diff --git "a/arxiv_mia_dev.jsonl" "b/arxiv_mia_dev.jsonl" new file mode 100644--- /dev/null +++ "b/arxiv_mia_dev.jsonl" @@ -0,0 +1,400 @@ +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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 $\\mathbb{R}^{n+1}$.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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 $\\mathcal{O}(\\epsilon^{-1}\\log(1/\\epsilon))$.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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 $n$.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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 $\\dot{B}^{0}_{\\infty, \\infty }$.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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/", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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 $2
7$, 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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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 .", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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 $\\tilde{A}_2$.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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\".", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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].", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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 Gr\u007fobner basis with respect to the graded reverse lexicographic order. This solves a conjecture by Robeva, Sturmfels and the last author.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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 $F$.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"text": "Title: Comptage des quiddit{\u00e9}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.", "label": 0, "field": "math"} +{"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 $m$.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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).", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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: [...]", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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 $O(\\sqrt{\\lambda})$.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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).", "label": 1, "field": "math"} +{"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}.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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 $G= SL_2(F_q)$.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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}.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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 $u_\\zeta$.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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}", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"text": "Title: The Yule-$\u039b$ 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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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].", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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 $\\gamma=1$.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"text": "Title: A minimal Gr\u00f6bner 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.", "label": 0, "field": "math"} +{"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", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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).", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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 $\\Gamma_i$.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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 $0 2000$ on the odd exponent $n$.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"text": "Title: On the $\u03b4$-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.", "label": 0, "field": "math"} +{"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", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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].)", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "cs"} +{"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 $n(G) = \\lceil \\frac{g}{2}\\rceil - 1$.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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 $p$.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 1, "field": "math"} +{"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.", "label": 0, "field": "cs"} +{"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.", "label": 0, "field": "math"} +{"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.", "label": 0, "field": "math"}