Title: Various Covering Spectra for Complete Metric Spaces
Abstract: 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.


Title: Aerial Manipulator Force Control Using Control Barrier Functions
Abstract: 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.


Title: Fourier-based schemes for computing the mechanical response of composites with accurate local fields
Abstract: 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.


Title: Group theoretic approach to cyclic cubic fields
Abstract: 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.


Title: Unified Diffusion-Based Rigid and Non-Rigid Editing with Text and Image Guidance
Abstract: 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.


Title: Isometric immersions of Riemannian manifolds in $k$-codimensional Euclidean space
Abstract: 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 $\mathbb{R}^{n+1}$.


Title: A Connected Component Labeling Algorithm for Implicitly-Defined Domains
Abstract: 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.


Title: On Cayley graphs of algebraic structures
Abstract: 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.


Title: Sample Complexity Bounds for Two Timescale Value-based Reinforcement Learning Algorithms
Abstract: 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 $\mathcal{O}(\epsilon^{-1}\log(1/\epsilon))$.


Title: Somos-4 and a quartic Surface in $\mathbb{RP}^{3}$
Abstract: 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.


Title: Predicting parametric spatiotemporal dynamics by multi-resolution PDE structure-preserved deep learning
Abstract: 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.


Title: Structure of betweenness uniform graphs with low values of betweenness centrality
Abstract: 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.


Title: Estimating Categorical Counterfactuals via Deep Twin Networks
Abstract: 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.


Title: The Mahler measure of exact polynomials in three variables
Abstract: 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.


Title: Category-Level 6D Object Pose Estimation with Flexible Vector-Based Rotation Representation
Abstract: 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.


Title: Cuckoo Trie: Exploiting Memory-Level Parallelism for Efficient DRAM Indexing
Abstract: 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.


Title: Every closed surface of genus at least $17$ is Loewner
Abstract: 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.


Title: On Language Varieties Without Boolean Operations
Abstract: 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.


Title: On the delooping of (framed) embedding spaces
Abstract: 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.


Title: Liberating dimension and spectral norm: A universal approach to spectral properties of sample covariance matrices
Abstract: 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 $n$.


Title: Some asymptotic formulae involving Cohen-Ramanujan expansions
Abstract: 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.


Title: The quasi-static plasmonic problem for polyhedra
Abstract: 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.


Title: Lower bounds for bulk deviations for the simple random walk on $\mathbb{Z}^d$, $d\geq 3$
Abstract: 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.


Title: Hopfield Neuronal Network of Fractional Order: A note on its numerical integration
Abstract: 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.


Title: Paraconsistent Existential Graphs Gamma Peirce System
Abstract: 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.


Title: A Finite Axiomatization of G-Dependence
Abstract: 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.


Title: Theory inspired deep network for instantaneous-frequency extraction and signal components recovery from discrete blind-source data
Abstract: 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.


Title: Branch Prediction in Hardcaml for a RISC-V 32im CPU
Abstract: 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.


Title: Fast and Smooth Interpolation on Wasserstein Space
Abstract: 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.


Title: Parabolic bifurcation loci in the spaces of rational functions
Abstract: 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.


Title: Pattern avoidance in ascent sequences
Abstract: 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.


Title: Anisotropy of quadratic forms over a global field of odd characteristic is diophantine
Abstract: 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.


Title: Good Things Come to Those Who Swap Objects on Paths
Abstract: 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.


Title: Shadow Generation with Decomposed Mask Prediction and Attentive Shadow Filling
Abstract: 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.


Title: Non-holomorphic Kaehler submanifolds of Euclidean space
Abstract: 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.


Title: Source-Free Online Domain Adaptive Semantic Segmentation of Satellite Images under Image Degradation
Abstract: 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.


Title: Transparent Contribution Evaluation for Secure Federated Learning on Blockchain
Abstract: 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.


Title: Kernel Theorems in Coorbit Theory
Abstract: 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 $\dot{B}^{0}_{\infty, \infty }$.


Title: Limitless HTTP in an HTTPS World: Inferring the Semantics of the HTTPS Protocol without Decryption
Abstract: 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.


Title: Novikov homology and noncommutative Alexander polynomials
Abstract: 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.


Title: Inequalities about the area bounded by three cevian lines of a triangle
Abstract: 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.


Title: On the lack of external response of a nonlinear medium in the second-harmonic generation process
Abstract: 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.


Title: Introducing Packet-Level Analysis in Programmable Data Planes to Advance Network Intrusion Detection
Abstract: 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.


Title: Transversal and Paving Positroids
Abstract: 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.


Title: On the parametrized Tate construction and two theories of real $p$-cyclotomic spectra
Abstract: 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.


Title: Lossy Compression of Individual Sequences Revisited: Fundamental Limits of Finite-State Encoders
Abstract: 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.


Title: On embeddings of certain spherical homogeneous spaces in prime characteristic
Abstract: 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.


Title: Regularity for Maxwell eigenproblems in photonic crystal fibre modelling
Abstract: 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.


Title: Time Protection: the Missing OS Abstraction
Abstract: 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.


Title: A New Criterion on Normal Bases of Finite Field Extensions
Abstract: 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.


Title: A new metric on the contactomorphism group of orderable contact manifolds
Abstract: 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.


Title: Unique equilibrium states for some intermediate beta transformations
Abstract: 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.


Title: Nonlinear analysis with resurgent functions
Abstract: 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.


Title: Tensor Ranks and the Fine-Grained Complexity of Dynamic Programming
Abstract: 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.


Title: A coordinate free characterization of certain quasidiagonal operators
Abstract: 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.


Title: A Survey of Protocol Fuzzing
Abstract: 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.


Title: Stable minimal hypersurfaces in $\mathbf{R}^5$
Abstract: We show that a complete, two-sided, stable minimal hypersurface in $\mathbf{R}^5$ is flat.


Title: Selling Data to a Competitor
Abstract: 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.


Title: A matrix concentration inequality for products
Abstract: 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.


Title: Counting symmetric and non-symmetric peaks in a set partition
Abstract: 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.


Title: Existence of Classic Solution of the Boussinesq Equation
Abstract: We generalize intermediate value Theorem to metric space,and make use of it to discuss existence of classic solution of the Boussinesq equation.


Title: Quantifying Deep Learning Model Uncertainty in Conformal Prediction
Abstract: 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.


Title: The Equity Framework: Fairness Beyond Equalized Predictive Outcomes
Abstract: 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.


Title: Convergence rate of alternating projection method for the intersection of an affine subspace and the second-order cone
Abstract: 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.


Title: Evaluating Language-Model Agents on Realistic Autonomous Tasks
Abstract: 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.


Title: Training-free Content Injection using h-space in Diffusion Models
Abstract: 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/


Title: Provable Computational and Statistical Guarantees for Efficient Learning of Continuous-Action Graphical Games
Abstract: 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.


Title: Existence and concentration of solutions for a class of biharmonic equations
Abstract: 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.


Title: Splitting Methods for differential equations
Abstract: 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.


Title: BA-SAM: Scalable Bias-Mode Attention Mask for Segment Anything Model
Abstract: 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.


Title: Taking Complete Finite Prefixes To High Level, Symbolically
Abstract: 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.


Title: Improving Automated Program Repair with Domain Adaptation
Abstract: 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.


Title: Closed categories vs. closed multicategories
Abstract: 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.


Title: The homology of the partition algebras
Abstract: 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.


Title: Can poachers find animals from public camera trap images?
Abstract: 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.


Title: Sub-Riemannian curvature of Carnot groups with rank-two distributions
Abstract: 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.


Title: Where You Are Is Who You Are: User Identification by Matching Statistics
Abstract: 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.


Title: A stratification of moduli of arbitrarily singular curves
Abstract: 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.


Title: Virtual rigid motives of semi-algebraic sets
Abstract: 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.


Title: Sharper Bounds for $\ell_p$ Sensitivity Sampling
Abstract: In large scale machine learning, random sampling is a popular way to approximate datasets by a small representative subset of examples. In particular, sensitivity sampling is an intensely studied technique which provides provable guarantees on the quality of approximation, while reducing the number of examples to the product of the VC dimension $d$ and the total sensitivity $\mathfrak S$ in remarkably general settings. However, guarantees going beyond this general bound of $\mathfrak S d$ are known in perhaps only one setting, for $\ell_2$ subspace embeddings, despite intense study of sensitivity sampling in prior work. In this work, we show the first bounds for sensitivity sampling for $\ell_p$ subspace embeddings for $p > 2$ that improve over the general $\mathfrak S d$ bound, achieving a bound of roughly $\mathfrak S^{2-2/p}$ for $2<p<\infty$. Furthermore, our techniques yield further new results in the study of sampling algorithms, showing that the root leverage score sampling algorithm achieves a bound of roughly $d$ for $1\leq p<2$, and that a combination of leverage score and sensitivity sampling achieves an improved bound of roughly $d^{2/p}\mathfrak S^{2-4/p}$ for $2<p<\infty$. Our sensitivity sampling results yield the best known sample complexity for a wide class of structured matrices that have small $\ell_p$ sensitivity.


Title: A Neural Lip-Sync Framework for Synthesizing Photorealistic Virtual News Anchors
Abstract: Lip sync has emerged as a promising technique for generating mouth movements from audio signals. However, synthesizing a high-resolution and photorealistic virtual news anchor is still challenging. Lack of natural appearance, visual consistency, and processing efficiency are the main problems with existing methods. This paper presents a novel lip-sync framework specially designed for producing high-fidelity virtual news anchors. A pair of Temporal Convolutional Networks are used to learn the cross-modal sequential mapping from audio signals to mouth movements, followed by a neural rendering network that translates the synthetic facial map into a high-resolution and photorealistic appearance. This fully trainable framework provides end-to-end processing that outperforms traditional graphics-based methods in many low-delay applications. Experiments also show the framework has advantages over modern neural-based methods in both visual appearance and efficiency.


Title: Algorithmically Effective Differentially Private Synthetic Data
Abstract: We present a highly effective algorithmic approach for generating $\varepsilon$-differentially private synthetic data in a bounded metric space with near-optimal utility guarantees under the 1-Wasserstein distance. In particular, for a dataset $X$ in the hypercube $[0,1]^d$, our algorithm generates synthetic dataset $Y$ such that the expected 1-Wasserstein distance between the empirical measure of $X$ and $Y$ is $O((\varepsilon n)^{-1/d})$ for $d\geq 2$, and is $O(\log^2(\varepsilon n)(\varepsilon n)^{-1})$ for $d=1$. The accuracy guarantee is optimal up to a constant factor for $d\geq 2$, and up to a logarithmic factor for $d=1$. Our algorithm has a fast running time of $O(\varepsilon dn)$ for all $d\geq 1$ and demonstrates improved accuracy compared to the method in (Boedihardjo et al., 2022) for $d\geq 2$.


Title: Formal multiple Eisenstein series and their derivations
Abstract: We introduce the algebra of formal multiple Eisenstein series and study its derivations. This algebra is motivated by the classical multiple Eisenstein series, introduced by Gangl-Kaneko-Zagier as a hybrid of classical Eisenstein series and multiple zeta values. In depth one, we obtain formal versions of the Eisenstein series satisfying the same algebraic relations as the classical Eisenstein series. In particular, they generate an algebra whose elements we call formal quasimodular forms. We show that the algebra of formal multiple Eisenstein series is an $\mathfrak{sl}_2$-algebra by formalizing the usual derivations for quasimodular forms and extending them naturally to the whole algebra. Additionally, we introduce some families of derivations for general quasi-shuffle algebras, providing a broader context for these derivations. Further, we prove that a quotient of this algebra is isomorphic to the algebra of formal multiple zeta values. This gives a novel and purely formal approach to classical (quasi)modular forms and builds a new link between (formal) multiple zeta values and modular forms.


Title: Jacobi polynomials and harmonic weight enumerators of the first-order Reed--Muller codes and the extended Hamming codes
Abstract: In the present paper, we give harmonic weight enumerators and Jacobi polynomials for the first-order Reed--Muller codes and the extended Hamming codes. As a corollary, we show the nonexistence of combinatorial $4$-designs in these codes.


Title: Existence of weak solutions to borderline double-phase problems with logarithmic convection term
Abstract: In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data. The proof is based on the surjectivity theorem for the pseudo-monotone operators and modular function spaces and embedding theorems in generalized Orlicz spaces. Our approach in this paper can be extended naturally to a larger class of unbalanced double-phase problems with logarithmic perturbation and gradient dependence on the right-hand sides.


Title: Generalised Dirac-Schrödinger operators and the Callias Theorem
Abstract: We consider generalised Dirac-Schr\"odinger operators, consisting of a self-adjoint elliptic first-order differential operator D with a skew-adjoint 'potential' given by a (suitable) family of unbounded operators on an auxiliary Hilbert module. The index of such an operator represents the pairing (Kasparov product) of the K-theory class of the potential with the K-homology class of D. Our main result in this paper is a generalisation of the Callias Theorem: the index of the Dirac-Schr\"odinger operator can be computed from its restriction to a hypersurface. Our theorem simultaneously generalises (and is inspired by) the well-known result that the spectral flow of a path of relatively compact perturbations depends only on the endpoints.


Title: Sub-Poissonian estimates for exponential moments of additive functionals over pairs of particles with respect to determinantal and symplectic Pfaffian point processes governed by entire functions
Abstract: The aim of this note is to estimate the tail of the distribution of the number of particles in an interval under determinantal and Pfaffian point processes. The main result of the note is that the square of the number of particles under the determinantal point process whose correlation kernel is an entire function of finite order has sub-Poissonian tails. The same result also holds in the symplectic Pfaffian case. As a corollary, sub-Poissonian estimates are also obtained for exponential moments of additive functionals over pairs of particles.


Title: The Effect of Learning Strategy versus Inherent Architecture Properties on the Ability of Convolutional Neural Networks to Develop Transformation Invariance
Abstract: As object recognition becomes an increasingly common ML task, and recent research demonstrating CNNs vulnerability to attacks and small image perturbations necessitate fully understanding the foundations of object recognition. We focus on understanding the mechanisms behind how neural networks generalize to spatial transformations of complex objects. While humans excel at discriminating between objects shown at new positions, orientations, and scales, past results demonstrate that this may be limited to familiar objects - humans demonstrate low tolerance of spatial-variances for purposefully constructed novel objects. Because training artificial neural networks from scratch is similar to showing novel objects to humans, we seek to understand the factors influencing the tolerance of CNNs to spatial transformations. We conduct a thorough empirical examination of seven Convolutional Neural Network (CNN) architectures. By training on a controlled face image dataset, we measure model accuracy across different degrees of 5 transformations: position, size, rotation, Gaussian blur, and resolution transformation due to resampling. We also examine how learning strategy affects generalizability by examining how different amounts of pre-training have on model robustness. Overall, we find that the most significant contributor to transformation invariance is pre-training on a large, diverse image dataset. Moreover, while AlexNet tends to be the least robust network, VGG and ResNet architectures demonstrate higher robustness for different transformations. Along with kernel visualizations and qualitative analyses, we examine differences between learning strategy and inherent architectural properties in contributing to invariance of transformations, providing valuable information towards understanding how to achieve greater robustness to transformations in CNNs.


Title: Global uniqueness of small representations
Abstract: We prove that automorphic representations whose local components are certain small representations have multiplicity one. The proof is based on the multiplicity-one theorem for certain functionals of small representations, also proved in this paper.


Title: The ghosts of departed quantities in switches and transitions
Abstract: Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the dynamics of the system significantly. Here we discuss the way transitions can be reduced to discontinuities without trivializing them, by preserving so-called hidden terms. We review the fundamental methodology, its motivations, and where their study seems to be heading. We derive a prototype for piecewise smooth models from the asymptotics of systems with rapid transitions, sharpening Filippov's convex combinations by encoding the tails of asymptotic series into nonlinear dependence on a switching parameter. We present a few examples that illustrate the impact of these on our standard picture of smooth or only piecewise smooth dynamics.


Title: A bridge between the circular and linear normal distributions
Abstract: In this short note, we present a refined approximation for the log-ratio of the density of the von Mises$(\mu,\kappa)$ distribution (also called the circular normal distribution) to the standard (linear) normal distribution when the concentration parameter \k{appa} is large. Our work complements the one of Hill (1976), who obtained a very similar approximation along with quantile couplings, using earlier approximations by Hill & Davis (1968) of Cornish-Fisher type. One motivation for this note is to highlight the connection between the circular and linear normal distributions through their circular variance and (linear) variance.


Title: On the non-transverse homoclinic channel of a center manifold
Abstract: We consider a scenario when a stable and unstable manifolds of compact center manifold of a saddle-center coincide. The normal form of the ODE governing the system near the center manifold is derived and so is the normal form of the return map to the neighbourhood of the center manifold. The limit dynamics of the return map is investigated by showing that it might take the form of a Henon-like map possessing a Lorenz-like attractor or satisfy 'cone-field condition' resulting in partial hyperbolicity. We consider also motivating example from game theory.


Title: Unconditional stability of equilibria in thermally driven compressible fluids
Abstract: We show that small perturbations of the spatially homogeneous equilibrium of a thermally driven compressible viscous fluid are globally stable. Specifically, any weak solution of the evolutionary Navier--Stokes--Fourier system driven by thermal convection converges to an equilibrium as time goes to infinity. The main difficulty to overcome is the fact the problem does not admit any obvious Lyapunov function. The result applies, in particular, to the Rayleigh--B\' enard convection problem.


Title: 3-anti-power uniform morphisms
Abstract: Words whose three successive factors of the same length are all different i.e. 3-anti-power words are a natural extension of square-free words (two successive factors of the same length are different). We give a way to verify whether a uniform morphism preserves 3-anti-power words (the image of a 3-anti-power word is a 3-anti-power word). A consequence of the existence of such morphisms is the possibility of generating an infinite 3-anti-power word.


Title: A binomial random multigraph
Abstract: Fix a positive integer $n$, a real number $p\in (0,1]$, and a (perhaps random) hypergraph $\mathcal{H}$ on $[n]$. We introduce and investigate the following random multigraph model, which we denote $\mathbb{G}(n,p\, ; \,\mathcal{H})$: begin with an empty graph on $n$ vertices, which are labelled by the set $[n]$. For every $H\in \mathcal{H}$ choose, independently from previous choices, a doubleton from $H$, say $D = \{i,j\} \subset H$, uniformly at random and then introduce an edge between the vertices $i$ and $j$ in the graph with probability $p$, where each edge is introduced independently of all other edges.


Title: On Probabilistic Completeness of Probabilistic Cell Decomposition
Abstract: Probabilistic Cell Decomposition (PCD) is a probabilistic path planning method combining the concepts of approximate cell decomposition with probabilistic sampling. It has been shown that the use of lazy evaluation techniques and supervised sampling in important areas result in a high performance path planning method. Even if it was postulated before that PCD is probabilistically complete, we present a detailed proof of probabilistic completeness here for the first time.


Title: Joint distribution in residue classes of families of polynomially-defined additive functions
Abstract: Let $g_1, \dots , g_M$ be additive functions for which there exist nonconstant polynomials $G_1, \dots , G_M$ satisfying $g_i(p) = G_i(p)$ for all primes $p$ and all $i \in \{1, \dots , M\}$. Under fairly general and nearly optimal hypotheses, we show that the functions $g_1, \dots , g_M$ are jointly equidistributed among the residue classes to moduli $q$ varying uniformly up to a fixed but arbitrary power of $\log x$. Thus, we obtain analogues of the Siegel-Walfisz Theorem for primes in arithmetic progressions, but with primes replaced by values of such additive functions. Our results partially extend work of Delange from fixed moduli to varying moduli, and also generalize recent work done for a single additive function.


Title: Minimizing the Weighted Number of Tardy Jobs is W[1]-hard
Abstract: We consider the $1||\sum w_J U_j$ problem, the problem of minimizing the weighted number of tardy jobs on a single machine. This problem is one of the most basic and fundamental problems in scheduling theory, with several different applications both in theory and practice. We prove that $1||\sum w_J U_j$ is W[1]-hard with respect to the number $p_{\#}$ of different processing times in the input, as well as with respect to the number $w_{\#}$ of different weights in the input. This, along with previous work, provides a complete picture for $1||\sum w_J U_j$ from the perspective of parameterized complexity, as well as almost tight complexity bounds for the problem under the Exponential Time Hypothesis (ETH).


Title: Graphon games: A statistical framework for network games and interventions
Abstract: In this paper, we present a unifying framework for analyzing equilibria and designing interventions for large network games sampled from a stochastic network formation process represented by a graphon. We first introduce a new class of infinite population games, termed graphon games, where a continuum of heterogeneous agents interact according to a graphon. After studying properties of equilibria in graphon games, we show that graphon equilibria can approximate equilibria of large network games sampled from the graphon. We next show that, under some regularity assumptions, the graphon approach enables the design of asymptotically optimal interventions via the solution of an optimization problem with much lower dimension than the one based on the entire network structure. We illustrate our framework on a synthetic dataset of rural villages and show that the graphon intervention can be computed efficiently and based solely on aggregated relational data.


Title: Passivity-Preserving Safety-Critical Control using Control Barrier Functions
Abstract: In this letter we propose a holistic analysis merging the techniques of passivity-based control (PBC) and control barrier functions (CBF). We constructively find conditions under which passivity of the closed-loop system is preserved under CBF-based safety-critical control. The results provide an energetic interpretation of safety-critical control schemes, and induce novel passive designs which are less conservative than standard methods based on damping injection. The results are specialised to port-Hamiltonian systems and simulations are performed on a cart-pole system.


Title: Functional Inequalities for Brownian Motion on Riemannian Manifolds with Sticky-Reflecting Boundary Diffusion
Abstract: We prove geometric upper bounds for the Poincar\'e and Logarithmic Sobolev constants for Brownian motion on manifolds with sticky reflecting boundary diffusion i.e. extended Wentzell-type boundary condition under general curvature assumptions on the manifold and its boundary. The method is based on an interpolation involving energy interactions between the boundary and the interior of the manifold. As side results we obtain explicit geometric bounds on the first nontrivial Steklov eigenvalue, for the norm of the boundary trace operator on Sobolev functions, and on the boundary trace logarithmic Sobolev constant. The case of Brownian motion with pure sticky reflection is also treated.


Title: Generalised Local Fractional Hermite-Hadamard Type Inequalities on Fractal Sets
Abstract: Fractal geometry and analysis constitute a growing field, with numerous applications, based on the principles of fractional calculus. Fractals sets are highly effective in improving convex inequalities and their generalisations. In this paper, we establish a generalized notion of convexity. By defining generalised $\phi_{h-s}$ convex functions, we extend the well known concepts of generalised convex functions, $P$-functions, Breckner $s$-convex functions, $h$-convex functions amongst others. With this definition, we prove Hermite-Hadamard type inequalities for generalized $\phi_{h-s}$ convex mappings onto fractal sets. Our results are then applied to probability theory.


Title: 5-Engel Lie algebras
Abstract: We prove that 5-Engel Lie algebras over a field of characteristic zero, or over a field of prime characteristic $p>7$, are nilpotent of class at most 11. We also prove that if $G$ is a finite 5-Engel $p$-group for $p>7$ then $G$ is nilpotent of class at most 10.


Title: Handling Collocations in Hierarchical Latent Tree Analysis for Topic Modeling
Abstract: 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.


Title: A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds
Abstract: 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 .


Title: Adversarial Machine Learning-Enabled Anonymization of OpenWiFi Data
Abstract: 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.


Title: Multi-segmented non-isothermal compositional liquid gas well model for geothermal processes
Abstract: 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.