Title: Reproducing formulas for generalized translation invariant systems on locally compact abelian groups
Abstract: In this paper we connect the well established discrete frame theory of generalized shift invariant systems to a continuous frame theory. To do so, we let $\Gamma_j$, $j \in J$, be a countable family of closed, co-compact subgroups of a second countable locally compact abelian group $G$ and study systems of the form $\cup_{j \in J}\{g_{j,p}(\cdot - \gamma)\}_{\gamma \in \Gamma_j, p \in P_j}$ with generators $g_{j,p}$ in $L^2(G)$ and with each $P_j$ being a countable or an uncountable index set. We refer to systems of this form as generalized translation invariant (GTI) systems. Many of the familiar transforms, e.g., the wavelet, shearlet and Gabor transform, both their discrete and continuous variants, are GTI systems. Under a technical $\alpha$ local integrability condition ($\alpha$-LIC) we characterize when GTI systems constitute tight and dual frames that yield reproducing formulas for $L^2(G)$. This generalizes results on generalized shift invariant systems, where each $P_j$ is assumed to be countable and each $\Gamma_j$ is a uniform lattice in $G$, to the case of uncountably many generators and (not necessarily discrete) closed, co-compact subgroups. Furthermore, even in the case of uniform lattices $\Gamma_j$, our characterizations improve known results since the class of GTI systems satisfying the $\alpha$-LIC is strictly larger than the class of GTI systems satisfying the previously used local integrability condition. As an application of our characterization results, we obtain new characterizations of translation invariant continuous frames and Gabor frames for $L^2(G)$. In addition, we will see that the admissibility conditions for the continuous and discrete wavelet and Gabor transform in $L^2(\mathbb{R}^n)$ are special cases of the same general characterizing equations.


Title: L3Cube-IndicNews: News-based Short Text and Long Document Classification Datasets in Indic Languages
Abstract: In this work, we introduce L3Cube-IndicNews, a multilingual text classification corpus aimed at curating a high-quality dataset for Indian regional languages, with a specific focus on news headlines and articles. We have centered our work on 10 prominent Indic languages, including Hindi, Bengali, Marathi, Telugu, Tamil, Gujarati, Kannada, Odia, Malayalam, and Punjabi. Each of these news datasets comprises 10 or more classes of news articles. L3Cube-IndicNews offers 3 distinct datasets tailored to handle different document lengths that are classified as: Short Headlines Classification (SHC) dataset containing the news headline and news category, Long Document Classification (LDC) dataset containing the whole news article and the news category, and Long Paragraph Classification (LPC) containing sub-articles of the news and the news category. We maintain consistent labeling across all 3 datasets for in-depth length-based analysis. We evaluate each of these Indic language datasets using 4 different models including monolingual BERT, multilingual Indic Sentence BERT (IndicSBERT), and IndicBERT. This research contributes significantly to expanding the pool of available text classification datasets and also makes it possible to develop topic classification models for Indian regional languages. This also serves as an excellent resource for cross-lingual analysis owing to the high overlap of labels among languages. The datasets and models are shared publicly at https://github.com/l3cube-pune/indic-nlp


Title: Beyond Efficiency: A Systematic Survey of Resource-Efficient Large Language Models
Abstract: The burgeoning field of Large Language Models (LLMs), exemplified by sophisticated models like OpenAI's ChatGPT, represents a significant advancement in artificial intelligence. These models, however, bring forth substantial challenges in the high consumption of computational, memory, energy, and financial resources, especially in environments with limited resource capabilities. This survey aims to systematically address these challenges by reviewing a broad spectrum of techniques designed to enhance the resource efficiency of LLMs. We categorize methods based on their optimization focus: computational, memory, energy, financial, and network resources and their applicability across various stages of an LLM's lifecycle, including architecture design, pretraining, finetuning, and system design. Additionally, the survey introduces a nuanced categorization of resource efficiency techniques by their specific resource types, which uncovers the intricate relationships and mappings between various resources and corresponding optimization techniques. A standardized set of evaluation metrics and datasets is also presented to facilitate consistent and fair comparisons across different models and techniques. By offering a comprehensive overview of the current sota and identifying open research avenues, this survey serves as a foundational reference for researchers and practitioners, aiding them in developing more sustainable and efficient LLMs in a rapidly evolving landscape.


Title: Fiedler Linearizations of Rectangular Rational Matrix Functions
Abstract: Linearization is a standard approach in the computation of eigenvalues, eigenvectors and invariant subspaces of matrix polynomials and rational matrix value functions. An important source of linearizations are the so called Fiedler linearizations, which are generalizations of the classical companion forms. In this paper the concept of Fiedler linearization is extended from square regular to rectangular rational matrix valued functions. The approach is applied to Rosenbrock functions arising in mathematical system theory.


Title: Towards a Foundation Purchasing Model: Pretrained Generative Autoregression on Transaction Sequences
Abstract: Machine learning models underpin many modern financial systems for use cases such as fraud detection and churn prediction. Most are based on supervised learning with hand-engineered features, which relies heavily on the availability of labelled data. Large self-supervised generative models have shown tremendous success in natural language processing and computer vision, yet so far they haven't been adapted to multivariate time series of financial transactions. In this paper, we present a generative pretraining method that can be used to obtain contextualised embeddings of financial transactions. Benchmarks on public datasets demonstrate that it outperforms state-of-the-art self-supervised methods on a range of downstream tasks. We additionally perform large-scale pretraining of an embedding model using a corpus of data from 180 issuing banks containing 5.1 billion transactions and apply it to the card fraud detection problem on hold-out datasets. The embedding model significantly improves value detection rate at high precision thresholds and transfers well to out-of-domain distributions.


Title: Efficient Private SCO for Heavy-Tailed Data via Clipping
Abstract: We consider stochastic convex optimization for heavy-tailed data with the guarantee of being differentially private (DP). Prior work on this problem is restricted to the gradient descent (GD) method, which is inefficient for large-scale problems. In this paper, we resolve this issue and derive the first high-probability bounds for the private stochastic method with clipping. For general convex problems, we derive excess population risks $\Tilde{O}\left(\frac{d^{1/7}\sqrt{\ln\frac{(n \epsilon)^2}{\beta d}}}{(n\epsilon)^{2/7}}\right)$ and $\Tilde{O}\left(\frac{d^{1/7}\ln\frac{(n\epsilon)^2}{\beta d}}{(n\epsilon)^{2/7}}\right)$ under bounded or unbounded domain assumption, respectively (here $n$ is the sample size, $d$ is the dimension of the data, $\beta$ is the confidence level and $\epsilon$ is the private level). Then, we extend our analysis to the strongly convex case and non-smooth case (which works for generalized smooth objectives with H$\ddot{\text{o}}$lder-continuous gradients). We establish new excess risk bounds without bounded domain assumption. The results above achieve lower excess risks and gradient complexities than existing methods in their corresponding cases. Numerical experiments are conducted to justify the theoretical improvement.


Title: Magnitude function identifies generic finite metric spaces
Abstract: We show that a ``generic'' finite metric space can be identified by the asymptotic behavior of the magnitude function. In particular, almost every finite set in Euclidean space can be determined by the magnitude function.


Title: Derivative-Based Diagnosis of Regular Expression Ambiguity
Abstract: Regular expressions are often ambiguous. We present a novel method based on Brzozowski's derivatives to aid the user in diagnosing ambiguous regular expressions. We introduce a derivative-based finite state transducer to generate parse trees and minimal counter-examples. The transducer can be easily customized to either follow the POSIX or Greedy disambiguation policy and based on a finite set of examples it is possible to examine if there are any differences among POSIX and Greedy.


Title: Igusa zeta functions and the non-archimedean SYZ fibration
Abstract: We explain the proof, obtained in collaboration with Chenyang Xu, of a 1999 conjecture of Veys about poles of maximal order of Igusa zeta functions. The proof technique is based on the Minimal Model Program in birational geometry, but the proof was heavily inspired by ideas coming from non-archimedean geometry and mirror symmetry; we will outline these relations at the end of the paper. This text is intended to be a low-tech introduction to these topics; we only assume that the reader has a basic knowledge of algebraic geometry.


Title: LSTMs Exploit Linguistic Attributes of Data
Abstract: While recurrent neural networks have found success in a variety of natural language processing applications, they are general models of sequential data. We investigate how the properties of natural language data affect an LSTM's ability to learn a nonlinguistic task: recalling elements from its input. We find that models trained on natural language data are able to recall tokens from much longer sequences than models trained on non-language sequential data. Furthermore, we show that the LSTM learns to solve the memorization task by explicitly using a subset of its neurons to count timesteps in the input. We hypothesize that the patterns and structure in natural language data enable LSTMs to learn by providing approximate ways of reducing loss, but understanding the effect of different training data on the learnability of LSTMs remains an open question.


Title: On the modulus of continuity of solutions to nonlocal parabolic equations
Abstract: A general modulus of continuity is quantified for locally bounded, local, weak solutions to nonlocal parabolic equations, under a minimal tail condition. H\"older modulus of continuity is then deduced under a slightly stronger tail condition. These regularity estimates are demonstrated under the framework of nonlocal $p$-Laplacian with measurable kernels.


Title: Quantum ergodicity on the Bruhat-Tits building for $\text{PGL}(3, F)$ in the Benjamini-Schramm limit
Abstract: We study joint eigenfunctions of the spherical Hecke algebra acting on $L^2(\Gamma_n \backslash G / K)$ where $G = \text{PGL}(3, F)$ with $F$ a non-archimedean local field of arbitrary characteristic, $K = \text{PGL}(3, O)$ with $O$ the ring of integers of $F$, and $(\Gamma_n)$ is a sequence of torsion-free lattices. We prove a form of equidistribution on average for eigenfunctions whose spectral parameters lie in the tempered spectrum when the associated sequence of quotients of the Bruhat-Tits building Benjamini-Schramm converges to the building itself. This result is a higher rank non-archimedean analogue of existing results for graphs and locally symmetric spaces. A recurring theme in the proof is the reduction of many computations to computing the sum of an exponential function over lattice points in a polytope; such expressions can subsequently be simplified using Brion's formula. Along the way of proving our main result we prove several other results which may be of independent interest including a "degenerate" version of Brion's formula which "interpolates" between the usual Brion's formula and the Ehrhart polynomial, an effective rate of convergence for the distribution of spectral parameters to the Plancherel measure under Benjamini-Schramm convergence, and a classification of relative positions of triples of points in buildings of type $\tilde{A}_2$.


Title: A spectral theorem for compact representations and non-unitary cusp forms
Abstract: We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms.


Title: Low level definability above large cardinals
Abstract: We study some connections between definability in generalized descriptive set theory and large cardinals, particularly measurable cardinals and limits thereof, working in ZFC. We show that if $\kappa$ is a limit of measurable cardinals then there is no $\Sigma_1(H_\kappa\cup\mathrm{OR})$ wellorder of a subset of $P(\kappa)$ of length $\geq\kappa^+$; this answers a question of L\"ucke and M\"uller. However, in $M_1$, the minimal proper class mouse with a Woodin cardinal, for every uncountable cardinal $\kappa$ which is not a limit of measurables, there is a $\Sigma_1(H_\kappa\cup\{\kappa\})$ good wellorder of $H_{\kappa^+}$. If $\kappa$ is a limit of measurables then there is no $\Sigma_1(H_\kappa\cup\mathrm{OR})$ mad family $F\subseteq P(\kappa)$ of cardinality $>\kappa$, and if also $\mathrm{cof}(\kappa)>\omega$ then there is no $\Sigma_1(H_\kappa\cup\mathrm{OR})$ almost disjoint family $F\subseteq P(\kappa)$ of cardinality $>\kappa$. However, relative to the consistency of large cardinals, $\Pi_1(\{\kappa\})$ mad families and maximal independent families $F\subseteq P(\kappa)$ can exist, when $\kappa$ is a limit of measurables, and even more. We also examine some of the features of $L[U]$, and answer another question of L\"ucke and M\"uller, showing that if $\kappa$ is a weakly compact cardinal such that every $\Sigma_1(H_\kappa\cup\{\kappa\})$ subset of $P(\kappa)$ of cardinality $>\kappa$ has a subset which is the range of a perfect function, then there is an inner model satisfying "there is a weakly compact limit of measurable cardinals".


Title: Second homotopy classes associated with non-cancellative monoids
Abstract: We construct second homotopy classes associated with twins of non-cancellative tuples of a monoid, where the monoid is defined by the semi-positive fundamental relations of the fundamental group of a CW-complex. As an application, we reconstruct the second homotopy classes for the complement of generic lines arrangement studied by Akio Hattori.


Title: Second-order Approximation of Exponential Random Graph Models
Abstract: Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\"os-R\'enyi random graphs, where edges are independent. In this paper, to distinguish ERGMs from Erd\"os-R\'enyi random graphs, we consider second-order approximations of ERGMs using two-stars and triangles. We prove that the second-order approximation indeed achieves second-order accuracy in the triangle-free case. The new approximation is formally obtained by Hoeffding decomposition and rigorously justified using Stein's method.


Title: Spatiotemporal Monitoring of Epidemics via Solution of a Coefficient Inverse Problem
Abstract: Let S,I and R be susceptible, infected and recovered populations in a city affected by an epidemic. The SIR model of Lee, Liu, Tembine, Li and Osher, \emph{SIAM J. Appl. Math.},~81, 190--207, 2021 of the spatiotemoral spread of epidemics is considered. This model consists of a system of three nonlinear coupled parabolic Partial Differential Equations with respect to the space and time dependent functions S,I and R. For the first time, a Coefficient Inverse Problem (CIP) for this system is posed. The so-called \textquotedblleft convexification" numerical method for this inverse problem is constructed. The presence of the Carleman Weight Function (CWF) in the resulting regularization functional ensures the global convergence of the gradient descent method of the minimization of this functional to the true solution of the CIP, as long as the noise level tends to zero. The CWF is the function, which is used as the weight in the Carleman estimate for the corresponding Partial Differential Operator. Numerical studies demonstrate an accurate reconstruction of unknown coefficients as well as S,I,R functions inside of that city. As a by-product, uniqueness theorem for this CIP is proven. Since the minimal measured input data are required, then the proposed methodology has a potential of a significant decrease of the cost of monitoring of epidemics.


Title: A comparison of the Spectral Ewald and Smooth Particle Mesh Ewald methods in GROMACS
Abstract: The smooth particle mesh Ewald (SPME) method is an FFT based method for the fast evaluation of electrostatic interactions under periodic boundary conditions. A highly optimized implementation of this method is available in GROMACS, a widely used software for molecular dynamics simulations. In this article, we compare a more recent method from the same family of methods, the spectral Ewald (SE) method, to the SPME method in terms of performance and efficiency. We consider serial and parallel implementations of both methods for single and multiple core computations on a desktop machine as well as the Beskow supercomputer at KTH Royal Institute of Technology. The implementation of the SE method has been well optimized, however not yet comparable to the level of the SPME implementation that has been improved upon for many years. We show that the SE method is very efficient whenever used to achieve high accuracy and that it already at this level of optimization can be competitive for low accuracy demands.


Title: Pointwise A posteriori error control of quadratic Discontinuous Galerkin Methods for the unilateral contact problem
Abstract: An a posteriori error bound for the pointwise error of the quadratic discontinuous Galerkin method for the unilateral contact problem on polygonal domain is presented. The pointwise a posteriori error analysis is based on the direct use of a priori estimates of the Green's matrix for the divergence type operators and the suitable construction of the discrete contact force density $\b{\sigma}_h$ and barrier functions for the continuous solution. Several numerical experiments (in two dimension) are presented to illustrate the reliability and efficiency properties of the proposed aposteriori error estimator.


Title: The (twisted/$L^2$)-Alexander polynomial of ideally triangulated 3-manifolds
Abstract: We establish a connection between the Alexander polynomial of a knot and its twisted and $L^2$-versions with the triangulations that appear in 3-dimensional hyperbolic geometry. Specifically, we introduce twisted Neumann--Zagier matrices of ordered ideal triangulations and use them to provide formulas for the Alexander polynomial and its variants, the twisted Alexander polynomial and the $L^2$-Alexander torsion.


Title: Hurewicz sets of reals without perfect subsets
Abstract: We show that even for subsets X of the real line which do not contain perfect sets, the Hurewicz property does not imply the property S1(Gamma,Gamma), asserting that for each countable family of open gamma-covers of X, there is a choice function whose image is a gamma-cover of X. This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszynski and Tsaban, and implies that for C_p(X), the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskii's property alpha_2.


Title: Affine Symmetries of Orbit Polytopes
Abstract: An orbit polytope is the convex hull of an orbit under a finite group $G \leq \operatorname{GL}(d,\mathbb{R})$. We develop a general theory of possible affine symmetry groups of orbit polytopes. For every group, we define an open and dense set of generic points such that the orbit polytopes of generic points have conjugated affine symmetry groups. We prove that the symmetry group of a generic orbit polytope is again $G$ if $G$ is itself the affine symmetry group of some orbit polytope, or if $G$ is absolutely irreducible. On the other hand, we describe some general cases where the affine symmetry group grows. We apply our theory to representation polytopes (the convex hull of a finite matrix group) and show that their affine symmetries can be computed effectively from a certain character. We use this to construct counterexamples to a conjecture of Baumeister et~al.\ on permutation polytopes [Advances in Math. 222 (2009), 431--452, Conjecture~5.4].


Title: The specialization index of a variety over a discretely valued field
Abstract: Let $X$ be a proper variety over a henselian discretely valued field. An important obstruction to the existence of a rational point on $X$ is the index, the minimal positive degree of a zero cycle on $X$. This paper introduces a new invariant, the specialization index, which is a closer approximation of the existence of a rational point. We provide an explicit formula for the specialization index in terms of an $snc$-model, and we give examples of curves where the index equals one but the specialization index is different from one, and thus explains the absence of a rational point. Our main result states that the specialization index of a smooth, proper, geometrically connected $\mathbb{C}((t))$-variety with trivial coherent cohomology is equal to one.


Title: Convergence of the discrete Redner-Ben-Avraham-Kahng coagulation equation
Abstract: This article looks at the relationship between the discrete and the continuous Redner-Ben-Avraham-Kahng (RBK) coagulation models. On the basis of a priori estimation, a weak stability principle and the weak compactness in $L_1$ for the continuous RBK model is shown. By employing a sequence of discrete models to approximate the continuous one, we show that how discrete model eventually converges to the the modified continuous one using the stability principle.


Title: Einstein Lorentzian solvable unimodular Lie groups
Abstract: The goal of this paper is to show that many key results found in the study of Einstein Lorentzian nilpotent Lie algebras can still hold in the more general settings of unimodular Lie algebras and (completely) solvable Lie algebras.


Title: SENS3: Multisensory Database of Finger-Surface Interactions and Corresponding Sensations
Abstract: The growing demand for natural interactions with technology underscores the importance of achieving realistic touch sensations in digital environments. Realizing this goal highly depends on comprehensive databases of finger-surface interactions, which need further development. Here, we present SENS3, an extensive open-access repository of multisensory data acquired from fifty surfaces when two participants explored them with their fingertips through static contact, pressing, tapping, and sliding. SENS3 encompasses high-fidelity visual, audio, and haptic information recorded during these interactions, including videos, sounds, contact forces, torques, positions, accelerations, skin temperature, heat flux, and surface photographs. Additionally, it incorporates thirteen participants' psychophysical sensation ratings while exploring these surfaces freely. We anticipate that SENS3 will be valuable for advancing multisensory texture rendering, user experience development, and touch sensing in robotics.


Title: A direct approach for function approximation on data defined manifolds
Abstract: In much of the literature on function approximation by deep networks, the function is assumed to be defined on some known domain, such as a cube or a sphere. In practice, the data might not be dense on these domains, and therefore, the approximation theory results are observed to be too conservative. In manifold learning, one assumes instead that the data is sampled from an unknown manifold; i.e., the manifold is defined by the data itself. Function approximation on this unknown manifold is then a two stage procedure: first, one approximates the Laplace-Beltrami operator (and its eigen-decomposition) on this manifold using a graph Laplacian, and next, approximates the target function using the eigen-functions. Alternatively, one estimates first some atlas on the manifold and then uses local approximation techniques based on the local coordinate charts. In this paper, we propose a more direct approach to function approximation on \emph{unknown}, data defined manifolds without computing the eigen-decomposition of some operator or an atlas for the manifold, and without any kind of training in the classical sense. Our constructions are universal; i.e., do not require the knowledge of any prior on the target function other than continuity on the manifold. We estimate the degree of approximation. For smooth functions, the estimates do not suffer from the so-called saturation phenomenon. We demonstrate via a property called good propagation of errors how the results can be lifted for function approximation using deep networks where each channel evaluates a Gaussian network on a possibly unknown manifold.


Title: 2-Representations of Lie 2-groups and 2-Vector Bundles
Abstract: Murray, Roberts and Wockel showed that there is no strict model of the string 2-group using the free loop group. Instead, they construct the next best thing, a coherent model for the string 2-group using the free loop group, with explicit formulas for all structure. Based on their expectations, we build a category of 2-representations for coherent Lie 2-groups and some concrete examples. We also discuss the relation between this category of 2-representations and the category of representations. In addition, we construct a model of equivariant 2-vector bundles. At the end, we discuss the adjoint action on the string 2-representations.


Title: Differentially Private Sketches for Jaccard Similarity Estimation
Abstract: This paper describes two locally-differential private algorithms for releasing user vectors such that the Jaccard similarity between these vectors can be efficiently estimated. The basic building block is the well known MinHash method. To achieve a privacy-utility trade-off, MinHash is extended in two ways using variants of Generalized Randomized Response and the Laplace Mechanism. A theoretical analysis provides bounds on the absolute error and experiments show the utility-privacy trade-off on synthetic and real-world data. The paper ends with a critical discussion of related work.


Title: Algebraic boundary of matrices of nonnegative rank at most three
Abstract: The Zariski closure of the boundary of the set of matrices of nonnegative rank at most 3 is reducible. We give a minimal generating set for the ideal of each irreducible component. In fact, this generating set is a Grobner basis with respect to the graded reverse lexicographic order. This solves a conjecture by Robeva, Sturmfels and the last author.


Title: Generalized integral type Hilbert operator acting on weighted Bloch space
Abstract: Let $\mu$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $$\mathcal{I}_{\mu_{\alpha+1}}(f)(z)=\int_{0}^{1}\frac{f(t)}{(1-tz)^{\alpha+1}}d\mu(t)\ \ \ (\alpha>-1).$$ The operator $\mathcal{I}_{\mu_{1}}$ has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of $\mathcal{I}_{\mu_{\alpha+1}}$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of $ \mathcal{I}_{\mu_{\alpha+1}}$ acting between Bloch type spaces, logarithmic Bloch spaces among others.


Title: An Open and Comprehensive Pipeline for Unified Object Grounding and Detection
Abstract: Grounding-DINO is a state-of-the-art open-set detection model that tackles multiple vision tasks including Open-Vocabulary Detection (OVD), Phrase Grounding (PG), and Referring Expression Comprehension (REC). Its effectiveness has led to its widespread adoption as a mainstream architecture for various downstream applications. However, despite its significance, the original Grounding-DINO model lacks comprehensive public technical details due to the unavailability of its training code. To bridge this gap, we present MM-Grounding-DINO, an open-source, comprehensive, and user-friendly baseline, which is built with the MMDetection toolbox. It adopts abundant vision datasets for pre-training and various detection and grounding datasets for fine-tuning. We give a comprehensive analysis of each reported result and detailed settings for reproduction. The extensive experiments on the benchmarks mentioned demonstrate that our MM-Grounding-DINO-Tiny outperforms the Grounding-DINO-Tiny baseline. We release all our models to the research community. Codes and trained models are released at https://github.com/open-mmlab/mmdetection/configs/mm_grounding_dino.


Title: Distributed Multi-Object Tracking Under Limited Field of View Heterogeneous Sensors with Density Clustering
Abstract: We consider the problem of tracking multiple, unknown, and time-varying numbers of objects using a distributed network of heterogeneous sensors. In an effort to derive a formulation for practical settings, we consider limited and unknown sensor field-of-views (FoVs), sensors with limited local computational resources and communication channel capacity. The resulting distributed multi-object tracking algorithm involves solving an NP-hard multidimensional assignment problem either optimally for small-size problems or sub-optimally for general practical problems. For general problems, we propose an efficient distributed multi-object tracking algorithm that performs track-to-track fusion using a clustering-based analysis of the state space transformed into a density space to mitigate the complexity of the assignment problem. The proposed algorithm can more efficiently group local track estimates for fusion than existing approaches. To ensure we achieve globally consistent identities for tracks across a network of nodes as objects move between FoVs, we develop a graph-based algorithm to achieve label consensus and minimise track segmentation. Numerical experiments with a synthetic and a real-world trajectory dataset demonstrate that our proposed method is significantly more computationally efficient than state-of-the-art solutions, achieving similar tracking accuracy and bandwidth requirements but with improved label consistency.


Title: 3D printed architected lattice structures by material jetting
Abstract: High-precision 3D printing technology opens to almost endless opportunities to design complex shapes present in tailored architected materials. The scope of this work is to review the latest studies regarding 3D printed lattice structures that involve the use of photopolymers fabricated by Material Jetting (MJ), with a focus on the widely used Polyjet and MultiJet techniques. The main aspects governing this printing process are introduced to determine their influence during the fabrication of 3D printed lattices. Performed experimental studies, considered assumptions, and constitutive models for the respective numerical simulations are analyzed. Furthermore, an overview of the latest extensively studied 3D printed architected lattice materials is exposed by emphasizing their achieved mechanical performances through the use of Ashby plots. Then, we highlight the advantages, limitations, and challenges of the material jetting technology to manufacture tunable architected materials for innovative devices, oriented to several engineering applications. Finally, possible approaches for future works and gaps to be covered by further research are indicated, including cost and environmental-related issues.


Title: The correspondence between silting objects and $t$-structures for non-positive dg algebras
Abstract: We establish a bijective correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures of $\mathsf{D}_{\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more generally, we work in the setting of ST-pair inside an algebraic triangulated category). For a non-positive (topologically) homologically smooth dg $k$-algebra $A$ whose zeroth cohomology is finite-dimensional, or for a non-positive proper dg $k$-algebra $A$, the one-to-one correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures on $\mathsf{D}_{\rm fd}(A)$ was already known. The main result of this paper generalizes the above two results to locally finite non-positive dg $k$-algebras.


Title: A characteristic-index inequality for closed embeddings of locally compact groups
Abstract: The characteristic index of a locally compact connected group $G$ is the non-negative integer $d$ for which we have a homeomorphism $G\cong K\times \mathbb{R}^d$ with $K\le G$ maximal compact. We prove that the characteristic indices of closed connected subgroups are dominated by those of the ambient groups.


Title: On the Lebesgue measure of the Feigenbaum Julia set
Abstract: We show that the Julia set of the Feigenbaum polynomial has Hausdorff dimension less than~2 (and consequently it has zero Lebesgue measure). This solves a long-standing open question.


Title: On the unicity of types in special linear groups
Abstract: Let $F$ be a non-archimedean local field. We show that any representation of a maximal compact subgroup of $\mathbf{SL}_N(F)$ which is typical for an essentially tame supercuspidal representation must be induced from a Bushnell--Kutzko maximal simple type. From this, we explicitly count and describe the conjugacy classes of such typical representations, and give an explicit description of an inertial Langlands correspondence for essentially tame irreducible $N$-dimensional projective representations of the Weil group of $F$.


Title: Poisson catenarity in Poisson nilpotent algebras
Abstract: We prove that for the iterated Poisson polynomial rings known as Poisson nilpotent algebras (or Poisson-CGL extensions), the Poisson prime spectrum is catenary, i.e., all saturated chains of inclusions of Poisson prime ideals between any two given Poisson prime ideals have the same length.


Title: Rotor-routing reachability is easy, chip-firing reachability is hard
Abstract: Chip-firing and rotor-routing are two well-studied examples of abelian networks. We study the complexity of their respective reachability problems. We show that the rotor-routing reachability problem is decidable in polynomial time, and we give a simple characterization of when a chip-and-rotor configuration is reachable from another one. For chip-firing, it has been known that the reachability problem is in P if we have a class of graphs whose period length is polynomial (for example, Eulerian digraphs). Here we show that in the general case, chip-firing reachability is hard in the sense that if the chip-firing reachability problem were in P for general digraphs, then the polynomial hierarchy would collapse to NP. We encode graphs by their adjacency matrix, and we encode ribbon structures "succinctly", only remembering the number of consecutive parallel edges.


Title: Multifunctions determined by integrable functions
Abstract: Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in the sense of Bochner, McShane or Birkhoff can be transferred to the generated multifunction while Henstock integrability does not guarantee it.


Title: Hamilton--Jacobi equations for Wasserstein controlled gradient flows: existence of viscosity solutions
Abstract: This work is the third part of a program initiated in arXiv:2111.13258, arXiv:2302.06571 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations related to controlled gradient flow problems in metric spaces. In this paper, we finish our analysis in the context of Wasserstein gradient flows with underlying energy functional satisfying McCann's condition. More prescisely, we establish that the value function for a linearly controlled gradient flow problem whose running cost is quadratic in the control variable and just continuous in the state variable yields a viscosity solution to the Hamilton-Jacobi equation in terms of two operators introduced in our former works, acting as rigorous upper and lower bounds for the formal Hamiltonian at hand. The definition of these operators is directly inspired by the Evolutional Variational Inequality formulation of gradient flows (EVI): one of the main innovations of this work is to introduce a controlled version of EVI, which turns out to be crucial in establishing regularity properties, energy and metric bounds along optimzing sequences in the controlled gradient flow problem that defines the candidate solution.


Title: The colouring number of infinite graphs
Abstract: We show that, given an infinite cardinal $\mu$, a graph has colouring number at most $\mu$ if and only if it contains neither of two types of subgraph. We also show that every graph with infinite colouring number has a well-ordering of its vertices that simultaneously witnesses its colouring number and its cardinality.


Title: Real-Time FJ/MAC PDE Solvers via Tensorized, Back-Propagation-Free Optical PINN Training
Abstract: Solving partial differential equations (PDEs) numerically often requires huge computing time, energy cost, and hardware resources in practical applications. This has limited their applications in many scenarios (e.g., autonomous systems, supersonic flows) that have a limited energy budget and require near real-time response. Leveraging optical computing, this paper develops an on-chip training framework for physics-informed neural networks (PINNs), aiming to solve high-dimensional PDEs with fJ/MAC photonic power consumption and ultra-low latency. Despite the ultra-high speed of optical neural networks, training a PINN on an optical chip is hard due to (1) the large size of photonic devices, and (2) the lack of scalable optical memory devices to store the intermediate results of back-propagation (BP). To enable realistic optical PINN training, this paper presents a scalable method to avoid the BP process. We also employ a tensor-compressed approach to improve the convergence and scalability of our optical PINN training. This training framework is designed with tensorized optical neural networks (TONN) for scalable inference acceleration and MZI phase-domain tuning for \textit{in-situ} optimization. Our simulation results of a 20-dim HJB PDE show that our photonic accelerator can reduce the number of MZIs by a factor of $1.17\times 10^3$, with only $1.36$ J and $1.15$ s to solve this equation. This is the first real-size optical PINN training framework that can be applied to solve high-dimensional PDEs.


Title: Imperfect Delayed CSIT can be as Useful as Perfect Delayed CSIT: DoF Analysis and Constructions for the BC
Abstract: In the setting of the two-user broadcast channel, where a two-antenna transmitter communicates information to two single-antenna receivers, recent work by Maddah-Ali and Tse has shown that perfect knowledge of delayed channel state information at the transmitter (perfect delayed CSIT) can be useful, even in the absence of any knowledge of current CSIT. Similar benefits of perfect delayed CSIT were revealed in recent work by Kobayashi et al., Yang et al., and Gou and Jafar, which extended the above to the case of perfect delayed CSIT and imperfect current CSIT. The work here considers the general problem of communicating, over the aforementioned broadcast channel, with imperfect delayed and imperfect current CSIT, and reveals that even substantially degraded and imperfect delayed-CSIT is in fact sufficient to achieve the aforementioned gains previously associated to perfect delayed CSIT. The work proposes novel multi-phase broadcasting schemes that properly utilize knowledge of imperfect delayed and imperfect current CSIT, to match in many cases the optimal degrees-of-freedom (DoF) region achieved with perfect delayed CSIT. In addition to the theoretical limits and explicitly constructed precoders, the work applies towards gaining practical insight as to when it is worth improving CSIT quality.


Title: Marginal Debiased Network for Fair Visual Recognition
Abstract: Deep neural networks (DNNs) are often prone to learn the spurious correlations between target classes and bias attributes, like gender and race, inherent in a major portion of training data (bias-aligned samples), thus showing unfair behavior and arising controversy in the modern pluralistic and egalitarian society. In this paper, we propose a novel marginal debiased network (MDN) to learn debiased representations. More specifically, a marginal softmax loss (MSL) is designed by introducing the idea of margin penalty into the fairness problem, which assigns a larger margin for bias-conflicting samples (data without spurious correlations) than for bias-aligned ones, so as to deemphasize the spurious correlations and improve generalization on unbiased test criteria. To determine the margins, our MDN is optimized through a meta learning framework. We propose a meta equalized loss (MEL) to perceive the model fairness, and adaptively update the margin parameters by metaoptimization which requires the trained model guided by the optimal margins should minimize MEL computed on an unbiased meta-validation set. Extensive experiments on BiasedMNIST, Corrupted CIFAR-10, CelebA and UTK-Face datasets demonstrate that our MDN can achieve a remarkable performance on under-represented samples and obtain superior debiased results against the previous approaches.


Title: Prescribed graphon symmetries and flavors of rigidity
Abstract: We prove that an arbitrary compact metrizable group can be realized as the automorphism group of a graphing; this is a continuous analogue to Frucht's theorem recovering arbitrary finite groups are automorphism groups of finite graphs. The paper also contains a number of results the persistence of transitivity of a compact-group action upon passing to a limit of graphons. Call a compact group $\mathbb{G}$ graphon-rigid if, whenever it acts transitively on each member $\Gamma_n$ of a convergent sequence of graphons, it also acts transitively on the limit $\lim_n \Gamma$. We show that for a compact Lie group $\mathbb{G}$ graphon rigidity is equivalent to the identity component $\mathbb{G}_0$ being semisimple; as a partial converse to a result of Lov\'{a}sz and Szegedy, this is also equivalent to weak randomness: the property that the group have only finitely many irreducible representations in each dimension. Similarly, call a compact group $\mathbb{G}$ image-rigid if for every compact Lie group $\mathbb{H}$ the images of morphisms $\mathbb{G}\to \mathbb{H}$ form a closed set (of closed subgroups, in the natural topology). We prove that graphon rigidity implies image rigidity for compact groups that are either connected or profinite, and the two conditions are equivalent (and also equivalent to being torsion) for profinite abelian groups.


Title: Comptage des quiddit{é}s sur les corps finis et sur quelques anneaux $\mathbb{Z}/N\mathbb{Z}$
Abstract: The $\lambda$-quiddities of size $n$ are $n$-tuples of elements of a fixed set, solutions of a matrix equation appearing in the study of Coxeter friezes. These can be considered on various sets with very different structures from one set to another. The main objective of this text is to obtain explicit formulas giving the number of $\lambda$-quiddities of size $n$ over finite fields and over the rings $\mathbb{Z}/N\mathbb{Z}$ with $N=4m$ and $m$ square free. We will also give some elements about the asymptotic behavior of the number of $\lambda$-quiddities verifying an irreducibility condition over $\mathbb{Z}/N\mathbb{Z}$ when $N$ goes to the infinity.


Title: On components of the tensor square of a Weyl module
Abstract: For a simple Lie algebra $\mathfrak{g}$ of type $A_n,B_n,C_n$ or $D_n$, we give a characterization of the set of dominant integral weights $\lambda$ such that for any rational point $\mu$ in the fundamental Weyl chamber, $2\lambda-\mu$ is a non-negative rational combination of the simple roots if and only if $V_{m\mu}\subseteq V_{m\lambda}\otimes V_{m\lambda}$ for some positive integer $m$.


Title: Entropy and the Kullback-Leibler Divergence for Bayesian Networks: Computational Complexity and Efficient Implementation
Abstract: Bayesian networks (BNs) are a foundational model in machine learning and causal inference. Their graphical structure can handle high-dimensional problems, divide them into a sparse collection of smaller ones, underlies Judea Pearl's causality, and determines their explainability and interpretability. Despite their popularity, there are almost no resources in the literature on how to compute Shannon's entropy and the Kullback-Leibler (KL) divergence for BNs under their most common distributional assumptions. In this paper, we provide computationally efficient algorithms for both by leveraging BNs' graphical structure, and we illustrate them with a complete set of numerical examples. In the process, we show it is possible to reduce the computational complexity of KL from cubic to quadratic for Gaussian BNs.


Title: Faster Projection-Free Augmented Lagrangian Methods via Weak Proximal Oracle
Abstract: This paper considers a convex composite optimization problem with affine constraints, which includes problems that take the form of minimizing a smooth convex objective function over the intersection of (simple) convex sets, or regularized with multiple (simple) functions. Motivated by high-dimensional applications in which exact projection/proximal computations are not tractable, we propose a \textit{projection-free} augmented Lagrangian-based method, in which primal updates are carried out using a \textit{weak proximal oracle} (WPO). In an earlier work, WPO was shown to be more powerful than the standard \textit{linear minimization oracle} (LMO) that underlies conditional gradient-based methods (aka Frank-Wolfe methods). Moreover, WPO is computationally tractable for many high-dimensional problems of interest, including those motivated by recovery of low-rank matrices and tensors, and optimization over polytopes which admit efficient LMOs. The main result of this paper shows that under a certain curvature assumption (which is weaker than strong convexity), our WPO-based algorithm achieves an ergodic rate of convergence of $O(1/T)$ for both the objective residual and feasibility gap. This result, to the best of our knowledge, improves upon the $O(1/\sqrt{T})$ rate for existing LMO-based projection-free methods for this class of problems. Empirical experiments on a low-rank and sparse covariance matrix estimation task and the Max Cut semidefinite relaxation demonstrate that of our method can outperform state-of-the-art LMO-based Lagrangian-based methods.


Title: Online minimum search for Brownian motion and the Cauchy process: Multiple approache
Abstract: The distribution for the minimum of Brownian motion or the Cauchy process is well-known using the reflection principle. Here we consider the problem of finding the sample-by-sample minimum, which we call the online minimum search. We consider the possibility of the golden search method, but we show quantitatively that the bisection method is more efficient. In the bisection method there is a hierarchical parameter, which tunes the depth to which each sub-search is conducted, somewhat similarly to how a depth-first search works to generate a topological ordering on nodes. Finally, we consider the possibility of using harmonic measure, which is a novel idea that has so far been unexplored.


Title: Ordered Ramsey numbers of powers of paths
Abstract: Given two vertex-ordered graphs $G$ and $H$, the ordered Ramsey number $R_<(G,H)$ is the smallest $N$ such that whenever the edges of a vertex-ordered complete graph $K_N$ are red/blue-coloured, then there is a red (ordered) copy of $G$ or a blue (ordered) copy of $H$. Let $P_n^t$ denote the $t$-th power of a monotone path on $n$ vertices. The ordered Ramsey numbers of powers of paths have been extensively studied. We prove that there exists an absolute constant $C$ such that $R_<(K_s,P_n^t)\leq R(K_s,K_t)^{C} \cdot n$ holds for all $s,t,n$, which is tight up to the value of $C$. As a corollary, we obtain that there is an absolute constant $C$ such that $R_<(K_n,P_n^t)\leq n^{Ct}$. These results resolve a problem and a conjecture of Gishboliner, Jin and Sudakov. Furthermore, we show that $R_<(P_n^t,P_n^t)\leq n^{4+o(1)}$ for any fixed $t$. This answers questions of Balko, Cibulka, Kr\'al and Kyn\v{c}l, and of Gishboliner, Jin and Sudakov.


Title: A survey on divisibility of ultrafilters
Abstract: An extension of the divisibility relation on $\mathbb{N}$ to the set $\beta\mathbb{N}$ of ultrafilters on $\mathbb{N}$ was defined and investigated in several papers during the last ten years. Here we make a survey of results obtained so far, adding a few simple results connecting the themes of different stages of the research. The main highlights include: separation into the lower part $L$ (with its division into levels) and the upper part; identifying basic ingredients (powers of primes) and fragmentation of each ultrafilter into them; finding the corresponding upward closed sets belonging to an ultrafilter; estimating cardinalities of divisibility-equivalence classes; extending the congruence relation (in two ways) and checking properties of the obtained relations.


Title: Physics-informed neural network for modeling dynamic linear elasticity
Abstract: In this work, we present the physics-informed neural network (PINN) model applied particularly to dynamic problems in solid mechanics. We focus on forward and inverse problems. Particularly, we show how a PINN model can be used efficiently for material identification in a dynamic setting. In this work, we assume linear continuum elasticity. We show results for two-dimensional (2D) plane strain problem and then we proceed to apply the same techniques for a three-dimensional (3D) problem. As for the training data we use the solution based on the finite element method. We rigorously show that PINN models are accurate, robust and computationally efficient, especially as a surrogate model for material identification problems. Also, we employ state-of-the-art techniques from the PINN literature which are an improvement to the vanilla implementation of PINN. Based on our results, we believe that the framework we have developed can be readily adapted to computational platforms for solving multiple dynamic problems in solid mechanics.


Title: Strongly Minimal Steiner Systems I: Existence
Abstract: A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner $k$-system (for $k \geq 2$) is a linear space such that each line has size exactly $k$. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a (bi-interpretable) vocabulary $\tau$ with a single ternary relation $R$. We prove that for every integer $k$ there exist $2^{\aleph_0}$-many integer valued functions $\mu$ such that each $\mu$ determines a distinct strongly minimal Steiner $k$-system $\mathcal{G}_\mu$, whose algebraic closure geometry has all the properties of the ab initio Hrushovski construction. Thus each is a counterexample to the Zilber Trichotomy Conjecture.


Title: Shadow Blade: A tool to interact with attack vectors
Abstract: The increased demand of cyber security professionals has also increased the development of new platforms and tools that help those professionals to improve their offensive skills. One of these platforms is HackTheBox, an online cyber security training platform that delivers a controlled and safe environment for those professionals to explore virtual machines in a Capture the Flag (CTF) competition style. Most of the tools used in a CTF, or even on real-world Penetration Testing (Pentest), were developed for specific reasons so each tool usually has different input and output formats. These different formats make it hard for cyber security professionals and CTF competitors to develop an attack graph. In order to help cyber security professionals and CTF competitors to discover, select and exploit an attack vector, this paper presents Shadow Blade, a tool to aid users to interact with their attack vectors.


Title: A Deep Reinforcement Learning Approach to Efficient Distributed Optimization
Abstract: In distributed optimization, the practical problem-solving performance is essentially sensitive to algorithm selection, parameter setting, problem type and data pattern. Thus, it is often laborious to acquire a highly efficient method for a given specific problem. In this paper, we propose a learning-based method to achieve efficient distributed optimization over networked systems. Specifically, a deep reinforcement learning (DRL) framework is developed for adaptive configuration within a parameterized unifying algorithmic form, which incorporates an abundance of decentralized first-order and second-order optimization algorithms. We exploit the local consensus and objective information to represent the regularities of problem instances and trace the solving progress, which constitute the states observed by a DRL agent. The framework is trained using Proximal Policy Optimization (PPO) on a number of practical problem instances of similar structures yet different problem data. Experiments on various smooth and non-smooth classes of objective functions demonstrate that our proposed learning-based method outperforms several state-of-the-art distributed optimization algorithms in terms of convergence speed and solution accuracy.


Title: The line bundles on the moduli stack of principal bundles on families of curves
Abstract: Given a connected reductive algebraic group G, we investigate the Picard group of the moduli stack of principal G-bundles over an arbitrary family of smooth curves.


Title: Notes on Nonrepetitive Graph Colouring
Abstract: A vertex colouring of a graph is \emph{nonrepetitive on paths} if there is no path $v_1,v_2,...,v_{2t}$ such that v_i and v_{t+i} receive the same colour for all i=1,2,...,t. We determine the maximum density of a graph that admits a k-colouring that is nonrepetitive on paths. We prove that every graph has a subdivision that admits a 4-colouring that is nonrepetitive on paths. The best previous bound was 5. We also study colourings that are nonrepetitive on walks, and provide a conjecture that would imply that every graph with maximum degree $\Delta$ has a $f(\Delta)$-colouring that is nonrepetitive on walks. We prove that every graph with treewidth k and maximum degree $\Delta$ has a $O(k\Delta)$-colouring that is nonrepetitive on paths, and a $O(k\Delta^3)$-colouring that is nonrepetitive on walks.


Title: Domination Polynomial of the Rook Graph
Abstract: A placement of chess pieces on a chessboard is called dominating, if each free square of the chessboard is under attack by at least one piece. In this contribution we compute the number of dominating arrangements of $k$ rooks on an $n\times m$ chessboard. To this end we derive an expression for the corresponding generating function, the domination polynomial of the $n\times m$ rook graph.


Title: Fourier quasicrystals with unit masses
Abstract: Every set $\Lambda\subset R$ such that the sum of $\delta$-measures sitting at the points of $\Lambda$ is a Fourier quasicrystal, is the zero set of an exponential polynomial with imaginary frequencies.


Title: Homogenization and nonselfadjoint spectral optimization for dissipative Maxwell eigenproblems
Abstract: The homogenization of eigenvalues of non-Hermitian Maxwell operators is studied by the H-convergence method. It is assumed that the Maxwell systems are equipped with suitable m-dissipative boundary conditions, namely, with Leontovich or generalized impedance boundary conditions of the form $n \times E = Z [(n \times H )\times n ] $. We show that, for a wide class of impedance operators $Z$, the nonzero spectrum of the corresponding Maxwell operator is discrete. To this end, a new continuous embedding theorem for domains of Maxwell operators is obtained. We prove the convergence of eigenvalues to an eigenvalue of a homogenized Maxwell operator under the assumption of the H-convergence of the material tensor-fields. This result is applied then to the existence of optimizers for eigenvalue optimization problems and to the existence of an eigenvalue-free region around zero. Connections with unique (and nonunique) continuation results are discussed.


Title: Two remarks on graph norms
Abstract: For a graph $H$, its homomorphism density in graphs naturally extends to the space of two-variable symmetric functions $W$ in $L^p$, $p\geq e(H)$, denoted by $t(H,W)$. One may then define corresponding functionals $\|W\|_{H}:=|t(H,W)|^{1/e(H)}$ and $\|W\|_{r(H)}:=t(H,|W|)^{1/e(H)}$ and say that $H$ is (semi-)norming if $\|.\|_{H}$ is a (semi-)norm and that $H$ is weakly norming if $\|.\|_{r(H)}$ is a norm. We obtain two results that contribute to the theory of (weakly) norming graphs. Firstly, answering a question of Hatami, who estimated the modulus of convexity and smoothness of $\|.\|_{H}$, we prove that $\|.\|_{r(H)}$ is not uniformly convex nor uniformly smooth, provided that $H$ is weakly norming. Secondly, we prove that every graph $H$ without isolated vertices is (weakly) norming if and only if each component is an isomorphic copy of a (weakly) norming graph. This strong factorisation result allows us to assume connectivity of $H$ when studying graph norms. In particular, we correct an error in the original statement of the aforementioned theorem by Hatami.


Title: The Total Matching Polytope of Complete Bipartite Graphs
Abstract: The total matching polytope generalizes the stable set polytope and the matching polytope. In this paper, we first propose new facet-defining inequalities for the total matching polytope. We then give an exponential-sized, non-redundant description in the original space and a compact description in an extended space of the total matching polytope of complete bipartite graphs.


Title: Buildings, spiders, and geometric Satake
Abstract: Let G be a simple algebraic group. Labelled trivalent graphs called webs can be used to product invariants in tensor products of minuscule representations. For each web, we construct a configuration space of points in the affine Grassmannian. Via the geometric Satake correspondence, we relate these configuration spaces to the invariant vectors coming from webs. In the case G = SL(3), non-elliptic webs yield a basis for the invariant spaces. The non-elliptic condition, which is equivalent to the condition that the dual diskoid of the web is CAT(0), is explained by the fact that affine buildings are CAT(0).


Title: A Hybrid Neural Coding Approach for Pattern Recognition with Spiking Neural Networks
Abstract: Recently, brain-inspired spiking neural networks (SNNs) have demonstrated promising capabilities in solving pattern recognition tasks. However, these SNNs are grounded on homogeneous neurons that utilize a uniform neural coding for information representation. Given that each neural coding scheme possesses its own merits and drawbacks, these SNNs encounter challenges in achieving optimal performance such as accuracy, response time, efficiency, and robustness, all of which are crucial for practical applications. In this study, we argue that SNN architectures should be holistically designed to incorporate heterogeneous coding schemes. As an initial exploration in this direction, we propose a hybrid neural coding and learning framework, which encompasses a neural coding zoo with diverse neural coding schemes discovered in neuroscience. Additionally, it incorporates a flexible neural coding assignment strategy to accommodate task-specific requirements, along with novel layer-wise learning methods to effectively implement hybrid coding SNNs. We demonstrate the superiority of the proposed framework on image classification and sound localization tasks. Specifically, the proposed hybrid coding SNNs achieve comparable accuracy to state-of-the-art SNNs, while exhibiting significantly reduced inference latency and energy consumption, as well as high noise robustness. This study yields valuable insights into hybrid neural coding designs, paving the way for developing high-performance neuromorphic systems.


Title: An Example of Evolutionary Computation + Large Language Model Beating Human: Design of Efficient Guided Local Search
Abstract: It is often very tedious for human experts to design efficient algorithms. Recently, we have proposed a novel Algorithm Evolution using Large Language Model (AEL) framework for automatic algorithm design. AEL combines the power of a large language model and the paradigm of evolutionary computation to design, combine, and modify algorithms automatically. In this paper, we use AEL to design the guide algorithm for guided local search (GLS) to solve the well-known traveling salesman problem (TSP). AEL automatically evolves elite GLS algorithms in two days, with minimal human effort and no model training. Experimental results on 1,000 TSP20-TSP100 instances and TSPLib instances show that AEL-designed GLS outperforms state-of-the-art human-designed GLS with the same iteration budget. It achieves a 0% gap on TSP20 and TSP50 and a 0.032% gap on TSP100 in 1,000 iterations. Our findings mark the emergence of a new era in automatic algorithm design.


Title: Speed Partitioning for Indexing Moving Objects
Abstract: Indexing moving objects has been extensively studied in the past decades. Moving objects, such as vehicles and mobile device users, usually exhibit some patterns on their velocities, which can be utilized for velocity-based partitioning to improve performance of the indexes. Existing velocity-based partitioning techniques rely on some kinds of heuristics rather than analytically calculate the optimal solution. In this paper, we propose a novel speed partitioning technique based on a formal analysis over speed values of the moving objects. We first show that speed partitioning will significantly reduce the search space expansion which has direct impacts on query performance of the indexes. Next we formulate the optimal speed partitioning problem based on search space expansion analysis and then compute the optimal solution using dynamic programming. We then build the partitioned indexing system where queries are duplicated and processed in each index partition. Extensive experiments demonstrate that our method dramatically improves the performance of indexes for moving objects and outperforms other state-of-the-art velocity-based partitioning approaches.


Title: A Case Study on Software Vulnerability Coordination
Abstract: Context: Coordination is a fundamental tenet of software engineering. Coordination is required also for identifying discovered and disclosed software vulnerabilities with Common Vulnerabilities and Exposures (CVEs). Motivated by recent practical challenges, this paper examines the coordination of CVEs for open source projects through a public mailing list. Objective: The paper observes the historical time delays between the assignment of CVEs on a mailing list and the later appearance of these in the National Vulnerability Database (NVD). Drawing from research on software engineering coordination, software vulnerabilities, and bug tracking, the delays are modeled through three dimensions: social networks and communication practices, tracking infrastructures, and the technical characteristics of the CVEs coordinated. Method: Given a period between 2008 and 2016, a sample of over five thousand CVEs is used to model the delays with nearly fifty explanatory metrics. Regression analysis is used for the modeling. Results: The results show that the CVE coordination delays are affected by different abstractions for noise and prerequisite constraints. These abstractions convey effects from the social network and infrastructure dimensions. Particularly strong effect sizes are observed for annual and monthly control metrics, a control metric for weekends, the degrees of the nodes in the CVE coordination networks, and the number of references given in NVD for the CVEs archived. Smaller but visible effects are present for metrics measuring the entropy of the emails exchanged, traces to bug tracking systems, and other related aspects. The empirical signals are weaker for the technical characteristics. Conclusion: [...]


Title: Multi-task learning for Joint Language Understanding and Dialogue State Tracking
Abstract: This paper presents a novel approach for multi-task learning of language understanding (LU) and dialogue state tracking (DST) in task-oriented dialogue systems. Multi-task training enables the sharing of the neural network layers responsible for encoding the user utterance for both LU and DST and improves performance while reducing the number of network parameters. In our proposed framework, DST operates on a set of candidate values for each slot that has been mentioned so far. These candidate sets are generated using LU slot annotations for the current user utterance, dialogue acts corresponding to the preceding system utterance and the dialogue state estimated for the previous turn, enabling DST to handle slots with a large or unbounded set of possible values and deal with slot values not seen during training. Furthermore, to bridge the gap between training and inference, we investigate the use of scheduled sampling on LU output for the current user utterance as well as the DST output for the preceding turn.


Title: Leveraging ParsBERT and Pretrained mT5 for Persian Abstractive Text Summarization
Abstract: Text summarization is one of the most critical Natural Language Processing (NLP) tasks. More and more researches are conducted in this field every day. Pre-trained transformer-based encoder-decoder models have begun to gain popularity for these tasks. This paper proposes two methods to address this task and introduces a novel dataset named pn-summary for Persian abstractive text summarization. The models employed in this paper are mT5 and an encoder-decoder version of the ParsBERT model (i.e., a monolingual BERT model for Persian). These models are fine-tuned on the pn-summary dataset. The current work is the first of its kind and, by achieving promising results, can serve as a baseline for any future work.


Title: Competitive Searching over Terrains
Abstract: We study a variant of the searching problem where the environment consists of a known terrain and the goal is to obtain visibility of an unknown target point on the surface of the terrain. The searcher starts on the surface of the terrain and is allowed to fly above the terrain. The goal is to devise a searching strategy that minimizes the competitive ratio, that is, the worst-case ratio between the distance traveled by the searching strategy and the minimum travel distance needed to detect the target. For $1.5$D terrains we show that any searching strategy has a competitive ratio of at least $\sqrt{82}$ and we present a nearly-optimal searching strategy that achieves a competitive ratio of $3\sqrt{19/2} \approx \sqrt{82} + 0.19$. This strategy extends directly to the case where the searcher has no knowledge of the terrain beforehand. For $2.5$D terrains we show that the optimal competitive ratio depends on the maximum slope $\lambda$ of the terrain, and is hence unbounded in general. Specifically, we provide a lower bound on the competitive ratio of $\Omega(\sqrt{\lambda})$. Finally, we complement the lower bound with a searching strategy based on the maximum slope of the known terrain, which achieves a competitive ratio of $O(\sqrt{\lambda})$.


Title: An Effective Baseline for Robustness to Distributional Shift
Abstract: Refraining from confidently predicting when faced with categories of inputs different from those seen during training is an important requirement for the safe deployment of deep learning systems. While simple to state, this has been a particularly challenging problem in deep learning, where models often end up making overconfident predictions in such situations. In this work we present a simple, but highly effective approach to deal with out-of-distribution detection that uses the principle of abstention: when encountering a sample from an unseen class, the desired behavior is to abstain from predicting. Our approach uses a network with an extra abstention class and is trained on a dataset that is augmented with an uncurated set that consists of a large number of out-of-distribution (OoD) samples that are assigned the label of the abstention class; the model is then trained to learn an effective discriminator between in and out-of-distribution samples. We compare this relatively simple approach against a wide variety of more complex methods that have been proposed both for out-of-distribution detection as well as uncertainty modeling in deep learning, and empirically demonstrate its effectiveness on a wide variety of of benchmarks and deep architectures for image recognition and text classification, often outperforming existing approaches by significant margins. Given the simplicity and effectiveness of this method, we propose that this approach be used as a new additional baseline for future work in this domain.


Title: Simplification of inclusion-exclusion on intersections of unions with application to network systems reliability
Abstract: Reliability of safety-critical systems is an important issue in system engineering and in most practical situations the reliability of a non series-parallel network system has to be calculated. Some methods for calculating reliability use the probability principle of inclusion-exclusion. When dealing with complex networks, this leads to very long mathematical expressions which are usually computationally very expensive to calculate. In this paper, we provide a new expression to simplify the probability principle of inclusion-exclusion's formula for intersections of unions, which appear when calculating reliability on non series parallel network systems. This new expression has much less terms, which reduces enormously the computational cost. We also show that the general form of the probability principle of inclusion-exclusion's formula has double exponential complexity whereas the simplified form has only exponential complexity with a linear exponent. Finally, we illustrate how to use this result when calculating the reliability of a door management system in aircraft engineering.


Title: Probability-graphons: Limits of large dense weighted graphs
Abstract: We introduce probability-graphons which are probability kernels that generalize graphons to the case of weighted graphs. Probability-graphons appear as the limit objects to study sequences of large weighted graphs whose distribution of subgraph sampling converge. The edge-weights are taken from a general Polish space, which also covers the case of decorated graphs. Here, graphs can be either directed or undirected. Starting from a distance $d_m$ inducing the weak topology on measures, we define a cut distance on probability-graphons, making it a Polish space, and study the properties of this cut distance. In particular, we exhibit a tightness criterion for probability-graphons related to relative compactness in the cut distance. We also prove that under some conditions on the distance $d_m$, which are satisfied for some well-know distances like the Prohorov distance, and the Fortet-Mourier and Kantorovitch-Rubinstein norms, the topology induced by the cut distance on the spaceof probability-graphons is independent from the choice of $d_m$. Eventually, we prove that this topology coincides with the topology induced by the convergence in distribution of the sampled subgraphs.


Title: Stable sets of primes in number fields
Abstract: We define a new class of sets -- stable sets -- of primes in number fields. For example, Chebotarev sets $P_{M/K}(\sigma)$, with $M/K$ Galois and $\sigma \in \Gal(M/K)$, are very often stable. These sets have positive (but arbitrary small) Dirichlet density and generalize sets with density 1 in the sense that arithmetic theorems like certain Hasse principles, the Grunwald-Wang theorem, the Riemann's existence theorem, etc. hold for them. Geometrically this allows to give examples of infinite sets $S$ with arbitrary small positive density such that $\Spec \mathcal{O}_{K,S}$ is algebraic $K(\pi,1)$ (for all $p$ simultaneous).


Title: Person Re-identification: Implicitly Defining the Receptive Fields of Deep Learning Classification Frameworks
Abstract: The \emph{receptive fields} of deep learning classification models determine the regions of the input data that have the most significance for providing correct decisions. The primary way to learn such receptive fields is to train the models upon masked data, which helps the networks to ignore any unwanted regions, but has two major drawbacks: 1) it often yields edge-sensitive decision processes; and 2) augments the computational cost of the inference phase considerably. This paper describes a solution for implicitly driving the inference of the networks' receptive fields, by creating synthetic learning data composed of interchanged segments that should be \emph{apriori} important/irrelevant for the network decision. In practice, we use a segmentation module to distinguish between the foreground (important)/background (irrelevant) parts of each learning instance, and randomly swap segments between image pairs, while keeping the class label exclusively consistent with the label of the deemed important segments. This strategy typically drives the networks to early convergence and appropriate solutions, where the identity and clutter descriptions are not correlated. Moreover, this data augmentation solution has various interesting properties: 1) it is parameter-free; 2) it fully preserves the label information; and, 3) it is compatible with the typical data augmentation techniques. In the empirical validation, we considered the person re-identification problem and evaluated the effectiveness of the proposed solution in the well-known \emph{Richly Annotated Pedestrian} (RAP) dataset for two different settings (\emph{upper-body} and \emph{full-body}), observing highly competitive results over the state-of-the-art. Under a reproducible research paradigm, both the code and the empirical evaluation protocol are available at \url{https://github.com/Ehsan-Yaghoubi/reid-strong-baseline}.


Title: UpFusion: Novel View Diffusion from Unposed Sparse View Observations
Abstract: We propose UpFusion, a system that can perform novel view synthesis and infer 3D representations for an object given a sparse set of reference images without corresponding pose information. Current sparse-view 3D inference methods typically rely on camera poses to geometrically aggregate information from input views, but are not robust in-the-wild when such information is unavailable/inaccurate. In contrast, UpFusion sidesteps this requirement by learning to implicitly leverage the available images as context in a conditional generative model for synthesizing novel views. We incorporate two complementary forms of conditioning into diffusion models for leveraging the input views: a) via inferring query-view aligned features using a scene-level transformer, b) via intermediate attentional layers that can directly observe the input image tokens. We show that this mechanism allows generating high-fidelity novel views while improving the synthesis quality given additional (unposed) images. We evaluate our approach on the Co3Dv2 and Google Scanned Objects datasets and demonstrate the benefits of our method over pose-reliant sparse-view methods as well as single-view methods that cannot leverage additional views. Finally, we also show that our learned model can generalize beyond the training categories and even allow reconstruction from self-captured images of generic objects in-the-wild.


Title: Polynomial-time Approximation Scheme for Equilibriums of Games
Abstract: Whether a PTAS (polynomial-time approximation scheme) exists for equilibriums of games has been an open question, which relates to the practicality of methods in algorithmic game theory and the problem of non-stationarity in training and curse of dimensionality in multi-agent reinforcement learning. This paper introduces our theory that implies a method that is sufficient and necessary to be the PTAS for perfect equilibriums of dynamic games. The theory consists of cone interior dynamic programming and primal-dual unbiased regret minimization. The former enables the dynamic programming operator to iteratively converge to a perfect equilibrium based on a concept called policy cone. The latter enables the line search method to approximate a Nash equilibrium based on two concepts called primal-dual bias and unbiased central path, solving a subproblem of the former. Validity of our discovery is cross-corroborated by a combination of theorem proofs, graphs of the three core concepts, and experimental results.


Title: Signal Detection for Ultra-Massive MIMO: An Information Geometry Approach
Abstract: In this paper, we propose an information geometry approach (IGA) for signal detection (SD) in ultra-massive multiple-input multiple-output (MIMO) systems. We formulate the signal detection as obtaining the marginals of the a posteriori probability distribution of the transmitted symbol vector. Then, a maximization of the a posteriori marginals (MPM) for signal detection can be performed. With the information geometry theory, we calculate the approximations of the a posteriori marginals. It is formulated as an iterative m-projection process between submanifolds with different constraints. We then apply the central-limit-theorem (CLT) to simplify the calculation of the m-projection since the direct calculation of the m-projection is of exponential-complexity. With the CLT, we obtain an approximate solution of the m-projection, which is asymptotically accurate. Simulation results demonstrate that the proposed IGA-SD emerges as a promising and efficient method to implement the signal detector in ultra-massive MIMO systems.


Title: The Knothe-Rosenblatt distance and its induced topology
Abstract: A basic and natural coupling between two probabilities on $\mathbb R^N$ is given by the Knothe-Rosenblatt coupling. It represents a multiperiod extension of the quantile coupling and is simple to calculate numerically. We consider the distance on $\mathcal P (\mathbb R^N)$ that is induced by considering the transport costs associated to the Knothe-Rosenblatt coupling. We show that this Knothe-Rosenblatt distance metrizes the adapted weak topology which is a stochastic process version of the usual weak topology and plays an important role, e.g. concerning questions on stability of stochastic control and probabilistic operations. We also establish that the Knothe-Rosenblatt distance is a geodesic distance, give a Skorokhod representation theorem for the adapted weak topology, and provide multi-dimensional versions of our results.


Title: Understanding Softmax Confidence and Uncertainty
Abstract: It is often remarked that neural networks fail to increase their uncertainty when predicting on data far from the training distribution. Yet naively using softmax confidence as a proxy for uncertainty achieves modest success in tasks exclusively testing for this, e.g., out-of-distribution (OOD) detection. This paper investigates this contradiction, identifying two implicit biases that do encourage softmax confidence to correlate with epistemic uncertainty: 1) Approximately optimal decision boundary structure, and 2) Filtering effects of deep networks. It describes why low-dimensional intuitions about softmax confidence are misleading. Diagnostic experiments quantify reasons softmax confidence can fail, finding that extrapolations are less to blame than overlap between training and OOD data in final-layer representations. Pre-trained/fine-tuned networks reduce this overlap.


Title: Towards an Automatic System for Extracting Planar Orientations from Software Generated Point Clouds
Abstract: In geology, a key activity is the characterisation of geological structures (surface formation topology and rock units) using Planar Orientation measurements such as Strike, Dip and Dip Direction. In general these measurements are collected manually using basic equipment; usually a compass/clinometer and a backboard, recorded on a map by hand. Various computing techniques and technologies, such as Lidar, have been utilised in order to automate this process and update the collection paradigm for these types of measurements. Techniques such as Structure from Motion (SfM) reconstruct of scenes and objects by generating a point cloud from input images, with detailed reconstruction possible on the decimetre scale. SfM-type techniques provide advantages in areas of cost and usability in more varied environmental conditions, while sacrificing the extreme levels of data fidelity. Here is presented a methodology of data acquisition and a Machine Learning-based software system: GeoStructure, developed to automate the measurement of orientation measurements. Rather than deriving measurements using a method applied to the input images, such as the Hough Transform, this method takes measurements directly from the reconstructed point cloud surfaces. Point cloud noise is mitigated using a Mahalanobis distance implementation. Significant structure is characterised using a k-nearest neighbour region growing algorithm, and final surface orientations are quantified using the plane, and normal direction cosines.


Title: Universal sequences of composition operators
Abstract: Let $G$ and $\Omega$ be two planar domains. We give necessary and sufficient conditions on a sequence $(\phi_n)$ of eventually injective holomorphic mappings from $G$ to $\Omega$ for the existence of a function $f\in H(\Omega)$ whose orbit under the composition by $(\phi_n)$ is dense in $H(G)$. This extends a result of the same nature obtained by Grosse-Erdmann and Mortini when $G=\Omega$. An interconnexion between the topological properties of $G$ and $\Omega$ appears. Further, in order to exhibit in a natural way holomorphic functions with wild boundary behaviour on planar domains, we study a certain type of universality for sequences of continuous mappings from a union of Jordan curves to a domain.


Title: Strongly minimal Steiner Systems III: Path graphs and sparse configurations
Abstract: We introduce a uniform method of proof for the following results. For {\em each} of the following conditions, there are $2^{\aleph_0}$ families of Steiner systems, satisfying that condition: i) Theorem~2.2.4: (extending \cite{Chicoetal}) each Steiner triple system is $\infty$-sparse and has a uniform but not perfect path graph; ii) (Theorem~5.4.2: (extending \cite{CameronWebb}) each Steiner $k$-system (for $k=p^n$) is $2$-transitive and has a uniform path graph (infinite cycles only); iii) Theorem~2.1.5: (extending \cite{Fujiwaramitre}, each is anti-Pasch (anti-mitre); iv) Theorem~3.6 has an explicit quasi-group structure. In each case all members of the family satisfy the same complete strongly minimal theory and it has $\aleph_0$ countable models and one model of each uncountable cardinal.


Title: Measurable functions on charge spaces
Abstract: The concept of measurability of functions on a charge space is generalised for functions taking values in a uniform space. Several existing forms of measurability generalise naturally in this context, and new forms of measurability are proposed. Conditions under which the various forms of measurability are logically equivalent are identified. Applying these concepts to real-valued functions, some recent characterisations of measurable functions on a bounded charge space are generalised to the unbounded case.


Title: Affine Metrics and Associated Algebroid Structures: Application to General Relativity
Abstract: In this paper, algebroid bundle associated to affine metrics provide an structure for unification of gravity and electromagnetism and, geometrization of matter.


Title: Channel Estimation for FAS-assisted Multiuser mmWave Systems
Abstract: This letter investigates the challenge of channel estimation in a multiuser millimeter-wave (mmWave) time-division duplexing (TDD) system. In this system, the base station (BS) employs a multi-antenna uniform linear array (ULA), while each mobile user is equipped with a fluid antenna system (FAS). Accurate channel state information (CSI) plays a crucial role in the precise placement of antennas in FAS. Traditional channel estimation methods designed for fixed-antenna systems are inadequate due to the high dimensionality of FAS. To address this issue, we propose a low-sample-size sparse channel reconstruction (L3SCR) method, capitalizing on the sparse propagation paths characteristic of mmWave channels. In this approach, each fluid antenna only needs to switch and measure the channel at a few specific locations. By observing this reduced-dimensional data, we can effectively extract angular and gain information related to the sparse channel, enabling us to reconstruct the full CSI. Simulation results demonstrate that our proposed method allows us to obtain precise CSI with minimal hardware switching and pilot overhead. As a result, the system sum-rate approaches the upper bound achievable with perfect CSI.


Title: The Zassenhaus variety of a reductive Lie algebra in positive characteristic
Abstract: Let g be the Lie algebra of a connected reductive group G over an algebraically closed field k of characteristic p>0. Let $Z$ be the centre of the universal enveloping algebra U=U(g) of g. Its maximal spectrum is called the Zassenhaus variety of g. We show that, under certain mild assumptions on G, the field of fractions Frac(Z) of Z is G-equivariantly isomorphic to the function field of the dual space g* with twisted G-action. In particular Frac(Z) is rational. This confirms a conjecture J. Alev. Furthermore we show that Z is a unique factorisation domain, confirming a conjecture of A. Braun and C. Hajarnavis. Recently, A. Premet used the above result about Frac(Z), a result of Colliot-Thelene, Kunyavskii, Popov and Reichstein and reduction mod p arguments to show that the Gelfand-Kirillov conjecture cannot hold for simple complex Lie algebras that are not of type A, C or G_2.


Title: Reconstructing almost all of a point set in $\mathbb{R}^d$ from randomly revealed pairwise distances
Abstract: Let $V$ be a set of $n$ points in $\mathbb{R}^d$, and suppose that the distance between each pair of points is revealed independently with probability $p$. We study when this information is sufficient to reconstruct large subsets of $V$, up to isometry. Strong results for $d=1$ have been obtained by Gir\~ao, Illingworth, Michel, Powierski, and Scott. In this paper, we investigate higher dimensions, and show that if $p>n^{-2/(d+4)}$, then we can reconstruct almost all of $V$ up to isometry, with high probability. We do this by relating it to a polluted graph bootstrap percolation result, for which we adapt the methods of Balogh, Bollob\'as, and Morris.


Title: On an inverse Robin spectral problem
Abstract: We consider the problem of the recovery of a Robin coefficient on a part $\gamma \subset \partial \Omega$ of the boundary of a bounded domain $\Omega$ from the principal eigenvalue and the boundary values of the normal derivative of the principal eigenfunction of the Laplace operator with Dirichlet boundary condition on $\partial \Omega \setminus \gamma$. We prove uniqueness, as well as local Lipschitz stability of the inverse problem. Moreover, we present an iterative reconstruction algorithm with numerical computations in two dimensions showing the accuracy of the method.


Title: Mechanism Design for Time Critical and Cost Critical Task Execution via Crowdsourcing
Abstract: An exciting application of crowdsourcing is to use social networks in complex task execution. In this paper, we address the problem of a planner who needs to incentivize agents within a network in order to seek their help in executing an {\em atomic task} as well as in recruiting other agents to execute the task. We study this mechanism design problem under two natural resource optimization settings: (1) cost critical tasks, where the planner's goal is to minimize the total cost, and (2) time critical tasks, where the goal is to minimize the total time elapsed before the task is executed. We identify a set of desirable properties that should ideally be satisfied by a crowdsourcing mechanism. In particular, {\em sybil-proofness} and {\em collapse-proofness} are two complementary properties in our desiderata. We prove that no mechanism can satisfy all the desirable properties simultaneously. This leads us naturally to explore approximate versions of the critical properties. We focus our attention on approximate sybil-proofness and our exploration leads to a parametrized family of payment mechanisms which satisfy collapse-proofness. We characterize the approximate versions of the desirable properties in cost critical and time critical domain.


Title: Quasi-Lie bialgebroids, Dirac structures and deformations of Poisson quasi-Nijenhuis manifolds
Abstract: We show how to deform a Poisson quasi-Nijenhuis manifold by means of a closed 2-form. Then we interpret this procedure in the context of quasi-Lie bialgebroids, as a particular case of the so called twisting of a quasi-Lie bialgebroid. Finally, we frame our result in the setting of Courant algebroids and Dirac structures.


Title: An Algorithm for Training Polynomial Networks
Abstract: We consider deep neural networks, in which the output of each node is a quadratic function of its inputs. Similar to other deep architectures, these networks can compactly represent any function on a finite training set. The main goal of this paper is the derivation of an efficient layer-by-layer algorithm for training such networks, which we denote as the \emph{Basis Learner}. The algorithm is a universal learner in the sense that the training error is guaranteed to decrease at every iteration, and can eventually reach zero under mild conditions. We present practical implementations of this algorithm, as well as preliminary experimental results. We also compare our deep architecture to other shallow architectures for learning polynomials, in particular kernel learning.


Title: Raphtory: The temporal graph engine for Rust and Python
Abstract: Raphtory is a platform for building and analysing temporal networks. The library includes methods for creating networks from a variety of data sources; algorithms to explore their structure and evolution; and an extensible GraphQL server for deployment of applications built on top. Raphtory's core engine is built in Rust, for efficiency, with Python interfaces, for ease of use. Raphtory is developed by network scientists, with a background in Physics, Applied Mathematics, Engineering and Computer Science, for use across academia and industry.


Title: Profinite equivariant spectra and their tensor-triangular geometry
Abstract: We study the tensor-triangular geometry of the category of equivariant $G$-spectra for $G$ a profinite group, $\mathsf{Sp}_G$. Our starting point is the construction of a ``continuous'' model for this category, which we show agrees with all other models in the literature. We describe the Balmer spectrum of finite $G$-spectra up to the ambiguity that is present in the finite group case; in particular, we obtain a thick subcategory theorem when $G$ is abelian. By verifying the bijectivity hypothesis for $\mathsf{Sp}_G$, we prove a nilpotence theorem for all profinite groups. Our study then moves to the realm of rational $G$-equivariant spectra. By exploiting the continuity of our model, we construct an equivalence between the category of rational $G$-spectra and the algebraic model of the second author and Sugrue, which improves their result to the symmetric monoidal and $\infty$-categorical level. Furthermore, we prove that the telescope conjecture holds in this category. Finally, we characterize when the category of rational $G$-spectra is stratified, resulting in a classification of the localizing ideals in terms of conjugacy classes of subgroups. To facilitate these results, we develop some foundational aspects of pro-tt-geometry. For instance, we establish and use the continuity of the homological spectrum and introduce a notion of von Neumann regular tt-categories, of which rational $G$-spectra is an example.


Title: Near Real-Time Data-Driven Control of Virtual Reality Traffic in Open Radio Access Network
Abstract: In mobile networks, Open Radio Access Network (ORAN) provides a framework for implementing network slicing that interacts with the resources at the lower layers. Both monitoring and Radio Access Network (RAN) control is feasible for both 4G and 5G systems. In this work, we consider how data-driven resource allocation in a 4G context can enable adaptive slice allocation to steer the experienced latency of Virtual Reality (VR) traffic towards a requested latency. We develop an xApp for the near real-time RAN Intelligent Controller (RIC) that embeds a heuristic algorithm for latency control, aiming to: (1) maintain latency of a VR stream around a requested value; and (2) improve the available RAN allocation to offer higher bit rate to another user. We have experimentally demonstrated the proposed approach in an ORAN testbed. Our results show that the data-driven approach can dynamically follow the variation of the traffic load while satisfying the required latency. This results in 15.8% more resources to secondary users than a latency-equivalent static allocation.


Title: Compensating trajectory bias for unsupervised patient stratification using adversarial recurrent neural networks
Abstract: Electronic healthcare records are an important source of information which can be used in patient stratification to discover novel disease phenotypes. However, they can be challenging to work with as data is often sparse and irregularly sampled. One approach to solve these limitations is learning dense embeddings that represent individual patient trajectories using a recurrent neural network autoencoder (RNN-AE). This process can be susceptible to unwanted data biases. We show that patient embeddings and clusters using previously proposed RNN-AE models might be impacted by a trajectory bias, meaning that results are dominated by the amount of data contained in each patients trajectory, instead of clinically relevant details. We investigate this bias on 2 datasets (from different hospitals) and 2 disease areas as well as using different parts of the patient trajectory. Our results using 2 previously published baseline methods indicate a particularly strong bias in case of an event-to-end trajectory. We present a method that can overcome this issue using an adversarial training scheme on top of a RNN-AE. Our results show that our approach can reduce the trajectory bias in all cases.


Title: Nested homotopy models of finite metric spaces and their spectral homology
Abstract: For a real $r\geq 0,$ we consider the notion of $r$-homotopy equivalence in the category quasimetric spaces, which includes metric spaces and directed graphs. We show that for a finite quasimetric space $X$ there is a unique (up to isometry) $r$-homotopy equivalent quasimetric space of the minimal possible cardinality. It is called $r$-minimal model of $X$. We use this to construct a decomposition of the magnitude-path spectral sequence of a digraph into a direct sum of spectral sequences with certain properties. We also construct an $r$-homotopy invariant ${\rm SH}^r_{n,I}(X)$ of a quasimetric space $X,$ called spectral homology, that generalises many other invariants: the pages of the magnitude-path spectral sequence, including path homology, magnitude homology, blurred magnitude homology and reachability homology.


Title: Will 6G be Semantic Communications? Opportunities and Challenges from Task Oriented and Secure Communications to Integrated Sensing
Abstract: This paper explores opportunities and challenges of task (goal)-oriented and semantic communications for next-generation (NextG) communication networks through the integration of multi-task learning. This approach employs deep neural networks representing a dedicated encoder at the transmitter and multiple task-specific decoders at the receiver, collectively trained to handle diverse tasks including semantic information preservation, source input reconstruction, and integrated sensing and communications. To extend the applicability from point-to-point links to multi-receiver settings, we envision the deployment of decoders at various receivers, where decentralized learning addresses the challenges of communication load and privacy concerns, leveraging federated learning techniques that distribute model updates across decentralized nodes. However, the efficacy of this approach is contingent on the robustness of the employed deep learning models. We scrutinize potential vulnerabilities stemming from adversarial attacks during both training and testing phases. These attacks aim to manipulate both the inputs at the encoder at the transmitter and the signals received over the air on the receiver side, highlighting the importance of fortifying semantic communications against potential multi-domain exploits. Overall, the joint and robust design of task-oriented communications, semantic communications, and integrated sensing and communications in a multi-task learning framework emerges as the key enabler for context-aware, resource-efficient, and secure communications ultimately needed in NextG network systems.


Title: Heat Kernel estimates for some elliptic operators with unbounded diffusion coefficients
Abstract: We prove heat kernel bounds for the operator (1 + |x|^{\alpha})\Delta in R^N, through Nash inequalities and weighted Hardy inequalities.