article, we addressed the numerical solution of a non-linear evolutionary variational inequality, which is encountered in the investigation of quasi-static contact problems. Our study encompasses both the semi-discrete and fully-discrete schemes, where we employ the backward Euler method for time discretization and utilize the lowest order Crouzeix-Raviart nonconforming finite element method for spatial discretization. By assuming appropriate regularity conditions on the solution, we establish \\emph{a priori} error analysis for these schemes, achieving the optimal convergence order for linear elements. To illustrate the numerical convergence rates, we provide numerical results on a two-dimensional test problem.", "field": "math", "label": 0}
{"text": "Title: Mid-point embedding of Hamiltonian systems and variational integrators\nAbstract: Following the discrete embedding formalism, we give a new derivation of the mid-point variational integrators as developed by J.M. Wendlandt and J.E. Marsden by defining an adapted order two discrete differential and integral calculus. This allows us to obtain a clearer correspondence between the discrete and continuous case. We also discuss the corresponding definition of a discrete Hamiltonian system. A complete comparaison with the results of J.M. Wendlandt and J.E. Marsden is provided.", "field": "math", "label": 1}
{"text": "Title: Faster Projection-Free Augmented Lagrangian Methods via Weak Proximal Oracle\nAbstract: This paper considers a convex composite optimization problem with affine constraints, which includes problems that take the form of minimizing a smooth convex objective function over the intersection of (simple) convex sets, or regularized with multiple (simple) functions. Motivated by high-dimensional applications in which exact projection/proximal computations are not tractable, we propose a \\textit{projection-free} augmented Lagrangian-based method, in which primal updates are carried out using a \\textit{weak proximal oracle} (WPO). In an earlier work, WPO was shown to be more powerful than the standard \\textit{linear minimization oracle} (LMO) that underlies conditional gradient-based methods (aka Frank-Wolfe methods). Moreover, WPO is computationally tractable for many high-dimensional problems of interest, including those motivated by recovery of low-rank matrices and tensors, and optimization over polytopes which admit efficient LMOs. The main result of this paper shows that under a certain curvature assumption (which is weaker than strong convexity), our WPO-based algorithm achieves an ergodic rate of convergence of $O(1/T)$ for both the objective residual and feasibility gap. This result, to the best of our knowledge, improves upon the $O(1/\\sqrt{T})$ rate for existing LMO-based projection-free methods for this class of problems. Empirical experiments on a low-rank and sparse covariance matrix estimation task and the Max Cut semidefinite relaxation demonstrate that of our method can outperform state-of-the-art LMO-based Lagrangian-based methods.", "field": "math", "label": 1}
{"text": "Title: Two dimensional dimers beyond planarity\nAbstract: We consider a generalisation of the double dimer model which includes several models of interest, such as the monomer double dimer model, the dimer model, the Spin O(N) model, and it is related to the loop O(N) model. We prove that on two-dimension like graphs (such as slabs), both the correlation function and the probability that a loop visits two vertices converge to zero as the distance between such vertices gets large. Our analysis is by introducing a new (complex) spin representation for all models belonging to this class, and by deriving a new proof of the Mermin-Wagner theorem which does not require the positivity of the Gibbs measure. Even for the well studied dimer and double dimer model our results are new since - not relying on solvability and Kasteleyn's theorem - they hold beyond the framework of planar graphs.", "field": "math", "label": 0}
{"text": "Title: Weyl modules and Levi subalgebras\nAbstract: For a simple complex Lie algebra of finite rank and classical type, we fix a triangular decomposition and consider the simple Levi subalgebras associated to closed subsets of roots. We study the restriction of global and local Weyl modules of current algebras to this Levi subalgebra. We identify necessary and sufficient conditions on a pair of a Levi subalgebra and a dominant integral weight, such that the restricted module is a global (resp. a local) Weyl module.", "field": "math", "label": 1}
{"text": "Title: Spatiotemporal Monitoring of Epidemics via Solution of a Coefficient Inverse Problem\nAbstract: Let S,I and R be susceptible, infected and recovered populations in a city affected by an epidemic. The SIR model of Lee, Liu, Tembine, Li and Osher, \\emph{SIAM J. Appl. Math.},~81, 190--207, 2021 of the spatiotemoral spread of epidemics is considered. This model consists of a system of three nonlinear coupled parabolic Partial Differential Equations with respect to the space and time dependent functions S,I and R. For the first time, a Coefficient Inverse Problem (CIP) for this system is posed. The so-called \\textquotedblleft convexification\" numerical method for this inverse problem is constructed. The presence of the Carleman Weight Function (CWF) in the resulting regularization functional ensures the global convergence of the gradient descent method of the minimization of this functional to the true solution of the CIP, as long as the noise level tends to zero. The CWF is the function, which is used as the weight in the Carleman estimate for the corresponding Partial Differential Operator. Numerical studies demonstrate an accurate reconstruction of unknown coefficients as well as S,I,R functions inside of that city. As a by-product, uniqueness theorem for this CIP is proven. Since the minimal measured input data are required, then the proposed methodology has a potential of a significant decrease of the cost of monitoring of epidemics.", "field": "math", "label": 0}
{"text": "Title: Hochschild and cyclic Homologies with bounded poles\nAbstract: We show that the classical Hochschild homology and (periodic and negative) cyclic homology groups are representable in the category of motives with modulus. We do this by constructing Hochschild homology and (periodic and negative) cyclic homologies for modulus pairs. We show a modulus version of HKR theorem, that is, there exists an isomorphism between modulus Hochschild homology and modulus K\\\"ahler differentials for affine normal crossing modulus pairs. By using the representability of modulus Hodge sheaves in the category of motives with modulus, we construct an object of the category of motives with modulus which represents modulus Hochschild homology. Similarly, We compare modulus de Rham cohomology and modulus cyclic homologies and obtain a representability of modulus cyclic homologies.", "field": "math", "label": 0}
{"text": "Title: Category-Level 6D Object Pose Estimation with Flexible Vector-Based Rotation Representation\nAbstract: In this paper, we propose a novel 3D graph convolution based pipeline for category-level 6D pose and size estimation from monocular RGB-D images. The proposed method leverages an efficient 3D data augmentation and a novel vector-based decoupled rotation representation. Specifically, we first design an orientation-aware autoencoder with 3D graph convolution for latent feature learning. The learned latent feature is insensitive to point shift and size thanks to the shift and scale-invariance properties of the 3D graph convolution. Then, to efficiently decode the rotation information from the latent feature, we design a novel flexible vector-based decomposable rotation representation that employs two decoders to complementarily access the rotation information. The proposed rotation representation has two major advantages: 1) decoupled characteristic that makes the rotation estimation easier; 2) flexible length and rotated angle of the vectors allow us to find a more suitable vector representation for specific pose estimation task. Finally, we propose a 3D deformation mechanism to increase the generalization ability of the pipeline. Extensive experiments show that the proposed pipeline achieves state-of-the-art performance on category-level tasks. Further, the experiments demonstrate that the proposed rotation representation is more suitable for the pose estimation tasks than other rotation representations.", "field": "cs", "label": 1}
{"text": "Title: The ghosts of departed quantities in switches and transitions\nAbstract: Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the dynamics of the system significantly. Here we discuss the way transitions can be reduced to discontinuities without trivializing them, by preserving so-called hidden terms. We review the fundamental methodology, its motivations, and where their study seems to be heading. We derive a prototype for piecewise smooth models from the asymptotics of systems with rapid transitions, sharpening Filippov's convex combinations by encoding the tails of asymptotic series into nonlinear dependence on a switching parameter. We present a few examples that illustrate the impact of these on our standard picture of smooth or only piecewise smooth dynamics.", "field": "math", "label": 1}
{"text": "Title: On the Effects of Battery Imperfections in an Energy Harvesting Device\nAbstract: Energy Harvesting allows the devices in a Wireless Sensor Network to recharge their batteries through environmental energy sources. While in the literature the main focus is on devices with ideal batteries, in reality several inefficiencies have to be considered to correctly design the operating regimes of an Energy Harvesting Device (EHD). In this work we describe how the throughput optimization problem changes under \\emph{real battery} constraints in an EHD. In particular, we consider imperfect knowledge of the state of charge of the battery and storage inefficiencies, \\emph{i.e.}, part of the harvested energy is wasted in the battery recharging process. We formulate the problem as a Markov Decision Process, basing our model on some realistic observations about transmission, consumption and harvesting power. We find the performance upper bound with a real battery and numerically discuss the novelty introduced by the real battery effects. We show that using the \\emph{old} policies obtained without considering the real battery effects is strongly sub-optimal and may even result in zero throughput.", "field": "cs", "label": 1}
{"text": "Title: CBD: A Certified Backdoor Detector Based on Local Dominant Probability\nAbstract: Backdoor attack is a common threat to deep neural networks. During testing, samples embedded with a backdoor trigger will be misclassified as an adversarial target by a backdoored model, while samples without the backdoor trigger will be correctly classified. In this paper, we present the first certified backdoor detector (CBD), which is based on a novel, adjustable conformal prediction scheme based on our proposed statistic local dominant probability. For any classifier under inspection, CBD provides 1) a detection inference, 2) the condition under which the attacks are guaranteed to be detectable for the same classification domain, and 3) a probabilistic upper bound for the false positive rate. Our theoretical results show that attacks with triggers that are more resilient to test-time noise and have smaller perturbation magnitudes are more likely to be detected with guarantees. Moreover, we conduct extensive experiments on four benchmark datasets considering various backdoor types, such as BadNet, CB, and Blend. CBD achieves comparable or even higher detection accuracy than state-of-the-art detectors, and it in addition provides detection certification. Notably, for backdoor attacks with random perturbation triggers bounded by $\\ell_2\\leq0.75$ which achieves more than 90\\% attack success rate, CBD achieves 100\\% (98\\%), 100\\% (84\\%), 98\\% (98\\%), and 72\\% (40\\%) empirical (certified) detection true positive rates on the four benchmark datasets GTSRB, SVHN, CIFAR-10, and TinyImageNet, respectively, with low false positive rates.", "field": "cs", "label": 0}
{"text": "Title: Starling: An I/O-Efficient Disk-Resident Graph Index Framework for High-Dimensional Vector Similarity Search on Data Segment\nAbstract: High-dimensional vector similarity search (HVSS) is receiving a spotlight as a powerful tool for various data science and AI applications. As vector data grows larger, in-memory indexes become extremely expensive because they necessitate substantial expansion of main memory resources. One possible solution is to use disk-based implementation, which stores and searches vector data in high-performance devices like NVMe SSDs. However, HVSS for data segments is still challenging in vector databases, where one machine has multiple segments for system features (like scaling) purposes. In this setting, each segment has limited memory and disk space, so HVSS on the data segment needs to balance accuracy, efficiency, and space cost. Existing disk-based methods are sub-optimal because they do not consider all these requirements together. In this paper, we present Starling, an I/O-efficient disk-resident graph index framework that optimizes data layout and search strategy in the segment. It has two main components: (1) a data layout that includes an in-memory navigation graph and a reordered disk-based graph with locality enhancement, which reduces the search path length and disk bandwidth wastage; and (2) a block search strategy that minimizes expensive disk I/Os when executing a vector query. We conduct extensive experiments to verify Starling's effectiveness, efficiency, and scalability. On a data segment with 2GB memory and 10GB disk capacity, Starling can maintain up to 33 million vectors in 128 dimensions, and serve HVSS with more than 0.9 average precision and top-10 recall rate, and latency of under 1 millisecond. The results show that Starling exhibits 43.9$\\times$ higher throughput with 98% lower query latency than state-of-the-art methods under the same accuracy.", "field": "cs", "label": 0}
{"text": "Title: $L^p$-spectral theory for the Laplacian on forms\nAbstract: In this article, we find sufficient conditions on an open Riemannian manifold so that a Weyl criterion holds for the $L^p$-spectrum of the Laplacian on $k$-forms, and also prove the decomposition of the $L^p$-spectrum depending on the order of the forms. We then show that the resolvent set of an operator such as the Laplacian on $L^p$ lies outside a parabola whenever the volume of the manifold has an exponential volume growth rate, removing the requirement on the manifold to be of bounded geometry. We conclude by providing a detailed description of the $L^p$ spectrum of the Laplacian on $k$-forms over hyperbolic space.", "field": "math", "label": 0}
{"text": "Title: On the number of perfect matchings in random lifts\nAbstract: Let G be a fixed connected multigraph with no loops. A random n-lift of G is obtained by replacing each vertex of G by a set of n vertices (where these sets are pairwise disjoint) and replacing each edge by a randomly chosen perfect matching between the n-sets corresponding to the endpoints of the edge. Let X_G be the number of perfect matchings in a random lift of G. We study the distribution of X_G in the limit as n tends to infinity, using the small subgraph conditioning method. We present several results including an asymptotic formula for the expectation of X_G when G is d-regular, d\\geq 3. The interaction of perfect matchings with short cycles in random lifts of regular multigraphs is also analysed. Partial calculations are performed for the second moment of X_G, with full details given for two example multigraphs, including the complete graph K_4. To assist in our calculations we provide a theorem for estimating a summation over multiple dimensions using Laplace's method. This result is phrased as a summation over lattice points, and may prove useful in future applications.", "field": "math", "label": 1}
{"text": "Title: Low level definability above large cardinals\nAbstract: We study some connections between definability in generalized descriptive set theory and large cardinals, particularly measurable cardinals and limits thereof, working in ZFC. We show that if $\\kappa$ is a limit of measurable cardinals then there is no $\\Sigma_1(H_\\kappa\\cup\\mathrm{OR})$ wellorder of a subset of $P(\\kappa)$ of length $\\geq\\kappa^+$; this answers a question of L\\\"ucke and M\\\"uller. However, in $M_1$, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal $\\kappa$ which is not a limit of measurables, there is a $\\Sigma_1(H_\\kappa\\cup\\{\\kappa\\})$ good wellorder of $H_{\\kappa^+}$. If $\\kappa$ is a limit of measurables then there is no $\\Sigma_1(H_\\kappa\\cup\\mathrm{OR})$ mad family $F\\subseteq P(\\kappa)$ of cardinality $>\\kappa$, and if also $\\mathrm{cof}(\\kappa)>\\omega$ then there is no $\\Sigma_1(H_\\kappa\\cup\\mathrm{OR})$ almost disjoint family $F\\subseteq P(\\kappa)$ of cardinality $>\\kappa$. However, relative to the consistency of large cardinals, $\\Pi_1(\\{\\kappa\\})$ mad families and maximal independent families $F\\subseteq P(\\kappa)$ can exist, when $\\kappa$ is a limit of measurables, and even more. We also examine some of the features of $L[U]$, and answer another question of L\\\"ucke and M\\\"uller, showing that if $\\kappa$ is a weakly compact cardinal such that every $\\Sigma_1(H_\\kappa\\cup\\{\\kappa\\})$ subset of $P(\\kappa)$ of cardinality $>\\kappa$ has a subset which is the range of a perfect function, then there is an inner model satisfying \"there is a weakly compact limit of measurable cardinals\".", "field": "math", "label": 0}
{"text": "Title: Twisted restricted conformal blocks of vertex operator algebras I: $g$-twisted correlation functions and fusion rules\nAbstract: In this paper, we introduce a notion of $g$-twisted restricted conformal block on the three-pointed twisted projective line $\\mathfrak{x}\\colon\\overline{C}\\to\\mathbb{P^1}$ associated with an untwisted module $M^1$ and the bottom levels of two $g$-twisted modules $M^2$ and $M^3$ over a vertex operator algebra $V$. We show that the space of twisted restricted conformal blocks is isomorphic to the space of $g$-twisted (restricted) correlation functions defined by the same datum and to the space of intertwining operators among these twisted modules. As an application, we derive a twisted version of the Fusion Rules Theorem.", "field": "math", "label": 0}
{"text": "Title: Optimal jump set in hyperbolic conservation laws\nAbstract: This paper deals with some qualitative properties of entropy solutions to hyperbolic conservation laws. In [11] the jump set of entropy solution to conservation laws has been introduced. We find an entropy solution to scalar conservation laws for which the jump set is not closed, in particular, it is dense in a space-time domain. In the later part of this article, we obtain a similar result for the hyperbolic system. We give two different approaches for scalar conservation laws and hyperbolic system to obtain the results. For the scalar case, obtained solutions are more explicitly calculated.", "field": "math", "label": 1}
{"text": "Title: Marginal Debiased Network for Fair Visual Recognition\nAbstract: Deep neural networks (DNNs) are often prone to learn the spurious correlations between target classes and bias attributes, like gender and race, inherent in a major portion of training data (bias-aligned samples), thus showing unfair behavior and arising controversy in the modern pluralistic and egalitarian society. In this paper, we propose a novel marginal debiased network (MDN) to learn debiased representations. More specifically, a marginal softmax loss (MSL) is designed by introducing the idea of margin penalty into the fairness problem, which assigns a larger margin for bias-conflicting samples (data without spurious correlations) than for bias-aligned ones, so as to deemphasize the spurious correlations and improve generalization on unbiased test criteria. To determine the margins, our MDN is optimized through a meta learning framework. We propose a meta equalized loss (MEL) to perceive the model fairness, and adaptively update the margin parameters by metaoptimization which requires the trained model guided by the optimal margins should minimize MEL computed on an unbiased meta-validation set. Extensive experiments on BiasedMNIST, Corrupted CIFAR-10, CelebA and UTK-Face datasets demonstrate that our MDN can achieve a remarkable performance on under-represented samples and obtain superior debiased results against the previous approaches.", "field": "cs", "label": 0}
{"text": "Title: Wasserstein gradient flows from large deviations of thermodynamic limits\nAbstract: We study the Fokker-Planck equation as the hydrodynamic limit of a stochastic particle system on one hand and as a Wasserstein gradient flow on the other. We write the rate functional, that characterizes the large deviations from the hydrodynamic limit, in a way that the free energy appears explicitly. Next we use this formulation via the contraction principle to prove that the discreet time rate functional is asymptotically equivalent in the Gamma-convergence sense to the functional derived from the Wasserstein gradient discretization scheme.", "field": "math", "label": 1}
{"text": "Title: The quantitative behaviour of polynomial orbits on nilmanifolds\nAbstract: A theorem of Leibman asserts that a polynomial orbit $(g(1),g(2),g(3),\\ldots)$ on a nilmanifold $G/\\Gamma$ is always equidistributed in a union of closed sub-nilmanifolds of $G/\\Gamma$. In this paper we give a quantitative version of Leibman's result, describing the uniform distribution properties of a finite polynomial orbit $(g(1),\\ldots,g(N))$ in a nilmanifold. More specifically we show that there is a factorization $g = \\epsilon g'\\gamma$, where $\\epsilon(n)$ is \"smooth\", $\\gamma(n)$ is periodic and \"rational\", and $(g'(a),g'(a+d),\\ldots,g'(a + d(l-1)))$ is uniformly distributed (up to a specified error $\\delta$) inside some subnilmanifold $G'/\\Gamma'$ of $G/\\Gamma$, for all sufficiently dense arithmetic progressions $a,a+d,\\ldots,a+d(l-1)$ inside $\\{1,..,N\\}$. Our bounds are uniform in $N$ and are polynomial in the error tolerance delta. In a subsequent paper we shall use this theorem to establish the Mobius and Nilsequences conjecture from our earlier paper \"Linear equations in primes\".", "field": "math", "label": 1}
{"text": "Title: Selection Collider Bias in Large Language Models\nAbstract: In this paper we motivate the causal mechanisms behind sample selection induced collider bias (selection collider bias) that can cause Large Language Models (LLMs) to learn unconditional dependence between entities that are unconditionally independent in the real world. We show that selection collider bias can become amplified in underspecified learning tasks, and although difficult to overcome, we describe a method to exploit the resulting spurious correlations for determination of when a model may be uncertain about its prediction. We demonstrate an uncertainty metric that matches human uncertainty in tasks with gender pronoun underspecification on an extended version of the Winogender Schemas evaluation set, and we provide an online demo where users can apply our uncertainty metric to their own texts and models.", "field": "cs", "label": 1}
{"text": "Title: On the local density problem for graphs of given odd-girth\nAbstract: Erd\\H{o}s conjectured that every $n$-vertex triangle-free graph contains a subset of $\\lfloor n/2\\rfloor$ vertices that spans at most $n^2/50$ edges. Extending a recent result of Norin and Yepremyan, we confirm this conjecture for graphs homomorphic to so-called Andr\\'asfai graphs. As a consequence, Erd\\H{o}s' conjecture holds for every triangle-free graph $G$ with minimum degree $\\delta (G)>10n/29$ and if $\\chi (G)\\leq 3$ the degree condition can be relaxed to $\\delta (G)> n/3$. In fact, we obtain a more general result for graphs of higher odd-girth.", "field": "math", "label": 1}
{"text": "Title: Moonshot: Optimizing Chain-Based Rotating Leader BFT via Optimistic Proposals\nAbstract: Existing chain-based rotating leader BFT SMR protocols for the partially synchronous network model that commit blocks with $O(1)$ minimum latency have block periods of at least $2\\delta$ (where $\\delta$ is the message transmission latency). While a protocol with a block period of $\\delta$ exists under the synchronous model, its minimum commit latency is linear in the size of the system. To close this gap, we present the first chain-based BFT SMR protocols with best-case delays of $\\delta$ between the proposals of distinct honest leaders, and minimum commit latencies of $3\\delta$. We present three protocols for the partially synchronous network model under different notions of optimistic responsiveness, two of which implement pipelining and one of which does not. All of our protocols achieve reorg resilience and two have short view lengths; properties that many existing chain-based BFT SMR protocols lack. We experimentally evaluate our protocols and show that they achieve significant increases in throughput and reductions in latency compared to the state-of-the-art, Jolteon. Our results also demonstrate that techniques commonly employed to reduce communication complexity$\\unicode{x2014}$such as vote-pipelining and the use of designated vote-aggregators$\\unicode{x2014}$actually reduce practical performance in many settings.", "field": "cs", "label": 0}
{"text": "Title: Quantum Geometry, Integrability, and Opers\nAbstract: This review article discusses recent progress in understanding of various families of integrable models in terms of algebraic geometry, representation theory, and physics. In particular, we address the connections between soluble many-body systems of Calogero-Ruijsenaars type, quantum spin chains, spaces of opers, representations of double affine Hecke algebras, enumerative counts to quiver varieties, to name just a few. We formulate several conjectures and open problems. This is a contribution to the proceedings of the conference on Elliptic Integrable Systems and Representation Theory, which was held in August 2023 at University of Tokyo.", "field": "math", "label": 0}
{"text": "Title: Lengths of three simple periodic geodesics on a Riemannian $2$-sphere\nAbstract: Let $M$ be a Riemannian $2$-sphere. A classical theorem of Lyusternik and Shnirelman asserts the existence of three distinct simple non-trivial periodic geodesics on $M$. In this paper we prove that there exist three simple periodic geodesics with lengths that do not exceed $20d$, where $d$ is the diameter of $M$. We also present an upper bound that depends only on the area and diameter for the lengths of the three simple periodic geodesics with positive indices that appear as minimax critical values in the classical proofs of the Lyusternik-Shnirelman theorem. Finally, we present better bounds for these three lengths for \"thin\" spheres, when the area $A$ is much less than $d^2$, where the bounds for the lengths of the first two simple periodic geodesics are asymptotically optimal, when ${A\\over d^2}\\longrightarrow 0$.", "field": "math", "label": 1}
{"text": "Title: The distance signatures of the incidence graphs of affine resolvable designs\nAbstract: In this note, we determined the distance signatures of the incidence matrices of affine resolvable designs. This proves a conjecture by Kohei Yamada.", "field": "math", "label": 1}
{"text": "Title: REDriver: Runtime Enforcement for Autonomous Vehicles\nAbstract: Autonomous driving systems (ADSs) integrate sensing, perception, drive control, and several other critical tasks in autonomous vehicles, motivating research into techniques for assessing their safety. While there are several approaches for testing and analysing them in high-fidelity simulators, ADSs may still encounter additional critical scenarios beyond those covered once they are deployed on real roads. An additional level of confidence can be established by monitoring and enforcing critical properties when the ADS is running. Existing work, however, is only able to monitor simple safety properties (e.g., avoidance of collisions) and is limited to blunt enforcement mechanisms such as hitting the emergency brakes. In this work, we propose REDriver, a general and modular approach to runtime enforcement, in which users can specify a broad range of properties (e.g., national traffic laws) in a specification language based on signal temporal logic (STL). REDriver monitors the planned trajectory of the ADS based on a quantitative semantics of STL, and uses a gradient-driven algorithm to repair the trajectory when a violation of the specification is likely. We implemented REDriver for two versions of Apollo (i.e., a popular ADS), and subjected it to a benchmark of violations of Chinese traffic laws. The results show that REDriver significantly improves Apollo's conformance to the specification with minimal overhead.", "field": "cs", "label": 0}
{"text": "Title: Beyond Extraction: Contextualising Tabular Data for Efficient Summarisation by Language Models\nAbstract: The conventional use of the Retrieval-Augmented Generation (RAG) architecture has proven effective for retrieving information from diverse documents. However, challenges arise in handling complex table queries, especially within PDF documents containing intricate tabular structures.This research introduces an innovative approach to enhance the accuracy of complex table queries in RAG-based systems. Our methodology involves storing PDFs in the retrieval database and extracting tabular content separately. The extracted tables undergo a process of context enrichment, concatenating headers with corresponding values. To ensure a comprehensive understanding of the enriched data, we employ a fine-tuned version of the Llama-2-chat language model for summarisation within the RAG architecture. Furthermore, we augment the tabular data with contextual sense using the ChatGPT 3.5 API through a one-shot prompt. This enriched data is then fed into the retrieval database alongside other PDFs. Our approach aims to significantly improve the precision of complex table queries, offering a promising solution to a longstanding challenge in information retrieval.", "field": "cs", "label": 0}
{"text": "Title: Ramsey numbers for bipartite graphs with small bandwidth\nAbstract: We estimate Ramsey numbers for bipartite graphs with small bandwidth and bounded maximum degree. In particular we determine asymptotically the two and three color Ramsey numbers for grid graphs. More generally, we determine asymptotically the two color Ramsey number for bipartite graphs with small bandwidth and bounded maximum degree and the three color Ramsey number for such graphs with the additional assumption that the bipartite graph is balanced.", "field": "math", "label": 1}
{"text": "Title: Analysis of Twisted Supercharge Families on Product Manifolds\nAbstract: Twisted supercharge families on product manifolds $\\mathbb{T} \\times M$ have been applied in the analysis of the odd twisted K-theory. We shall suspend these families to the even twisted K-theory and solve their twisted families index problem. This is applied to give analytic representatives of the twisted K-theory classes on tori - including all the torsion classes.", "field": "math", "label": 1}
{"text": "Title: On Picard groups and Jacobians of directed graphs\nAbstract: The Picard group of an undirected graph is a finitely generated abelian group, and the Jacobian is the torsion subgroup of the Picard group. These groups can be computed by using the Smith normal form of the Laplacian matrix of the graph or by using chip-firing games associated with the graph. One may consider its generalization to directed graphs based on the Laplacian matrix. We compute Picard groups and Jacobians for several classes of directed trees, cycles, wheel, and multipartite graphs.", "field": "math", "label": 1}
{"text": "Title: Mitigating Procrastination in Crowdsourcing Via Efficient Scheduling Algorithm\nAbstract: Several works related to crowdsourcing have been proposed in the direction where the task executors are to perform the tasks within the stipulated deadlines. Though the deadlines are set, it may be a practical scenario that majority of the task executors submit the tasks as late as possible. This situation where the task executors may delay their task submission is termed as procrastination in behavioural economics. In many applications, these late submission of tasks may be problematic for task requesters. In literature, how to prevent this procrastination within the deadline is not addressed in crowdsourcing scenario. However, in a bipartite graph setting one procrastination aware scheduling is proposed but balanced job distribution in different slots (also termed as schedules) is not considered there. In this paper, a procrastination aware scheduling of jobs is proliferated by proposing an (randomized) algorithm in crowdsourcing scenario (also applicable in mobile and spatial crowdsourcing). Our algorithm ensures that balancing of jobs in different schedules are maintained. Our scheme is compared with the existing algorithm through extensive simulation and in terms of balancing effect, our proposed algorithm outperforms the existing one. Analytically it is shown that our proposed algorithm maintains the balanced distribution.", "field": "cs", "label": 0}
{"text": "Title: Extended Special Linear group $ESL_2(\\mathbb{F})$ and square roots in matrix groups $SL_2(\\mathbb{F})$, $SL_2(\\mathbb{Z})$, $ESL_2(\\mathbb{F})$, $GL_2(\\mathbb{F}_p)$\nAbstract: First time, we introduce Extended special linear group $ESL_2(F)$, which is generalization of matrix group $SL_2(F)$ over arbitrary field $F$. Extended special linear group $ESL_2(k)$, where $k$ is arbitrary perfect field, is storage of all square matrix roots from $ESL_2(k)$. The analytical formulas of roots of 2-nd, 3-rd, 4-th and $n$-th powers in $ SL_2(\\mathbb{F}_p)$ are found by us. Also for roots in $ SL_2(\\mathbb{Z})$, $ ESL_2(\\mathbb{Z})$ and in $ SL_2({k})$ as well as in $ESL_2({k})$, where $k$ is arbitrary perfect field, is found by us. New linear group which is storage of square roots from $ SL_2{\\mathbb{F}_p}$ is found and investigated by us. The criterion of roots existing for different classes of matrix -- simple and semisimple matrixes from $ SL_2({\\mathbb{F}_p})$, $ SL_2({\\mathbb{Z}})$ are established. The problems of square root from group element existing in $SL_2(F_p)$, $SL_2(F_p)$ and $GL_2(F_p)$ for arbitrary prime $p$ are solved in this paper. The similar goal of root finding was reached in the GM algorithm adjoining an $n$-th root of a generator \\cite{GM} results in a discrete group for group $SL(2,R)$, but we consider this question over finite field $F_p$. Over method gives answer about existing $\\sqrt{ M^n}$ without exponenting $M$ to $n$-th power. We only use the trace of $M$ or only eigenvalues of $M$. In \\cite{Amit} only the Anisotropic case of group $SL_1(Q)$, where $Q$ is a quaternion division algebra over $k$ was considered. The authors of \\cite{Amit} considered criterion to be square only for the case $F_p$ is a field of characteristics not equal 2. We solve this problem even for fields $F_2$ and $F_{2^n}$. The criterion to $g \\in SL_2 (F_2)$ be square in $SL_2(F_2)$ was not found by them what was declared in a separate sentence in \\cite{Amit}. We consider more general case \\cite{SkSq} consisting in whole group $G= SL_2(F_q)$.", "field": "math", "label": 0}
{"text": "Title: Application of the Cartier Operator in Coding Theory\nAbstract: The $a$-number is an invariant of the isomorphism class of the $p$-torsion group scheme. We use the Cartier operator on $H^0(\\mathcal{A}_2,\\Omega^1)$ to find a closed formula for the $a$-number of the form $\\mathcal{A}_2 = v(Y^{\\sqrt{q}}+Y-x^{\\frac{\\sqrt{q}+1}{2}})$ where $q=p^s$ over the finite field $\\mathbb{F}_{q^2}$. The application of the computed $a$-number in coding theory is illustrated by the relationship between the algebraic properties of the curve and the parameters of codes that are supported by it.", "field": "cs", "label": 0}
{"text": "Title: The continuum limit of higher-order Follow-the-Leader models\nAbstract: We study a generalized Follow-the-Leader model where the driver considers the position of an arbitrary but finite number of vehicles ahead, as well as the position of the vehicle directly behind the driver. It is proved that this model converges to the classical Lighthill-Whitham-Richards model for traffic flow when traffic becomes dense. This also underscores the robustness of the Lighthill-Whitham-Richards model.", "field": "math", "label": 0}
{"text": "Title: Multi-scale Discriminant Saliency with Wavelet-based Hidden Markov Tree Modelling\nAbstract: The bottom-up saliency, an early stage of humans' visual attention, can be considered as a binary classification problem between centre and surround classes. Discriminant power of features for the classification is measured as mutual information between distributions of image features and corresponding classes . As the estimated discrepancy very much depends on considered scale level, multi-scale structure and discriminant power are integrated by employing discrete wavelet features and Hidden Markov Tree (HMT). With wavelet coefficients and Hidden Markov Tree parameters, quad-tree like label structures are constructed and utilized in maximum a posterior probability (MAP) of hidden class variables at corresponding dyadic sub-squares. Then, a saliency value for each square block at each scale level is computed with discriminant power principle. Finally, across multiple scales is integrated the final saliency map by an information maximization rule. Both standard quantitative tools such as NSS, LCC, AUC and qualitative assessments are used for evaluating the proposed multi-scale discriminant saliency (MDIS) method against the well-know information based approach AIM on its released image collection with eye-tracking data. Simulation results are presented and analysed to verify the validity of MDIS as well as point out its limitation for further research direction.", "field": "cs", "label": 1}
{"text": "Title: Stationary Distributions for Two-Dimensional Sticky Brownian Motions: Exact Tail Asymptotics and Extreme Value Distributions\nAbstract: In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and mathematical finance. For example, a sticky Brownian motion can be used to model a storage system.with exceptional services. In this paper, we focus on stationary distributions for sticky Brownian motions. The main results obtained here include tail asymptotic properties in boundary stationary distributions, marginal distributions, and joint distributions. The kernel method, copula concept and extreme value theory are main tools used in our analysis.", "field": "math", "label": 1}
{"text": "Title: Non-unital polygraphs form a presheaf category\nAbstract: We prove, as claimed by A.Carboni and P.T.Johnstone, that the category of non-unital polygraphs, i.e. polygraphs where the source and target of each generator are not identity arrows, is a presheaf category. More generally we develop a new criterion for proving that certain classes of polygraphs are presheaf categories. This criterion also applies to the larger class of polygraphs where only the source of each generator is not an identity, and to the class of \"many-to-one polygraphs\", producing a new, more direct, proof that this is a presheaf category. The criterion itself seems to be extendable to more general type of operads over possibly different combinatorics, but we leave this question for future work. In an appendix we explain why this result is relevant if one wants to fix the arguments of a famous paper of M.Kapranov and V.Voevodsky and make them into a proof of C.Simpson's semi-strictification conjecture. We present a program aiming at proving this conjecture, which will be continued in subsequent papers.", "field": "math", "label": 1}
{"text": "Title: On the center of near-group fusion category of type $\\mathbb{Z}_3+6$\nAbstract: Let $\\mathcal{A}$ be a near-group fusion category of type $\\mathbb{Z}_3+6$. We show that there is a modular tensor equivalence $\\mathcal{Z}(\\mathcal{A})\\cong\\mathcal{C}(\\mathbb{Z}_3,\\eta)\\boxtimes\\mathcal{C}(\\mathfrak{sl}_3,9)_{\\mathbb{Z}_3}^0$. Moreover, we construct two non-trivial faithful extensions of $\\mathcal{A}$ explicitly, whose Drinfeld centers can also be obtained from representation categories quantum groups at root of unity.", "field": "math", "label": 0}
{"text": "Title: Affine Symmetries of Orbit Polytopes\nAbstract: An orbit polytope is the convex hull of an orbit under a finite group $G \\leq \\operatorname{GL}(d,\\mathbb{R})$. We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense set of generic points such that the orbit polytopes of generic points have conjugated affine symmetry groups. We prove that the symmetry group of a generic orbit polytope is again $G$ if $G$ is itself the affine symmetry group of some orbit polytope, or if $G$ is absolutely irreducible. On the other hand, we describe some general cases where the affine symmetry group grows. We apply our theory to representation polytopes (the convex hull of a finite matrix group) and show that their affine symmetries can be computed effectively from a certain character. We use this to construct counterexamples to a conjecture of Baumeister et~al.\\ on permutation polytopes [Advances in Math. 222 (2009), 431--452, Conjecture~5.4].", "field": "math", "label": 1}
{"text": "Title: Stability Conditions and Semiorthogonal Decompositions I: Quasi-convergence\nAbstract: We develop a framework relating semiorthogonal decompositions of a triangulated category $\\mathcal{C}$ to paths in its space of stability conditions. We prove that when $\\mathcal{C}$ is the homotopy category of a smooth and proper pre-triangulated dg-category, every semiorthogonal decomposition whose semiorthogonal factors admit a Bridgeland stability condition can be obtained from our framework.", "field": "math", "label": 0}
{"text": "Title: Vietnamese Poem Generation & The Prospect Of Cross-Language Poem-To-Poem Translation\nAbstract: Poetry generation has been a challenging task in the field of Natural Language Processing, as it requires the model to understand the nuances of language, sentiment, and style. In this paper, we propose using Large Language Models to generate Vietnamese poems of various genres from natural language prompts, thereby facilitating an intuitive process with enhanced content control. Our most efficacious model, the GPT-3 Babbage variant, achieves a custom evaluation score of 0.8, specifically tailored to the \"luc bat\" genre of Vietnamese poetry. Furthermore, we also explore the idea of paraphrasing poems into normal text prompts and yield a relatively high score of 0.781 in the \"luc bat\" genre. This experiment presents the potential for cross-Language poem-to-poem translation with translated poems as the inputs while concurrently maintaining complete control over the generated content.", "field": "cs", "label": 0}
{"text": "Title: Covariant Dirac Operators on Quantum Groups\nAbstract: We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space $U_q(\\g) \\otimes \\mathrm{cl}_q(\\g)$ where the second tensor factor is a $q$-deformation of the classical Clifford algebra. The tensor space $ U_q(\\g) \\otimes \\mathrm{cl}_q(\\g)$ is given a structure of the adjoint module of the quantum group and the Dirac operator is invariant under this action. The purpose of this approach is to construct equivariant Fredholm modules and $K$-homology cycles. This work generalizes the operator introduced by Bibikov and Kulish in \\cite{BK}.", "field": "math", "label": 1}
{"text": "Title: Sub-Poissonian estimates for exponential moments of additive functionals over pairs of particles with respect to determinantal and symplectic Pfaffian point processes governed by entire functions\nAbstract: The aim of this note is to estimate the tail of the distribution of the number of particles in an interval under determinantal and Pfaffian point processes. The main result of the note is that the square of the number of particles under the determinantal point process whose correlation kernel is an entire function of finite order has sub-Poissonian tails. The same result also holds in the symplectic Pfaffian case. As a corollary, sub-Poissonian estimates are also obtained for exponential moments of additive functionals over pairs of particles.", "field": "math", "label": 0}
{"text": "Title: Law of large numbers and fluctuations in the sub-critical and $L^2$ regions for SHE and KPZ equation in dimension $d\\geq 3$\nAbstract: There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $d\\geq 3$ as the smoothing parameter is switched off, but most of the results did not hold in the full temperature regions where they should. Inspired by martingale techniques coming from the directed polymers literature, we first extend the law of large numbers for SHE obtained in [MSZ16] to the full weak disorder region of the associated polymer model and to more general initial conditions. We further extend the Edwards-Wilkinson regime of the SHE and KPZ equation studied in [GRZ18,MU17,DGRZ20] to the full $L^2$-region, along with multidimensional convergence and general initial conditions for the KPZ equation (and SHE), which were not proven before. To do so, we rely on a martingale CLT combined with a refinement of the local limit theorem for polymers.", "field": "math", "label": 1}
{"text": "Title: Towards Higher Spectral Efficiency: Rate-2 Full-Diversity Complex Space-Time Block Codes\nAbstract: The upcoming 5G networks demand high-speed and high spectral-efficiency communications to keep up with the proliferating traffic demands. To this end, Massive multiple-input multiple-output (MIMO) techniques have gained significant traction owing to its ability to achieve these without increasing bandwidth or density of base stations. The preexisting space-time block code (STBC) designs cannot achieve a rate of more than 1 for more than two transmit antennas while preserving the orthogonality and full diversity conditions. In this paper, we present Jagannath codes - a novel complex modulation STBC, that achieves a very high rate of 2 for three and four transmit antennas. The presented designs achieve full diversity and overcome the previously achieved rates with the three and four antenna MIMO systems. We present a detailed account of the code construction of the proposed designs, orthogonality and full diversity analysis, transceiver model and conditional maximum likelihood (ML) decoding. In an effort to showcase the improvement achieved with the presented designs, we compare the rates and delays of some of the known STBCs with the proposed designs. The effective spectral efficiency and coding gain of the presented designs are compared to the Asymmetric Coordinate Interleaved design (ACIOD) and Jafarkhani code. We presented an effective spectral efficiency improvement by a factor of 2 with the proposed Jagannath codes. Owing to the full diversity of the presented designs, we demonstrate significant coding gains (6 dB and 12 dB) with the proposed designs.", "field": "cs", "label": 1}
{"text": "Title: Concurrent Brainstorming & Hypothesis Satisfying: An Iterative Framework for Enhanced Retrieval-Augmented Generation (R2CBR3H-SR)\nAbstract: Addressing the complexity of comprehensive information retrieval, this study introduces an innovative, iterative retrieval-augmented generation system. Our approach uniquely integrates a vector-space driven re-ranking mechanism with concurrent brainstorming to expedite the retrieval of highly relevant documents, thereby streamlining the generation of potential queries. This sets the stage for our novel hybrid process, which synergistically combines hypothesis formulation with satisfying decision-making strategy to determine content adequacy, leveraging a chain of thought-based prompting technique. This unified hypothesize-satisfied phase intelligently distills information to ascertain whether user queries have been satisfactorily addressed. Upon reaching this criterion, the system refines its output into a concise representation, maximizing conceptual density with minimal verbosity. The iterative nature of the workflow enhances process efficiency and accuracy. Crucially, the concurrency within the brainstorming phase significantly accelerates recursive operations, facilitating rapid convergence to solution satisfaction. Compared to conventional methods, our system demonstrates a marked improvement in computational time and cost-effectiveness. This research advances the state-of-the-art in intelligent retrieval systems, setting a new benchmark for resource-efficient information extraction and abstraction in knowledge-intensive applications.", "field": "cs", "label": 0}
{"text": "Title: Complementing Model Learning with Mutation-Based Fuzzing\nAbstract: An ongoing challenge for learning algorithms formulated in the Minimally Adequate Teacher framework is to efficiently obtain counterexamples. In this paper we compare and combine conformance testing and mutation-based fuzzing methods for obtaining counterexamples when learning finite state machine models for the reactive software systems of the Rigorous Exampination of Reactive Systems (RERS) challenge. We have found that for the LTL problems of the challenge the fuzzer provided an independent confirmation that the learning process had been successful, since no additional counterexamples were found. For the reachability problems of the challenge, however, the fuzzer discovered more reachable error states than the learner and tester, albeit in some cases the learner and tester found some that were not discovered by the fuzzer. This leads us to believe that these orthogonal approaches are complementary in the context of model learning.", "field": "cs", "label": 1}
{"text": "Title: A conjecture of Stanley on alternating permutations\nAbstract: We give two simple proofs of a conjecture of Richard Stanley concerning the equidistribution of derangements and alternating permutations with the maximal number of fixed points.", "field": "math", "label": 1}
{"text": "Title: Frequency Domain Nuances Mining for Visible-Infrared Person Re-identification\nAbstract: The key of visible-infrared person re-identification (VIReID) lies in how to minimize the modality discrepancy between visible and infrared images. Existing methods mainly exploit the spatial information while ignoring the discriminative frequency information. To address this issue, this paper aims to reduce the modality discrepancy from the frequency domain perspective. Specifically, we propose a novel Frequency Domain Nuances Mining (FDNM) method to explore the cross-modality frequency domain information, which mainly includes an amplitude guided phase (AGP) module and an amplitude nuances mining (ANM) module. These two modules are mutually beneficial to jointly explore frequency domain visible-infrared nuances, thereby effectively reducing the modality discrepancy in the frequency domain. Besides, we propose a center-guided nuances mining loss to encourage the ANM module to preserve discriminative identity information while discovering diverse cross-modality nuances. To the best of our knowledge, this is the first work that explores the potential frequency information for VIReID research. Extensive experiments show that the proposed FDNM has significant advantages in improving the performance of VIReID. Specifically, our method outperforms the second-best method by 5.2\\% in Rank-1 accuracy and 5.8\\% in mAP on the SYSU-MM01 dataset under the indoor search mode, respectively. Besides, we also validate the effectiveness and generalization of our method on the challenging visible-infrared face recognition task. \\textcolor{magenta}{The code will be available.}", "field": "cs", "label": 0}
{"text": "Title: Riemann surface of the Riemann zeta function\nAbstract: In this paper we treat the classical Riemann zeta function as a function of three variables: one is the usual complex $\\adyn$-dimensional, customly denoted as $s$, another two are complex infinite dimensional, we denote it as $\\b = \\{b_n\\}_{n=1}^{\\infty}$ and $\\z =\\{z_n\\}_{n=1}^{\\infty}$. When $\\b = \\{1\\}_{n=1}^{\\infty}$ and $\\z = \\{\\frac{1}{n}\\}_{n=1}^{\\infty}$ one gets the usual Riemann zeta function. Our goal in this paper is to study the meromorphic continuation of $\\zeta (\\b , \\z ,s)$ as a function of the triple $(\\a , \\z , s)$. Minor corrections, to appear in the Journal of Mathematical Analysis and Applications.", "field": "math", "label": 1}
{"text": "Title: Autonomous Reinforcement Learning via Subgoal Curricula\nAbstract: Reinforcement learning (RL) promises to enable autonomous acquisition of complex behaviors for diverse agents. However, the success of current reinforcement learning algorithms is predicated on an often under-emphasised requirement -- each trial needs to start from a fixed initial state distribution. Unfortunately, resetting the environment to its initial state after each trial requires substantial amount of human supervision and extensive instrumentation of the environment which defeats the goal of autonomous acquisition of complex behaviors. In this work, we propose Value-accelerated Persistent Reinforcement Learning (VaPRL), which generates a curriculum of initial states such that the agent can bootstrap on the success of easier tasks to efficiently learn harder tasks. The agent also learns to reach the initial states proposed by the curriculum, minimizing the reliance on human interventions into the learning. We observe that VaPRL reduces the interventions required by three orders of magnitude compared to episodic RL while outperforming prior state-of-the art methods for reset-free RL both in terms of sample efficiency and asymptotic performance on a variety of simulated robotics problems.", "field": "cs", "label": 1}
{"text": "Title: Not all Minorities are Equal: Empty-Class-Aware Distillation for Heterogeneous Federated Learning\nAbstract: Data heterogeneity, characterized by disparities in local data distribution across clients, poses a significant challenge in federated learning. Substantial efforts have been devoted to addressing the heterogeneity in local label distribution. As minority classes suffer from worse accuracy due to overfitting on local imbalanced data, prior methods often incorporate class-balanced learning techniques during local training. Despite the improved mean accuracy across all classes, we observe that empty classes-referring to categories absent from a client's data distribution-are still not well recognized. This paper introduces FedED, a novel approach in heterogeneous federated learning that integrates both empty-class distillation and logit suppression simultaneously. Specifically, empty-class distillation leverages knowledge distillation during local training on each client to retain essential information related to empty classes from the global model. Moreover, logit suppression directly penalizes network logits for non-label classes, effectively addressing misclassifications in minority classes that may be biased toward majority classes. Extensive experiments validate the efficacy of FedED, surpassing previous state-of-the-art methods across diverse datasets with varying degrees of label distribution shift.", "field": "cs", "label": 0}
{"text": "Title: Test ideals in mixed characteristic: a unified theory up to perturbation\nAbstract: Let $X$ be an integral scheme of finite type over a complete DVR of mixed characteristic. We provide a definition of a test ideal which agrees with the multiplier ideal after inverting $p$, can be computed from a sufficiently large alteration, agrees with previous mixed characteristic BCM test ideals after localizing and completing at any point of residue characteristic $p$ (up to small perturbation), and which satisfies the full suite of expected properties of a multiplier or test ideal. This object is obtained via the $p$-adic Riemann-Hilbert functor.", "field": "math", "label": 0}
{"text": "Title: Slot-guided Volumetric Object Radiance Fields\nAbstract: We present a novel framework for 3D object-centric representation learning. Our approach effectively decomposes complex scenes into individual objects from a single image in an unsupervised fashion. This method, called slot-guided Volumetric Object Radiance Fields (sVORF), composes volumetric object radiance fields with object slots as a guidance to implement unsupervised 3D scene decomposition. Specifically, sVORF obtains object slots from a single image via a transformer module, maps these slots to volumetric object radiance fields with a hypernetwork and composes object radiance fields with the guidance of object slots at a 3D location. Moreover, sVORF significantly reduces memory requirement due to small-sized pixel rendering during training. We demonstrate the effectiveness of our approach by showing top results in scene decomposition and generation tasks of complex synthetic datasets (e.g., Room-Diverse). Furthermore, we also confirm the potential of sVORF to segment objects in real-world scenes (e.g., the LLFF dataset). We hope our approach can provide preliminary understanding of the physical world and help ease future research in 3D object-centric representation learning.", "field": "cs", "label": 0}
{"text": "Title: Mining Fine-Grained Image-Text Alignment for Zero-Shot Captioning via Text-Only Training\nAbstract: Image captioning aims at generating descriptive and meaningful textual descriptions of images, enabling a broad range of vision-language applications. Prior works have demonstrated that harnessing the power of Contrastive Image Language Pre-training (CLIP) offers a promising approach to achieving zero-shot captioning, eliminating the need for expensive caption annotations. However, the widely observed modality gap in the latent space of CLIP harms the performance of zero-shot captioning by breaking the alignment between paired image-text features. To address this issue, we conduct an analysis on the CLIP latent space which leads to two findings. Firstly, we observe that the CLIP's visual feature of image subregions can achieve closer proximity to the paired caption due to the inherent information loss in text descriptions. In addition, we show that the modality gap between a paired image-text can be empirically modeled as a zero-mean Gaussian distribution. Motivated by the findings, we propose a novel zero-shot image captioning framework with text-only training to reduce the modality gap. In particular, we introduce a subregion feature aggregation to leverage local region information, which produces a compact visual representation for matching text representation. Moreover, we incorporate a noise injection and CLIP reranking strategy to boost captioning performance. We also extend our framework to build a zero-shot VQA pipeline, demonstrating its generality. Through extensive experiments on common captioning and VQA datasets such as MSCOCO, Flickr30k and VQAV2, we show that our method achieves remarkable performance improvements. Code is available at https://github.com/Artanic30/MacCap.", "field": "cs", "label": 0}
{"text": "Title: The six-vertex model on random planar maps revisited\nAbstract: We address the six vertex model on a random lattice, which in combinatorial terms corresponds to the enumeration of weighted 4-valent planar maps equipped with an Eulerian orientation. This problem was exactly, albeit non-rigorously solved by Ivan Kostov in 2000 using matrix integral techniques. We convert Kostov's work to a combinatorial argument involving functional equations coming from recursive decompositions of the maps, which we solve rigorously using complex analysis. We then investigate modular properties of the solution, which lead to simplifications in certain special cases. In particular, in two special cases of combinatorial interest we rederive the formulae discovered by Bousquet-M\\'elou and the first author.", "field": "math", "label": 1}
{"text": "Title: Learning Discretized Neural Networks under Ricci Flow\nAbstract: In this paper, we study Discretized Neural Networks (DNNs) composed of low-precision weights and activations, which suffer from either infinite or zero gradients due to the non-differentiable discrete function during training. Most training-based DNNs in such scenarios employ the standard Straight-Through Estimator (STE) to approximate the gradient w.r.t. discrete values. However, the use of STE introduces the problem of gradient mismatch, arising from perturbations in the approximated gradient. To address this problem, this paper reveals that this mismatch can be interpreted as a metric perturbation in a Riemannian manifold, viewed through the lens of duality theory. Building on information geometry, we construct the Linearly Nearly Euclidean (LNE) manifold for DNNs, providing a background for addressing perturbations. By introducing a partial differential equation on metrics, i.e., the Ricci flow, we establish the dynamical stability and convergence of the LNE metric with the $L^2$-norm perturbation. In contrast to previous perturbation theories with convergence rates in fractional powers, the metric perturbation under the Ricci flow exhibits exponential decay in the LNE manifold. Experimental results across various datasets demonstrate that our method achieves superior and more stable performance for DNNs compared to other representative training-based methods.", "field": "cs", "label": 0}
{"text": "Title: A note on concentration for polynomials in the Ising model\nAbstract: We present precise multilevel exponential concentration inequalities for polynomials in Ising models satisfying the Dobrushin condition. The estimates have the same form as two-sided tail estimates for polynomials in Gaussian variables due to Lata{\\l}a. In particular, for quadratic forms we obtain a Hanson-Wright type inequality. We also prove concentration results for convex functions and estimates for nonnegative definite quadratic forms, analogous as for quadratic forms in i.i.d. Rademacher variables, for more general random vectors satisfying the approximate tensorization property for entropy.", "field": "math", "label": 1}
{"text": "Title: Sieve in discrete groups, especially sparse\nAbstract: We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.", "field": "math", "label": 1}
{"text": "Title: Radio Map-Based Spectrum Sharing for Joint Communication and Sensing\nAbstract: The sixth-generation (6G) network is expected to provide both communication and sensing (C&S) services. However, spectrum scarcity poses a major challenge to the harmonious coexistence of C&S systems. Without effective cooperation, the interference resulting from spectrum sharing impairs the performance of both systems. This paper addresses C&S interference within a distributed network. Different from traditional schemes that require pilot-based high-frequency interactions between C&S systems, we introduce a third party named the radio map to provide the large-scale channel state information (CSI). With large-scale CSI, we optimize the transmit power of C&S systems to maximize the signal-to-interference-plus-noise ratio (SINR) for the radar detection, while meeting the ergodic rate requirement of the interfered user. Given the non-convexity of both the objective and constraint, we employ the techniques of auxiliary-function-based scaling and fraction programming for simplification. Subsequently, we propose an iterative algorithm to solve this problem. Simulation results collaborate our idea that the extrinsic information, i.e., positions and surroundings, is effective to decouple C&S interference.", "field": "cs", "label": 0}
{"text": "Title: Generative Optimization Networks for Memory Efficient Data Generation\nAbstract: In standard generative deep learning models, such as autoencoders or GANs, the size of the parameter set is proportional to the complexity of the generated data distribution. A significant challenge is to deploy resource-hungry deep learning models in devices with limited memory to prevent system upgrade costs. To combat this, we propose a novel framework called generative optimization networks (GON) that is similar to GANs, but does not use a generator, significantly reducing its memory footprint. GONs use a single discriminator network and run optimization in the input space to generate new data samples, achieving an effective compromise between training time and memory consumption. GONs are most suited for data generation problems in limited memory settings. Here we illustrate their use for the problem of anomaly detection in memory-constrained edge devices arising from attacks or intrusion events. Specifically, we use a GON to calculate a reconstruction-based anomaly score for input time-series windows. Experiments on a Raspberry-Pi testbed with two existing and a new suite of datasets show that our framework gives up to 32% higher detection F1 scores and 58% lower memory consumption, with only 5% higher training overheads compared to the state-of-the-art.", "field": "cs", "label": 1}
{"text": "Title: Clique number of Xor products of Kneser graphs\nAbstract: In this article we investigate a problem in graph theory, which has an equivalent reformulation in extremal set theory similar to the problems researched in \"A general 2-part Erd\\H{o}s-Ko-Rado theorem\" by Gyula O.H. Katona, who proposed our problem as well. In the graph theoretic form we examine the clique number of the Xor product of two isomorphic $KG(N,k)$ Kneser graphs. Denote this number with $f(k,N)$. We give lower and upper bounds on $f(k,N)$, and we solve the problem up to a constant deviation depending only on $k$, and find the exact value for $f(2,N)$ if $N$ is large enough. We also compute that $f(k,k^2)$ is asymptotically equivalent to $k^2$.", "field": "math", "label": 1}
{"text": "Title: Thread With Caution: Proactively Helping Users Assess and Deescalate Tension in Their Online Discussions\nAbstract: Incivility remains a major challenge for online discussion platforms, to such an extent that even conversations between well-intentioned users can often derail into uncivil behavior. Traditionally, platforms have relied on moderators to -- with or without algorithmic assistance -- take corrective actions such as removing comments or banning users. In this work we propose a complementary paradigm that directly empowers users by proactively enhancing their awareness about existing tension in the conversation they are engaging in and actively guides them as they are drafting their replies to avoid further escalation. As a proof of concept for this paradigm, we design an algorithmic tool that provides such proactive information directly to users, and conduct a user study in a popular discussion platform. Through a mixed methods approach combining surveys with a randomized controlled experiment, we uncover qualitative and quantitative insights regarding how the participants utilize and react to this information. Most participants report finding this proactive paradigm valuable, noting that it helps them to identify tension that they may have otherwise missed and prompts them to further reflect on their own replies and to revise them. These effects are corroborated by a comparison of how the participants draft their reply when our tool warns them that their conversation is at risk of derailing into uncivil behavior versus in a control condition where the tool is disabled. These preliminary findings highlight the potential of this user-centered paradigm and point to concrete directions for future implementations.", "field": "cs", "label": 1}
{"text": "Title: Limited Feedback on Measurements: Sharing a Codebook or a Generative Model?\nAbstract: Discrete Fourier transform (DFT) codebook-based solutions are well-established for limited feedback schemes in frequency division duplex (FDD) systems. In recent years, data-aided solutions have been shown to achieve higher performance, enabled by the adaptivity of the feedback scheme to the propagation environment of the base station (BS) cell. In particular, a versatile limited feedback scheme utilizing Gaussian mixture models (GMMs) was recently introduced. The scheme supports multi-user communications, exhibits low complexity, supports parallelization, and offers significant flexibility concerning various system parameters. Conceptually, a GMM captures environment knowledge and is subsequently transferred to the mobile terminals (MTs) for online inference of feedback information. Afterward, the BS designs precoders using either directional information or a generative modeling-based approach. A major shortcoming of recent works is that the assessed system performance is only evaluated through synthetic simulation data that is generally unable to fully characterize the features of real-world environments. It raises the question of how the GMM-based feedback scheme performs on real-world measurement data, especially compared to the well-established DFT-based solution. Our experiments reveal that the GMM-based feedback scheme tremendously improves the system performance measured in terms of sum-rate, allowing to deploy systems with fewer pilots or feedback bits.", "field": "cs", "label": 0}
{"text": "Title: On the embedding complexity of Liouville manifolds\nAbstract: We define a family of symplectic invariants which obstruct exact symplectic embeddings between Liouville manifolds, using the general formalism of linearized contact homology and its L-infinity structure. As our primary application, we investigate embeddings between normal crossing divisor complements in complex projective space, giving a complete characterization in many cases. Our main embedding results are deduced explicitly from pseudoholomorphic curves, without appealing to Hamiltonian or virtual perturbations.", "field": "math", "label": 1}
{"text": "Title: Foundations and Scoping of Data Science\nAbstract: There has been an increasing recognition of the value of data and of data-based decision making. As a consequence, the development of data science as a field of study has intensified in recent years. However, there is no systematic and comprehensive treatment and understanding of data science. This article describes a systematic and end-to-end framing of the field based on an inclusive definition. It identifies the core components making up the data science ecosystem, presents its lifecycle modeling the development process, and argues its interdisciplinarity.", "field": "cs", "label": 0}
{"text": "Title: A BDI Agent-Based Task Scheduling Framework for Cloud Computing\nAbstract: Cloud computing is an attractive technology for providing computing resources over the Internet. Task scheduling is a critical issue in cloud computing, where an efficient task scheduling method can improve overall cloud performance. Since cloud computing is a large-scale and geographically distributed environment, traditional scheduling methods that allocate resources in a centralized manner are ineffective. Besides, traditional methods are difficult to make rational decisions timely when the external environment changes. This paper proposes a decentralized BDI (belief-desire-intention) agent-based scheduling framework for cloud computing. BDI agents have advantages in modelling dynamic environments because BDI agents can update their beliefs, change desires, and trigger behaviours based on environmental changes. Besides, to avoid communication stuck caused by environmental uncertainties, the asynchronous communication mode with a notify listener is employed. The proposed framework covers both the task scheduling and rescheduling stages with the consideration of uncertain events that can interrupt task executions. Two agent-based algorithms are proposed to implement the task scheduling and rescheduling processes, and a novel recommendation mechanism is presented in the scheduling stage to reduce the impact of information synchronization delays. The proposed framework is implemented by JADEX and tested on CloudSim. The experimental results show that our framework can minimize the task makespan, balance the resource utilization in a large-scale environment, and maximize the task success rate when uncertain events occur.", "field": "cs", "label": 0}
{"text": "Title: Improving the Design of Linear Controllers for Homogeneous Platooning under Disturbances\nAbstract: This paper addresses the problem of longitudinal platooning control of homogeneous vehicles subject to external disturbances, such as wind gusts, road slopes, and parametric uncertainties. Our control objective is to maintain the relative distance of the cars regarding their nearby teammates in a decentralized manner. Therefore, we proposed a novel control law to compute the acceleration commands of each vehicle that includes the integral of the spacing error, which endows the controller with the capability to mitigate external disturbances in steady-state conditions. We adopt a constant distance spacing policy and employ generalized look-ahead and bidirectional network topologies. We provide formal conditions for the controller synthesis that ensure the internal stability of the platoon under the proposed control law in the presence of constant and bounded disturbances affecting multiple vehicles. Experiments considering nonlinear vehicle models in the high-fidelity CARLA simulator environment under different disturbances, parametric uncertainties, and several network topologies demonstrate the effectiveness of our approach.", "field": "cs", "label": 0}
{"text": "Title: Multi-Auxiliary Augmented Collaborative Variational Auto-encoder for Tag Recommendation\nAbstract: Recommending appropriate tags to items can facilitate content organization, retrieval, consumption and other applications, where hybrid tag recommender systems have been utilized to integrate collaborative information and content information for better recommendations. In this paper, we propose a multi-auxiliary augmented collaborative variational auto-encoder (MA-CVAE) for tag recommendation, which couples item collaborative information and item multi-auxiliary information, i.e., content and social graph, by defining a generative process. Specifically, the model learns deep latent embeddings from different item auxiliary information using variational auto-encoders (VAE), which could form a generative distribution over each auxiliary information by introducing a latent variable parameterized by deep neural network. Moreover, to recommend tags for new items, item multi-auxiliary latent embeddings are utilized as a surrogate through the item decoder for predicting recommendation probabilities of each tag, where reconstruction losses are added in the training phase to constrict the generation for feedback predictions via different auxiliary embeddings. In addition, an inductive variational graph auto-encoder is designed where new item nodes could be inferred in the test phase, such that item social embeddings could be exploited for new items. Extensive experiments on MovieLens and citeulike datasets demonstrate the effectiveness of our method.", "field": "cs", "label": 1}
{"text": "Title: Bordered and Framed Toeplitz and Hankel Determinants with Applications to Integrable Probability\nAbstract: Bordered and framed Toeplitz/Hankel determinants have the same structure as Toeplitz/Hankel determinants except in small number of matrix rows and/or columns. We review these structured determinants and their connections to orthogonal polynomials, collecting well-known and perhaps less well-known results. We present some applications for these structured determinants to ensembles of non-intersecting paths and the six-vertex model, with an eye towards asymptotic analysis. We also prove some asymptotic formulae for the probability of non-intersection for an ensemble of continuous time random walks for certain choices of starting and ending points as the number of random walkers tends to infinity.", "field": "math", "label": 0}
{"text": "Title: An insertion algorithm for catabolizability\nAbstract: Motivated by our recent work relating canonical bases to combinatorics of Garsia-Procesi modules \\cite{B}, we give an insertion algorithm that computes the catabolizability of the insertion tableau of a standard word. This allows us to characterize catabolizability as the statistic on words invariant under Knuth transformations, certain (co)rotations, and a new operation called a catabolism transformation. We also prove a Greene's Theorem-like characterization of catabolizability, and a result about how cocyclage changes catabolizability, strengthening a similar result in \\cite{SW}.", "field": "math", "label": 1}
{"text": "Title: Dissipative SymODEN: Encoding Hamiltonian Dynamics with Dissipation and Control into Deep Learning\nAbstract: In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size, Dissipative SymODEN encodes the port-Hamiltonian dynamics with energy dissipation and external input into the design of its computation graph and learns the dynamics in a structured way. The learned model, by revealing key aspects of the system, such as the inertia, dissipation, and potential energy, paves the way for energy-based controllers.", "field": "cs", "label": 1}
{"text": "Title: Balanced infinitesimal bialgebras, double Poisson gebras and pre-Calabi-Yau algebras\nAbstract: We consider the properad that governs the balanced infinitesimal bialgebras equipped with a coproduct of degree $1-d$. This properad naturally encodes a tiny part of the structure of the pre-Calabi-Yau algebras of dimension $d$. We compute its cobar construction and show that its gebras are \"in between\" the homotopy double Poisson gebras and the pre-Calabi-Yau algebras. Finally, we show that, if one is willing to consider their curved version, the two resulting notions of curved homotopy balanced infinitesimal bialgebra and curved homotopy double Poisson gebra are equivalent. A relation with the homotopy odd Lie bialgebras is also discussed.", "field": "math", "label": 0}
{"text": "Title: Free Brownian motion and free convolution semigroups: multiplicative case\nAbstract: We consider a pair of probability measures $\\mu,\\nu$ on the unit circle such that $\\Sigma_{\\lambda}(\\eta_{\\nu}(z))=z/\\eta_{\\mu}(z)$. We prove that the same type of equation holds for any $t\\geq 0$ when we replace $\\nu$ by $\\nu\\boxtimes\\lambda_t$ and $\\mu$ by $\\mathbb{M}_t(\\mu)$, where $\\lambda_t$ is the free multiplicative analogue of the normal distribution on the unit circle of $\\mathbb{C}$ and $\\mathbb{M}_t$ is the map defined by Arizmendi and Hasebe. These equations are a multiplicative analogue of equations studied by Belinschi and Nica. In order to achieve this result, we study infinite divisibility of the measures associated with subordination functions in multiplicative free Brownian motion and multiplicative free convolution semigroups. We use the modified $\\mathcal{S}$-transform introduced by Raj Rao and Speicher to deal with the case that $\\nu$ has mean zero. The same type of the result holds for convolutions on the positive real line. We also obtain some regularity properties for the free multiplicative analogue of the normal distributions.", "field": "math", "label": 1}
{"text": "Title: Lossy Compression of Individual Sequences Revisited: Fundamental Limits of Finite-State Encoders\nAbstract: We extend Ziv and Lempel's model of finite-state encoders to the realm of lossy compression of individual sequences. In particular, the model of the encoder includes a finite-state reconstruction codebook followed by an information lossless finite-state encoder that compresses the reconstruction codeword with no additional distortion. We first derive two different lower bounds to the compression ratio that depend on the number of states of the lossless encoder. Both bounds are asymptotically achievable by conceptually simple coding schemes. We then show that when the number of states of the lossless encoder is large enough in terms of the reconstruction block-length, the performance can be improved, sometimes significantly so. In particular, the improved performance is achievable using a random-coding ensemble that is universal, not only in terms of the source sequence, but also in terms of the distortion measure.", "field": "cs", "label": 0}
{"text": "Title: Error Inhibiting Block One-Step Schemes for Ordinary Differential Equations\nAbstract: The commonly used one step methods and linear multi-step methods all have a global error that is of the same order as the local truncation error (as defined in \\cite{gustafsson1995time,quarteroni2010numerical,AllenIsaacson,IsaacsonKeller,Sewell}). In fact, this is true of the entire class of general linear methods. In practice, this means that the order of the method is typically defined solely by the order conditions which are derived by studying the local truncation error. In this work, we investigate the interplay between the local truncation error and the global error, and develop a methodology which defines the construction of explicit {\\em error inhibiting} block one-step methods (alternatively written as explicit general linear methods \\cite{butcher1993a}). These {\\em error inhibiting schemes} are constructed so that the accumulation of the local truncation error over time is controlled, which results in a global error that is one order higher than the local truncation error. In this work, we delineate how to carefully choose the coefficient matrices so that the growth of the local truncation error is inhibited. We then use this theoretical understanding to construct several methods that have higher order global error than local truncation error, and demonstrate their enhanced order of accuracy on test cases. These methods demonstrate that the error inhibiting concept is realizable. Future work will further develop new error inhibiting methods and will analyze the computational efficiency and linear stability properties of these methods.", "field": "math", "label": 1}
{"text": "Title: Local wellposedness for the quasilinear Schrödinger equations via the generalized energy method\nAbstract: We study the global Cauchy problem of the quasilinear Schr\\\"odinger equations, for which KENIG et al. (Invent Math, 2004; Adv Math, 2006) obtained short time local wellposedness with large data by pseudo-differential techniques and viscosity methods, while MARZUOLA et al. (Adv Math, 2012; Kyoto J Math, 2014; Arch Ration Mech Anal, 2021) improved the results by dispersive arguments. In this paper, we introduce the generalized energy method that can close the bounds by combining momentum and energy estimates and derive the results by viscosity methods. The whole arguments basically only involve integration by parts and Sobolev embedding inequalities, just like the classical local existence theorem for semilinear Schr\\\"odinger equations. For quadratic interaction problem with small data, we derive low regularity local wellposedness in the same function spaces as in the works of Kenig et al. For cubic interaction problem, we obtain the same low regularity results as in Marzuola et al. (Kyoto J Math, 2014).", "field": "math", "label": 0}
{"text": "Title: Characteristic Mode Decomposition Using the Scattering Dyadic in Arbitrary Full-Wave Solvers\nAbstract: Characteristic modes are formulated using the scattering dyadic, which maps incident plane waves to scattered far fields generated by an object of arbitrary material composition. Numerical construction of the scattering dyadic using arbitrary full-wave electromagnetic solvers is demonstrated in examples involving a variety of dielectric and magnetic materials. Wrapper functions for computing characteristic modes in method-of-moments, finite-difference time domain, and finite element solvers are provided as supplementary material.", "field": "cs", "label": 1}
{"text": "Title: A note about the invariance of the basic reproduction number for stochastically perturbed SIS models\nAbstract: We try to justify rigorously, using a Wong-Zakai approximation argument, the susceptible-infected-susceptible (SIS) stochastic differential equation proposed in [2]. We discover that according to this approach the \"right\" stochastic model to be considered should be the Stratonovich version of the It\\^o equation analyzed in [2]. Surprisingly, this alternative model presents the following feature: the threshold value characterizing the two different asymptotic regimes of the solution coincides with the one describing the classical SIS deterministic equation.", "field": "math", "label": 1}
{"text": "Title: Multiclass Common Spatial Pattern for EEG based Brain Computer Interface with Adaptive Learning Classifier\nAbstract: In Brain Computer Interface (BCI), data generated from Electroencephalogram (EEG) is non-stationary with low signal to noise ratio and contaminated with artifacts. Common Spatial Pattern (CSP) algorithm has been proved to be effective in BCI for extracting features in motor imagery tasks, but it is prone to overfitting. Many algorithms have been devised to regularize CSP for two class problem, however they have not been effective when applied to multiclass CSP. Outliers present in data affect extracted CSP features and reduces performance of the system. In addition to this non-stationarity present in the features extracted from the CSP present a challenge in classification. We propose a method to identify and remove artifact present in the data during pre-processing stage, this helps in calculating eigenvectors which in turn generates better CSP features. To handle the non-stationarity, Self-Regulated Interval Type-2 Neuro-Fuzzy Inference System (SRIT2NFIS) was proposed in the literature for two class EEG classification problem. This paper extends the SRIT2NFIS to multiclass using Joint Approximate Diagonalization (JAD). The results on standard data set from BCI competition IV shows significant increase in the accuracies from the current state of the art methods for multiclass classification.", "field": "cs", "label": 1}
{"text": "Title: The Density Formula: One Lemma to Bound Them All\nAbstract: We introduce the Density Formula for (topological) drawings of graphs in the plane or on the sphere, which relates the number of edges, vertices, crossings, and sizes of cells in the drawing. We demonstrate its capability by providing several applications: we prove tight upper bounds on the edge density of various beyond-planar graph classes, including so-called $k$-planar graphs with $k=1,2$, fan-crossing / fan-planar graphs, $k$-bend RAC-graphs with $k=0,1,2$, and quasiplanar graphs. In some cases ($1$-bend and $2$-bend RAC-graphs and fan-crossing / fan-planar graphs), we thereby obtain the first tight upper bounds on the edge density of the respective graph classes. In other cases, we give new streamlined and significantly shorter proofs for bounds that were already known in the literature. Thanks to the Density Formula, all of our proofs are mostly elementary counting and mostly circumvent the typical intricate case analysis found in earlier proofs. Further, in some cases (simple and non-homotopic quasiplanar graphs), our alternative proofs using the Density Formula lead to the first tight lower bound examples.", "field": "math", "label": 0}
{"text": "Title: BPS algebras and generalised Kac-Moody algebras from 2-Calabi-Yau categories\nAbstract: We determine the structure of the BPS algebra of $2$-Calabi-Yau Abelian categories whose stack of objects admits a good moduli space. We prove that this algebra is isomorphic to the positive part of the enveloping algebra of a generalised Kac-Moody Lie algebra generated by the intersection cohomology of certain connected components (corresponding to roots) of the good moduli space. Some major examples include the BPS algebras of (1) the category of semistable coherent sheaves of given slope on a K3 surface or, more generally, quasiprojective symplectic surface, (2) semistable Higgs bundles on smooth projective curves, (3) preprojective algebras of quivers, (4) multiplicative preprojective algebras and (5) fundamental groups of (quiver) Riemann surfaces. We define the BPS Lie algebras of $2$-Calabi-Yau categories and prove that they coincide with the ones obtained by dimensional reduction from the critical cohomological Hall algebra in the case in which the 2-Calabi-Yau category is the category of representations of a preprojective algebra. Consequences include (1) A proof in full generality of the Bozec-Schiffmann positivity conjecture for absolutely cuspidal polynomials, a strengthening of the Kac positivity conjecture (2) A proof of the cohomological integrality conjecture for the category of semistable coherent sheaves on local K3 surfaces (3) A description of the cohomology (in all degrees) of Nakajima quiver varieties as direct sums of irreducible lowest weight representations over the BPS Lie algebra.", "field": "math", "label": 0}
{"text": "Title: Neural Additive Vector Autoregression Models for Causal Discovery in Time Series\nAbstract: Causal structure discovery in complex dynamical systems is an important challenge for many scientific domains. Although data from (interventional) experiments is usually limited, large amounts of observational time series data sets are usually available. Current methods that learn causal structure from time series often assume linear relationships. Hence, they may fail in realistic settings that contain nonlinear relations between the variables. We propose Neural Additive Vector Autoregression (NAVAR) models, a neural approach to causal structure learning that can discover nonlinear relationships. We train deep neural networks that extract the (additive) Granger causal influences from the time evolution in multi-variate time series. The method achieves state-of-the-art results on various benchmark data sets for causal discovery, while providing clear interpretations of the mapped causal relations.", "field": "cs", "label": 1}
{"text": "Title: Identifiability of Covariance Kernels in the Gaussian Process Regression Model\nAbstract: Gaussian process regression (GPR) model is a popular nonparametric regression model. In GPR, features of the regression function such as varying degrees of smoothness and periodicities are modeled through combining various covarinace kernels, which are supposed to model certain effects. The covariance kernels have unknown parameters which are estimated by the EM-algorithm or Markov Chain Monte Carlo. The estimated parameters are keys to the inference of the features of the regression functions, but identifiability of these parameters has not been investigated. In this paper, we prove identifiability of covariance kernel parameters in two radial basis mixed kernel GPR and radial basis and periodic mixed kernel GPR. We also provide some examples about non-identifiable cases in such mixed kernel GPRs.", "field": "math", "label": 1}
{"text": "Title: The Natural Selection of Conservative Science\nAbstract: Social epistemologists have argued that high risk, high reward science has an important role to play in scientific communities. Recently, though, it has also been argued that various scientific fields seem to be trending towards conservatism -- the increasing production of what Kuhn (1970) would have called `normal science'. This paper will explore a possible explanation for this sort of trend: that the process by which scientific research groups form, grow, and dissolve might be inherently hostile to high risk science. In particular, I employ a paradigm developed by Smaldino and McElreath (2016) that treats a scientific community as a population undergoing selection. As will become clear, perhaps counter-intuitively this sort of process in some ways promotes high risk, high reward science. But, as I will point out, high risk high reward science is, in general, the sort of thing that is hard to repeat. While more conservative scientists will be able to train students capable of continuing their successful projects, and so create thriving lineages, successful risky science may not be the sort of thing one can easily pass on. In such cases, the structure of scientific communities selects against high risk, high rewards projects. More generally, this paper makes clear that there are at least two processes to consider in thinking about how incentives shape scientific communities -- the process by which individual scientists make choices about their careers and research, and the selective process governing the formation of new research groups.", "field": "cs", "label": 1}
{"text": "Title: Set-valued propagation of chaos for controlled path-dependent McKean-Vlasov SPDEs\nAbstract: We develop a limit theory for controlled path-dependent mean field stochastic partial differential equations (SPDEs) within the semigroup approach of Da Prato and Zabczyk. More precisely, we prove existence results for mean field limits and particle approximations, and we establish set-valued propagation of chaos in the sense that we show convergence of sets of empirical distributions to sets of mean field limits in the Hausdorff metric topology. Furthermore, we discuss consequences of our results to stochastic optimal control. As another application, we deduce a propagation of chaos result for Peng's $G$-Brownian motion with drift interaction.", "field": "math", "label": 0}
{"text": "Title: Two Equivalent Families of Linear Fully Coupled Forward Backward Stochastic Differential Equations\nAbstract: In this paper, we investigate two families of fully coupled linear Forward-Backward Stochastic Differential Equations (FBSDE). Within these families, one could get the same well-posedness of FBSDEs with totally different structures. The first family of FBSDEs are proved to be equivalent with respect to the Unified Approach. Thus one could get the well-posedness of the whole family if one member exists a unique solution. Another equivalent family of FBSDEs are investigated by introducing a linear transformation method. By reason of the fully coupling structure between the forward and backward equations, it leads to a highly interdependence in solutions. We are able to lower the coupling of FBSDEs, by virtue of the idea of transformation, without losing the well-posedness. Moreover, owing to the non-degeneracy of the transformation matrix, the solution to original FBSDE is totally determined by solutions of FBSDE after transformation. In addition, an example of optimal Linear Quadratic (LQ) problem is presented to illustrate.", "field": "math", "label": 1}
{"text": "Title: Preference as Reward, Maximum Preference Optimization with Importance Sampling\nAbstract: Preference learning is a key technology for aligning language models with human values. Reinforcement Learning from Human Feedback (RLHF) is a model based algorithm to optimize preference learning, which first fitting a reward model for preference score, and then optimizing generating policy with on-policy PPO algorithm to maximize the reward. The processing of RLHF is complex, time-consuming and unstable. Direct Preference Optimization (DPO) algorithm using off-policy algorithm to direct optimize generating policy and eliminating the need for reward model, which is data efficient and stable. DPO use Bradley-Terry model and log-loss which leads to over-fitting to the preference data at the expense of ignoring KL-regularization term when preference near deterministic. IPO uses a root-finding pairwise MSE loss to solve the ignoring KL-regularization problem, and learning an optimal policy. But IPO's pairwise loss still can't s make the KL-regularization to work. In this paper, we design a simple and intuitive off-policy preferences optimization algorithm from an importance sampling view, and add an off-policy KL-regularization term which makes KL-regularization truly effective. To simplify the learning process and save memory usage, we can generate regularization data in advance, which eliminate the needs for both reward model and reference policy in the stage of optimization.", "field": "cs", "label": 0}
{"text": "Title: On Choosing Committees Based on Approval Votes in the Presence of Outliers\nAbstract: We study the computational complexity of committee selection problem for several approval-based voting rules in the presence of outliers. Our first result shows that outlier consideration makes committee selection problem intractable for approval, net approval, and minisum approval voting rules. We then study parameterized complexity of this problem with five natural parameters, namely the target score, the size of the committee (and its dual parameter, the number of candidates outside the committee), the number of outliers (and its dual parameter, the number of non-outliers). For net approval and minisum approval voting rules, we provide a dichotomous result, resolving the parameterized complexity of this problem for all subsets of five natural parameters considered (by showing either FPT or W[1]-hardness for all subsets of parameters). For the approval voting rule, we resolve the parameterized complexity of this problem for all subsets of parameters except one. We also study approximation algorithms for this problem. We show that there does not exist any alpha(.) factor approximation algorithm for approval and net approval voting rules, for any computable function alpha(.), unless P=NP. For the minisum voting rule, we provide a pseudopolynomial (1+eps) factor approximation algorithm.", "field": "cs", "label": 1}
{"text": "Title: Quantum ergodicity on the Bruhat-Tits building for $\\text{PGL}(3, F)$ in the Benjamini-Schramm limit\nAbstract: We study joint eigenfunctions of the spherical Hecke algebra acting on $L^2(\\Gamma_n \\backslash G / K)$ where $G = \\text{PGL}(3, F)$ with $F$ a non-archimedean local field of arbitrary characteristic, $K = \\text{PGL}(3, O)$ with $O$ the ring of integers of $F$, and $(\\Gamma_n)$ is a sequence of torsion-free lattices. We prove a form of equidistribution on average for eigenfunctions whose spectral parameters lie in the tempered spectrum when the associated sequence of quotients of the Bruhat-Tits building Benjamini-Schramm converges to the building itself. This result is a higher rank non-archimedean analogue of existing results for graphs and locally symmetric spaces. A recurring theme in the proof is the reduction of many computations to computing the sum of an exponential function over lattice points in a polytope; such expressions can subsequently be simplified using Brion's formula. Along the way of proving our main result we prove several other results which may be of independent interest including a \"degenerate\" version of Brion's formula which \"interpolates\" between the usual Brion's formula and the Ehrhart polynomial, an effective rate of convergence for the distribution of spectral parameters to the Plancherel measure under Benjamini-Schramm convergence, and a classification of relative positions of triples of points in buildings of type $\\tilde{A}_2$.", "field": "math", "label": 0}
{"text": "Title: On irrationality measure of Thue-Morse constant\nAbstract: We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant.", "field": "math", "label": 1}
{"text": "Title: Filtrations for $\\mathbb{wK4}$ and its relatives\nAbstract: We study the finite model property of subframe logics with expressible transitive reflexive closure modality. For $m>0$, let $\\mathrm{L}_m$ be the logic given by axiom $\\lozenge^{m+1} p\\to \\lozenge p\\vee p$. We construct filtrations for the logics $\\mathrm{L}_m$. It follows that these logics and their tense counterparts have the finite model property. Then we show that every canonical subframe logic that contains $\\mathrm{L}_m$ have the finite model property.", "field": "math", "label": 0}
{"text": "Title: Examining the Challenges in Archiving Instagram\nAbstract: To prevent the spread of disinformation on Instagram, we need to study the accounts and content of disinformation actors. However, due to their malicious nature, Instagram often bans accounts that are responsible for spreading disinformation, making these accounts inaccessible from the live web. The only way we can study the content of banned accounts is through public web archives such as the Internet Archive. However, there are many issues present with archiving Instagram pages. Specifically, we focused on the issue that many Wayback Machine Instagram mementos redirect to the Instagram login page. In this study, we determined that mementos of Instagram account pages on the Wayback Machine began redirecting to the Instagram login page in August 2019. We also found that Instagram mementos on Archive.today, Arquivo.pt, and Perma.cc are also not well archived in terms of quantity and quality. Moreover, we were unsuccessful in all our attempts to archive Katy Perry's Instagram account page on Archive.today, Arquivo.pt, and Conifer. Although in the minority, replayable Instagram mementos exist in public archives and contain valuable data for studying disinformation on Instagram. With that in mind, we developed a Python script to web scrape Instagram mementos. As of August 2023, the Python script can scrape Wayback Machine archives of Instagram account pages between November 7, 2012 and June 8, 2018.", "field": "cs", "label": 0}
{"text": "Title: Effective Aspects of Bernoulli Randomness\nAbstract: In this paper, we study Bernoulli random sequences, i.e., sequences that are Martin-L\\\"of random with respect to a Bernoulli measure $\\mu_p$ for some $p\\in[0,1]$, where we allow for the possibility that $p$ is noncomputable. We focus in particular on the case in which the underlying Bernoulli parameter $p$ is proper (that is, Martin-L\\\"of random with respect to some computable measure). We show for every Bernoulli parameter $p$, if there is a sequence that is both proper and Martin-L\\\"of random with respect to $\\mu_p$, then $p$ itself must be proper, and explore further consequences of this result. We also study the Turing degrees of Bernoulli random sequences, showing, for instance, that the Turing degrees containing a Bernoulli random sequence do not coincide with the Turing degrees containing a Martin-L\\\"of random sequence. Lastly, we consider several possible approaches to characterizing blind Bernoulli randomness, where the corresponding Martin-L\\\"of tests do not have access to the Bernoulli parameter $p$, and show that these fail to characterize blind Bernoulli randomness.", "field": "math", "label": 1}
{"text": "Title: Lifespan of Solution to MHD Boundary Layer Equations with Analytic Perturbation of General Shear Flow\nAbstract: In this paper, we consider the lifespan of solution to the MHD boundary layer system as an analytic perturbation of general shear flow. By using the cancellation mechanism in the system observed in \\cite{LXY1}, the lifespan of solution is shown to have a lower bound in the order of $\\varepsilon^{-2+}$ if the strength of the perturbation is of the order of $\\varepsilon$. Since there is no restriction on the strength of the shear flow and the lifespan estimate is larger than the one obtained for the classical Prandtl system in this setting, it reveals the stabilizing effect of the magnetic field on the electrically conducting fluid near the boundary.", "field": "math", "label": 1}
{"text": "Title: The combinatorics of Farey words and their traces\nAbstract: The set of Kleinian groups which are free on two parabolic generators is parameterised by the closed Riley slice of Schottky space. A Farey word is a word in such a group which represents a non-boundary-parallel geodesic that can be pinched down to a puncture; in the interior of the Riley slice such a word is loxodromic, and the pinching process corresponds to deforming the word to be parabolic. Keen and Series showed that the geometry of the Riley slice is detected by the real loci of the trace polynomials of these words. We study these trace polynomials from a combinatorial viewpoint, and give a recursion formula for them which enables efficient calculation of the polynomials without performing matrix multiplication; we also present some intriguing examples to show that there is much still to be learned about them.", "field": "math", "label": 1}
{"text": "Title: The Zilber-Pink Conjecture and the Generalized Cosmetic Surgery Conjecture\nAbstract: In this paper, we generalize the Cosmetic Surgery Conjecture to an $n$-cusped hyperbolic $3$-manifold and prove it under the assumption of another well-known conjecture in number theory, so called the Zilber-Pink Conjecture. For $n=1$ and $2$, we show them without the assumption.", "field": "math", "label": 1}
{"text": "Title: On the lack of external response of a nonlinear medium in the second-harmonic generation process\nAbstract: This paper concerns the scattering problem for a nonlinear medium of compact support, $D$, with second-harmonic generation. Such a medium, when probed with monochromatic light beams at frequency $\\omega$, generates additional waves at frequency $2\\omega$. The response of the medium is governed by a system of two coupled semilinear partial differential equations for the electric fields at frequency $\\omega$ and $2\\omega$. We investigate whether there are situations in which the generated $2\\omega$ wave is localized inside $D$, that is, the nonlinear interaction of the medium with the probing wave is invisible to an outside observer. This leads to the analysis of a semilinear elliptic system formulated in $D$ with non-standard boundary conditions. The analysis presented here sets up a mathematical framework needed to investigate a multitude of questions related to nonlinear scattering with second-harmonic generation.", "field": "math", "label": 0}
{"text": "Title: On the hierarchical Bayesian modelling of frequency response functions\nAbstract: For situations that may benefit from information sharing among datasets, e.g., population-based SHM of similar structures, the hierarchical Bayesian approach provides a useful modelling structure. Hierarchical Bayesian models learn statistical distributions at the population (or parent) and the domain levels simultaneously, to bolster statistical strength among the parameters. As a result, variance is reduced among the parameter estimates, particularly when data are limited. In this paper, a combined probabilistic FRF model is developed for a small population of nominally-identical helicopter blades, using a hierarchical Bayesian structure, to support information transfer in the context of sparse data. The modelling approach is also demonstrated in a traditional SHM context, for a single helicopter blade exposed to varying temperatures, to show how the inclusion of physics-based knowledge can improve generalisation beyond the training data, in the context of scarce data. These models address critical challenges in SHM, by accommodating benign variations that present as differences in the underlying dynamics, while also considering (and utilising), the similarities among the domains.", "field": "cs", "label": 0}
{"text": "Title: Extremal results for random discrete structures\nAbstract: We study thresholds for extremal properties of random discrete structures. We determine the threshold for Szemer\\'edi's theorem on arithmetic progressions in random subsets of the integers and its multidimensional extensions and we determine the threshold for Tur\\'an-type problems for random graphs and hypergraphs. In particular, we verify a conjecture of Kohayakawa, \\L uczak, and R\\\"odl for Tur\\'an-type problems in random graphs. Similar results were obtained by Conlon and Gowers.", "field": "math", "label": 1}
{"text": "Title: Mixing trichotomy for an Ehrenfest urn with impurities\nAbstract: We consider a version of the classical Ehrenfest urn model with two urns and two types of balls: regular and heavy. Each ball is selected independently according to a Poisson process having rate $1$ for regular balls and rate $\\alpha\\in(0,1)$ for heavy balls, and once a ball it is selected is placed in a urn uniformly at random. We study the asymptotic behavior when the total number of balls, $N$, goes to infinity, and the number of heavy ball is set to $\\lfloor N^\\beta\\rfloor$ for some $\\beta\\in[0,1]$. We focus on the observable given by the total number of balls in the left urn, which converges to a binomial distribution of parameter $1/2$, regardless of the choice of the two parameters, $\\alpha$ and $\\beta$. We study the speed of convergence and show that this can exhibit three different phenomenologies depending on the choice of the two parameters of the model.", "field": "math", "label": 0}
{"text": "Title: On the Ideal Number of Groups for Isometric Gradient Propagation\nAbstract: Recently, various normalization layers have been proposed to stabilize the training of deep neural networks. Among them, group normalization is a generalization of layer normalization and instance normalization by allowing a degree of freedom in the number of groups it uses. However, to determine the optimal number of groups, trial-and-error-based hyperparameter tuning is required, and such experiments are time-consuming. In this study, we discuss a reasonable method for setting the number of groups. First, we find that the number of groups influences the gradient behavior of the group normalization layer. Based on this observation, we derive the ideal number of groups, which calibrates the gradient scale to facilitate gradient descent optimization. Our proposed number of groups is theoretically grounded, architecture-aware, and can provide a proper value in a layer-wise manner for all layers. The proposed method exhibited improved performance over existing methods in numerous neural network architectures, tasks, and datasets.", "field": "cs", "label": 1}
{"text": "Title: Weyl modules for the hyperspecial current algebra\nAbstract: We develop the theory of global and local Weyl modules for the hyperspecial maximal parabolic subalgebra of type $A_{2n}^{(2)}$. We prove that the dimension of a local Weyl module depends only on its highest weight, thus establishing a freeness result for global Weyl modules. Furthermore, we show that the graded local Weyl modules are level one Demazure modules for the corresponding affine Lie algebra. In the last section we derive the same results for the special maximal parabolic subalgebras of the twisted affine Lie algebras not of type $A_{2n}^{(2)}$.", "field": "math", "label": 1}
{"text": "Title: On sets of graded attribute implications with witnessed non-redundancy\nAbstract: We study properties of particular non-redundant sets of if-then rules describing dependencies between graded attributes. We introduce notions of saturation and witnessed non-redundancy of sets of graded attribute implications are show that bases of graded attribute implications given by systems of pseudo-intents correspond to non-redundant sets of graded attribute implications with saturated consequents where the non-redundancy is witnessed by antecedents of the contained graded attribute implications. We introduce an algorithm which transforms any complete set of graded attribute implications parameterized by globalization into a base given by pseudo-intents. Experimental evaluation is provided to compare the method of obtaining bases for general parameterizations by hedges with earlier graph-based approaches.", "field": "cs", "label": 1}
{"text": "Title: The limiting shape of a full mailbox\nAbstract: We study a model for email communication due to Gabrielli and Caldarelli, where someone receives and answers emails at the times of independent Poisson processes with intensities $\\lambda_{\\rm in}>\\lambda_{\\rm out}$. The receiver assigns i.i.d. priorities to incoming emails according to some atomless law and always answers the email in the mailbox with the highest priority. Since the frequency of incoming emails is higher than the frequency of answering, below a critical priority, the mailbox fills up ad infinitum. We prove a theorem about the limiting shape of the mailbox just above the critical point, linking it to the convex hull of Brownian motion. We conjecture that this limiting shape is universal in a class of similar models, including a model for the evolution of an order book due to Stigler and Luckock.", "field": "math", "label": 1}
{"text": "Title: A reduced order variational multiscale approach for turbulent flows\nAbstract: The purpose of this work is to present a reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method. The Reduced Order Models (ROMs) presented in this manuscript are based on a POD-Galerkin approach with a VMS stabilization technique. Two different reduced order models are presented, which differ on the stabilization used during the Galerkin projection. In the first case the VMS stabilization method is used at both the full order and the reduced order level. In the second case, the VMS stabilization is used only at the full order level, while the projection of the standard Navier-Stokes equations is performed instead at the reduced order level. The former method is denoted as consistent ROM, while the latter is named non-consistent ROM, in order to underline the different choices made at the two levels. Particular attention is also devoted to the role of inf-sup stabilization by means of supremizers in ROMs based on a VMS formulation. Finally, the developed methods are tested on a numerical benchmark.", "field": "math", "label": 1}
{"text": "Title: How Do Pedestrians' Perception Change toward Autonomous Vehicles during Unmarked Midblock Multilane Crossings: Role of AV Operation and Signal Indication\nAbstract: One of the primary impediments hindering the widespread acceptance of autonomous vehicles (AVs) among pedestrians is their limited comprehension of AVs. This study employs virtual reality (VR) to provide pedestrians with an immersive environment for engaging with and comprehending AVs during unmarked midblock multilane crossings. Diverse AV driving behaviors were modeled to exhibit negotiation behavior with a yellow signal indication or non-yielding behavior with a blue signal indication. This paper aims to investigate the impact of various factors, such as AV behavior and signaling, pedestrian past behavior, etc., on pedestrians' perception change of AVs. Before and after the VR experiment, participants completed surveys assessing their perception of AVs, focusing on two main aspects: \"Attitude\" and \"System Effectiveness.\" The Wilcoxon signed-rank test results demonstrated that both pedestrians' overall attitude score toward AVs and trust in the effectiveness of AV systems significantly increased following the VR experiment. Notably, individuals who exhibited a greater trust in the yellow signals were more inclined to display a higher attitude score toward AVs and to augment their trust in the effectiveness of AV systems. This indicates that the design of the yellow signal instills pedestrians with greater confidence in their interactions with AVs. Further, pedestrians who exhibit more aggressive crossing behavior are less likely to change their perception towards AVs as compared to those pedestrians with more positive crossing behaviors. It is concluded that integrating this paper's devised AV behavior and signaling within an immersive VR setting facilitated pedestrian engagement with AVs, thereby changing their perception of AVs.", "field": "cs", "label": 0}
{"text": "Title: To Push or To Pull: On Reducing Communication and Synchronization in Graph Computations\nAbstract: We reduce the cost of communication and synchronization in graph processing by analyzing the fastest way to process graphs: pushing the updates to a shared state or pulling the updates to a private state.We investigate the applicability of this push-pull dichotomy to various algorithms and its impact on complexity, performance, and the amount of used locks, atomics, and reads/writes. We consider 11 graph algorithms, 3 programming models, 2 graph abstractions, and various families of graphs. The conducted analysis illustrates surprising differences between push and pull variants of different algorithms in performance, speed of convergence, and code complexity; the insights are backed up by performance data from hardware counters.We use these findings to illustrate which variant is faster for each algorithm and to develop generic strategies that enable even higher speedups. Our insights can be used to accelerate graph processing engines or libraries on both massively-parallel shared-memory machines as well as distributed-memory systems.", "field": "cs", "label": 1}
{"text": "Title: The correspondence between silting objects and $t$-structures for non-positive dg algebras\nAbstract: We establish a bijective correspondence between isomorphism classes of basic silting objects of $\\mathsf{per}(A)$ and algebraic $t$-structures of $\\mathsf{D}_{\\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more generally, we work in the setting of ST-pair inside an algebraic triangulated category). For a non-positive (topologically) homologically smooth dg $k$-algebra $A$ whose zeroth cohomology is finite-dimensional, or for a non-positive proper dg $k$-algebra $A$, the one-to-one correspondence between isomorphism classes of basic silting objects of $\\mathsf{per}(A)$ and algebraic $t$-structures on $\\mathsf{D}_{\\rm fd}(A)$ was already known. The main result of this paper generalizes the above two results to locally finite non-positive dg $k$-algebras.", "field": "math", "label": 0}
{"text": "Title: Improving Sequential Query Recommendation with Immediate User Feedback\nAbstract: We propose an algorithm for next query recommendation in interactive data exploration settings, like knowledge discovery for information gathering. The state-of-the-art query recommendation algorithms are based on sequence-to-sequence learning approaches that exploit historical interaction data. Due to the supervision involved in the learning process, such approaches fail to adapt to immediate user feedback. We propose to augment the transformer-based causal language models for query recommendations to adapt to the immediate user feedback using multi-armed bandit (MAB) framework. We conduct a large-scale experimental study using log files from a popular online literature discovery service and demonstrate that our algorithm improves the per-round regret substantially, with respect to the state-of-the-art transformer-based query recommendation models, which do not make use of immediate user feedback. Our data model and source code are available at https://github.com/shampp/exp3_ss", "field": "cs", "label": 1}
{"text": "Title: Same Influenza, Different Responses: Social Media Can Sense a Regional Spectrum of Symptoms\nAbstract: Influenza is an acute respiratory infection caused by a virus. It is highly contagious and rapidly mutative. However, its epidemiological characteristics are conventionally collected in terms of outpatient records. In fact, the subjective bias of the doctor emphasizes exterior signs, and the necessity of face-to-face inquiry results in an inaccurate and time-consuming manner of data collection and aggregation. Accordingly, the inferred spectrum of syndromes can be incomplete and lagged. With a massive number of users being sensors, online social media can indeed provide an alternative approach. Voluntary reports in Twitter and its variants can deliver not only exterior signs but also interior feelings such as emotions. These sophisticated signals can further be efficiently collected and aggregated in a real-time manner, and a comprehensive spectrum of syndromes could thus be inferred. Taking Weibo as an example, it is confirmed that a regional spectrum of symptoms can be credibly sensed. Aside from the differences in symptoms and treatment incentives between northern and southern China, it is also surprising that patients in the south are more optimistic, while those in the north demonstrate more intense emotions. The differences sensed from Weibo can even help improve the performance of regressions in monitoring influenza. Our results suggest that self-reports from social media can be profound supplements to the existing clinic-based systems for influenza surveillance.", "field": "cs", "label": 1}
{"text": "Title: Product Formula of Artin Symbols in Non-abelian Extensions\nAbstract: The product formula of Artin symbols (norm residue symbols) is an important equality that connects local and global class field theory. Usually, the product formula of Artin symbols is considered in abelian extensions of global fields. In this paper, however, the product is considered in non-abelian extensions such that each symbol is well-defined. As an application, some properties on fundamental units of real quadratic fields are obtained and will be presented here.", "field": "math", "label": 0}
{"text": "Title: Unified Diffusion-Based Rigid and Non-Rigid Editing with Text and Image Guidance\nAbstract: Existing text-to-image editing methods tend to excel either in rigid or non-rigid editing but encounter challenges when combining both, resulting in misaligned outputs with the provided text prompts. In addition, integrating reference images for control remains challenging. To address these issues, we present a versatile image editing framework capable of executing both rigid and non-rigid edits, guided by either textual prompts or reference images. We leverage a dual-path injection scheme to handle diverse editing scenarios and introduce an integrated self-attention mechanism for fusion of appearance and structural information. To mitigate potential visual artifacts, we further employ latent fusion techniques to adjust intermediate latents. Compared to previous work, our approach represents a significant advance in achieving precise and versatile image editing. Comprehensive experiments validate the efficacy of our method, showcasing competitive or superior results in text-based editing and appearance transfer tasks, encompassing both rigid and non-rigid settings.", "field": "cs", "label": 0}
{"text": "Title: Cohomology for quantum groups via the geometry of the nullcone\nAbstract: Let $\\zeta$ be a complex $\\ell$th root of unity for an odd integer $\\ell>1$. For any complex simple Lie algebra $\\mathfrak g$, let $u_\\zeta=u_\\zeta({\\mathfrak g})$ be the associated \"small\" quantum enveloping algebra. In general, little is known about the representation theory of quantum groups (resp., algebraic groups) when $l$ (resp., $p$) is smaller than the Coxeter number $h$ of the underlying root system. For example, Lusztig's conjecture concerning the characters of the rational irreducible $G$-modules stipulates that $p \\geq h$. The main result in this paper provides a surprisingly uniform answer for the cohomology algebra $\\opH^\\bullet(u_\\zeta,{\\mathbb C})$ of the small quantum group. When $\\ell>h$, this cohomology algebra has been calculated by Ginzburg and Kumar \\cite{GK}. Our result requires powerful tools from complex geometry and a detailed knowledge of the geometry of the nullcone of $\\mathfrak g$. In this way, the methods point out difficulties present in obtaining similar results for the restricted enveloping algebra $u$ in small characteristics, though they do provide some clarification of known results there also. Finally, we establish that if $M$ is a finite dimensional $u_\\zeta$-module, then $\\opH^\\bullet(u_\\zeta,M)$ is a finitely generated $\\opH^\\bullet(u_\\zeta,\\mathbb C)$-module, and we obtain new results on the theory of support varieties for $u_\\zeta$.", "field": "math", "label": 1}
{"text": "Title: Bounds for the Quartic Weyl Sum\nAbstract: We improve the standard Weyl estimate for quartic exponential sums in which the argument is a quadratic irrational. Specifically we show that \\[\\sum_{n\\le N} e(\\alpha n^4)\\ll_{\\ep,\\alpha}N^{5/6+\\ep}\\] for any $\\ep>0$ and any quadratic irrational $\\alpha\\in\\R-\\Q$. Classically one would have had the exponent $7/8+\\ep$ for such $\\alpha$. In contrast to the author's earlier work \\cite{cubweyl} on cubic Weyl sums (which was conditional on the $abc$-conjecture), we show that the van der Corput $AB$-steps are sufficient for the quartic case, rather than the $BAAB$-process needed for the cubic sum.", "field": "math", "label": 0}
{"text": "Title: R(3,10) <= 41\nAbstract: We improve the upper bound on the Ramsey number R(3,10) from 42 to 41. Hence R(3,10) is equal to 40 or 41.", "field": "math", "label": 0}
{"text": "Title: Transparent Contribution Evaluation for Secure Federated Learning on Blockchain\nAbstract: Federated Learning is a promising machine learning paradigm when multiple parties collaborate to build a high-quality machine learning model. Nonetheless, these parties are only willing to participate when given enough incentives, such as a fair reward based on their contributions. Many studies explored Shapley value based methods to evaluate each party's contribution to the learned model. However, they commonly assume a semi-trusted server to train the model and evaluate the data owners' model contributions, which lacks transparency and may hinder the success of federated learning in practice. In this work, we propose a blockchain-based federated learning framework and a protocol to transparently evaluate each participant's contribution. Our framework protects all parties' privacy in the model building phase and transparently evaluates contributions based on the model updates. The experiment with the handwritten digits dataset demonstrates that the proposed method can effectively evaluate the contributions.", "field": "cs", "label": 1}
{"text": "Title: Multiple Access Techniques for Intelligent and Multi-Functional 6G: Tutorial, Survey, and Outlook\nAbstract: Multiple access (MA) is a crucial part of any wireless system and refers to techniques that make use of the resource dimensions to serve multiple users/devices/machines/services, ideally in the most efficient way. Given the needs of multi-functional wireless networks for integrated communications, sensing, localization, computing, coupled with the surge of machine learning / artificial intelligence (AI) in wireless networks, MA techniques are expected to experience a paradigm shift in 6G and beyond. In this paper, we provide a tutorial, survey and outlook of past, emerging and future MA techniques and pay a particular attention to how wireless network intelligence and multi-functionality will lead to a re-thinking of those techniques. The paper starts with an overview of orthogonal, physical layer multicasting, space domain, power domain, ratesplitting, code domain MAs, and other domains, and highlight the importance of researching universal multiple access to shrink instead of grow the knowledge tree of MA schemes by providing a unified understanding of MA schemes across all resource dimensions. It then jumps into rethinking MA schemes in the era of wireless network intelligence, covering AI for MA such as AI-empowered resource allocation, optimization, channel estimation, receiver designs, user behavior predictions, and MA for AI such as federated learning/edge intelligence and over the air computation. We then discuss MA for network multi-functionality and the interplay between MA and integrated sensing, localization, and communications. We finish with studying MA for emerging intelligent applications before presenting a roadmap toward 6G standardization. We also point out numerous directions that are promising for future research.", "field": "cs", "label": 0}
{"text": "Title: Secure Multiparty Computation with Partial Fairness\nAbstract: A protocol for computing a functionality is secure if an adversary in this protocol cannot cause more harm than in an ideal computation where parties give their inputs to a trusted party which returns the output of the functionality to all parties. In particular, in the ideal model such computation is fair -- all parties get the output. Cleve (STOC 1986) proved that, in general, fairness is not possible without an honest majority. To overcome this impossibility, Gordon and Katz (Eurocrypt 2010) suggested a relaxed definition -- 1/p-secure computation -- which guarantees partial fairness. For two parties, they construct 1/p-secure protocols for functionalities for which the size of either their domain or their range is polynomial (in the security parameter). Gordon and Katz ask whether their results can be extended to multiparty protocols. We study 1/p-secure protocols in the multiparty setting for general functionalities. Our main result is constructions of 1/p-secure protocols when the number of parties is constant provided that less than 2/3 of the parties are corrupt. Our protocols require that either (1) the functionality is deterministic and the size of the domain is polynomial (in the security parameter), or (2) the functionality can be randomized and the size of the range is polynomial. If the size of the domain is constant and the functionality is deterministic, then our protocol is efficient even when the number of parties is O(log log n) (where n is the security parameter). On the negative side, we show that when the number of parties is super-constant, 1/p-secure protocols are not possible when the size of the domain is polynomial.", "field": "cs", "label": 1}
{"text": "Title: Neighbourhood Evaluation Criteria for Vertex Cover Problem\nAbstract: Neighbourhood Evaluation Criteria is a heuristical approximate algorithm that attempts to solve the Minimum Vertex Cover. degree count is kept in check for each vertex and the highest count based vertex is included in our cover set. In the case of multiple equivalent vertices, the one with the lowest neighbourhood influence is selected. In the case of still existing multiple equivalent vertices, the one with the lowest remaining active vertex count (the highest Independent Set enabling count) is selected as a tie-breaker.", "field": "cs", "label": 1}
{"text": "Title: On the boundary of the central quadratic hyperbolic component\nAbstract: We give a concrete description for the boundary of the central quadratic hyperbolic component. The connectedness of the Julia sets of the boundary maps are also considered.", "field": "math", "label": 0}
{"text": "Title: The dynamics of the heterochaos baker maps\nAbstract: The heterochaos baker maps are piecewise affine maps of the unit square or cube introduced by Saiki et al. (2018), to provide a hands-on, elementary understanding of complicated phenomena in systems of large degrees of freedom. We review recent progress on a dynamical systems theory of the heterochaos baker maps, and present new results on properties of measures of maximal entropy and the underlying Lebesgue measure. We address several conjectures and questions that may illuminate new aspects of heterochaos and inspire future research.", "field": "math", "label": 0}
{"text": "Title: A Decision Method for Elementary Stream Calculus\nAbstract: The main result is a doubly exponential decision procedure for the first-order equality theory of streams with both arithmetic and control-oriented stream operations. This stream logic is expressive for elementary problems of stream calculus.", "field": "cs", "label": 0}
{"text": "Title: Non-associative Frobenius algebras of type $E_7$\nAbstract: Recently, Maurice Chayet and Skip Garibaldi introduced a class of commutative non-associative algebras. In previous work, we gave an explicit description of these algebras for groups of type $G_2,F_4$ and certain forms of $E_6$ in terms of octonion and Albert algebras. In this paper, we extend this further by dealing with $E_7$ in terms of generalised Freudenthal triple systems.", "field": "math", "label": 0}
{"text": "Title: Scale invariant elliptic operators with singular coefficients\nAbstract: We show that a realization of the operator $L=|x|^\\alpha\\Delta +c|x|^{\\alpha-1}\\frac{x}{|x|}\\cdot\\nabla -b|x|^{\\alpha-2}$ generates a semigroup in $L^p(\\mathbb {R}^N)$ if and only if $D_c=b+(N-2+c)^2/4 > 0$ and $s_1+\\min\\{0,2-\\alpha\\}<N/p<s_2+\\max\\{0,2-\\alpha\\}$, where $s_i$ are the roots of the equation $b+s(N-2+c-s)=0$, or $D_c=0$ and $s_0+\\min\\{0,2-\\alpha\\} \\le N/p \\le s_0+\\max\\{0,2-\\alpha\\}$, where $s_0$ is the unique root of the above equation. The domain of the generator is also characterized.", "field": "math", "label": 1}
{"text": "Title: On Cayley graphs of algebraic structures\nAbstract: We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.", "field": "cs", "label": 1}
{"text": "Title: Deployment and configuration of MEC apps with Simu5G\nAbstract: Multi-access Edge Computing (MEC) is expected to act as the enabler for the integration of 5G (and future 6G) communication technologies with cloud-computing-based capabilities at the edge of the network. This will enable low-latency and context-aware applications for users of such mobile networks. In this paper we describe the implementation of a MEC model for the Simu5G simulator and illustrate how to configure the environment to evaluate MEC applications in both simulation and real-time emulation modes.", "field": "cs", "label": 1}
{"text": "Title: Hamilton--Jacobi equations for Wasserstein controlled gradient flows: existence of viscosity solutions\nAbstract: This work is the third part of a program initiated in arXiv:2111.13258, arXiv:2302.06571 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations related to controlled gradient flow problems in metric spaces. In this paper, we finish our analysis in the context of Wasserstein gradient flows with underlying energy functional satisfying McCann's condition. More prescisely, we establish that the value function for a linearly controlled gradient flow problem whose running cost is quadratic in the control variable and just continuous in the state variable yields a viscosity solution to the Hamilton-Jacobi equation in terms of two operators introduced in our former works, acting as rigorous upper and lower bounds for the formal Hamiltonian at hand. The definition of these operators is directly inspired by the Evolutional Variational Inequality formulation of gradient flows (EVI): one of the main innovations of this work is to introduce a controlled version of EVI, which turns out to be crucial in establishing regularity properties, energy and metric bounds along optimzing sequences in the controlled gradient flow problem that defines the candidate solution.", "field": "math", "label": 0}
{"text": "Title: Propagation of chaos and Poisson Hypothesis for replica mean-field models of intensity-based neural networks\nAbstract: Neural computations arising from myriads of interactions between spiking neurons can be modeled as network dynamics with punctuate interactions. However, most relevant dynamics do not allow for computational tractability. To circumvent this difficulty, the Poisson Hypothesis regime replaces interaction times between neurons by Poisson processes. We prove that the Poisson Hypothesis holds at the limit of an infinite number of replicas in the replica-mean-field model, which consists of randomly interacting copies of the network of interest. The proof is obtained through a novel application of the Chen-Stein method to the case of a random sum of Bernoulli random variables and a fixed point approach to prove a law of large numbers for exchangeable random variables.", "field": "math", "label": 1}
{"text": "Title: Simplified Information Geometry Approach for Massive MIMO-OFDM Channel Estimation -- Part I: Algorithm and Fixed Point Analysis\nAbstract: In this two-part paper, we investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. In Part I, we revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By using the constant magnitude property of the entries of the measurement matrix in the massive MIMO-OFDM channel estimation and the asymptotic analysis, we find that the second-order natural parameters of the distributions on all the auxiliary manifolds are equivalent to each other at each iteration of IGA, and the first-order natural parameters of the distributions on all the auxiliary manifolds are asymptotically equivalent to each other at the fixed point of IGA. Motivated by these results, we simplify the iterative process of IGA and propose a simplified IGA for massive MIMO-OFDM channel estimation. It is proved that at the fixed point, the a posteriori mean obtained by the simplified IGA is asymptotically optimal. The simplified IGA allows efficient implementation with fast Fourier transformation (FFT). Simulations confirm that the simplified IGA can achieve near the optimal performance with low complexity in a limited number of iterations.", "field": "cs", "label": 0}
{"text": "Title: Integral Representations of Three Novel Multiple Zeta Functions for Barnes Type: A Probabilistic Approach\nAbstract: Integral representation is one of the powerful tools for studying analytic continuation of the zeta functions. It is known that Hurwitz zeta function generalizes the famous Riemann zeta function which plays an important role in analytic number theory. They both have several multiple versions in the literature. In this paper, we introduce three novel multiple zeta functions for Barnes type and study their integral representations through hyperbolic probability distributions given by Pitman and Yor (2003, Canad. J. Math., 55, 292-330). The analytically continued properties of the three multiple zeta functions are also investigated. Surprisingly, two of them, unlike the previous results, can extend analytically to entire functions in the whole complex plane.", "field": "math", "label": 0}
{"text": "Title: Effects of forward scattering on the onset of phototactic bioconvection in an algal suspension under diffuse flux without collimated flux\nAbstract: Phototaxis refers to the directed swimming response influenced by the sensed light intensity in microorganisms. Positive phototaxis involves motion toward the light source, while negative phototaxis entails motion away from it. This study explores the phototactic bioconvection in a suspension of anisotropic scattering phototactic algae, illuminated by diffuse flux without direct collimated flux. The basic state is characterized by zero fluid flow, with the balance between upward and downward swimming due to positive and negative phototaxis, respectively, counteracted by microorganism diffusion. The paper conducts a thorough numerical analysis of linear stability, placing particular emphasis on the impact of forward scattering. The onset of bioconvection manifests either through a stationary mode or an oscillatory mode. The transition between these modes is observed with varying anisotropic coefficients for specific parameter values.", "field": "math", "label": 0}
{"text": "Title: Behavior of Totally Positive Differential Systems Near a Periodic Solution\nAbstract: A time-varying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tri-diagonal with positive entries on the super- and sub-diagonals. If the vector field of a TPDS is T-periodic then every bounded trajectory converges to a T-periodic solution. In particular, when the vector field is time-invariant every bounded trajectory of a TPDS converges to an equlbrium. Here, we use the spectral theory of oscillatory matrices to analyze the behavior near a periodic solution of a TPDS. This yields information on the perturbation directions that lead to the fastest and slowest convergence to or divergence from the periodic solution. We demonstrate the theoretical results using a model from systems biology called the ribosome flow model.", "field": "math", "label": 1}
{"text": "Title: Hille's theorem for Bochner integrals of functions with values in locally convex spaces\nAbstract: Hille's theorem is a powerful classical result in vector measure theory. It asserts that the application of a closed, unbounded linear operator commutes with strong/Bochner integration of functions taking values in a Banach space. This note shows that Hille's theorem also holds in the setting of complete locally convex spaces.", "field": "math", "label": 0}
{"text": "Title: Spikformer V2: Join the High Accuracy Club on ImageNet with an SNN Ticket\nAbstract: Spiking Neural Networks (SNNs), known for their biologically plausible architecture, face the challenge of limited performance. The self-attention mechanism, which is the cornerstone of the high-performance Transformer and also a biologically inspired structure, is absent in existing SNNs. To this end, we explore the potential of leveraging both self-attention capability and biological properties of SNNs, and propose a novel Spiking Self-Attention (SSA) and Spiking Transformer (Spikformer). The SSA mechanism eliminates the need for softmax and captures the sparse visual feature employing spike-based Query, Key, and Value. This sparse computation without multiplication makes SSA efficient and energy-saving. Further, we develop a Spiking Convolutional Stem (SCS) with supplementary convolutional layers to enhance the architecture of Spikformer. The Spikformer enhanced with the SCS is referred to as Spikformer V2. To train larger and deeper Spikformer V2, we introduce a pioneering exploration of Self-Supervised Learning (SSL) within the SNN. Specifically, we pre-train Spikformer V2 with masking and reconstruction style inspired by the mainstream self-supervised Transformer, and then finetune the Spikformer V2 on the image classification on ImageNet. Extensive experiments show that Spikformer V2 outperforms other previous surrogate training and ANN2SNN methods. An 8-layer Spikformer V2 achieves an accuracy of 80.38% using 4 time steps, and after SSL, a 172M 16-layer Spikformer V2 reaches an accuracy of 81.10% with just 1 time step. To the best of our knowledge, this is the first time that the SNN achieves 80+% accuracy on ImageNet. The code will be available at Spikformer V2.", "field": "cs", "label": 0}
{"text": "Title: The model theory of the curve graph\nAbstract: In this paper we develop a bridge between model theory, geometric topology, and geometric group theory. In particular, we investigate the Ivanov Metaconjecture from the point of view of model theory, and more broadly we seek to answer the general question: why does the curve graph of a surface play such a central role in the study of surfaces and mapping class groups? More specifically, we consider a surface $\\Sigma$ of finite type and its curve graph $\\mathcal C(\\Sigma)$, and we investigate its first-order theory in the language of graph theory. Crucially, $\\mathcal C(\\Sigma)$ is bi-interpretable with a certain object called the augmented Cayley graph of the mapping class group of the surface. We use this bi-interpretation to prove that the theory of the curve graph is $\\omega$--stable, to compute its Morley rank, and to show that it has quantifier elimination with respect to the class of $\\forall\\exists$--formulae. We also show that many of the complexes which are naturally associated to a surface are interpretable in $\\mathcal C(\\Sigma)$. This shows that these complexes are all $\\omega$--stable and admit certain a priori bounds on their Morley ranks. We are able to use Morley ranks to prove that various complexes are not bi--interpretable with the curve graph. As a consequence of quantifier elimination, we show that algebraic intersection number is not definable in the first order theory of the curve graph. Finally, we prove that the curve graph of a surface enjoys a novel phenomenon that we call interpretation rigidity. That is, if surfaces $\\Sigma_1$ and $\\Sigma_2$ admits curve graphs that are mutually interpretable, then $\\Sigma_1$ and $\\Sigma_2$ are homeomorphic to each other. Along the way, numerous technical results are obtained.", "field": "math", "label": 1}
{"text": "Title: Pointwise A posteriori error control of quadratic Discontinuous Galerkin Methods for the unilateral contact problem\nAbstract: An a posteriori error bound for the pointwise error of the quadratic discontinuous Galerkin method for the unilateral contact problem on polygonal domain is presented. The pointwise a posteriori error analysis is based on the direct use of a priori estimates of the Green's matrix for the divergence type operators and the suitable construction of the discrete contact force density $\\b{\\sigma}_h$ and barrier functions for the continuous solution. Several numerical experiments (in two dimension) are presented to illustrate the reliability and efficiency properties of the proposed aposteriori error estimator.", "field": "math", "label": 0}
{"text": "Title: Simpler Context-Dependent Logical Forms via Model Projections\nAbstract: We consider the task of learning a context-dependent mapping from utterances to denotations. With only denotations at training time, we must search over a combinatorially large space of logical forms, which is even larger with context-dependent utterances. To cope with this challenge, we perform successive projections of the full model onto simpler models that operate over equivalence classes of logical forms. Though less expressive, we find that these simpler models are much faster and can be surprisingly effective. Moreover, they can be used to bootstrap the full model. Finally, we collected three new context-dependent semantic parsing datasets, and develop a new left-to-right parser.", "field": "cs", "label": 1}
{"text": "Title: Optimizing Information Freshness in Uplink Multiuser MIMO Networks with Partial Observations\nAbstract: This paper investigates a multiuser scheduling problem within an uplink multiple-input multi-output (MIMO) status update network, consisting of a multi-antenna base station (BS) and multiple single-antenna devices. The presence of multiple antennas at the BS introduces spatial degrees-of-freedom, enabling concurrent transmission of status updates from multiple devices in each time slot. Our objective is to optimize network-wide information freshness, quantified by the age of information (AoI) metric, by determining how the BS can best schedule device transmissions, while taking into account the random arrival of status updates at the device side.To address this decision-making problem, we model it as a partially observable Markov decision process (POMDP) and establish that the evolution of belief states for different devices is independent.We also prove that feasible belief states can be described by finite-dimensional vectors. Building on these observations, we develop a dynamic scheduling (DS) policy to solve the POMDP, and then derive an upper bound of its AoI performance, which is used to optimize the parameter configuration. To gain more design insights, we investigate a symmetric network, and put forth a fixed scheduling (FS) policy with lower computational complexity. An action space reduction strategy is applied to further reduce the computational complexity of both DS and FS policies. Our numerical results validate our analyses and indicate that the DS policy with the reduced action space performs almost identically to the original DS policy, and both outperform the baseline policies.", "field": "cs", "label": 0}
{"text": "Title: Cyclotomic generating functions\nAbstract: It is a remarkable fact that for many statistics on finite sets of combinatorial objects, the roots of the corresponding generating function are each either a complex root of unity or zero. We call such polynomials \\textbf{cyclotomic generating functions} (CGF's). Previous work studied the support and asymptotic distribution of the coefficients of several families of CGF's arising from tableau and forest combinatorics. In this paper, we continue these explorations by studying general CGF's from algebraic, analytic, and asymptotic perspectives. We review some of the many known examples of CGF's; describe their coefficients, moments, cumulants, and characteristic functions; and give a variety of necessary and sufficient conditions for their existence arising from probability, commutative algebra, and invariant theory. We further show that CGF's are ``generically'' asymptotically normal, generalizing a result of Diaconis. We include several open problems concerning CGF's.", "field": "math", "label": 0}
{"text": "Title: A Cybersecurity Risk Analysis Framework for Systems with Artificial Intelligence Components\nAbstract: The introduction of the European Union Artificial Intelligence Act, the NIST Artificial Intelligence Risk Management Framework, and related norms demands a better understanding and implementation of novel risk analysis approaches to evaluate systems with Artificial Intelligence components. This paper provides a cybersecurity risk analysis framework that can help assessing such systems. We use an illustrative example concerning automated driving systems.", "field": "cs", "label": 0}
{"text": "Title: Multi-stages attention Breast cancer classification based on nonlinear spiking neural P neurons with autapses\nAbstract: Breast cancer(BC) is a prevalent type of malignant tumor in women. Early diagnosis and treatment are vital for enhancing the patients' survival rate. Downsampling in deep networks may lead to loss of information, so for compensating the detail and edge information and allowing convolutional neural networks to pay more attention to seek the lesion region, we propose a multi-stages attention architecture based on NSNP neurons with autapses. First, unlike the single-scale attention acquisition methods of existing methods, we set up spatial attention acquisition at each feature map scale of the convolutional network to obtain an fusion global information on attention guidance. Then we introduce a new type of NSNP variants called NSNP neurons with autapses. Specifically, NSNP systems are modularized as feature encoders, recoding the features extracted from convolutional neural network as well as the fusion of attention information and preserve the key characteristic elements in feature maps. This ensures the retention of valuable data while gradually transforming high-dimensional complicated info into low-dimensional ones. The proposed method is evaluated on the public dataset BreakHis at various magnifications and classification tasks. It achieves a classification accuracy of 96.32% at all magnification cases, outperforming state-of-the-art methods. Ablation studies are also performed, verifying the proposed model's efficacy. The source code is available at XhuBobYoung/Breast-cancer-Classification.", "field": "cs", "label": 0}
{"text": "Title: Selling Data to a Competitor\nAbstract: We study the costs and benefits of selling data to a competitor. Although selling all consumers' data may decrease total firm profits, there exist other selling mechanisms -- in which only some consumers' data is sold -- that render both firms better off. We identify the profit-maximizing mechanism, and show that the benefit to firms comes at a cost to consumers. We then construct Pareto-improving mechanisms, in which each consumers' welfare, as well as both firms' profits, increase. Finally, we show that consumer opt-in can serve as an instrument to induce firms to choose a Pareto-improving mechanism over a profit-maximizing one.", "field": "cs", "label": 1}
{"text": "Title: Propagation Path Loss Models for 5G Urban Micro- and Macro-Cellular Scenarios\nAbstract: This paper presents and compares two candidate large-scale propagation path loss models, the alpha-beta-gamma (ABG) model and the close-in (CI) free space reference distance model, for the design of fifth generation (5G) wireless communication systems in urban micro- and macro-cellular scenarios. Comparisons are made using the data obtained from 20 propagation measurement campaigns or ray-tracing studies from 2 GHz to 73.5 GHz over distances ranging from 5 m to 1429 m. The results show that the one-parameter CI model has a very similar goodness of fit (i.e., the shadow fading standard deviation) in both line-of-sight and non-line-of-sight environments, while offering substantial simplicity and more stable behavior across frequencies and distances, as compared to the three-parameter ABG model. Additionally, the CI model needs only one very subtle and simple modification to the existing 3GPP floating-intercept path loss model (replacing a constant with a close-in free space reference value) in order to provide greater simulation accuracy, more simplicity, better repeatability across experiments, and higher stability across a vast range of frequencies.", "field": "cs", "label": 1}
{"text": "Title: Finiteness conjecture for 3-manifolds obtained from handlebodies by attaching 2-handles\nAbstract: We study a generalized Witten's finiteness conjecture for the skein modules of oriented compact 3-manifolds with boundary. We formulate an equivalent version of the generalized finiteness conjecture using handlebodies and 2-handles, and prove the conjecture for some classes with the handlebodies of genus 2 and 3 using the equivalent version.", "field": "math", "label": 0}
{"text": "Title: Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes\nAbstract: In the present paper, we give harmonic weight enumerators and Jacobi polynomials for the first-order Reed--Muller codes and the extended Hamming codes. As a corollary, we show the nonexistence of combinatorial $4$-designs in these codes.", "field": "math", "label": 0}
{"text": "Title: Dimension-Minimality and Primality of Counter Nets\nAbstract: A $k$-Counter Net ($k$-CN) is a finite-state automaton equipped with $k$ integer counters that are not allowed to become negative, but do not have explicit zero tests. This language-recognition model can be thought of as labelled vector addition systems with states, some of which are accepting. Certain decision problems for $k$-CNs become easier, or indeed decidable, when the dimension $k$ is small. Yet, little is known about the effect that the dimension $k$ has on the class of languages recognised by $k$-CNs. Specifically, it would be useful if we could simplify algorithmic reasoning by reducing the dimension of a given CN. To this end, we introduce the notion of dimension-primality for $k$-CN, whereby a $k$-CN is prime if it recognises a language that cannot be decomposed into a finite intersection of languages recognised by $d$-CNs, for some $d<k$. We show that primality is undecidable. We also study two related notions: dimension-minimality (where we seek a single language-equivalent $d$-CN of lower dimension) and language regularity. Additionally, we explore the trade-offs in expressiveness between dimension and non-determinism for CN.", "field": "cs", "label": 0}
{"text": "Title: Finite central extensions of type I\nAbstract: Let $\\mathbb{G}$ be a Lie group with solvable connected component and finitely-generated component group and $\\alpha\\in H^2(\\mathbb{G},\\mathbb{S}^1)$ a cohomology class. We prove that if $(\\mathbb{G},\\alpha)$ is of type I then the same holds for the finite central extensions of $\\mathbb{G}$. In particular, finite central extensions of type-I connected solvable Lie groups are again of type I. This is by contrast with the general case, whereby the type-I property does not survive under finite central extensions. We also show that ad-algebraic hulls of connected solvable Lie groups operate on these even when the latter are not simply connected, and give a group-theoretic characterization of the intersection of all Euclidean subgroups of a connected, simply-connected solvable group $\\mathbb{G}$ containing a given central subgroup of $\\mathbb{G}$.", "field": "math", "label": 1}
{"text": "Title: The GDPR Enforcement Fines at Glance\nAbstract: The General Data Protection Regulation (GDPR) came into force in 2018. After this enforcement, many fines have already been imposed by national data protection authorities in Europe. This paper examines the individual GDPR articles referenced in the enforcement decisions, as well as predicts the amount of enforcement fines with available meta-data and text mining features extracted from the enforcement decision documents. According to the results, three articles related to the general principles, lawfulness, and information security have been the most frequently referenced ones. Although the amount of fines imposed vary across the articles referenced, these three particular articles do not stand out. Furthermore, a better statistical evidence is available with other meta-data features, including information about the particular European countries in which the enforcements were made. Accurate predictions are attainable even with simple machine learning techniques for regression analysis. Basic text mining features outperform the meta-data features in this regard. In addition to these results, the paper reflects the GDPR's enforcement against public administration obstacles in the European Union (EU), as well as discusses the use of automatic decision-making systems in judiciary.", "field": "cs", "label": 1}
{"text": "Title: Deep nets for local manifold learning\nAbstract: The problem of extending a function $f$ defined on a training data $\\mathcal{C}$ on an unknown manifold $\\mathbb{X}$ to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For $\\mathbb{X}$ embedded in a high dimensional ambient Euclidean space $\\mathbb{R}^D$, a deep learning algorithm is developed for finding a local coordinate system for the manifold {\\bf without eigen--decomposition}, which reduces the problem to the classical problem of function approximation on a low dimensional cube. Deep nets (or multilayered neural networks) are proposed to accomplish this approximation scheme by using the training data. Our methods do not involve such optimization techniques as back--propagation, while assuring optimal (a priori) error bounds on the output in terms of the number of derivatives of the target function. In addition, these methods are universal, in that they do not require a prior knowledge of the smoothness of the target function, but adjust the accuracy of approximation locally and automatically, depending only upon the local smoothness of the target function. Our ideas are easily extended to solve both the pre--image problem and the out--of--sample extension problem, with a priori bounds on the growth of the function thus extended.", "field": "cs", "label": 1}
{"text": "Title: Knight's paths towards Catalan numbers\nAbstract: We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the $x$-axis are enumerated by the generalized Catalan numbers, and we give a constructive bijection with peakless Motzkin paths of a given length. After enumerating partial knight's paths of a given length, we prove that zigzag knight's paths of a given length ending on the $x$-axis are counted by the Catalan numbers. Finally, we give a constructive bijection with Dyck paths of a given length.", "field": "math", "label": 1}
{"text": "Title: On in-plane drill rotations for Cosserat surfaces\nAbstract: We show under some natural smoothness assumptions that pure in-plane drill rotations as deformation mappings of a $C^2$-smooth regular shell surface to another one parametrized over the same domain are impossible provided that the rotations are fixed at a portion of the boundary. Put otherwise, if the tangent vectors of the new surface are obtained locally by only rotating the given tangent vectors, and if these rotations have a rotation axis which coincides everywhere with the normal of the initial surface, then the two surfaces are equal provided they coincide at a portion of the boundary. In the language of differential geometry of surfaces we show that any isometry which leaves normals invariant and which coincides with the given surface at a portion of the boundary, is the identity mapping.", "field": "math", "label": 1}
{"text": "Title: Signal Processing in the Retina: Interpretable Graph Classifier to Predict Ganglion Cell Responses\nAbstract: It is a popular hypothesis in neuroscience that ganglion cells in the retina are activated by selectively detecting visual features in an observed scene. While ganglion cell firings can be predicted via data-trained deep neural nets, the networks remain indecipherable, thus providing little understanding of the cells' underlying operations. To extract knowledge from the cell firings, in this paper we learn an interpretable graph-based classifier from data to predict the firings of ganglion cells in response to visual stimuli. Specifically, we learn a positive semi-definite (PSD) metric matrix $\\mathbf{M} \\succeq 0$ that defines Mahalanobis distances between graph nodes (visual events) endowed with pre-computed feature vectors; the computed inter-node distances lead to edge weights and a combinatorial graph that is amenable to binary classification. Mathematically, we define the objective of metric matrix $\\mathbf{M}$ optimization using a graph adaptation of large margin nearest neighbor (LMNN), which is rewritten as a semi-definite programming (SDP) problem. We solve it efficiently via a fast approximation called Gershgorin disc perfect alignment (GDPA) linearization. The learned metric matrix $\\mathbf{M}$ provides interpretability: important features are identified along $\\mathbf{M}$'s diagonal, and their mutual relationships are inferred from off-diagonal terms. Our fast metric learning framework can be applied to other biological systems with pre-chosen features that require interpretation.", "field": "cs", "label": 0}
{"text": "Title: Pendant appearances and components in random graphs from structured classes\nAbstract: We consider random graphs sampled uniformly from a structured class of graphs, such as the class of graphs embeddable in a given surface. We sharpen and extend earlier results on pendant appearances, concerning for example numbers of leaves; and obtain results on the asymptotic distribution of components other than the giant component, under quite general conditions.", "field": "math", "label": 1}
{"text": "Title: The Equity Framework: Fairness Beyond Equalized Predictive Outcomes\nAbstract: Machine Learning (ML) decision-making algorithms are now widely used in predictive decision-making, for example, to determine who to admit and give a loan. Their wide usage and consequential effects on individuals led the ML community to question and raise concerns on how the algorithms differently affect different people and communities. In this paper, we study fairness issues that arise when decision-makers use models (proxy models) that deviate from the models that depict the physical and social environment in which the decisions are situated (intended models). We also highlight the effect of obstacles on individual access and utilization of the models. To this end, we formulate an Equity Framework that considers equal access to the model, equal outcomes from the model, and equal utilization of the model, and consequentially achieves equity and higher social welfare than current fairness notions that aim for equality. We show how the three main aspects of the framework are connected and provide an equity scoring algorithm and questions to guide decision-makers towards equitable decision-making. We show how failure to consider access, outcome, and utilization would exacerbate proxy gaps leading to an infinite inequity loop that reinforces structural inequities through inaccurate and incomplete ground truth curation. We, therefore, recommend a more critical look at the model design and its effect on equity and a shift towards equity achieving predictive decision-making models.", "field": "cs", "label": 1}
{"text": "Title: Mitigating Face Recognition Bias via Group Adaptive Classifier\nAbstract: Face recognition is known to exhibit bias - subjects in a certain demographic group can be better recognized than other groups. This work aims to learn a fair face representation, where faces of every group could be more equally represented. Our proposed group adaptive classifier mitigates bias by using adaptive convolution kernels and attention mechanisms on faces based on their demographic attributes. The adaptive module comprises kernel masks and channel-wise attention maps for each demographic group so as to activate different facial regions for identification, leading to more discriminative features pertinent to their demographics. Our introduced automated adaptation strategy determines whether to apply adaptation to a certain layer by iteratively computing the dissimilarity among demographic-adaptive parameters. A new de-biasing loss function is proposed to mitigate the gap of average intra-class distance between demographic groups. Experiments on face benchmarks (RFW, LFW, IJB-A, and IJB-C) show that our work is able to mitigate face recognition bias across demographic groups while maintaining the competitive accuracy.", "field": "cs", "label": 1}
{"text": "Title: Deformed Hamiltonian vector fields and Lagrangian fibrations\nAbstract: Certain dissipative physical systems closely resemble Hamiltonian systems in $\\mathbb{R}^{2n}$, but with the canonical equation for one of the variables in each conjugate pair rescaled by a real parameter. To generalise these dynamical systems to symplectic manifolds in this paper we introduce and study the properties of deformed Hamiltonian vector fields on Lagrangian fibrations. We describe why these objects have some interesting applications to symplectic geometry and discuss how their physical interpretation motivates new problems in mathematics.", "field": "math", "label": 1}
{"text": "Title: The irregularity of cyclic multiple planes after Zariski\nAbstract: A formula for the irregularity of a cyclic multiple plane associated to a branch curve that has arbitrary singularities and is transverse to the line at infinity is established. The irregularity is expressed as a sum of superabundances of linear systems associated to some multiplier ideals of the branch curve and the proof rests on the theory of standard cyclic coverings. Explicit computations of multiplier ideals are performed and some applications are presented.", "field": "math", "label": 1}
{"text": "Title: A new version of Toom's proof\nAbstract: There are several proofs now for the stability of Toom's example of a two-dimensional stable cellular automaton and its application to fault-tolerant computation. Simon and Berman simplified and strengthened Toom's original proof: the present report is a simplified exposition of their proof.", "field": "cs", "label": 1}
{"text": "Title: Relative Entropy for Quantum Channels\nAbstract: We introduce an quantum entropy for bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy. The relative entropy for Fourier multipliers of bimodule quantum channels establishes an upper bound of the quantum entropy. Additionally, we present the Araki relative entropy for bimodule quantum channels, revealing its equivalence to the relative entropy for Fourier multipliers and demonstrating its left/right monotonicities and convexity. Notably, the quantum entropy attains its maximum if there is a downward Jones basic construction. By considering R\\'{e}nyi entropy for Fourier multipliers, we find a continuous bridge between the logarithm of the Pimsner-Popa index and the Pimsner-Popa entropy. As a consequence, the R\\'{e}nyi entropy at $1/2$ serves a criterion for the existence of a downward Jones basic construction.", "field": "math", "label": 0}
{"text": "Title: Open Transactions on Shared Memory\nAbstract: Transactional memory has arisen as a good way for solving many of the issues of lock-based programming. However, most implementations admit isolated transactions only, which are not adequate when we have to coordinate communicating processes. To this end, in this paper we present OCTM, an Haskell-like language with open transactions over shared transactional memory: processes can join transactions at runtime just by accessing to shared variables. Thus a transaction can co-operate with the environment through shared variables, but if it is rolled-back, also all its effects on the environment are retracted. For proving the expressive power of TCCS we give an implementation of TCCS, a CCS-like calculus with open transactions.", "field": "cs", "label": 1}
{"text": "Title: Fast & Fair: Efficient Second-Order Robust Optimization for Fairness in Machine Learning\nAbstract: This project explores adversarial training techniques to develop fairer Deep Neural Networks (DNNs) to mitigate the inherent bias they are known to exhibit. DNNs are susceptible to inheriting bias with respect to sensitive attributes such as race and gender, which can lead to life-altering outcomes (e.g., demographic bias in facial recognition software used to arrest a suspect). We propose a robust optimization problem, which we demonstrate can improve fairness in several datasets, both synthetic and real-world, using an affine linear model. Leveraging second order information, we are able to find a solution to our optimization problem more efficiently than a purely first order method.", "field": "cs", "label": 0}
{"text": "Title: $F$-pure and $F$-injective singularities in equal characteristic zero\nAbstract: Inspired by Schoutens' results, we introduce a variant of sharp $F$-purity and sharp $F$-injectivity in equal characteristic zero via ultraproducts. As an application, we show that if $R\\to S$ is pure and $S$ is of dense $F$-pure type, then $R$ is of dense $F$-pure type.", "field": "math", "label": 0}
{"text": "Title: Shift Graphs, Chromatic Number and Acyclic One-Path Orientations\nAbstract: Shift graphs, which were introduced by Erd\\H{o}s and Hajnal, have been used to answer various questions in extremal graph theory. In this paper, we prove two new results using shift graphs and their induced subgraphs. 1. Recently Girao [Combinatorica2023], showed that for every graph $F$ with at least one edge, there is a constant $c_F$ such that there are graphs of arbitrarily large chromatic number and the same clique number as $F$, in which every $F$-free induced subgraph has chromatic number at most $c_F$. We significantly improve the value of the constant $c_F$ for the special case where $F$ is the complete bipartite graph $K_{a,b}$. We show that any $K_{a,b}$-free induced subgraph of the triangle-free shift graph $G_{n,2}$ has chromatic number at most $a+b$. 2. An undirected simple graph $G$ is said to have the AOP Property if it can be acyclically oriented such that there is at most one directed path between any two vertices. We prove that the shift graph $G_{n,2}$ does not have the AOP property for all $n\\geq 9$. We then construct induced subgraphs of shift graph $G_{n,2}$ with an arbitrarily high chromatic number and odd-girth which have the AOP property. To the best of our knowledge, this gives the first constructive proof of the existence of graphs with arbitrarily high chromatic number and odd-girth that have the AOP property. Furthermore, we construct graphs with arbitrarily high odd-girth that do not have the AOP Property and also prove the existence of graphs with girth equal to $5$ that do not have the AOP property.", "field": "math", "label": 0}
{"text": "Title: The Log-Volume of Optimal Codes for Memoryless Channels, Asymptotically Within A Few Nats\nAbstract: Shannon's analysis of the fundamental capacity limits for memoryless communication channels has been refined over time. In this paper, the maximum volume $M_\\avg^*(n,\\epsilon)$ of length-$n$ codes subject to an average decoding error probability $\\epsilon$ is shown to satisfy the following tight asymptotic lower and upper bounds as $n \\to \\infty$: \\[ \\underline{A}_\\epsilon + o(1) \\le \\log M_\\avg^*(n,\\epsilon) - [nC - \\sqrt{nV_\\epsilon} \\,Q^{-1}(\\epsilon) + \\frac{1}{2} \\log n] \\le \\overline{A}_\\epsilon + o(1) \\] where $C$ is the Shannon capacity, $V_\\epsilon$ the $\\epsilon$-channel dispersion, or second-order coding rate, $Q$ the tail probability of the normal distribution, and the constants $\\underline{A}_\\epsilon$ and $\\overline{A}_\\epsilon$ are explicitly identified. This expression holds under mild regularity assumptions on the channel, including nonsingularity. The gap $\\overline{A}_\\epsilon - \\underline{A}_\\epsilon$ is one nat for weakly symmetric channels in the Cover-Thomas sense, and typically a few nats for other symmetric channels, for the binary symmetric channel, and for the $Z$ channel. The derivation is based on strong large-deviations analysis and refined central limit asymptotics. A random coding scheme that achieves the lower bound is presented. The codewords are drawn from a capacity-achieving input distribution modified by an $O(1/\\sqrt{n})$ correction term.", "field": "cs", "label": 1}
{"text": "Title: Discrete Uniqueness Sets for Functions with Spectral Gaps\nAbstract: It is well-known that entire functions whose spectrum belongs to a fixed bounded set $S$ admit real uniformly discrete uniqueness sets $\\Lambda$. We show that the same is true for much wider spaces of continuous functions. In particular, Sobolev spaces have this property whenever $S$ is a set of infinite measure having \"periodic gaps\". The periodicity condition is crucial. For sets $S$ with randomly distributed gaps, we show that the uniformly discrete sets $\\Lambda$ satisfy a strong non-uniqueness property: Every discrete function $c(\\lambda)\\in l^2(\\Lambda)$ can be interpolated by an analytic $L^2$-function with spectrum in $S$.", "field": "math", "label": 1}
{"text": "Title: Quasi-Lie bialgebroids, Dirac structures and deformations of Poisson quasi-Nijenhuis manifolds\nAbstract: We show how to deform a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Then we interpret this procedure in the context of quasi-Lie bialgebroids, as a particular case of the so called twisting of a quasi-Lie bialgebroid. Finally, we frame our result in the setting of Courant algebroids and Dirac structures.", "field": "math", "label": 0}
{"text": "Title: Parabolic Anderson model in bounded domains of recurrent metric measure spaces\nAbstract: A metric measure space equipped with a Dirichlet form is called recurrent if its Hausdorff dimension is less than its walk dimension. In bounded domains of such spaces we study the parabolic Anderson models \\[ \\partial_{t} u(t,x) = \\Delta u(t,x) + \\beta u(t,x) \\, \\dot{W}_\\alpha(t,x) \\] where the noise $W_\\alpha$ is white in time and colored in space when $\\alpha >0$ while for $\\alpha=0$ it is also white in space. Both Dirichlet and Neumann boundary conditions are considered. Besides proving existence and uniqueness in the It\\^o sense we also get precise $L^p$ estimates for the moments and intermittency properties of the solution as a consequence. Our study reveals new exponents which are intrinsically associated to the geometry of the underlying space and the results for instance apply in metric graphs or fractals like the Sierpi\\'nski gasket for which we prove scaling invariance properties of the models.", "field": "math", "label": 0}
{"text": "Title: Buildings, spiders, and geometric Satake\nAbstract: Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).", "field": "math", "label": 1}
{"text": "Title: Competitive Searching over Terrains\nAbstract: We study a variant of the searching problem where the environment consists of a known terrain and the goal is to obtain visibility of an unknown target point on the surface of the terrain. The searcher starts on the surface of the terrain and is allowed to fly above the terrain. The goal is to devise a searching strategy that minimizes the competitive ratio, that is, the worst-case ratio between the distance traveled by the searching strategy and the minimum travel distance needed to detect the target. For $1.5$D terrains we show that any searching strategy has a competitive ratio of at least $\\sqrt{82}$ and we present a nearly-optimal searching strategy that achieves a competitive ratio of $3\\sqrt{19/2} \\approx \\sqrt{82} + 0.19$. This strategy extends directly to the case where the searcher has no knowledge of the terrain beforehand. For $2.5$D terrains we show that the optimal competitive ratio depends on the maximum slope $\\lambda$ of the terrain, and is hence unbounded in general. Specifically, we provide a lower bound on the competitive ratio of $\\Omega(\\sqrt{\\lambda})$. Finally, we complement the lower bound with a searching strategy based on the maximum slope of the known terrain, which achieves a competitive ratio of $O(\\sqrt{\\lambda})$.", "field": "cs", "label": 0}
{"text": "Title: Short note on the behavior of recurrent neural network for noisy dynamical system\nAbstract: The behavior of recurrent neural network for the data-driven simulation of noisy dynamical systems is studied by training a set of Long Short-Term Memory Networks (LSTM) on the Mackey-Glass time series with a wide range of noise level. It is found that, as the training noise becomes larger, LSTM learns to depend more on its autonomous dynamics than the noisy input data. As a result, LSTM trained on noisy data becomes less susceptible to the perturbation in the data, but has a longer relaxation timescale. On the other hand, when trained on noiseless data, LSTM becomes extremely sensitive to a small perturbation, but is able to adjusts to the changes in the input data.", "field": "cs", "label": 1}
{"text": "Title: The Optimal Paper Moebius Band\nAbstract: In this paper we prove that a smooth embedded paper Moebius band must have aspect ratio greater than $\\sqrt 3$. We also prove that any sequence of smooth embedded paper Moebius bands whose aspect ratio converges to $\\sqrt 3$ must converge, up to isometry, to the famous triangular Moebius band. These results answer the minimum aspect ratio question discussed by W. Wunderlich in 1962 and prove the more specific conjecture of B Halpern and C. Weaver from 1977.", "field": "math", "label": 0}
{"text": "Title: Nonlinear analysis with resurgent functions\nAbstract: We provide estimates for the convolution product of an arbitrary number of \"resurgent functions\", that is holomorphic germs at the origin of $C$ that admit analytic continuation outside a closed discrete subset of $C$ which is stable under addition. Such estimates are then used to perform nonlinear operations like substitution in a convergent series, composition or functional inversion with resurgent functions, and to justify the rules of \"alien calculus\"; they also yield implicitly defined resurgent functions. The same nonlinear operations can be performed in the framework of Borel-Laplace summability.", "field": "math", "label": 1}
{"text": "Title: Codes and Designs in Johnson Graphs From Symplectic Actions on Quadratic Forms\nAbstract: The Johnson graph $J(v, k)$ has as vertices the $k$-subsets of $\\mathcal{V}=\\{1,\\ldots, v\\}$, and two vertices are joined by an edge if their intersection has size $k-1$. An \\emph{$X$-strongly incidence-transitive code} in $J (v, k)$ is a proper vertex subset $\\Gamma$ such that the subgroup $X$ of graph automorphisms leaving $\\Gamma$ invariant is transitive on the set $\\Gamma$ of `codewords', and for each codeword $\\Delta$, the setwise stabiliser $X_\\Delta$ is transitive on $\\Delta \\times (\\mathcal{V}\\setminus \\Delta)$. We classify the \\emph{$X$-strongly incidence-transitive codes} in $J(v,k)$ for which $X$ is the symplectic group $\\mathrm{Sp}_{2n}(2)$ acting as a $2$-transitive permutation group of degree $2^{2n-1}\\pm 2^{n-1}$, where the stabiliser $X_\\Delta$ of a codeword $\\Delta$ is contained in a \\emph{geometric} maximal subgroup of $X$. In particular, we construct two new infinite families of strongly incidence-transitive codes associated with the reducible maximal subgroups of $\\mathrm{Sp}_{2n}(2)$.", "field": "math", "label": 1}
{"text": "Title: A Connected Component Labeling Algorithm for Implicitly-Defined Domains\nAbstract: A connected component labeling algorithm is developed for implicitly-defined domains specified by multivariate polynomials. The algorithm operates by recursively subdividing the constraint domain into hyperrectangular subcells until the topology thereon is sufficiently simple; in particular, we devise a topology test using properties of Bernstein polynomials. In many cases the algorithm produces a certificate guaranteeing its correctness, i.e., two points yield the same label if and only if they are path-connected. To robustly handle various kinds of edge cases, the algorithm may assign identical labels to distinct components, but only when they are exactly or nearly touching, relative to a user-controlled length scale. A variety of numerical experiments assess the effectiveness of the overall approach, including statistical analyses on randomly generated multi-component geometry in 2D and 3D, as well as specific examples involving cusps, self-intersections, junctions, and other kinds of singularities.", "field": "math", "label": 1}
{"text": "Title: Percolation threshold for metric graph loop soup\nAbstract: In this short note, we show that the critical threshold for the percolation of metric graph loop soup on a large class of transient metric graphs (including quasi-transitive graphs such as $\\mathbb{Z}^d$, $d\\geq 3$) is $1/2$.", "field": "math", "label": 0}
{"text": "Title: Evasive Hardware Trojan through Adversarial Power Trace\nAbstract: The globalization of the Integrated Circuit (IC) supply chain, driven by time-to-market and cost considerations, has made ICs vulnerable to hardware Trojans (HTs). Against this threat, a promising approach is to use Machine Learning (ML)-based side-channel analysis, which has the advantage of being a non-intrusive method, along with efficiently detecting HTs under golden chip-free settings. In this paper, we question the trustworthiness of ML-based HT detection via side-channel analysis. We introduce a HT obfuscation (HTO) approach to allow HTs to bypass this detection method. Rather than theoretically misleading the model by simulated adversarial traces, a key aspect of our approach is the design and implementation of adversarial noise as part of the circuitry, alongside the HT. We detail HTO methodologies for ASICs and FPGAs, and evaluate our approach using TrustHub benchmark. Interestingly, we found that HTO can be implemented with only a single transistor for ASIC designs to generate adversarial power traces that can fool the defense with 100% efficiency. We also efficiently implemented our approach on a Spartan 6 Xilinx FPGA using 2 different variants: (i) DSP slices-based, and (ii) ring-oscillator-based design. Additionally, we assess the efficiency of countermeasures like spectral domain analysis, and we show that an adaptive attacker can still design evasive HTOs by constraining the design with a spectral noise budget. In addition, while adversarial training (AT) offers higher protection against evasive HTs, AT models suffer from a considerable utility loss, potentially rendering them unsuitable for such security application. We believe this research represents a significant step in understanding and exploiting ML vulnerabilities in a hardware security context, and we make all resources and designs openly available online: https://dev.d18uu4lqwhbmka.amplifyapp.com", "field": "cs", "label": 0}
{"text": "Title: On PFH and HF spectral invariants\nAbstract: In this note, we define the link spectral invariants by using the cylindrical formulation of the quantitative Heegaard Floer homology. We call them HF spectral invariants. We deduce a relation between the HF spectral invariants and the PFH spectral invariants by using closed-open morphisms and open-closed morphisms. For the sphere, we prove that the homogenized HF spectral invariants at the unit are equal to the homogenized PFH spectral invariants. Moreover, we show that the homogenized PFH spectral invariants are quasimorphisms.", "field": "math", "label": 1}
{"text": "Title: Network Structure, Efficiency, and Performance in WikiProjects\nAbstract: The internet has enabled collaborations at a scale never before possible, but the best practices for organizing such large collaborations are still not clear. Wikipedia is a visible and successful example of such a collaboration which might offer insight into what makes large-scale, decentralized collaborations successful. We analyze the relationship between the structural properties of WikiProject coeditor networks and the performance and efficiency of those projects. We confirm the existence of an overall performance-efficiency trade-off, while observing that some projects are higher than others in both performance and efficiency, suggesting the existence factors correlating positively with both. Namely, we find an association between low-degree coeditor networks and both high performance and high efficiency. We also confirm results seen in previous numerical and small-scale lab studies: higher performance with less skewed node distributions, and higher performance with shorter path lengths. We use agent-based models to explore possible mechanisms for degree-dependent performance and efficiency. We present a novel local-majority learning strategy designed to satisfy properties of real-world collaborations. The local-majority strategy as well as a localized conformity-based strategy both show degree-dependent performance and efficiency, but in opposite directions, suggesting that these factors depend on both network structure and learning strategy. Our results suggest possible benefits to decentralized collaborations made of smaller, more tightly-knit teams, and that these benefits may be modulated by the particular learning strategies in use.", "field": "cs", "label": 1}
{"text": "Title: Urban Surface Reconstruction in SAR Tomography by Graph-Cuts\nAbstract: SAR (Synthetic Aperture Radar) tomography reconstructs 3-D volumes from stacks of SAR images. High-resolution satellites such as TerraSAR-X provide images that can be combined to produce 3-D models. In urban areas, sparsity priors are generally enforced during the tomographic inversion process in order to retrieve the location of scatterers seen within a given radar resolution cell. However, such priors often miss parts of the urban surfaces. Those missing parts are typically regions of flat areas such as ground or rooftops. This paper introduces a surface segmentation algorithm based on the computation of the optimal cut in a flow network. This segmentation process can be included within the 3-D reconstruction framework in order to improve the recovery of urban surfaces. Illustrations on a TerraSAR-X tomographic dataset demonstrate the potential of the approach to produce a 3-D model of urban surfaces such as ground, fa\\c{c}ades and rooftops.", "field": "cs", "label": 1}
{"text": "Title: 2-Representations of Lie 2-groups and 2-Vector Bundles\nAbstract: Murray, Roberts and Wockel showed that there is no strict model of the string 2-group using the free loop group. Instead, they construct the next best thing, a coherent model for the string 2-group using the free loop group, with explicit formulas for all structure. Based on their expectations, we build a category of 2-representations for coherent Lie 2-groups and some concrete examples. We also discuss the relation between this category of 2-representations and the category of representations. In addition, we construct a model of equivariant 2-vector bundles. At the end, we discuss the adjoint action on the string 2-representations.", "field": "math", "label": 1}
{"text": "Title: Remarks on the point character of Banach spaces and non-linear embeddings into~$c_0(\\Ga)$\nAbstract: We give a brief survey of the results on coarse or uniform embeddings of Banach spaces into $c_0(\\Ga)$ and the point character of Banach spaces. In the process we prove several new results in this direction (for example we determine the point character of the spaces $L_p(\\mu)$, $1\\le p\\le2$) solving open problems posed by C.~Avart, P.~Komjath, and V.~Roedl and by G.~Godefroy, G.~Lancien, and V.~Zizler. In particular, we show that $X=L_p(\\mu)$, $1\\le p<\\infty$, bi-Lipschitz embeds into $c_0(\\Ga)$ if and only if $\\dens X<\\om_\\om$.", "field": "math", "label": 0}
{"text": "Title: Robust Collective Classification against Structural Attacks\nAbstract: Collective learning methods exploit relations among data points to enhance classification performance. However, such relations, represented as edges in the underlying graphical model, expose an extra attack surface to the adversaries. We study adversarial robustness of an important class of such graphical models, Associative Markov Networks (AMN), to structural attacks, where an attacker can modify the graph structure at test time. We formulate the task of learning a robust AMN classifier as a bi-level program, where the inner problem is a challenging non-linear integer program that computes optimal structural changes to the AMN. To address this technical challenge, we first relax the attacker problem, and then use duality to obtain a convex quadratic upper bound for the robust AMN problem. We then prove a bound on the quality of the resulting approximately optimal solutions, and experimentally demonstrate the efficacy of our approach. Finally, we apply our approach in a transductive learning setting, and show that robust AMN is much more robust than state-of-the-art deep learning methods, while sacrificing little in accuracy on non-adversarial data.", "field": "cs", "label": 1}
{"text": "Title: Sampling probabilities, diffusions, ancestral graphs, and duality under strong selection\nAbstract: Wright-Fisher diffusions and their dual ancestral graphs occupy a central role in the study of allele frequency change and genealogical structure, and they provide expressions, explicit in some special cases but generally implicit, for the sampling probability, a crucial quantity in inference. Under a finite-allele mutation model, with possibly parent-dependent mutation, we consider the asymptotic regime where the selective advantage of one allele grows to infinity, while the other parameters remain fixed. In this regime, we show that the Wright-Fisher diffusion can be approximated either by a Gaussian process or by a process whose components are independent continuous-state branching processes with immigration, aligning with analogous results for Wright-Fisher models but employing different methods. While the first process becomes degenerate at stationarity, the latter does not and provides a simple, analytic approximation for the leading term of the sampling probability. Furthermore, using another approach based on a recursion formula, we characterise all remaining terms to provide a full asymptotic expansion for the sampling probability. Finally, we study the asymptotic behaviour of the rates of the block-counting process of the conditional ancestral selection graph and establish an asymptotic duality relationship between this and the diffusion.", "field": "math", "label": 0}
{"text": "Title: An infinite family of counterexamples to a conjecture on distance magic labeling\nAbstract: This work is about a partition problem which is an instance of the distance magic graph labeling problem. Given positive integers $n,k$ and $p_1\\le p_2\\le \\cdots\\le p_k$ such that $p_1+\\cdots+p_k=n$ and $k$ divides $\\sum_{i=1}^ni$, we study the problem of characterizing the cases where it is possible to find a partition of the set $\\{1,2,\\ldots,n\\}$ into $k$ subsets of respective sizes $p_1,\\dots,p_k$, such that the element sum in each subset is equal. Using a computerized search we found examples showing that the necessary condition, $\\sum_{i=1}^{p_1+\\cdots+p_j} (n-i+1)\\ge j{\\binom{n+1}{2}}/k$ for all $j=1,\\ldots,k$, is not generally sufficient, refuting a past conjecture. Moreover, we show that there are infinitely many such counter-examples. The question whether there is a simple characterization is left open and for all we know the corresponding decision problem might be NP-complete.", "field": "math", "label": 0}
{"text": "Title: On geometry of the unit ball of Paley-Wiener space over two symmetric intervals\nAbstract: Let $PW_S^1$ be the space of integrable functions on $\\mathbb{R}$ whose Fourier transform vanishes outside $S$, where $S = [-\\sigma,-\\rho]\\cup[\\rho,\\sigma]$, $0<\\rho<\\sigma$. In the case $\\rho>\\sigma/2$, we present a complete description of the set of extreme and the set of exposed points of the unit ball of $PW^1_S$. The structure of these sets becomes more complicated when $\\rho<\\sigma/2$.", "field": "math", "label": 1}
{"text": "Title: Synchrony in Gene Regulatory Networks\nAbstract: We consider two mathematical dynamical models of gene regulatory networks (GRNs) and obtain results on robust synchronization on these dynamical models based on the existing theoretical results in the coupled cell network formalism. We also explore the concepts of quotient networks and network lifting in the context of GRNs which are related to the process of gene duplication and the phenomenon of genetic redundancy.", "field": "math", "label": 1}
{"text": "Title: Bayesian Neural Network Versus Ex-Post Calibration For Prediction Uncertainty\nAbstract: Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on non-probabilistic neural networks which by default do not capture this inherent uncertainty. This well-known problem has led to the development of post-hoc calibration procedures, such as Platt scaling (logistic), isotonic and beta calibration, which transforms the scores into well calibrated empirical probabilities. A plausible alternative to the calibration approach is to use Bayesian neural networks, which directly models a predictive distribution. Although they have been applied to images and text datasets, they have seen limited adoption in the tabular and small data regime. In this paper, we demonstrate that Bayesian neural networks yields competitive performance when compared to calibrated neural networks and conduct experiments across a wide array of datasets.", "field": "cs", "label": 1}
{"text": "Title: Fusion Categories over Non-Algebriacally Closed Fields\nAbstract: Several complications arise when attempting to work with fusion categories over arbitrary fields. Here we describe some of the new phenomena that occur when the field is not algebraically closed, and we adapt tools such as the Frobenius-Perron dimension in order to accommodate these new effects.", "field": "math", "label": 0}
{"text": "Title: Exact upper and lower bounds on the misclassification probability\nAbstract: Exact lower and upper bounds on the best possible misclassification probability for a finite number of classes are obtained in terms of the total variation norms of the differences between the sub-distributions over the classes. These bounds are compared with the exact bounds in terms of the conditional entropy obtained by Feder and Merhav.", "field": "math", "label": 1}
{"text": "Title: The Mahler measure of exact polynomials in three variables\nAbstract: We prove that under certain explicit conditions, the Mahler measure of a three-variable exact polynomial can be expressed in terms of elliptic curve $L$-functions and values of the Bloch-Wigner dilogarithm, conditionally on Beilinson's conjecture. In some cases, these dilogarithmic values simplify to Dirichlet $L$-values. This generalizes a result of Lal\\'in for the polynomial $z + (x+1)(y+1)$. We apply our method to several other Mahler measure identities conjectured by Boyd and Brunault.", "field": "math", "label": 0}
{"text": "Title: Unleashing the Emergent Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration\nAbstract: Human intelligence thrives on cognitive synergy, where collaboration among different minds yield superior outcomes compared to isolated individuals. In this work, we propose Solo Performance Prompting (SPP), which transforms a single LLM into a cognitive synergist by engaging in multi-turn self-collaboration with multiple personas. A cognitive synergist is an intelligent agent that collaboratively combines multiple minds' strengths and knowledge to enhance problem-solving in complex tasks. By dynamically identifying and simulating different personas based on task inputs, SPP unleashes the potential of cognitive synergy in LLMs. Our in-depth analysis shows that assigning multiple fine-grained personas in LLMs improves problem-solving abilities compared to using a single or fixed number of personas. We evaluate SPP on three challenging tasks: Trivia Creative Writing, Codenames Collaborative, and Logic Grid Puzzle, encompassing both knowledge-intensive and reasoning-intensive types. Unlike previous works, such as Chain-of-Thought, that solely enhance the reasoning abilities in LLMs, experimental results demonstrate that SPP effectively reduces factual hallucination, and maintains strong reasoning capabilities. Additionally, comparative experiments show that cognitive synergy only emerges in GPT-4 and does not appear in less capable models, such as GPT-3.5-turbo and Llama2-13b-chat, which draws an interesting analogy to human development. Code, data, and prompts can be found at: https://github.com/MikeWangWZHL/Solo-Performance-Prompting.git.", "field": "cs", "label": 0}
{"text": "Title: Applications of Gorenstein projective $τ$-rigid modules\nAbstract: We first introduce the notion of $CM$-$\\tau$-tilting free algebras as the generalization of $CM$-free algebras and show the homological properties of $CM$-$\\tau$-tilting free algebras. Then we give a bijection between Gorenstein projective $\\tau$-rigid modules and certain modules by using an equivalence established by Kong and Zhang. Finally, we give a partial answer to Tachikawa's first conjecture by using Gorenstein projective $\\tau$-rigid modules.", "field": "math", "label": 0}
{"text": "Title: Challenges and Opportunities in High-dimensional Variational Inference\nAbstract: Current black-box variational inference (BBVI) methods require the user to make numerous design choices -- such as the selection of variational objective and approximating family -- yet there is little principled guidance on how to do so. We develop a conceptual framework and set of experimental tools to understand the effects of these choices, which we leverage to propose best practices for maximizing posterior approximation accuracy. Our approach is based on studying the pre-asymptotic tail behavior of the density ratios between the joint distribution and the variational approximation, then exploiting insights and tools from the importance sampling literature. Our framework and supporting experiments help to distinguish between the behavior of BBVI methods for approximating low-dimensional versus moderate-to-high-dimensional posteriors. In the latter case, we show that mass-covering variational objectives are difficult to optimize and do not improve accuracy, but flexible variational families can improve accuracy and the effectiveness of importance sampling -- at the cost of additional optimization challenges. Therefore, for moderate-to-high-dimensional posteriors we recommend using the (mode-seeking) exclusive KL divergence since it is the easiest to optimize, and improving the variational family or using model parameter transformations to make the posterior and optimal variational approximation more similar. On the other hand, in low-dimensional settings, we show that heavy-tailed variational families and mass-covering divergences are effective and can increase the chances that the approximation can be improved by importance sampling.", "field": "cs", "label": 1}
{"text": "Title: Hopfield Neuronal Network of Fractional Order: A note on its numerical integration\nAbstract: In this paper, the commensurate fractional-order variant of an Hopfield neuronal network is analyzed. The system is integrated with the ABM method for fractional-order equations. Beside the standard stability analysis of equilibria, the divergence of fractional order is proposed to determine the instability of the equilibria. The bifurcation diagrams versus the fractional order, and versus one parameter, reveal a strange phenomenon suggesting that the bifurcation branches generated by initial conditions outside neighborhoods of unstable equilibria are spurious sets although they look similar with those generated by initial conditions close to the equilibria. These spurious sets look ``delayed'' in the considered bifurcation scenario. Once the integration step-size is reduced, the spurious branches maintain their shapes but tend to the branches obtained from initial condition within neighborhoods of equilibria. While the spurious branches move once the integration step size reduces, the branches generated by the initial conditions near the equilibria maintain their positions in the considered bifurcation space. This phenomenon does not depend on the integration-time interval, and repeats in the parameter bifurcation space.", "field": "math", "label": 1}
{"text": "Title: A Finite Axiomatization of G-Dependence\nAbstract: We show that a form of dependence known as G-dependence (originally introduced by Grelling) admits a very natural finite axiomatization, as well as Armstrong relations. We also give an explicit translation between functional dependence and G-dependence.", "field": "math", "label": 1}
{"text": "Title: The built-in selection bias of hazard ratios formalized\nAbstract: It is known that the hazard ratio lacks a useful causal interpretation. Even for data from a randomized controlled trial, the hazard ratio suffers from built-in selection bias as, over time, the individuals at risk in the exposed and unexposed are no longer exchangeable. In this work, we formalize how the observed hazard ratio evolves and deviates from the causal hazard ratio of interest in the presence of heterogeneity of the hazard of unexposed individuals (frailty) and heterogeneity in effect (individual modification). For the case of effect heterogeneity, we define the causal hazard ratio. We show that the observed hazard ratio equals the ratio of expectations of the latent variables (frailty and modifier) conditionally on survival in the world with and without exposure, respectively. Examples with gamma, inverse Gaussian and compound Poisson distributed frailty, and categorical (harming, beneficial or neutral) effect modifiers are presented for illustration. This set of examples shows that an observed hazard ratio with a particular value can arise for all values of the causal hazard ratio. Therefore, the hazard ratio can not be used as a measure of the causal effect without making untestable assumptions, stressing the importance of using more appropriate estimands such as contrasts of the survival probabilities.", "field": "math", "label": 1}
{"text": "Title: Complete Geodesic Metrics in Big Classes\nAbstract: Let $(X,\\omega)$ be a compact K\\\"ahler manifold and $\\theta$ be a smooth closed real $(1,1)$-form that represents a big cohomology class. In this paper, we show that for $p\\geq 1$, the high energy space $\\mathcal{E}^{p}(X,\\theta)$ can be endowed with a metric $d_{p}$ that makes $(\\mathcal{E}^{p}(X,\\theta),d_{p})$ a complete geodesic metric space. The weak geodesics in $\\mathcal{E}^{p}(X,\\theta)$ are the metric geodesic for $(\\mathcal{E}^{p}(X,\\theta), d_{p})$. Moreover, for $p > 1$, the geodesic metric space $(\\mathcal{E}^{p}(X,\\theta), d_{p})$ is uniformly convex.", "field": "math", "label": 0}
{"text": "Title: Trajectory Optimization for Completion Time Minimization in UAV-Enabled Multicasting\nAbstract: This paper studies an unmanned aerial vehicle (UAV)-enabled multicasting system, where a UAV is dispatched to disseminate a common file to a number of geographically distributed ground terminals (GTs). Our objective is to design the UAV trajectory to minimize its mission completion time, while ensuring that each GT is able to successfully recover the file with a high probability required. We consider the use of practical random linear network coding (RLNC) for UAV multicasting, so that each GT is able to recover the file as long as it receives a sufficiently large number of coded packets. However, the formulated UAV trajectory optimization problem is non-convex and difficult to be directly solved. To tackle this issue, we first derive an analytical lower bound for the success probability of each GT's file recovery. Based on this result, we then reformulate the problem into a more tractable form, where the UAV trajectory only needs to be designed to meet a set of constraints each on the minimum connection time with a GT, during which their distance is below a designed threshold. We show that the optimal UAV trajectory only needs to constitute connected line segments, thus it can be obtained by determining first the optimal set of waypoints and then UAV speed along the lines connecting the waypoints. We propose practical schemes for the waypoints design based on a novel concept of virtual base station (VBS) placement and by applying convex optimization techniques. Furthermore, for given set of waypoints, we obtain the optimal UAV speed over the resulting path efficiently by solving a linear programming (LP) problem. Numerical results show that the proposed UAV-enabled multicasting with optimized trajectory design achieves significant performance gains as compared to benchmark schemes.", "field": "cs", "label": 1}
{"text": "Title: The near-parabolic geometry of external rays\nAbstract: Using Lavaurs maps and near-parabolic renormalization, we describe the degenerating geometry of external rays for quadratic polynomials when a periodic cycle becomes parabolic. We similarly describe the geometry of parameter rays for the Mandelbrot set near parabolic points. Using this geometric control we establish new bounds on the size of limbs of the Mandelbrot set, for example providing a quadratic Pommerenke-Levin-Yoccoz inequality in the near-parabolic setting.", "field": "math", "label": 0}
{"text": "Title: Analytic Regularity for Linear Elliptic Systems in Polygons and Polyhedra\nAbstract: We prove weighted anisotropic analytic estimates for solutions of second order elliptic boundary value problems in polyhedra. The weighted analytic classes which we use are the same as those introduced by Guo in 1993 in view of establishing exponential convergence for hp finite element methods in polyhedra. We first give a simple proof of the known weighted analytic regularity in a polygon, relying on a new formulation of elliptic a priori estimates in smooth domains with analytic control of derivatives. The technique is based on dyadic partitions near the corners. This technique can successfully be extended to polyhedra, providing isotropic analytic regularity. This is not optimal, because it does not take advantage of the full regularity along the edges. We combine it with a nested open set technique to obtain the desired three-dimensional anisotropic analytic regularity result. Our proofs are global and do not require the analysis of singular functions.", "field": "math", "label": 1}
{"text": "Title: A homological reformulation of the link condition\nAbstract: We prove an equivalent condition for the existence of a link between prime ideals in terms of the structure of a certain cohomology module. We use this formulation to answer an open question regarding the nature of module extensions over one sided noetherian rings. We apply the techniques developed in this paper to the local link structure of prime ideals of small homological height and examine when certain noetherian rings satisfy the density condition.", "field": "math", "label": 1}
{"text": "Title: Drinfeld rational fractions for affine Kac-Moody quantum symmetric pairs\nAbstract: We formulate a precise connection between the new Drinfeld presentation of a quantum affine algebra $U_q\\widehat{\\mathfrak{g}}$ and the new Drinfeld presentation of affine coideal subalgebras of split type recently discovered by Lu and Wang. In particular, we establish a ``factorization formula'', expressing the commuting ``affine Cartan''-type operators $\\Theta_{i,k}$ in a coideal subalgebra in terms of the corresponding Drinfeld generators of $U_q\\widehat{\\mathfrak{g}}$, modulo the ``Drinfeld positive half\" of $U_q\\widehat{\\mathfrak{g}}$. We study the spectra of these operators on finite dimensional representations, and describe them in terms of rational functions with an extra symmetry. These results can be seen as the starting point of a $q$-character theory for affine Kac--Moody quantum symmetric pairs. Additionally, we prove a compatibility result linking Lusztig's and the Lu-Ruan-Wang-Zhang braid group actions.", "field": "math", "label": 0}
{"text": "Title: Can We Distinguish Machine Learning from Human Learning?\nAbstract: What makes a task relatively more or less difficult for a machine compared to a human? Much AI/ML research has focused on expanding the range of tasks that machines can do, with a focus on whether machines can beat humans. Allowing for differences in scale, we can seek interesting (anomalous) pairs of tasks T, T'. We define interesting in this way: The \"harder to learn\" relation is reversed when comparing human intelligence (HI) to AI. While humans seems to be able to understand problems by formulating rules, ML using neural networks does not rely on constructing rules. We discuss a novel approach where the challenge is to \"perform well under rules that have been created by human beings.\" We suggest that this provides a rigorous and precise pathway for understanding the difference between the two kinds of learning. Specifically, we suggest a large and extensible class of learning tasks, formulated as learning under rules. With these tasks, both the AI and HI will be studied with rigor and precision. The immediate goal is to find interesting groundtruth rule pairs. In the long term, the goal will be to understand, in a generalizable way, what distinguishes interesting pairs from ordinary pairs, and to define saliency behind interesting pairs. This may open new ways of thinking about AI, and provide unexpected insights into human learning.", "field": "cs", "label": 1}
{"text": "Title: Limit theorems for a supercritical remaining-lifetime age-structured branching process\nAbstract: In a previous paper [9] we studied an age-structured branching model without immigration. Here we consider a special case of the model, where the system is founded by a single particle with a random lifetime and the reproduction regime is supercritical. We show that there is a necessary and sufficient condition for the convergence of the Malthus normalized random measures $e^{-\\tilde{\\alpha}t} X_t$, where $\\tilde{\\alpha}$ is a strictly positive Malthusian parameter. The convergence of $e^{-\\tilde{\\alpha}t} \\langle X_t,f\\rangle$ can be strengthened to hold with probability one under conditions weaker than those given in Jagers [24]. A central limit theorem of $\\langle X_t,f\\rangle$ is further proved.", "field": "math", "label": 0}
{"text": "Title: Bounded Homotopy Path Approach to Find the Solution of Linear Complementarity Problems\nAbstract: In this article, we introduce a new homotopy function to trace the trajectory by applying modified homotopy continuation method for finding the solution of the linear complementarity problem. Earlier several authors attempted to propose homotopy functions based on original problems. We propose the homotopy function based on the Karush-Kuhn-Tucker condition of the corresponding quadratic programming problem. The proposed approach extends the processability of the larger class of linear complementarity problem and overcomes the limitations of other existing homotopy approaches. We show that the homotopy path approaching the solution is smooth and bounded with positive tangent direction of the homotopy path. Various classes of numerical examples are illustrated to show the effectiveness of the proposed algorithm and the superiority of the algorithm among other existing iterative methods.", "field": "math", "label": 1}
{"text": "Title: A Borsuk--Ulam theorem for well separated maps\nAbstract: Suppose that $f_1,\\ldots ,f_m : S(V)\\to R$ are $m$ ($\\geq 1$) continuous functions defined on the unit sphere in a Euclidean vector space $V$ of dimension $m+1$ satisfying $f_i(-v)=-f_i(v)$ for all $v\\in S(V)$. The classical Borsuk-Ulam theorem asserts that the image of the map $(f_1,\\ldots ,f_m) :S(V)\\to R^m$ contains $0=(0,\\ldots ,0)$. Pursuing ideas in papers of B\\'ar\\'any, Hubard and J\\'eronimo (2008) and Frick and Wellner (2023), we show that a certain separation property will guarantee that the image contains an $m$-cube.", "field": "math", "label": 0}
{"text": "Title: On the Barcode Entropy of Reeb Flows\nAbstract: In this paper we continue investigating connections between Floer theory and dynamics of Hamiltonian systems, focusing on the barcode entropy of Reeb flows. Barcode entropy is the exponential growth rate of the number of not-too-short bars in the Floer or symplectic homology persistence module. The key novel result is that the barcode entropy is bounded from below by the topological entropy of any hyperbolic invariant set. This, combined with the fact that the topological entropy bounds the barcode entropy from above, established by Fender, Lee and Sohn, implies that in dimension three the two types of entropy agree. The main new ingredient of the proof is a variant of the Crossing Energy Theorem for Reeb flows.", "field": "math", "label": 0}
{"text": "Title: Gesture-to-Gesture Translation in the Wild via Category-Independent Conditional Maps\nAbstract: Recent works have shown Generative Adversarial Networks (GANs) to be particularly effective in image-to-image translations. However, in tasks such as body pose and hand gesture translation, existing methods usually require precise annotations, e.g. key-points or skeletons, which are time-consuming to draw. In this work, we propose a novel GAN architecture that decouples the required annotations into a category label - that specifies the gesture type - and a simple-to-draw category-independent conditional map - that expresses the location, rotation and size of the hand gesture. Our architecture synthesizes the target gesture while preserving the background context, thus effectively dealing with gesture translation in the wild. To this aim, we use an attention module and a rolling guidance approach, which loops the generated images back into the network and produces higher quality images compared to competing works. Thus, our GAN learns to generate new images from simple annotations without requiring key-points or skeleton labels. Results on two public datasets show that our method outperforms state of the art approaches both quantitatively and qualitatively. To the best of our knowledge, no work so far has addressed the gesture-to-gesture translation in the wild by requiring user-friendly annotations.", "field": "cs", "label": 1}
{"text": "Title: Proof of Halin's normal spanning tree conjecture\nAbstract: Halin conjectured 20 years ago that a graph has a normal spanning tree if and only if every minor of it has countable colouring number. We prove Halin's conjecture. This implies a forbidden minor characterisation for the property of having a normal spanning tree.", "field": "math", "label": 1}
{"text": "Title: An Algorithm for Training Polynomial Networks\nAbstract: We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of this paper is the derivation of an efficient layer-by-layer algorithm for training such networks, which we denote as the \\emph{Basis Learner}. The algorithm is a universal learner in the sense that the training error is guaranteed to decrease at every iteration, and can eventually reach zero under mild conditions. We present practical implementations of this algorithm, as well as preliminary experimental results. We also compare our deep architecture to other shallow architectures for learning polynomials, in particular kernel learning.", "field": "cs", "label": 1}
{"text": "Title: Physics-Inspired Discrete-Phase Optimization for 3D Beamforming with PIN-Diode Extra-Large Antenna Arrays\nAbstract: Large antenna arrays can steer narrow beams towards a target area, and thus improve the communications capacity of wireless channels and the fidelity of radio sensing. Hardware that is capable of continuously-variable phase shifts is expensive, presenting scaling challenges. PIN diodes that apply only discrete phase shifts are promising and cost-effective; however, unlike continuous phase shifters, finding the best phase configuration across elements is an NP-hard optimization problem. Thus, the complexity of optimization becomes a new bottleneck for large-antenna arrays. To address this challenge, this paper suggests a procedure for converting the optimization objective function from a ratio of quadratic functions to a sequence of more easily solvable quadratic unconstrained binary optimization (QUBO) sub-problems. This conversion is an exact equivalence, and the resulting QUBO forms are standard input formats for various physics-inspired optimization methods. We demonstrate that a simulated annealing approach is very effective for solving these sub-problems, and we give performance metrics for several large array types optimized by this technique. Through numerical experiments, we report 3D beamforming performance for extra-large arrays with up to 10,000 elements.", "field": "cs", "label": 0}
{"text": "Title: A Learning-Based Fast Uplink Grant for Massive IoT via Support Vector Machines and Long Short-Term Memory\nAbstract: The current random access (RA) allocation techniques suffer from congestion and high signaling overhead while serving massive machine type communication (mMTC) applications. To this end, 3GPP introduced the need to use fast uplink grant (FUG) allocation in order to reduce latency and increase reliability for smart internet-of-things (IoT) applications with strict QoS constraints. We propose a novel FUG allocation based on support vector machine (SVM), First, MTC devices are prioritized using SVM classifier. Second, LSTM architecture is used for traffic prediction and correction techniques to overcome prediction errors. Both results are used to achieve an efficient resource scheduler in terms of the average latency and total throughput. A Coupled Markov Modulated Poisson Process (CMMPP) traffic model with mixed alarm and regular traffic is applied to compare the proposed FUG allocation to other existing allocation techniques. In addition, an extended traffic model based CMMPP is used to evaluate the proposed algorithm in a more dense network. We test the proposed scheme using real-time measurement data collected from the Numenta Anomaly Benchmark (NAB) database. Our simulation results show the proposed model outperforms the existing RA allocation schemes by achieving the highest throughput and the lowest access delay of the order of 1 ms by achieving prediction accuracy of 98 $\\%$ when serving the target massive and critical MTC applications with a limited number of resources.", "field": "cs", "label": 1}
{"text": "Title: On Einstein Lorentzian nilpotent Lie groups\nAbstract: In this paper, we study Lorentzian left invariant Einstein metrics on nilpotent Lie groups. We show that if the center of such Lie groups is degenerate then they are Ricci-flat and their Lie algebras can be obtained by the double extension process from an abelian Euclidean Lie algebra. We show that all nilpotent Lie groups up to dimension $5$ endowed with a Lorentzian Einstein left invariant metric have degenerate center and we use this fact to give a complete classification of these metrics. We show that if $\\mathfrak{g}$ is the Lie algebra of a nilpotent Lie group endowed with a Lorentzian left invariant Einstein metric with non zero scalar curvature then the center $Z(\\mathfrak{g})$ of $\\mathfrak{g}$ is nondegenerate Euclidean, the derived ideal $[\\mathfrak{g},\\mathfrak{g}]$ is nondegenerate Lorentzian and $Z(\\mathfrak{g})\\subset[\\mathfrak{g},\\mathfrak{g}]$. We give the first examples of Ricci-flat Lorentzian nilpotent Lie algebra with nondegenerate center.", "field": "math", "label": 1}
{"text": "Title: Hyperlinear approximations to amenable groups come from sofic approximations\nAbstract: We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is essentially produced from a sofic approximation. The proof is probabilistic, using the concentration of measure in high dimensional spheres to control the deviation of an operator's matrix coefficients from its trace. As a corollary, we obtain a result connecting stability of sofic approximations with stability of hyperlinear approximations.", "field": "math", "label": 1}
{"text": "Title: Microsoft COCO: Common Objects in Context\nAbstract: We present a new dataset with the goal of advancing the state-of-the-art in object recognition by placing the question of object recognition in the context of the broader question of scene understanding. This is achieved by gathering images of complex everyday scenes containing common objects in their natural context. Objects are labeled using per-instance segmentations to aid in precise object localization. Our dataset contains photos of 91 objects types that would be easily recognizable by a 4 year old. With a total of 2.5 million labeled instances in 328k images, the creation of our dataset drew upon extensive crowd worker involvement via novel user interfaces for category detection, instance spotting and instance segmentation. We present a detailed statistical analysis of the dataset in comparison to PASCAL, ImageNet, and SUN. Finally, we provide baseline performance analysis for bounding box and segmentation detection results using a Deformable Parts Model.", "field": "cs", "label": 1}
{"text": "Title: Orthogonal webs and semisimplification\nAbstract: We define a diagrammatic category that is equivalent to tilting representations for the orthogonal group. Our construction works in characteristic not equal to two. We also describe the semisimplification of this category.", "field": "math", "label": 0}
{"text": "Title: VBFT: Veloce Byzantine Fault Tolerant Consensus for Blockchains\nAbstract: Low latency is one of the most desirable features of partially synchronous Byzantine consensus protocols. Existing low-latency protocols have achieved consensus with just two communication steps by reducing the maximum number of faults the protocol can tolerate (from $f = \\frac{n-1}{3}$ to $f = \\frac{n+1}{5}$), \\textcolor{black}{by relaxing protocol safety guarantees}, or by using trusted hardware like Trusted Execution Environment. Furthermore, these two-step protocols don't support rotating primary and low-cost view change (leader replacement), which are important features of many blockchain use cases. In this paper, we propose a protocol called VBFT which achieves consensus in just two communication steps without scarifying desirable features. In particular, VBFT tolerates $f = \\frac{n-1}{3}$ faults (which is the best possible), guarantees strong safety for honest primaries, and requires no trusted hardware. Moreover, VBFT supports primary rotation and low-cost view change, thereby improving prior art on multiple axes.", "field": "cs", "label": 0}
{"text": "Title: Rings Whose Clean and Nil-Clean Elements Have Some Clean-Like Properties\nAbstract: We define two types of rings, namely the so-called CSNC and NCUC that are those rings whose clean elements are strongly nil-clean, respectively, whose nil-clean elements are uniquely clean. Our results obtained in this paper somewhat expand these obtained by Calugareanu-Zhou in Mediterr. J. Math. (2023) and by Cui-Danchev-Jin in Publ. Math. Debrecen (2024), respectively.", "field": "math", "label": 0}
{"text": "Title: Runs in Sequences of Random Ordered Variables\nAbstract: We determine the distributions of lengths of runs in sequences of random elements from a total or partial order. In particular, we derive formulas for the expected value, variance, and probability generating function (PGF) of such lengths in the case of total orders (focusing on distributions with atoms). To do this, we define novel generating functions associated with a measure on an order. These generating functions behave nicely when splitting and combining measures on orders allowing us to solve the case of total orders.", "field": "math", "label": 0}
{"text": "Title: Inherently robust suboptimal MPC for autonomous racing with anytime feasible SQP\nAbstract: In recent years, the increasing need for high-performance controllers in applications like autonomous driving has motivated the development of optimization routines tailored to specific control problems. In this paper, we propose an efficient inexact model predictive control (MPC) strategy for autonomous miniature racing with inherent robustness properties. We rely on a feasible sequential quadratic programming (SQP) algorithm capable of generating feasible intermediate iterates such that the solver can be stopped after any number of iterations, without jeopardizing recursive feasibility. In this way, we provide a strategy that computes suboptimal and yet feasible solutions with a computational footprint that is much lower than state-of-the-art methods based on the computation of locally optimal solutions. Under suitable assumptions on the terminal set and on the controllability properties of the system, we can state that, for any sufficiently small disturbance affecting the system's dynamics, recursive feasibility can be guaranteed. We validate the effectiveness of the proposed strategy in simulation and by deploying it onto a physical experiment with autonomous miniature race cars. Both the simulation and experimental results demonstrate that, using the feasible SQP method, a feasible solution can be obtained with moderate additional computational effort compared to strategies that resort to early termination without providing a feasible solution. At the same time, the proposed method is significantly faster than the state-of-the-art solver Ipopt.", "field": "math", "label": 0}
{"text": "Title: Miscellaneous problems about packing and covering\nAbstract: In this paper we discuss various special problems on packing and covering. Among others we survey the problems and results concerning finite arrangements, Minkowskian, saturated, compact, and totally separable packings. We discuss shortest path problems and questions about stability of packings.", "field": "math", "label": 1}
{"text": "Title: Numerical solution of the Burgers' equation with high order splitting methods\nAbstract: In this work, high order splitting methods have been used for calculating the numerical solutions of the Burgers' equation in one space dimension with periodic and Dirichlet boundary conditions. However, splitting methods with real coefficients of order higher than two necessarily have negative coefficients and can not be used for time-irreversible systems, such as Burgers equations, due to the time-irreversibility of the Laplacian operator. Therefore, the splitting methods with complex coefficients and extrapolation methods with real and positive coefficients have been employed. If we consider the system as the perturbation of an exactly solvable problem(or can be easily approximated numerically), it is possible to employ highly efficient methods to approximate Burgers' equation. The numerical results show that the methods with complex time steps having one set of coefficients real and positive, say $a_i\\in\\mathbb{R}^+$ and $b_i\\in\\mathbb{C}^+$, and high order extrapolation methods derived from a lower order splitting method produce very accurate solutions of the Burgers' equation.", "field": "math", "label": 1}
{"text": "Title: Nonexistence of Exceptional 5-class Association Schemes with Two $Q$-polynomial Structures\nAbstract: In [H. Suzuki, Association schemes with multiple $Q$-polynomial structures, J. Algebraic Combin. 7 (1998) 181-196], Suzuki gave a classification of association schemes with multiple $Q$-polynomial structures, allowing for one exceptional case which has five classes. In this paper, we rule out the existence of this case. Hence Suzuki's theorem mirrors exactly the well-known counterpart for association schemes with multiple $P$-polynomial structures, a result due to Eiichi Bannai and Etsuko Bannai in 1980.", "field": "math", "label": 1}
{"text": "Title: On the classification of multiplicity-free Hamiltonian actions by regular proper symplectic groupoids\nAbstract: In this paper we study a natural generalization of symplectic toric manifolds in the context of regular Poisson manifolds of compact types. To be more precise, we consider a class of multiplicity-free Hamiltonian actions by regular proper symplectic groupoids that we call faithful. Given such a groupoid, we classify its faithful multiplicity-free Hamiltonian actions in terms of what we call Delzant subspaces of its orbit space -- certain `suborbifolds with corners' satisfying the Delzant condition relative to the integral affine orbifold structure of the orbit space. This encompasses both the classification of symplectic toric manifolds (due to Delzant) in terms of Delzant polytopes and the classification of proper Lagrangian fibrations over an integral affine base manifold (due to Duistermaat) in terms of a sheaf cohomology group. Each Delzant subspace comes with an orbifold version of this cohomology, the degree one part of which classifies faithful multiplicity-free Hamiltonian actions with momentum map image equal to the Delzant subspace, provided there exists such an action. The obstruction to existence is encoded by a degree two class in this cohomology: the Lagrangian Dixmier-Douady class. In addition to the above, we introduce another invariant, which leads to a variation of our classification result involving only classical sheaf cohomology and the group cohomology of certain modules for the isotropy groups of the groupoid.", "field": "math", "label": 0}
{"text": "Title: Modification method for single-stage object detectors that allows to exploit the temporal behaviour of a scene to improve detection accuracy\nAbstract: A simple modification method for single-stage generic object detection neural networks, such as YOLO and SSD, is proposed, which allows for improving the detection accuracy on video data by exploiting the temporal behavior of the scene in the detection pipeline. It is shown that, using this method, the detection accuracy of the base network can be considerably improved, especially for occluded and hidden objects. It is shown that a modified network is more prone to detect hidden objects with more confidence than an unmodified one. A weakly supervised training method is proposed, which allows for training a modified network without requiring any additional annotated data.", "field": "cs", "label": 1}
{"text": "Title: Variational Bandwidth Auto-encoder for Hybrid Recommender Systems\nAbstract: Hybrid recommendations have recently attracted a lot of attention where user features are utilized as auxiliary information to address the sparsity problem caused by insufficient user-item interactions. However, extracted user features generally contain rich multimodal information, and most of them are irrelevant to the recommendation purpose. Therefore, excessive reliance on these features will make the model overfit on noise and difficult to generalize. In this article, we propose a variational bandwidth auto-encoder (VBAE) for recommendations, aiming to address the sparsity and noise problems simultaneously. VBAE first encodes user collaborative and feature information into Gaussian latent variables via deep neural networks to capture non-linear user similarities. Moreover, by considering the fusion of collaborative and feature variables as a virtual communication channel from an information-theoretic perspective, we introduce a user-dependent channel to dynamically control the information allowed to be accessed from the feature embeddings. A quantum-inspired uncertainty measurement of the hidden rating embeddings is proposed accordingly to infer the channel bandwidth by disentangling the uncertainty information in the ratings from the semantic information. Through this mechanism, VBAE incorporates adequate auxiliary information from user features if collaborative information is insufficient, while avoiding excessive reliance on noisy user features to improve its generalization ability to new users. Extensive experiments conducted on three real-world datasets demonstrate the effectiveness of the proposed method. Codes and datasets are released at https://github.com/yaochenzhu/vbae.", "field": "cs", "label": 1}
{"text": "Title: Classifying Words with 3-sort Automata\nAbstract: Grammatical inference consists in learning a language or a grammar from data. In this paper, we consider a number of models for inferring a non-deterministic finite automaton (NFA) with 3 sorts of states, that must accept some words, and reject some other words from a given sample. We then propose a transformation from this 3-sort NFA into weighted-frequency and probabilistic NFA, and we apply the latter to a classification task. The experimental evaluation of our approach shows that the probabilistic NFAs can be successfully applied for classification tasks on both real-life and superficial benchmark data sets.", "field": "cs", "label": 0}
{"text": "Title: Approximate Equilibria in Generalized Colonel Blotto and Generalized Lottery Blotto Games\nAbstract: In the Colonel Blotto game, two players with a fixed budget simultaneously allocate their resources across n battlefields to maximize the aggregate value gained from the battlefields where they have the higher allocation. Despite its long-standing history and important applications, the Colonel Blotto game still lacks a complete Nash equilibrium characterization in its most general form where players are asymmetric and battlefields' values are heterogeneous across battlefields and different between the two players---this is called the Generalized Colonel Blotto game. In this work, we propose a simply-constructed class of strategies---the independently uniform strategies---and we prove that they are approximate equilibria of the Generalized Colonel Blotto game; moreover, we characterize the approximation error according to the game's parameters. We also consider an extension called the Generalized Lottery Blotto game, with stochastic winner-determination rules allowing more flexibility in modeling practical contests. We prove that the proposed strategies are also approximate equilibria of the Generalized Lottery Blotto game.", "field": "cs", "label": 1}
{"text": "Title: New results in vertex sedentariness\nAbstract: A vertex in a graph is said to be sedentary if a quantum state assigned on that vertex tends to stay on that vertex. Under mild conditions, we show that the direct product and join operations preserve vertex sedentariness. We also completely characterize sedentariness in blow-up graphs. These results allow us to construct new infinite families of graphs with sedentary vertices. We prove that a vertex with a twin is either sedentary or admits pretty good state transfer. Moreover, we give a complete characterization of twin vertices that are sedentary, and provide sharp bounds on their sedentariness. As an application, we determine the conditions in which perfect state transfer, pretty good state transfer and sedentariness occur in complete bipartite graphs and threshold graphs of any order.", "field": "math", "label": 0}
{"text": "Title: A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, the decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group\nAbstract: The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to the taking of the reduced Palm measure at infinity for our decomposing measures. The proof proceeds by finite-dimensional approximation of our measures by orthogonal polynomial ensembles. The key remark is that the taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems.", "field": "math", "label": 0}
{"text": "Title: A Look at the Time Delays in CVSS Vulnerability Scoring\nAbstract: This empirical paper examines the time delays that occur between the publication of Common Vulnerabilities and Exposures (CVEs) in the National Vulnerability Database (NVD) and the Common Vulnerability Scoring System (CVSS) information attached to published CVEs. According to the empirical results based on regularized regression analysis of over eighty thousand archived vulnerabilities, (i) the CVSS content does not statistically influence the time delays, which, however, (ii) are strongly affected by a decreasing annual trend. In addition to these results, the paper contributes to the empirical research tradition of software vulnerabilities by a couple of insights on misuses of statistical methodology.", "field": "cs", "label": 1}
{"text": "Title: A Note on Nesting in Dyadic Deontic Logic\nAbstract: The paper reports on some results concerning Aqvist's dyadic logic known as system G, which is one of the most influential logics for reasoning with dyadic obligations (\"it ought to be the case that ... if it is the case that ...\"). Although this logic has been known in the literature for a while, many of its properties still await in-depth consideration. In this short paper we show: that any formula in system G including nested modal operators is equivalent to some formula with no nesting; that the universal modality introduced by Aqvist in the first presentation of the system is definable in terms of the deontic modality.", "field": "cs", "label": 1}
{"text": "Title: ShapeAug: Occlusion Augmentation for Event Camera Data\nAbstract: Recently, Dynamic Vision Sensors (DVSs) sparked a lot of interest due to their inherent advantages over conventional RGB cameras. These advantages include a low latency, a high dynamic range and a low energy consumption. Nevertheless, the processing of DVS data using Deep Learning (DL) methods remains a challenge, particularly since the availability of event training data is still limited. This leads to a need for event data augmentation techniques in order to improve accuracy as well as to avoid over-fitting on the training data. Another challenge especially in real world automotive applications is occlusion, meaning one object is hindering the view onto the object behind it. In this paper, we present a novel event data augmentation approach, which addresses this problem by introducing synthetic events for randomly moving objects in a scene. We test our method on multiple DVS classification datasets, resulting in an relative improvement of up to 6.5 % in top1-accuracy. Moreover, we apply our augmentation technique on the real world Gen1 Automotive Event Dataset for object detection, where we especially improve the detection of pedestrians by up to 5 %.", "field": "cs", "label": 0}
{"text": "Title: Analyzing Misinformation Claims During the 2022 Brazilian General Election on WhatsApp, Twitter, and Kwai\nAbstract: This study analyzes misinformation from WhatsApp, Twitter, and Kwai during the 2022 Brazilian general election. Given the democratic importance of accurate information during elections, multiple fact-checking organizations collaborated to identify and respond to misinformation via WhatsApp tiplines and power a fact-checking feature within a chatbot operated by Brazil's election authority, the TSE. WhatsApp is installed on over 99% of smartphones in Brazil, and the TSE chatbot was used by millions of citizens in the run-up to the elections. During the same period, we collected social media data from Twitter (now X) and Kwai (a popular video-sharing app similar to TikTok). Using the WhatsApp, Kwai, and Twitter data along with fact-checks from three Brazilian fact-checking organizations, we find unique claims on each platform. Even when the same claims are present on different platforms, they often differ in format, detail, length, or other characteristics. Our research highlights the limitations of current claim matching algorithms to match claims across platforms with such differences and identifies areas for further algorithmic development. Finally, we perform a descriptive analysis examining the formats (image, video, audio, text) and content themes of popular misinformation claims.", "field": "cs", "label": 0}
{"text": "Title: Symmetry Breaking in Symmetric Tensor Decomposition\nAbstract: In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by standard gradient based methods are \\emph{symmetry breaking} with respect to the target tensor. The phenomena, seen for different choices of target tensors and norms, make possible the use of recently developed analytic and algebraic tools for studying nonconvex optimization landscapes exhibiting symmetry breaking phenomena of similar nature.", "field": "math", "label": 1}
{"text": "Title: Towards a Solution to Bongard Problems: A Causal Approach\nAbstract: Even though AI has advanced rapidly in recent years displaying success in solving highly complex problems, the class of Bongard Problems (BPs) yet remain largely unsolved by modern ML techniques. In this paper, we propose a new approach in an attempt to not only solve BPs but also extract meaning out of learned representations. This includes the reformulation of the classical BP into a reinforcement learning (RL) setting which will allow the model to gain access to counterfactuals to guide its decisions but also explain its decisions. Since learning meaningful representations in BPs is an essential sub-problem, we further make use of contrastive learning for the extraction of low level features from pixel data. Several experiments have been conducted for analyzing the general BP-RL setup, feature extraction methods and using the best combination for the feature space analysis and its interpretation.", "field": "cs", "label": 1}
{"text": "Title: Nilpotent dessins: Decomposition theorem and classification of the abelian dessins\nAbstract: A map is a 2-cell decomposition of an orientable closed surface. A dessin is a bipartite map with a fixed colouring of vertices. A dessin is regular if its group of colour- and orientation-preserving automorphisms acts transitively on the edges, and a regular dessin is symmetric if it admits an additional external symmetry transposing the vertex colours. Regular dessins with nilpotent automorphism groups are investigated. We show that each such dessin is a parallel product of regular dessins whose automorphism groups are the Sylow subgroups. Regular and symmetric dessins with abelian automorphism groups are classified and enumerated.", "field": "math", "label": 1}
{"text": "Title: Strauss- and Lions-type results for a class of Orlicz-Sobolev spaces and applications\nAbstract: The main goal this work is to prove two results like Strauss and Lions for Orlicz-Sobolev spaces. After, we use these results for study the existence of solutions for a class of quasilinear problems in $\\mathbb{R}^{N}$.", "field": "math", "label": 1}
{"text": "Title: Planar Para Algebras, Reflection Positivity\nAbstract: We define a planar para algebra, which arises naturally from combining planar algebras with the idea of $\\mathbb{Z}_{N}$ para symmetry in physics. A subfactor planar para algebra is a Hilbert space representation of planar tangles with parafermionic defects, that are invariant under para isotopy. For each $\\mathbb{Z}_{N}$, we construct a family of subfactor planar para algebras which play the role of Temperley-Lieb-Jones planar algebras. The first example in this family is the parafermion planar para algebra (PAPPA). Based on this example, we introduce parafermion Pauli matrices, quaternion relations, and braided relations for parafermion algebras which one can use in the study of quantum information. An important ingredient in planar para algebra theory is the string Fourier transform (SFT), that we use on the matrix algebra generated by the Pauli matrices. Two different reflections play an important role in the theory of planar para algebras. One is the adjoint operator; the other is the modular conjugation in Tomita-Takesaki theory. We use the latter one to define the double algebra and to introduce reflection positivity. We give a new and geometric proof of reflection positivity, by relating the two reflections through the string Fourier transform.", "field": "math", "label": 1}
{"text": "Title: Explore Human Parsing Modality for Action Recognition\nAbstract: Multimodal-based action recognition methods have achieved high success using pose and RGB modality. However, skeletons sequences lack appearance depiction and RGB images suffer irrelevant noise due to modality limitations. To address this, we introduce human parsing feature map as a novel modality, since it can selectively retain effective semantic features of the body parts, while filtering out most irrelevant noise. We propose a new dual-branch framework called Ensemble Human Parsing and Pose Network (EPP-Net), which is the first to leverage both skeletons and human parsing modalities for action recognition. The first human pose branch feeds robust skeletons in graph convolutional network to model pose features, while the second human parsing branch also leverages depictive parsing feature maps to model parsing festures via convolutional backbones. The two high-level features will be effectively combined through a late fusion strategy for better action recognition. Extensive experiments on NTU RGB+D and NTU RGB+D 120 benchmarks consistently verify the effectiveness of our proposed EPP-Net, which outperforms the existing action recognition methods. Our code is available at: https://github.com/liujf69/EPP-Net-Action.", "field": "cs", "label": 0}
{"text": "Title: Propagation of Chaos for Mean Field Interacting Particle System with Multiplicative Noise\nAbstract: In this paper, the quantitative propagation of chaos for mean field interacting particle system with multiplicative noise in $L^2$-Wasserstein distance is derived. When the diffusion is distribution free, the quantitative propagation of chaos in relative entropy as well as total variation distance is also obtained, where the initial distribution of mean field interacting particles is allowed to be singular with that of the limit equation. Furthermore, a general result on the long time quantitative propagation of chaos in relative entropy as well as in $L^2$-Wasserstein distance is provided and is applied in (path dependent) mean field interacting particle system as well as stochastic Hamiltonian system under dissipative condition.", "field": "math", "label": 0}
{"text": "Title: General Berndt-Type Integrals and Series Associated with Jacobi Elliptic Functions\nAbstract: n this paper, we prove two structural theorems on the general Berndt-type integrals with the denominator having arbitrary positive degrees by contour integrations involving hyperbolic and trigonometric functions, and hyperbolic sums associated with Jacobi elliptic functions. We first establish explicit relations between these integrals and four classes of hyperbolic sums. Then, using our previous results on hyperbolic series and applying the matrix method from linear algebra, we compute explicitly several general hyperbolic sums and their higher derivatives. These enable us to express two families of general Berndt-type integrals as polynomials in $\\Gamma^4(1/4)$ and $\\pi^{-1}$ with rational coefficients, where $\\Gamma$ is the Euler gamma function. At the end of the paper, we provide some conjectures of general Berndt-type integrals.", "field": "math", "label": 0}
{"text": "Title: Cofinal elements and fractional Dehn twist coefficients\nAbstract: We show that for a surface $S$ with positive genus and one boundary component, the mapping class of a Dehn twist along a curve parallel to the boundary is cofinal in every left ordering of the mapping class group $\\operatorname{Mod}(S)$. We apply this result to show that one of the usual definitions of the fractional Dehn twist coefficient -- via translation numbers of a particular action of $\\operatorname{Mod}(S)$ on $\\mathbb{R}$ -- is in fact independent of the underlying action when $S$ has genus larger than one. As an algebraic counterpart to this, we provide a formula that recovers the fractional Dehn twist coefficient of a homeomorphism of $S$ from an arbitrary left ordering of $\\operatorname{Mod}(S)$.", "field": "math", "label": 1}
{"text": "Title: Radial Laplacian on rotation groups\nAbstract: The Laplacian on the rotation group is invariant by conjugation. Hence, it maps class functions to class functions. A maximal torus consists of block diagonal matrices whose blocks are planar rotations. Class functions are determined by their values of this maximal torus. Hence, the Laplacian induces a second order operator on the maximal torus called the radial Laplacian. In this paper, we derive the expression of the radial Laplacian. Then, we use it to find the eigenvalues of the Laplacian, using that characters are class functions whose expressions are given by the Weyl character formula. Although this material is familiar to Lie-group experts, we gather it here in a synthetic and accessible way which may be useful to non experts who need to work with these concepts.", "field": "math", "label": 1}
{"text": "Title: Directed polymers in a random environment: a review of the phase transitions\nAbstract: The model of directed polymer in a random environment is a fundamental model of interaction between a simple random walk and ambient disorder. This interaction gives rise to complex phenomena and transitions from a central limit theory to novel statistical behaviours. Despite its intense study, there are still many aspects and phases which have not yet been identified. In this review we focus on the current status of our understanding of the transition between weak and strong disorder phases, give an account of some of the methods that the study of the model has motivated and highlight some open questions.", "field": "math", "label": 0}
{"text": "Title: A Feynman-Kac type formula for a fixed delay CIR model\nAbstract: Stochastic delay differential equations (SDDE's) have been used for financial modeling. In this article, we study a SDDE obtained by the equation of a CIR process, with an additional fixed delay term in drift; in particular, we prove that there exists a unique strong solution (positive and integrable) which we call fixed delay CIR process. Moreover, for the fixed delay CIR process, we derive a Feynman-Kac type formula, leading to a generalized exponential-affine formula, which is used to determine a bond pricing formula when the interest rate follows the delay's equation. It turns out that, for each maturity time T, the instantaneous forward rate is an affine function (with time dependent coefficients) of the rate process and of an auxiliary process (also depending on T). The coefficients satisfy a system of deterministic delay differential equations.", "field": "math", "label": 1}
{"text": "Title: A note on Jones polynomial and cosmetic surgery\nAbstract: We show that two Dehn surgeries on a knot $K$ never yield manifolds that are homeomorphic as oriented manifolds if $V_K''(1)\\neq 0$ or $V_K'''(1)\\neq 0$. As an application, we verify the cosmetic surgery conjecture for all knots with no more than $11$ crossings except for three $10$-crossing knots and five $11$-crossing knots. We also compute the finite type invariant of order $3$ for two-bridge knots and Whitehead doubles, from which we prove several nonexistence results of purely cosmetic surgery.", "field": "math", "label": 1}
{"text": "Title: Probabilistic Galois Theory in Function Fields\nAbstract: We study the irreducibility and Galois group of random polynomials over function fields. We prove that a random polynomial $f=y^n+\\sum_{i=0}^{n-1}a_i(x)y^i\\in\\mathbb F_q[x][y]$ with i.i.d coefficients $a_i$ taking values in the set $\\{a(x)\\in\\mathbb{F}_q[x]: \\mathrm{deg}\\, a\\leq d\\}$ with uniform probability, is irreducible with probability tending to $1-\\frac{1}{q^d}$ as $n\\to\\infty$, where $d$ and $q$ are fixed. We also prove that with the same probability, the Galois group of this random polynomial contains the alternating group $A_n$. Moreover, we prove that if we assume a version of the polynomial Chowla conjecture over $\\mathbb{F}_q[x]$, then the Galois group of this polynomial is actually equal to the symmetric group $S_n$ with probability tending to $1-\\frac{1}{q^d}$. We also study the other possible Galois groups occurring with positive limit probability. Finally, we study the same problems with $n$ fixed and $d\\to\\infty$.", "field": "math", "label": 0}
{"text": "Title: CPG graphs: Some structural and hardness results\nAbstract: In this paper we continue the systematic study of Contact graphs of Paths on a Grid (CPG graphs) initiated in [Deniz et al., 2018]. A CPG graph is a graph for which there exists a collection of pairwise interiorly disjoint paths on a grid in one-to-one correspondence with its vertex set such that two vertices are adjacent if and only if the corresponding paths touch at a grid-point. If every such path has at most $k$ bends for some $k \\geq 0$, the graph is said to be $B_k$-CPG. We first show that, for any $k \\geq 0$, the class of $B_k$-CPG graphs is strictly contained in the class of $B_{k+1}$-CPG graphs even within the class of planar graphs, thus implying that there exists no $k \\geq 0$ such that every planar CPG graph is $B_k$-CPG. The main result of the paper is that recognizing CPG graphs and $B_k$-CPG graphs with $k \\geq 1$ is $\\mathsf{NP}$-complete. Moreover, we show that the same remains true even within the class of planar graphs in the case $k \\geq 3$. We then consider several graph problems restricted to CPG graphs and show, in particular, that Independent Set and Clique Cover remain $\\mathsf{NP}$-hard for $B_0$-CPG graphs. Finally, we consider the related classes $B_k$-EPG of edge-intersection graphs of paths with at most $k$ bends on a grid. Although it is possible to optimally color a $B_0$-EPG graph in polynomial time, as this class coincides with that of interval graphs, we show that, in contrast, 3-Colorability is $\\mathsf{NP}$-complete for $B_1$-EPG graphs.", "field": "cs", "label": 1}
{"text": "Title: Early Record of Divisibility and Primality\nAbstract: We provide textual evidence on divisibility and primality in the ancient Vedic texts of India. Concern with divisibility becomes clear from the listing of all the fifteen pairs of divisors of the number 720. The total number of pairs of divisors of 10,800 is also given. The motivation behind finding the divisors was the theory that the number of divisors of a certain periodic process is related to the count associated with some other periodic process. For example, 720 (days and nights of the year) has 15 pairs of divisors, and this was related to the 15 days of the waxing and waning of the moon. Numbers that have no divisors appeared to have been used to symbolize the \"transcendent\" that is beyond periodicity and change.", "field": "math", "label": 1}
{"text": "Title: Essential dimension via prismatic cohomology\nAbstract: For $X$ a smooth, proper complex variety such that $h^{0,i}_X \\neq 0,$ we show that for almost all primes $p,$ the restriction of the mod $p$ cohomology $H^i(X,\\mathbb{F}_p)$ to any Zariski open is nonzero. The proof uses the prismatic cohomology of Bhatt-Scholze. We use this result to obtain lower bounds on the $p$-essential dimension of covers of complex varieties. For example, we prove the $p$-incompressibility of the mod $p$ homology cover of an abelian variety, confirming a conjecture of Brosnan for sufficiently large $p.$ By combining these techniques with the theory of toroidal compactifications of Shimura varieties, we show that for any Hermitian symmetric domain $X,$ there exist $p$-congruence covers that are $p$-incompressible.", "field": "math", "label": 1}
{"text": "Title: Involutions under Bruhat order and labeled Motzkin Paths\nAbstract: In this note, we introduce a statistic on Motzkin paths that describes the rank generating function of Bruhat order for involutions. Our proof relies on a bijection introduced by Philippe Biane from permutations to certain labeled Motzkin paths and a recently introduced interpretation of this rank generating function in terms of visible inversions. By restricting our identity to fixed-point-free (FPF) involutions, we recover an identity due to Louis Billera, Lionel Levine and Karola M\\'esz\\'aros with a previous bijective proof by Matthew Watson. Our work sheds new light on the Ethiopian dinner game.", "field": "math", "label": 1}
{"text": "Title: Virtual critical regularity of mapping class group actions on the circle\nAbstract: We show that if $G_1$ and $G_2$ are non-solvable groups, then no $C^{1,\\tau}$ action of $(G_1\\times G_2)*\\mathbb{Z}$ on $S^1$ is faithful for $\\tau>0$. As a corollary, if $S$ is an orientable surface of complexity at least three then the critical regularity of an arbitrary finite index subgroup of the mapping class group $\\mathrm{Mod}(S)$ with respect to the circle is at most one, thus strengthening a result of the first two authors with Baik.", "field": "math", "label": 1}
{"text": "Title: Error Approximation and Bias Correction in Dynamic Problems using a Recurrent Neural Network/Finite Element Hybrid Model\nAbstract: This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to perform bias correction of the low-fidelity models. The hybrid model uses FE basis functions as a spatial basis and RNNs for the approximation of the time dependencies of the FE basis' degrees of freedom. The training data sets consist of sparse, non-uniformly sampled snapshots of the discrepancy function, pre-computed from trajectory data of low- and high-fidelity dynamic FE models. To account for data sparsity and prevent overfitting, data upsampling and local weighting factors are employed, to instigate a trade-off between physically conforming model behavior and neural network regression. The proposed hybrid modeling methodology is showcased in three highly non-trivial engineering test-cases, all featuring transient FE models, namely, heat diffusion out of a heat sink, eddy-currents in a quadrupole magnet, and sound wave propagation in a cavity. The results show that the proposed hybrid model is capable of approximating model discrepancies to a high degree of accuracy and accordingly correct low-fidelity models.", "field": "cs", "label": 0}
{"text": "Title: Human-in-the-Loop Policy Optimization for Preference-Based Multi-Objective Reinforcement Learning\nAbstract: Multi-objective reinforcement learning (MORL) aims to find a set of high-performing and diverse policies that address trade-offs between multiple conflicting objectives. However, in practice, decision makers (DMs) often deploy only one or a limited number of trade-off policies. Providing too many diversified trade-off policies to the DM not only significantly increases their workload but also introduces noise in multi-criterion decision-making. With this in mind, we propose a human-in-the-loop policy optimization framework for preference-based MORL that interactively identifies policies of interest. Our method proactively learns the DM's implicit preference information without requiring any a priori knowledge, which is often unavailable in real-world black-box decision scenarios. The learned preference information is used to progressively guide policy optimization towards policies of interest. We evaluate our approach against three conventional MORL algorithms that do not consider preference information and four state-of-the-art preference-based MORL algorithms on two MORL environments for robot control and smart grid management. Experimental results fully demonstrate the effectiveness of our proposed method in comparison to the other peer algorithms.", "field": "cs", "label": 0}
{"text": "Title: The compressible Euler equations in a physical vacuum: a comprehensive Eulerian approach\nAbstract: This article is concerned with the local well-posedness problem for the compressible Euler equations in gas dynamics. For this system we consider the free boundary problem which corresponds to a physical vacuum. Despite the clear physical interest in this system, the prior work on this problemis limited to Lagrangian coordinates, in high regularity spaces. Instead, the objective of the present work is to provide a new, fully Eulerian approach to this problem, which provides a complete, Hadamard style well-posedness theory for this problem in low regularity Sobolev spaces. In particular we give new proofs for both existence, uniqueness, and continuous dependence on the data with sharp, scale invariant energy estimates, and continuation criterion.", "field": "math", "label": 1}
{"text": "Title: Fractional hypergraph isomorphism and fractional invariants\nAbstract: Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like connectivity, clique and independence numbers, chromatic number, vertex and edge cover numbers, matching number, domination and total domination numbers. In this work, we extend the concept of fractional graph isomorphism to hypergraphs, and give an alternative characterization, analogous to one of those that are known for graphs. With this new concept we prove that the fractional packing, covering, matching and transversal numbers on hypergraphs are invariant under fractional hypergraph isomorphism. As a consequence, fractional matching, vertex and edge cover, independence, domination and total domination numbers are invariant under fractional graph isomorphism. This is not the case of fractional chromatic, clique, and clique cover numbers. In this way, most of the classical fractional parameters are classified with respect to their invariance under fractional graph isomorphism.", "field": "math", "label": 1}
{"text": "Title: On the heteroclinic connection problem for multi-well gradient systems\nAbstract: We revisit the existence problem of heteroclinic connections in $\\mathbb{R}^N$ associated with Hamiltonian systems involving potentials $W:\\mathbb{R}^N\\to \\mathbb{R}$ having several global minima. Under very mild assumptions on $W$ we present a simple variational approach to first find geodesics minimizing length of curves joining any two of the potential wells, where length is computed with respect to a degenerate metric having conformal factor $\\sqrt{W}.$ Then we show that when such a minimizing geodesic avoids passing through other wells of the potential at intermediate times, it gives rise to a heteroclinic connection between the two wells. This work improves upon the approach of P.Sternberg in $\\texttt{Vector-valued local minimizers of nonconvex}$ $\\texttt{variational problems}$, and represents a more geometric alternative to the approaches for finding such connections described, for example, by N.D. Alikakos and G.Fusco in $\\texttt{On the connection problem for potentials with}$ $\\texttt{several global minima}$, by S.V. Bolotin in $\\texttt{Libration motions of natural dynamical systems}$, by J. Byeon, P. Montecchiari, and P. Rabinowitz in $\\texttt{A double well potential}$ $\\texttt{system}$, and by P. Rabinowitz in $\\texttt{Homoclinic and heteroclinic orbits for a class of Hamiltonian}$ $\\texttt{systems}$.", "field": "math", "label": 1}
{"text": "Title: Nested homotopy models of finite metric spaces and their spectral homology\nAbstract: For a real $r\\geq 0,$ we consider the notion of $r$-homotopy equivalence in the category quasimetric spaces, which includes metric spaces and directed graphs. We show that for a finite quasimetric space $X$ there is a unique (up to isometry) $r$-homotopy equivalent quasimetric space of the minimal possible cardinality. It is called $r$-minimal model of $X$. We use this to construct a decomposition of the magnitude-path spectral sequence of a digraph into a direct sum of spectral sequences with certain properties. We also construct an $r$-homotopy invariant ${\\rm SH}^r_{n,I}(X)$ of a quasimetric space $X,$ called spectral homology, that generalises many other invariants: the pages of the magnitude-path spectral sequence, including path homology, magnitude homology, blurred magnitude homology and reachability homology.", "field": "math", "label": 0}
{"text": "Title: Group theoretic approach to cyclic cubic fields\nAbstract: Let (k1,k2,k3,k4) be a quartet of cyclic cubic number fields sharing a common conductor c=pqr divisible by exactly three prime(power)s p,q,r. For those components k of the quartet whose 3-class group Cl(3,k) = Z/3Z x Z/3Z is elementary bicyclic, the automorphism group M = Gal(F(3,2,k)/k) of the maximal metabelian unramified 3-extension of k is determined by conditions for cubic residue symbols between p,q,r and for ambiguous principal ideals in subfields of the common absolute 3-genus field k* of k1,k2,k3,k4. With the aid of the relation rank d2(M), it is decided whether M coincides with the Galois group G = Gal(F(3,infinity,k)/k) of the maximal unramified pro-3-extension of k.", "field": "math", "label": 0}
{"text": "Title: Reciprocity between partitions and compositions\nAbstract: In this paper, we extend the work of Andrews, Beck and Hopkins by considering partitions and compositions with bounded gaps between each pair of consecutive parts. We show that both their generating functions and two matrices determined by them satisfy certain reciprocal relations.", "field": "math", "label": 1}
{"text": "Title: The dimension of ergodic random sequences\nAbstract: Let \\mu be a computable ergodic shift-invariant measure over the Cantor space. Providing a constructive proof of Shannon-McMillan-Breiman theorem, V'yugin proved that if a sequence x is Martin-L\\\"of random w.r.t. \\mu then the strong effective dimension Dim(x) of x equals the entropy of \\mu. Whether its effective dimension dim(x) also equals the entropy was left as an problem question. In this paper we settle this problem, providing a positive answer. A key step in the proof consists in extending recent results on Birkhoff's ergodic theorem for Martin-L\\\"of random sequences.", "field": "cs", "label": 1}
{"text": "Title: Implications of some mass-capacity inequalities\nAbstract: Applying a family of mass-capacity related inequalities proved in \\cite{M22}, we obtain sufficient conditions that imply the nonnegativity as well as positive lower bounds of the mass, on a class of manifolds with nonnegative scalar curvature with or without a singularity.", "field": "math", "label": 0}
{"text": "Title: Asymptotic Stability for Relativistic Vlasov-Maxwell-Landau System in Bounded Domain\nAbstract: The control of plasma-wall interaction is one of the keys in a fusion device from both physical and mathematical standpoints. A classical perfect conducting boundary causes the Lorentz force to penetrate inside the domain, which may lead to grazing set singularity in the phase space, preventing the construction of global dynamics for PDEs in any kinetic plasma models. We establish the first global asymptotic stability for the relativistic Vlasov-Maxwell-Landau system for describing a collisional plasma specularly reflected at a perfect conducting boundary.", "field": "math", "label": 0}
{"text": "Title: Edge ideals of some edge-weighted graphs\nAbstract: This paper presents exact formulas for the regularity and depth of powers of edge ideals of an edge-weighted star graph. Additionally, we provide exact formulas for the regularity of powers of the edge ideal of an edge-weighted integrally closed path, as well as lower bounds on the depth of powers of such an edge ideal.", "field": "math", "label": 0}
{"text": "Title: Integer-Forcing Message Recovering in Interference Channels\nAbstract: In this paper, we propose a scheme referred to as integer-forcing message recovering (IFMR) to enable receivers to recover their desirable messages in interference channels. Compared to the state-of-the- art integer-forcing linear receiver (IFLR), our proposed IFMR approach needs to decode considerably less number of messages. In our method, each receiver recovers independent linear integer combinations of the desirable messages each from two independent equations. We propose an efficient algorithm to sequentially find the equations and integer combinations with maximum rates. We evaluate the performance of our scheme and compare the results with the minimum mean-square error (MMSE) and zero-forcing (ZF), as well as the IFLR schemes. The results indicate that our IFMR scheme outperforms the MMSE and ZF schemes, in terms of achievable rate, considerably. Also, compared to IFLR, the IFMR scheme achieves slightly less rates in moderate signal-to-noise ratios, with significantly less implementation complexity.", "field": "cs", "label": 1}
{"text": "Title: Linked partition ideals, directed graphs and $q$-multi-summations\nAbstract: Finding an Andrews--Gordon type generating function identity for a linked partition ideal is difficult in most cases. In this paper, we will handle this problem in the setting of graph theory. With the generating function of directed graphs with an ``empty'' vertex, we then turn our attention to a $q$-difference system. This $q$-difference system eventually yields a factorization problem of a special type of column functional vectors involving $q$-multi-summations. Finally, using a recurrence relation satisfied by certain $q$-multi-summations, we are able to provide non-computer-assisted proofs of some Andrews--Gordon type generating function identities. These proofs also have an interesting connection with binary trees.", "field": "math", "label": 1}
{"text": "Title: Distributed Compute-and-Forward Based Relaying Strategies in Multi-User Multi-Relay Networks\nAbstract: In this paper, we propose different practical distributed schemes to solve the rank failure problem in the compute and forward (CMF)-based multi-user multi-relay networks without central coordinator, in which the relays have no prior information about each other. First, a new relaying strategy based on CMF, named incremental compute-and-forward (ICMF), is proposed that performs quite well in terms of the outage probability. We show that the distributed ICMF scheme can even outperform the achievable rate of centralized optimal CMF in strong enough inter relay links, with much less complexity. Then, as the second scheme, amplify-forward and compute (AFC) is introduced in which the equations are recovered in the destination rather than in the relays. Finally, ICMF and AFC schemes are combined to present hybrid compute-amplify and forward (HCAF) relaying scheme, which takes advantages of both ICMF, and AFC and improves the performance of the ICMF considerably. We evaluate the performance of the proposed strategies in terms of the outage probability and compare the results with those of the conventional CMF strategy, the Decode and Forward (DF) strategy, and also the centralized optimal CMF. The results indicate the substantial superiority of the proposed schemes compared with the conventional schemes, specially for high number of users and relays.", "field": "cs", "label": 1}
{"text": "Title: Handling Collocations in Hierarchical Latent Tree Analysis for Topic Modeling\nAbstract: Topic modeling has been one of the most active research areas in machine learning in recent years. Hierarchical latent tree analysis (HLTA) has been recently proposed for hierarchical topic modeling and has shown superior performance over state-of-the-art methods. However, the models used in HLTA have a tree structure and cannot represent the different meanings of multiword expressions sharing the same word appropriately. Therefore, we propose a method for extracting and selecting collocations as a preprocessing step for HLTA. The selected collocations are replaced with single tokens in the bag-of-words model before running HLTA. Our empirical evaluation shows that the proposed method led to better performance of HLTA on three of the four data sets tested.", "field": "cs", "label": 1}
{"text": "Title: Enriched Annotations for Tumor Attribute Classification from Pathology Reports with Limited Labeled Data\nAbstract: Precision medicine has the potential to revolutionize healthcare, but much of the data for patients is locked away in unstructured free-text, limiting research and delivery of effective personalized treatments. Generating large annotated datasets for information extraction from clinical notes is often challenging and expensive due to the high level of expertise needed for high quality annotations. To enable natural language processing for small dataset sizes, we develop a novel enriched hierarchical annotation scheme and algorithm, Supervised Line Attention (SLA), and apply this algorithm to predicting categorical tumor attributes from kidney and colon cancer pathology reports from the University of California San Francisco (UCSF). Whereas previous work only annotated document level labels, we in addition ask the annotators to enrich the traditional label by asking them to also highlight the relevant line or potentially lines for the final label, which leads to a 20% increase of annotation time required per document. With the enriched annotations, we develop a simple and interpretable machine learning algorithm that first predicts the relevant lines in the document and then predicts the tumor attribute. Our results show across the small dataset sizes of 32, 64, 128, and 186 labeled documents per cancer, SLA only requires half the number of labeled documents as state-of-the-art methods to achieve similar or better micro-f1 and macro-f1 scores for the vast majority of comparisons that we made. Accounting for the increased annotation time, this leads to a 40% reduction in total annotation time over the state of the art.", "field": "cs", "label": 1}
{"text": "Title: Solving Fokker-Planck equations using the zeros of Fokker-Planck operators and the Feynman-Kac formula\nAbstract: First we show that physics-informed neural networks are not suitable for a large class of parabolic partial differential equations including the Fokker-Planck equation. Then we devise an algorithm to compute solutions of the Fokker-Planck equation using the zeros of Fokker-Planck operator and the Feynman-Kac formula. The resulting algorithm is mesh-free, highly parallelizable and able to compute solutions pointwise, thus mitigating the curse of dimensionality in a practical sense. We analyze various nuances of this algorithm that are determined by the drift term in the Fokker-Planck equation. We work with problems ranging in dimensions from 2 to 10. We demonstrate that this algorithm requires orders of magnitude fewer trajectories for each point in space when compared to Monte-Carlo. We also prove that under suitable conditions the error that is caused by letting some trajectories (associated with the Feynman-Kac expectation) escape our domain of knowledge is proportional to the fraction of trajectories that escape.", "field": "math", "label": 0}
{"text": "Title: On the uniqueness and computation of commuting extensions\nAbstract: A tuple (Z_1,...,Z_p) of matrices of size r is said to be a commuting extension of a tuple (A_1,...,A_p) of matrices of size n <r if the Z_i pairwise commute and each A_i sits in the upper left corner of a block decomposition of Z_i. This notion was discovered and rediscovered in several contexts including algebraic complexity theory (in Strassen's work on tensor rank), in numerical analysis for the construction of cubature formulas and in quantum mechanics for the study of computational methods and the study of the so-called \"quantum Zeno dynamics.\" Commuting extensions have also attracted the attention of the linear algebra community. In this paper we present 3 types of results: (i) Theorems on the uniqueness of commuting extensions for three matrices or more. (ii) Algorithms for the computation of commuting extensions of minimal size. These algorithms work under the same assumptions as our uniqueness theorems. They are applicable up to r=4n/3, and are apparently the first provably efficient algorithms for this problem applicable beyond r=n+1. (iii) A genericity theorem showing that our algorithms and uniqueness theorems can be applied to a wide range of input matrices.", "field": "cs", "label": 0}
{"text": "Title: Periodicity of Adams operations on the Green ring of a finite group\nAbstract: The Adams operations $\\psi_\\Lambda^n$ and $\\psi_S^n$ on the Green ring of a group $G$ over a field $K$ provide a framework for the study of the exterior powers and symmetric powers of $KG$-modules. When $G$ is finite and $K$ has prime characteristic $p$ we show that $\\psi_\\Lambda^n$ and $\\psi_S^n$ are periodic in $n$ if and only if the Sylow $p$-subgroups of $G$ are cyclic. In the case where $G$ is a cyclic $p$-group we find the minimum periods and use recent work of Symonds to express $\\psi_S^n$ in terms of $\\psi_\\Lambda^n$.", "field": "math", "label": 1}
{"text": "Title: Hybrid and Oriented Harmonic Potentials for Safe Task Execution in Unknown Environment\nAbstract: Harmonic potentials provide globally convergent potential fields that are provably free of local minima. Due to its analytical format, it is particularly suitable for generating safe and reliable robot navigation policies. However, for complex environments that consist of a large number of overlapping non-sphere obstacles, the computation of associated transformation functions can be tedious. This becomes more apparent when: (i) the workspace is initially unknown and the underlying potential fields are updated constantly as the robot explores it; (ii) the high-level mission consists of sequential navigation tasks among numerous regions, requiring the robot to switch between different potentials. Thus, this work proposes an efficient and automated scheme to construct harmonic potentials incrementally online as guided by the task automaton. A novel two-layer harmonic tree (HT) structure is introduced that facilitates the hybrid combination of oriented search algorithms for task planning and harmonic-based navigation controllers for non-holonomic robots. Both layers are adapted efficiently and jointly during online execution to reflect the actual feasibility and cost of navigation within the updated workspace. Global safety and convergence are ensured both for the high-level task plan and the low-level robot trajectory. Known issues such as oscillation or long-detours for purely potential-based methods and sharp-turns or high computation complexity for purely search-based methods are prevented. Extensive numerical simulation and hardware experiments are conducted against several strong baselines.", "field": "cs", "label": 0}
{"text": "Title: Morphisms of rational motivic homotopy types\nAbstract: We investigate several interrelated foundational questions pertaining to the study of motivic dga's of Dan-Cohen--Schlank [8] and Iwanari [13]. In particular, we note that morphisms of motivic dga's can reasonably be thought of as a nonabelian analog of motivic cohomology. Just as abelian motivic cohomology is a homotopy group of a spectrum coming from K-theory, the space of morphisms of motivic dga's is a certain limit of such spectra; we give an explicit formula for this limit --- a possible first step towards explicit computations or dimension bounds. We also consider commutative comonoids in Chow motives, which we call ``motivic Chow coalgebras''. We discuss the relationship between motivic Chow coalgebras and motivic dga's of smooth proper schemes. As a small first application of our results, we show that among schemes which are finite \\'etale over a number field, morphisms of associated motivic dga's are no different than morphisms of schemes. This may be regarded as a small consequence of a plausible generalization of Kim's relative unipotent section conjecture, hence as an ounce of evidence for the latter.", "field": "math", "label": 1}
{"text": "Title: Symplectic leaves in projective spaces of bundle extensions\nAbstract: Fix a stable degree-$n$ rank-$k$ bundle $\\mathcal{F}$ on a complex elliptic curve for (coprime) $1\\le k<n\\ge 3$. We identify the symplectic leaves of the Poisson structure introduced independently by Polishchuk and Feigin-Odesskii on $\\mathbb{P}^{n-1}\\cong \\mathbb{P}\\mathrm{Ext}^1(\\mathcal{F},\\mathcal{O})$ as precisely the loci classifying extensions $0\\to \\mathcal{O}\\to \\mathcal{E}\\to \\mathcal{F}\\to 0$ with $\\mathcal{E}$ fitting into a fixed isomorphism class, verifying a claim of Feigin-Odesskii. We also classify the bundles $\\mathcal{E}$ which do fit into such extensions in geometric / combinatorial terms, involving their Harder-Narasimhan polygons introduced by Shatz.", "field": "math", "label": 0}
{"text": "Title: The Balkans Continued Fraction\nAbstract: In a previous escapade we gave a collection of continued fractions involving Catalan's constant. This paper provides more general formulae governing those continued fractions. Having distinguished different cases associated to regions in the plan, we nickname those continued fractions \\enquote{The Balkans} as they divide into areas which are related but still different in nature. Because we do not provide formal proofs of those machine-constructed formulae we do not claim them to be theorems. Still, each and every proposed formula was extensively tested numerically.", "field": "math", "label": 0}
{"text": "Title: Rational Construction of Stochastic Numerical Methods for Molecular Sampling\nAbstract: In this article, we focus on the sampling of the configurational Gibbs-Boltzmann distribution, that is, the calculation of averages of functions of the position coordinates of a molecular $N$-body system modelled at constant temperature. We show how a formal series expansion of the invariant measure of a Langevin dynamics numerical method can be obtained in a straightforward way using the Baker-Campbell-Hausdorff lemma. We then compare Langevin dynamics integrators in terms of their invariant distributions and demonstrate a superconvergence property (4th order accuracy where only 2nd order would be expected) of one method in the high friction limit; this method, moreover, can be reduced to a simple modification of the Euler-Maruyama method for Brownian dynamics involving a non-Markovian (coloured noise) random process. In the Brownian dynamics case, 2nd order accuracy of the invariant density is achieved. All methods considered are efficient for molecular applications (requiring one force evaluation per timestep) and of a simple form. In fully resolved (long run) molecular dynamics simulations, for our favoured method, we observe up to two orders of magnitude improvement in configurational sampling accuracy for given stepsize with no evident reduction in the size of the largest usable timestep compared to common alternative methods.", "field": "math", "label": 1}
{"text": "Title: Stochastic Approach for Price Optimization Problems with Decision-dependent Uncertainty\nAbstract: Price determination is a central research topic of revenue management in marketing. The important aspect in pricing is controlling the stochastic behavior of demand, and the previous studies have tackled price optimization problems with uncertainties. However, many of those studies assumed that uncertainties are independent of decision variables (i.e., prices) and did not consider situations where demand uncertainty depends on price. Although some price optimization studies have dealt with decision-dependent uncertainty, they make application-specific assumptions in order to obtain an optimal solution or an approximation solution. To handle a wider range of applications with decision-dependent uncertainty, we propose a general non-convex stochastic optimization formulation. This approach aims to maximize the expectation of a revenue function with respect to a random variable representing demand under a decision-dependent distribution. We derived an unbiased stochastic gradient estimator by using a well-tuned variance reduction parameter and used it for a projected stochastic gradient descent method to find a stationary point of our problem. We conducted synthetic experiments and simulation experiments with real data on a retail service application. The results show that the proposed method outputs solutions with higher total revenues than baselines.", "field": "math", "label": 0}
{"text": "Title: The rational (non-)formality of the non-3-equal manifolds\nAbstract: Let $M^{(k)}_{d}(n)$ be the manifold of $n$-tuples $(x_1,\\ldots,x_n)\\in(\\mathbb{R}^d)^n$ having non-$k$-equal coordinates. We show that, for $d\\geq2$, $M^{(3)}_{d}(n)$ is rationally formal if and only if $n\\leq 6$. This stands in sharp contrast with the fact that all classical configuration spaces $M^{(2)}_d(n)=\\text{Conf}(\\hspace{.2mm}\\mathbb{R}^d,n)$ are rationally formal, just as are all complements of arrangements of arbitrary complex subspaces with geometric lattice of intersections. The rational non formality of $M^{(3)}_{d}(n)$ for $n>6$ is established via detection of non-trivial triple Massey products assessed through Poincar\\'e duality.", "field": "math", "label": 0}
{"text": "Title: Inner conjugate pair of Hadamard subfactors and vertex model\nAbstract: We show that any pair of Hadamard subfactors arising from complex Hadamard matrices of order 3 are either equal or inner conjugate. If the pair of Hadamard subfactors are distinct, their intersection is shown to be a subfactor of the hyperfinite type $II_1$ factor $R$. We compute its first relative commutant and characterize this subfactor by identifying it with a vertex model subfactor of the Krishnan-Sunder type. A few key invariants, including the Pimsner-Popa probabilistic number, the angle, and the Connes-St{\\o}rmer relative entropy for the pair of Hadamard subfactors are computed to understand their relative position.", "field": "math", "label": 0}
{"text": "Title: Super-extensions of tensor algebras and their applications\nAbstract: Following arXiv:0909.5586 and arXiv:1411.4125, we construct two super-extensions of the usual tensor algebra through the super-actions of symmetric groups and Hecke algebras respectively. For each extension, we consider a special type of derivations coming from covectors, and study the the space generated, in some special manner, by these derivations and operators from left multiplication by vectors and permutations. Duality theorems of these spaces and the super-actions are proved. As an application, we provide a new proof of the Schur-Sergeev duality theorem, as well as its quantum version.", "field": "math", "label": 0}
{"text": "Title: A note on odd partition numbers\nAbstract: Ramanujan's celebrated partition congruences modulo $\\ell\\in \\{5, 7, 11\\}$ assert that $$ p(\\ell n+\\delta_{\\ell})\\equiv 0\\pmod{\\ell}, $$ where $0<\\delta_{\\ell}<\\ell$ satisfies $24\\delta_{\\ell}\\equiv 1\\pmod{\\ell}.$ By proving Subbarao's Conjecture, Radu showed that there are no such congruences when it comes to parity. There are infinitely many odd (resp. even) partition numbers in every arithmetic progression. For primes $\\ell \\geq 5,$ we give a new proof of the conclusion that there are infinitely many $m$ for which $p(\\ell m+\\delta_{\\ell})$ is odd. This proof uses a generalization, due to the second author and Ramsey, of a result of Mazur in his classic paper on the Eisenstein ideal. We also refine a classical criterion of Sturm for modular form congruences, which allows us to show that the smallest such $m$ satisfies $m<(\\ell^2-1)/24,$ representing a significant improvement to the previous bound.", "field": "math", "label": 0}
{"text": "Title: Algebraic structures in set-theoretic Yang-Baxter & reflection equations\nAbstract: We present resent results regarding invertible, non-degenerate solutions of the set-theoretic Yang-Baxter and reflection equations. We recall the notion of braces and we present and prove various fundamental properties required for the solutions of the set theoretic Yang-Baxter equation. We then restrict our attention on involutive solutions and consider lambda parametric set-theoretic solutions of the Yang-Baxter equation and we extract the associated quantum algebra. We also discuss the notion of the Drinfeld twist for involutive solutions and their relation to the Yangian. We next focus on reflections and we derive the associated defining algebra relations for R-matrices being Baxterized solutions of the symmetric group. We show that there exists a ``reflection'' finite sub-algebra for some special choice of reflection maps.", "field": "math", "label": 0}
{"text": "Title: Fano threefolds with noncyclic torsion in the divisor class group\nAbstract: In this note we study Fano threefolds with noncyclic torsion in the divisor class group. Since they can all be obtained as quotients of Fano threefolds, we get also all examples that can be obtained as quotients of low codimension Fanos in the weighted projective space.", "field": "math", "label": 1}
{"text": "Title: Knot concordance, the point class in instanton homology and Donaldson invariants\nAbstract: We define an invariant ${\\varphi}$ for knots in the 3-sphere by means of Donaldson invariants and Floer's instanton homology. Some basic properties of this invariant are established and it is shown that ${\\varphi}$ coincides with a special case of an invariant defined by Froyshov", "field": "math", "label": 0}
{"text": "Title: A matrix concentration inequality for products\nAbstract: We present a non-asymptotic concentration inequality for the random matrix product \\begin{equation}\\label{eq:Zn} Z_n = \\left(I_d-\\alpha X_n\\right)\\left(I_d-\\alpha X_{n-1}\\right)\\cdots \\left(I_d-\\alpha X_1\\right), \\end{equation} where $\\left\\{X_k \\right\\}_{k=1}^{+\\infty}$ is a sequence of bounded independent random positive semidefinite matrices with common expectation $\\mathbb{E}\\left[X_k\\right]=\\Sigma$. Under these assumptions, we show that, for small enough positive $\\alpha$, $Z_n$ satisfies the concentration inequality \\begin{equation}\\label{eq:CTbound} \\mathbb{P}\\left(\\left\\Vert Z_n-\\mathbb{E}\\left[Z_n\\right]\\right\\Vert \\geq t\\right) \\leq 2d^2\\cdot\\exp\\left(\\frac{-t^2}{\\alpha \\sigma^2} \\right) \\quad \\text{for all } t\\geq 0, \\end{equation} where $\\sigma^2$ denotes a variance parameter.", "field": "math", "label": 1}
{"text": "Title: A limit theory for controlled McKean-Vlasov SPDEs\nAbstract: We develop a limit theory for controlled mean field stochastic partial differential equations in a variational framework. More precisely, we prove existence results for mean field limits and particle approximations, and we establish a set-valued propagation of chaos result which shows that sets of empirical distributions converge to sets of mean field limits in the Hausdorff metric topology. Further, we discuss limit theorems related to stochastic optimal control theory. To illustrate our findings, we apply them to a controlled interacting particle system of stochastic porous media equations.", "field": "math", "label": 0}
{"text": "Title: Von Neumann entropy of the angle operator between a pair of intermediate subalgebras\nAbstract: Given a pair of intermediate $C^*$-subalgebras of a unital inclusion of simple $C^*$-algebras with a conditional expectation of finite Watatani index, we discuss the corresponding angle operator and its Fourier transform. We provide a calculable formula for the von Neumann entropy of the (Fourier) dual angle operator for a large class of quadruple of simple $C^*$-algebras.", "field": "math", "label": 0}
{"text": "Title: Quantum cohomology of minuscule homogeneous spaces\nAbstract: We study the quantum cohomology of (co)minuscule homogeneous varieties under a unified perspective. We show that three points Gromov-Witten invariants can always be interpreted as classical intersection numbers on auxiliary varieties. Our main combinatorial tools are certain quivers, in terms of which we obtain a quantum Chevalley formula and a higher quantum Poincar\\'{e} duality. In particular we compute the quantum cohomology of the two exceptional minuscule homogeneous varieties.", "field": "math", "label": 1}
{"text": "Title: An Open and Comprehensive Pipeline for Unified Object Grounding and Detection\nAbstract: Grounding-DINO is a state-of-the-art open-set detection model that tackles multiple vision tasks including Open-Vocabulary Detection (OVD), Phrase Grounding (PG), and Referring Expression Comprehension (REC). Its effectiveness has led to its widespread adoption as a mainstream architecture for various downstream applications. However, despite its significance, the original Grounding-DINO model lacks comprehensive public technical details due to the unavailability of its training code. To bridge this gap, we present MM-Grounding-DINO, an open-source, comprehensive, and user-friendly baseline, which is built with the MMDetection toolbox. It adopts abundant vision datasets for pre-training and various detection and grounding datasets for fine-tuning. We give a comprehensive analysis of each reported result and detailed settings for reproduction. The extensive experiments on the benchmarks mentioned demonstrate that our MM-Grounding-DINO-Tiny outperforms the Grounding-DINO-Tiny baseline. We release all our models to the research community. Codes and trained models are released at https://github.com/open-mmlab/mmdetection/configs/mm_grounding_dino.", "field": "cs", "label": 0}
{"text": "Title: Policy-regularized Offline Multi-objective Reinforcement Learning\nAbstract: In this paper, we aim to utilize only offline trajectory data to train a policy for multi-objective RL. We extend the offline policy-regularized method, a widely-adopted approach for single-objective offline RL problems, into the multi-objective setting in order to achieve the above goal. However, such methods face a new challenge in offline MORL settings, namely the preference-inconsistent demonstration problem. We propose two solutions to this problem: 1) filtering out preference-inconsistent demonstrations via approximating behavior preferences, and 2) adopting regularization techniques with high policy expressiveness. Moreover, we integrate the preference-conditioned scalarized update method into policy-regularized offline RL, in order to simultaneously learn a set of policies using a single policy network, thus reducing the computational cost induced by the training of a large number of individual policies for various preferences. Finally, we introduce Regularization Weight Adaptation to dynamically determine appropriate regularization weights for arbitrary target preferences during deployment. Empirical results on various multi-objective datasets demonstrate the capability of our approach in solving offline MORL problems.", "field": "cs", "label": 0}
{"text": "Title: Spiker+: a framework for the generation of efficient Spiking Neural Networks FPGA accelerators for inference at the edge\nAbstract: Including Artificial Neural Networks in embedded systems at the edge allows applications to exploit Artificial Intelligence capabilities directly within devices operating at the network periphery. This paper introduces Spiker+, a comprehensive framework for generating efficient, low-power, and low-area customized Spiking Neural Networks (SNN) accelerators on FPGA for inference at the edge. Spiker+ presents a configurable multi-layer hardware SNN, a library of highly efficient neuron architectures, and a design framework, enabling the development of complex neural network accelerators with few lines of Python code. Spiker+ is tested on two benchmark datasets, the MNIST and the Spiking Heidelberg Digits (SHD). On the MNIST, it demonstrates competitive performance compared to state-of-the-art SNN accelerators. It outperforms them in terms of resource allocation, with a requirement of 7,612 logic cells and 18 Block RAMs (BRAMs), which makes it fit in very small FPGA, and power consumption, draining only 180mW for a complete inference on an input image. The latency is comparable to the ones observed in the state-of-the-art, with 780us/img. To the authors' knowledge, Spiker+ is the first SNN accelerator tested on the SHD. In this case, the accelerator requires 18,268 logic cells and 51 BRAM, with an overall power consumption of 430mW and a latency of 54 us for a complete inference on input data. This underscores the significance of Spiker+ in the hardware-accelerated SNN landscape, making it an excellent solution to deploy configurable and tunable SNN architectures in resource and power-constrained edge applications.", "field": "cs", "label": 0}
{"text": "Title: The infinite Arnoldi exponential integrator for linear inhomogeneous ODEs\nAbstract: Exponential integrators that use Krylov approximations of matrix functions have turned out to be efficient for the time-integration of certain ordinary differential equations (ODEs). This holds in particular for linear homogeneous ODEs, where the exponential integrator is equivalent to approximating the product of the matrix exponential and a vector. In this paper, we consider linear inhomogeneous ODEs, $y'(t)=Ay(t)+g(t)$, where the function $g(t)$ is assumed to satisfy certain regularity conditions. We derive an algorithm for this problem which is equivalent to approximating the product of the matrix exponential and a vector using Arnoldi's method. The construction is based on expressing the function $g(t)$ as a linear combination of given basis functions $[\\phi_i]_{i=0}^\\infty$ with particular properties. The properties are such that the inhomogeneous ODE can be restated as an infinite-dimensional linear homogeneous ODE. Moreover, the linear homogeneous infinite-dimensional ODE has properties that directly allow us to extend a Krylov method for finite-dimensional linear ODEs. Although the construction is based on an infinite-dimensional operator, the algorithm can be carried out with operations involving matrices and vectors of finite size. This type of construction resembles in many ways the infinite Arnoldi method for nonlinear eigenvalue problems. We prove convergence of the algorithm under certain natural conditions, and illustrate properties of the algorithm with examples stemming from the discretization of partial differential equations.", "field": "math", "label": 1}
{"text": "Title: A Unified Framework for Rank-based Loss Minimization\nAbstract: The empirical loss, commonly referred to as the average loss, is extensively utilized for training machine learning models. However, in order to address the diverse performance requirements of machine learning models, the use of the rank-based loss is prevalent, replacing the empirical loss in many cases. The rank-based loss comprises a weighted sum of sorted individual losses, encompassing both convex losses like the spectral risk, which includes the empirical risk and conditional value-at-risk, and nonconvex losses such as the human-aligned risk and the sum of the ranked range loss. In this paper, we introduce a unified framework for the optimization of the rank-based loss through the utilization of a proximal alternating direction method of multipliers. We demonstrate the convergence and convergence rate of the proposed algorithm under mild conditions. Experiments conducted on synthetic and real datasets illustrate the effectiveness and efficiency of the proposed algorithm.", "field": "math", "label": 0}
{"text": "Title: Cost Minimization in Multi-cloud Systems with Runtime Microservice Re-orchestration\nAbstract: Multi-cloud systems facilitate a cost-efficient and geographically-distributed deployment of microservice-based applications by temporary leasing virtual nodes with diverse pricing models. To preserve the cost-efficiency of multi-cloud deployments, it is essential to redeploy microservices onto the available nodes according to a dynamic resource configuration, which is often performed to better accommodate workload variations. However, this approach leads to frequent service disruption since applications are continuously shutdown and redeployed in order to apply the new resource assignment. To overcome this issue, we propose a re-orchestration scheme that migrates microservice at runtime based on a rolling update scheduling logic. Specifically, we propose an integer linear optimization problem that minimizes the cost associated to multi-cloud virtual nodes and that ensures that delay-sensitive microservices are co-located on the same regional cluster. The resulting rescheduling order guarantees no service disruption by repacking microservices between the available nodes without the need to turn off the outdated microservice instance before redeploying the updated version. In addition, we propose a two-step heuristic scheme that effectively approximates the optimal solution at the expense of close-to-zero service disruption and QoS violation probability. Results show that proposed schemes achieve better performance in terms of cost mitigation, low service disruption and low QoS violation probability compared to baseline schemes replicating Kubernetes scheduler functionalities.", "field": "cs", "label": 0}
{"text": "Title: Log-concave Density Estimation with Independent Components\nAbstract: We propose a method for estimating a log-concave density on $\\mathbb R^d$ from samples, under the assumption that there exists an orthogonal transformation that makes the components of the random vector independent. While log-concave density estimation is hard both computationally and statistically, the independent components assumption alleviates both issues, while still maintaining a large non-parametric class. We prove that under mild conditions, at most $\\tilde{\\mathcal{O}}(\\epsilon^{-4})$ samples (suppressing constants and log factors) suffice for our proposed estimator to be within $\\epsilon$ of the original density in squared Hellinger distance. On the computational front, while the usual log-concave maximum likelihood estimate can be obtained via a finite-dimensional convex program, it is slow to compute -- especially in higher dimensions. We demonstrate through numerical experiments that our estimator can be computed efficiently, making it more practical to use.", "field": "math", "label": 0}
{"text": "Title: Subdifferentials of convex matrix-valued functions\nAbstract: Subdifferentials (in the sense of convex analysis) of matrix-valued functions defined on $\\mathbb{R}^d$ that are convex with respect to the L\\\"{o}wner partial order can have a complicated structure and might be very difficult to compute even in simple cases. The aim of this paper is to study subdifferential calculus for such functions and properties of their subdifferentials. We show that many standard results from convex analysis no longer hold true in the matrix-valued case. For example, in this case the subdifferential of the sum is not equal to the sum of subdifferentials, the Clarke subdifferential is not equal to the subdifferential in the sense of convex analysis, etc. Nonetheless, it is possible to provide simple rules for computing nonempty subsets of subdifferentials (in particular, individual subgradients) of convex matrix-valued functions in the general case and to completely describe subdifferentials of such functions defined on the real line. As a by-product of our analysis, we derive some interesting properties of convex matrix-valued functions, e.g. we show that if such function is nonsmooth, then its diagonal elements must be nonsmooth as well.", "field": "math", "label": 0}
{"text": "Title: Nodal solutions for Neumann systems with gradient dependence\nAbstract: We consider the following convective Neumann systems:\\begin{equation*}\\left(\\mathrm{S}\\right)\\qquad\\left\\{\\begin{array}{ll}-\\Delta_{p_1}u_1+\\frac{|\\nabla u_1|^{p_1}}{u_1+\\delta_1}=f_1(x,u_1,u_2,\\nabla u_1,\\nabla u_2) & \\text{in}\\;\\Omega,\\\\ -\\Delta _{p_2}u_2+\\frac{|\\nabla u_2|^{p_2}}{u_2+\\delta_2}=f_2(x,u_1,u_2,\\nabla u_1,\\nabla u_2)&\\text{in}\\;\\Omega, \\\\ |\\nabla u_1|^{p_1-2}\\frac{\\partial u_1}{\\partial \\eta }=0=|\\nabla u_2|^{p_2-2}\\frac{\\partial u_2}{\\partial \\eta}&\\text{on}\\;\\partial\\Omega,\\end{array}\\right.\\end{equation*}where $\\Omega$ is a bounded domain in $\\mathbb{R}^{N}$ ($N\\geq 2$) with a smooth boundary $\\partial\\Omega$,$\\delta_1,\\,\\delta_2 >0$ are small parameters, $\\eta$ is the outward unit vector normal to $\\partial \\Omega,$ $f_1,\\,f_2:\\Omega\\times\\mathbb{R}^2\\times\\mathbb{R}^{2N}\\rightarrow \\mathbb{R}$ are Carath\\'{e}odory functions that satisfy certain growth conditions, and $\\Delta _{p_i}$ ($1<p_i<N,$ for $i=1,2$) are the $p$-Laplace operators $\\Delta _{p_i}u_i=\\mathrm{div}(|\\nabla u_i|^{p_i-2}\\nabla u_i)$,for every $\\,u_i\\in W^{1,p_i}(\\Omega).$ In order to prove the existence of solutions to such systems, we use a sub-supersolution method. We also obtain nodal solutions by constructing appropriate sub-solution and super-solution pairs. To the best of our knowledge, such systems have not been studied yet.", "field": "math", "label": 0}
{"text": "Title: HEMlets PoSh: Learning Part-Centric Heatmap Triplets for 3D Human Pose and Shape Estimation\nAbstract: Estimating 3D human pose from a single image is a challenging task. This work attempts to address the uncertainty of lifting the detected 2D joints to the 3D space by introducing an intermediate state-Part-Centric Heatmap Triplets (HEMlets), which shortens the gap between the 2D observation and the 3D interpretation. The HEMlets utilize three joint-heatmaps to represent the relative depth information of the end-joints for each skeletal body part. In our approach, a Convolutional Network (ConvNet) is first trained to predict HEMlets from the input image, followed by a volumetric joint-heatmap regression. We leverage on the integral operation to extract the joint locations from the volumetric heatmaps, guaranteeing end-to-end learning. Despite the simplicity of the network design, the quantitative comparisons show a significant performance improvement over the best-of-grade methods (e.g. $20\\%$ on Human3.6M). The proposed method naturally supports training with \"in-the-wild\" images, where only weakly-annotated relative depth information of skeletal joints is available. This further improves the generalization ability of our model, as validated by qualitative comparisons on outdoor images. Leveraging the strength of the HEMlets pose estimation, we further design and append a shallow yet effective network module to regress the SMPL parameters of the body pose and shape. We term the entire HEMlets-based human pose and shape recovery pipeline HEMlets PoSh. Extensive quantitative and qualitative experiments on the existing human body recovery benchmarks justify the state-of-the-art results obtained with our HEMlets PoSh approach.", "field": "cs", "label": 1}
{"text": "Title: Cubic bent functions outside the completed Maiorana-McFarland class\nAbstract: In this paper we prove that in opposite to the cases of 6 and 8 variables, the Maiorana-McFarland construction does not describe the whole class of cubic bent functions in $n$ variables for all $n\\ge 10$. Moreover, we show that for almost all values of $n$, these functions can simultaneously be homogeneous and have no affine derivatives.", "field": "math", "label": 1}
{"text": "Title: Universal Homotopy Theories and Associated Homological Algebras\nAbstract: Let $\\mathscr{C}$ be a small category. For every commutative ring $R$ with unity, we associate an $R\\mathrm{-linear}$ abelian category with the universal homotopy category of $\\mathscr{C}$, where we can do the corresponding homological algebra.", "field": "math", "label": 0}
{"text": "Title: The Drinfel'd Double and Twisting in Stringy Orbifold Theory\nAbstract: This paper exposes the fundamental role that the Drinfel'd double $\\dkg$ of the group ring of a finite group $G$ and its twists $\\dbkg$, $\\beta \\in Z^3(G,\\uk)$ as defined by Dijkgraaf--Pasquier--Roche play in stringy orbifold theories and their twistings. The results pertain to three different aspects of the theory. First, we show that $G$--Frobenius algebras arising in global orbifold cohomology or K-theory are most naturally defined as elements in the braided category of $\\dkg$--modules. Secondly, we obtain a geometric realization of the Drinfel'd double as the global orbifold $K$--theory of global quotient given by the inertia variety of a point with a $G$ action on the one hand and more stunningly a geometric realization of its representation ring in the braided category sense as the full $K$--theory of the stack $[pt/G]$. Finally, we show how one can use the co-cycles $\\beta$ above to twist a) the global orbifold $K$--theory of the inertia of a global quotient and more importantly b) the stacky $K$--theory of a global quotient $[X/G]$. This corresponds to twistings with a special type of 2--gerbe.", "field": "math", "label": 1}
{"text": "Title: Bring Metric Functions into Diffusion Models\nAbstract: We introduce a Cascaded Diffusion Model (Cas-DM) that improves a Denoising Diffusion Probabilistic Model (DDPM) by effectively incorporating additional metric functions in training. Metric functions such as the LPIPS loss have been proven highly effective in consistency models derived from the score matching. However, for the diffusion counterparts, the methodology and efficacy of adding extra metric functions remain unclear. One major challenge is the mismatch between the noise predicted by a DDPM at each step and the desired clean image that the metric function works well on. To address this problem, we propose Cas-DM, a network architecture that cascades two network modules to effectively apply metric functions to the diffusion model training. The first module, similar to a standard DDPM, learns to predict the added noise and is unaffected by the metric function. The second cascaded module learns to predict the clean image, thereby facilitating the metric function computation. Experiment results show that the proposed diffusion model backbone enables the effective use of the LPIPS loss, leading to state-of-the-art image quality (FID, sFID, IS) on various established benchmarks.", "field": "cs", "label": 0}
{"text": "Title: HCIZ integral formula as unitarity of a canonical map between reproducing kernel spaces\nAbstract: In this article we prove that the Harish-Chandra-Itzykson-Zuber (HCIZ) integral formula is equivalent to the unitarity of a canonical map between invariant subspaces of Segal-Bargmann spaces. As a consequence, we provide alternative proofs of the HCIZ integral and other results.", "field": "math", "label": 0}
{"text": "Title: Mod-$p$ isogeny classes on Shimura varieties with parahoric level structure\nAbstract: We study the special fiber of the integral models for Shimura varieties of Hodge type with parahoric level structure constructed by Kisin and Pappas in [KP]. We show that when the group is residually split, the points in the mod $p$ isogeny classes have the form predicted by the Langlands Rapoport conjecture in [LR]. We also verify most of the He-Rapoport axioms for these integral models without the residually split assumption. This allows us to prove that all Newton strata are non-empty for these models.", "field": "math", "label": 1}
{"text": "Title: Effective Ways to Build and Evaluate Individual Survival Distributions\nAbstract: An accurate model of a patient's individual survival distribution can help determine the appropriate treatment for terminal patients. Unfortunately, risk scores (e.g., from Cox Proportional Hazard models) do not provide survival probabilities, single-time probability models (e.g., the Gail model, predicting 5 year probability) only provide for a single time point, and standard Kaplan-Meier survival curves provide only population averages for a large class of patients meaning they are not specific to individual patients. This motivates an alternative class of tools that can learn a model which provides an individual survival distribution which gives survival probabilities across all times - such as extensions to the Cox model, Accelerated Failure Time, an extension to Random Survival Forests, and Multi-Task Logistic Regression. This paper first motivates such \"individual survival distribution\" (ISD) models, and explains how they differ from standard models. It then discusses ways to evaluate such models - namely Concordance, 1-Calibration, Brier score, and various versions of L1-loss - and then motivates and defines a novel approach \"D-Calibration\", which determines whether a model's probability estimates are meaningful. We also discuss how these measures differ, and use them to evaluate several ISD prediction tools, over a range of survival datasets.", "field": "cs", "label": 1}
{"text": "Title: Fourier quasicrystals with unit masses\nAbstract: Every set $\\Lambda\\subset R$ such that the sum of $\\delta$-measures sitting at the points of $\\Lambda$ is a Fourier quasicrystal, is the zero set of an exponential polynomial with imaginary frequencies.", "field": "math", "label": 1}
{"text": "Title: Properly Outer and Strictly Outer Actions of Finite Groups on Prime C*-algebras\nAbstract: An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper I define the notion of strictly outer action (similar to the definition for von Neumann factors in [11]) and prove that for finite groups it is equivalent with proper outerness of the action. For finite abelian groups this is equivalent with other relevant properities of the action.", "field": "math", "label": 0}
{"text": "Title: Using Locality-sensitive Hashing for Rendezvous Search\nAbstract: The multichannel rendezvous problem is a fundamental problem for neighbor discovery in many IoT applications. The existing works in the literature focus mostly on improving the worst-case performance, and the average-case performance is often not as good as that of the random algorithm. As IoT devices (users) are close to each other, their available channel sets, though they might be different, are similar. Using the locality-sensitive hashing (LSH) technique in data mining, we propose channel hopping algorithms that exploit the similarity between the two available channel sets to increase the rendezvous probability. For the synchronous setting, our algorithms have the expected time-to-rendezvous (ETTR) inversely proportional to a well-known similarity measure called the Jaccard index. For the asynchronous setting, we use dimensionality reduction to speed up the rendezvous process. Our numerical results show that our algorithms can outperform the random algorithm in terms of ETTR.", "field": "cs", "label": 1}
{"text": "Title: Politics and Propaganda on Social Media: How Twitter and Meta Moderate State-Linked Information Operations\nAbstract: Why do Social Media Corporations (SMCs) engage in state-linked information operations? Social media can significantly influence the global political landscape, allowing governments and other political entities to engage in concerted information operations, shaping or manipulating domestic and foreign political agendas. In response to state-linked political manipulation tactics on social media, Twitter and Meta carried out take-down operations against propaganda networks, accusing them of interfering foreign elections, organizing disinformation campaigns, manipulating political debates and many other issues. This research investigates the two SMCs' policy orientation to explain which factors can affect these two companies' reaction against state-linked information operations. We find that good governance indicators such as democracy are significant elements of SMCs' country-focus. This article also examines whether Meta and Twitter's attention to political regime characteristics is influenced by international political alignments. This research illuminates recent trends in SMCs' take-down operations and illuminating interplay between geopolitics and domestic regime characteristics.", "field": "cs", "label": 0}
{"text": "Title: On Language Varieties Without Boolean Operations\nAbstract: Eilenberg's variety theorem marked a milestone in the algebraic theory of regular languages by establishing a formal correspondence between properties of regular languages and properties of finite monoids recognizing them. Motivated by classes of languages accepted by quantum finite automata, we introduce basic varieties of regular languages, a weakening of Eilenberg's original concept that does not require closure under any boolean operations, and prove a variety theorem for them. To do so, we investigate the algebraic recognition of languages by lattice bimodules, generalizing Klima and Polak's lattice algebras, and we utilize the duality between algebraic completely distributive lattices and posets.", "field": "cs", "label": 1}
{"text": "Title: Closed and asymptotic formulae for harmonic and quadratic harmonic sums\nAbstract: We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.", "field": "cs", "label": 0}
{"text": "Title: Learning Compact Reward for Image Captioning\nAbstract: Adversarial learning has shown its advances in generating natural and diverse descriptions in image captioning. However, the learned reward of existing adversarial methods is vague and ill-defined due to the reward ambiguity problem. In this paper, we propose a refined Adversarial Inverse Reinforcement Learning (rAIRL) method to handle the reward ambiguity problem by disentangling reward for each word in a sentence, as well as achieve stable adversarial training by refining the loss function to shift the generator towards Nash equilibrium. In addition, we introduce a conditional term in the loss function to mitigate mode collapse and to increase the diversity of the generated descriptions. Our experiments on MS COCO and Flickr30K show that our method can learn compact reward for image captioning.", "field": "cs", "label": 1}
{"text": "Title: Topological generation and matrix models for quantum reflection groups\nAbstract: We establish several new topological generation results for the quantum permutation groups $S^+_N$ and the quantum reflection groups $H^{s+}_N$. We use these results to show that these quantum groups admit sufficiently many \"matrix models\". In particular, all of these quantum groups have residually finite discrete duals (and are, in particular, hyperlinear), and certain \"flat\" matrix models for $S_N^+$ are inner faithful.", "field": "math", "label": 1}
{"text": "Title: Structure and Design of HoloGen\nAbstract: Increasing popularity of augmented and mixed reality systems has seen a similar increase of interest in 2D and 3D computer generated holography (CGH). Unlike stereoscopic approaches, CGH can fully represent a light field including depth of focus, accommodation and vergence. Along with existing telecommunications, imaging, projection, lithography, beam shaping and optical tweezing applications, CGH is an exciting technique applicable to a wide array of photonic problems including full 3D representation. Traditionally, the primary roadblock to acceptance has been the significant numerical processing required to generate holograms requiring both significant expertise and significant computational power. This article discusses the structure and design of HoloGen. HoloGen is an MIT licensed application that may be used to generate holograms using a wide array of algorithms without expert guidance. HoloGen uses a Cuda C and C++ backend with a C# and Windows Presentation Framework graphical user interface. The article begins by introducing HoloGen before providing an in-depth discussion of its design and structure. Particular focus is given to the communication, data transfer and algorithmic aspects.", "field": "cs", "label": 1}
{"text": "Title: Horizontal Goodman surgery and almost equivalence of pseudo-Anosov flows\nAbstract: We provide an exposition of a `horizontal' generalization of Goodman's surgery operation on (pseudo-)Anosov flows. This operation is performed by cutting along a specific kind of annulus that is transverse to the flow and regluing with a Dehn twist of the appropriate sign. We then show that performing horizontal Goodman surgery on a transitive pseudo-Anosov flow yields an almost equivalent flow, i.e. the original flow and the surgered flow are orbit equivalent after drilling out a finite collection of closed orbits. We obtain some almost equivalence results by applying this theorem on examples of the surgery operation. Along the way, we also show a structural stability result for pseudo-Anosov flows.", "field": "math", "label": 0}
{"text": "Title: KK-duality for the Cuntz-Pimsner algebras of Temperley-Lieb subproduct systems\nAbstract: We prove that the Cuntz-Pimsner algebra of every Temperley-Lieb subproduct system is KK-self-dual. We show also that every such Cuntz-Pimsner algebra has a canonical KMS-state, which we use to construct a Fredholm module representative for the fundamental class of the duality. This allows us to describe the K-homology of the Cuntz-Pimsner algebras by explicit Fredholm modules. Both the construction of the dual class and the proof of duality rely in a crucial way on quantum symmetries of Temperley-Lieb subproduct systems. In the simplest case of Arveson's $2$-shift our work establishes $U(2)$-equivariant KK-self-duality of $S^3$.", "field": "math", "label": 0}
{"text": "Title: An experimental sorting method for improving metagenomic data encoding\nAbstract: Minimizing data storage poses a significant challenge in large-scale metagenomic projects. In this paper, we present a new method for improving the encoding of FASTQ files generated by metagenomic sequencing. This method incorporates metagenomic classification followed by a recursive filter for clustering reads by DNA sequence similarity to improve the overall reference-free compression. In the results, we show an overall improvement in the compression of several datasets. As hypothesized, we show a progressive compression gain for higher coverage depth and number of identified species. Additionally, we provide an implementation that is freely available at https://github.com/cobilab/mizar and can be customized to work with other FASTQ compression tools.", "field": "cs", "label": 0}
{"text": "Title: The quasi-static plasmonic problem for polyhedra\nAbstract: We characterize the essential spectrum of the plasmonic problem for polyhedra in $\\mathbb{R}^3$. The description is particularly simple for convex polyhedra and permittivities $\\epsilon < - 1$. The plasmonic problem is interpreted as a spectral problem through a boundary integral operator, the direct value of the double layer potential, also known as the Neumann--Poincar\\'e operator. We therefore study the spectral structure of the the double layer potential for polyhedral cones and polyhedra.", "field": "math", "label": 1}
{"text": "Title: TR-DETR: Task-Reciprocal Transformer for Joint Moment Retrieval and Highlight Detection\nAbstract: Video moment retrieval (MR) and highlight detection (HD) based on natural language queries are two highly related tasks, which aim to obtain relevant moments within videos and highlight scores of each video clip. Recently, several methods have been devoted to building DETR-based networks to solve both MR and HD jointly. These methods simply add two separate task heads after multi-modal feature extraction and feature interaction, achieving good performance. Nevertheless, these approaches underutilize the reciprocal relationship between two tasks. In this paper, we propose a task-reciprocal transformer based on DETR (TR-DETR) that focuses on exploring the inherent reciprocity between MR and HD. Specifically, a local-global multi-modal alignment module is first built to align features from diverse modalities into a shared latent space. Subsequently, a visual feature refinement is designed to eliminate query-irrelevant information from visual features for modal interaction. Finally, a task cooperation module is constructed to refine the retrieval pipeline and the highlight score prediction process by utilizing the reciprocity between MR and HD. Comprehensive experiments on QVHighlights, Charades-STA and TVSum datasets demonstrate that TR-DETR outperforms existing state-of-the-art methods. Codes are available at \\url{https://github.com/mingyao1120/TR-DETR}.", "field": "cs", "label": 0}
{"text": "Title: Bow varieties as symplectic reductions of $T^*(G/P)$\nAbstract: Cherkis bow varieties were introduced as ADHM type description of moduli space of instantons on the Taub-NUT space equivariant under a cyclic group action. They are also models of Coulomb branches of quiver gauge theories of affine type A. In this paper, we realize each bow variety with torus fixed points as a symplectic reduction of a cotangent bundle of a partial flag variety by a unipotent group, and find a slice of this action. By this description, we calculate the equivariant cohomology (and ordinary cohomology) of some of them and answer some questions raisedbefore. This also uses a new result about circle-equivariant cohomology proven in an appendix. We also give an explicit generalized Mirkovic-Vybornov isomorphism for bow varieties in the appendix.", "field": "math", "label": 0}
{"text": "Title: Gradient-Based Optimization of Lattice Quantizers\nAbstract: Lattices with minimal normalized second moments are designed using a new numerical optimization algorithm. Starting from a random lower-triangular generator matrix and applying stochastic gradient descent, all elements are updated towards the negative gradient, which makes it the most efficient algorithm proposed so far for this purpose. A graphical illustration of the theta series, called theta image, is introduced and shown to be a powerful tool for converting numerical lattice representations into their underlying exact forms. As a proof of concept, optimized lattices are designed in dimensions up to 16. In all dimensions, the algorithm converges to either the previously best known lattice or a better one. The dual of the 15-dimensional laminated lattice is conjectured to be optimal in its dimension.", "field": "cs", "label": 0}
{"text": "Title: Regularity for Maxwell eigenproblems in photonic crystal fibre modelling\nAbstract: The convergence behaviour and the design of numerical methods for modelling the flow of light in photonic crystal fibres depend critically on an understanding of the regularity of solutions to time-harmonic Maxwell equations in a three-dimensional, periodic, translationally invariant, heterogeneous medium. In this paper we determine the strength of the dominant singularities that occur at the interface between materials. By modifying earlier regularity theory for polygonal interfaces we find that on each subdomain, where the material in the fibre is constant, the regularity of in-plane components of the magnetic field are $H^{2-\\eta}$ for all $\\eta > 0$. This estimate is sharp in the sense that these components do not belong to $H^2$, in general. However, global regularity is restricted by the presence of an interface between these subdomains and the interface conditions imply only $H^{3/2-\\eta}$ regularity across the interface. The results are useful to anyone applying a numerical method such as a finite element method or a planewave expansion method to model photonic crystal fibres or similar materials.", "field": "math", "label": 1}
{"text": "Title: Deplatforming Norm-Violating Influencers on Social Media Reduces Overall Online Attention Toward Them\nAbstract: From politicians to podcast hosts, online platforms have systematically banned (``deplatformed'') influential users for breaking platform guidelines. Previous inquiries on the effectiveness of this intervention are inconclusive because 1) they consider only few deplatforming events; 2) they consider only overt engagement traces (e.g., likes and posts) but not passive engagement (e.g., views); 3) they do not consider all the potential places users impacted by the deplatforming event might migrate to. We address these limitations in a longitudinal, quasi-experimental study of 165 deplatforming events targeted at 101 influencers. We collect deplatforming events from Reddit posts and then manually curate the data, ensuring the correctness of a large dataset of deplatforming events. Then, we link these events to Google Trends and Wikipedia page views, platform-agnostic measures of online attention that capture the general public's interest in specific influencers. Through a difference-in-differences approach, we find that deplatforming reduces online attention toward influencers. After 12 months, we estimate that online attention toward deplatformed influencers is reduced by -63% (95% CI [-75%,-46%]) on Google and by -43% (95% CI [-57%,-24%]) on Wikipedia. Further, as we study over a hundred deplatforming events, we can analyze in which cases deplatforming is more or less impactful, revealing nuances about the intervention. Notably, we find that both permanent and temporary deplatforming reduce online attention toward influencers; Overall, this work contributes to the ongoing effort to map the effectiveness of content moderation interventions, driving platform governance away from speculation.", "field": "cs", "label": 0}
{"text": "Title: Robust Regret Optimal Control\nAbstract: This paper presents a synthesis method for robust, regret optimal control. The plant is modeled in discrete-time by an uncertain linear time-invariant (LTI) system. An optimal non-causal controller is constructed using the nominal plant model and given full knowledge of the disturbance. Robust regret is defined relative to the performance of this optimal non-causal control. It is shown that a controller achieves robust regret if and only if it satisfies a robust $H_\\infty$ performance condition. DK-iteration can be used to synthesize a controller that satisfies this condition and hence achieve a given level of robust regret. The approach is demonstrated three examples: (i) a simple single-input, single-output classical design, (ii) a longitudinal control for a simplified model for a Boeing 747 model, and (iii) an active suspension for a quarter car model. All examples compare the robust regret optimal against regret optimal controllers designed without uncertainty.", "field": "math", "label": 0}
{"text": "Title: A Survey Analyzing Generalization in Deep Reinforcement Learning\nAbstract: Reinforcement learning research obtained significant success and attention with the utilization of deep neural networks to solve problems in high dimensional state or action spaces. While deep reinforcement learning policies are currently being deployed in many different fields from medical applications to self driving vehicles, there are still ongoing questions the field is trying to answer on the generalization capabilities of deep reinforcement learning policies. In this paper, we will outline the fundamental reasons why deep reinforcement learning policies encounter overfitting problems that limit their robustness and generalization capabilities. Furthermore, we will formalize and unify the diverse solution approaches to increase generalization, and overcome overfitting in state-action value functions. We believe our study can provide a compact systematic unified analysis for the current advancements in deep reinforcement learning, and help to construct robust deep neural policies with improved generalization abilities.", "field": "cs", "label": 0}
{"text": "Title: Robust and Adaptive Planning under Model Uncertainty\nAbstract: Planning under model uncertainty is a fundamental problem across many applications of decision making and learning. In this paper, we propose the Robust Adaptive Monte Carlo Planning (RAMCP) algorithm, which allows computation of risk-sensitive Bayes-adaptive policies that optimally trade off exploration, exploitation, and robustness. RAMCP formulates the risk-sensitive planning problem as a two-player zero-sum game, in which an adversary perturbs the agent's belief over the models. We introduce two versions of the RAMCP algorithm. The first, RAMCP-F, converges to an optimal risk-sensitive policy without having to rebuild the search tree as the underlying belief over models is perturbed. The second version, RAMCP-I, improves computational efficiency at the cost of losing theoretical guarantees, but is shown to yield empirical results comparable to RAMCP-F. RAMCP is demonstrated on an n-pull multi-armed bandit problem, as well as a patient treatment scenario.", "field": "cs", "label": 1}
{"text": "Title: Characters of Representations of Quantum Groups of Type $A_n$\nAbstract: We introduce the notion of characters of comodules over coribbon Hopf algebras. The case of quantum groups of type $A_n$ is studied. We establish a characteristic equation for the quantum matrix and a q-analogue of Harish-Chandra- Itzykson-Zuber integral", "field": "math", "label": 1}
{"text": "Title: Connected sums and directed systems in knot Floer homologies\nAbstract: We prove a number of fundamental properties about instanton knot Floer homology. Our arguments rely on general properties of sutured Floer theories and apply also in the Heegaard Floer and monopole Floer settings, where many of our results were already known. Our main result is the connected sum formula for instanton knot Floer homology. An extension of this result proves the oriented skein exact triangle for the minus version of instanton knot Floer homology. Finally, we derive a new model of the minus version of instanton knot Floer homology, which takes the form of a free, finitely generated chain complex over a polynomial ring, as opposed to a direct limit. This construction is new to all of the Floer theories. We explore these results also in the context of Heegaard Floer theory as well.", "field": "math", "label": 0}
{"text": "Title: Solutions to complex $m$-Hessian type equation and its application\nAbstract: In this paper, we introduce the class $\\mathcal{E}_{m,F}(\\Omega)$ and prove the existence of solutions of the complex $m-$Hessian type equation $-F(u(z),z)H_{m}(u)=\\mu$ where $\\mu$ vanishes on all of $m-$polar sets in the class $\\mathcal{E}_{m,F}(\\Omega).$ Next, we prove the existence of solutions of this equation in the class $\\mathcal{E}_{m,F}(\\Omega)$ if there exists subsolution in this class. Using the above results, we study subextension in the class $\\mathcal{E}_{m,F}(\\Omega).$", "field": "math", "label": 0}
{"text": "Title: An Example of Evolutionary Computation + Large Language Model Beating Human: Design of Efficient Guided Local Search\nAbstract: It is often very tedious for human experts to design efficient algorithms. Recently, we have proposed a novel Algorithm Evolution using Large Language Model (AEL) framework for automatic algorithm design. AEL combines the power of a large language model and the paradigm of evolutionary computation to design, combine, and modify algorithms automatically. In this paper, we use AEL to design the guide algorithm for guided local search (GLS) to solve the well-known traveling salesman problem (TSP). AEL automatically evolves elite GLS algorithms in two days, with minimal human effort and no model training. Experimental results on 1,000 TSP20-TSP100 instances and TSPLib instances show that AEL-designed GLS outperforms state-of-the-art human-designed GLS with the same iteration budget. It achieves a 0% gap on TSP20 and TSP50 and a 0.032% gap on TSP100 in 1,000 iterations. Our findings mark the emergence of a new era in automatic algorithm design.", "field": "cs", "label": 0}
{"text": "Title: Representation stability in the level 4 braid group\nAbstract: We investigate the cohomology of the level 4 subgroup of the braid group, namely, the kernel of the mod 4 reduction of the Burau representation at $t=-1$. This group is also equal to the kernel of the mod 2 abelianization of the pure braid group. We give an exact formula for the first Betti number; it is a quartic polynomial in the number of strands. We also show that, like the pure braid group, the first homology satisfies uniform representation stability in the sense of Church and Farb. Unlike the pure braid group, the group of symmetries - the quotient of the braid group by the level 4 subgroup - is one for which the representation theory has not been well studied; we develop its representation theory. This group is a non-split extension of the symmetric group. As applications of our main results, we show that the rational cohomology ring of the level 4 braid group is not generated in degree 1 when the number of strands is at least 15, and we compute all Betti numbers of the level 4 braid group when the number of strands is at most 4. We also derive a new lower bound on the first rational Betti number of the hyperelliptic Torelli group and on the top rational Betti number of the level 4 mapping class group in genus 2. Finally, we apply our results to locate all of the 2-torsion points on the characteristic varieties of the pure braid group.", "field": "math", "label": 1}
{"text": "Title: Randomly coupled differential equations with elliptic correlations\nAbstract: We consider the long time asymptotic behavior of a large system of $N$ linear differential equations with random coefficients. We allow for general elliptic correlation structures among the coefficients, thus we substantially generalize our previous work [14] that was restricted to the independent case. In particular, we analyze a recent model in the theory of neural networks [27] that specifically focused on the effect of the distributional asymmetry in the random connectivity matrix $X$. We rigorously prove and slightly correct the explicit formula from [28] on the time decay as a function of the asymmetry parameter. Our main tool is an asymptotically precise formula for the normalized trace of $f(X) g(X^*)$, in the large $N$ limit, where $f$ and $g$ are analytic functions.", "field": "math", "label": 1}
{"text": "Title: Grounding Complex Navigational Instructions Using Scene Graphs\nAbstract: Training a reinforcement learning agent to carry out natural language instructions is limited by the available supervision, i.e. knowing when the instruction has been carried out. We adapt the CLEVR visual question answering dataset to generate complex natural language navigation instructions and accompanying scene graphs, yielding an environment-agnostic supervised dataset. To demonstrate the use of this data set, we map the scenes to the VizDoom environment and use the architecture in \\citet{gatedattention} to train an agent to carry out these more complex language instructions.", "field": "cs", "label": 1}
{"text": "Title: Offset Hypersurfaces and Persistent Homology of Algebraic Varieties\nAbstract: In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology and algebraic optimization. Namely, we express the degree corresponding to the distance variable of the offset hypersurface in terms of the Euclidean Distance Degree of the starting variety, obtaining a new way to compute these degrees. Finally, we describe the non-properness locus of the offset construction and use this to describe the set of points that are topologically interesting (the medial axis and center points of the bounded components of the complement of the variety) and relevant to the computation of persistent homology.", "field": "math", "label": 1}
{"text": "Title: Roots of crosscap slides and crosscap transpositions\nAbstract: Let $N_{g}$ denote a closed nonorientable surface of genus $g$. For $g \\geq 2$ the mapping class group $\\mathcal{M}(N_{g})$ is generated by Dehn twists and one crosscap slide ($Y$-homeomorphism) or by Dehn twists and a crosscap transposition. Margalit and Schleimer observed that Dehn twists have nontrivial roots. We give necessary and sufficient conditions for the existence of a root of a crosscap slide and a crosscap transposition.", "field": "math", "label": 1}
{"text": "Title: Higher dimensional Calabi-Yau manifolds of Kummer type\nAbstract: Based on Cynk-Hulek method we construct complex Calabi-Yau varieties of arbitrary dimensions using elliptic curves with automorphism of order 6. Also we give formulas for Hodge numbers of varieties obtained from that construction. We shall generalize result of Katsura and Sch\\\"utt to obtain arbitrarily dimensional Calabi-Yau manifolds which are Zariski in any characteristic $p\\not\\equiv 1\\pmod{12}.$", "field": "math", "label": 1}
{"text": "Title: Shifted Composition II: Shift Harnack Inequalities and Curvature Upper Bounds\nAbstract: We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for the first time, allowing us to investigate their relationship with other properties of the diffusion. Namely, we show that they are equivalent to a sharp \"local gradient-entropy\" bound, and that they imply curvature upper bounds in a compelling reflection of the Bakry-Emery theory of curvature lower bounds. Finally, we show that the local gradient-entropy inequality implies optimal concentration of the score, a.k.a. the logarithmic gradient of the density.", "field": "math", "label": 0}
{"text": "Title: Convergence of boundary layers of chemotaxis models with physical boundary conditions~I: degenerate initial data\nAbstract: The celebrated experiment of Tuval et al. \\cite{tuval2005bacterial} showed that the bacteria living a water drop can form a thin layer near the air-water interface, where a so-called chemotaxis-fluid system with physical boundary conditions was proposed to interpret the mechanism underlying the pattern formation alongside numerical simulations. However, the rigorous proof for the existence and convergence of the boundary layer solutions to the proposed model still remains open. This paper shows that the model with physical boundary conditions proposed in \\cite{tuval2005bacterial} in one dimension can generate boundary layer solution as the oxygen diffusion rate $\\varepsilon>0$ is small. Specifically, we show that the solution of the model with $\\varepsilon>0$ will converge to the solution with $\\varepsilon=0$ (outer-layer solution) plus the boundary layer profiles (inner-layer solution) with a sharp transition near the boundary as $ \\varepsilon \\rightarrow 0$. There are two major difficulties in our analysis. First, the global well-posedness of the model is hard to prove since the Dirichlet boundary condition can not contribute to the gradient estimates needed for the cross-diffusion structure in the model. Resorting to the technique of taking anti-derivative, we remove the cross-diffusion structure such that the Dirichlet boundary condition can facilitate the needed estimates. Second, the outer-layer profile of bacterial density is required to be degenerate at the boundary as $ t \\rightarrow 0 ^{+}$, which makes the traditional cancellation technique incapable. Here we employ the Hardy inequality and delicate weighted energy estimates to overcome this obstacle and derive the requisite uniform-in-$\\varepsilon$ estimates allowing us to pass the limit $\\varepsilon \\to 0$ to achieve our results.", "field": "math", "label": 0}
{"text": "Title: Gromov's Oka principle, fiber bundles and the conformal module\nAbstract: The conformal module of conjugacy classes of braids is an invariant that appeared earlier than the entropy of conjugacy classes of braids, and is inverse proportional to the entropy. Using the relation between the two invariants we give a short conceptional proof of an earlier result on the conformal module. Mainly, we consider situations, when the conformal module of conjugacy classes of braids serves as obstruction for the existence of homotopies (or isotopies) of smooth objects involving braids to the respective holomorphic objects, and present theorems on the restricted validity of Gromov's Oka principle in these situations.", "field": "math", "label": 1}
{"text": "Title: Weighted Proportional Allocations of Indivisible Goods and Chores: Insights via Matchings\nAbstract: We study the fair allocation of indivisible goods and chores under ordinal valuations for agents with unequal entitlements. We show the existence and polynomial time computation of weighted necessarily proportional up to one item (WSD-PROP1) allocations for both goods and chores, by reducing it to a problem of finding perfect matchings in a bipartite graph. We give a complete characterization of these allocations as corner points of a perfect matching polytope. Using this polytope, we can optimize over all allocations to find a min-cost WSD-PROP1 allocation of goods or most efficient WSD-PROP1 allocation of chores. Additionally, we show the existence and computation of sequencible (SEQ) WSD-PROP1 allocations by using rank-maximal perfect matching algorithms and show incompatibility of Pareto optimality under all valuations and WSD-PROP1. We also consider the Best-of-Both-Worlds (BoBW) fairness notion. By using our characterization, we show the existence and polynomial time computation of Ex-ante envy free (WSD-EF) and Ex-post WSD-PROP1 allocations under ordinal valuations for both chores and goods.", "field": "cs", "label": 0}
{"text": "Title: Joint Matrix-Tensor Factorization for Knowledge Base Inference\nAbstract: While several matrix factorization (MF) and tensor factorization (TF) models have been proposed for knowledge base (KB) inference, they have rarely been compared across various datasets. Is there a single model that performs well across datasets? If not, what characteristics of a dataset determine the performance of MF and TF models? Is there a joint TF+MF model that performs robustly on all datasets? We perform an extensive evaluation to compare popular KB inference models across popular datasets in the literature. In addition to answering the questions above, we remove a limitation in the standard evaluation protocol for MF models, propose an extension to MF models so that they can better handle out-of-vocabulary (OOV) entity pairs, and develop a novel combination of TF and MF models. We also analyze and explain the results based on models and dataset characteristics. Our best model is robust, and obtains strong results across all datasets.", "field": "cs", "label": 1}
{"text": "Title: VSFormer: Visual-Spatial Fusion Transformer for Correspondence Pruning\nAbstract: Correspondence pruning aims to find correct matches (inliers) from an initial set of putative correspondences, which is a fundamental task for many applications. The process of finding is challenging, given the varying inlier ratios between scenes/image pairs due to significant visual differences. However, the performance of the existing methods is usually limited by the problem of lacking visual cues (\\eg texture, illumination, structure) of scenes. In this paper, we propose a Visual-Spatial Fusion Transformer (VSFormer) to identify inliers and recover camera poses accurately. Firstly, we obtain highly abstract visual cues of a scene with the cross attention between local features of two-view images. Then, we model these visual cues and correspondences by a joint visual-spatial fusion module, simultaneously embedding visual cues into correspondences for pruning. Additionally, to mine the consistency of correspondences, we also design a novel module that combines the KNN-based graph and the transformer, effectively capturing both local and global contexts. Extensive experiments have demonstrated that the proposed VSFormer outperforms state-of-the-art methods on outdoor and indoor benchmarks. Our code is provided at the following repository: https://github.com/sugar-fly/VSFormer.", "field": "cs", "label": 0}
{"text": "Title: LaDe: The First Comprehensive Last-mile Delivery Dataset from Industry\nAbstract: Real-world last-mile delivery datasets are crucial for research in logistics, supply chain management, and spatio-temporal data mining. Despite a plethora of algorithms developed to date, no widely accepted, publicly available last-mile delivery dataset exists to support research in this field. In this paper, we introduce \\texttt{LaDe}, the first publicly available last-mile delivery dataset with millions of packages from the industry. LaDe has three unique characteristics: (1) Large-scale. It involves 10,677k packages of 21k couriers over 6 months of real-world operation. (2) Comprehensive information. It offers original package information, such as its location and time requirements, as well as task-event information, which records when and where the courier is while events such as task-accept and task-finish events happen. (3) Diversity. The dataset includes data from various scenarios, including package pick-up and delivery, and from multiple cities, each with its unique spatio-temporal patterns due to their distinct characteristics such as populations. We verify LaDe on three tasks by running several classical baseline models per task. We believe that the large-scale, comprehensive, diverse feature of LaDe can offer unparalleled opportunities to researchers in the supply chain community, data mining community, and beyond. The dataset homepage is publicly available at https://huggingface.co/datasets/Cainiao-AI/LaDe.", "field": "cs", "label": 0}
{"text": "Title: 3-anti-power uniform morphisms\nAbstract: Words whose three successive factors of the same length are all different i.e. 3-anti-power words are a natural extension of square-free words (two successive factors of the same length are different). We give a way to verify whether a uniform morphism preserves 3-anti-power words (the image of a 3-anti-power word is a 3-anti-power word). A consequence of the existence of such morphisms is the possibility of generating an infinite 3-anti-power word.", "field": "cs", "label": 0}
{"text": "Title: Ramified covering maps of singular curves and stability of pulled back bundles\nAbstract: Let $f : X \\rightarrow Y$ be a generically smooth nonconstant morphism between irreducible projective curves, defined over an algebraically closed field, which is \\'etale on an open subset of $Y$ that contains both the singular locus of $Y$ and the image, in $Y$, of the singular locus of $X$. We prove that the following statements are equivalent: \\begin{enumerate} \\item The homomorphism of \\'etale fundamental groups $$f_* : \\pi_1^{\\rm et}(X) \\rightarrow\\pi_1^{\\rm et}(Y)$$ induced by $f$ is surjective. \\item There is no nontrivial \\'etale covering $\\phi : Y' \\rightarrow Y$ admitting a morphism $q: X \\rightarrow Y'$ such that $\\phi\\circ q = f$. \\item The fiber product $X\\times_Y X$ is connected. \\item $\\dim H^0(X, f^*f_* {\\mathcal O}_X)= 1$. \\item ${\\mathcal O}_Y \\subset f_*{\\mathcal O}_X$ is the maximal semistable subsheaf. \\item The pullback $f^*E$ of every stable sheaf $E$ on $Y$ is also stable. \\end{enumerate}", "field": "math", "label": 0}
{"text": "Title: The Adjoint Representation of a Higher Lie Groupoid\nAbstract: We extend the standard construction of the adjoint representation of a Lie groupoid to the case of an arbitrary higher Lie groupoid. As for a Lie groupoid, the adjoint representation of a higher Lie groupoid turns out to be a representation up to homotopy which is well defined up to isomorphism. Its existence and uniqueness are immediate consequences of a more general result in the theory of simplicial vector bundles: the representation up to homotopy obtained by splitting a higher vector bundle by means of a cleavage is, to within isomorphism, independent of the choice of the cleavage.", "field": "math", "label": 0}
{"text": "Title: On Nontrivial Winning and Losing Parameters of Schmidt Games\nAbstract: In this paper we completely describe the winning and losing conditions different from the only ``trivial'' conditions known before. In other words, we solve the open question of finding a complete nontrivial Schmidt diagram. In addition, we give the new bounds for two family of sets: one related to frequencies of digits in base-$2$ expansions, and one connected to the set of the badly approximable numbers.", "field": "math", "label": 0}
{"text": "Title: SuperEdge: Towards a Generalization Model for Self-Supervised Edge Detection\nAbstract: Edge detection is a fundamental technique in various computer vision tasks. Edges are indeed effectively delineated by pixel discontinuity and can offer reliable structural information even in textureless areas. State-of-the-art heavily relies on pixel-wise annotations, which are labor-intensive and subject to inconsistencies when acquired manually. In this work, we propose a novel self-supervised approach for edge detection that employs a multi-level, multi-homography technique to transfer annotations from synthetic to real-world datasets. To fully leverage the generated edge annotations, we developed SuperEdge, a streamlined yet efficient model capable of concurrently extracting edges at pixel-level and object-level granularity. Thanks to self-supervised training, our method eliminates the dependency on manual annotated edge labels, thereby enhancing its generalizability across diverse datasets. Comparative evaluations reveal that SuperEdge advances edge detection, demonstrating improvements of 4.9% in ODS and 3.3% in OIS over the existing STEdge method on BIPEDv2.", "field": "cs", "label": 0}
{"text": "Title: Investigating the Suitability of Concept Drift Detection for Detecting Leakages in Water Distribution Networks\nAbstract: Leakages are a major risk in water distribution networks as they cause water loss and increase contamination risks. Leakage detection is a difficult task due to the complex dynamics of water distribution networks. In particular, small leakages are hard to detect. From a machine-learning perspective, leakages can be modeled as concept drift. Thus, a wide variety of drift detection schemes seems to be a suitable choice for detecting leakages. In this work, we explore the potential of model-loss-based and distribution-based drift detection methods to tackle leakage detection. We additionally discuss the issue of temporal dependencies in the data and propose a way to cope with it when applying distribution-based detection. We evaluate different methods systematically for leakages of different sizes and detection times. Additionally, we propose a first drift-detection-based technique for localizing leakages.", "field": "cs", "label": 0}
{"text": "Title: Design and Actuator Optimization of Lightweight and Compliant Knee Exoskeleton for Mobility Assistance of Children with Crouch Gait\nAbstract: Pediatric exoskeletons offer great promise to increase mobility for children with crouch gait caused by cerebral palsy. A lightweight, compliant and user-specific actuator is critical for maximizing the benefits of an exoskeleton to users. To date, pediatric exoskeletons generally use the same actuators as adult exoskeletons, which are heavy and resistive to natural movement. There is yet no easy way for robotic exoskeletons to accommodate the changes in design requirements that occur as a child ages. We developed a lightweight (1.65 kg unilateral mass) and compliant pediatric knee exoskeleton with a bandwidth of 22.6 Hz that can provide torque assistance to children with crouch gait using high torque density motor. Experimental results demonstrated that the robot exhibited low mechanical impedance (1.79 Nm average backdrive torque) under the unpowered condition and 0.32 Nm with zero-torque tracking control. Root mean square (RMS) error of torque tracking result is less than 0.73 Nm (5.7% with respect to 12 Nm torque). To achieve optimal age-specific performance, we proposed the first optimization framework that considered both motor and transmission of the actuator system that can produce optimal settings for children between 3 and 18 years old. The optimization generated an optimal motor air gap radius that monotonically increases with age from 0.011 to 0.033 meters, and optimal gear ratio varies from 2.6 to 11.6 (3-13 years old) and 11.6 to 10.2 (13-18 years old), leading to actuators of minimal mass.", "field": "cs", "label": 1}
{"text": "Title: Clairvoyant embedding in one dimension\nAbstract: Let v, w be infinite 0-1 sequences, and m a positive integer. We say that w is m-embeddable in v, if there exists an increasing sequence n_{i} of integers with n_{0}=0, such that 0< n_{i} - n_{i-1} < m, w(i) = v(n_i) for all i > 0. Let X and Y be independent coin-tossing sequences. We will show that there is an m with the property that Y is m-embeddable into X with positive probability. This answers a question that was open for a while. The proof generalizes somewhat the hierarchical method of an earlier paper of the author on dependent percolation.", "field": "math", "label": 1}
{"text": "Title: Learning circuits with few negations\nAbstract: Monotone Boolean functions, and the monotone Boolean circuits that compute them, have been intensively studied in complexity theory. In this paper we study the structure of Boolean functions in terms of the minimum number of negations in any circuit computing them, a complexity measure that interpolates between monotone functions and the class of all functions. We study this generalization of monotonicity from the vantage point of learning theory, giving near-matching upper and lower bounds on the uniform-distribution learnability of circuits in terms of the number of negations they contain. Our upper bounds are based on a new structural characterization of negation-limited circuits that extends a classical result of A. A. Markov. Our lower bounds, which employ Fourier-analytic tools from hardness amplification, give new results even for circuits with no negations (i.e. monotone functions).", "field": "cs", "label": 1}
{"text": "Title: Affine homogeneous varieties and suspensions\nAbstract: An algebraic variety $X$ is called a homogeneous variety if the automorphism group $\\mathrm{Aut}(X)$ acts on $X$ transitively, and a homogeneous space if there exists a transitive action of an algebraic group on $X$. We prove a criterion of smoothness of a suspension to construct a wide class of homogeneous varieties. As an application, we give criteria for a Danielewski surface to be a homogeneous variety and a homogeneous space. Also, we construct affine suspensions of arbitrary dimension that are homogeneous varieties but not homogeneous spaces.", "field": "math", "label": 0}
{"text": "Title: A comparison of the Spectral Ewald and Smooth Particle Mesh Ewald methods in GROMACS\nAbstract: The smooth particle mesh Ewald (SPME) method is an FFT based method for the fast evaluation of electrostatic interactions under periodic boundary conditions. A highly optimized implementation of this method is available in GROMACS, a widely used software for molecular dynamics simulations. In this article, we compare a more recent method from the same family of methods, the spectral Ewald (SE) method, to the SPME method in terms of performance and efficiency. We consider serial and parallel implementations of both methods for single and multiple core computations on a desktop machine as well as the Beskow supercomputer at KTH Royal Institute of Technology. The implementation of the SE method has been well optimized, however not yet comparable to the level of the SPME implementation that has been improved upon for many years. We show that the SE method is very efficient whenever used to achieve high accuracy and that it already at this level of optimization can be competitive for low accuracy demands.", "field": "math", "label": 1}
{"text": "Title: tmf Is Not a Ring Spectrum Quotient of String Bordism\nAbstract: This paper shows that $\\mathrm{tmf}[1/6]$ is not a ring spectrum quotient of $\\mathrm{MO}\\langle8\\rangle[1/6]$. In fact, for any prime $p>3$ and any sequence $X$ of homogeneous elements of $\\pi_*\\mathrm{MO}\\langle8\\rangle$, the $\\pi_*\\mathrm{MO}\\langle8\\rangle$-module $$\\pi_*\\big(\\mathrm{MO}\\langle8\\rangle_{(p)}/X\\big)$$ is not (even abstractly) isomorphic to $\\pi_*\\mathrm{tmf}_{(p)}$. It does so by showing that, for any commutative ring spectrum $R$ and any sequence $X$ of homogeneous elements of $\\pi_*(R)$, there is an isomorphism of graded $\\mathbf{Q}$-vector spaces $$\\pi_*(R/X)\\otimes\\mathbf{Q} \\cong \\mathrm{H}_*(\\mathrm{Tot}(\\mathrm{K}(X)))\\otimes\\mathbf{Q},$$ where the right-hand side is the rational homology of the (total) Koszul complex of $X$, which is strictly bigger than $\\pi_*(R)/(X)\\otimes\\mathbf{Q}$ unless $X$ is a $\\pi_*(R)\\otimes\\mathbf{Q}$-quasi-regular sequence. The result then follows from the fact that the kernel of the $p$-local Witten genus cannot be generated by a $\\pi_*\\mathrm{MO}\\langle8\\rangle\\otimes\\mathbf{Q}$-quasi-regular sequence.", "field": "math", "label": 1}
{"text": "Title: A note on minor antichains of uncountable graphs\nAbstract: A simplified construction is presented for Komj\\'ath's result that for every uncountable cardinal $\\kappa$, there are $2^\\kappa$ graphs of size $\\kappa$ none of them being a minor of another.", "field": "math", "label": 1}
{"text": "Title: Introduction of Probabilistic Algebraic Variety\nAbstract: Historically, probability theory has been studied for a long time, and Kolmogorov, Levy Ito Kiyoshi, and others have mathematically developed modern probability in conjunction with measurement theory. On the other hand, commutative algebra and algebraic geometry have historically been the subject of interdisciplinary research led by Grothendiek. Many Japanese, notably Matsumura, Hironaka, and Kodaira, have contributed to this field. This paper is an attempt to focus on the research theme of Professor Sumio Watanabe of Tokyo Institute of Technology, \"Algebraic Geometry and Probability Theory,\" from my own perspective. The mathematical theory development starts from Kolmogorov's axioms, and the proof and introduction of \"Probabilistic Algebraic Variety\" are given. Problems in computation and applications, analysis by computational homology, and unsolved problems in regression problems will be introduced as applications to statistics.", "field": "math", "label": 0}
{"text": "Title: The Constrained Round Robin Algorithm for Fair and Efficient Allocation\nAbstract: We consider a multi-agent resource allocation setting that models the assignment of papers to reviewers. A recurring issue in allocation problems is the compatibility of welfare/efficiency and fairness. Given an oracle to find a welfare-achieving allocation, we embed such an oracle into a flexible algorithm called the Constrained Round Robin (CRR) algorithm, that achieves the required welfare level. Our algorithm also allows the system designer to lower the welfare requirements in order to achieve a higher degree of fairness. If the welfare requirement is lowered enough, a strengthening of envy-freeness up to one item is guaranteed. Hence, our algorithm can be viewed as a computationally efficient way to interpolate between welfare and approximate envy-freeness in allocation problems.", "field": "cs", "label": 1}
{"text": "Title: A Generalized Variable Projection Algorithm for Least Squares Problems in Atmospheric Remote Sensing\nAbstract: This paper presents a solution for efficiently and accurately solving separable least squares problems with multiple datasets. These problems involve determining linear parameters that are specific to each dataset while ensuring that the nonlinear parameters remain consistent across all datasets. A well-established approach for solving such problems is the variable projection algorithm introduced by Golub and LeVeque, which effectively reduces a separable problem to its nonlinear component. However, this algorithm assumes that the datasets have equal sizes and identical auxiliary model parameters. This article is motivated by a real-world remote sensing application where these assumptions do not apply. Consequently, we propose a generalized algorithm that extends the original theory to overcome these limitations. The new algorithm has been implemented and tested using both synthetic and real satellite data for atmospheric carbon dioxide retrievals. It has also been compared to conventional state-of-the-art solvers, and its advantages are thoroughly discussed. The experimental results demonstrate that the proposed algorithm significantly outperforms all other methods in terms of computation time, while maintaining comparable accuracy and stability. Hence, this novel method can have a positive impact on future applications in remote sensing and could be valuable for other scientific fitting problems with similar properties.", "field": "math", "label": 0}
{"text": "Title: Phenotype switching in chemotaxis aggregation models controls the spontaneous emergence of large densities\nAbstract: We consider a phenotype-switching chemotaxis model for aggregation, in which a chemotactic population is capable of switching back and forth between a chemotaxing state (performing chemotactic movement) and a secreting state (producing the attractant). We show that the switching rate provides a powerful mechanism for controlling the densities of spontaneously emerging aggregates. Specifically, in two- and three-dimensional settings it is shown that when both switching rates coincide and are suitably large, then the densities of both the chemotaxing and the secreting population will exceed any prescribed level at some points in the considered domain. This is complemented by two results asserting the absence of such aggregation phenomena in corresponding scenarios in which one of the switching rates remains within some bounded interval.", "field": "math", "label": 1}
{"text": "Title: Lower Bounds on Cardinality of Reducts for Decision Tables from Closed Classes\nAbstract: In this paper, we consider classes of decision tables closed under removal of attributes (columns) and changing of decisions attached to rows. For decision tables from closed classes, we study lower bounds on the minimum cardinality of reducts, which are minimal sets of attributes that allow us to recognize, for a given row, the decision attached to it. We assume that the number of rows in decision tables from the closed class is not bounded from above by a constant. We divide the set of such closed classes into two families. In one family, only standard lower bounds $\\Omega (\\log $ ${\\rm cl}(T))$ on the minimum cardinality of reducts for decision tables hold, where ${\\rm cl}(T)$ is the number of decision classes in the table $T$. In another family, these bounds can be essentially tightened up to $\\Omega ({\\rm cl}(T)^{1/q})$ for some natural $q$.", "field": "cs", "label": 0}
{"text": "Title: CAD-compatible structural shape optimization with a movable Bézier tetrahedral mesh\nAbstract: This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with B\\'ezier tetrahedra. The tetrahedral mesh is obtained from the mesh generator software Gmsh. A methodology to reconstruct the NURBS surfaces from the triangular faces of the boundary mesh is presented. The description of the boundary is used for the computation of the analytical sensitivities with respect to the control points employed in surface design. Further, the mesh is updated at each iteration of the structural optimization process by a pseudo-elastic moving mesh method. In this procedure, the existing mesh is deformed to match the updated surface and therefore reduces the need for remeshing. Numerical examples are presented to test the performance of the proposed method. The use of the movable mesh technique results in a considerable decrease in the computational effort for the numerical examples.", "field": "cs", "label": 0}
{"text": "Title: Descent distribution on Catalan words avoiding a pattern of length at most three\nAbstract: Catalan words are particular growth-restricted words over the set of non-negative integers, and they represent still another combinatorial class counted by the Catalan numbers. We study the distribution of descents on the sets of Catalan words avoiding a pattern of length at most three: for each such a pattern $p$ we provide a bivariate generating function where the coefficient of $x^ny^k$ in its series expansion is the number of length $n$ Catalan words with $k$ descents and avoiding $p$. As a byproduct, we enumerate the set of Catalan words avoiding $p$, and we provide the popularity of descents on this set. Some of the obtained enumerating sequences are not yet recorded in the On-line Encyclopedia of Integer Sequences.", "field": "math", "label": 1}
{"text": "Title: DEWP: Deep Expansion Learning for Wind Power Forecasting\nAbstract: Wind is one kind of high-efficient, environmentally-friendly and cost-effective energy source. Wind power, as one of the largest renewable energy in the world, has been playing a more and more important role in supplying electricity. Though growing dramatically in recent years, the amount of generated wind power can be directly or latently affected by multiple uncertain factors, such as wind speed, wind direction, temperatures, etc. More importantly, there exist very complicated dependencies of the generated power on the latent composition of these multiple time-evolving variables, which are always ignored by existing works and thus largely hinder the prediction performances. To this end, we propose DEWP, a novel Deep Expansion learning for Wind Power forecasting framework to carefully model the complicated dependencies with adequate expressiveness. DEWP starts with a stack-by-stack architecture, where each stack is composed of (i) a variable expansion block that makes use of convolutional layers to capture dependencies among multiple variables; (ii) a time expansion block that applies Fourier series and backcast/forecast mechanism to learn temporal dependencies in sequential patterns. These two tailored blocks expand raw inputs into different latent feature spaces which can model different levels of dependencies of time-evolving sequential data. Moreover, we propose an inference block corresponding for each stack, which applies multi-head self-attentions to acquire attentive features and maps expanded latent representations into generated wind power. In addition, to make DEWP more expressive in handling deep neural architectures, we adapt doubly residue learning to process stack-by-stack outputs. Finally, we present extensive experiments in the real-world wind power forecasting application on two datasets from two different turbines to demonstrate the effectiveness of our approach.", "field": "cs", "label": 0}
{"text": "Title: A quatum inspired neural network for geometric modeling\nAbstract: By conceiving physical systems as 3D many-body point clouds, geometric graph neural networks (GNNs), such as SE(3)/E(3) equivalent GNNs, have showcased promising performance. In particular, their effective message-passing mechanics make them adept at modeling molecules and crystalline materials. However, current geometric GNNs only offer a mean-field approximation of the many-body system, encapsulated within two-body message passing, thus falling short in capturing intricate relationships within these geometric graphs. To address this limitation, tensor networks, widely employed by computational physics to handle manybody systems using high-order tensors, have been introduced. Nevertheless, integrating these tensorized networks into the message-passing framework of GNNs faces scalability and symmetry conservation (e.g., permutation and rotation) challenges. In response, we introduce an innovative equivariant Matrix Product State (MPS)-based message-passing strategy, through achieving an efficient implementation of the tensor contraction operation. Our method effectively models complex many-body relationships, suppressing mean-field approximations, and captures symmetries within geometric graphs. Importantly, it seamlessly replaces the standard message-passing and layer-aggregation modules intrinsic to geometric GNNs. We empirically validate the superior accuracy of our approach on benchmark tasks, including predicting classical Newton systems and quantum tensor Hamiltonian matrices. To our knowledge, our approach represents the inaugural utilization of parameterized geometric tensor networks.", "field": "cs", "label": 0}
{"text": "Title: The colouring number of infinite graphs\nAbstract: We show that, given an infinite cardinal $\\mu$, a graph has colouring number at most $\\mu$ if and only if it contains neither of two types of subgraph. We also show that every graph with infinite colouring number has a well-ordering of its vertices that simultaneously witnesses its colouring number and its cardinality.", "field": "math", "label": 1}
{"text": "Title: Constant Step Size Least-Mean-Square: Bias-Variance Trade-offs and Optimal Sampling Distributions\nAbstract: We consider the least-squares regression problem and provide a detailed asymptotic analysis of the performance of averaged constant-step-size stochastic gradient descent (a.k.a. least-mean-squares). In the strongly-convex case, we provide an asymptotic expansion up to explicit exponentially decaying terms. Our analysis leads to new insights into stochastic approximation algorithms: (a) it gives a tighter bound on the allowed step-size; (b) the generalization error may be divided into a variance term which is decaying as O(1/n), independently of the step-size $\\gamma$, and a bias term that decays as O(1/$\\gamma$ 2 n 2); (c) when allowing non-uniform sampling, the choice of a good sampling density depends on whether the variance or bias terms dominate. In particular, when the variance term dominates, optimal sampling densities do not lead to much gain, while when the bias term dominates, we can choose larger step-sizes that leads to significant improvements.", "field": "cs", "label": 1}
{"text": "Title: First mixed Laplace eigenfunctions with no hot spots\nAbstract: The hot spots conjecture of J. Rauch states that the second Neumann eigenfunction of the Laplace operator on a bounded Lipschitz domain in $\\mathbb{R}^n$ attains its extrema only on the boundary of the domain. We present an analogous problem for domains with mixed Dirichlet-Neumann boundary conditions. We then solve this problem for Euclidean triangles and a class of planar domains bounded by the graphs of certain piecewise smooth functions.", "field": "math", "label": 0}
{"text": "Title: An obstruction relating locally finite polygons to translation quadrangles\nAbstract: One of the most fundamental open problems in Incidence Geometry, posed by Tits in the 1960s, asks for the existence of so-called \"locally finite generalized polygons\" | that is, generalized polygons with \"mixed parameters\" (one being finite and the other not). In a more specialized context, another long-standing problem (from the 1990s) is as to whether the endomorphism ring of any translation generalized quadrangle is a skew field (the answer of which is known in the finite case). (The analogous problem for projective planes, and its positive solution, the \"Bruck-Bose construction,\" lies at the very base of the whole theory of translation planes.) In this short note, we introduce a category, representing certain very specific embeddings of generalized polygons, which surprisingly controls the solution of both (apparently entirely unrelated) problems.", "field": "math", "label": 1}
{"text": "Title: Universal height and width bounds for random trees\nAbstract: We prove non-asymptotic stretched exponential tail bounds on the height of a randomly sampled node in a random combinatorial tree, which we use to prove bounds on the heights and widths of random trees from a variety of models. Our results allow us to prove a conjecture and settle an open problem of Janson (https://doi.org/10.1214/11-PS188), and nearly prove another conjecture and settle another open problem from the same work (up to a polylogarithmic factor). The key tool for our work is an equivalence in law between the degrees along the path to a random node in a random tree with given degree statistics, and a random truncation of a size-biased ordering of the degrees of such a tree. We also exploit a Poissonization trick introduced by Camarri and Pitman (https://doi.org/10.1214/EJP.v5-58) in the context of inhomogeneous continuum random trees, which we adapt to the setting of random trees with fixed degrees. Finally, we propose and justify a change to the conventions of branching process nomenclature: the name \"Galton-Watson trees\" should be permanently retired by the community, and replaced with the name \"Bienaym\\'e trees\".", "field": "math", "label": 1}
{"text": "Title: Approximation of polynomials from Walsh tail spaces\nAbstract: We derive various bounds for the $L_p$ distance of polynomials on the hypercube from Walsh tail spaces, extending some of Oleszkiewicz's results (2017) for Rademacher sums.", "field": "math", "label": 0}
{"text": "Title: The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds\nAbstract: We establish a connection between the Alexander polynomial of a knot and its twisted and $L^2$-versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier matrices of ordered ideal triangulations and use them to provide formulas for the Alexander polynomial and its variants, the twisted Alexander polynomial and the $L^2$-Alexander torsion.", "field": "math", "label": 0}
{"text": "Title: Age-Aware Dynamic Frame Slotted ALOHA for Machine-Type Communications\nAbstract: Information aging has gained prominence in characterizing communication protocols for timely remote estimation and control applications. This work proposes an Age of Information (AoI)-aware threshold-based dynamic frame slotted ALOHA (T-DFSA) for contention resolution in random access machine-type communication networks. Unlike conventional DFSA that maximizes the throughput in each frame, the frame length and age-gain threshold in T-DFSA are determined to minimize the normalized average AoI reduction of the network in each frame. At the start of each frame in the proposed protocol, the common Access Point (AP) stores an estimate of the age-gain distribution of a typical node. Depending on the observed status of the slots, age-gains of successful nodes, and maximum available AoI, the AP adjusts its estimation in each frame. The maximum available AoI is exploited to derive the maximum possible age-gain at each frame and thus, to avoid overestimating the age-gain threshold, which may render T-DFSA unstable. Numerical results validate our theoretical analysis and demonstrate the effectiveness of the proposed T-DFSA compared to the existing optimal frame slotted ALOHA, threshold-ALOHA, and age-based thinning protocols in a considerable range of update generation rates.", "field": "cs", "label": 0}
{"text": "Title: A note on a Sung-Wang's paper\nAbstract: The purpose of this note is to study the connectedness at infinity of manifold by using the theory of $p$-harmonic functions. We show that if the first eigenvalue $\\lambda_{1,p}$ for the $p$-Laplacian achievies its maximal value on a K\\\"{a}hler manifold or a quaternionic K\\\"{a}hler manifold then such a manifold must be connected at infinity unless it is a topological cylinder with an explicit warped product metric.", "field": "math", "label": 1}
{"text": "Title: Derivative-Based Diagnosis of Regular Expression Ambiguity\nAbstract: Regular expressions are often ambiguous. We present a novel method based on Brzozowski's derivatives to aid the user in diagnosing ambiguous regular expressions. We introduce a derivative-based finite state transducer to generate parse trees and minimal counter-examples. The transducer can be easily customized to either follow the POSIX or Greedy disambiguation policy and based on a finite set of examples it is possible to examine if there are any differences among POSIX and Greedy.", "field": "cs", "label": 1}
{"text": "Title: Cartesian closed and stable subconstructs of Q-Ord\nAbstract: It is shown that the category of fuzzy ordered sets and order-preserving maps valued in the quantale based on a continuous triangular norm on the unit interval contains a largest Cartesian closed and stable subconstruct which contains all crisp ordered sets.", "field": "math", "label": 0}
{"text": "Title: Quantum rigidity of negatively curved manifolds\nAbstract: We show that an isometric action of a compact quantum group on the underlying geodesic metric space of a compact connected Riemannian manifold $(M,g)$ with strictly negative curvature is automatically classical, in the sense that it factors through the action of the isometry group of $(M,g)$. This partially answers a question by D. Goswami.", "field": "math", "label": 1}
{"text": "Title: Using Schur Rings to Produce GRRs for Dihedral Groups\nAbstract: In this paper we shall be looking at several results relating Schur rings to sufficient conditions for a graph to be a graphical regular representation (GRR) of a finite group, and then applying these specifically in the case of certain subfamilies of dihedral groups. Numerical methods are given for constructing trivalent GRRs for these dihedral groups very quickly.", "field": "math", "label": 0}
{"text": "Title: Investigating EEG-Based Functional Connectivity Patterns for Multimodal Emotion Recognition\nAbstract: Compared with the rich studies on the motor brain-computer interface (BCI), the recently emerging affective BCI presents distinct challenges since the brain functional connectivity networks involving emotion are not well investigated. Previous studies on emotion recognition based on electroencephalography (EEG) signals mainly rely on single-channel-based feature extraction methods. In this paper, we propose a novel emotion-relevant critical subnetwork selection algorithm and investigate three EEG functional connectivity network features: strength, clustering coefficient, and eigenvector centrality. The discrimination ability of the EEG connectivity features in emotion recognition is evaluated on three public emotion EEG datasets: SEED, SEED-V, and DEAP. The strength feature achieves the best classification performance and outperforms the state-of-the-art differential entropy feature based on single-channel analysis. The experimental results reveal that distinct functional connectivity patterns are exhibited for the five emotions of disgust, fear, sadness, happiness, and neutrality. Furthermore, we construct a multimodal emotion recognition model by combining the functional connectivity features from EEG and the features from eye movements or physiological signals using deep canonical correlation analysis. The classification accuracies of multimodal emotion recognition are 95.08/6.42% on the SEED dataset, 84.51/5.11% on the SEED-V dataset, and 85.34/2.90% and 86.61/3.76% for arousal and valence on the DEAP dataset, respectively. The results demonstrate the complementary representation properties of the EEG connectivity features with eye movement data. In addition, we find that the brain networks constructed with 18 channels achieve comparable performance with that of the 62-channel network in multimodal emotion recognition and enable easier setups for BCI systems in real scenarios.", "field": "cs", "label": 1}
{"text": "Title: Strongly Minimal Steiner Systems I: Existence\nAbstract: A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner $k$-system (for $k \\geq 2$) is a linear space such that each line has size exactly $k$. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a (bi-interpretable) vocabulary $\\tau$ with a single ternary relation $R$. We prove that for every integer $k$ there exist $2^{\\aleph_0}$-many integer valued functions $\\mu$ such that each $\\mu$ determines a distinct strongly minimal Steiner $k$-system $\\mathcal{G}_\\mu$, whose algebraic closure geometry has all the properties of the ab initio Hrushovski construction. Thus each is a counterexample to the Zilber Trichotomy Conjecture.", "field": "math", "label": 1}
{"text": "Title: Learning to Generate Training Datasets for Robust Semantic Segmentation\nAbstract: Semantic segmentation methods have advanced significantly. Still, their robustness to real-world perturbations and object types not seen during training remains a challenge, particularly in safety-critical applications. We propose a novel approach to improve the robustness of semantic segmentation techniques by leveraging the synergy between label-to-image generators and image-to-label segmentation models. Specifically, we design Robusta, a novel robust conditional generative adversarial network to generate realistic and plausible perturbed images that can be used to train reliable segmentation models. We conduct in-depth studies of the proposed generative model, assess the performance and robustness of the downstream segmentation network, and demonstrate that our approach can significantly enhance the robustness in the face of real-world perturbations, distribution shifts, and out-of-distribution samples. Our results suggest that this approach could be valuable in safety-critical applications, where the reliability of perception modules such as semantic segmentation is of utmost importance and comes with a limited computational budget in inference. We release our code at https://github.com/ENSTA-U2IS/robusta.", "field": "cs", "label": 0}
{"text": "Title: Homogenization and nonselfadjoint spectral optimization for dissipative Maxwell eigenproblems\nAbstract: The homogenization of eigenvalues of non-Hermitian Maxwell operators is studied by the H-convergence method. It is assumed that the Maxwell systems are equipped with suitable m-dissipative boundary conditions, namely, with Leontovich or generalized impedance boundary conditions of the form $n \\times E = Z [(n \\times H )\\times n ] $. We show that, for a wide class of impedance operators $Z$, the nonzero spectrum of the corresponding Maxwell operator is discrete. To this end, a new continuous embedding theorem for domains of Maxwell operators is obtained. We prove the convergence of eigenvalues to an eigenvalue of a homogenized Maxwell operator under the assumption of the H-convergence of the material tensor-fields. This result is applied then to the existence of optimizers for eigenvalue optimization problems and to the existence of an eigenvalue-free region around zero. Connections with unique (and nonunique) continuation results are discussed.", "field": "math", "label": 0}
{"text": "Title: Stochastic Analysis of an Adaptive Cubic Regularisation Method under Inexact Gradient Evaluations and Dynamic Hessian Accuracy\nAbstract: We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still considered, this novel variant inherits the innovative use of adaptive accuracy requirements for Hessian approximations introduced in [3] and additionally employs inexact computations of the gradient. Without restrictions on the variance of the errors, we assume that these approximations are available within a sufficiently large, but fixed, probability and we extend, in the spirit of [18], the deterministic analysis of the framework to its stochastic counterpart, showing that the expected number of iterations to reach a first-order stationary point matches the well known worst-case optimal complexity. This is, in fact, still given by O(epsilon^(-3/2)), with respect to the first-order epsilon tolerance. Finally, numerical tests on nonconvex finite-sum minimisation confirm that using inexact first and second-order derivatives can be beneficial in terms of the computational savings.", "field": "math", "label": 1}
{"text": "Title: SwitchTab: Switched Autoencoders Are Effective Tabular Learners\nAbstract: Self-supervised representation learning methods have achieved significant success in computer vision and natural language processing, where data samples exhibit explicit spatial or semantic dependencies. However, applying these methods to tabular data is challenging due to the less pronounced dependencies among data samples. In this paper, we address this limitation by introducing SwitchTab, a novel self-supervised method specifically designed to capture latent dependencies in tabular data. SwitchTab leverages an asymmetric encoder-decoder framework to decouple mutual and salient features among data pairs, resulting in more representative embeddings. These embeddings, in turn, contribute to better decision boundaries and lead to improved results in downstream tasks. To validate the effectiveness of SwitchTab, we conduct extensive experiments across various domains involving tabular data. The results showcase superior performance in end-to-end prediction tasks with fine-tuning. Moreover, we demonstrate that pre-trained salient embeddings can be utilized as plug-and-play features to enhance the performance of various traditional classification methods (e.g., Logistic Regression, XGBoost, etc.). Lastly, we highlight the capability of SwitchTab to create explainable representations through visualization of decoupled mutual and salient features in the latent space.", "field": "cs", "label": 0}
{"text": "Title: An Inversion Formula for the Gaussian Radon Transform for Banach Spaces\nAbstract: We provide a disintegration theorem for the Gaussian Radon transform Gf on Banach spaces and use the Segal-Bargmann transform on abstract Wiener spaces to find a procedure to obtain f from its Gaussian Radon transform Gf.", "field": "math", "label": 1}
{"text": "Title: Further Explanations on \"SAT Requires Exhaustive Search\"\nAbstract: Recently, Xu and Zhou [2023] introduced a constructive approach for exploring computational hardness, proving that SAT requires exhaustive search. In light of certain misinterpretations concerning the contributions and proofs in that paper, we focus on providing detailed explanations in this work. We begin by delineating the core innovation of the constructive approach, shedding light on the pivotal concept of algorithm designability. We address the overlooked white-box diagonalization method and highlight the concept of an almost independent solution space. In response to specific misunderstandings, such as the concerns surrounding the assumptions of Lemma 3.1, we offer comprehensive clarifications aimed at improving the comprehension of the proof. We are grateful for the feedback received on our prior paper and hope this work can foster a more well-informed discussion.", "field": "cs", "label": 0}
{"text": "Title: Complexity Classes and Completeness in Algebraic Geometry\nAbstract: We study the computational complexity of sequences of projective varieties. We define analogues of the complexity classes P and NP for these and prove the NP-completeness of a sequence called the universal circuit resultant. This is the first family of compact spaces shown to be NP-complete in a geometric setting.", "field": "math", "label": 1}
{"text": "Title: Lower bounds for the eigenvalue estimates of the submanifold Dirac operator\nAbstract: We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets several known results in this direction.", "field": "math", "label": 1}
{"text": "Title: Boltzmann equation with mixed boundary condition\nAbstract: We study the Boltzmann equation in a smooth bounded domain featuring a mixed boundary condition. Specifically, gas particles experience specular reflection in two parallel plates, while diffusive reflection occurs in the remaining portion between these two specular regions. The boundary is assumed to be motionless and isothermal. Our main focus is on constructing global-in-time small-amplitude solutions around global Maxwellians for the corresponding initial-boundary value problem. The proof relies on the $L^2$ hypocoercivity at the linear level, utilizing the weak formulation and various functional inequalities on the test functions, such as Poincar\\'e and Korn inequalities. It also extends to the linear problem involving Maxwell boundary conditions, where the accommodation coefficient can be a piecewise constant function on the boundary, allowing for more general bounded domains. Moreover, we develop a delicate application of the $L^2-L^\\infty$ bootstrap argument, which relies on the specific geometry of our domains, to effectively handle this mixed-type boundary condition.", "field": "math", "label": 0}
{"text": "Title: The triviality of a certain invariant of link maps in the four-sphere\nAbstract: It is an open problem whether Kirk's $\\sigma$ invariant is the complete obstruction to a link map $S^2\\cup S^2\\to S^4$ being link homotopically trivial. With the objective of constructing counterexamples, Li proposed a link homotopy invariant $\\omega$ that is defined on the kernel of $\\sigma$ and also obstructs link nullhomotopy. We show that $\\omega$ is determined by $\\sigma$, and is a strictly weaker invariant.", "field": "math", "label": 1}
{"text": "Title: Precondition and Effect Reasoning for Action Recognition\nAbstract: Human action recognition has drawn a lot of attention in the recent years due to the research and application significance. Most existing works on action recognition focus on learning effective spatial-temporal features from videos, but neglect the strong causal relationship among the precondition, action and effect. Such relationships are also crucial to the accuracy of action recognition. In this paper, we propose to model the causal relationships based on the precondition and effect to improve the performance of action recognition. Specifically, a Cycle-Reasoning model is proposed to capture the causal relationships for action recognition. To this end, we annotate precondition and effect for a large-scale action dataset. Experimental results show that the proposed Cycle-Reasoning model can effectively reason about the precondition and effect and can enhance action recognition performance.", "field": "cs", "label": 1}
{"text": "Title: A compactness result for the CR Yamabe problem in three dimensions\nAbstract: We prove the compactness of the set of solutions to the CR Yamabe problem on a compact strictly pseudoconvex CR manifold of dimension three whose blow-up manifolds at every point have positive p-mass. As a corollary we deduce that compactness holds for CR-embeddable manifolds which are not CR-equivalent to $S^3$. The theorem is proved by blow-up analysis.", "field": "math", "label": 0}
{"text": "Title: Software Testing, AI and Robotics (STAIR) Learning Lab\nAbstract: In this paper we presented the Software Testing, AI and Robotics (STAIR) Learning Lab. STAIR is an initiative started at the University of Innsbruck to bring robotics, Artificial Intelligence (AI) and software testing into schools. In the lab physical and virtual learning units are developed in parallel and in sync with each other. Its core learning approach is based the develop of both a physical and simulated robotics environment. In both environments AI scenarios (like traffic sign recognition) are deployed and tested. We present and focus on our newly designed MiniBot that are both built on hardware which was designed for educational and research purposes as well as the simulation environment. Additionally, we describe first learning design concepts and a showcase scenario (i.e., AI-based traffic sign recognition) with different exercises which can easily be extended.", "field": "cs", "label": 1}
{"text": "Title: From Merging Frameworks to Merging Stars: Experiences using HPX, Kokkos and SIMD Types\nAbstract: Octo-Tiger, a large-scale 3D AMR code for the merger of stars, uses a combination of HPX, Kokkos and explicit SIMD types, aiming to achieve performance-portability for a broad range of heterogeneous hardware. However, on A64FX CPUs, we encountered several missing pieces, hindering performance by causing problems with the SIMD vectorization. Therefore, we add std::experimental::simd as an option to use in Octo-Tiger's Kokkos kernels alongside Kokkos SIMD, and further add a new SVE (Scalable Vector Extensions) SIMD backend. Additionally, we amend missing SIMD implementations in the Kokkos kernels within Octo-Tiger's hydro solver. We test our changes by running Octo-Tiger on three different CPUs: An A64FX, an Intel Icelake and an AMD EPYC CPU, evaluating SIMD speedup and node-level performance. We get a good SIMD speedup on the A64FX CPU, as well as noticeable speedups on the other two CPU platforms. However, we also experience a scaling issue on the EPYC CPU.", "field": "cs", "label": 1}
{"text": "Title: DB-GPT: Empowering Database Interactions with Private Large Language Models\nAbstract: The recent breakthroughs in large language models (LLMs) are positioned to transition many areas of software. Database technologies particularly have an important entanglement with LLMs as efficient and intuitive database interactions are paramount. In this paper, we present DB-GPT, a revolutionary and production-ready project that integrates LLMs with traditional database systems to enhance user experience and accessibility. DB-GPT is designed to understand natural language queries, provide context-aware responses, and generate complex SQL queries with high accuracy, making it an indispensable tool for users ranging from novice to expert. The core innovation in DB-GPT lies in its private LLM technology, which is fine-tuned on domain-specific corpora to maintain user privacy and ensure data security while offering the benefits of state-of-the-art LLMs. We detail the architecture of DB-GPT, which includes a novel retrieval augmented generation (RAG) knowledge system, an adaptive learning mechanism to continuously improve performance based on user feedback and a service-oriented multi-model framework (SMMF) with powerful data-driven agents. Our extensive experiments and user studies confirm that DB-GPT represents a paradigm shift in database interactions, offering a more natural, efficient, and secure way to engage with data repositories. The paper concludes with a discussion of the implications of DB-GPT framework on the future of human-database interaction and outlines potential avenues for further enhancements and applications in the field. The project code is available at https://github.com/eosphoros-ai/DB-GPT. Experience DB-GPT for yourself by installing it with the instructions https://github.com/eosphoros-ai/DB-GPT#install and view a concise 10-minute video at https://www.youtube.com/watch?v=KYs4nTDzEhk.", "field": "cs", "label": 0}
{"text": "Title: Towards Abstract Wiener Model Spaces\nAbstract: Wiener spaces are in many ways the decisive setting for fundamental results on Gaussian measures: large deviations (Schilder), quasi-invariance (Cameron--Martin), differential calculus (Malliavin), support description (Stroock--Varadhan), concentration of measure (Fernique), ... Analogues of these classical results have been derived in the \"enhanced\" context of Gaussian rough paths and, more recently, regularity structures equipped with Gaussian models. The aim of this article is to propose a notion of \"abstract Wiener model space\" that encompasses the aforementioned. More specifically, we focus here on enhanced Schilder type results, Cameron--Martin shifts and Fernique estimates, offering a somewhat unified view on results in Friz--Victoir 2007 and Hairer--Weber 2015.", "field": "math", "label": 0}
{"text": "Title: Charatheodory and Smirnov type theorem for harmonic mappings\nAbstract: We prove a version of Smirnov type theorem and Charatheodory type theorem for a harmonic homeomorphism of the unit disk onto a Jordan surface with rectifiable boundary. Further we establish the classical isoperimetric inequality and Riesz--Zygmund inequality for Jordan harmonic surfaces without any smoothness assumptions of the boundary.", "field": "math", "label": 1}
{"text": "Title: Minimizing the Weighted Number of Tardy Jobs is W[1]-hard\nAbstract: We consider the $1||\\sum w_J U_j$ problem, the problem of minimizing the weighted number of tardy jobs on a single machine. This problem is one of the most basic and fundamental problems in scheduling theory, with several different applications both in theory and practice. We prove that $1||\\sum w_J U_j$ is W[1]-hard with respect to the number $p_{\\#}$ of different processing times in the input, as well as with respect to the number $w_{\\#}$ of different weights in the input. This, along with previous work, provides a complete picture for $1||\\sum w_J U_j$ from the perspective of parameterized complexity, as well as almost tight complexity bounds for the problem under the Exponential Time Hypothesis (ETH).", "field": "cs", "label": 0}
{"text": "Title: (Universal) Unconditional Verifiability in E-Voting without Trusted Parties\nAbstract: In traditional e-voting protocols, privacy is often provided by a trusted authority that learns the votes and computes the tally. Some protocols replace the trusted authority by a set of authorities, and privacy is guaranteed if less than a threshold number of authorities are corrupt. For verifiability, stronger security guarantees are demanded. Typically, corrupt authorities that try to fake the result of the tally must always be detected. To provide verifiability, many e-voting protocols use Non-Interactive Zero-Knowledge proofs (NIZKs). Thanks to their non-interactive nature, NIZKs allow anybody, including third parties that do not participate in the protocol, to verify the correctness of the tally. Therefore, NIZKs can be used to obtain universal verifiability. Additionally, NIZKs also improve usability because they allow voters to cast a vote using a non-interactive protocol. The disadvantage of NIZKs is that their security is based on setup assumptions such as the common reference string (CRS) or the random oracle (RO) model. The former requires a trusted party for the generation of a common reference string. The latter, though a popular methodology for designing secure protocols, has been shown to be unsound. In this paper, we address the design of an e-voting protocol that provides verifiability without any trust assumptions, where verifiability here is meant without eligibility verification. We show that Non-Interactive Witness-Indistinguishable proofs (NIWI) can be used for this purpose. The e-voting scheme is private under the Decision Linear assumption, while verifiability holds unconditionally. To our knowledge, this is the first private e-voting scheme with perfect universal verifiability, i.e. one in which the probability of a fake tally not being detected is 0, and with {\\em non-interactive} protocols that does not rely on trust assumptions.", "field": "cs", "label": 1}
{"text": "Title: The anti-Ramsey numbers of cliques in complete multi-partite graphs\nAbstract: A subgraph of an edge-colored graph is rainbow if all of its edges have different colors. Let $G$ and $H$ be two graphs. The anti-Ramsey number $\\ar(G, H)$ is the maximum number of colors of an edge-coloring of $G$ that does not contain a rainbow copy of $H$. In this paper, we study the anti-Ramsey numbers of $K_k$ in complete multi-partite graphs. We determine the values of the anti-Ramsey numbers of $K_k$ in complete $k$-partite graphs and in balanced complete $r$-partite graphs for $r\\geq k$.", "field": "math", "label": 0}
{"text": "Title: Radical subgroups of finite reductive groups\nAbstract: Radical subgroups play an important role in both group theory and representation theory. In this paper we present a strategy of classifying radical subgroups of finite reductive groups. As an application, we complete the proof of the inductive blockwise Alperin weight condition for the Chevalley groups $\\F_4(q)$, contributing to the program to prove the Alperin weight conjecture by verifying its inductive condition for simple groups.", "field": "math", "label": 0}
{"text": "Title: Log-Gamma polymer free energy fluctuations via a Fredholm determinant identity\nAbstract: We prove that under n^{1/3} scaling, the limiting distribution as n goes to infinity of the free energy of Seppalainen's log-Gamma discrete directed polymer is GUE Tracy-Widom. The main technical innovation we provide is a general identity between a class of n-fold contour integrals and a class of Fredholm determinants. Applying this identity to the integral formula proved in [Corwin-O'Connell-Seppalainen-Zygouras] for the Laplace transform of the log-Gamma polymer partition function, we arrive at a Fredholm determinant which lends itself to asymptotic analysis (and thus yields the free energy limit theorem). The Fredholm determinant was anticipated in [Borodin-Corwin] via the formalism of Macdonald processes yet its rigorous proof was so far lacking because of the nontriviality of certain decay estimates required by that approach.", "field": "math", "label": 1}
{"text": "Title: Uniform regularity estimates and invisicid limit for the compressible non-resistive magnetohydrodynamics system\nAbstract: We are concerned with the uniform regularity estimates of solutions to the two dimensional compressible non-resistive magnetohydrodynamics (MHD) equations with the no-slip boundary condition on velocity in the half plane. Under the assumption that the initial magnetic field is transverse to the boundary, the uniform conormal energy estimates are established for the solutions to compressible MHD equations with respect to small viscosity coefficients. As a direct consequence, we proved the inviscid limit of solutions from viscous MHD systems to the ideal MHD systems in $L^\\infty$ sense. It shows that the transverse magnetic field can prevent the boundary layers from occurring in some physical regime.", "field": "math", "label": 1}
{"text": "Title: On internal categories and crossed objects in the category of monoids\nAbstract: It is a well-known fact that the category $\\mathsf{Cat}(\\mathbf{C})$ of internal categories in a category $\\mathbf{C}$ has a description in terms of crossed modules, when $\\mathbf{C}=\\mathbf{Gr}$ is the category of groups. The proof of this result heavily uses the fact that any split epimorphism decomposes as a semi-direct product. An equivalent statement does not hold in the category $\\mathbf{Mon}$ of monoids. In a previous work on quadratic algebras, I constructed an internal category in the category of monoids, see Section 6. Based on this construction, this paper will introduce the notion of a crossed semi-bimodule and show that it gives rise to an object in $\\mathsf{Cat}(\\mathbf{Mon})$. I will also relate this new notion to the crossed semi-modules introduced earlier by A. Patchkoria.", "field": "math", "label": 0}
{"text": "Title: Filtered fiber functors over a general base\nAbstract: We prove that every filtered fiber functor on the category of dualizable representations of a smooth affine group scheme with enough dualizable representations comes from a graded fiber functor.", "field": "math", "label": 0}
{"text": "Title: Rotor-routing reachability is easy, chip-firing reachability is hard\nAbstract: Chip-firing and rotor-routing are two well-studied examples of abelian networks. We study the complexity of their respective reachability problems. We show that the rotor-routing reachability problem is decidable in polynomial time, and we give a simple characterization of when a chip-and-rotor configuration is reachable from another one. For chip-firing, it has been known that the reachability problem is in P if we have a class of graphs whose period length is polynomial (for example, Eulerian digraphs). Here we show that in the general case, chip-firing reachability is hard in the sense that if the chip-firing reachability problem were in P for general digraphs, then the polynomial hierarchy would collapse to NP. We encode graphs by their adjacency matrix, and we encode ribbon structures \"succinctly\", only remembering the number of consecutive parallel edges.", "field": "math", "label": 1}
{"text": "Title: Correlations of the divisor function\nAbstract: In this paper we study linear correlations of the divisor function tau(n) = sum_{d|n} 1 using methods developed by Green and Tao. For example, we obtain an asymptotic for sum_{n,d} tau(n) tau(n+d) ... tau(n+ (k-1)d).", "field": "math", "label": 1}
{"text": "Title: Matchings in hypercubes extend to long cycles\nAbstract: The $d$-dimensional hypercube graph $Q_d$ has as vertices all subsets of $\\{1,\\ldots,d\\}$, and an edge between any two sets that differ in a single element. The Ruskey-Savage conjecture asserts that every matching of $Q_d$, $d\\ge 2$, can be extended to a Hamilton cycle, i.e., to a cycle that visits every vertex exactly once. We prove that every matching of $Q_d$, $d\\ge 2$, can be extended to a cycle that visits at least a $2/3$-fraction of all vertices.", "field": "math", "label": 0}
{"text": "Title: Vectorization of Multibyte Floating Point Data Formats\nAbstract: We propose a scheme for reduced-precision representation of floating point data on a continuum between IEEE-754 floating point types. Our scheme enables the use of lower precision formats for a reduction in storage space requirements and data transfer volume. We describe how our scheme can be accelerated using existing hardware vector units on a general-purpose processor (GPP). Exploiting native vector hardware allows us to support reduced precision floating point with low overhead. We demonstrate that supporting reduced precision in the compiler as opposed to using a library approach can yield a low overhead solution for GPPs.", "field": "cs", "label": 1}
{"text": "Title: Sampling projections in the uniform norm\nAbstract: We show that there are sampling projections on arbitrary $n$-dimensional subspaces of $B(D)$ with at most $2n$ samples and norm of order $\\sqrt{n}$, where $B(D)$ is the space of complex-valued bounded functions on a set $D$. This gives a more explicit form of the Kadets-Snobar theorem for the uniform norm and improves upon Auerbach's lemma. We discuss consequences for optimal recovery in $L_p$.", "field": "math", "label": 0}
{"text": "Title: Near Real-Time Data-Driven Control of Virtual Reality Traffic in Open Radio Access Network\nAbstract: In mobile networks, Open Radio Access Network (ORAN) provides a framework for implementing network slicing that interacts with the resources at the lower layers. Both monitoring and Radio Access Network (RAN) control is feasible for both 4G and 5G systems. In this work, we consider how data-driven resource allocation in a 4G context can enable adaptive slice allocation to steer the experienced latency of Virtual Reality (VR) traffic towards a requested latency. We develop an xApp for the near real-time RAN Intelligent Controller (RIC) that embeds a heuristic algorithm for latency control, aiming to: (1) maintain latency of a VR stream around a requested value; and (2) improve the available RAN allocation to offer higher bit rate to another user. We have experimentally demonstrated the proposed approach in an ORAN testbed. Our results show that the data-driven approach can dynamically follow the variation of the traffic load while satisfying the required latency. This results in 15.8% more resources to secondary users than a latency-equivalent static allocation.", "field": "cs", "label": 0}
{"text": "Title: Reconstruction of curves from their theta hyperplanes in genera $6$ and $7$\nAbstract: We derive a formula for reconstructing a generic complex canonical curve $C$ of genus 6 and 7 in terms of the theta hyperplanes of $C$. Hence, we get a generic inverse to the Torelli map, as well as a complete description of the Schottky locus in these genera. The computational part of the proof relies on a certified numerical argument.", "field": "math", "label": 0}
{"text": "Title: The Evolving Ecosystem of Predatory Journals: A Case Study in Indian Perspective\nAbstract: Digital advancement in scholarly repositories has led to the emergence of a large number of open access predatory publishers that charge high article processing fees from authors but fail to provide necessary editorial and publishing services. Identifying and blacklisting such publishers has remained a research challenge due to the highly volatile scholarly publishing ecosystem. This paper presents a data-driven approach to study how potential predatory publishers are evolving and bypassing several regularity constraints. We empirically show the close resemblance of predatory publishers against reputed publishing groups. In addition to verifying standard constraints, we also propose distinctive signals gathered from network-centric properties to understand this evolving ecosystem better.", "field": "cs", "label": 1}
{"text": "Title: Quantization effects for multi-component Ginzburg-Landau vortices\nAbstract: In this paper, we are concerned with $n$-component Ginzburg-Landau equations on $\\rtwo$.By introducing a diffusion constant for each component, we discuss that the $n$-component equations are different from $n$-copies of the single Ginzburg-Landau equations.Then, the results of Brezis-Merle-Riviere for the single Ginzburg-Landau equation can be nontrivially extended to the multi-component case.First, we show that if the solutions have their gradients in $L^2$ space, they are trivial solutions.Second, we prove that if the potential is square summable, then it has quantized integrals, i.e., there exists one-to-one correspondence between the possible values of the potential energy and $\\nat^n$.Third, we show that different diffusion coefficients in the system are important to obtain nontrivial solutions of $n$-component equations.", "field": "math", "label": 0}
{"text": "Title: Deterministic Identity Testing for Sum of Read-Once Oblivious Arithmetic Branching Programs\nAbstract: A read-once oblivious arithmetic branching program (ROABP) is an arithmetic branching program (ABP) where each variable occurs in at most one layer. We give the first polynomial time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial time complexity $n^{O(\\log n)}$. In both the cases, our time complexity is double exponential in the number of ROABPs. ROABPs are a generalization of set-multilinear depth-$3$ circuits. The prior results for the sum of constantly many set-multilinear depth-$3$ circuits were only slightly better than brute-force, i.e. exponential-time. Our techniques are a new interplay of three concepts for ROABP: low evaluation dimension, basis isolating weight assignment and low-support rank concentration. We relate basis isolation to rank concentration and extend it to a sum of two ROABPs using evaluation dimension (or partial derivatives).", "field": "cs", "label": 1}
{"text": "Title: Post-hoc evaluation of nodes influence in information cascades: the case of coordinated accounts\nAbstract: In the last years, social media has gained an unprecedented amount of attention, playing a pivotal role in shaping the contemporary landscape of communication and connection. However, Coordinated Inhautentic Behaviour (CIB), defined as orchestrated efforts by entities to deceive or mislead users about their identity and intentions, has emerged as a tactic to exploit the online discourse. In this study, we quantify the efficacy of CIB tactics by defining a general framework for evaluating the influence of a subset of nodes in a directed tree. We design two algorithms that provide optimal and greedy post-hoc placement strategies that lead to maximising the configuration influence. We then consider cascades from information spreading on Twitter to compare the observed behaviour with our algorithms. The results show that, according to our model, coordinated accounts are quite inefficient in terms of their network influence, thus suggesting that they may play a less pivotal role than expected. Moreover, the causes of these poor results may be found in two separate aspects: a bad placement strategy and a scarcity of resources.", "field": "cs", "label": 0}
{"text": "Title: The Cauchy problem on large time for the Water Waves equations with large topography variations\nAbstract: We prove the local existence for the Water Waves equations with large bathymetric variations on a time interval of size 1/\\epsilon, where $\\epsilon$ measures the amplitude of the wave. We just need the presence of surface tension.", "field": "math", "label": 1}
{"text": "Title: Superimposed Pilots are Superior for Mitigating Pilot Contamination in Massive MIMO\nAbstract: In this paper, superimposed pilots are introduced as an alternative to time-multiplexed pilot and data symbols for mitigating pilot contamination in massive multiple-input multiple-output (MIMO) systems. We propose a non-iterative scheme for uplink channel estimation based on superimposed pilots and derive an expression for the uplink signal-to-interference-plus-noise ratio (SINR) at the output of a matched filter employing this channel estimate. Based on this expression, we observe that power control is essential when superimposed pilots are employed. Moreover, the quality of the channel estimate can be improved by reducing the interference that results from transmitting data alongside the pilots, and an intuitive iterative data-aided scheme that reduces this component of interference is also proposed. Approximate expressions for the uplink SINR are provided for the iterative data-aided method as well. In addition, we show that a hybrid system with users utilizing both time-multiplexed and superimposed pilots is superior to an optimally designed system that employs only time-multiplexed pilots, even when the non-iterative channel estimate is used to build the detector and precoder. We also describe a simple approach to implement this hybrid system by minimizing the overall inter and intra-cell interference. Numerical simulations demonstrating the performance of the proposed channel estimation schemes and the superiority of the hybrid system are also provided.", "field": "cs", "label": 1}
{"text": "Title: Global existence and Hadamard differentiability of hysteresis-reaction-diffusion systems\nAbstract: We consider a class of semilinear parabolic evolution equations subject to a hysteresis operator and a Bochner-Lebesgue integrable source term. The underlying spatial domain is allowed to have a very general boundary. In the first part of the paper, we apply semigroup theory to prove well-posedness and boundedness of the solution operator. Rate independence in reaction-diffusion systems complicates the analysis, since the reaction term acts no longer local in time. This demands careful estimates when working with semigroup methods. In the second part, we show Lipschitz continuity and Hadamard differentiability of the solution operator. We use fixed point arguments to derive a representation for the derivative in terms of the evolution system. Finally, we apply our results to an optimal control problem in which the source term acts as a control function and show existence of an optimal solution.", "field": "math", "label": 1}
{"text": "Title: Outage Analysis for Active Reconfigurable Intelligent Surface-Enhanced Wireless Powered Communication Networks\nAbstract: Wireless powered communication (WPC) involves the integration of energy harvesting and data transmission. This allows devices to communicate without constant battery replacements or wired power sources. Reconfigurable intelligent surfaces (RISs) can dynamically manipulate radio signals. In this paper, we explore the use of active elements to mitigate double-fading challenges inherent in RIS-aided links. We enhance the reliability performance for an energy-constrained user by combining active RIS and WPC. The theoretical closed-form analysis, which includes transmission rate, harvested energy, and outage probability, provides valuable insights that inform parameter selection.", "field": "cs", "label": 0}
{"text": "Title: Classification and Treatment Learning with Constraints via Composite Heaviside Optimization: a Progressive MIP Method\nAbstract: This paper proposes a Heaviside composite optimization approach and presents a progressive (mixed) integer programming (PIP) method for solving multi-class classification and multi-action treatment problems with constraints. A Heaviside composite function is a composite of a Heaviside function (i.e., the indicator function of either the open $( \\, 0,\\infty )$ or closed $[ \\, 0,\\infty \\, )$ interval) with a possibly nondifferentiable function. Modeling-wise, we show how Heaviside composite optimization provides a unified formulation for learning the optimal multi-class classification and multi-action treatment rules, subject to rule-dependent constraints stipulating a variety of domain restrictions. A Heaviside composite function has an equivalent discrete formulation %in terms of integer variables, and the resulting optimization problem can in principle be solved by integer programming (IP) methods. Nevertheless, for constrained learning problems with large data sets, %of modest or large sizes, a straightforward application of off-the-shelf IP solvers is usually ineffective in achieving global optimality. To alleviate such a computational burden, our major contribution is the proposal of the PIP method by leveraging the effectiveness of state-of-the-art IP solvers for problems of modest sizes. We provide the theoretical advantage of the PIP method with the connection to continuous optimization and show that the computed solution is locally optimal for a broad class of Heaviside composite optimization problems. The numerical performance of the PIP method is demonstrated by extensive computational experimentation.", "field": "math", "label": 0}
{"text": "Title: LLM Harmony: Multi-Agent Communication for Problem Solving\nAbstract: Large Language Models (LLMs) have revolutionized Natural Language Processing but exhibit limitations, particularly in autonomously addressing novel challenges such as reasoning and problem-solving. Traditional techniques like chain-of-thought prompting necessitate explicit human guidance. This paper introduces a novel multi-agent communication framework, inspired by the CAMEL model, to enhance LLMs' autonomous problem-solving capabilities. The framework employs multiple LLM agents, each with a distinct persona, engaged in role-playing communication, offering a nuanced and adaptable approach to diverse problem scenarios. Extensive experimentation demonstrates the framework's superior performance and adaptability, providing valuable insights into the collaborative potential of multiple agents in overcoming the limitations of individual models.", "field": "cs", "label": 0}
{"text": "Title: Beyond Efficiency: A Systematic Survey of Resource-Efficient Large Language Models\nAbstract: The burgeoning field of Large Language Models (LLMs), exemplified by sophisticated models like OpenAI's ChatGPT, represents a significant advancement in artificial intelligence. These models, however, bring forth substantial challenges in the high consumption of computational, memory, energy, and financial resources, especially in environments with limited resource capabilities. This survey aims to systematically address these challenges by reviewing a broad spectrum of techniques designed to enhance the resource efficiency of LLMs. We categorize methods based on their optimization focus: computational, memory, energy, financial, and network resources and their applicability across various stages of an LLM's lifecycle, including architecture design, pretraining, finetuning, and system design. Additionally, the survey introduces a nuanced categorization of resource efficiency techniques by their specific resource types, which uncovers the intricate relationships and mappings between various resources and corresponding optimization techniques. A standardized set of evaluation metrics and datasets is also presented to facilitate consistent and fair comparisons across different models and techniques. By offering a comprehensive overview of the current sota and identifying open research avenues, this survey serves as a foundational reference for researchers and practitioners, aiding them in developing more sustainable and efficient LLMs in a rapidly evolving landscape.", "field": "cs", "label": 0}
{"text": "Title: Enhancing NOMA Networks via Reconfigurable Multi-Functional Surface\nAbstract: By flexibly manipulating the radio propagation environment, reconfigurable intelligent surface (RIS) is a promising technique for future wireless communications. However, the single-side coverage and double-fading attenuation faced by conventional RISs largely restrict their applications. To address this issue, we propose a novel concept of multi-functional RIS (MF-RIS), which provides reflection, transmission, and amplification simultaneously for the incident signal. With the aim of enhancing the performance of a non-orthogonal multiple-access (NOMA) downlink multiuser network, we deploy an MF-RIS to maximize the sum rate by jointly optimizing the active beamforming and MF-RIS coefficients. Then, an alternating optimization algorithm is proposed to solve the formulated non-convex problem by exploiting successive convex approximation and penalty-based method. Numerical results show that the proposed MF-RIS outperforms conventional RISs under different settings.", "field": "cs", "label": 1}
{"text": "Title: Fast Certification of Vision-Language Models Using Incremental Randomized Smoothing\nAbstract: A key benefit of deep vision-language models such as CLIP is that they enable zero-shot open vocabulary classification; the user has the ability to define novel class labels via natural language prompts at inference time. However, while CLIP-based zero-shot classifiers have demonstrated competitive performance across a range of domain shifts, they remain highly vulnerable to adversarial attacks. Therefore, ensuring the robustness of such models is crucial for their reliable deployment in the wild. In this work, we introduce Open Vocabulary Certification (OVC), a fast certification method designed for open-vocabulary models like CLIP via randomized smoothing techniques. Given a base \"training\" set of prompts and their corresponding certified CLIP classifiers, OVC relies on the observation that a classifier with a novel prompt can be viewed as a perturbed version of nearby classifiers in the base training set. Therefore, OVC can rapidly certify the novel classifier using a variation of incremental randomized smoothing. By using a caching trick, we achieve approximately two orders of magnitude acceleration in the certification process for novel prompts. To achieve further (heuristic) speedups, OVC approximates the embedding space at a given input using a multivariate normal distribution bypassing the need for sampling via forward passes through the vision backbone. We demonstrate the effectiveness of OVC on through experimental evaluation using multiple vision-language backbones on the CIFAR-10 and ImageNet test datasets.", "field": "cs", "label": 0}
{"text": "Title: Global Sobolev persistence for the fractional Boussinesq equations with zero diffusivity\nAbstract: We address the persistence of regularity for the 2D $\\alpha$-fractional Boussinesq equations with positive viscosity and zero diffusivity in general Sobolev spaces, i.e., for $(u_{0}, \\rho_{0}) \\in W^{s,q}(\\mathbb R^2) \\times W^{s,q}(\\mathbb R^2)$, where $s> 1$ and $q \\in (2, \\infty)$. We prove that the solution $(u(t), \\rho(t))$ exists and belongs to $W^{s,q}(\\mathbb R^2) \\times W^{s,q}(\\mathbb R^2)$ for all positive time $t$ for $q>2$, where $\\alpha\\in(1,2)$ is arbitrary.", "field": "math", "label": 1}
{"text": "Title: The specialization index of a variety over a discretely valued field\nAbstract: Let $X$ be a proper variety over a henselian discretely valued field. An important obstruction to the existence of a rational point on $X$ is the index, the minimal positive degree of a zero cycle on $X$. This paper introduces a new invariant, the specialization index, which is a closer approximation of the existence of a rational point. We provide an explicit formula for the specialization index in terms of an $snc$-model, and we give examples of curves where the index equals one but the specialization index is different from one, and thus explains the absence of a rational point. Our main result states that the specialization index of a smooth, proper, geometrically connected $\\mathbb{C}((t))$-variety with trivial coherent cohomology is equal to one.", "field": "math", "label": 1}
{"text": "Title: When ideals properly extend the class of Arbault sets\nAbstract: In this article we continue the investigation of generalized version of Arbault sets, that was initiated in \\cite{DGT} but look at the picture from the most general point of view where ideals come into play. While Arbault sets can be naturally associated with the Frechet ideal $Fin$, in \\cite{DGT} it was observed that when $Fin$ is replaced by the natural density ideal $\\mathcal{I}_d$ one can obtain a strictly larger class of trigonometric thin sets containing Arbault sets. From the set theoretic point of view a natural question arises as whether one can broaden the picture and specify a class of ideals (instead of a single ideal) each of which would have the similar effect. As a natural candidate, we focus on a special class of ideals, namely, non-$snt$ ideals ($snt$ stands for ``strongly non translation invariant\") which properly contains the class of translation invariant ideals ($\\varsupsetneq Fin$) and happens to contain ideals generated by simple density functions as also certain non-negative regular summability matrices (but not all) which can be seen from \\cite{DG6}. We consider the resulting class of $\\mathcal{I}$-Arbault sets and it is observed that for each such ideal, the class of $\\mathcal{I}$-Arbault sets not only properly contains the class of classical Arbault sets \\cite{Ar} but also a large subfamily of $\\mathbf{N}$-sets (also called ``sets of absolute convergence\") \\cite{Ft} while being contained in the class of weak Dirichlet sets. %In particular it properly contains the family of $\\mathbf{N}_0$-sets which have been extensively used in the literature (see \\cite{Ar, Ka, Ko}). Though distinct from the class of $\\mathbf{N}$-sets, this happens to be a new class strictly lying between the class of Arbault sets and the class of weak Dirichlet sets.", "field": "math", "label": 0}
{"text": "Title: Two trees are better than one\nAbstract: We consider partitions of a point set into two parts, and the lengths of the minimum spanning trees of the original set and of the two parts. If $w(P)$ denotes the length of a minimum spanning tree of $P$, we show that every set $P$ of $n \\geq 12$ points admits a bipartition $P= R \\cup B$ for which the ratio $\\frac{w(R)+w(B)}{w(P)}$ is strictly larger than $1$; and that $1$ is the largest number with this property. Furthermore, we provide a very fast algorithm that computes such a bipartition in $O(1)$ time and one that computes the corresponding ratio in $O(n \\log{n})$ time. In certain settings, a ratio larger than $1$ can be expected and sometimes guaranteed. For example, if $P$ is a set of $n$ random points uniformly distributed in $[0,1]^2$ ($n \\to \\infty$), then for any $\\eps>0$, the above ratio in a maximizing partition is at least $\\sqrt2 -\\eps$ with probability tending to $1$. As another example, if $P$ is a set of $n$ points with spread at most $\\alpha \\sqrt{n}$, for some constant $\\alpha>0$, then the aforementioned ratio in a maximizing partition is $1 + \\Omega(\\alpha^{-2})$. All our results and techniques are extendable to higher dimensions.", "field": "cs", "label": 0}
{"text": "Title: Existence of solutions to the nonlinear equations characterizing the precise error of M-estimators\nAbstract: Major progress has been made in the previous decade to characterize the asymptotic behavior of regularized M-estimators in high-dimensional regression problems in the proportional asymptotic regime where the sample size $n$ and the number of features $p$ are increasing simultaneously such that $n/p\\to \\delta \\in(0,\\infty)$, using powerful tools such as Approximate Message Passing or the Convex Gaussian Min-Max Theorem (CGMT). The asymptotic error and behavior of the regularized M-estimator is then typically described by a system of nonlinear equations with a few scalar unknowns, and the solution to this system precisely characterize the asymptotic error. Application of the CGMT and related machinery requires the existence of a solution to this low-dimensional system of equations. This paper resolves the question of existence of solution to this low-dimensional system for the case of linear models with independent additive noise, when both the data-fitting loss function and regularization penalty are separable and convex. Such existence result for solution to the nonlinear system were previously known under strong convexity for specific estimators such as the Lasso. The main idea behind this existence result is inspired by an argument developed \\cite{montanari2019generalization,celentano2020lasso} in different contexts: By constructing an ad-hoc convex minimization problem in an infinite dimensional Hilbert space, the existence of the Lagrange multiplier for this optimization problem makes it possible to construct explicitly solutions to the low-dimensional system of interest. The conditions under which we derive this existence result exactly correspond to the side of the phase transition where perfect recovery $\\hat x= x_0$ fails, so that these conditions are optimal.", "field": "math", "label": 0}
{"text": "Title: Maximal Sections of Sheaves of Data over an Abstract Simplicial Complex\nAbstract: We employ techniques from topological data analysis to model sensor networks. Our approach to sensor integration uses the topological method of sheaves over cell complexes. The internal consistency of data from individual sensors is determined by a set of consistency functions assigned to elements of the complex. Using these functions we determine, for any collection of data, the unique set of maximal sections of consistent data received from the sensors. We offer a proof for the existence and uniqueness of these sections and illustrate the ideas with examples.", "field": "cs", "label": 1}
{"text": "Title: Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words\nAbstract: Any finite state automaton gives rise to a Boolean one-dimensional TQFT with defects and inner endpoints of cobordisms. This paper extends the correspondence to Boolean TQFTs where defects accumulate toward inner endpoints, relating such TQFTs and topological theories to sofic systems and $\\omega$-automata.", "field": "math", "label": 0}
{"text": "Title: Calculus and applications\nAbstract: This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\\mathbb R\\to\\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and of the integral $\\int_a^bf(x)dx$. Then we investigate the case of the complex functions $f:\\mathbb C\\to\\mathbb C$, and notably the holomorphic functions, and harmonic functions. Then, we discuss the multivariable functions, $f:\\mathbb R^N\\to\\mathbb R^M$ or $f:\\mathbb R^N\\to\\mathbb C^M$ or $f:\\mathbb C^N\\to\\mathbb C^M$, with general theory, integration results, maximization questions, and basic applications to physics.", "field": "math", "label": 0}
{"text": "Title: Explicit Generators for the Stabilizers of Rational Points in Thompson's Group $F$\nAbstract: We construct explicit finite generating sets for the stabilizers in Thompson's group $F$ of rational points of a unit interval or a Cantor set. Our technique is based on the Reidemeister-Schreier procedure in the context of Schreier graphs of such stabilizers in $F$. It is well known that the stabilizers of dyadic rational points are isomorphic to $F\\times F$ and can thus be generated by 4 explicit elements. We show that the stabilizer of every non-dyadic rational point $b\\in (0,1)$ is generated by 5 elements that are explicitly calculated as words in generators $x_0, x_1$ of $F$ that depend on the binary expansion of $b$. We also provide an alternative simple proof that the stabilizers of all rational points are finitely presented.", "field": "math", "label": 0}
{"text": "Title: Lorentzian connections with parallel twistor-free torsion\nAbstract: We describe Lorentzian manifolds that admit metric connections with parallel torsion having zero twistorial component and non-zero vectorial component. We also describe Lorentzian manifolds admitting metric connections with closed parallel skew-symmetric torsion.", "field": "math", "label": 0}
{"text": "Title: The convolution algebra of an absolutely locally compact topos\nAbstract: We introduce a class of toposes called \"absolutely locally compact\" toposes and of \"admissible\" sheaf of rings over such toposes. To any such ringed topos $(\\mathcal{T},A)$ we attach an involutive convolution algebra $\\mathcal{C}_c(\\mathcal{T},A)$ which is well defined up to Morita equivalence and characterized by the fact that the category of non-degenerate modules over $\\mathcal{C}_c(\\mathcal{T},A)$ is equivalent to the category of sheaf of $A$-module over $\\mathcal{T}$. In the case where $A$ is the sheaf of real or complex Dedekind numbers, we construct several norms on this involutive algebra that allows to complete it in various Banach and $C^*$-algebras: $L^1(\\mathcal{T},A)$, $C^*_{red}(\\mathcal{T},A)$ and $C^*_{max}(\\mathcal{T},A)$. We also give some examples where this construction corresponds to well known constructions of involutive algebras, like groupoids convolution algebra and Leavitt path algebras.", "field": "math", "label": 1}
{"text": "Title: Quantifying Deep Learning Model Uncertainty in Conformal Prediction\nAbstract: Precise estimation of predictive uncertainty in deep neural networks is a critical requirement for reliable decision-making in machine learning and statistical modeling, particularly in the context of medical AI. Conformal Prediction (CP) has emerged as a promising framework for representing the model uncertainty by providing well-calibrated confidence levels for individual predictions. However, the quantification of model uncertainty in conformal prediction remains an active research area, yet to be fully addressed. In this paper, we explore state-of-the-art CP methodologies and their theoretical foundations. We propose a probabilistic approach in quantifying the model uncertainty derived from the produced prediction sets in conformal prediction and provide certified boundaries for the computed uncertainty. By doing so, we allow model uncertainty measured by CP to be compared by other uncertainty quantification methods such as Bayesian (e.g., MC-Dropout and DeepEnsemble) and Evidential approaches.", "field": "cs", "label": 0}
{"text": "Title: Person Re-identification: Implicitly Defining the Receptive Fields of Deep Learning Classification Frameworks\nAbstract: The \\emph{receptive fields} of deep learning classification models determine the regions of the input data that have the most significance for providing correct decisions. The primary way to learn such receptive fields is to train the models upon masked data, which helps the networks to ignore any unwanted regions, but has two major drawbacks: 1) it often yields edge-sensitive decision processes; and 2) augments the computational cost of the inference phase considerably. This paper describes a solution for implicitly driving the inference of the networks' receptive fields, by creating synthetic learning data composed of interchanged segments that should be \\emph{apriori} important/irrelevant for the network decision. In practice, we use a segmentation module to distinguish between the foreground (important)/background (irrelevant) parts of each learning instance, and randomly swap segments between image pairs, while keeping the class label exclusively consistent with the label of the deemed important segments. This strategy typically drives the networks to early convergence and appropriate solutions, where the identity and clutter descriptions are not correlated. Moreover, this data augmentation solution has various interesting properties: 1) it is parameter-free; 2) it fully preserves the label information; and, 3) it is compatible with the typical data augmentation techniques. In the empirical validation, we considered the person re-identification problem and evaluated the effectiveness of the proposed solution in the well-known \\emph{Richly Annotated Pedestrian} (RAP) dataset for two different settings (\\emph{upper-body} and \\emph{full-body}), observing highly competitive results over the state-of-the-art. Under a reproducible research paradigm, both the code and the empirical evaluation protocol are available at \\url{https://github.com/Ehsan-Yaghoubi/reid-strong-baseline}.", "field": "cs", "label": 1}
{"text": "Title: Acyclicity of Preferences, Nash Equilibria, and Subgame Perfect Equilibria: a Formal and Constructive Equivalence\nAbstract: In 1953, Kuhn showed that every sequential game has a Nash equilibrium by showing that a procedure, named ``backward induction'' in game theory, yields a Nash equilibrium. It actually yields Nash equilibria that define a proper subclass of Nash equilibria. In 1965, Selten named this proper subclass subgame perfect equilibria. In game theory, payoffs are rewards usually granted at the end of a game. Although traditional game theory mainly focuses on real-valued payoffs that are implicitly ordered by the usual total order over the reals, works of Simon or Blackwell already involved partially ordered payoffs. This paper generalises the notion of sequential game by replacing real-valued payoff functions with abstract atomic objects, called outcomes, and by replacing the usual total order over the reals with arbitrary binary relations over outcomes, called preferences. This introduces a general abstract formalism where Nash equilibrium, subgame perfect equilibrium, and ``backward induction'' can still be defined. This paper proves that the following three propositions are equivalent: 1) Preferences over the outcomes are acyclic. 2) Every sequential game has a Nash equilibrium. 3) Every sequential game has a subgame perfect equilibrium. The result is fully computer-certified using Coq. Beside the additional guarantee of correctness, the activity of formalisation using Coq also helps clearly identify the useful definitions and the main articulations of the proof.", "field": "cs", "label": 1}
{"text": "Title: ClassWise-SAM-Adapter: Parameter Efficient Fine-tuning Adapts Segment Anything to SAR Domain for Semantic Segmentation\nAbstract: In the realm of artificial intelligence, the emergence of foundation models, backed by high computing capabilities and extensive data, has been revolutionary. Segment Anything Model (SAM), built on the Vision Transformer (ViT) model with millions of parameters and vast training dataset SA-1B, excels in various segmentation scenarios relying on its significance of semantic information and generalization ability. Such achievement of visual foundation model stimulates continuous researches on specific downstream tasks in computer vision. The ClassWise-SAM-Adapter (CWSAM) is designed to adapt the high-performing SAM for landcover classification on space-borne Synthetic Aperture Radar (SAR) images. The proposed CWSAM freezes most of SAM's parameters and incorporates lightweight adapters for parameter efficient fine-tuning, and a classwise mask decoder is designed to achieve semantic segmentation task. This adapt-tuning method allows for efficient landcover classification of SAR images, balancing the accuracy with computational demand. In addition, the task specific input module injects low frequency information of SAR images by MLP-based layers to improve the model performance. Compared to conventional state-of-the-art semantic segmentation algorithms by extensive experiments, CWSAM showcases enhanced performance with fewer computing resources, highlighting the potential of leveraging foundational models like SAM for specific downstream tasks in the SAR domain. The source code is available at: https://github.com/xypu98/CWSAM.", "field": "cs", "label": 0}
{"text": "Title: Almost spanning distance trees in subsets of finite vector spaces\nAbstract: For $d\\ge 2$ and an odd prime power $q$, consider the vector space $\\mathbb{F}_q^d$ over the finite field $\\mathbb{F}_q$, where the distance between two points $(x_1,\\ldots,x_d)$ and $(y_1,\\ldots,y_d)$ is defined as $\\sum_{i=1}^d (x_i-y_i)^2$. A distance graph is a graph associated with a non-zero distance to each of its edges. We show that large subsets of vector spaces over finite fields contain every nearly spanning distance tree with bounded degree in each distance. This quantitatively improves results by Bennett, Chapman, Covert, Hart, Iosevich, and Pakianathan on finding distance paths, and results by Pham, Senger, Tait, and Thu on finding distance trees. A key ingredient in proving our main result is to obtain a colorful generalization of a classical result of Haxell about finding nearly spanning bounded-degree trees in an expander.", "field": "math", "label": 0}
{"text": "Title: Extremal spectral radius of nonregular graphs with prescribed maximum degree\nAbstract: Let $G$ be a graph attaining the maximum spectral radius among all connected nonregular graphs of order $n$ with maximum degree $\\Delta$. Let $\\lambda_1(G)$ be the spectral radius of $G$. A nice conjecture due to Liu, Shen and Wang [On the largest eigenvalue of non-regular graphs, J. Combin. Theory Ser. B, 97 (2007) 1010--1018] asserts that \\[ \\lim_{n\\to\\infty} \\frac{n^2(\\Delta-\\lambda_1(G))}{\\Delta-1} = \\pi^2 \\] for each fixed $\\Delta$. Concerning an important structural property of the extremal graphs $G$, Liu and Li present another conjecture which states that $G$ has degree sequence $\\Delta,\\ldots,\\Delta,\\delta$. Here, $\\delta=\\Delta-1$ or $\\delta=\\Delta-2$ depending on the parity of $n\\Delta$. In this paper, we make progress on the two conjectures. To be precise, we disprove the first conjecture for all $\\Delta\\geq 3$ by showing that the limit superior is at most $\\pi^2/2$. For small $\\Delta$, we determine the precise asymptotic behavior of $\\Delta-\\lambda_1(G)$. In particular, we show that $\\lim\\limits_{n\\to\\infty} n^2 (\\Delta - \\lambda_1(G)) /(\\Delta - 1) = \\pi^2/4$ if $\\Delta=3$; and $\\lim\\limits_{n\\to\\infty} n^2 (\\Delta - \\lambda_1(G)) /(\\Delta - 2) = \\pi^2/2$ if $\\Delta = 4$. We also confirm the second conjecture for $\\Delta = 3$ and $\\Delta = 4$ by determining the precise structure of extremal graphs. Particularly, we show that the extremal graphs for $\\Delta\\in\\{3,4\\}$ must have a path-like structure built from specific blocks.", "field": "math", "label": 1}
{"text": "Title: Explicit stabilized multirate methods for the monodomain model in cardiac electrophysiology\nAbstract: Fully explicit stabilized multirate (mRKC) methods are well-suited for the numerical solution of large multiscale systems of stiff ordinary differential equations thanks to their improved stability properties. To demonstrate their efficiency for the numerical solution of stiff, multiscale, nonlinear parabolic PDE's, we apply mRKC methods to the monodomain equation from cardiac electrophysiology. In doing so, we propose an improved version, specifically tailored to the monodomain model, which leads to the explicit exponential multirate stabilized (emRKC) method. Several numerical experiments are conducted to evaluate the efficiency of both mRKC and emRKC, while taking into account different finite element meshes (structured and unstructured) and realistic ionic models. The new emRKC method typically outperforms a standard implicit-explicit baseline method for cardiac electrophysiology. Code profiling and strong scalability results further demonstrate that emRKC is faster and inherently parallel without sacrificing accuracy.", "field": "math", "label": 0}
{"text": "Title: A stochastic approximation scheme and convergence theorem for particle interactions with perfectly reflecting boundaries\nAbstract: We prove the existence of a solution to an equation governing the number density within a compact domain of a discrete particle system for a prescribed class of particle interactions taking into account the effects of the diffusion and drift of the set of particles. Each particle carries a number of internal coordinates which may evolve continuously in time, determined by what we will refer to as the internal drift, or discretely via the interaction kernels. Perfectly reflecting boundary conditions are imposed on the system and all the processes may be spatially and temporally inhomogeneous. We use a relative compactness argument to construct a sequence of measures that converge weakly to a solution of the governing equation. Since the proof of existence is a constructive one, it provides a stochastic approximation scheme that can be used for the numerical study of molecular dynamics.", "field": "math", "label": 1}
{"text": "Title: The Implicit Bias of Benign Overfitting\nAbstract: The phenomenon of benign overfitting, where a predictor perfectly fits noisy training data while attaining near-optimal expected loss, has received much attention in recent years, but still remains not fully understood beyond well-specified linear regression setups. In this paper, we provide several new results on when one can or cannot expect benign overfitting to occur, for both regression and classification tasks. We consider a prototypical and rather generic data model for benign overfitting of linear predictors, where an arbitrary input distribution of some fixed dimension $k$ is concatenated with a high-dimensional distribution. For linear regression which is not necessarily well-specified, we show that the minimum-norm interpolating predictor (that standard training methods converge to) is biased towards an inconsistent solution in general, hence benign overfitting will generally not occur. Moreover, we show how this can be extended beyond standard linear regression, by an argument proving how the existence of benign overfitting on some regression problems precludes its existence on other regression problems. We then turn to classification problems, and show that the situation there is much more favorable. Specifically, we prove that the max-margin predictor (to which standard training methods are known to converge in direction) is asymptotically biased towards minimizing a weighted \\emph{squared hinge loss}. This allows us to reduce the question of benign overfitting in classification to the simpler question of whether this loss is a good surrogate for the misclassification error, and use it to show benign overfitting in some new settings.", "field": "cs", "label": 1}
{"text": "Title: Weierstrass Bridges\nAbstract: We introduce a new class of stochastic processes called fractional Wiener-Weierstrass bridges. They arise by applying the convolution from the construction of the classical, fractal Weierstrass functions to an underlying fractional Brownian bridge. By analyzing the $p$-th variation of the fractional Wiener-Weierstrass bridge along the sequence of $b$-adic partitions, we identify two regimes in which the processes exhibit distinct sample path properties. We also analyze the critical case between those two regimes for Wiener-Weierstrass bridges that are based on standard Brownian bridge. We furthermore prove that fractional Wiener-Weierstrass bridges are never semimartingales, and we show that their covariance functions are typically fractal functions. Some of our results are extended to Weierstrass bridges based on bridges derived from a general continuous Gaussian martingale.", "field": "math", "label": 0}
{"text": "Title: Positroids, knots, and $q,t$-Catalan numbers\nAbstract: We relate the mixed Hodge structure on the cohomology of open positroid varieties (in particular, their Betti numbers over $\\mathbb{C}$ and point counts over $\\mathbb{F}_q$) to Khovanov--Rozansky homology of associated links. We deduce that the mixed Hodge polynomials of top-dimensional open positroid varieties are given by rational $q,t$-Catalan numbers. Via the curious Lefschetz property of cluster varieties, this implies the $q,t$-symmetry and unimodality properties of rational $q,t$-Catalan numbers. We show that the $q,t$-symmetry phenomenon is a manifestation of Koszul duality for category $\\mathcal{O}$, and discuss relations with open Richardson varieties and extension groups of Verma modules.", "field": "math", "label": 1}
{"text": "Title: Fredholm-type Operators and Index\nAbstract: While in \\cite{HB} we studied classes of Fredholm-type operators defined by the homomorphism $\\Pi$ from $L(X)$ onto the Calkin algebra $\\mathcal{C}(X)$, $X$ being a Banach space, we study in this paper two classes of Fredholm-type operators defined by the homomorphism $\\pi$ from $L(X)$ onto the algebra $\\mathcal{C}_0(X)= L(X)/F_0(X),$ where $F_0(X)$ is the ideal of finite rank operators in $L(X).$ Then we define an index for Fredholm-type operators and we show that this new index satisfies similar properties as the usual Fredholm index.", "field": "math", "label": 0}
{"text": "Title: Unique Triangulated 1-Planar Graphs\nAbstract: It is well-known that every 3-connected planar graph has a unique planar embedding on the sphere. We study the extension to triangulated 1-planar graphs, T1P graphs for short, which admit an embedding in which each edge is crossed at most once and each face is a triangle, and obtain an algorithmic solution by a cubic time recognition algorithm that also counts the number of T1P embeddings. In particular, we show that every triangulated planar graph has a unique T1P embedding, although it may admit many 1-planar embeddings, and that any 6-connected T1P graph has a unique 1-planar embedding, except for full generalized two-stars that admit two or eight 1-planar embeddings. Our algorithm extends, refines, and corrects a previous recognition algorithm by Chen, Grigni and Papadimitiou (``Recognizing Hole-Free 4-Map Graphs in Cubic Time'', Algorithmica 45 (2006)).", "field": "cs", "label": 0}
{"text": "Title: On games and simulators as a platform for development of artificial intelligence for command and control\nAbstract: Games and simulators can be a valuable platform to execute complex multi-agent, multiplayer, imperfect information scenarios with significant parallels to military applications: multiple participants manage resources and make decisions that command assets to secure specific areas of a map or neutralize opposing forces. These characteristics have attracted the artificial intelligence (AI) community by supporting development of algorithms with complex benchmarks and the capability to rapidly iterate over new ideas. The success of artificial intelligence algorithms in real-time strategy games such as StarCraft II have also attracted the attention of the military research community aiming to explore similar techniques in military counterpart scenarios. Aiming to bridge the connection between games and military applications, this work discusses past and current efforts on how games and simulators, together with the artificial intelligence algorithms, have been adapted to simulate certain aspects of military missions and how they might impact the future battlefield. This paper also investigates how advances in virtual reality and visual augmentation systems open new possibilities in human interfaces with gaming platforms and their military parallels.", "field": "cs", "label": 1}
{"text": "Title: Sample Complexity Bounds for Two Timescale Value-based Reinforcement Learning Algorithms\nAbstract: Two timescale stochastic approximation (SA) has been widely used in value-based reinforcement learning algorithms. In the policy evaluation setting, it can model the linear and nonlinear temporal difference learning with gradient correction (TDC) algorithms as linear SA and nonlinear SA, respectively. In the policy optimization setting, two timescale nonlinear SA can also model the greedy gradient-Q (Greedy-GQ) algorithm. In previous studies, the non-asymptotic analysis of linear TDC and Greedy-GQ has been studied in the Markovian setting, with diminishing or accuracy-dependent stepsize. For the nonlinear TDC algorithm, only the asymptotic convergence has been established. In this paper, we study the non-asymptotic convergence rate of two timescale linear and nonlinear TDC and Greedy-GQ under Markovian sampling and with accuracy-independent constant stepsize. For linear TDC, we provide a novel non-asymptotic analysis and show that it attains an $\\epsilon$-accurate solution with the optimal sample complexity of $\\mathcal{O}(\\epsilon^{-1}\\log(1/\\epsilon))$ under a constant stepsize. For nonlinear TDC and Greedy-GQ, we show that both algorithms attain $\\epsilon$-accurate stationary solution with sample complexity $\\mathcal{O}(\\epsilon^{-2})$. It is the first non-asymptotic convergence result established for nonlinear TDC under Markovian sampling and our result for Greedy-GQ outperforms the previous result orderwisely by a factor of $\\mathcal{O}(\\epsilon^{-1}\\log(1/\\epsilon))$.", "field": "cs", "label": 1}
{"text": "Title: Periodic Strategies II: Generalizations and Extensions\nAbstract: At a mixed Nash equilibrium, the payoff of a player does not depend on her own action, as long as her opponent sticks to his. In a periodic strategy, a concept developed in a previous paper (arXiv:1307.2035v4), in contrast, the own payoff does not depend on the opponent's action. Here, we generalize this to multi-player simultaneous perfect information strategic form games. We show that also in this class of games, there always exists at least one periodic strategy, and we investigate the mathematical properties of such periodic strategies. In addition, we demonstrate that periodic strategies may exist in games with incomplete information; we shall focus on Bayesian games. Moreover we discuss the differences between the periodic strategies formalism and cooperative game theory. In fact, the periodic strategies are obtained in a purely non-cooperative way, and periodic strategies are as cooperative as the Nash equilibria are. Finally, we incorporate the periodic strategies in an epistemic game theory framework, and discuss several features of this approach.", "field": "cs", "label": 1}
{"text": "Title: Stochastic Approximation Approaches to Group Distributionally Robust Optimization\nAbstract: This paper investigates group distributionally robust optimization (GDRO), with the purpose to learn a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem, and demonstrate that stochastic mirror descent (SMD), using $m$ samples in each iteration, achieves an $O(m (\\log m)/\\epsilon^2)$ sample complexity for finding an $\\epsilon$-optimal solution, which matches the $\\Omega(m/\\epsilon^2)$ lower bound up to a logarithmic factor. Then, we make use of techniques from online learning to reduce the number of samples required in each round from $m$ to $1$, keeping the same sample complexity. Specifically, we cast GDRO as a two-players game where one player simply performs SMD and the other executes an online algorithm for non-oblivious multi-armed bandits. Next, we consider a more practical scenario where the number of samples that can be drawn from each distribution is different, and propose a novel formulation of weighted GDRO, which allows us to derive distribution-dependent convergence rates. Denote by $n_i$ the sample budget for the $i$-th distribution, and assume $n_1 \\geq n_2 \\geq \\cdots \\geq n_m$. In the first approach, we incorporate non-uniform sampling into SMD such that the sample budget is satisfied in expectation, and prove that the excess risk of the $i$-th distribution decreases at an $O(\\sqrt{n_1 \\log m}/n_i)$ rate. In the second approach, we use mini-batches to meet the budget exactly and also reduce the variance in stochastic gradients, and then leverage stochastic mirror-prox algorithm, which can exploit small variances, to optimize a carefully designed weighted GDRO problem. Under appropriate conditions, it attains an $O((\\log m)/\\sqrt{n_i})$ convergence rate, which almost matches the optimal $O(\\sqrt{1/n_i})$ rate of only learning from the $i$-th distribution with $n_i$ samples.", "field": "cs", "label": 0}
{"text": "Title: Correctness Comparison of ChatGPT-4, Bard, Claude-2, and Copilot for Spatial Tasks\nAbstract: Generative AI including large language models (LLMs) have recently gained significant interest in the geo-science community through its versatile task-solving capabilities including coding, spatial computations, generation of sample data, time-series forecasting, toponym recognition, or image classification. So far, the assessment of LLMs for spatial tasks has primarily focused on ChatGPT, arguably the most prominent AI chatbot, whereas other chatbots received less attention. To narrow this research gap, this study evaluates the correctness of responses for a set of 54 spatial tasks assigned to four prominent chatbots, i.e., ChatGPT-4, Bard, Claude-2, and Copilot. Overall, the chatbots performed well on spatial literacy, GIS theory, and interpretation of programming code and given functions, but revealed weaknesses in mapping, code generation, and code translation. ChatGPT-4 outperformed other chatbots across most task categories.", "field": "cs", "label": 0}
{"text": "Title: Solution of the Kolmogorov equation for TASEP\nAbstract: We provide a direct and elementary proof that the formula obtained in [MQR17] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP particle system.", "field": "math", "label": 1}
{"text": "Title: LLM Augmented LLMs: Expanding Capabilities through Composition\nAbstract: Foundational models with billions of parameters which have been trained on large corpora of data have demonstrated non-trivial skills in a variety of domains. However, due to their monolithic structure, it is challenging and expensive to augment them or impart new skills. On the other hand, due to their adaptation abilities, several new instances of these models are being trained towards new domains and tasks. In this work, we study the problem of efficient and practical composition of existing foundation models with more specific models to enable newer capabilities. To this end, we propose CALM -- Composition to Augment Language Models -- which introduces cross-attention between models to compose their representations and enable new capabilities. Salient features of CALM are: (i) Scales up LLMs on new tasks by 're-using' existing LLMs along with a few additional parameters and data, (ii) Existing model weights are kept intact, and hence preserves existing capabilities, and (iii) Applies to diverse domains and settings. We illustrate that augmenting PaLM2-S with a smaller model trained on low-resource languages results in an absolute improvement of up to 13\\% on tasks like translation into English and arithmetic reasoning for low-resource languages. Similarly, when PaLM2-S is augmented with a code-specific model, we see a relative improvement of 40\\% over the base model for code generation and explanation tasks -- on-par with fully fine-tuned counterparts.", "field": "cs", "label": 0}
{"text": "Title: LLaVA-$φ$: Efficient Multi-Modal Assistant with Small Language Model\nAbstract: In this paper, we introduce LLaVA-$\\phi$ (LLaVA-Phi), an efficient multi-modal assistant that harnesses the power of the recently advanced small language model, Phi-2, to facilitate multi-modal dialogues. LLaVA-Phi marks a notable advancement in the realm of compact multi-modal models. It demonstrates that even smaller language models, with as few as 2.7B parameters, can effectively engage in intricate dialogues that integrate both textual and visual elements, provided they are trained with high-quality corpora. Our model delivers commendable performance on publicly available benchmarks that encompass visual comprehension, reasoning, and knowledge-based perception. Beyond its remarkable performance in multi-modal dialogue tasks, our model opens new avenues for applications in time-sensitive environments and systems that require real-time interaction, such as embodied agents. It highlights the potential of smaller language models to achieve sophisticated levels of understanding and interaction, while maintaining greater resource efficiency.The project is available at {https://github.com/zhuyiche/llava-phi}.", "field": "cs", "label": 0}
{"text": "Title: Actions of right-angled Artin groups in low dimensions\nAbstract: We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one--dimensional manifolds. For compact one--manifolds, every right-angled Artin group acts faithfully by $C^1$ diffeomorphisms, but the right-angled Artin groups which act faithfully by $C^2$ diffeomorphisms are very restricted. For the real line, every right-angled Artin group acts faithfully by $C^{\\infty}$ diffeomorphisms, though analytic actions are again more limited. In dimensions two and higher, every right-angled Artin group acts faithfully on every manifold by $C^{\\infty}$ diffeomorphisms. We give applications of this discussion to mapping class groups of surfaces and related groups.", "field": "math", "label": 1}
{"text": "Title: Some combinatorial problems arising in the dimer model\nAbstract: We discuss some diverse open problems in the dimer model, motivated by a geometric viewpoint. This is part of a conference proceedings for the OPAC 2022 conference.", "field": "math", "label": 0}
{"text": "Title: Microlocal approach to Lusztig's symmetries\nAbstract: We reformulate the De Concini -- Toledano Laredo conjecture about the monodromy of the Casimir connection in terms of a relation between Lusztig's symmetries of quantum group modules and the monodromy in the vanishing cycles of factorizable sheaves.", "field": "math", "label": 1}
{"text": "Title: A fourth-order Cherrier-Escobar problem with prescribed corner behavior on the half-ball\nAbstract: We show that the half-ball in $\\mathbb{R}^4$ can be conformally changed so that the only contribution to the Gauss--Bonnet formula is a constant term at the corner. This may be seen as a fourth-order Cherrier--Escobar-type problem on the half-ball.", "field": "math", "label": 0}
{"text": "Title: Act as You Learn: Adaptive Decision-Making in Non-Stationary Markov Decision Processes\nAbstract: A fundamental (and largely open) challenge in sequential decision-making is dealing with non-stationary environments, where exogenous environmental conditions change over time. Such problems are traditionally modeled as non-stationary Markov decision processes (NSMDP). However, existing approaches for decision-making in NSMDPs have two major shortcomings: first, they assume that the updated environmental dynamics at the current time are known (although future dynamics can change); and second, planning is largely pessimistic, i.e., the agent acts ``safely'' to account for the non-stationary evolution of the environment. We argue that both these assumptions are invalid in practice -- updated environmental conditions are rarely known, and as the agent interacts with the environment, it can learn about the updated dynamics and avoid being pessimistic, at least in states whose dynamics it is confident about. We present a heuristic search algorithm called \\textit{Adaptive Monte Carlo Tree Search (ADA-MCTS)} that addresses these challenges. We show that the agent can learn the updated dynamics of the environment over time and then act as it learns, i.e., if the agent is in a region of the state space about which it has updated knowledge, it can avoid being pessimistic. To quantify ``updated knowledge,'' we disintegrate the aleatoric and epistemic uncertainty in the agent's updated belief and show how the agent can use these estimates for decision-making. We compare the proposed approach with the multiple state-of-the-art approaches in decision-making across multiple well-established open-source problems and empirically show that our approach is faster and highly adaptive without sacrificing safety.", "field": "cs", "label": 0}
{"text": "Title: Theory inspired deep network for instantaneous-frequency extraction and signal components recovery from discrete blind-source data\nAbstract: This paper is concerned with the inverse problem of recovering the unknown signal components, along with extraction of their instantaneous frequencies (IFs), governed by the adaptive harmonic model (AHM), from discrete (and possibly non-uniform) samples of the blind-source composite signal. None of the existing decomposition methods and algorithms, including the most popular empirical mode decomposition (EMD) computational scheme and its current modifications, is capable of solving this inverse problem. In order to meet the AHM formulation and to extract the IFs of the decomposed components, called intrinsic mode functions (IMFs), each IMF of EMD is extended to an analytic function in the upper half of the complex plane via the Hilbert transform, followed by taking the real part of the polar form of the analytic extension. Unfortunately, this approach most often fails to resolve the inverse problem satisfactorily. More recently, to resolve the inverse problem, the notion of synchrosqueezed wavelet transform (SST) was proposed by Daubechies and Maes, and further developed in many other papers, while a more direct method, called signal separation operation (SSO), was proposed and developed in our previous work published in the journal, Applied and Computational Harmonic Analysis, vol. 30(2):243-261, 2016. In the present paper, we propose a synthesis of SSO using a deep neural network, based directly on a discrete sample set, that may be non-uniformly sampled, of the blind-source signal. Our method is localized, as illustrated by a number of numerical examples, including components with different signal arrival and departure times. It also yields short-term prediction of the signal components, along with their IFs. Our neural networks are inspired by theory, designed so that they do not require any training in the traditional sense.", "field": "cs", "label": 1}
{"text": "Title: The Least Common Multiple of Polynomial Values over Function Fields\nAbstract: Cilleruelo conjectured that for an irreducible polynomial $f \\in \\mathbb{Z}[X]$ of degree $d \\geq 2$ one has $$\\log\\left[\\mathrm{lcm}(f(1),f(2),\\ldots f(N))\\right]\\sim(d-1)N\\log N$$ as $N \\to \\infty$. He proved it in the case $d=2$ but it remains open for every polynomial with $d>2$. We investigate the function field analogue of the problem by considering polynomials over the ring $\\mathbb F_q[T]$. We state an analog of Cilleruelo's conjecture in this setting: denoting by $$L_f(n) := \\mathrm{lcm} \\left(f\\left(Q\\right)\\ : \\ Q \\in \\mathbb F_q[T]\\mbox{ monic},\\, \\mathrm{deg}\\,Q = n\\right)$$ we conjecture that \\begin{equation}\\label{eq:conjffabs}\\mathrm{deg}\\, L_f(n) \\sim c_f \\left(d-1\\right) nq^n,\\ n \\to \\infty\\end{equation} ($c_f$ is an explicit constant dependent only on $f$, typically $c_f=1$). We give both upper and lower bounds for $L_f(n)$ and show that the conjectured asymptotic holds for a class of ``special\" polynomials, initially considered by Leumi in this context, which includes all quadratic polynomials and many other examples as well. We fully classify these special polynomials. We also show that $\\mathrm{deg}\\, L_f(n) \\sim \\mathrm{deg}\\,\\mathrm{rad}\\left(L_f(n)\\right)$ (in other words the corresponding LCM is close to being squarefree), which is not known over $\\mathbb Z$.", "field": "math", "label": 0}
{"text": "Title: A simple proof for generalized Fibonacci numbers with dying rabbits\nAbstract: We consider the generalized Fibonacci counting problem with rabbits that become fertile at age $f$ and die at age $d$, with $1<=f<=d$ and $d$ finite or infinite. We provide a simple proof, based exclusively on a counting argumentation, for a recursive formula that gives the $n$th generalized Fibonacci number as a function of at most 3 previous numbers. The formula generalizes both the original Fibonacci sequence, for $f=2$ and $d=\\infty$ (or $f=1$ and $d=2$), and other Fibonacci-related sequences, such as the Padovan sequence, for $f=2$ and $d=3$, the Tribonacci, for $f=1$ and $d=3$, Tetranacci, for $f=1$ and $d=4$, and alike sequences, for $f=1$ and finite values of $d$.", "field": "math", "label": 0}
{"text": "Title: Travelers: A scalable fair ordering BFT system\nAbstract: Many blockchain platform are subject to maximal value extraction (MEV), and users on the platform are losing money while sending transactions because the transaction order can be manipulated to extract value from them. Consensus protocols have been augmented with different notion of fair ordering in order to counter the problem. Out of all practical protocols, the most efficient BFT consensus requires $O(nTL + n^2T)$ communication complexity, where $n$ is number node, $T$ is number of transactions and $L$ is average transaction size. In this work, we propose a new system of BFT fair ordering protocols, Travelers, that substantially reduce the communication complexity. The proposed system of protocols satisfy a new notion of fair ordering, called probabilistic fair ordering, which is an extension to some existing notions of fairness. The new notion allows a small probability of error $\\epsilon$, that adversary can insert some transactions at any location in a block, but for the remaining $1-\\epsilon$ the a modified version of ordering linearizability holds. Our mechanism neither require a dissemination network nor direct submissions to all consensus nodes. The key innovation comes from a routing protocol, that is both flexible and efficient. We construct a protocol with $O(c\\log({n})TL + n^2)$ communication complexity with $\\epsilon = 1/n^c$ for some system parameter $c\\ge 1$.", "field": "cs", "label": 0}
{"text": "Title: Marked random graphs with given degree sequence: large deviations on the local topology\nAbstract: We investigate the behavior of the empirical neighbourhood distribution of marked graphs in the framework of local weak convergence. We establish a large deviation principle for such families of empirical measures. The proof builds on Bordenave and Caputo's seminal 2015 paper, and Delgosha and Anantharam's 2019 introduction of BC entropy, relying on combinatorial lemmas that allow one to construct suitable approximations of measures supported on marked trees.", "field": "math", "label": 0}
{"text": "Title: An alternative approach to large deviations for the almost-critical Erdős-Rényi random graph\nAbstract: We study the near-critical behavior of the sparse Erd\\H{o}s-R\\'enyi random graph $\\mathcal{G}(n,p)$ on $n\\gg1$ vertices, where the connection probability $p$ satisfies $np = 1+\\theta(b_n^2/n)^{1/3}$, with $n^{3/10}\\ll {b_n}\\ll n^{1/2}$, and $\\theta\\in\\mathbb{R}$. To this end, we introduce an empirical measure that describes connected components of $\\mathcal{G}(n,p)$ of mesoscopic size $\\propto (nb_n)^{2/3}$, and we characterize its large deviation behavior. The proof hinges on detailed combinatorial estimates and optimization procedures. In particular, we give precise estimates for the probability that the graph has no connected component of mesoscopic size or larger. We argue that these are a stepping stone for the analysis of more general inhomogeneous random graphs. Our proof strategy gives new and accurate estimates of the probability that the sparse Erd\\H{o}s-R\\'enyi graph is connected.", "field": "math", "label": 0}
{"text": "Title: Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes\nAbstract: We consider a non-isothermal compositional gas liquid model for the simulation of well operations in geothermal processes. The model accounts for phase transitions assumed to be at thermodynamical equilibrium and is based on an hydrodynamical Drift Flux Model (DFM) combined with a No Pressure Wave approximation of the momentum equation. The focus of this work is on the design of a robust discretization accounting for slanted and multibranch wells with the ability to simulate both transient behavior such as well opening as well as coupled simulations at the time scale of the reservoir. It is based on a staggered finite volume scheme in space combined with a fully implicit Euler time integration. The construction of consistent and stable numerical fluxes is a key feature for a robust numerical method. It is achieved by combining a monotone flux approximation for the phase superficial velocities with an upwind approximation of the phase molar fractions, density and enthalpy. In order to facilitate the coupling of the well and reservoir models, the Newton linearization accounts for the elimination of the hydrodynamical unknowns leading to Jacobian systems using the same primary unknowns than those of the reservoir model. The efficiency of our approach is investigated on both stand alone well test cases without and with cross flow, and on a fully coupled well-reservoir simulation.", "field": "math", "label": 0}
{"text": "Title: A study in sums of products\nAbstract: We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory.", "field": "math", "label": 1}
{"text": "Title: Affine Metrics and Associated Algebroid Structures: Application to General Relativity\nAbstract: In this paper, algebroid bundle associated to affine metrics provide an structure for unification of gravity and electromagnetism and, geometrization of matter.", "field": "math", "label": 1}
{"text": "Title: Fourier-based schemes for computing the mechanical response of composites with accurate local fields\nAbstract: We modify the Green operator involved in Fourier-based computational schemes in elasticity, in 2D and 3D. The new operator is derived by expressing continuum mechanics in terms of centered differences on a rotated grid. Use of the modified Green operator leads, in all systems investigated, to more accurate strain and stress fields than using the discretizations proposed by Moulinec and Suquet (1994) or Willot and Pellegrini (2008). Moreover, we compared the convergence rates of the \"direct\" and \"accelerated\" FFT schemes with the different discretizations. The discretization method proposed in this work allows for much faster FFT schemes with respect to two criteria: stress equilibrium and effective elastic moduli.", "field": "math", "label": 1}
{"text": "Title: Physics-informed Generalizable Wireless Channel Modeling with Segmentation and Deep Learning: Fundamentals, Methodologies, and Challenges\nAbstract: Channel modeling is fundamental in advancing wireless systems and has thus attracted considerable research focus. Recent trends have seen a growing reliance on data-driven techniques to facilitate the modeling process and yield accurate channel predictions. In this work, we first provide a concise overview of data-driven channel modeling methods, highlighting their limitations. Subsequently, we introduce the concept and advantages of physics-informed neural network (PINN)-based modeling and a summary of recent contributions in this area. Our findings demonstrate that PINN-based approaches in channel modeling exhibit promising attributes such as generalizability, interpretability, and robustness. We offer a comprehensive architecture for PINN methodology, designed to inform and inspire future model development. A case-study of our recent work on precise indoor channel prediction with semantic segmentation and deep learning is presented. The study concludes by addressing the challenges faced and suggesting potential research directions in this field.", "field": "cs", "label": 0}
{"text": "Title: Gland Segmentation in Colon Histology Images: The GlaS Challenge Contest\nAbstract: Colorectal adenocarcinoma originating in intestinal glandular structures is the most common form of colon cancer. In clinical practice, the morphology of intestinal glands, including architectural appearance and glandular formation, is used by pathologists to inform prognosis and plan the treatment of individual patients. However, achieving good inter-observer as well as intra-observer reproducibility of cancer grading is still a major challenge in modern pathology. An automated approach which quantifies the morphology of glands is a solution to the problem. This paper provides an overview to the Gland Segmentation in Colon Histology Images Challenge Contest (GlaS) held at MICCAI'2015. Details of the challenge, including organization, dataset and evaluation criteria, are presented, along with the method descriptions and evaluation results from the top performing methods.", "field": "cs", "label": 1}
{"text": "Title: Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training\nAbstract: Solving partial differential equations (PDEs) numerically often requires huge computing time, energy cost, and hardware resources in practical applications. This has limited their applications in many scenarios (e.g., autonomous systems, supersonic flows) that have a limited energy budget and require near real-time response. Leveraging optical computing, this paper develops an on-chip training framework for physics-informed neural networks (PINNs), aiming to solve high-dimensional PDEs with fJ/MAC photonic power consumption and ultra-low latency. Despite the ultra-high speed of optical neural networks, training a PINN on an optical chip is hard due to (1) the large size of photonic devices, and (2) the lack of scalable optical memory devices to store the intermediate results of back-propagation (BP). To enable realistic optical PINN training, this paper presents a scalable method to avoid the BP process. We also employ a tensor-compressed approach to improve the convergence and scalability of our optical PINN training. This training framework is designed with tensorized optical neural networks (TONN) for scalable inference acceleration and MZI phase-domain tuning for \\textit{in-situ} optimization. Our simulation results of a 20-dim HJB PDE show that our photonic accelerator can reduce the number of MZIs by a factor of $1.17\\times 10^3$, with only $1.36$ J and $1.15$ s to solve this equation. This is the first real-size optical PINN training framework that can be applied to solve high-dimensional PDEs.", "field": "cs", "label": 0}
{"text": "Title: Quantum Polynomial Hierarchies: Karp-Lipton, error reduction, and lower bounds\nAbstract: The Polynomial-Time Hierarchy ($\\mathsf{PH}$) is a staple of classical complexity theory, with applications spanning randomized computation to circuit lower bounds to ''quantum advantage'' analyses for near-term quantum computers. Quantumly, however, despite the fact that at least \\emph{four} definitions of quantum $\\mathsf{PH}$ exist, it has been challenging to prove analogues for these of even basic facts from $\\mathsf{PH}$. This work studies three quantum-verifier based generalizations of $\\mathsf{PH}$, two of which are from [Gharibian, Santha, Sikora, Sundaram, Yirka, 2022] and use classical strings ($\\mathsf{QCPH}$) and quantum mixed states ($\\mathsf{QPH}$) as proofs, and one of which is new to this work, utilizing quantum pure states ($\\mathsf{pureQPH}$) as proofs. We first resolve several open problems from [GSSSY22], including a collapse theorem and a Karp-Lipton theorem for $\\mathsf{QCPH}$. Then, for our new class $\\mathsf{pureQPH}$, we show one-sided error reduction for $\\mathsf{pureQPH}$, as well as the first bounds relating these quantum variants of $\\mathsf{PH}$, namely $\\mathsf{QCPH}\\subseteq \\mathsf{pureQPH} \\subseteq \\mathsf{EXP}^{\\mathsf{PP}}$.", "field": "cs", "label": 0}
{"text": "Title: Improved Online Algorithm for Weighted Flow Time\nAbstract: We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a $O(\\log P)$-competitive algorithm, where $P$ is the maximum-to-minimum processing time ratio, improving upon the $O(\\log^{2}P)$-competitive algorithm of Chekuri, Khanna and Zhu (STOC 2001). We also design a $O(\\log D)$-competitive algorithm, where $D$ is the maximum-to-minimum density ratio of jobs. Finally, we show how to combine these results with the result of Bansal and Dhamdhere (SODA 2003) to achieve a $O(\\log(\\min(P,D,W)))$-competitive algorithm (where $W$ is the maximum-to-minimum weight ratio), without knowing $P,D,W$ in advance. As shown by Bansal and Chan (SODA 2009), no constant-competitive algorithm is achievable for this problem.", "field": "cs", "label": 1}
{"text": "Title: General runner removal and the Mullineux map\nAbstract: We prove a new `runner removal theorem' for $q$-decomposition numbers of the level 1 Fock space of type $A^{(1)}_{e-1}$, generalising earlier theorems of James--Mathas and the author. By combining this with another theorem relating to the Mullineux map, we show that the problem of finding all $q$-decomposition numbers indexed by partitions of a given weight is a finite computation.", "field": "math", "label": 1}
{"text": "Title: Geometric structures of late points of a two-dimensional simple random walk\nAbstract: We consider the problem, as suggested by Dembo ($2003$, $2006$), of late points of a simple random walk in two dimensions. It has been shown that the exponents for the numbers of pairs of late points coincide with those of nearly favorite points and high points in the Gaussian free field, whose exact values are known. We estimate the exponents for the numbers of a multipoint set of late points in average. While there have been observed certain similarities between among three classes of points, our results exhibit a difference.", "field": "math", "label": 1}
{"text": "Title: The novel Tauberian conditions associated with the $(\\overline{N},p,q)$ summability of double sequences\nAbstract: In this paper, our primary objective is to provide a fresh perspective on the relationship between the $(\\overline{N},p,q)$ method, which is a product of relevant one-dimensional summability methods, and $P$-convergence for double sequences. To accomplish this objective, we establish certain Tauberian conditions that control the behavior of a double sequence in terms of both $O_L$-oscillation and $O$-oscillation in certain senses, building a bridge between $(\\overline{N},p,q)$ summability and $P$-convergence, while imposing certain restrictions on the weight sequences. As special circumstances of our findings, we demonstrate that Landau-type $O_L$ condition with respect to $(P_m)$ and $(Q_n),$ as well as Hardy-type $O$ condition with respect to $(P_m)$ and $(Q_n),$ serve as Tauberian conditions for $(\\overline{N},p,q)$ summability under particular additional conditions. Consequently, these results encompass all classical Tauberian theorems, including conditions such as slow decrease or slow oscillation in certain senses.", "field": "math", "label": 0}
{"text": "Title: Penalty Parameter Selection in Deconvolution by Estimating the Risk for a Smaller Sample Size\nAbstract: We address the choice of penalty parameter in the Smoothness-Penalized Deconvolution (SPeD) method of estimating a probability density under additive measurement error. Cross-validation gives an unbiased estimate of the risk (for the present sample size n) with a given penalty parameter, and this function can be minimized as a function of the penalty parameter. Least-squares cross-validation, which has been proposed for the similar Deconvoluting Kernel Density Estimator (DKDE), performs quite poorly for SPeD. We instead estimate the risk function for a smaller sample size n_1 < n with a given penalty parameter, using this to choose the penalty parameter for sample size n_1, and then use the asymptotics of the optimal penalty parameter to choose for sample size n. In a simulation study, we find that this has dramatically better performance than cross-validation, is an improvement over a SURE-type method previously proposed for this estimator, and compares favorably to the classic DKDE with its recommended plug-in method. We prove that the maximum error in estimating the risk function is of smaller order than its optimal rate of convergence.", "field": "math", "label": 0}
{"text": "Title: On the safe set of Cartesian product of two complete graphs\nAbstract: For a connected graph $G$, a vertex subset $S$ of $V(G)$ is a safe set if for every component $C$ of the subgraph of $G$ induced by $S$, $|C| \\ge |D|$ holds for every component $D$ of $G-S$ such that there exists an edge between $C$ and $D$, and, in particular, if the subgraph induced by $S$ is connected, then $S$ is called a connected safe set. For a connected graph $G$, the safe number and the connected safe number of $G$ are the minimum among sizes of the safe sets and the minimum among sizes of the connected safe sets, respectively, of $G$. Fujita et al. introduced these notions in connection with a variation of the facility location problem. In this paper, we study the safe number and the connected safe number of Cartesian product of two complete graphs. Figuring out a way to reduce the number of components to two without changing the size of safe set makes it sufficient to consider only partitions of an integer into two parts without which it would be much more complicated to take care of all the partitions. In this way, we could show that the safe number and the connected safe number of Cartesian product of two complete graphs are equal and present a polynomial-time algorithm to compute them. Especially, in the case where one of complete components has order at most four, we precisely formulate those numbers.", "field": "math", "label": 1}
{"text": "Title: Integrated Sensing and Communication with Massive MIMO: A Unified Tensor Approach for Channel and Target Parameter Estimation\nAbstract: Benefitting from the vast spatial degrees of freedom, the amalgamation of integrated sensing and communication (ISAC) and massive multiple-input multiple-output (MIMO) is expected to simultaneously improve spectral and energy efficiencies as well as the sensing capability. However, a large number of antennas deployed in massive MIMO-ISAC raises critical challenges in acquiring both accurate channel state information and target parameter information. To overcome these two challenges with a unified framework, we first analyze their underlying system models and then propose a novel tensor-based approach that addresses both the channel estimation and target sensing problems. Specifically, by parameterizing the high-dimensional communication channel exploiting a small number of physical parameters, we associate the channel state information with the sensing parameters of targets in terms of angular, delay, and Doppler dimensions. Then, we propose a shared training pattern adopting the same time-frequency resources such that both the channel estimation and target parameter estimation can be formulated as a canonical polyadic decomposition problem with a similar mathematical expression. On this basis, we first investigate the uniqueness condition of the tensor factorization and the maximum number of resolvable targets by utilizing the specific Vandermonde", "field": "cs", "label": 0}
{"text": "Title: On the existence of analytic families of stable lattices in trianguline representations and their reductions\nAbstract: In this article, we prove the existence of rigid analytic families of $G$-stable lattices with locally constant reductions inside families of representations of a topologically compact group $G$, extending a result of Hellman obtained in the semi-simple residual case. Implementing this generalization in the context of Galois representations, we prove a local constancy result for reductions modulo prime powers of trianguline representations of generic dimension $d$. Moreover, we present two explicit applications. First, in dimension two, we extend to a prime power setting and to the whole rigid projective line a recent result of Bergdall, Levin and Liu concerning reductions of semi-stable representations of $\\text{Gal}(\\overline{\\mathbb{Q}}_p / \\mathbb{Q}_p)$ with fixed Hodge-Tate weights and large $\\mathcal{L}$-invariant. Second, in dimension $d$, let $V_n$ be a sequence of crystalline representations converging in a certain geometric sense to a crystalline representation $V$. We show that for any refined version $(V, \\sigma)$ of $V$ (or equivalently for any chosen triangulation of its attached $(\\varphi, \\Gamma)$-module $D_{\\text{rig}} (V)$ over the Robba ring), there exists a sequence of refinement $\\sigma_n$ of each of the $V_n$ such that the limit as refined representations $(V_n , \\sigma_n )$ converges to the $(V, \\sigma)$. This result does not hold under the weaker assumption that $V_n$ converges only uniformly $p$-adically to $V$ (in the sense of Chenevier, Khare and Larsen).", "field": "math", "label": 0}
{"text": "Title: The Stanley Conjecture Revisited\nAbstract: In the seminal work of Stanley, several conjectures were made on the structure of Littlewood-Richardson coefficients for the multiplication of Jack symmetric functions. Motivated by recent results of Alexandersson and the present author, we postulate that a certain 'windowing' property holds for all such Jack L-R coefficients. This property provides a vast set of relations between these coefficients and allows for their direct computation in certain novel cases. We demonstrate compatibility between our windowing conjecture and the conjectures of Stanley, with the hope of illuminating the structures within.", "field": "math", "label": 0}
{"text": "Title: The Effect of Noise on the Emergence of Continuous Norms and its Evolutionary Dynamics\nAbstract: We examine the effect of noise on societies of agents using an agent-based model of evolutionary norm emergence. Generally, we see that noisy societies are more selfish, smaller and discontent, and are caught in rounds of perpetual punishment preventing them from flourishing. Surprisingly, despite the effect of noise on the population, it does not seem to evolve away. We carry out further analysis and provide reasons for why this may be the case. Furthermore, we claim that our framework that evolves the noise/ambiguity of norms may be a new way to model the tight/loose framework of norms, suggesting that despite ambiguous norms detrimental effect on society, evolution does not favour clarity.", "field": "cs", "label": 0}
{"text": "Title: Locally dualizable modules abound\nAbstract: It is proved that given any prime ideal $\\mathfrak{p}$ of height at least 2 in a countable commutative noetherian ring $A$, there are uncountably many more dualizable objects in the $\\mathfrak{p}$-local $\\mathfrak{p}$-torsion stratum of the derived category of $A$ than those that are obtained as retracts of images of perfect $A$-complexes. An analogous result is established dealing with the stable module category of the group algebra, over a countable field of positive characteristic $p$, of an elementary abelian $p$-group of rank at least 3.", "field": "math", "label": 0}
{"text": "Title: On Brown-York mass and compactly conformal deformations of scalar curvature\nAbstract: In this article, we found a connection between Brown-York mass and the first Dirichlet Eigenvalue of a Schr\\\"odingier type operator. In particular, we proved a local positive mass type theorem for metrics conformal to the background one with suitable presumptions. As applications, we investigated compactly conformal deformations which either increase or decrease scalar curvature. We found local conformal rigidity phenomena occur in both cases for small domains and as for manifolds with nonpositive scalar curvature it is even more rigid in particular. On the other hand, such deformations exist for closed manifolds with positive scalar curvature. We also constructed such kind of deformations on a type of product manifolds that either increase or decrease their scalar curvature compactly and conformally. These results together answered a natural question arises in \\cite{Corvino, Lohkamp}.", "field": "math", "label": 1}
{"text": "Title: Singularity-agnostic incomplete U-statistics for testing polynomial constraints in Gaussian covariance matrices\nAbstract: Testing the goodness-of-fit of a model with its defining functional constraints in the parameters could date back to Spearman (1927), who analyzed the famous \"tetrad\" polynomial in the covariance matrix of the observed variables in a single-factor model. Despite its long history, the Wald test typically employed to operationalize this approach could produce very inaccurate test sizes in many situations, even when the regular conditions for the classical normal asymptotics are met and a very large sample is available. Focusing on testing a polynomial constraint in a Gaussian covariance matrix, we obtained a new understanding of this baffling phenomenon: When the null hypothesis is true but \"near-singular\", the standardized Wald test exhibits slow weak convergence, owing to the sophisticated dependency structure inherent to the underlying U-statistic that ultimately drives its limiting distribution; this can also be rigorously explained by a key ratio of moments encoded in the Berry-Esseen bound quantifying the normal approximation error involved. As an alternative, we advocate the use of an incomplete U-statistic to mildly tone down the dependence thereof and render the speed of convergence agnostic to the singularity status of the hypothesis. In parallel, we develop a Berry-Esseen bound that is mathematically descriptive of the singularity-agnostic nature of our standardized incomplete U-statistic, using some of the finest exponential-type inequalities in the literature.", "field": "math", "label": 0}
{"text": "Title: Characterizing BigBench queries, Hive, and Spark in multi-cloud environments\nAbstract: BigBench is the new standard (TPCx-BB) for benchmarking and testing Big Data systems. The TPCx-BB specification describes several business use cases -- queries -- which require a broad combination of data extraction techniques including SQL, Map/Reduce (M/R), user code (UDF), and Machine Learning to fulfill them. However, currently, there is no widespread knowledge of the different resource requirements and expected performance of each query, as is the case to more established benchmarks. At the same time, cloud providers currently offer convenient on-demand managed big data clusters (PaaS) with a pay-as-you-go model. In PaaS, analytical engines such as Hive and Spark come ready to use, with a general-purpose configuration and upgrade management. The study characterizes both the BigBench queries and the out-of-the-box performance of Spark and Hive versions in the cloud. At the same time, comparing popular PaaS offerings in terms of reliability, data scalability (1GB to 10TB), versions, and settings from Azure HDinsight, Amazon Web Services EMR, and Google Cloud Dataproc. The query characterization highlights the similarities and differences in Hive an Spark frameworks, and which queries are the most resource consuming according to CPU, memory, and I/O. Scalability results show how there is a need for configuration tuning in most cloud providers as data scale grows, especially with Sparks memory usage. These results can help practitioners to quickly test systems by picking a subset of the queries which stresses each of the categories. At the same time, results show how Hive and Spark compare and what performance can be expected of each in PaaS.", "field": "cs", "label": 1}
{"text": "Title: Randomness Requirements and Asymmetries in Nash Equilibria\nAbstract: In general, Nash equilibria in normal-form games may require players to play (probabilistically) mixed strategies. We define a measure of the complexity of finite probability distributions and study the complexity required to play NEs in finite two player $n\\times n$ games with rational payoffs. Our central results show that there exist games in which there is an exponential vs. linear gap in the complexity of the mixed distributions that the two players play at (the unique) NE. This gap induces gaps in the amount of space required to represent and sample from the corresponding distributions using known state-of-the-art sampling algorithms. We also establish upper and lower bounds on the complexity of any NE in the games that we study. These results highlight (i) the nontriviality of the assumption that players can any mixed strategy and (ii) the disparities in resources that players may require to play NEs in the games that we study.", "field": "cs", "label": 0}
{"text": "Title: Hilbert modular forms and Galois representations\nAbstract: In this expository article, we present a brief introduction to the theory of Hilbert modular forms and Galois representations, and describe what it means to attach a compatible system of Galois representations to a Hilbert modular form.", "field": "math", "label": 0}
{"text": "Title: Section Rings of $\\mathbb{Q}$-Divisors on Genus-$1$ Curves\nAbstract: We compute generators and relations for the section ring of a rational divisor on an elliptic curve. Our technique is a generalization of \\cite{O'Dorney} and \\cite{VZB} that accounts for the additional subtlety that genus one curves pose: their group structure. We give explicit minimal presentations for section rings of divisors supported at one point and for section rings of effective divisors supported at two points. Our results for one-point divisors are quite similar to the corresponding case in genus zero from \\cite{O'Dorney}, and are a combination of the one-point cases in genera one and zero for two-point effective divisors.", "field": "math", "label": 0}
{"text": "Title: Multifractality and intermittency in the limit evolution of polygonal vortex filaments\nAbstract: With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann's non-differentiable functions \\begin{equation} R_{x_0}(t) = \\sum_{n \\neq 0} \\frac{e^{2\\pi i ( n^2 t + n x_0 ) } }{n^2}, \\qquad x_0 \\in [0,1]. \\end{equation} These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments that evolve according to the binormal flow. When $x_0$ is rational, we show that $R_{x_0}$ is multifractal and intermittent by completely determining the spectrum of singularities of $R_{x_0}$ and computing the $L^p$ norms of its Fourier high-pass filters, which are analogues of structure functions. We prove that $R_{x_0}$ has a multifractal behavior also when $x_0$ is irrational. The proofs rely on a careful design of Diophantine sets that depend on $x_0$, which we study by crucially using the Duffin-Schaeffer theorem and the Mass Transference Principle.", "field": "math", "label": 0}
{"text": "Title: DIALIGHT: Lightweight Multilingual Development and Evaluation of Task-Oriented Dialogue Systems with Large Language Models\nAbstract: We present DIALIGHT, a toolkit for developing and evaluating multilingual Task-Oriented Dialogue (ToD) systems which facilitates systematic evaluations and comparisons between ToD systems using fine-tuning of Pretrained Language Models (PLMs) and those utilising the zero-shot and in-context learning capabilities of Large Language Models (LLMs). In addition to automatic evaluation, this toolkit features (i) a secure, user-friendly web interface for fine-grained human evaluation at both local utterance level and global dialogue level, and (ii) a microservice-based backend, improving efficiency and scalability. Our evaluations reveal that while PLM fine-tuning leads to higher accuracy and coherence, LLM-based systems excel in producing diverse and likeable responses. However, we also identify significant challenges of LLMs in adherence to task-specific instructions and generating outputs in multiple languages, highlighting areas for future research. We hope this open-sourced toolkit will serve as a valuable resource for researchers aiming to develop and properly evaluate multilingual ToD systems and will lower, currently still high, entry barriers in the field.", "field": "cs", "label": 0}
{"text": "Title: Rational trigonometry via projective geometric algebra\nAbstract: We show that main results of rational trigonometry (as developed by NJ Wildberger, \"Divine Proportions\", 2005) can be succinctly expressed using projective geometric algebra (PGA). In fact, the PGA representation exhibits distinct advantages over the original vector-based approach. These include the advantages intrinsic to geometric algebra: it is coordinate-free, treats lines and points in a unified framework, and handles many special cases in a uniform and seamless fashion. It also reveals structural patterns not visible in the original formulation, for example, the exact duality of spread and quadrance. The current article handles only a representative (euclidean) subset of the full content of Wildberger's work, but enough to establish the value of this approach for further development. The metric-neutral framework of PGA makes it especially promising also to handle universal geometry, which extends rational trigonometry to the hyperbolic plane.", "field": "math", "label": 1}
{"text": "Title: Non-Wire Alternatives to Capacity Expansion\nAbstract: Distributed energy resources (DERs) can serve as non-wire alternatives to capacity expansion by managing peak load to avoid or defer traditional expansion projects. In this paper, we study a planning problem that co-optimizes DERs investment and operation (e.g., energy efficiency, energy storage, demand response, solar photovoltaic) and the timing of capacity expansion. We formulate the problem as a large scale (in the order of millions of variables because we model the operation of DERs over a period of decades) non-convex optimization problem. Despite its non-convexities, we find its optimal solution by decomposing it using the Dantzig-Wolfe Decomposition Algorithm and solving a series of small linear problems. Finally, we present a real planning problem at the University of Washington Seattle Campus.", "field": "math", "label": 1}
{"text": "Title: Deep Learning Based Superposition Coded Modulation for Hierarchical Semantic Communications over Broadcast Channels\nAbstract: We consider multi-user semantic communications over broadcast channels. While most existing works consider that each receiver requires either the same or independent semantic information, this paper explores the scenario where the semantic information desired by different receivers is different but correlated. In particular, we investigate semantic communications over Gaussian broadcast channels where the transmitter has a common observable source but the receivers wish to recover hierarchical semantic information in adaptation to their channel conditions. Inspired by the capacity achieving property of superposition codes, we propose a deep learning based superposition coded modulation (DeepSCM) scheme. Specifically, the hierarchical semantic information is first extracted and encoded into basic and enhanced feature vectors. A linear minimum mean square error (LMMSE) decorrelator is then developed to obtain a refinement from the enhanced features that is uncorrelated with the basic features. Finally, the basic features and their refinement are superposed for broadcasting after probabilistic modulation. Experiments are conducted for two-receiver image semantic broadcasting with coarse and fine classification as hierarchical semantic tasks. DeepSCM outperforms the benchmarking coded-modulation scheme without a superposition structure, especially with large channel disparity and high order modulation. It also approaches the performance upperbound as if there were only one receiver.", "field": "cs", "label": 0}
{"text": "Title: Analytic problems for elliptic curves\nAbstract: We consider some problems of analytic number theory for elliptic curves which can be considered as analogues of classical questions around the distribution of primes in arithmetic progressions to large moduli, and of the question of twin primes. This leads to some local results on the distribution of the group structures of elliptic curves defined over a prime finite field, exhibiting an interesting dichotomy for the occurence of the possible groups. (Note : This paper was initially written in 2000/01, but after a four year wait for a referee report, it is now withdrawn and deposited in the arXiv).", "field": "math", "label": 1}
{"text": "Title: Fiedler Linearizations of Rectangular Rational Matrix Functions\nAbstract: Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler linearizations, which are generalizations of the classical companion forms. In this paper the concept of Fiedler linearization is extended from square regular to rectangular rational matrix valued functions. The approach is applied to Rosenbrock functions arising in mathematical system theory.", "field": "math", "label": 1}
{"text": "Title: On Borkar and Young Relaxed Control Topologies and Continuous Dependence of Invariant Measures on Control Policy\nAbstract: In deterministic and stochastic control theory, relaxed or randomized control policies allow for versatile mathematical analysis (on continuity, compactness, convexity and approximations) to be applicable with no artificial restrictions on the classes of control policies considered, leading to very general existence results on optimal measurable policies under various setups and information structures. On relaxed controls, two studied topologies are the Young and Borkar (weak$^*$) topologies on spaces of functions from a state/measurement space to the space of probability measures on control action spaces; the former via a weak convergence topology on probability measures on a product space with a fixed marginal on the input (state) space, and the latter via a weak$^*$ topology on randomized policies viewed as maps from states/measurements to the space of signed measures with bounded variation. We establish implication and equivalence conditions between the Young and Borkar topologies on control policies. We then show that, under some conditions, for a controlled Markov chain with standard Borel spaces the invariant measure is weakly continuous on the space of stationary control policies defined by either of these topologies. An implication is near optimality of quantized stationary policies in state and actions or continuous stationary and deterministic policies for average cost control under two sets of continuity conditions (with either weak continuity in the state-action pair or strong continuity in the action for each state) on transition kernels.", "field": "math", "label": 0}
{"text": "Title: Maximal polarization for periodic configurations on the real line\nAbstract: We prove that among all 1-periodic configurations $\\Gamma$ of points on the real line $\\mathbb{R}$ the quantities $$ \\min_{x \\in \\mathbb{R}} \\sum_{\\gamma \\in \\Gamma} e^{- \\pi \\alpha (x - \\gamma)^2} \\quad \\text{and} \\quad \\max_{x \\in \\mathbb{R}} \\sum_{\\gamma \\in \\Gamma} e^{- \\pi \\alpha (x - \\gamma)^2}$$ are maximized and minimized, respectively, if and only if the points are equispaced and whenever the number of points $n$ per period is sufficiently large (depending on $\\alpha$). This solves the polarization problem for periodic configurations with a Gaussian weight on $\\mathbb{R}$ for large $n$. The first result is shown using Fourier series. The second result follows from work of Cohn and Kumar on universal optimality and holds for all $n$ (independent of $\\alpha$).", "field": "math", "label": 0}
{"text": "Title: The Power of Training: How Different Neural Network Setups Influence the Energy Demand\nAbstract: This work examines the effects of variations in machine learning training regimes and learning paradigms on the corresponding energy consumption. While increasing data availability and innovation in high-performance hardware fuels the training of sophisticated models, it also supports the fading perception of energy consumption and carbon emission. Therefore, the goal of this work is to create awareness about the energy impact of general training parameters and processes, from learning rate over batch size to knowledge transfer. Multiple setups with different hyperparameter initializations are evaluated on two different hardware configurations to obtain meaningful results. Experiments on pretraining and multitask training are conducted on top of the baseline results to determine their potential towards sustainable machine learning.", "field": "cs", "label": 0}
{"text": "Title: Entropy-based Probing Beam Selection and Beam Prediction via Deep Learning\nAbstract: Hierarchical beam search in mmWave communications incurs substantial training overhead, necessitating deep learning-enabled beam predictions to effectively leverage channel priors and mitigate this overhead. In this study, we introduce a comprehensive probabilistic model of power distribution in beamspace, and formulate the joint optimization problem of probing beam selection and probabilistic beam prediction as an entropy minimization problem. Then, we propose a greedy scheme to iteratively and alternately solve this problem, where a transformer-based beam predictor is trained to estimate the conditional power distribution based on the probing beams and user location within each iteration, and the trained predictor selects an unmeasured beam that minimizes the entropy of remaining beams. To further reduce the number of interactions and the computational complexity of the iterative scheme, we propose a two-stage probing beam selection scheme. Firstly, probing beams are selected from a location-specific codebook designed by an entropy-based criterion, and predictions are made with corresponding feedback. Secondly, the optimal beam is identified using additional probing beams with the highest predicted power values. Simulation results demonstrate the superiority of the proposed schemes compared to hierarchical beam search and beam prediction with uniform probing beams.", "field": "cs", "label": 0}
{"text": "Title: Equivariant Morse theory for Lie algebra actions on Riemannian foliations\nAbstract: Consider the transverse isometric action of a finite dimensional Lie algebra g on a Riemannian foliation. This paper studies the equivariant Morse-Bott theory on the leaf space of the Riemannian foliations in this setting. Among other things, we establish a foliated version of the Morse-Bott lemma for a g-invariant basic Morse-Bott function, and a foliated version of the usual handle presentation theorem. In the non-equivariant case, we apply these results to present a new proof of the Morse inequalities on Riemannian foliations. In the equivariant case, we apply these results to study Hamiltonian action of an abelian Lie algebra on a presymplectic manifold whose underlying foliation is also Riemannian, and extend the Kirwan surjectivity and injectivity theorem in equivariant symplectic geometry to this situation. Among other things, this implies the Kirwan surjectivity and injectivity hold for Hamiltonian torus actions on symplectic orbifolds.", "field": "math", "label": 0}
{"text": "Title: Order of uniform approximation by polynomial interpolation in the complex plane and beyond\nAbstract: For Lagrange polynomial interpolation on open arcs $X=\\gamma$ in $\\mathbb{C}$, it is well-known that the Lebesgue constant for the family of Chebyshev points ${\\bf{x}}_n:=\\{x_{n,j}\\}^{n}_{j=0}$ on $[-1,1]\\subset \\mathbb{R}$ has growth order of $O(log(n))$. The same growth order was shown in [45] for the Lebesgue constant of the family ${\\bf {z^{**}_n}}:=\\{z_{n,j}^{**}\\}^{n}_{j=0}$ of some properly adjusted Fej\\'er points on a rectifiable smooth open arc $\\gamma\\subset \\mathbb{C}$. On the other hand, in our recent work [15], it was observed that if the smooth open arc $\\gamma$ is replaced by an $L$-shape arc $\\gamma_0 \\subset \\mathbb{C}$ consisting of two line segments, numerical experiments suggest that the Marcinkiewicz-Zygmund inequalities are no longer valid for the family of Fej\\'er points ${\\bf z}_n^{*}:=\\{z_{n,j}^{*}\\}^{n}_{j=0}$ on $\\gamma$, and that the rate of growth for the corresponding Lebesgue constant $L_{{\\bf {z}}^{*}_n}$ is as fast as $c\\,log^2(n)$ for some constant $c>0$. The main objective of the present paper is 3-fold: firstly, it will be shown that for the special case of the $L$-shape arc $\\gamma_0$ consisting of two line segments of the same length that meet at the angle of $\\pi/2$, the growth rate of the Lebesgue constant $L_{{\\bf {z}}_n^{*}}$ is at least as fast as $O(Log^2(n))$, with $\\lim\\sup \\frac{L_{{\\bf {z}}_n^{*}}}{log^2(n)} = \\infty$; secondly, the corresponding (modified) Marcinkiewicz-Zygmund inequalities fail to hold; and thirdly, a proper adjustment ${\\bf z}_n^{**}:=\\{z_{n,j}^{**}\\}^{n}_{j=0}$ of the Fej\\'er points on $\\gamma$ will be described to assure the growth rate of $L_{{\\bf z}_n^{**}}$ to be exactly $O(Log^2(n))$.", "field": "math", "label": 1}
{"text": "Title: Periodic solutions of one-dimensional cellular automata with random rules\nAbstract: We study cellular automata with randomly selected rules. Our setting are two-neighbor rules with a large number $n$ of states. The main quantity we analyze is the asymptotic probability, as $n \\to \\infty$, that the random rule has a periodic solution with given spatial and temporal periods. We prove that this limiting probability is non-trivial when the spatial and temporal periods are confined to a finite range. The main tool we use is the Chen-Stein method for Poisson approximation. The limiting probability distribution of the smallest temporal period for a given spatial period is deduced as a corollary and relevant empirical simulations are presented.", "field": "math", "label": 1}
{"text": "Title: Graphon games: A statistical framework for network games and interventions\nAbstract: In this paper, we present a unifying framework for analyzing equilibria and designing interventions for large network games sampled from a stochastic network formation process represented by a graphon. We first introduce a new class of infinite population games, termed graphon games, where a continuum of heterogeneous agents interact according to a graphon. After studying properties of equilibria in graphon games, we show that graphon equilibria can approximate equilibria of large network games sampled from the graphon. We next show that, under some regularity assumptions, the graphon approach enables the design of asymptotically optimal interventions via the solution of an optimization problem with much lower dimension than the one based on the entire network structure. We illustrate our framework on a synthetic dataset of rural villages and show that the graphon intervention can be computed efficiently and based solely on aggregated relational data.", "field": "cs", "label": 1}
{"text": "Title: A new approach to convergence analysis of iterative models with optimal error bounds\nAbstract: In this paper, we study a new approach related to the convergence analysis of Ishikawa-type iterative models to a common fixed point of two non-expansive mappings in Banach spaces. The main novelty of our contribution lies in the so-called \\emph{optimal error bounds}, which established some necessary and sufficient conditions for convergence and derived both the error estimates and bounds on the convergence rates for iterative schemes. Although a special interest here is devoted to the Ishikawa and modified Ishikawa iterative sequences, the theory of \\emph{optimal error bounds} proposed in this paper can also be favorably applied to various types of iterative models to approximate common fixed points of non-expansive mappings.", "field": "math", "label": 0}
{"text": "Title: Towards a Foundation Purchasing Model: Pretrained Generative Autoregression on Transaction Sequences\nAbstract: Machine learning models underpin many modern financial systems for use cases such as fraud detection and churn prediction. Most are based on supervised learning with hand-engineered features, which relies heavily on the availability of labelled data. Large self-supervised generative models have shown tremendous success in natural language processing and computer vision, yet so far they haven't been adapted to multivariate time series of financial transactions. In this paper, we present a generative pretraining method that can be used to obtain contextualised embeddings of financial transactions. Benchmarks on public datasets demonstrate that it outperforms state-of-the-art self-supervised methods on a range of downstream tasks. We additionally perform large-scale pretraining of an embedding model using a corpus of data from 180 issuing banks containing 5.1 billion transactions and apply it to the card fraud detection problem on hold-out datasets. The embedding model significantly improves value detection rate at high precision thresholds and transfers well to out-of-domain distributions.", "field": "cs", "label": 0}
{"text": "Title: Cluster algebras and monotone Lagrangian tori\nAbstract: Motivated by recent developments in the construction of Newton--Okounkov bodies and toric degenerations via cluster algebras in [GHKK18, FO20], we consider a family of Newton--Okounkov polytopes of a complex smooth projective variety $X$ related by a composition of tropicalized cluster mutations. According to the work of [HK15], the toric degeneration associated with each Newton--Okounkov polytope $\\Delta$ in the family produces a Lagrangian torus fibration of $X$ over $\\Delta$. We investigate circumstances in which each Lagrangian torus fibration possesses a monotone Lagrangian torus fiber. We provide a sufficient condition, based on the data of tropical integer points and exchange matrices, for the family of constructed monotone Lagrangian tori to contain infinitely many monotone Lagrangian tori, no two of which are related by any symplectomorphisms. By employing this criterion and exploiting the correspondence between the tropical integer points and the dual canonical basis elements, we generate infinitely many distinct monotone Lagrangian tori on flag manifolds of arbitrary type except in a few cases.", "field": "math", "label": 0}
{"text": "Title: A sample iterated small cancellation theory for groups of Burnside type\nAbstract: We develop yet another technique to present the free Burnside group $B(m,n)$ of odd exponent $n$ with $m\\ge2$ generators as a group satisfying a certain iterated small cancellation condition. Using the approach, we provide a reasonably accessible proof that $B(m,n)$ is infinite with a moderate bound $n > 2000$ on the odd exponent $n$.", "field": "math", "label": 1}
{"text": "Title: Uncovering the Disentanglement Capability in Text-to-Image Diffusion Models\nAbstract: Generative models have been widely studied in computer vision. Recently, diffusion models have drawn substantial attention due to the high quality of their generated images. A key desired property of image generative models is the ability to disentangle different attributes, which should enable modification towards a style without changing the semantic content, and the modification parameters should generalize to different images. Previous studies have found that generative adversarial networks (GANs) are inherently endowed with such disentanglement capability, so they can perform disentangled image editing without re-training or fine-tuning the network. In this work, we explore whether diffusion models are also inherently equipped with such a capability. Our finding is that for stable diffusion models, by partially changing the input text embedding from a neutral description (e.g., \"a photo of person\") to one with style (e.g., \"a photo of person with smile\") while fixing all the Gaussian random noises introduced during the denoising process, the generated images can be modified towards the target style without changing the semantic content. Based on this finding, we further propose a simple, light-weight image editing algorithm where the mixing weights of the two text embeddings are optimized for style matching and content preservation. This entire process only involves optimizing over around 50 parameters and does not fine-tune the diffusion model itself. Experiments show that the proposed method can modify a wide range of attributes, with the performance outperforming diffusion-model-based image-editing algorithms that require fine-tuning. The optimized weights generalize well to different images. Our code is publicly available at https://github.com/UCSB-NLP-Chang/DiffusionDisentanglement.", "field": "cs", "label": 1}
{"text": "Title: Decay rates for cubic and higher order nonlinear wave equations on asymptotically flat spacetimes\nAbstract: In this paper, we prove pointwise decay rates for cubic and higher order nonlinear wave equations, including quasilinear wave equations, on asymptotically flat and time-dependent spacetimes. We assume that the solution to the linear equation (rather than the nonlinear equation) satisfies a weaker form of the standard integrated local energy decay, or Morawetz, estimate. For nonlinearities with a total derivative structure, we prove better pointwise decay rates.", "field": "math", "label": 1}
{"text": "Title: JPEG XT Image Compression with Hue Compensation for Two-Layer HDR Coding\nAbstract: We propose a novel JPEG XT image compression with hue compensation for two-layer HDR coding. LDR images produced from JPEG XT bitstreams have some distortion in hue due to tone mapping operations. In order to suppress the color distortion, we apply a novel hue compensation method based on the maximally saturated colors. Moreover, the bitstreams generated by using the proposed method are fully compatible with the JPEG XT standard. In an experiment, the proposed method is demonstrated not only to produce images with small hue degradation but also to maintain well-mapped luminance, in terms of three kinds of criterion: TMQI, hue value in CIEDE2000, and the maximally saturated color on the constant-hue plane.", "field": "cs", "label": 1}
{"text": "Title: The second largest component in the supercritical 2D Hamming graph\nAbstract: The 2-dimensional Hamming graph H(2,n) consists of the $n^2$ vertices $(i,j)$, $1\\leq i,j\\leq n$, two vertices being adjacent when they share a common coordinate. We examine random subgraphs of H(2,n) in percolation with edge probability $p$, so that the average degree $2(n-1)p=1+\\epsilon$. Previous work by van der Hofstad and Luczak had shown that in the barely supercritical region $n^{-2/3}\\ln^{1/3}n\\ll \\epsilon \\ll 1$ the largest component has size $\\sim 2\\epsilon n$. Here we show that the second largest component has size close to $\\epsilon^{-2}$, so that the dominant component has emerged. This result also suggests that a {\\it discrete duality principle} might hold, whereby, after removing the largest connected component in the supercritical regime, the remaining random subgraphs behave as in the subcritical regime.", "field": "math", "label": 1}
{"text": "Title: Thermodynamic Consistent Neural Networks for Learning Material Interfacial Mechanics\nAbstract: For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings, which is critical to understand and predict interfacial failures under complex loadings. However, existing theoretical models have limitations on enough complexity and flexibility to well learn the real-world TSR from experimental observations. A neural network can fit well along with the loading paths but often fails to obey the laws of physics, due to a lack of experimental data and understanding of the hidden physical mechanism. In this paper, we propose a thermodynamic consistent neural network (TCNN) approach to build a data-driven model of the TSR with sparse experimental data. The TCNN leverages recent advances in physics-informed neural networks (PINN) that encode prior physical information into the loss function and efficiently train the neural networks using automatic differentiation. We investigate three thermodynamic consistent principles, i.e., positive energy dissipation, steepest energy dissipation gradient, and energy conservative loading path. All of them are mathematically formulated and embedded into a neural network model with a novel defined loss function. A real-world experiment demonstrates the superior performance of TCNN, and we find that TCNN provides an accurate prediction of the whole TSR surface and significantly reduces the violated prediction against the laws of physics.", "field": "cs", "label": 1}
{"text": "Title: Learning Safe, Generalizable Perception-based Hybrid Control with Certificates\nAbstract: Many robotic tasks require high-dimensional sensors such as cameras and Lidar to navigate complex environments, but developing certifiably safe feedback controllers around these sensors remains a challenging open problem, particularly when learning is involved. Previous works have proved the safety of perception-feedback controllers by separating the perception and control subsystems and making strong assumptions on the abilities of the perception subsystem. In this work, we introduce a novel learning-enabled perception-feedback hybrid controller, where we use Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs) to show the safety and liveness of a full-stack perception-feedback controller. We use neural networks to learn a CBF and CLF for the full-stack system directly in the observation space of the robot, without the need to assume a separate perception-based state estimator. Our hybrid controller, called LOCUS (Learning-enabled Observation-feedback Control Using Switching), can safely navigate unknown environments, consistently reach its goal, and generalizes safely to environments outside of the training dataset. We demonstrate LOCUS in experiments both in simulation and in hardware, where it successfully navigates a changing environment using feedback from a Lidar sensor.", "field": "cs", "label": 1}
{"text": "Title: Squared chromatic number without claws or large cliques\nAbstract: Let $G$ be a claw-free graph on $n$ vertices with clique number $\\omega$, and consider the chromatic number $\\chi(G^2)$ of the square $G^2$ of $G$. Writing $\\chi'_s(d)$ for the supremum of $\\chi(L^2)$ over the line graphs $L$ of simple graphs of maximum degree at most $d$, we prove that $\\chi(G^2)\\le \\chi'_s(\\omega)$ for $\\omega \\in \\{3,4\\}$. For $\\omega=3$, this implies the sharp bound $\\chi(G^2) \\leq 10$. For $\\omega=4$, this implies $\\chi(G^2)\\leq 22$, which is within $2$ of the conjectured best bound. This work is motivated by a strengthened form of a conjecture of Erd\\H{o}s and Ne\\v{s}et\\v{r}il.", "field": "math", "label": 1}
{"text": "Title: Notes on exotic and perverse-coherent sheaves\nAbstract: Exotic sheaves are certain complexes of coherent sheaves on the cotangent bundle of the flag variety of a reductive group. They are closely related to perverse-coherent sheaves on the nilpotent cone. This expository article includes the definitions of these two categories, applications, and some structure theory, as well as detailed calculations for SL(2).", "field": "math", "label": 1}
{"text": "Title: Local limit theorem for time-inhomogeneous functions of Markov processes\nAbstract: In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear dynamical systems.", "field": "math", "label": 0}
{"text": "Title: GridFormer: Point-Grid Transformer for Surface Reconstruction\nAbstract: Implicit neural networks have emerged as a crucial technology in 3D surface reconstruction. To reconstruct continuous surfaces from discrete point clouds, encoding the input points into regular grid features (plane or volume) has been commonly employed in existing approaches. However, these methods typically use the grid as an index for uniformly scattering point features. Compared with the irregular point features, the regular grid features may sacrifice some reconstruction details but improve efficiency. To take full advantage of these two types of features, we introduce a novel and high-efficiency attention mechanism between the grid and point features named Point-Grid Transformer (GridFormer). This mechanism treats the grid as a transfer point connecting the space and point cloud. Our method maximizes the spatial expressiveness of grid features and maintains computational efficiency. Furthermore, optimizing predictions over the entire space could potentially result in blurred boundaries. To address this issue, we further propose a boundary optimization strategy incorporating margin binary cross-entropy loss and boundary sampling. This approach enables us to achieve a more precise representation of the object structure. Our experiments validate that our method is effective and outperforms the state-of-the-art approaches under widely used benchmarks by producing more precise geometry reconstructions. The code is available at https://github.com/list17/GridFormer.", "field": "cs", "label": 0}
{"text": "Title: Luna's fundamental lemma for diagonalizable groups\nAbstract: We study relatively affine actions of a diagonalizable group $G$ on locally noetherian schemes. In particular, we generalize Luna's fundamental lemma when applied to a diagonalizable group: we obtain criteria for a $G$-equivariant morphism $f: X'\\to X$ to be $strongly\\ equivariant$, namely the base change of the morphism $f/\\!/G$ of quotient schemes, and establish descent criteria for $f/\\!/G$ to be an open embedding, \\'etale, smooth, regular, syntomic, or lci.", "field": "math", "label": 1}
{"text": "Title: Existence and rigidity of quantum isometry groups for compact metric spaces\nAbstract: We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed probability measure. In the former case it also follows from recent results of the second author that the quantum isometry group is classical, i.e. the commutative $C^*$-algebra of continuous functions on the Riemannian isometry group.", "field": "math", "label": 1}
{"text": "Title: On an inverse Robin spectral problem\nAbstract: We consider the problem of the recovery of a Robin coefficient on a part $\\gamma \\subset \\partial \\Omega$ of the boundary of a bounded domain $\\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the principal eigenfunction of the Laplace operator with Dirichlet boundary condition on $\\partial \\Omega \\setminus \\gamma$. We prove uniqueness, as well as local Lipschitz stability of the inverse problem. Moreover, we present an iterative reconstruction algorithm with numerical computations in two dimensions showing the accuracy of the method.", "field": "math", "label": 1}
{"text": "Title: Randomization can be as helpful as a glimpse of the future in online computation\nAbstract: We provide simple but surprisingly useful direct product theorems for proving lower bounds on online algorithms with a limited amount of advice about the future. As a consequence, we are able to translate decades of research on randomized online algorithms to the advice complexity model. Doing so improves significantly on the previous best advice complexity lower bounds for many online problems, or provides the first known lower bounds. For example, if $n$ is the number of requests, we show that: (1) A paging algorithm needs $\\Omega(n)$ bits of advice to achieve a competitive ratio better than $H_k=\\Omega(\\log k)$, where $k$ is the cache size. Previously, it was only known that $\\Omega(n)$ bits of advice were necessary to achieve a constant competitive ratio smaller than $5/4$. (2) Every $O(n^{1-\\varepsilon})$-competitive vertex coloring algorithm must use $\\Omega(n\\log n)$ bits of advice. Previously, it was only known that $\\Omega(n\\log n)$ bits of advice were necessary to be optimal. For certain online problems, including the MTS, $k$-server, paging, list update, and dynamic binary search tree problem, our results imply that randomization and sublinear advice are equally powerful (if the underlying metric space or node set is finite). This means that several long-standing open questions regarding randomized online algorithms can be equivalently stated as questions regarding online algorithms with sublinear advice. For example, we show that there exists a deterministic $O(\\log k)$-competitive $k$-server algorithm with advice complexity $o(n)$ if and only if there exists a randomized $O(\\log k)$-competitive $k$-server algorithm without advice. Technically, our main direct product theorem is obtained by extending an information theoretical lower bound technique due to Emek, Fraigniaud, Korman, and Ros\\'en [ICALP'09].", "field": "cs", "label": 1}
{"text": "Title: Root multiplicities for Borcherds algebras and graph coloring\nAbstract: We establish a connection between root multiplicities for Borcherds-Kac-Moody algebras and graph coloring. We show that the generalized chromatic polynomial of the graph associated to a given Borcherds algebra can be used to give a closed formula for certain root multiplicities. Using this connection we give a second interpretation, namely that the root multiplicity of a given root coincides with the number of acyclic orientations with a unique sink of a certain graph (depending on the root). Finally, using the combinatorics of Lyndon words we construct a basis for the root spaces corresponding to these roots and determine the Hilbert series in the case when all simple roots are imaginary. As an application we give a Lie theoretic proof of Stanley's reciprocity theorem of chromatic polynomials.", "field": "math", "label": 1}
{"text": "Title: Perspective Plane Program Induction from a Single Image\nAbstract: We study the inverse graphics problem of inferring a holistic representation for natural images. Given an input image, our goal is to induce a neuro-symbolic, program-like representation that jointly models camera poses, object locations, and global scene structures. Such high-level, holistic scene representations further facilitate low-level image manipulation tasks such as inpainting. We formulate this problem as jointly finding the camera pose and scene structure that best describe the input image. The benefits of such joint inference are two-fold: scene regularity serves as a new cue for perspective correction, and in turn, correct perspective correction leads to a simplified scene structure, similar to how the correct shape leads to the most regular texture in shape from texture. Our proposed framework, Perspective Plane Program Induction (P3I), combines search-based and gradient-based algorithms to efficiently solve the problem. P3I outperforms a set of baselines on a collection of Internet images, across tasks including camera pose estimation, global structure inference, and down-stream image manipulation tasks.", "field": "cs", "label": 1}
{"text": "Title: Eulerian partitions for configurations of skew lines\nAbstract: In this paper, which is a complement of \\cite{BG}, we study a few elementary invariants for configurations of skew lines, as introduced and analyzed first by Viro and his collaborators. We slightly simplify the exposition of some known invariants and use them to define a natural partition of the lines in a skew configuration. We also describe an algorithm which constructs a spindle-permutation for a given switching class, or proves non-existence of such a spindle-permutation.", "field": "math", "label": 1}
{"text": "Title: STAS: Spatial-Temporal Return Decomposition for Multi-agent Reinforcement Learning\nAbstract: Centralized Training with Decentralized Execution (CTDE) has been proven to be an effective paradigm in cooperative multi-agent reinforcement learning (MARL). One of the major challenges is credit assignment, which aims to credit agents by their contributions. While prior studies have shown great success, their methods typically fail to work in episodic reinforcement learning scenarios where global rewards are revealed only at the end of the episode. They lack the functionality to model complicated relations of the delayed global reward in the temporal dimension and suffer from inefficiencies. To tackle this, we introduce Spatial-Temporal Attention with Shapley (STAS), a novel method that learns credit assignment in both temporal and spatial dimensions. It first decomposes the global return back to each time step, then utilizes the Shapley Value to redistribute the individual payoff from the decomposed global reward. To mitigate the computational complexity of the Shapley Value, we introduce an approximation of marginal contribution and utilize Monte Carlo sampling to estimate it. We evaluate our method on an Alice & Bob example and MPE environments across different scenarios. Our results demonstrate that our method effectively assigns spatial-temporal credit, outperforming all state-of-the-art baselines.", "field": "cs", "label": 0}
{"text": "Title: Coverage Explorer: Coverage-guided Test Generation for Cyber Physical Systems\nAbstract: Given the safety-critical functions of autonomous cyber-physical systems (CPS) across diverse domains, testing these systems is essential. While conventional software and hardware testing methodologies offer partial insights, they frequently do not provide adequate coverage in a CPS. In this study, we introduce a testing framework designed to systematically formulate test cases, effectively exploring the state space of CPS. This framework introduces a coverage-centric sampling technique, coupled with a cluster-based methodology for training a surrogate model. The framework then uses model predictive control within the surrogate model to generates test cases tailored to CPS specifications. To evaluate the efficacy of the framework, we applied it on several benchmarks, spanning from a kinematic car to systems like an unmanned aircraft collision avoidance system (ACAS XU) and automatic transmission system. Comparative analyses were conducted against alternative test generation strategies, including randomized testing, as well as falsification using S-TaLiRo.", "field": "cs", "label": 0}
{"text": "Title: A Simple Generalization of a Result for Random Matrices with Independent Sub-Gaussian Rows\nAbstract: In this short note, we give a very simple but useful generalization of a result of Vershynin (Theorem 5.39 of [1]) for a random matrix with independent sub-Gaussian rows. We also explain with an example where our generalization is useful.", "field": "math", "label": 1}
{"text": "Title: A load balanced chemistry model with analytical Jacobian for faster reactive simulations in OpenFOAM\nAbstract: In this study, we introduce a novel open-source chemistry model for OpenFOAM to speed-up the reactive computational fluid dynamics (CFD) simulations using finite-rate chemistry. First, a dynamic load balancing model called DLBFoam is introduced to balance the chemistry load during runtime in parallel simulations. In addition, the solution of the cell-based chemistry problem is improved by utilizing an analytical Jacobian using an open-source library called pyJac and an efficient linear algebra library LAPACK. Combination of the aforementioned efforts yields a speed-up factor 200 for a high-fidelity large-eddy simulation spray combustion case compared to the standard OpenFOAM implementation. It is worth noting that the present implementation does not compromise the solution accuracy.", "field": "cs", "label": 1}
{"text": "Title: Uncertainty Estimates for Ordinal Embeddings\nAbstract: To investigate objects without a describable notion of distance, one can gather ordinal information by asking triplet comparisons of the form \"Is object $x$ closer to $y$ or is $x$ closer to $z$?\" In order to learn from such data, the objects are typically embedded in a Euclidean space while satisfying as many triplet comparisons as possible. In this paper, we introduce empirical uncertainty estimates for standard embedding algorithms when few noisy triplets are available, using a bootstrap and a Bayesian approach. In particular, simulations show that these estimates are well calibrated and can serve to select embedding parameters or to quantify uncertainty in scientific applications.", "field": "cs", "label": 1}
{"text": "Title: On metrically complete Bruhat-Tits buildings\nAbstract: Metrical completeness for Bruhat-Tits buildings is a natural and useful condition. In this paper we determine which Bruhat-Tits buildings are metrically complete up to certain cases involving infinite-dimensionality and residue characteristic two.", "field": "math", "label": 1}
{"text": "Title: Chordal graphs, even-hole-free graphs and sparse obstructions to bounded treewidth\nAbstract: We present and study the following conjecture: for an integer $t\\geq 4$ and a graph $H$, every even-hole-free graph of large enough treewidth has an induced subgraph isomorphic to either $K_t$ or $H$, if (and only if) $H$ is a $K_4$-free chordal graph. The ``only if'' part follows from the properties of the so-called layered wheels due to Sintiari and Trotignon. Alecu, Chudnovsky, Spirkl and the author recently proved the conjecture in two special cases: (a) when $t=4$; and (b) when $H=cone (F)$ for some forest $F$; that is, $H$ is obtained from $F$ by adding a universal vertex. Our first result is a common strengthening: for an integer $t\\geq 4$ and graphs $F$ and $H$, (even-hole, $cone(cone (F))$, $H$, $K_t$)-free graphs have bounded treewidth if and only if $F$ is a forest and $H$ is a $K_4$-free chordal graph. For general $t\\geq 4$, we push the current state of the art further than (b) by settling the conjecture for the smallest choices of $H$ that are not coned forests. This follows from our second result: we prove the conjecture when $H$ is a crystal; that is, a graph obtained from several coned double stars by gluing them together along the middle edges of the double stars. We also propose another conjecture motivated by the following observation: except for complete graphs and complete bipartite graphs, all the constructions of graphs with unbounded treewidth which have been discovered so far are $2$-degenerate. Specifically, we conjecture that for every $t\\geq 1$, every graph of sufficiently large treewidth has an induced subgraph of treewidth $t$ which is either complete, complete bipartite, or $2$-degenerate. This conjecture is the first to predict a grid-type theorem for induced subgraphs, and what makes it even more relevant is somewhat serendipitous: if true, it would imply our former conjecture by reducing it to (a).", "field": "math", "label": 0}
{"text": "Title: Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions\nAbstract: In this survey, we dive into Tabular Data Learning (TDL) using Graph Neural Networks (GNNs), a domain where deep learning-based approaches have increasingly shown superior performance in both classification and regression tasks compared to traditional methods. The survey highlights a critical gap in deep neural TDL methods: the underrepresentation of latent correlations among data instances and feature values. GNNs, with their innate capability to model intricate relationships and interactions between diverse elements of tabular data, have garnered significant interest and application across various TDL domains. Our survey provides a systematic review of the methods involved in designing and implementing GNNs for TDL (GNN4TDL). It encompasses a detailed investigation into the foundational aspects and an overview of GNN-based TDL methods, offering insights into their evolving landscape. We present a comprehensive taxonomy focused on constructing graph structures and representation learning within GNN-based TDL methods. In addition, the survey examines various training plans, emphasizing the integration of auxiliary tasks to enhance the effectiveness of instance representations. A critical part of our discussion is dedicated to the practical application of GNNs across a spectrum of GNN4TDL scenarios, demonstrating their versatility and impact. Lastly, we discuss the limitations and propose future research directions, aiming to spur advancements in GNN4TDL. This survey serves as a resource for researchers and practitioners, offering a thorough understanding of GNNs' role in revolutionizing TDL and pointing towards future innovations in this promising area.", "field": "cs", "label": 0}
{"text": "Title: Leveraging SAM for Single-Source Domain Generalization in Medical Image Segmentation\nAbstract: Domain Generalization (DG) aims to reduce domain shifts between domains to achieve promising performance on the unseen target domain, which has been widely practiced in medical image segmentation. Single-source domain generalization (SDG) is the most challenging setting that trains on only one source domain. Although existing methods have made considerable progress on SDG of medical image segmentation, the performances are still far from the applicable standards when faced with a relatively large domain shift. In this paper, we leverage the Segment Anything Model (SAM) to SDG to greatly improve the ability of generalization. Specifically, we introduce a parallel framework, the source images are sent into the SAM module and normal segmentation module respectively. To reduce the calculation resources, we apply a merging strategy before sending images to the SAM module. We extract the bounding boxes from the segmentation module and send the refined version as prompts to the SAM module. We evaluate our model on a classic DG dataset and achieve competitive results compared to other state-of-the-art DG methods. Furthermore, We conducted a series of ablation experiments to prove the effectiveness of the proposed method. The code is publicly available at https://github.com/SARIHUST/SAMMed.", "field": "cs", "label": 0}
{"text": "Title: Virtual rigid motives of semi-algebraic sets\nAbstract: Let $k$ be a field of characteristic zero containing all roots of unity and $K=k((t))$. We build a ring morphism from the Grothendieck group of semi-algebraic sets over $K$ to the Grothendieck group of motives of rigid analytic varieties over $K$. It extend the morphism sending the class of an algebraic variety over $K$ to its cohomological motive with compact support. We show that it fits inside a commutative diagram involving Hrushovski and Kazhdan's motivic integration and Ayoub's equivalence between motives of rigid analytic varieties over $K$ and quasi-unipotent motives over $k$ ; we also show that it satisfies a form of duality. This allows us to answer a question by Ayoub, Ivorra and Sebag about the analytic Milnor fiber.", "field": "math", "label": 1}
{"text": "Title: Word-Representability of Graphs with respect to Split Recomposition\nAbstract: In this work, we show that the class of word-representable graphs is closed under split recomposition and determine the representation number of the graph obtained by recomposing two word-representable graphs. Accordingly, we show that the class of parity graphs is word-representable. Further, we obtain a characteristic property by which the recomposition of comparability graphs is a comparability graph. Consequently, we also establish the permutation-representation number (prn) of the resulting comparability graph. We also introduce a subclass of comparability graphs, called prn-irreducible graphs. We provide a criterion such that the split recomposition of two prn-irreducible graphs is a comparability graph and determine the prn of the resultant graph.", "field": "cs", "label": 0}
{"text": "Title: Counterexamples to the B-spline conjecture for Gabor frames\nAbstract: The frame set conjecture for B-splines $B_n$, $n \\ge 2$, states that the frame set is the maximal set that avoids the known obstructions. We show that any hyperbola of the form $ab=r$, where $r$ is a rational number smaller than one and $a$ and $b$ denote the sampling and modulation rates, respectively, has infinitely many pieces, located around $b=2,3,\\dots$, \\emph{not} belonging to the frame set of the $n$th order B-spline. This, in turn, disproves the frame set conjecture for B-splines. On the other hand, we uncover a new region belonging to the frame set for B-splines $B_n$, $n \\ge 2$.", "field": "math", "label": 1}
{"text": "Title: A Simple Construction of Tournaments with Finite and Uncountable Dichromatic Number\nAbstract: The dichromatic number $\\chi(\\vec{G})$ of a digraph $\\vec{G}$ is the minimum number of colors needed to color the vertices $V(\\vec{G})$ in such a way that no monochromatic directed cycle is obtained. In this note, for any $k\\in \\mathbb{N}$, we give a simple construction of tournaments with dichromatic number exactly equal to $k$. The proofs are based on a combinatorial lemma on partitioning a checkerboard which may be of independent interest. We also generalize our finite construction to give an elementary construction of a complete digraph of cardinality equal to the cardinality of $\\mathbb{R}$ and having an uncountable dichromatic number. Furthermore, we also construct an oriented balanced complete $n$-partite graph $\\vec{K}^{(m)}_n$, such that the minimum number of colors needed to color its vertices such that there is no monochromatic directed triangle is greater than or equal to $nm/(n+2m-2)$.", "field": "math", "label": 0}
{"text": "Title: On the Structure of Boolean Functions with Small Spectral Norm\nAbstract: In this paper we prove results regarding Boolean functions with small spectral norm (the spectral norm of f is $\\|\\hat{f}\\|_1=\\sum_{\\alpha}|\\hat{f}(\\alpha)|$). Specifically, we prove the following results for functions $f:\\{0,1\\}^n \\to \\{0,1\\}$ with $\\|\\hat{f}\\|_1=A$. 1. There is a subspace $V$ of co-dimension at most $A^2$ such that $f|_V$ is constant. 2. f can be computed by a parity decision tree of size $2^{A^2}n^{2A}$. (a parity decision tree is a decision tree whose nodes are labeled with arbitrary linear functions.) 3. If in addition f has at most s nonzero Fourier coefficients, then f can be computed by a parity decision tree of depth $A^2 \\log s$. 4. For every $0<\\epsilon$ there is a parity decision tree of depth $O(A^2 + \\log(1/\\epsilon))$ and size $2^{O(A^2)} \\cdot \\min\\{1/\\epsilon^2,O(\\log(1/\\epsilon))^{2A}\\}$ that \\epsilon-approximates f. Furthermore, this tree can be learned, with probability $1-\\delta$, using $\\poly(n,\\exp(A^2),1/\\epsilon,\\log(1/\\delta))$ membership queries. All the results above also hold (with a slight change in parameters) to functions $f:Z_p^n\\to \\{0,1\\}$.", "field": "cs", "label": 1}
{"text": "Title: Boundary regularity of stochastic PDEs\nAbstract: The boundary behaviour of solutions of stochastic PDEs with Dirichlet boundary conditions can be surprisingly - and in a sense, arbitrarily - bad: as shown by Krylov, for any $\\alpha>0$ one can find a simple $1$-dimensional constant coefficient linear equation whose solution at the boundary is not $\\alpha$-H\\\"older continuous. We obtain a positive counterpart of this: under some mild regularity assumptions on the coefficients, solutions of semilinear SPDEs on $C^1$ domains are proved to be $\\alpha$-H\\\"older continuous up to the boundary with some $\\alpha>0$.", "field": "math", "label": 1}
{"text": "Title: Biharmonic and harmonic homomorphisms between Riemannian three dimensional unimodular Lie groups\nAbstract: We classify biharmonic and harmonic homomorphisms $f:(G,g_1)\\rightarrow(G,g_2)$ where $G$ is a connected and simply connected three-dimensional unimodular Lie group and $g_1$ and $g_2$ are left invariant Riemannian metrics.", "field": "math", "label": 1}
{"text": "Title: Current Trends in Digital Twin Development, Maintenance, and Operation: An Interview Study\nAbstract: Digital twins (DT) are often defined as a pairing of a physical entity and a corresponding virtual entity (VE), mimicking certain aspects of the former depending on the use-case. In recent years, this concept has facilitated numerous use-cases ranging from design to validation and predictive maintenance of large and small high-tech systems. Various heterogeneous cross-domain models are essential for such systems and model-driven engineering plays a pivotal role in the design, development, and maintenance of these models. We believe models and model-driven engineering play a similarly crucial role in the context of a VE of a DT. Due to the rapidly growing popularity of DTs and their use in diverse domains and use-cases, the methodologies, tools, and practices for designing, developing, and maintaining the corresponding VEs differ vastly. To better understand these differences and similarities, we performed a semi-structured interview research with 19 professionals from industry and academia who are closely associated with different lifecycle stages of digital twins. In this paper, we present our analysis and findings from this study, which is based on seven research questions. In general, we identified an overall lack of uniformity in terms of the understanding of digital twins and used tools, techniques, and methodologies for the development and maintenance of the corresponding VEs. Furthermore, considering that digital twins are software intensive systems, we recognize a significant growth potential for adopting more software engineering practices, processes, and expertise in various stages of a digital twin's lifecycle.", "field": "cs", "label": 0}
{"text": "Title: On the Notion of Equal Figures in Euclid\nAbstract: Euclid uses an undefined notion of \"equal figures\", to which he applies the common notions about equals added to equals or subtracted from equals. When (in previous work) we formalized Euclid Book~I for computer proof-checking, we had to add fifteen axioms about undefined relations \"equal triangles\" and \"equal quadrilaterals\" to replace Euclid's use of the common notions. In this paper, we offer definitions of \"equal triangles\" and \"equal quadrilaterals\", that Euclid could have given, and prove that they have the required properties. This removes the need for adding new axioms. The proof uses the theory of proportions. Hence we also discuss the \"early theory of proportions\", which has a long history.", "field": "math", "label": 1}
{"text": "Title: Mean Value Theorems for Binary Egyptian Fractions\nAbstract: In this paper, we establish two mean value theorems for the number of solutions of the Diophantine equation $\\frac{a}{n}=\\frac{1}{x}+\\frac{1}{y}$, in the case when $a$ is fixed and $n$ varies and in the case when both $a$ and $n$ vary.", "field": "math", "label": 1}
{"text": "Title: Several new classes of MDS symbol-pair codes derived from matrix-product codes\nAbstract: In order to correct the pair-errors generated during the transmission of modern high-density data storage that the outputs of the channels consist of overlapping pairs of symbols, a new coding scheme named symbol-pair code is proposed. The error-correcting capability of the symbol-pair code is determined by its minimum symbol-pair distance. For such codes, the larger the minimum symbol-pair distance, the better. It is a challenging task to construct symbol-pair codes with optimal parameters, especially, maximum-distance-separable (MDS) symbol-pair codes. In this paper, the permutation equivalence codes of matrix-product codes with underlying matrixes of orders 3 and 4 are used to extend the minimum symbol-pair distance, and six new classes of MDS symbol-pair codes are derived.", "field": "cs", "label": 0}
{"text": "Title: Backward propagation of warped product structures and asymptotically conical shrinkers\nAbstract: We establish sufficient conditions which ensure that a locally-warped product structure propagates backward in time under the Ricci flow. As an application, we prove that if an asymptotically conical gradient shrinking soliton is asymptotic to a cone whose cross-section is a product of Einstein manifolds, the soliton must itself be a multiply-warped product over the same manifolds.", "field": "math", "label": 0}
{"text": "Title: Subgroups of bounded rank in hyperbolic 3-manifold groups\nAbstract: We prove a finiteness theorem for subgroups of bounded rank in hyperbolic $3$-manifold groups. As a consequence, we show that every bounded rank covering tower of closed hyperbolic $3$-manifolds is a tower of finite covers associated to a fibration over a $1$-orbifold.", "field": "math", "label": 0}
{"text": "Title: Two improvements in Brauer's theorem on forms\nAbstract: Let $k$ be a Brauer field, that is, a field over which every diagonal form in sufficiently many variables has a nonzero solution; for instance, $k$ could be an imaginary quadratic number field. Brauer proved that if $f_1, \\ldots, f_r$ are homogeneous polynomials on a $k$-vector space $V$ of degrees $d_1, \\ldots, d_r$, then the variety $Z$ defined by the $f_i$'s has a non-trivial $k$-point, provided that $\\dim{V}$ is sufficiently large compared to the $d_i$'s and $k$. We offer two improvements to this theorem, assuming $k$ is infinite. First, we show that the Zariski closure of the set $Z(k)$ of $k$-points has codimension $<C$, where $C$ is a constant depending only on the $d_i$'s and $k$. And second, we show that if the strength of the $f_i$'s is sufficiently large in terms of the $d_i$'s and $k$, then $Z(k)$ is actually Zariski dense in $Z$. The proofs rely on recent work of Ananyan and Hochster on high strength polynomials.", "field": "math", "label": 0}
{"text": "Title: Natural real algebraic maps of non-positive codimensions with prescribed images whose boundaries consist of non-singular real algebraic hypersurfaces intersecting with transversality\nAbstract: We present new real algebraic maps of non-positive codimensions with prescribed images whose boundaries consist of explicit non-singular real algebraic hypersurfaces intersecting with so-called \"transversality\". We also have the maps with explicit information on important real polynomials. This gives new construction of explicit real algebraic maps of non-positive codimensions with explicit information on images, preimages and important real polynomials. Thanks to some celebrated theory of Nash, smooth closed manifolds are {\\it non-singular} real algebraic manifolds and the zero sets of some real polynomials. In considerable cases, we can approximate smooth functions or more generally, maps, by real algebraic ones. It is in general difficult to have explicit examples. We have constructed some previously. We have ones of some new type with explicit information on global structures of the maps.", "field": "math", "label": 0}
{"text": "Title: Free constructions of geometries of Coxeter type\nAbstract: We establish two free constructions of geometries of Coxeter type. The first construction deals with any Coxeter diagram having no subdiagram of type A_3, the second one with diagrams of type C_n and H_4.", "field": "math", "label": 1}
{"text": "Title: Approximate Distance and Shortest-Path Oracles for Fault-Tolerant Geometric Spanners\nAbstract: In this paper, we present approximate distance and shortest-path oracles for fault-tolerant Euclidean spanners motivated by the routing problem in real-world road networks. An $f$-fault-tolerant Euclidean $t$-spanner for a set $V$ of $n$ points in $\\mathbb{R}^d$ is a graph $G=(V,E)$ where, for any two points $p$ and $q$ in $V$ and a set $F$ of $f$ vertices of $V$, the distance between $p$ and $q$ in $G-F$ is at most $t$ times their Euclidean distance. Given an $f$-fault-tolerant Euclidean $t$-spanner $G$ with $O(n)$ edges and a constant $\\varepsilon$, our data structure has size $O_{t,f}(n\\log n)$, and this allows us to compute an $(1+\\varepsilon)$-approximate distance in $G-F$ between $s$ and $s'$ can be computed in constant time for any two vertices $s$ and $s'$ and a set $F$ of $f$ failed vertices. Also, with a data structure of size $O_{t,f}(n\\log n\\log\\log n)$, we can compute an $(1+\\varepsilon)$-approximate shortest path in $G-F$ between $s$ and $s'$ in $O_{t,f}(\\log^2 n\\log\\log n+\\textsf{sol})$ time for any two vertices $s$ and $s'$ and a set $F$ of failed vertices, where $\\textsf{sol}$ denotes the number of vertices in the returned path.", "field": "cs", "label": 0}
{"text": "Title: KCES: A Workflow Containerization Scheduling Scheme Under Cloud-Edge Collaboration Framework\nAbstract: As more IoT applications gradually move towards the cloud-edge collaborative mode, the containerized scheduling of workflows extends from the cloud to the edge. However, given the high delay of the communication network, loose coupling of structure, and resource heterogeneity between cloud and edge, workflow containerization scheduling in the cloud-edge scenarios faces the difficulty of resource coordination and application collaboration management. To address these two issues, we propose a KubeEdge-Cloud-Edge-Scheduling scheme named KCES, a workflow containerization scheduling scheme for the KubeEdge cloud-edge framework. The KCES includes a cloud-edge workflow scheduling engine for KubeEdge and workflow scheduling strategies for task horizontal roaming and vertical offloading. Considering the scheduling optimization of cloud-edge workflows, this paper proposes a cloud-edge workflow scheduling model and cloud-edge node model and designs a cloud-edge workflow scheduling engine to maximize cloud-edge resource utilization under the constraint of workflow task delay. A cloud-edge resource hybrid management technology is used to design the cloud-edge resource evaluation and resource allocation algorithms to achieve cloud-edge resource collaboration. Based on the ideas of distributed functional roles and the hierarchical division of computing power, the horizontal roaming among the edges and vertical offloading strategies between the cloud and edges for workflow tasks are designed to realize the cloud-edge application collaboration. Through a customized IoT application workflow instance, experimental results show that KCES is superior to the baseline in total workflow duration, average workflow duration, and resource usage and has the capabilities of horizontal roaming and vertical offloading for workflow tasks.", "field": "cs", "label": 0}
{"text": "Title: Oscillator representations of quantum affine orthosymplectic superalgebras\nAbstract: We introduce a category of $q$-oscillator representations over the quantum affine superalgebras of type $D$ and construct a new family of its irreducible representations. Motivated by the theory of super duality, we show that these irreducible representations naturally interpolate the irreducible $q$-oscillator representations of type $X_n^{(1)}$ and the finite-dimensional irreducible representations of type $Y_n^{(1)}$ for $(X,Y)=(C,D),(D,C)$ under exact monoidal functors. This can be viewed as a quantum (untwisted) affine analogue of the correspondence between irreducible oscillator and irreducible finite-dimensional representations of classical Lie algebras arising from Howe's reductive dual pairs $(\\mathfrak{g},G)$, where $\\mathfrak{g}=\\mathfrak{sp}_{2n}, \\mathfrak{so}_{2n}$ and $G=O_\\ell, Sp_{2\\ell}$.", "field": "math", "label": 0}
{"text": "Title: A new combinatorial approach for edge universality of Wigner matrices\nAbstract: In this paper we introduce a new combinatorial approach to analyze the trace of large powers of Wigner matrices. Our approach is motivated from the paper by \\citet{sosh}. However the counting approach is different. We start with classical word sentence approach similar to \\citet{AZ05} and take the motivation from \\citet{sinaisosh}, \\citet{sosh} and \\citet{peche2009universality} to encode the words to objects similar to Dyck paths. To be precise the map takes a word to a Dyck path with some edges removed from it. Using this new counting we prove edge universality for large Wigner matrices with sub-Gaussian entries. One novelty of this approach is unlike \\citet{sinaisosh}, \\citet{sosh} and \\citet{peche2009universality} we do not need to assume the entries of the matrices are symmetrically distributed around $0$. The main technical contribution of this paper is two folded. Firstly we produce an encoding of the ``contributing words\" (for definition one might look at Section \\ref{sec:word}) of the Wigner matrix which retrieves the edge universality. Hence this is the best one can do. We hope this method will be applicable to many other scenarios in random matrices. Secondly in course of the paper we give a combinatorial description of the GOE Tracy Widom law. The explanation for GUE is very similar. This explanation might be important for the models where exact calculations are not available but some combinatorial structures are present.", "field": "math", "label": 1}
{"text": "Title: Lower bounds for bulk deviations for the simple random walk on $\\mathbb{Z}^d$, $d\\geq 3$\nAbstract: This article investigates the behavior of the continuous-time simple random walk on $\\mathbb{Z}^d$, $d \\geq 3$. We derive an asymptotic lower bound on the principal exponential rate of decay for the probability that the average value over a large box of some non-decreasing local function of the field of occupation times of the walk exceeds a given positive value. This bound matches at leading order the corresponding upper bound derived by Sznitman in arXiv:1906.05809, and is given in terms of a certain constrained minimum of the Dirichlet energy of functions on $\\mathbb{R}^d$ decaying at infinity. Our proof utilizes a version of tilted random walks, a model originally constructed by Li in arXiv:1412.3959 to derive lower bounds on the probability of the event that the trace of a simple random walk disconnects a macroscopic set from an enclosing box.", "field": "math", "label": 0}
{"text": "Title: Linear stability of compact shrinking Ricci solitons\nAbstract: In this paper, we continue to investigate the second variation of Perelman's $\\nu$-entropy for compact shrinking Ricci solitons. In particular, we improve some of our previous work in \"H.-D. Cao and M. Zhu, Math. Ann. 353 (2012), No. 3, 747-763\" and the more recent work in \"M. Mansour and R. Asadollah, arXiv:2104.08343\" and obtain a necessary and sufficient condition for a compact shrinking Ricci soliton to be linearly stable. Our work also extends similar results of Hamilton, Ilmanen and the first author in \"arXiv:math.DG/0404165\" (see also \"H.-D. Cao and C. He, J. Reine Angew. Math. 2015 (2015), no. 709, 229-246.\") for positive Einstein manifolds to the compact shrinking Ricci soliton case.", "field": "math", "label": 0}
{"text": "Title: Holonomic D-modules on abelian varieties\nAbstract: We study the Fourier-Mukai transform for holonomic D-modules on complex abelian varieties. Among other things, we show that the cohomology support loci of a holonomic D-module are finite unions of linear subvarieties, which go through points of finite order for objects of geometric origin; that the standard t-structure on the derived category of holonomic complexes corresponds, under the Fourier-Mukai transform, to a certain perverse coherent t-structure in the sense of Kashiwara and Arinkin-Bezrukavnikov; and that Fourier-Mukai transforms of simple holonomic D-modules are intersection complexes in this t-structure. This supports the conjecture that Fourier-Mukai transforms of holonomic D-modules are \"hyperk\\\"ahler perverse sheaves\".", "field": "math", "label": 1}
{"text": "Title: The Yule-$Λ$ Nested Coalescent: Distribution of the Number of Lineages\nAbstract: We study a model of a population with individuals sampled from different species. The Yule-$\\Lambda$ nested coalescent describes the genealogy of the sample when each species merges with another randomly chosen species with a constant rate $c$ and the mergers of individuals in each species follow the $\\Lambda$-coalescent. For the Yule-$\\Lambda$ nested coalescent with $c<\\int_0^1x^{-1}\\Lambda(dx)<\\infty$, where $\\Lambda$ is the measure that characterizes the $\\Lambda$-coalescent, we show that under some initial conditions, the distribution of the number of individual lineages belonging to one species converges weakly to the distribution $\\nu_c^*$, which is the solution to some recursive distributional equation (RDE) with finite mean. In addition, we show that for some values of $c$, the RDE has another solution with infinite mean.", "field": "math", "label": 0}
{"text": "Title: Singular degree of a rational matrix pseudodifferential operator\nAbstract: In our previous work we studied minimal fractional decompositions of a rational matrix pseudodifferential operator: H=A/B, where A and B are matrix differential operators, and B is non-degenerate of minimal possible degree deg(B). In the present paper we introduce the singular degree sdeg(H)=deg(B), and show that for an arbitrary rational expression H=sum_a (A^a_1)/(B^a_1)...(A^a_n)/(B^a_n), we have that sdeg(H) is less than or equal to sum_{a,i} deg(B^a_i). If the equality holds, we call such an expression minimal. We study the properties of the singular degree and of minimal rational expressions. These results are important for the computations involved in the Lenard-Magri scheme of integrability.", "field": "math", "label": 1}
{"text": "Title: Demystifying $μ$\nAbstract: We develop the theory of illfounded and cyclic proof systems in the context of the modal $\\mu$-calculus. A fine analysis of provability and admissibility bridges the finitary, cyclic and illfounded notions of proof for this logic and re-enforces the subtlety of two important normal form theorems: guardedness and disjunctiveness.", "field": "math", "label": 0}
{"text": "Title: Splitting of Uniform bundles on generalized Grassmannians and Kumar's conjecture\nAbstract: Let $E$ be a uniform bundle on an arbitrary generalised Grassmannian $X$. We show that if the rank of $E$ is smaller than $e.d.(\\mathrm{VMRT})$, then $E$ is necessarily splitting. For some generalised Grassmannians, we prove that the upper bound $e.d.(\\mathrm{VMRT})$ is optimal. On the other hand, Kumar's conjecture predicts that if the minss rank of $G'/P'$ is bigger that the maxss rank of $G/P$, then any morphism $f:G'/P'\\rightarrow G/P$ is constant. We prove some partially affirmative results about this conjecture.", "field": "math", "label": 0}
{"text": "Title: Asymptotic expansion and optimal symmetry of minimal gradient graph equations in dimension 2\nAbstract: In this paper, we study asymptotic expansion at infinity and symmetry of zero mean curvature equations of gradient graph in dimension 2, which include the Monge--Amp\\`ere equation, inverse harmonic Hessian equation and the special Lagrangian equation. This refines the research of asymptotic behavior, gives the precise gap between exterior minimal gradient graph and the entire case, and extends the classification results of Monge--Amp\\`ere equations.", "field": "math", "label": 1}
{"text": "Title: Analysis of the embedded cell method for the numerical homogenization of metal-ceramic composite materials\nAbstract: In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the coincidence of the material properties predicted by the limit with the effective material properties provided by the analytical homogenization theory in three situations, namely for a one dimensional linear elasticity model, a simple one dimensional plasticity model and a two dimensional model of linear hyperelastic isotropic materials with constant shear modulus and slightly varying first Lam\\'e parameter.", "field": "math", "label": 1}
{"text": "Title: On the homology of locally finite graphs\nAbstract: We show that the topological cycle space of a locally finite graph is a canonical quotient of the first singular homology group of its Freudenthal compactification, and we characterize the graphs for which the two coincide. We construct a new singular-type homology for non-compact spaces with ends, which in dimension~1 captures precisely the topological cycle space of graphs but works in any dimension.", "field": "math", "label": 1}
{"text": "Title: On positivity of the two-parameter bivariate kernel built of q-ultraspherical polynomials and other Lancaster-type expansions of bivariate distributions\nAbstract: Our most important result concerns the positivity of certain kernels built of the so-called $q-$ultraspherical polynomials. Since this result appears at first sight as primarily important for those who are working in orthogonal polynomials, $q-$series theory and the so-called quantum polynomials, it might have a limited number of interested researchers. That is why, we put our result into a broader context. We recall the theory of Hilbert-Schmidt operators, Lancaster expansions and their applications in Mathematical statistics, or bivariate distributions absolutely continuous with respect to the product of their marginal distributions leading to the generation of Markov process with polynomial conditional moments (the main representative of such processes is a famous Wiener process).", "field": "math", "label": 0}
{"text": "Title: Reciprocity obstructions in semigroup orbits in SL(2, Z)\nAbstract: We study orbits of semigroups of $\\text{SL}(2,\\mathbb{Z})$, and demonstrate reciprocity obstructions: we show that certain such orbits avoid squares, but not as a consequence of such obstructions on the Zariski closure, and not as a consequence of congruence obstructions. This is in analogy to the reciprocity obstructions recently used to disprove the Apollonian local-global conjecture. We give an example of such an orbit which is known exactly, and misses all squares together with an explicit finite list of sporadic values: the corresponding semigroup is not thin, but its Zariski closure does not miss squares. We also demonstrate thin semigroups with reciprocity obstructions, including semigroups associated to continued fractions formed from finite alphabets. Zaremba's conjecture states that for continued fractions with coefficients chosen from $\\{1,\\ldots,5\\}$, every positive integer appears as a denominator. Bourgain and Kontorovich proposed a generalization of Zaremba's conjecture in the context of semigroups associated to finite alphabets. We disprove their conjecture. In particular, we demonstrate classes of finite continued fraction expansions which never represent rationals with square denominator, but not as a consequence of congruence obstructions, and for which the limit set has Hausdorff dimension exceeding $1/2$. An example of such a class is continued fractions of the form $[0; a_1, a_2, \\ldots, a_n,1,1,2]$, where the $a_i$ are chosen from the set $\\{4,8,12,\\ldots,128\\}$. The object at the heart of these results is a semigroup $\\Psi\\subseteq\\Gamma_1(4)$ which preserves Kronecker symbols.", "field": "math", "label": 0}
{"text": "Title: A binomial random multigraph\nAbstract: Fix a positive integer $n$, a real number $p\\in (0,1]$, and a (perhaps random) hypergraph $\\mathcal{H}$ on $[n]$. We introduce and investigate the following random multigraph model, which we denote $\\mathbb{G}(n,p\\, ; \\,\\mathcal{H})$: begin with an empty graph on $n$ vertices, which are labelled by the set $[n]$. For every $H\\in \\mathcal{H}$ choose, independently from previous choices, a doubleton from $H$, say $D = \\{i,j\\} \\subset H$, uniformly at random and then introduce an edge between the vertices $i$ and $j$ in the graph with probability $p$, where each edge is introduced independently of all other edges.", "field": "math", "label": 0}
{"text": "Title: Survey of 3D Human Body Pose and Shape Estimation Methods for Contemporary Dance Applications\nAbstract: 3D human body shape and pose estimation from RGB images is a challenging problem with potential applications in augmented/virtual reality, healthcare and fitness technology and virtual retail. Recent solutions have focused on three types of inputs: i) single images, ii) multi-view images and iii) videos. In this study, we surveyed and compared 3D body shape and pose estimation methods for contemporary dance and performing arts, with a special focus on human body pose and dressing, camera viewpoint, illumination conditions and background conditions. We demonstrated that multi-frame methods, such as PHALP, provide better results than single-frame method for pose estimation when dancers are performing contemporary dances.", "field": "cs", "label": 0}
{"text": "Title: Einstein Lorentzian solvable unimodular Lie groups\nAbstract: The goal of this paper is to show that many key results found in the study of Einstein Lorentzian nilpotent Lie algebras can still hold in the more general settings of unimodular Lie algebras and (completely) solvable Lie algebras.", "field": "math", "label": 1}
{"text": "Title: An Adjusted Nearest Neighbor Algorithm Maximizing the F-Measure from Imbalanced Data\nAbstract: In this paper, we address the challenging problem of learning from imbalanced data using a Nearest-Neighbor (NN) algorithm. In this setting, the minority examples typically belong to the class of interest requiring the optimization of specific criteria, like the F-Measure. Based on simple geometrical ideas, we introduce an algorithm that reweights the distance between a query sample and any positive training example. This leads to a modification of the Voronoi regions and thus of the decision boundaries of the NN algorithm. We provide a theoretical justification about the weighting scheme needed to reduce the False Negative rate while controlling the number of False Positives. We perform an extensive experimental study on many public imbalanced datasets, but also on large scale non public data from the French Ministry of Economy and Finance on a tax fraud detection task, showing that our method is very effective and, interestingly, yields the best performance when combined with state of the art sampling methods.", "field": "cs", "label": 1}
{"text": "Title: Calabi-Yau structures on Drinfeld quotients and Amiot's conjecture\nAbstract: In 2009, Claire Amiot gave a construction of Calabi-Yau structures on Verdier quotients. We sketch how to lift it to the dg setting. We use this construction as an important step in an outline of the proof of her conjecture on the structure of 2-Calabi-Yau triangulated categories with a cluster-tilting object.", "field": "math", "label": 0}
{"text": "Title: Bounds on the number of squares in recurrence sequences\nAbstract: We investigate the number of squares in a very broad family of binary recurrence sequences with $u_{0}=1$. We show that there are at most two distinct squares in such sequences (the best possible result), except under such very special conditions where we prove there are at most three such squares.", "field": "math", "label": 0}
{"text": "Title: The Effects of Generative AI on Computing Students' Help-Seeking Preferences\nAbstract: Help-seeking is a critical way for students to learn new concepts, acquire new skills, and get unstuck when problem-solving in their computing courses. The recent proliferation of generative AI tools, such as ChatGPT, offers students a new source of help that is always available on-demand. However, it is unclear how this new resource compares to existing help-seeking resources along dimensions of perceived quality, latency, and trustworthiness. In this paper, we investigate the help-seeking preferences and experiences of computing students now that generative AI tools are available to them. We collected survey data (n=47) and conducted interviews (n=8) with computing students. Our results suggest that although these models are being rapidly adopted, they have not yet fully eclipsed traditional help resources. The help-seeking resources that students rely on continue to vary depending on the task and other factors. Finally, we observed preliminary evidence about how help-seeking with generative AI is a skill that needs to be developed, with disproportionate benefits for those who are better able to harness the capabilities of LLMs. We discuss potential implications for integrating generative AI into computing classrooms and the future of help-seeking in the era of generative AI.", "field": "cs", "label": 0}
{"text": "Title: Stable minimal hypersurfaces in $\\mathbf{R}^5$\nAbstract: We show that a complete, two-sided, stable minimal hypersurface in $\\mathbf{R}^5$ is flat.", "field": "math", "label": 0}
{"text": "Title: Disentangle Estimation of Causal Effects from Cross-Silo Data\nAbstract: Estimating causal effects among different events is of great importance to critical fields such as drug development. Nevertheless, the data features associated with events may be distributed across various silos and remain private within respective parties, impeding direct information exchange between them. This, in turn, can result in biased estimations of local causal effects, which rely on the characteristics of only a subset of the covariates. To tackle this challenge, we introduce an innovative disentangle architecture designed to facilitate the seamless cross-silo transmission of model parameters, enriched with causal mechanisms, through a combination of shared and private branches. Besides, we introduce global constraints into the equation to effectively mitigate bias within the various missing domains, thereby elevating the accuracy of our causal effect estimation. Extensive experiments conducted on new semi-synthetic datasets show that our method outperforms state-of-the-art baselines.", "field": "cs", "label": 0}
{"text": "Title: Hypergraph reconstruction from noisy pairwise observations\nAbstract: The network reconstruction task aims to estimate a complex system's structure from various data sources such as time series, snapshots, or interaction counts. Recent work has examined this problem in networks whose relationships involve precisely two entities-the pairwise case. Here we investigate the general problem of reconstructing a network in which higher-order interactions are also present. We study a minimal example of this problem, focusing on the case of hypergraphs with interactions between pairs and triplets of vertices, measured imperfectly and indirectly. We derive a Metropolis-Hastings-within-Gibbs algorithm for this model and use the algorithms to highlight the unique challenges that come with estimating higher-order models. We show that this approach tends to reconstruct empirical and synthetic networks more accurately than an equivalent graph model without higher-order interactions.", "field": "cs", "label": 1}
{"text": "Title: Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain\nAbstract: We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms.", "field": "math", "label": 1}
{"text": "Title: Splines and Wavelets on Circulant Graphs\nAbstract: We present novel families of wavelets and associated filterbanks for the analysis and representation of functions defined on circulant graphs. In this work, we leverage the inherent vanishing moment property of the circulant graph Laplacian operator, and by extension, the e-graph Laplacian, which is established as a parameterization of the former with respect to the degree per node, for the design of vertex-localized and critically-sampled higher-order graph (e-)spline wavelet filterbanks, which can reproduce and annihilate classes of (exponential) polynomial signals on circulant graphs. In addition, we discuss similarities and analogies of the detected properties and resulting constructions with splines and spline wavelets in the Euclidean domain. Ultimately, we consider generalizations to arbitrary graphs in the form of graph approximations, with focus on graph product decompositions. In particular, we proceed to show how the use of graph products facilitates a multi-dimensional extension of the proposed constructions and properties.", "field": "cs", "label": 1}
{"text": "Title: Construction of Jacobi forms using adjoint of Jacobi-Serre derivative\nAbstract: In the article, we study the Oberdieck derivative defined on the space of weak Jacobi forms. We prove that the Oberdieck derivative maps a Jacobi form to a Jacobi form. Moreover, we study the adjoint of Oberdieck derivative of a Jacobi cusp form with respect to Petersson scalar product defined on the space of Jacobi forms. As a consequence, we also obtain the adjoint of Jacobi-Serre derivative (defined in an unpublished work of Oberdieck). As an application, we obtain certain relations among the Fourier coefficients of Jacobi forms.", "field": "math", "label": 0}
{"text": "Title: Submodular Mutual Information for Targeted Data Subset Selection\nAbstract: With the rapid growth of data, it is becoming increasingly difficult to train or improve deep learning models with the right subset of data. We show that this problem can be effectively solved at an additional labeling cost by targeted data subset selection(TSS) where a subset of unlabeled data points similar to an auxiliary set are added to the training data. We do so by using a rich class of Submodular Mutual Information (SMI) functions and demonstrate its effectiveness for image classification on CIFAR-10 and MNIST datasets. Lastly, we compare the performance of SMI functions for TSS with other state-of-the-art methods for closely related problems like active learning. Using SMI functions, we observe ~20-30% gain over the model's performance before re-training with added targeted subset; ~12% more than other methods.", "field": "cs", "label": 1}
{"text": "Title: Decentralized Multi-Task Online Convex Optimization Under Random Link Failures\nAbstract: Decentralized optimization methods often entail information exchange between neighbors. Transmission failures can happen due to network congestion, hardware/software issues, communication outage, and other factors. In this paper, we investigate the random link failure problem in decentralized multi-task online convex optimization, where agents have individual decisions that are coupled with each other via pairwise constraints. Although widely used in constrained optimization, conventional saddle-point algorithms are not directly applicable here because of random packet dropping. To address this issue, we develop a robust decentralized saddle-point algorithm against random link failures with heterogeneous probabilities by replacing the missing decisions of neighbors with their latest received values. Then, by judiciously bounding the accumulated deviation stemming from this replacement, we first establish that our algorithm achieves $\\mathcal{O}(\\sqrt{T})$ regret and $\\mathcal{O}(T^\\frac{3}{4})$ constraint violations for the full information scenario, where the complete information on the local cost function is revealed to each agent at the end of each time slot. These two bounds match, in order sense, the performance bounds of algorithms with perfect communications. Further, we extend our algorithm and analysis to the two-point bandit feedback scenario, where only the values of the local cost function at two random points are disclosed to each agent sequentially. Performance bounds of the same orders as the full information case are derived. Finally, we corroborate the efficacy of the proposed algorithms and the analytical results through numerical simulations.", "field": "cs", "label": 0}
{"text": "Title: Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation\nAbstract: We present a unifying framework encompassing many social choice settings. Viewing each social choice setting as voting in a suitable metric space, we consider a general model of social choice over metric spaces, in which---similarly to the spatial model of elections---each voter specifies an ideal element of the metric space. The ideal element functions as a vote, where each voter prefers elements that are closer to her ideal element. But it also functions as a proposal, thus making all participants equal not only as voters but also as proposers. We consider Condorcet aggregation and a continuum of solution concepts, ranging from minimizing the sum of distances to minimizing the maximum distance. We study applications of the abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters, and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making.", "field": "cs", "label": 1}
{"text": "Title: Aerial Manipulator Force Control Using Control Barrier Functions\nAbstract: This article studies the problem of applying normal forces on a surface, using an underactuated aerial vehicle equipped with a dexterous robotic arm. A force-motion high-level controller is designed based on a Lyapunov function encompassing alignment and exerted force errors. This controller is coupled with a Control Barrier Function constraint under an optimization scheme using Quadratic Programming. This aims to enforce a prescribed relationship between the approaching motion for the end-effector and its alignment with the surface, thus ensuring safe operation. An adaptive low-level controller is devised for the aerial vehicle, capable of tracking velocity commands generated by the high-level controller. Simulations and experiments are presented to demonstrate the force exertion stability and safety of the controller in cases of large disturbances.", "field": "cs", "label": 0}
{"text": "Title: Inequity aversion improves cooperation in intertemporal social dilemmas\nAbstract: Groups of humans are often able to find ways to cooperate with one another in complex, temporally extended social dilemmas. Models based on behavioral economics are only able to explain this phenomenon for unrealistic stateless matrix games. Recently, multi-agent reinforcement learning has been applied to generalize social dilemma problems to temporally and spatially extended Markov games. However, this has not yet generated an agent that learns to cooperate in social dilemmas as humans do. A key insight is that many, but not all, human individuals have inequity averse social preferences. This promotes a particular resolution of the matrix game social dilemma wherein inequity-averse individuals are personally pro-social and punish defectors. Here we extend this idea to Markov games and show that it promotes cooperation in several types of sequential social dilemma, via a profitable interaction with policy learnability. In particular, we find that inequity aversion improves temporal credit assignment for the important class of intertemporal social dilemmas. These results help explain how large-scale cooperation may emerge and persist.", "field": "cs", "label": 1}
{"text": "Title: Investigation of the Sense of Agency in Social Cognition, based on frameworks of Predictive Coding and Active Inference: A simulation study on multimodal imitative interaction\nAbstract: When agents interact socially with different intentions, conflicts are difficult to avoid. Although how agents can resolve such problems autonomously has not been determined, dynamic characteristics of agency may shed light on underlying mechanisms. The current study focused on the sense of agency (SoA), a specific aspect of agency referring to congruence between the agent's intention in acting and the outcome. Employing predictive coding and active inference as theoretical frameworks of perception and action generation, we hypothesize that regulation of complexity in the evidence lower bound of an agent's model should affect the strength of the agent's SoA and should have a critical impact on social interactions. We built a computational model of imitative interaction between a robot and a human via visuo-proprioceptive sensation with a variational Bayes recurrent neural network, and simulated the model in the form of pseudo-imitative interaction using recorded human body movement data. A key feature of the model is that each modality's complexity can be regulated differently with a hyperparameter assigned to each module. We first searched for an optimal setting that endows the model with appropriate coordination of multimodal sensation. This revealed that the vision module's complexity should be more tightly regulated than that of the proprioception module. Using the optimally trained model, we examined how changing the tightness of complexity regulation after training affects the strength of the SoA during interactions. The results showed that with looser regulation, an agent tends to act more egocentrically, without adapting to the other. In contrast, with tighter regulation, the agent tends to follow the other by adjusting its intention. We conclude that the tightness of complexity regulation crucially affects the strength of the SoA and the dynamics of interactions between agents.", "field": "cs", "label": 1}
{"text": "Title: Collective Choice Theory in Collaborative Computing\nAbstract: This paper presents some fundamental collective choice theory for information system designers, particularly those working in the field of computer-supported cooperative work. This paper is focused on a presentation of Arrow's Possibility and Impossibility theorems which form the fundamental boundary on the efficacy of collective choice: voting and selection procedures. It restates the conditions that Arrow placed on collective choice functions in more rigorous second-order logic, which could be used as a set of test conditions for implementations, and a useful probabilistic result for analyzing votes on issue pairs. It also describes some simple collective choice functions. There is also some discussion of how enterprises should approach putting their resources under collective control: giving an outline of a superstructure of performative agents to carry out this function and what distributing processing technology would be needed.", "field": "cs", "label": 1}
{"text": "Title: DeepOnet Based Preconditioning Strategies For Solving Parametric Linear Systems of Equations\nAbstract: We introduce a new class of hybrid preconditioners for solving parametric linear systems of equations. The proposed preconditioners are constructed by hybridizing the deep operator network, namely DeepONet, with standard iterative methods. Exploiting the spectral bias, DeepONet-based components are harnessed to address low-frequency error components, while conventional iterative methods are employed to mitigate high-frequency error components. Our preconditioning framework comprises two distinct hybridization approaches: direct preconditioning (DP) and trunk basis (TB) approaches. In the DP approach, DeepONet is used to approximate an action of an inverse operator to a vector during each preconditioning step. In contrast, the TB approach extracts basis functions from the trained DeepONet to construct a map to a smaller subspace, in which the low-frequency component of the error can be effectively eliminated. Our numerical results demonstrate that utilizing the TB approach enhances the convergence of Krylov methods by a large margin compared to standard non-hybrid preconditioning strategies. Moreover, the proposed hybrid preconditioners exhibit robustness across a wide range of model parameters and problem resolutions.", "field": "math", "label": 0}
{"text": "Title: Optimal cross-learning for contextual bandits with unknown context distributions\nAbstract: We consider the problem of designing contextual bandit algorithms in the ``cross-learning'' setting of Balseiro et al., where the learner observes the loss for the action they play in all possible contexts, not just the context of the current round. We specifically consider the setting where losses are chosen adversarially and contexts are sampled i.i.d. from an unknown distribution. In this setting, we resolve an open problem of Balseiro et al. by providing an efficient algorithm with a nearly tight (up to logarithmic factors) regret bound of $\\widetilde{O}(\\sqrt{TK})$, independent of the number of contexts. As a consequence, we obtain the first nearly tight regret bounds for the problems of learning to bid in first-price auctions (under unknown value distributions) and sleeping bandits with a stochastic action set. At the core of our algorithm is a novel technique for coordinating the execution of a learning algorithm over multiple epochs in such a way to remove correlations between estimation of the unknown distribution and the actions played by the algorithm. This technique may be of independent interest for other learning problems involving estimation of an unknown context distribution.", "field": "cs", "label": 0}
{"text": "Title: Evaluating Language-Model Agents on Realistic Autonomous Tasks\nAbstract: In this report, we explore the ability of language model agents to acquire resources, create copies of themselves, and adapt to novel challenges they encounter in the wild. We refer to this cluster of capabilities as \"autonomous replication and adaptation\" or ARA. We believe that systems capable of ARA could have wide-reaching and hard-to-anticipate consequences, and that measuring and forecasting ARA may be useful for informing measures around security, monitoring, and alignment. Additionally, once a system is capable of ARA, placing bounds on a system's capabilities may become significantly more difficult. We construct four simple example agents that combine language models with tools that allow them to take actions in the world. We then evaluate these agents on 12 tasks relevant to ARA. We find that these language model agents can only complete the easiest tasks from this list, although they make some progress on the more challenging tasks. Unfortunately, these evaluations are not adequate to rule out the possibility that near-future agents will be capable of ARA. In particular, we do not think that these evaluations provide good assurance that the ``next generation'' of language models (e.g. 100x effective compute scaleup on existing models) will not yield agents capable of ARA, unless intermediate evaluations are performed during pretraining. Relatedly, we expect that fine-tuning of the existing models could produce substantially more competent agents, even if the fine-tuning is not directly targeted at ARA.", "field": "cs", "label": 0}
{"text": "Title: New Perspective on Progressive GANs Distillation for One-class Novelty Detection\nAbstract: One-class novelty detection is conducted to identify anomalous instances, with different distributions from the expected normal instances. In this paper, the Generative Adversarial Network based on the Encoder-Decoder-Encoder scheme (EDE-GAN) achieves state-of-the-art performance. The two factors bellow serve the above purpose: 1) The EDE-GAN calculates the distance between two latent vectors as the anomaly score, which is unlike the previous methods by utilizing the reconstruction error between images. 2) The model obtains best results when the batch size is set to 1. To illustrate their superiority, we design a new GAN architecture, and compare performances according to different batch sizes. Moreover, with experimentation leads to discovery, our result implies there is also evidence of just how beneficial constraint on the latent space are when engaging in model training. In an attempt to learn compact and fast models, we present a new technology, Progressive Knowledge Distillation with GANs (P-KDGAN), which connects two standard GANs through the designed distillation loss. Two-step progressive learning continuously augments the performance of student GANs with improved results over single-step approach. Our experimental results on CIFAR-10, MNIST, and FMNIST datasets illustrate that P-KDGAN improves the performance of the student GAN by 2.44%, 1.77%, and 1.73% when compressing the computationat ratios of 24.45:1, 311.11:1, and 700:1, respectively.", "field": "cs", "label": 1}
{"text": "Title: Factorial Moments of the Geometric Distribution of Order $k$\nAbstract: We derive a simple expression for the $r^{th}$ factorial moment $\\mu_{(r)}$ of the geometric distribution of order $k$ with success parameter $p\\in(0,1)$ (and $q=1-p$) in terms of its probability mass function $f_k(n)$. Specifically, $\\mu_{(r)} = r!f_k((r+1)k+r)/((qp^k)^{r+1})$.", "field": "math", "label": 0}
{"text": "Title: Quantum Sets of Compact Quantum Groups\nAbstract: Q-system completion can be thought of as a notion of higher idempotent completion of C*-2-categories. We introduce a notion of quantum bi-elements, and study Q-system completion in the context of compact quantum groups. We relate our notion of quantum bi-elements to already known notions of quantum sets and quantum functions, and provide a description of Q-system completion of the C*-2-category of compact quantum groups using quantum bi-elements", "field": "math", "label": 0}
{"text": "Title: Representing General Stochastic Processes as Martingale Laws\nAbstract: Random variables $X^i$, $i=1,2$ are 'probabilistically equivalent' if they have the same law. Moreover, in any class of equivalent random variables it is easy to select canonical representatives. The corresponding questions are more involved for processes $X^i$ on filtered stochastic bases $(\\Omega^i, \\mathcal F^i, \\mathbb P^i, (\\mathcal F^i_t)_{t\\in [0,1]})$. Here equivalence in law does not capture relevant properties of processes such as the solutions to stochastic control or multistage decision problems. This motivates Aldous to introduce the stronger notion of synonymity based on prediction processes. Stronger still, Hoover--Keisler formalize what it means that $X^i$, $i=1,2$ have the same probabilistic properties. We establish that canonical representatives of the Hoover--Keisler equivalence classes are given precisely by the set of all Markov-martingale laws on a specific nested path space $\\mathsf M_\\infty$. As a consequence we obtain that, modulo Hoover--Keisler equivalence, the class of stochastic processes forms a Polish space. On this space, processes are topologically close iff they model similar probabilistic phenomena. In particular this means that their laws as well as the information encoded in the respective filtrations are similar. Importantly, compact sets of processes admit a Prohorov-type characterization. We also obtain that for every stochastic process, defined on some abstract basis, there exists a process with identical probabilistic properties which is defined on a standard Borel space.", "field": "math", "label": 0}
{"text": "Title: The number of points from a random lattice that lie inside a ball\nAbstract: We prove a sharp bound for the remainder term of the number of lattice points inside a ball, when averaging over a compact set of (not necessarily unimodular) lattices, in dimensions two and three. We also prove that such a bound cannot hold if one averages over the space of all lattices.", "field": "math", "label": 1}
{"text": "Title: Generalizing Tanisaki's ideal via ideals of truncated symmetric functions\nAbstract: We define a family of ideals $I_h$ in the polynomial ring $\\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define $I_h$, we use polynomials in a proper subset of the variables ${x_1,...,x_n}$ that are symmetric under the corresponding permutation subgroup. We call these polynomials {\\em truncated symmetric functions} and show combinatorial identities relating different kinds of truncated symmetric polynomials. We then prove several key properties of $I_h$, including that if $h>h'$ in the natural partial order on Dyck paths then $I_{h} \\subset I_{h'}$, and explicitly construct a Gr\\\"{o}bner basis for $I_h$. We use a second family of ideals $J_h$ for which some of the claims are easier to see, and prove that $I_h = J_h$. The ideals $J_h$ arise in work of Ding, Develin-Martin-Reiner, and Gasharov-Reiner on a family of Schubert varieties called partition varieties. Using earlier work of the first author, the current manuscript proves that the ideals $I_h = J_h$ generalize the Tanisaki ideals both algebraically and geometrically, from Springer varieties to a family of nilpotent Hessenberg varieties.", "field": "math", "label": 1}
{"text": "Title: Semi-Infinite Cycles in Floer Theory: Viterbo's Theorem\nAbstract: This is the first of a series of papers on foundations of Floer theory. We give an axiomatic treatment of the geometric notion of a semi-infinite cycle. Using this notion, we introduce a bordism version of Floer theory for the cotangent bundle of a compact manifold M. Our construction is geometric and does not require the compactness and gluing results traditionally used to setup Floer theory. Finally, we prove a bordism version of Viterbo's theorem relating Floer bordism of the cotangent bundle to the ordinary bordism groups of the free loop space of M.", "field": "math", "label": 1}
{"text": "Title: Carleman estimates for third order operators of KdV and non KdV-type and applications\nAbstract: In this paper we study a class of variable coefficient third order partial differential operators on $\\mathbb{R}^{n+1}$, containing, as a subclass, some variable coefficient operators of KdV-type in any space dimension. For such a class, as well as for the adjoint class, we obtain a Carleman estimate and the local solvability at any point of $\\mathbb{R}^{n+1}$. A discussion of possible applications in the context of dispersive equations is provided.", "field": "math", "label": 0}
{"text": "Title: Knowledge Enhanced Conditional Imputation for Healthcare Time-series\nAbstract: This study presents a novel approach to addressing the challenge of missing data in multivariate time series, with a particular focus on the complexities of healthcare data. Our Conditional Self-Attention Imputation (CSAI) model, grounded in a transformer-based framework, introduces a conditional hidden state initialization tailored to the intricacies of medical time series data. This methodology diverges from traditional imputation techniques by specifically targeting the imbalance in missing data distribution, a crucial aspect often overlooked in healthcare datasets. By integrating advanced knowledge embedding and a non-uniform masking strategy, CSAI adeptly adjusts to the distinct patterns of missing data in Electronic Health Records (EHRs).", "field": "cs", "label": 0}
{"text": "Title: Mutual-visibility problems on graphs of diameter two\nAbstract: The mutual-visibility problem in a graph $G$ asks for the cardinality of a largest set of vertices $S\\subseteq V(G)$ so that for any two vertices $x,y\\in S$ there is a shortest $x,y$-path $P$ so that all internal vertices of $P$ are not in $S$. This is also said as $x,y$ are visible with respect to $S$, or $S$-visible for short. Variations of this problem are known, based on the extension of the visibility property of vertices that are in and/or outside $S$. Such variations are called total, outer and dual mutual-visibility problems. This work is focused on studying the corresponding four visibility parameters in graphs of diameter two, throughout showing bounds and/or closed formulae for these parameters. The mutual-visibility problem in the Cartesian product of two complete graphs is equivalent to (an instance of) the celebrated Zarankievicz's problem. Here we study the dual and outer mutual-visibility problem for the Cartesian product of two complete graphs and all the mutual-visibility problems for the direct product of such graphs as well. We also study all the mutual-visibility problems for the line graphs of complete and complete bipartite graphs. As a consequence of this study, we present several relationships between the mentioned problems and some instances of the classical Tur\\'an problem. Moreover, we study the visibility problems for cographs and several non-trivial diameter-two graphs of minimum size.", "field": "math", "label": 0}
{"text": "Title: Local semicircle law with imprimitive variance matrix\nAbstract: We extend the proof of the local semicircle law for generalized Wigner matrices given in [4] to the case when the matrix of variances has an eigenvalue $ -1 $. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices $ \\boldsymbol{\\mathrm{X}}^\\ast \\boldsymbol{\\mathrm{X}} $, where the variances of the entries of $ \\boldsymbol{\\mathrm{X}} $ may vary.", "field": "math", "label": 1}
{"text": "Title: Passivity-Preserving Safety-Critical Control using Control Barrier Functions\nAbstract: In this letter we propose a holistic analysis merging the techniques of passivity-based control (PBC) and control barrier functions (CBF). We constructively find conditions under which passivity of the closed-loop system is preserved under CBF-based safety-critical control. The results provide an energetic interpretation of safety-critical control schemes, and induce novel passive designs which are less conservative than standard methods based on damping injection. The results are specialised to port-Hamiltonian systems and simulations are performed on a cart-pole system.", "field": "cs", "label": 0}
{"text": "Title: Generalized integral type Hilbert operator acting on weighted Bloch space\nAbstract: Let $\\mu$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $$\\mathcal{I}_{\\mu_{\\alpha+1}}(f)(z)=\\int_{0}^{1}\\frac{f(t)}{(1-tz)^{\\alpha+1}}d\\mu(t)\\ \\ \\ (\\alpha>-1).$$ The operator $\\mathcal{I}_{\\mu_{1}}$ has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of $\\mathcal{I}_{\\mu_{\\alpha+1}}$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of $ \\mathcal{I}_{\\mu_{\\alpha+1}}$ acting between Bloch type spaces, logarithmic Bloch spaces among others.", "field": "math", "label": 1}
{"text": "Title: A finite difference scheme for two-dimensional singularly perturbed convection-diffusion problem with discontinuous source term\nAbstract: We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution features interacting boundary and interior layers, the latter due to discontinuities in source term. The problem is posed on the unit square. The second derivative is multiplied by a singular perturbation parameter, $\\epsilon$, while the nature of the first derivative term is such that flow is aligned with a boundary. These two facts mean that solutions tend to exhibit layers of both exponential and characteristic type. We solve the problem using a finite difference method, specially adapted to the discontinuities, and applied on a piecewise-uniform (Shishkin). We prove that that the computed solution converges to the true one at a rate that is independent of the perturbation parameter, and is nearly first-order. We present numerical results that verify that these results are sharp.", "field": "math", "label": 0}
{"text": "Title: On Spectral Approximations With Nonstandard Weight Functions and Their Implementations to Generalized Chaos Expansions\nAbstract: In this manuscript, we analyze the expansions of functions in orthogonal polynomials associated with a general weight function in a multidimensional setting. Such orthogonal polynomials can be obtained by Gram-Schmidt orthogonalization. However, in most cases, they are not eigenfunctions of some singular Sturm-Liouville problem, as is the case for classical polynomials. Therefore, standard results regarding convergence cannot be applied. Furthermore, since in general, the weight functions are not a tensor product of one-dimensional functions, the orthogonal polynomials are not a tensor product of one-dimensional orthogonal polynomials, as well. In this work, we determine the convergence rate using a comparison Lemma. We also present a spectrally convergent, multidimensional, integration method. Numerical examples demonstrate the efficacy of the proposed method. We show that the use of nonstandard weight functions can allow for efficient integration of singular functions. We also apply this method to Generalized Polynomial Chaos Expansions in the case of dependent random variables.", "field": "math", "label": 1}
{"text": "Title: Towards an Automatic System for Extracting Planar Orientations from Software Generated Point Clouds\nAbstract: In geology, a key activity is the characterisation of geological structures (surface formation topology and rock units) using Planar Orientation measurements such as Strike, Dip and Dip Direction. In general these measurements are collected manually using basic equipment; usually a compass/clinometer and a backboard, recorded on a map by hand. Various computing techniques and technologies, such as Lidar, have been utilised in order to automate this process and update the collection paradigm for these types of measurements. Techniques such as Structure from Motion (SfM) reconstruct of scenes and objects by generating a point cloud from input images, with detailed reconstruction possible on the decimetre scale. SfM-type techniques provide advantages in areas of cost and usability in more varied environmental conditions, while sacrificing the extreme levels of data fidelity. Here is presented a methodology of data acquisition and a Machine Learning-based software system: GeoStructure, developed to automate the measurement of orientation measurements. Rather than deriving measurements using a method applied to the input images, such as the Hough Transform, this method takes measurements directly from the reconstructed point cloud surfaces. Point cloud noise is mitigated using a Mahalanobis distance implementation. Significant structure is characterised using a k-nearest neighbour region growing algorithm, and final surface orientations are quantified using the plane, and normal direction cosines.", "field": "cs", "label": 1}
{"text": "Title: The cyclic open-closed map, u-connections and R-matrices\nAbstract: This paper considers the (negative) cyclic open-closed map $\\mathcal{OC}^{-}$, which maps the cyclic homology of the Fukaya category of a symplectic manifold to its $S^1$-equivariant quantum cohomology. We prove (under simplifying technical hypotheses) that this map respects the respective natural connections in the direction of the equivariant parameter. In the monotone setting this allows us to conclude that $\\mathcal{OC}^{-}$ intertwines the decomposition of the Fukaya category by eigenvalues of quantum cup product with the first Chern class, with the Hukuhara-Levelt-Turrittin decomposition of the quantum cohomology. We also explain how our results relate to the Givental-Teleman classification of semisimple cohomological field theories: in particular, how the R-matrix is related to $\\mathcal{OC}^{-}$ in the semisimple case; we also consider the non-semisimple case.", "field": "math", "label": 1}
{"text": "Title: Near-optimal constructions of constant weight codes and constant composition codes asymptotically attaining the Johnson bound: the odd distances\nAbstract: Constant weight codes (CWCs) and constant composition codes (CCCs) are two important classes of codes that have been studied extensively in both combinatorics and coding theory for nearly sixty years. In this paper we show that for {\\it all} fixed odd distances, there exist near-optimal CWCs and CCCs asymptotically achieving the classic Johnson-type upper bounds. Let $A_q(n,w,d)$ denote the maximum size of $q$-ary CWCs of length $n$ with constant weight $w$ and minimum distance $d$. One of our main results shows that for {\\it all} fixed $q,w$ and odd $d$, one has $\\lim_{n\\rightarrow\\infty}\\frac{A_q(n,d,w)}{\\binom{n}{t}}=\\frac{(q-1)^t}{\\binom{w}{t}}$, where $t=\\frac{2w-d+1}{2}$. This implies the existence of near-optimal generalized Steiner systems originally introduced by Etzion, and can be viewed as a counterpart of a celebrated result of R\\\"odl on the existence of near-optimal Steiner systems. Note that prior to our work, very little is known about $A_q(n,w,d)$ for $q\\ge 3$. A similar result is proved for the maximum size of CCCs. We provide different proofs for our two main results, based on two strengthenings of the well-known Frankl-R\\\"odl-Pippenger theorem on the existence of near-optimal matchings in hypergraphs: the first proof follows by Kahn's linear programming variation of the above theorem, and the second follows by the recent independent work of Delcour-Postle, and Glock-Joos-Kim-K\\\"uhn-Lichev on the existence of near-optimal matchings avoiding certain forbidden configurations. We also present several intriguing open questions for future research.", "field": "math", "label": 0}
{"text": "Title: Finite variations on the isoperimetric problem\nAbstract: The isoperimetric problem asks for the maximum area of a region of given perimeter. It is natural to consider other measurements of a region, such as the diameter and width, and ask for the extreme value of one when another is fixed. The solution of these problems is known if the competing regions are general convex disks, however several of these problems are still open if the competing regions are polygons with at most a given number of sides. The present work surveys these problems.", "field": "math", "label": 1}
{"text": "Title: Human activity recognition from mobile inertial sensors using recurrence plots\nAbstract: Inertial sensors are present in most mobile devices nowadays and such devices are used by people during most of their daily activities. In this paper, we present an approach for human activity recognition based on inertial sensors by employing recurrence plots (RP) and visual descriptors. The pipeline of the proposed approach is the following: compute RPs from sensor data, compute visual features from RPs and use them in a machine learning protocol. As RPs generate texture visual patterns, we transform the problem of sensor data classification to a problem of texture classification. Experiments for classifying human activities based on accelerometer data showed that the proposed approach obtains the highest accuracies, outperforming time- and frequency-domain features directly extracted from sensor data. The best results are obtained when using RGB RPs, in which each RGB channel corresponds to the RP of an independent accelerometer axis.", "field": "cs", "label": 1}
{"text": "Title: A conformal integral invariant on Riemannian foliations\nAbstract: Let $M$ be a closed manifold which admits a foliation structure $\\mathcal{F}$ of codimension $q\\geq 2$ and a bundle-like metric $g_0$. Let $[g_0]_B$ be the space of bundle-like metrics which differ from $g_0$ only along the horizontal directions by a multiple of a positive basic function. Assume $Y$ is a transverse conformal vector field and the mean curvature of the leaves of $(M,\\mathcal{F},g_0)$ vanishes. We show that the integral $\\int_MY(R^T_{g^T})d\\mu_g$ is independent of the choice of $g\\in [g_0]_B$, where $g^T$ is the transverse metric induced by $g$ and $R^T$ is the transverse scalar curvature. Moreover if $q\\geq 3$, we have $\\int_MY(R^T_{g^T})d\\mu_g=0$ for any $g\\in [g_0]_B$. However there exist codimension 2 minimal Riemannian foliations $(M,\\mathcal{F},g)$ and transverse conformal vector fields $Y$ such that $\\int_MY(R^T_{g^T})d\\mu_g\\neq 0$. Therefore, it is a nontrivial obstruction for the transverse Yamabe problem on minimal Riemannian foliation of codimension 2.", "field": "math", "label": 1}
{"text": "Title: A Moebius inversion formula to discard tangled hyperbolic surfaces\nAbstract: Recent literature on Weil-Petersson random hyperbolic surfaces has met a consistent obstacle: the necessity to condition the model, prohibiting certain rare geometric patterns (which we call tangles), such as short closed geodesics or embedded surfaces of short boundary length. The main result of this article is a Moebius inversion formula, allowing to integrate the indicator function of the set of tangle-free surfaces in a systematic, tractable way. It is inspired by a key step of Friedman's celebrated proof of Alon's conjecture. We further prove that our tangle-free hypothesis significantly reduces the number of local topological types of short geodesics, replacing the exponential proliferation observed on tangled surfaces by a polynomial growth.", "field": "math", "label": 0}
{"text": "Title: Distillation-based fabric anomaly detection\nAbstract: Unsupervised texture anomaly detection has been a concerning topic in a vast amount of industrial processes. Patterned textures inspection, particularly in the context of fabric defect detection, is indeed a widely encountered use case. This task involves handling a diverse spectrum of colors and textile types, encompassing a wide range of fabrics. Given the extensive variability in colors, textures, and defect types, fabric defect detection poses a complex and challenging problem in the field of patterned textures inspection. In this article, we propose a knowledge distillation-based approach tailored specifically for addressing the challenge of unsupervised anomaly detection in textures resembling fabrics. Our method aims to redefine the recently introduced reverse distillation approach, which advocates for an encoder-decoder design to mitigate classifier bias and to prevent the student from reconstructing anomalies. In this study, we present a new reverse distillation technique for the specific task of fabric defect detection. Our approach involves a meticulous design selection that strategically highlights high-level features. To demonstrate the capabilities of our approach both in terms of performance and inference speed, we conducted a series of experiments on multiple texture datasets, including MVTEC AD, AITEX, and TILDA, alongside conducting experiments on a dataset acquired from a textile manufacturing facility. The main contributions of this paper are the following: a robust texture anomaly detector utilizing a reverse knowledge-distillation technique suitable for both anomaly detection and domain generalization and a novel dataset encompassing a diverse range of fabrics and defects.", "field": "cs", "label": 0}
{"text": "Title: Twice $Q$-polynomial distance-regular graphs of diameter 4\nAbstract: It is known that a distance-regular graph with valency $k$ at least three admits at most two Q-polynomial structures. % In this note we show that all distance-regular graphs with diameter four and valency at least three admitting two $Q$-polynomial structures are either dual bipartite or almost dual imprimitive. By the work of Dickie \\cite{Dickie} this implies that any distance-regular graph with diameter $d$ at least four and valency at least three admitting two $Q$-polynomial structures is, provided it is not a Hadamard graph, either the cube $H(d,2)$ with $d$ even, the half cube ${1}/{2} H(2d+1,2)$, the folded cube $\\tilde{H}(2d+1,2)$, or the dual polar graph on $[^2A_{2d-1}(q)]$ with $q\\ge 2$ a prime power.", "field": "math", "label": 1}
{"text": "Title: Sommets fortement critiques d'un tournoi indécomposable\nAbstract: Let $T=(V,A)$ be a tournament. For $X\\subseteq V$, the subtournament of $T$ induced by $X$ is denoted by $T[X]$. A subset $I$ of $V$ is an interval of $T$ provided that for every $a,b\\in I$ and $x\\in V\\setminus I$, $(a,x)\\in A$ if and only if $(b,x)\\in A$. For example, $\\varnothing $, ${x}$ ($x \\in V$) and $V$ are intervals of $T$, called trivial intervals. The tournament $T$ is indecomposable if all its intervals are trivial, otherwise, it is decomposable. A critical tournament is an indecomposable tournament $T$ of cardinality $\\geqslant 5$ such that every vertex $x$ of $T$ is critical, i.e., the subtournament $T[V(T)\\setminus\\{x\\}]$ is decomposable. Given an indecomposable tournament $T$, a vertex $x$ of $T$ is strongly critical, if for every $X\\subseteq V(T)$ such that $x\\in X$, $\\vert X\\vert \\geqslant 5$ and $T[X]$ is indecomposable, $x$ is a critical vertex of $T[X]$. Let $T$ be an indecomposable tournament and let $\\mathscr{C}(T)$ be the set of the strongly critical vertices of $T$. We prove that, if $T$ is non-critical, then $f(T):=\\vert \\mathscr{C}(T)\\vert \\leqslant 4$, and that the correspondence $f(T)$ is decreasing from the class of indecomposable and non-critical tournaments (defined by means of embedding) to $\\{0,1,2,3,4\\}$. By giving examples, we also verify that the bounds 0 and 4 are optimal. This article is an extract from my master's thesis \\cite{mon mast\\`ere}.", "field": "math", "label": 0}
{"text": "Title: Wide Neural Networks Forget Less Catastrophically\nAbstract: A primary focus area in continual learning research is alleviating the \"catastrophic forgetting\" problem in neural networks by designing new algorithms that are more robust to the distribution shifts. While the recent progress in continual learning literature is encouraging, our understanding of what properties of neural networks contribute to catastrophic forgetting is still limited. To address this, instead of focusing on continual learning algorithms, in this work, we focus on the model itself and study the impact of \"width\" of the neural network architecture on catastrophic forgetting, and show that width has a surprisingly significant effect on forgetting. To explain this effect, we study the learning dynamics of the network from various perspectives such as gradient orthogonality, sparsity, and lazy training regime. We provide potential explanations that are consistent with the empirical results across different architectures and continual learning benchmarks.", "field": "cs", "label": 1}
{"text": "Title: A Soft Recommender System for Social Networks\nAbstract: Recent social recommender systems benefit from friendship graph to make an accurate recommendation, believing that friends in a social network have exactly the same interests and preferences. Some studies have benefited from hard clustering algorithms (such as K-means) to determine the similarity between users and consequently to define degree of friendships. In this paper, we went a step further to identify true friends for making even more realistic recommendations. we calculated the similarity between users, as well as the dependency between a user and an item. Our hypothesis is that due to the uncertainties in user preferences, the fuzzy clustering, instead of the classical hard clustering, is beneficial in accurate recommendations. We incorporated the C-means algorithm to get different membership degrees of soft users' clusters. Then, the users' similarity metric is defined according to the soft clusters. Later, in a training scheme we determined the latent representations of users and items, extracting from the huge and sparse user-item-tag matrix using matrix factorization. In the parameter tuning, we found the optimum coefficients for the influence of our soft social regularization and the user-item dependency terms. Our experimental results convinced that the proposed fuzzy similarity metric improves the recommendations in real data compared to the baseline social recommender system with the hard clustering.", "field": "cs", "label": 1}
{"text": "Title: The Gossiping Insert-Eliminate Algorithm for Multi-Agent Bandits\nAbstract: We consider a decentralized multi-agent Multi Armed Bandit (MAB) setup consisting of $N$ agents, solving the same MAB instance to minimize individual cumulative regret. In our model, agents collaborate by exchanging messages through pairwise gossip style communications on an arbitrary connected graph. We develop two novel algorithms, where each agent only plays from a subset of all the arms. Agents use the communication medium to recommend only arm-IDs (not samples), and thus update the set of arms from which they play. We establish that, if agents communicate $\\Omega(\\log(T))$ times through any connected pairwise gossip mechanism, then every agent's regret is a factor of order $N$ smaller compared to the case of no collaborations. Furthermore, we show that the communication constraints only have a second order effect on the regret of our algorithm. We then analyze this second order term of the regret to derive bounds on the regret-communication tradeoffs. Finally, we empirically evaluate our algorithm and conclude that the insights are fundamental and not artifacts of our bounds. We also show a lower bound which gives that the regret scaling obtained by our algorithm cannot be improved even in the absence of any communication constraints. Our results thus demonstrate that even a minimal level of collaboration among agents greatly reduces regret for all agents.", "field": "cs", "label": 1}
{"text": "Title: Effective randomness, strong reductions and Demuth's theorem\nAbstract: We study generalizations of Demuth's Theorem, which states that the image of a Martin-L\\\"of random real under a tt-reduction is either computable or Turing equivalent to a Martin-L\\\"of random real. We show that Demuth's Theorem holds for Schnorr randomness and computable randomness (answering a question of Franklin), but that it cannot be strengthened by replacing the Turing equivalence in the statement of the theorem with wtt-equivalence. We also provide some additional results about the Turing and tt-degrees of reals that are random with respect to some computable measure.", "field": "math", "label": 1}
{"text": "Title: Almost periodic invariant tori for the NLS on the circle\nAbstract: In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain (2005) on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract \"counter-term theorem\" `a la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find \"many more\" almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs.", "field": "math", "label": 1}
{"text": "Title: From microscopic theory to macroscopic theory: dynamics of the rod-like liquid crystal molecules\nAbstract: Starting from Doi-Onsager equation for the liquid crystal, we first derive the Q-tensor equation by the Bingham closure. Then we derive the Ericksen-Leslie equation from the Q-tensor equation by taking the small Deborah number limit.", "field": "math", "label": 1}
{"text": "Title: Presentations of configuration categories\nAbstract: The configuration category of a manifold is a topological category which we view as a Segal space, via the nerve construction. Our main result is that the unordered configuration category, suitably truncated, admits a finite presentation as a complete Segal space if the manifold in question is the interior of a compact manifold.", "field": "math", "label": 0}
{"text": "Title: Learning Multi-Step Manipulation Tasks from A Single Human Demonstration\nAbstract: Learning from human demonstrations has exhibited remarkable achievements in robot manipulation. However, the challenge remains to develop a robot system that matches human capabilities and data efficiency in learning and generalizability, particularly in complex, unstructured real-world scenarios. We propose a system that processes RGBD videos to translate human actions to robot primitives and identifies task-relevant key poses of objects using Grounded Segment Anything. We then address challenges for robots in replicating human actions, considering the human-robot differences in kinematics and collision geometry. To test the effectiveness of our system, we conducted experiments focusing on manual dishwashing. With a single human demonstration recorded in a mockup kitchen, the system achieved 50-100% success for each step and up to a 40% success rate for the whole task with different objects in a home kitchen. Videos are available at https://robot-dishwashing.github.io", "field": "cs", "label": 0}
{"text": "Title: Revisiting Norm Estimation in Data Streams\nAbstract: The problem of estimating the pth moment F_p (p nonnegative and real) in data streams is as follows. There is a vector x which starts at 0, and many updates of the form x_i <-- x_i + v come sequentially in a stream. The algorithm also receives an error parameter 0 < eps < 1. The goal is then to output an approximation with relative error at most eps to F_p = ||x||_p^p. Previously, it was known that polylogarithmic space (in the vector length n) was achievable if and only if p <= 2. We make several new contributions in this regime, including: (*) An optimal space algorithm for 0 < p < 2, which, unlike previous algorithms which had optimal dependence on 1/eps but sub-optimal dependence on n, does not rely on a generic pseudorandom generator. (*) A near-optimal space algorithm for p = 0 with optimal update and query time. (*) A near-optimal space algorithm for the \"distinct elements\" problem (p = 0 and all updates have v = 1) with optimal update and query time. (*) Improved L_2 --> L_2 dimensionality reduction in a stream. (*) New 1-pass lower bounds to show optimality and near-optimality of our algorithms, as well as of some previous algorithms (the \"AMS sketch\" for p = 2, and the L_1-difference algorithm of Feigenbaum et al.). As corollaries of our work, we also obtain a few separations in the complexity of moment estimation problems: F_0 in 1 pass vs. 2 passes, p = 0 vs. p > 0, and F_0 with strictly positive updates vs. arbitrary updates.", "field": "cs", "label": 1}
{"text": "Title: Provable Computational and Statistical Guarantees for Efficient Learning of Continuous-Action Graphical Games\nAbstract: In this paper, we study the problem of learning the set of pure strategy Nash equilibria and the exact structure of a continuous-action graphical game with quadratic payoffs by observing a small set of perturbed equilibria. A continuous-action graphical game can possibly have an uncountable set of Nash euqilibria. We propose a $\\ell_{12}-$ block regularized method which recovers a graphical game, whose Nash equilibria are the $\\epsilon$-Nash equilibria of the game from which the data was generated (true game). Under a slightly stringent condition on the parameters of the true game, our method recovers the exact structure of the graphical game. Our method has a logarithmic sample complexity with respect to the number of players. It also runs in polynomial time.", "field": "cs", "label": 1}
{"text": "Title: Knutson ideals and determinantal ideals of Hankel matrices\nAbstract: Motivated by a work of Knutson, in a recent paper Conca and Varbaro have defined a new class of ideals, namely \"Knutson ideals\", starting from a polynomial $f$ with squarefree leading term. We will show that the main properties that this class has in polynomial rings over fields of characteristic $p$ are preserved when one introduces the definition of Knutson ideal also in polynomial rings over fields of characteristic zero. Then we will show that determinantal ideals of Hankel matrices are Knutson ideals for a suitable choice of the polynomial $f$.", "field": "math", "label": 1}
{"text": "Title: Modeling Image Structure with Factorized Phase-Coupled Boltzmann Machines\nAbstract: We describe a model for capturing the statistical structure of local amplitude and local spatial phase in natural images. The model is based on a recently developed, factorized third-order Boltzmann machine that was shown to be effective at capturing higher-order structure in images by modeling dependencies among squared filter outputs (Ranzato and Hinton, 2010). Here, we extend this model to $L_p$-spherically symmetric subspaces. In order to model local amplitude and phase structure in images, we focus on the case of two dimensional subspaces, and the $L_2$-norm. When trained on natural images the model learns subspaces resembling quadrature-pair Gabor filters. We then introduce an additional set of hidden units that model the dependencies among subspace phases. These hidden units form a combinatorial mixture of phase coupling distributions, concentrated in the sum and difference of phase pairs. When adapted to natural images, these distributions capture local spatial phase structure in natural images.", "field": "cs", "label": 1}
{"text": "Title: Standing waves with prescribed $L^2$-norm to nonlinear Schrödinger equations with combined inhomogeneous nonlinearities\nAbstract: In this paper, we are concerned with solutions to the following nonlinear Schr\\\"odinger equation with combined inhomogeneous nonlinearities, $$ -\\Delta u + \\lambda u= \\mu |x|^{-b}|u|^{q-2} u + |x|^{-b}|u|^{p-2} u \\quad \\mbox{in} \\,\\, \\R^N, $$ under the $L^2$-norm constraint $$ \\int_{\\R^N} |u|^2 \\, dx=c>0, $$ where $N \\geq 1$, $\\mu =\\pm 1$, $2<q<p<{2(N-b)}/{(N-2)^+}$, $0<b<\\min\\{2, N\\}$ and the parameter $\\lambda \\in \\R$ appearing as Lagrange multiplier is unknown. In the mass subcritical case, we establish the compactness of any minimizing sequence to the minimization problem given by the underlying energy functional restricted on the constraint. As a consequence of the compactness of any minimizing sequence, orbital stability of minimizers is derived. In the mass critical and supercritical cases, we investigate the existence, radial symmetry and orbital instability of solutions. Meanwhile, we consider the existence, radial symmetry and algebraical decay of ground states to the corresponding zero mass equation with defocusing perturbation. In addition, dynamical behaviors of solutions to the Cauchy problem for the associated dispersive equation are discussed.", "field": "math", "label": 0}
{"text": "Title: Comparative Analysis of Engagement, Themes, and Causality of Ukraine-Related Debunks and Disinformation\nAbstract: This paper compares quantitatively the spread of Ukraine-related disinformation and its corresponding debunks, first by considering re-tweets, replies, and favourites, which demonstrate that despite platform efforts Ukraine-related disinformation is still spreading wider than its debunks. Next, bidirectional post-hoc analysis is carried out using Granger causality tests, impulse response analysis and forecast error variance decomposition, which demonstrate that the spread of debunks has a positive impact on reducing Ukraine-related disinformation eventually, albeit not instantly. Lastly, the paper investigates the dominant themes in Ukraine-related disinformation and their spatiotemporal distribution. With respect to debunks, we also establish that around 18% of fact-checks are debunking claims which have already been fact-checked in another language. The latter finding highlights an opportunity for better collaboration between fact-checkers, so they can benefit from and amplify each other's debunks through translation, citation, and early publication online.", "field": "cs", "label": 1}
{"text": "Title: Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics\nAbstract: Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are insufficient to meet the growing requirements for large-scale and long-period simulations. Fortunately, the rapid advancement in neural networks, especially neural operator learning mappings between function spaces, has introduced novel approaches to tackle these challenges via data-driven modeling. In this paper, we propose a Fourier neural operator-based fluid-structure interaction solver (FNO-based FSI solver) for efficient simulation of FSI problems, where the solid solver based on the finite difference method is seamlessly integrated with the Fourier neural operator to predict incompressible flow using the immersed boundary method. We analyze the performance of the FNO-based FSI solver in the following three situations: training data with or without the steady state, training method with one-step label or multi-step labels, and prediction in interpolation or extrapolation. We find that the best performance for interpolation is achieved by training the operator with multi-step labels using steady-state data. Finally, we train the FNO-based FSI solver using this optimal training method and apply it to vesicle dynamics. The results show that the FNO-based FSI solver is capable of capturing the variations in the fluid and the vesicle.", "field": "math", "label": 0}
{"text": "Title: Universal sequences of composition operators\nAbstract: Let $G$ and $\\Omega$ be two planar domains. We give necessary and sufficient conditions on a sequence $(\\phi_n)$ of eventually injective holomorphic mappings from $G$ to $\\Omega$ for the existence of a function $f\\in H(\\Omega)$ whose orbit under the composition by $(\\phi_n)$ is dense in $H(G)$. This extends a result of the same nature obtained by Grosse-Erdmann and Mortini when $G=\\Omega$. An interconnexion between the topological properties of $G$ and $\\Omega$ appears. Further, in order to exhibit in a natural way holomorphic functions with wild boundary behaviour on planar domains, we study a certain type of universality for sequences of continuous mappings from a union of Jordan curves to a domain.", "field": "math", "label": 1}
{"text": "Title: On mild solutions to some dissipative SPDEs on $L^p$ spaces with additive noise\nAbstract: We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations on $L^p$ spaces on bounded domains of $\\mathbb{R}^n$ with a nonlinear drift term given by the superposition operator generated by a monotone function on the real line with power-like growth. The noise is of additive type with respect to a cylindrical Wiener process, with diffusion coefficient not necessarily of $\\gamma$-Radonifying type.", "field": "math", "label": 0}
{"text": "Title: $q$-deformation of Aomoto complex\nAbstract: A degree one element of the Orlik-Solomon algebra of a hyperplane arrangement defines a cochain complex known as the Aomoto complex. The Aomoto complex can be considerd as the ``linear approximation'' of the twisted cochain complex with coefficients in a complex rank one local system. In this paper, we discuss $q$-deformations of the Aomoto complex. The $q$-deformation is defined by replacing the entries of representation matrices of the coboundary maps with their $q$-analogues. While the resulting maps do not generally define cochain complexes, for certain special basis derived from real structures, the $q$-deformation becomes again a cochain complex. Moreover, it exhibits universality in the sense that any specialization of $q$ to a complex number yields the cochain complex computing the corresponding local system cohomology group.", "field": "math", "label": 0}
{"text": "Title: A Pragmatic Look at Deep Imitation Learning\nAbstract: The introduction of the generative adversarial imitation learning (GAIL) algorithm has spurred the development of scalable imitation learning approaches using deep neural networks. Many of the algorithms that followed used a similar procedure, combining on-policy actor-critic algorithms with inverse reinforcement learning. More recently there have been an even larger breadth of approaches, most of which use off-policy algorithms. However, with the breadth of algorithms, everything from datasets to base reinforcement learning algorithms to evaluation settings can vary, making it difficult to fairly compare them. In this work we re-implement 6 different IL algorithms, updating 3 of them to be off-policy, base them on a common off-policy algorithm (SAC), and evaluate them on a widely-used expert trajectory dataset (D4RL) for the most common benchmark (MuJoCo). After giving all algorithms the same hyperparameter optimisation budget, we compare their results for a range of expert trajectories. In summary, GAIL, with all of its improvements, consistently performs well across a range of sample sizes, AdRIL is a simple contender that performs well with one important hyperparameter to tune, and behavioural cloning remains a strong baseline when data is more plentiful.", "field": "cs", "label": 1}
{"text": "Title: Quotient polynomials with positive coefficients\nAbstract: We give an optimal necessary and sufficient condition for the quotient polynomial and remainder in the division algorithm to have positive coefficients.", "field": "math", "label": 1}
{"text": "Title: A Neural Lip-Sync Framework for Synthesizing Photorealistic Virtual News Anchors\nAbstract: Lip sync has emerged as a promising technique for generating mouth movements from audio signals. However, synthesizing a high-resolution and photorealistic virtual news anchor is still challenging. Lack of natural appearance, visual consistency, and processing efficiency are the main problems with existing methods. This paper presents a novel lip-sync framework specially designed for producing high-fidelity virtual news anchors. A pair of Temporal Convolutional Networks are used to learn the cross-modal sequential mapping from audio signals to mouth movements, followed by a neural rendering network that translates the synthetic facial map into a high-resolution and photorealistic appearance. This fully trainable framework provides end-to-end processing that outperforms traditional graphics-based methods in many low-delay applications. Experiments also show the framework has advantages over modern neural-based methods in both visual appearance and efficiency.", "field": "cs", "label": 1}
{"text": "Title: Large deviation principle for slow-fast rough differential equations via controlled rough paths\nAbstract: We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\\in (1/3,1/2)$. Our approach is based on the continuity of the solution mapping and the variational framework for mixed fractional Brownian motion. By utilizing the variational representation, our problem is transformed into a qualitative property of the controlled system. In particular, the fast rough differential equation coincides with It\\^o SDE almost surely, which possesses a unique invariant probability measure with frozen slow component. We then demonstrate the weak convergence of the controlled slow component by averaging with respect to the invariant measure of the fast equation and exploiting the continuity of the solution mapping.", "field": "math", "label": 0}
{"text": "Title: Adversarial Machine Learning-Enabled Anonymization of OpenWiFi Data\nAbstract: Data privacy and protection through anonymization is a critical issue for network operators or data owners before it is forwarded for other possible use of data. With the adoption of Artificial Intelligence (AI), data anonymization augments the likelihood of covering up necessary sensitive information; preventing data leakage and information loss. OpenWiFi networks are vulnerable to any adversary who is trying to gain access or knowledge on traffic regardless of the knowledge possessed by data owners. The odds for discovery of actual traffic information is addressed by applied conditional tabular generative adversarial network (CTGAN). CTGAN yields synthetic data; which disguises as actual data but fostering hidden acute information of actual data. In this paper, the similarity assessment of synthetic with actual data is showcased in terms of clustering algorithms followed by a comparison of performance for unsupervised cluster validation metrics. A well-known algorithm, K-means outperforms other algorithms in terms of similarity assessment of synthetic data over real data while achieving nearest scores 0.634, 23714.57, and 0.598 as Silhouette, Calinski and Harabasz and Davies Bouldin metric respectively. On exploiting a comparative analysis in validation scores among several algorithms, K-means forms the epitome of unsupervised clustering algorithms ensuring explicit usage of synthetic data at the same time a replacement for real data. Hence, the experimental results aim to show the viability of using CTGAN-generated synthetic data in lieu of publishing anonymized data to be utilized in various applications.", "field": "cs", "label": 0}
{"text": "Title: A scalable computational platform for particulate Stokes suspensions\nAbstract: We describe a computational framework for simulating suspensions of rigid particles in Newtonian Stokes flow. One central building block is a collision-resolution algorithm that overcomes the numerical constraints arising from particle collisions. This algorithm extends the well-known complementarity method for non-smooth multi-body dynamics to resolve collisions in dense rigid body suspensions. This approach formulates the collision resolution problem as a linear complementarity problem with geometric `non-overlapping' constraints imposed at each timestep. It is then reformulated as a constrained quadratic programming problem and the Barzilai-Borwein projected gradient descent method is applied for its solution. This framework is designed to be applicable for any convex particle shape, e.g., spheres and spherocylinders, and applicable to any Stokes mobility solver, including the Rotne-Prager-Yamakawa approximation, Stokesian Dynamics, and PDE solvers (e.g., boundary integral and immersed boundary methods). In particular, this method imposes Newton's Third Law and records the entire contact network. Further, we describe a fast, parallel, and spectrally-accurate boundary integral method tailored for spherical particles, capable of resolving lubrication effects. We show weak and strong parallel scalings up to $8\\times 10^4$ particles with approximately $4\\times 10^7$ degrees of freedom on $1792$ cores. We demonstrate the versatility of this framework with several examples, including sedimentation of particle clusters, and active matter systems composed of ensembles of particles driven to rotate.", "field": "cs", "label": 1}
{"text": "Title: Kodaira-Saito vanishing for the irregular Hodge filtration\nAbstract: After making correct, and then improving, our definition of the category of irregular mixed Hodge modules thanks to Mochizuki's recent results arXiv:2108.03843, we show how these results allow us to obtain Kodaira-Saito-type vanishing theorems for the irregular Hodge filtration of irregular mixed Hodge modules.", "field": "math", "label": 0}
{"text": "Title: Kernel Theorems in Coorbit Theory\nAbstract: We prove general kernel theorems for operators acting between coorbit spaces. These are Banach spaces associated to an integrable representation of a locally compact group and contain most of the usual function spaces (Besov spaces, modulation spaces, etc.). A kernel theorem describes the form of every bounded operator between a coorbit space of test functions and distributions by means of a kernel in a coorbit space associated to the tensor product representation. As special cases we recover Feichtinger's kernel theorem for modulation spaces and the recent generalizations by Cordero and Nicola. We also obtain a kernel theorem for operators between the Besov spaces $\\dot{B}^0_{1,1}$ and $\\dot{B}^{0}_{\\infty, \\infty }$.", "field": "math", "label": 1}
{"text": "Title: Some asymptotic formulae involving Cohen-Ramanujan expansions\nAbstract: Some necessary and sufficient conditions for the existence of Cohen-Ramanujan expansions for arithmetical functions were provided by these authors in [\\textit{arXive preprint arXive:2205.08466}, 2022]. Given two arithmetical functions $f$ and $g$ with absolutely convergent Cohen-Ramanujan expansions, we derive an asymptotic formula for $\\sum_{n\\leq N}f(n)g(n+h)$ where $h$ is a fixed positive integer. We also provide Cohen-Ramanujan expansions for certain functions to illustrate some of the results we prove consequently.", "field": "math", "label": 0}
{"text": "Title: Long time behavior for collisional strongly magnetized plasma in three space dimensions\nAbstract: We consider the long time evolution of a population of charged particles, under strong magnetic fields and collision mechanisms. We derive a fluid model and justify the asymptotic behavior toward smooth solutions of this regime. In three space dimensions, a constraint ocurs along the parallel direction. For eliminating the corresponding Lagrange multiplier, we average along the magnetic lines.", "field": "math", "label": 0}
{"text": "Title: On the Composability of Statistically Secure Random Oblivious Transfer\nAbstract: We show that stand-alone statistically secure random oblivious transfer protocols based on two-party stateless primitives are statistically universally composable. I.e. they are simulatable secure with an unlimited adversary, an unlimited simulator and an unlimited environment machine. Our result implies that several previous oblivious transfer protocols in the literature which were proven secure under weaker, non-composable definitions of security can actually be used in arbitrary statistically secure applications without lowering the security.", "field": "cs", "label": 1}
{"text": "Title: Igusa zeta functions and the non-archimedean SYZ fibration\nAbstract: We explain the proof, obtained in collaboration with Chenyang Xu, of a 1999 conjecture of Veys about poles of maximal order of Igusa zeta functions. The proof technique is based on the Minimal Model Program in birational geometry, but the proof was heavily inspired by ideas coming from non-archimedean geometry and mirror symmetry; we will outline these relations at the end of the paper. This text is intended to be a low-tech introduction to these topics; we only assume that the reader has a basic knowledge of algebraic geometry.", "field": "math", "label": 1}
{"text": "Title: WFTNet: Exploiting Global and Local Periodicity in Long-term Time Series Forecasting\nAbstract: Recent CNN and Transformer-based models tried to utilize frequency and periodicity information for long-term time series forecasting. However, most existing work is based on Fourier transform, which cannot capture fine-grained and local frequency structure. In this paper, we propose a Wavelet-Fourier Transform Network (WFTNet) for long-term time series forecasting. WFTNet utilizes both Fourier and wavelet transforms to extract comprehensive temporal-frequency information from the signal, where Fourier transform captures the global periodic patterns and wavelet transform captures the local ones. Furthermore, we introduce a Periodicity-Weighted Coefficient (PWC) to adaptively balance the importance of global and local frequency patterns. Extensive experiments on various time series datasets show that WFTNet consistently outperforms other state-of-the-art baseline. Code is available at https://github.com/Hank0626/WFTNet.", "field": "cs", "label": 0}
{"text": "Title: $L^p$ Maximal regularity for vector-valued Schrödinger operators\nAbstract: In this paper we consider the vector-valued Schr\\\"{o}dinger operator $-\\Delta + V$, where the potential term $V$ is a matrix-valued function whose entries belong to $L^1_{\\rm loc}(\\mathbb{R}^d)$ and, for every $x\\in\\mathbb{R}^d$, $V(x)$ is a symmetric and nonnegative definite matrix, with non positive off-diagonal terms and with eigenvalues comparable each other. For this class of potential terms we obtain maximal inequality in $L^1(\\mathbb{R}^d,\\mathbb{R}^m).$ Assuming further that the minimal eigenvalue of $V$ belongs to some reverse H\\\"older class of order $q\\in(1,\\infty)\\cup\\{\\infty\\}$, we obtain maximal inequality in $L^p(\\mathbb{R}^d,\\mathbb{R}^m)$, for $p$ in between $1$ and some $q$.", "field": "math", "label": 0}
{"text": "Title: Probabilistic representation for mild solution of the Navier-Stokes equations\nAbstract: This paper is based on a formulation of the Navier-Stokes equations developed by Iyer and Constantin \\cite{Cont} , where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. Our contribution is to establish this probabilistic representation formula for mild solutions of the Navier-Stokes equations on $\\mathbb{R}^{d} $.", "field": "math", "label": 1}
{"text": "Title: Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems\nAbstract: Despite the great promise of the physics-informed neural networks (PINNs) in solving forward and inverse problems, several technical challenges are present as roadblocks for more complex and realistic applications. First, most existing PINNs are based on point-wise formulation with fully-connected networks to learn continuous functions, which suffer from poor scalability and hard boundary enforcement. Second, the infinite search space over-complicates the non-convex optimization for network training. Third, although the convolutional neural network (CNN)-based discrete learning can significantly improve training efficiency, CNNs struggle to handle irregular geometries with unstructured meshes. To properly address these challenges, we present a novel discrete PINN framework based on graph convolutional network (GCN) and variational structure of PDE to solve forward and inverse partial differential equations (PDEs) in a unified manner. The use of a piecewise polynomial basis can reduce the dimension of search space and facilitate training and convergence. Without the need of tuning penalty parameters in classic PINNs, the proposed method can strictly impose boundary conditions and assimilate sparse data in both forward and inverse settings. The flexibility of GCNs is leveraged for irregular geometries with unstructured meshes. The effectiveness and merit of the proposed method are demonstrated over a variety of forward and inverse computational mechanics problems governed by both linear and nonlinear PDEs.", "field": "cs", "label": 1}
{"text": "Title: Asymptotic $l_p$ spaces and bounded distortions\nAbstract: The new class of Banach spaces, so-called asymptotic $l_p$ spaces, is introduced and it is shown that every Banach space with bounded distortions contains a subspace from this class. The proof is based on an investigation of certain functions, called enveloping functions, which are intimately connected with stabilization properties of the norm.", "field": "math", "label": 1}
{"text": "Title: On gamma factors for representations of finite general linear groups\nAbstract: We use the Langlands--Shahidi method in order to define the Shahidi gamma factor for a pair of irreducible generic representations of $\\operatorname{GL}_n\\left(\\mathbb{F}_q\\right)$ and $\\operatorname{GL}_m\\left(\\mathbb{F}_q\\right)$. We prove that the Shahidi gamma factor is multiplicative and show that it is related to the Jacquet--Piatetski-Shapiro--Shalika gamma factor. As an application, we prove a converse theorem based on the absolute value of the Shahidi gamma factor, and improve the converse theorem of Nien. As another application, we give explicit formulas for special values of the Bessel function of an irreducible generic representation of $\\operatorname{GL}_n\\left(\\mathbb{F}_q\\right)$.", "field": "math", "label": 0}
{"text": "Title: Locally anti de Sitter spaces and deformation quantization\nAbstract: In the first part we define a \"BTZ\" black hole in anti de Sitter space in any dimension by defining as \"singular\" the closed orbits of the Iwasawa component of SO(2,n). In the second part, a strict quantization of the black hole by action of group is performed and its Dirac operator is computed. We introduce, in the appendix, most of the notions about homogeneous spaces and Iwasawa decompositions that are needed. Explicit matricial decompositions are given for every Lie algebra that will be used in the thesis: sl(2,R), so(1,n), so(2,n), sl(2,C) and sp(2,R).", "field": "math", "label": 1}
{"text": "Title: Detection and Discovery of Misinformation Sources using Attributed Webgraphs\nAbstract: Website reliability labels underpin almost all research in misinformation detection. However, misinformation sources often exhibit transient behavior, which makes many such labeled lists obsolete over time. We demonstrate that Search Engine Optimization (SEO) attributes provide strong signals for predicting news site reliability. We introduce a novel attributed webgraph dataset with labeled news domains and their connections to outlinking and backlinking domains. We demonstrate the success of graph neural networks in detecting news site reliability using these attributed webgraphs, and show that our baseline news site reliability classifier outperforms current SoTA methods on the PoliticalNews dataset, achieving an F1 score of 0.96. Finally, we introduce and evaluate a novel graph-based algorithm for discovering previously unknown misinformation news sources.", "field": "cs", "label": 0}
{"text": "Title: How to Scale Up the Spectral Efficiency of Multi-way Massive MIMO Relaying?\nAbstract: This paper considers a decode-and-forward (DF) multi-way massive multiple-input multiple-output (MIMO) relay system where many users exchange their data with the aid of a relay station equipped with a massive antenna array. We propose a new transmission protocol which leverages successive cancelation decoding and zero-forcing (ZF) at the users. By using properties of massive MIMO, a tight analytical approximation of the spectral efficiency is derived. We show that our proposed scheme uses only half of the time-slots required in the conventional scheme (in which the number of time-slots is equal to the number of users [1]), to exchange data across different users. As a result, the sum spectral efficiency of our proposed scheme is nearly double the one of the conventional scheme, thereby boosting the performance of multi-way massive MIMO to unprecedented levels.", "field": "cs", "label": 1}
{"text": "Title: Smooth invariant foliations and Koopman eigenfunctions about stable equilibria of semiflows\nAbstract: We consider a $C^r$ semiflow $\\{ \\varphi_t \\}_{t \\geq 0}$ on a Banach space $X$ admitting a stable fixed point $x$. We show, along the lines of the parameterization method (Cabr\\'e et al., 2003), the existence of a $C^r$ invariant foliation tangent to $X_1$ at $x$, for an arbitrary $D \\varphi_t(x)$-invariant subspace $X_1 \\subset X$ satisfying some additional spectral conditions. Uniqueness ensues in a subclass of sufficiently smooth invariant foliations tangent to $X_1$ at $x$. We then draw relations to Koopman theory, and thereby establish the existence and uniqueness, in some appropriate sense, of $C^r$ Koopman eigenfunctions. We demonstrate that these results apply to the case of the Navier-Stokes system, the archetypal example considered by the modern upheaval of applied 'Koopmanism'.", "field": "math", "label": 0}
{"text": "Title: DCR-Consistency: Divide-Conquer-Reasoning for Consistency Evaluation and Improvement of Large Language Models\nAbstract: Evaluating the quality and variability of text generated by Large Language Models (LLMs) poses a significant, yet unresolved research challenge. Traditional evaluation methods, such as ROUGE and BERTScore, which measure token similarity, often fail to capture the holistic semantic equivalence. This results in a low correlation with human judgments and intuition, which is especially problematic in high-stakes applications like healthcare and finance where reliability, safety, and robust decision-making are highly critical. This work proposes DCR, an automated framework for evaluating and improving the consistency of LLM-generated texts using a divide-conquer-reasoning approach. Unlike existing LLM-based evaluators that operate at the paragraph level, our method employs a divide-and-conquer evaluator (DCE) that breaks down the paragraph-to-paragraph comparison between two generated responses into individual sentence-to-paragraph comparisons, each evaluated based on predefined criteria. To facilitate this approach, we introduce an automatic metric converter (AMC) that translates the output from DCE into an interpretable numeric score. Beyond the consistency evaluation, we further present a reason-assisted improver (RAI) that leverages the analytical reasons with explanations identified by DCE to generate new responses aimed at reducing these inconsistencies. Through comprehensive and systematic empirical analysis, we show that our approach outperforms state-of-the-art methods by a large margin (e.g., +19.3% and +24.3% on the SummEval dataset) in evaluating the consistency of LLM generation across multiple benchmarks in semantic, factual, and summarization consistency tasks. Our approach also substantially reduces nearly 90% of output inconsistencies, showing promise for effective hallucination mitigation.", "field": "cs", "label": 0}
{"text": "Title: The Unreasonable Effectiveness of Deep Evidential Regression\nAbstract: There is a significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware regression-based neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, notably with the capabilities to disentangle aleatoric and epistemic uncertainties. Despite some empirical success of Deep Evidential Regression (DER), there are important gaps in the mathematical foundation that raise the question of why the proposed technique seemingly works. We detail the theoretical shortcomings and analyze the performance on synthetic and real-world data sets, showing that Deep Evidential Regression is a heuristic rather than an exact uncertainty quantification. We go on to discuss corrections and redefinitions of how aleatoric and epistemic uncertainties should be extracted from NNs.", "field": "cs", "label": 1}
{"text": "Title: An Improved Algorithm for Computing All the Best Swap Edges of a Tree Spanner\nAbstract: A tree $\\sigma$-spanner of a positively real-weighted $n$-vertex and $m$-edge undirected graph $G$ is a spanning tree $T$ of $G$ which approximately preserves (i.e., up to a multiplicative stretch factor $\\sigma$) distances in $G$. Tree spanners with provably good stretch factors find applications in communication networks, distributed systems, and network design. However, finding an optimal or even a good tree spanner is a very hard computational task. Thus, if one has to face a transient edge failure in $T$, the overall effort that has to be afforded to rebuild a new tree spanner (i.e., computational costs, set-up of new links, updating of the routing tables, etc.) can be rather prohibitive. To circumvent this drawback, an effective alternative is that of associating with each tree edge a best possible (in terms of resulting stretch) swap edge -- a well-established approach in the literature for several other tree topologies. Correspondingly, the problem of computing all the best swap edges of a tree spanner is a challenging algorithmic problem, since solving it efficiently means to exploit the structure of shortest paths not only in $G$, but also in all the scenarios in which an edge of $T$ has failed. For this problem we provide a very efficient solution, running in $O(n^2 \\log^4 n)$ time, which drastically improves (almost by a quadratic factor in $n$ in dense graphs!) on the previous known best result.", "field": "cs", "label": 1}
{"text": "Title: Force-Based Atomistic/Continuum Blending for Multilattices\nAbstract: We formulate the blended force-based quasicontinuum (BQCF) method for multilattices and develop rigorous error estimates in terms of the approximation parameters: atomistic region, blending region and continuum finite element mesh. Balancing the approximation parameters yields a convergent atomistic/continuum multiscale method for multilattices with point defects, including a rigorous convergence rate in terms of the computational cost. The analysis is illustrated with numerical results for a Stone--Wales defect in graphene.", "field": "math", "label": 1}
{"text": "Title: Adaptive Population-based Simulated Annealing for Uncertain Resource Constrained Job Scheduling\nAbstract: Transporting ore from mines to ports is of significant interest in mining supply chains. These operations are commonly associated with growing costs and a lack of resources. Large mining companies are interested in optimally allocating their resources to reduce operational costs. This problem has been previously investigated in the literature as resource constrained job scheduling (RCJS). While a number of optimisation methods have been proposed to tackle the deterministic problem, the uncertainty associated with resource availability, an inevitable challenge in mining operations, has received less attention. RCJS with uncertainty is a hard combinatorial optimisation problem that cannot be solved efficiently with existing optimisation methods. This study proposes an adaptive population-based simulated annealing algorithm that can overcome the limitations of existing methods for RCJS with uncertainty including the premature convergence, the excessive number of hyper-parameters, and the inefficiency in coping with different uncertainty levels. This new algorithm is designed to effectively balance exploration and exploitation, by using a population, modifying the cooling schedule in the Metropolis-Hastings algorithm, and using an adaptive mechanism to select perturbation operators. The results show that the proposed algorithm outperforms existing methods across a wide range of benchmark RCJS instances and uncertainty levels. Moreover, new best known solutions are discovered for all but one problem instance across all uncertainty levels.", "field": "cs", "label": 1}
{"text": "Title: Improved estimators in Bell regression model with application\nAbstract: In this paper, we propose the application of shrinkage strategies to estimate coefficients in the Bell regression models when prior information about the coefficients is available. The Bell regression models are well-suited for modeling count data with multiple covariates. Furthermore, we provide a detailed explanation of the asymptotic properties of the proposed estimators, including asymptotic biases and mean squared errors. To assess the performance of the estimators, we conduct numerical studies using Monte Carlo simulations and evaluate their simulated relative efficiency. The results demonstrate that the suggested estimators outperform the unrestricted estimator when prior information is taken into account. Additionally, we present an empirical application to demonstrate the practical utility of the suggested estimators.", "field": "math", "label": 0}
{"text": "Title: An algorithm for estimating the crossing number of dense graphs, and continuous analogs of the crossing and rectilinear crossing numbers\nAbstract: We present a deterministic $n^{2+o(1)}$-time algorithm that approximates the crossing number of any graph $G$ of order $n$ up to an additive error of $o(n^4)$. We also provide a randomized polynomial-time algorithm that constructs a drawing of $G$ with $\\text{cr}(G)+o(n^4)$ crossings. These results are made interesting by the well known fact that every dense $n$-vertex graph has crossing number $\\Theta(n^4)$. Our work builds on a technique developed by Fox, Pach and S\\'uk, who obtained very similar results for the rectilinear crossing number. The results by the aforementioned authors and in this paper imply that the (normalized) crossing and rectilinear crossing numbers are estimable parameters. Motivated by this, we introduce two graphon parameters, the \\textit{crossing density} and the \\textit{rectilinear crossing density}, and then we prove that, in a precise sense, these are the correct continuous analogs of the crossing and rectilinear crossing numbers of graphs.", "field": "math", "label": 0}
{"text": "Title: Nonlinear diffusion equations with nonlinear gradient noise\nAbstract: We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the one-dimensional stochastic mean curvature flow in graph form.", "field": "math", "label": 1}
{"text": "Title: The Solvability of Interpretability Evaluation Metrics\nAbstract: Feature attribution methods are popular for explaining neural network predictions, and they are often evaluated on metrics such as comprehensiveness and sufficiency. In this paper, we highlight an intriguing property of these metrics: their solvability. Concretely, we can define the problem of optimizing an explanation for a metric, which can be solved by beam search. This observation leads to the obvious yet unaddressed question: why do we use explainers (e.g., LIME) not based on solving the target metric, if the metric value represents explanation quality? We present a series of investigations showing strong performance of this beam search explainer and discuss its broader implication: a definition-evaluation duality of interpretability concepts. We implement the explainer and release the Python solvex package for models of text, image and tabular domains.", "field": "cs", "label": 1}
{"text": "Title: Hadwiger's conjecture and topological bounds\nAbstract: The Odd Hadwiger's conjecture, formulated by Gerards and Seymour in 1995, is a substantial strengthening of Hadwiger's famous coloring conjecture from 1943. We investigate whether the hierarchy of topological lower bounds on the chromatic number, introduced by Matou\\v{s}ek and Ziegler (2003) and refined recently by Daneshpajouh and Meunier (2023), forms a potential avenue to a disproof of Hadwiger's conjecture or its odd-minor variant. In this direction, we prove that, in a very general sense, every graph $G$ that admits a topological lower bound of $t$ on its chromatic number, contains $K_{\\lfloor t/2\\rfloor +1}$ as an odd-minor. This solves a problem posed by Simonyi and Zsb\\'{a}n [European Journal of Combinatorics, 31(8), 2110--2119 (2010)]. We also prove that if for a graph $G$ the Dol'nikov-K\\v{r}\\'{i}\\v{z} lower bound on the chromatic number (one of the lower bounds in the aforementioned hierarchy) attains a value of at least $t$, then $G$ contains $K_t$ as a minor. Finally, extending results by Simonyi and Zsb\\'{a}n, we show that the Odd Hadwiger's conjecture holds for Schrijver and Kneser graphs for any choice of the parameters. The latter are canonical examples of graphs for which topological lower bounds on the chromatic number are tight.", "field": "math", "label": 0}
{"text": "Title: Joint distribution in residue classes of families of polynomially-defined multiplicative functions\nAbstract: We study the distribution of families of multiplicative functions among the coprime residue classes to moduli varying uniformly in a wide range, when the multiplicative functions can be controlled by the values of polynomials at the first few prime powers. We obtain complete uniform extensions of a criterion of Narkiewicz for families of such multiplicative functions, thus also generalizing and improving upon previous work for a single such function and establishing results that are optimal in most parameters and hypotheses. As a special case of our results, for any fixed $\\epsilon>0$, the Euler totient function $\\phi(n)$ and sum of divisors function $\\sigma(n)$ are jointly asymptotically equidistributed among the reduced residue classes to moduli $q$ coprime to $6$ varying uniformly up to $(\\log x)^{(1-\\epsilon)\\alpha(q)}$, where $\\alpha(q) = \\prod_{\\ell \\mid q} (\\ell-3)/(\\ell-1)$; furthermore, the coprimality restriction is necessary and the range of $q$ is essentially optimal.", "field": "math", "label": 0}
{"text": "Title: The extension problem in free harmonic analysis\nAbstract: This paper studies certain aspects of harmonic analysis on nonabelian free groups. We focus on the concept of a positive definite function on the free group and our primary goal is to understand how such functions can be extended from balls of finite radius to the entire group. Previous work showed that such extensions always exist and we study the problem of simultaneous extension of multiple positive definite functions. More specifically, we define a concept of 'relative energy' which measures the proximity between a pair of positive definite functions, and show that a pair of positive definite functions on a finite ball can be extended to the entire group without increasing their relative energy. The proof is analytic, involving differentiation of noncommutative Szego parameters.", "field": "math", "label": 1}