Title: Generalized Divide and Color models
Abstract: In this paper, we initiate the study of "Generalized Divide and Color Models". A very special interesting case of this is the "Divide and Color Model" (which motivates the name we use) introduced and studied by Olle H\"aggstr\"om. In this generalized model, one starts with a finite or countable set $V$, a random partition of $V$ and a parameter $p\in [0,1]$. The corresponding Generalized Divide and Color Model is the $\{0,1\}$-valued process indexed by $V$ obtained by independently, for each partition element in the random partition chosen, with probability $p$, assigning all the elements of the partition element the value 1, and with probability $1-p$, assigning all the elements of the partition element the value 0. Some of the questions which we study here are the following. Under what situations can different random partitions give rise to the same color process? What can one say concerning exchangeable random partitions? What is the set of product measures that a color process stochastically dominates? For random partitions which are translation invariant, what ergodic properties do the resulting color processes have? The motivation for studying these processes is twofold; on the one hand, we believe that this is a very natural and interesting class of processes that deserves investigation and on the other hand, a number of quite varied well-studied processes actually fall into this class such as (1) the Ising model, (2) the fuzzy Potts model, (3) the stationary distributions for the Voter Model, (4) random walk in random scenery and of course (5) the original Divide and Color Model.


Title: SuperEdge: Towards a Generalization Model for Self-Supervised Edge Detection
Abstract: Edge detection is a fundamental technique in various computer vision tasks. Edges are indeed effectively delineated by pixel discontinuity and can offer reliable structural information even in textureless areas. State-of-the-art heavily relies on pixel-wise annotations, which are labor-intensive and subject to inconsistencies when acquired manually. In this work, we propose a novel self-supervised approach for edge detection that employs a multi-level, multi-homography technique to transfer annotations from synthetic to real-world datasets. To fully leverage the generated edge annotations, we developed SuperEdge, a streamlined yet efficient model capable of concurrently extracting edges at pixel-level and object-level granularity. Thanks to self-supervised training, our method eliminates the dependency on manual annotated edge labels, thereby enhancing its generalizability across diverse datasets. Comparative evaluations reveal that SuperEdge advances edge detection, demonstrating improvements of 4.9% in ODS and 3.3% in OIS over the existing STEdge method on BIPEDv2.


Title: Unicron: Economizing Self-Healing LLM Training at Scale
Abstract: Training large-scale language models is increasingly critical in various domains, but it is hindered by frequent failures, leading to significant time and economic costs. Current failure recovery methods in cloud-based settings inadequately address the diverse and complex scenarios that arise, focusing narrowly on erasing downtime for individual tasks without considering the overall cost impact on a cluster. We introduce Unicron, a workload manager designed for efficient self-healing in large-scale language model training. Unicron optimizes the training process by minimizing failure-related costs across multiple concurrent tasks within a cluster. Its key features include in-band error detection for real-time error identification without extra overhead, a dynamic cost-aware plan generation mechanism for optimal reconfiguration, and an efficient transition strategy to reduce downtime during state changes. Deployed on a 128-GPU distributed cluster, Unicron demonstrates up to a 1.9x improvement in training efficiency over state-of-the-art methods, significantly reducing failure recovery costs and enhancing the reliability of large-scale language model training.


Title: Stochastic Approximation Approaches to Group Distributionally Robust Optimization
Abstract: This paper investigates group distributionally robust optimization (GDRO), with the purpose to learn a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem, and demonstrate that stochastic mirror descent (SMD), using $m$ samples in each iteration, achieves an $O(m (\log m)/\epsilon^2)$ sample complexity for finding an $\epsilon$-optimal solution, which matches the $\Omega(m/\epsilon^2)$ lower bound up to a logarithmic factor. Then, we make use of techniques from online learning to reduce the number of samples required in each round from $m$ to $1$, keeping the same sample complexity. Specifically, we cast GDRO as a two-players game where one player simply performs SMD and the other executes an online algorithm for non-oblivious multi-armed bandits. Next, we consider a more practical scenario where the number of samples that can be drawn from each distribution is different, and propose a novel formulation of weighted GDRO, which allows us to derive distribution-dependent convergence rates. Denote by $n_i$ the sample budget for the $i$-th distribution, and assume $n_1 \geq n_2 \geq \cdots \geq n_m$. In the first approach, we incorporate non-uniform sampling into SMD such that the sample budget is satisfied in expectation, and prove that the excess risk of the $i$-th distribution decreases at an $O(\sqrt{n_1 \log m}/n_i)$ rate. In the second approach, we use mini-batches to meet the budget exactly and also reduce the variance in stochastic gradients, and then leverage stochastic mirror-prox algorithm, which can exploit small variances, to optimize a carefully designed weighted GDRO problem. Under appropriate conditions, it attains an $O((\log m)/\sqrt{n_i})$ convergence rate, which almost matches the optimal $O(\sqrt{1/n_i})$ rate of only learning from the $i$-th distribution with $n_i$ samples.


Title: The relationship between Biological and Artificial Intelligence
Abstract: Intelligence can be defined as a predominantly human ability to accomplish tasks that are generally hard for computers and animals. Artificial Intelligence [AI] is a field attempting to accomplish such tasks with computers. AI is becoming increasingly widespread, as are claims of its relationship with Biological Intelligence. Often these claims are made to imply higher chances of a given technology succeeding, working on the assumption that AI systems which mimic the mechanisms of Biological Intelligence should be more successful. In this article I will discuss the similarities and differences between AI and the extent of our knowledge about the mechanisms of intelligence in biology, especially within humans. I will also explore the validity of the assumption that biomimicry in AI systems aids their advancement, and I will argue that existing similarity to biological systems in the way Artificial Neural Networks [ANNs] tackle tasks is due to design decisions, rather than inherent similarity of underlying mechanisms. This article is aimed at people who understand the basics of AI (especially ANNs), and would like to be better able to evaluate the often wild claims about the value of biomimicry in AI.


Title: Hyperlinear approximations to amenable groups come from sofic approximations
Abstract: We provide a quantitative formulation of the equivalence between hyperlinearity and soficity for amenable groups, showing that every hyperlinear approximation to such a group is essentially produced from a sofic approximation. The proof is probabilistic, using the concentration of measure in high dimensional spheres to control the deviation of an operator's matrix coefficients from its trace. As a corollary, we obtain a result connecting stability of sofic approximations with stability of hyperlinear approximations.


Title: Integration of physics-informed operator learning and finite element method for parametric learning of partial differential equations
Abstract: We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase contrast. Similar equations manifest in diverse applications like chemical diffusion, electrostatics, and Darcy flow. The neural network aims to establish the link between the complex thermal conductivity profiles and temperature distributions, as well as heat flux components within the microstructure, under fixed boundary conditions. A distinctive aspect is our independence from classical solvers like finite element methods for data. A noteworthy contribution lies in our novel approach to defining the loss function, based on the discretized weak form of the governing equation. This not only reduces the required order of derivatives but also eliminates the need for automatic differentiation in the construction of loss terms, accepting potential numerical errors from the chosen discretization method. As a result, the loss function in this work is an algebraic equation that significantly enhances training efficiency. We benchmark our methodology against the standard finite element method, demonstrating accurate yet faster predictions using the trained neural network for temperature and flux profiles. We also show higher accuracy by using the proposed method compared to purely data-driven approaches for unforeseen scenarios.


Title: Knutson ideals and determinantal ideals of Hankel matrices
Abstract: Motivated by a work of Knutson, in a recent paper Conca and Varbaro have defined a new class of ideals, namely "Knutson ideals", starting from a polynomial $f$ with squarefree leading term. We will show that the main properties that this class has in polynomial rings over fields of characteristic $p$ are preserved when one introduces the definition of Knutson ideal also in polynomial rings over fields of characteristic zero. Then we will show that determinantal ideals of Hankel matrices are Knutson ideals for a suitable choice of the polynomial $f$.


Title: Domination structure for number three
Abstract: From a research of several recent papers, in the first part, we are concerned with domination number in cubic graphs and give a sufficient condition of Reed's conjecture. In the second part, from a perspective, we study the structure of a minimum dominating set in 3-connected graphs. It is derived from a collection of cycles with length 0 mod 3.


Title: Stanley decompositions of modules of covariants
Abstract: For a complex reductive group $H$ with finite-dimensional representations $W$ and $U$, the module of covariants for $W$ of type $U$ is the space of all $H$-equivariant polynomial functions $W \longrightarrow U$. In this paper, we take $H$ to be one of the classical groups $\operatorname{GL}(V)$, $\operatorname{Sp}(V)$, or $\operatorname{O}(V)$ arising in Howe's dual pair setting, where $W$ is a direct sum of copies of $V$ and $V^*$. Our main result is a uniform combinatorial model for Stanley decompositions of the modules of covariants, using visualizations that we call jellyfish. Our decompositions allow us to interpret the Hilbert series as a positive combination of rational expressions which have concrete combinatorial interpretations in terms of lattice paths; significantly, this interpretation does not depend on the Cohen-Macaulay property. As a corollary, we recover a major result of Nishiyama-Ochiai-Taniguchi (2001) regarding the Bernstein degree of unitary highest weight $(\mathfrak{g},K)$-modules. We also extend our methods to compute the Hilbert series of the invariant rings for the groups $\operatorname{SL}(V)$ and $\operatorname{SO}(V)$, as well as the Wallach representations of type ADE.


Title: Radial Laplacian on rotation groups
Abstract: The Laplacian on the rotation group is invariant by conjugation. Hence, it maps class functions to class functions. A maximal torus consists of block diagonal matrices whose blocks are planar rotations. Class functions are determined by their values of this maximal torus. Hence, the Laplacian induces a second order operator on the maximal torus called the radial Laplacian. In this paper, we derive the expression of the radial Laplacian. Then, we use it to find the eigenvalues of the Laplacian, using that characters are class functions whose expressions are given by the Weyl character formula. Although this material is familiar to Lie-group experts, we gather it here in a synthetic and accessible way which may be useful to non experts who need to work with these concepts.


Title: Clairaut Anti-invariant Riemannian maps from/to Kähler manifolds admitting Ricci soliton
Abstract: The aim of this article is to study the Clairaut anti-invariant Riemannian maps from/to K\"ahler manifolds admitting Ricci solitons. We find the curvature relations and calculate the Ricci tensor under different conditions. We obtain conditions for the range and kernel of these maps to be Einstein. Next, we find the scalar curvature for range. Finally, we give some non-trivial examples of Clairaut anti-invariant Riemannian maps from/to K\"ahler manifolds admitting Ricci solitons.


Title: Fourier neural operator based fluid-structure interaction for predicting the vesicle dynamics
Abstract: Solving complex fluid-structure interaction (FSI) problems, characterized by nonlinear partial differential equations, is crucial in various scientific and engineering applications. Traditional computational fluid dynamics (CFD) solvers are insufficient to meet the growing requirements for large-scale and long-period simulations. Fortunately, the rapid advancement in neural networks, especially neural operator learning mappings between function spaces, has introduced novel approaches to tackle these challenges via data-driven modeling. In this paper, we propose a Fourier neural operator-based fluid-structure interaction solver (FNO-based FSI solver) for efficient simulation of FSI problems, where the solid solver based on the finite difference method is seamlessly integrated with the Fourier neural operator to predict incompressible flow using the immersed boundary method. We analyze the performance of the FNO-based FSI solver in the following three situations: training data with or without the steady state, training method with one-step label or multi-step labels, and prediction in interpolation or extrapolation. We find that the best performance for interpolation is achieved by training the operator with multi-step labels using steady-state data. Finally, we train the FNO-based FSI solver using this optimal training method and apply it to vesicle dynamics. The results show that the FNO-based FSI solver is capable of capturing the variations in the fluid and the vesicle.


Title: Synergizing Beyond Diagonal Reconfigurable Intelligent Surface and Rate-Splitting Multiple Access
Abstract: This work focuses on the synergy of rate-splitting multiple access (RSMA) and beyond diagonal reconfigurable intelligent surface (BD-RIS) to enlarge the coverage, improve the performance, and save on antennas. Specifically, we employ a multi-sector BD-RIS modeled as a prism, which can achieve highly directional full-space coverage, in a multiuser multiple input single output communication system. With the multi-sector BD-RIS aided RSMA model, we jointly design the transmit precoder and BD-RIS matrix under the imperfect channel state information (CSI) conditions. The robust design is performed by solving a stochastic average sum-rate maximization problem. With sample average approximation and weighted minimum mean square error-rate relationship, the stochastic problem is transformed into a deterministic one with multiple blocks, each of which is iteratively designed. Simulation results show that multi-sector BD-RIS aided RSMA outperforms space division multiple access schemes. More importantly, synergizing multi-sector BD-RIS with RSMA is an efficient strategy to reduce the number of active antennas at the transmitter and the number of passive antennas in BD-RIS.


Title: Self-Stabilizing Indulgent Zero-degrading Binary Consensus
Abstract: Guerraoui proposed an indulgent solution for the binary consensus problem. Namely, he showed that an arbitrary behavior of the failure detector never violates safety requirements even if it compromises liveness. Consensus implementations are often used in a repeated manner. Dutta and Guerraoui proposed a zero-degrading solution, \ie during system runs in which the failure detector behaves perfectly, a node failure during one consensus instance has no impact on the performance of future instances. Our study, which focuses on indulgent zero-degrading binary consensus, aims at the design of an even more robust communication abstraction. We do so through the lenses of self-stabilization - a very strong notion of fault-tolerance. In addition to node and communication failures, self-stabilizing algorithms can recover after the occurrence of arbitrary transient faults; these faults represent any violation of the assumptions according to which the system was designed to operate (as long as the algorithm code stays intact). This work proposes the first, to the best of our knowledge, self-stabilizing algorithm for indulgent zero-degrading binary consensus for time-free message-passing systems prone to detectable process failures. The proposed algorithm has an O(1) stabilization time (in terms of asynchronous cycles) from arbitrary transient faults. Since the proposed solution uses an {\Omega} failure detector, we also present the first, to the best of our knowledge, self-stabilizing asynchronous {\Omega} failure detector, which is a variation on the one by Most\'efaoui, Mourgaya, and Raynal.


Title: Speeding Up Distributed Machine Learning Using Codes
Abstract: Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes, system failures, or communication bottlenecks -- but there has been little interaction cutting across codes, machine learning, and distributed systems. In this work, we provide theoretical insights on how coded solutions can achieve significant gains compared to uncoded ones. We focus on two of the most basic building blocks of distributed learning algorithms: matrix multiplication and data shuffling. For matrix multiplication, we use codes to alleviate the effect of stragglers, and show that if the number of homogeneous workers is $n$, and the runtime of each subtask has an exponential tail, coded computation can speed up distributed matrix multiplication by a factor of $\log n$. For data shuffling, we use codes to reduce communication bottlenecks, exploiting the excess in storage. We show that when a constant fraction $\alpha$ of the data matrix can be cached at each worker, and $n$ is the number of workers, \emph{coded shuffling} reduces the communication cost by a factor of $(\alpha + \frac{1}{n})\gamma(n)$ compared to uncoded shuffling, where $\gamma(n)$ is the ratio of the cost of unicasting $n$ messages to $n$ users to multicasting a common message (of the same size) to $n$ users. For instance, $\gamma(n) \simeq n$ if multicasting a message to $n$ users is as cheap as unicasting a message to one user. We also provide experiment results, corroborating our theoretical gains of the coded algorithms.


Title: Knight's paths towards Catalan numbers
Abstract: We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the $x$-axis are enumerated by the generalized Catalan numbers, and we give a constructive bijection with peakless Motzkin paths of a given length. After enumerating partial knight's paths of a given length, we prove that zigzag knight's paths of a given length ending on the $x$-axis are counted by the Catalan numbers. Finally, we give a constructive bijection with Dyck paths of a given length.


Title: Composition method for chromatic symmetric functions: Neat noncommutative analogs
Abstract: This work is inspired by Shareshian and Wachs's exquisite formula for the chromatic symmetric function of paths. We develop a composition method to unearth neat noncommutative analogs of chromatic symmetric functions. A symmetric function is $e$-positive if and only if it has a $\Lambda$-positive noncommutative analog. We bring to light short and sweet $\Lambda$-positive noncommutative analogs for the chromatic symmetric functions of tadpoles and barbells, with cycles and lollipops as specifications. Using these elegant formulas and the composition method, we discover a new family of $e$-positive graphs and call them hats, which are the unicyclic graphs obtained by adding an edge to a path. A compact ribbon Schur analog for cycles is also obtained as a by-product.


Title: Simpler Specifications and Easier Proofs of Distributed Algorithms Using History Variables
Abstract: This paper studies specifications and proofs of distributed algorithms when only message history variables are used, using the Basic Paxos and Multi-Paxos algorithms for distributed consensus as precise case studies. We show that not using and maintaining other state variables yields simpler specifications that are more declarative and easier to understand. It also allows easier proofs to be developed by needing fewer invariants and facilitating proof derivations. Furthermore, the proofs are mechanically checked more efficiently. We show that specifications in TLA+, Lamport's temporal logic of actions, and proofs in TLAPS, the TLA+ Proof System (TLAPS) are reduced by a quarter or more for single-value Paxos and by about half or more for multi-value Paxos. Overall we need about half as many manually written invariants and proof obligations. Our proof for Basic Paxos takes about 25% less time for TLAPS to check, and our proofs for Multi-Paxos are checked within 1.5 minutes whereas prior proofs fail to be checked by TLAPS.


Title: Structure and Design of HoloGen
Abstract: Increasing popularity of augmented and mixed reality systems has seen a similar increase of interest in 2D and 3D computer generated holography (CGH). Unlike stereoscopic approaches, CGH can fully represent a light field including depth of focus, accommodation and vergence. Along with existing telecommunications, imaging, projection, lithography, beam shaping and optical tweezing applications, CGH is an exciting technique applicable to a wide array of photonic problems including full 3D representation. Traditionally, the primary roadblock to acceptance has been the significant numerical processing required to generate holograms requiring both significant expertise and significant computational power. This article discusses the structure and design of HoloGen. HoloGen is an MIT licensed application that may be used to generate holograms using a wide array of algorithms without expert guidance. HoloGen uses a Cuda C and C++ backend with a C# and Windows Presentation Framework graphical user interface. The article begins by introducing HoloGen before providing an in-depth discussion of its design and structure. Particular focus is given to the communication, data transfer and algorithmic aspects.


Title: On Classes of Fredholm Type Operators
Abstract: Given an idempotent $p$ in a Banach algebra and following the study in \cite{P50} of p-invertibility, we consider here left p-invertibility, right p-invertibility and p-invertibility in the Calkin Algebra $\mathcal{C}(X),$ where $X$ is a Banach space. Then we define and study left and right generalized Drazin invertibility and we characterize left and right Drazin invertible elements in the Calkin algebra. Globally, this leads to define and characterize the classes of P-Fredholm, pseudo B-Fredholm and weak B-Fredholm operators.


Title: Kernel Search approach to solve the Minimum Spanning Tree Problem with conflicting edge pairs
Abstract: The Minimum Spanning Tree Problem with Conflicts consists in finding the minimum conflict-free spanning tree of a graph, i.e., the spanning tree of minimum cost, including no pairs of edges that are in conflict. In this paper, we solve this problem using a tailored Kernel Search heuristic method, which consists in solving iteratively improved restrictions of the problem. The main novelty of the approach consists in using an independent set of the conflict graph within the algorithm. We test our approach on the benchmark instances and we compare our results with the ones obtained by other heuristics available in the literature.


Title: Quasi-streamwise vortices and enhanced dissipation for the incompressible 3D Navier-Stokes equations
Abstract: We consider the 3D incompressible Navier-Stokes equations under the following $2+\frac{1}{2}$-dimensional situation: vertical vortex blob (quasi-streamwise vortices) being stretched by two-dimensional shear flow. We prove enhanced dissipation induced by such quasi-streamwise vortices.


Title: Dorfman connections and Courant algebroids
Abstract: We define Dorfman connections, which are to Courant algebroids what connections are to Lie algebroids. Several examples illustrate this analogy. A linear connection $\nabla\colon \mathfrak{X}(M)\times\Gamma(E)\to\Gamma(E)$ on a vector bundle $E$ over a smooth manifold $M$ is tantamount to a linear splitting $TE\simeq T^{q_E}E\oplus H_\nabla$, where $T^{q_E}E$ is the set of vectors tangent to the fibres of $E$. Furthermore, the curvature of the connection measures the failure of the horizontal space $H_\nabla$ to be integrable. We show that linear horizontal complements to $T^{q_E}E\oplus (T^{q_E}E)^\circ$ in the Pontryagin bundle over the vector bundle $E$ can be described in the same manner via a certain class of Dorfman connections $\Delta\colon \Gamma(TM\oplus E^*)\times\Gamma(E\oplus T^*M)\to\Gamma(E\oplus T^*M)$. Similarly to the tangent bundle case, we find that, after the choice of a linear splitting, the standard Courant algebroid structure of $TE\oplus T^*E\to E$ can be completely described by properties of the Dorfman connection. As an application, we study splittings of $TA\oplus T^*A$ over a Lie algebroid $A$ and, following Gracia-Saz and Mehta, we compute the representations up to homotopy defined by any linear splitting of $TA\oplus T^*A$ and the linear Lie algebroid $TA\oplus T^*A\to TM\oplus A^*$. Further, we characterise VB- and LA-Dirac structures in $TA\oplus T^*A$ via Dorfman connections.


Title: A simple proof for generalized Fibonacci numbers with dying rabbits
Abstract: We consider the generalized Fibonacci counting problem with rabbits that become fertile at age $f$ and die at age $d$, with $1<=f<=d$ and $d$ finite or infinite. We provide a simple proof, based exclusively on a counting argumentation, for a recursive formula that gives the $n$th generalized Fibonacci number as a function of at most 3 previous numbers. The formula generalizes both the original Fibonacci sequence, for $f=2$ and $d=\infty$ (or $f=1$ and $d=2$), and other Fibonacci-related sequences, such as the Padovan sequence, for $f=2$ and $d=3$, the Tribonacci, for $f=1$ and $d=3$, Tetranacci, for $f=1$ and $d=4$, and alike sequences, for $f=1$ and finite values of $d$.


Title: Some Grönwall inequalities for a class of discretizations of time fractional equations on nonuniform meshes
Abstract: We consider the completely positive discretizations of fractional ordinary differential equations (FODEs) on nonuniform meshes. Making use of the resolvents for nonuniform meshes, we first establish comparison principles for the discretizations. Then we prove some discrete Gr\"onwall inequalities using the comparison principles and careful analysis of the solutions to the time continuous FODEs. Our results do not have any restrictions on the step size ratio. The Gr\"onwall inequalities for dissipative equations can be used to obtain the uniform-in-time error control and decay estimates of the numerical solutions. The Gr\"onwall inequalities are then applied to subdiffusion problems and the time fractional Allen-Cahn equations for illustration.


Title: Configuration space, moduli space and 3-fold covering space
Abstract: A function from configuration space to moduli space of surface may induce a homomorphism between their fundamental groups which are braid groups and mapping class groups of surface, respectively. This map $\phi: B_k \rightarrow \Gamma_{g,b}$ is induced by 3-fold branched covering over a disk with some branch points. In this thesis we give a concrete description of this map and show that it is injective by Birman-Hilden theory. This gives us a new interesting non-geometric embedding of braid group into mapping class group. On the other hand, we show that the map on the level of classifying spaces of groups is compatible with the action of little 2-cube operad so that it induces a trivial homomorphim between stable homology group of braid groups and that of mapping class groups(Harer conjecture). We also show how the lift $\tilde{\beta_i}$ acts on the fundamental group of the surface and through this we prove that $\tilde{\beta_i}$ equals the product of two inverse Dehn twists.


Title: Euclidean algorithms are Gaussian over imaginary quadratic fields
Abstract: The distributional analysis of Euclidean algorithms was carried out by Baladi and Vall\'{e}e. They showed the asymptotic normality of the number of division steps and associated costs in the Euclidean algorithm as a random variable on the set of rational numbers with bounded denominator based on the transfer operator methods. We extend their result to the Euclidean algorithm over appropriate imaginary quadratic fields by studying dynamics of the nearest integer complex continued fraction map, which is piecewise analytic and expanding but not a full branch map. By observing a finite Markov partition with a regular CW-structure, which enables us to associate the transfer operator acting on a direct sum of spaces of $C^1$-functions, we obtain the limit Gaussian distribution as well as residual equidistribution.


Title: Training Single-Layer Morphological Perceptron Using Convex-Concave Programming
Abstract: This paper concerns the training of a single-layer morphological perceptron using disciplined convex-concave programming (DCCP). We introduce an algorithm referred to as K-DDCCP, which combines the existing single-layer morphological perceptron (SLMP) model proposed by Ritter and Urcid with the weighted disciplined convex-concave programming (WDCCP) algorithm by Charisopoulos and Maragos. The proposed training algorithm leverages the disciplined convex-concave procedure (DCCP) and formulates a non-convex optimization problem for binary classification. To tackle this problem, the constraints are expressed as differences of convex functions, enabling the application of the DCCP package. The experimental results confirm the effectiveness of the K-DDCCP algorithm in solving binary classification problems. Overall, this work contributes to the field of morphological neural networks by proposing an algorithm that extends the capabilities of the SLMP model.


Title: VSFormer: Visual-Spatial Fusion Transformer for Correspondence Pruning
Abstract: Correspondence pruning aims to find correct matches (inliers) from an initial set of putative correspondences, which is a fundamental task for many applications. The process of finding is challenging, given the varying inlier ratios between scenes/image pairs due to significant visual differences. However, the performance of the existing methods is usually limited by the problem of lacking visual cues (\eg texture, illumination, structure) of scenes. In this paper, we propose a Visual-Spatial Fusion Transformer (VSFormer) to identify inliers and recover camera poses accurately. Firstly, we obtain highly abstract visual cues of a scene with the cross attention between local features of two-view images. Then, we model these visual cues and correspondences by a joint visual-spatial fusion module, simultaneously embedding visual cues into correspondences for pruning. Additionally, to mine the consistency of correspondences, we also design a novel module that combines the KNN-based graph and the transformer, effectively capturing both local and global contexts. Extensive experiments have demonstrated that the proposed VSFormer outperforms state-of-the-art methods on outdoor and indoor benchmarks. Our code is provided at the following repository: https://github.com/sugar-fly/VSFormer.


Title: Fractional hypergraph isomorphism and fractional invariants
Abstract: Fractional graph isomorphism is the linear relaxation of an integer programming formulation of graph isomorphism. It preserves some invariants of graphs, like degree sequences and equitable partitions, but it does not preserve others like connectivity, clique and independence numbers, chromatic number, vertex and edge cover numbers, matching number, domination and total domination numbers. In this work, we extend the concept of fractional graph isomorphism to hypergraphs, and give an alternative characterization, analogous to one of those that are known for graphs. With this new concept we prove that the fractional packing, covering, matching and transversal numbers on hypergraphs are invariant under fractional hypergraph isomorphism. As a consequence, fractional matching, vertex and edge cover, independence, domination and total domination numbers are invariant under fractional graph isomorphism. This is not the case of fractional chromatic, clique, and clique cover numbers. In this way, most of the classical fractional parameters are classified with respect to their invariance under fractional graph isomorphism.


Title: Reuse-Aware Cache Partitioning Framework for Data-Sharing Multicore Systems
Abstract: Multi-core processors improve performance, but they can create unpredictability owing to shared resources such as caches interfering. Cache partitioning is used to alleviate the Worst-Case Execution Time (WCET) estimation by isolating the shared cache across each thread to reduce interference. It does, however, prohibit data from being transferred between parallel threads running on different cores. In this paper we present (SRCP) a cache replacement mechanism for partitioned caches that is aware of data being shared across threads, prevents shared data from being replicated across partitions and frequently used data from being evicted from caches. Our technique outperforms TA-DRRIP and EHC, which are existing state-of-the-art cache replacement algorithms, by 13.34% in cache hit-rate and 10.4% in performance over LRU (least recently used) cache replacement policy.


Title: Braid variety cluster structures, II: general type
Abstract: We show that braid varieties for any complex simple algebraic group $G$ are cluster varieties. This includes open Richardson varieties inside the flag variety $G/B$.


Title: An upwind method for genuine weakly hyperbolic systems
Abstract: In this article, we attempted to develop an upwind scheme based on Flux Difference Splitting using Jordan canonical forms to simulate genuine weakly hyperbolic systems. Theory of Jordan Canonical Forms is being used to complete defective set of linear independent eigenvectors. Proposed FDS-J scheme is capable of recognizing various shocks accurately.


Title: Twice $Q$-polynomial distance-regular graphs of diameter 4
Abstract: It is known that a distance-regular graph with valency $k$ at least three admits at most two Q-polynomial structures. % In this note we show that all distance-regular graphs with diameter four and valency at least three admitting two $Q$-polynomial structures are either dual bipartite or almost dual imprimitive. By the work of Dickie \cite{Dickie} this implies that any distance-regular graph with diameter $d$ at least four and valency at least three admitting two $Q$-polynomial structures is, provided it is not a Hadamard graph, either the cube $H(d,2)$ with $d$ even, the half cube ${1}/{2} H(2d+1,2)$, the folded cube $\tilde{H}(2d+1,2)$, or the dual polar graph on $[^2A_{2d-1}(q)]$ with $q\ge 2$ a prime power.


Title: Influence Maximization in Ising Models
Abstract: Given a complex high-dimensional distribution over $\{\pm 1\}^n$, what is the best way to increase the expected number of $+1$'s by controlling the values of only a small number of variables? Such a problem is known as influence maximization and has been widely studied in social networks, biology, and computer science. In this paper, we consider influence maximization on the Ising model which is a prototypical example of undirected graphical models and has wide applications in many real-world problems. We establish a sharp computational phase transition for influence maximization on sparse Ising models under a bounded budget: In the high-temperature regime, we give a linear-time algorithm for finding a small subset of variables and their values which achieve nearly optimal influence; In the low-temperature regime, we show that the influence maximization problem cannot be solved in polynomial time under commonly-believed complexity assumption. The critical temperature coincides with the tree uniqueness/non-uniqueness threshold for Ising models which is also a critical point for other computational problems including approximate sampling and counting.


Title: Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
Abstract: In this work, we study the reproducing kernel (RK) collocation method for the peridynamic Navier equation. We first apply a linear RK approximation on both displacements and dilatation, then back-substitute dilatation, and solve the peridynamic Navier equation in a pure displacement form. The RK collocation scheme converges to the nonlocal limit and also to the local limit as nonlocal interactions vanish. The stability is shown by comparing the collocation scheme with the standard Galerkin scheme using Fourier analysis. We then apply the RK collocation to the quasi-discrete peridynamic Navier equation and show its convergence to the correct local limit when the ratio between the nonlocal length scale and the discretization parameter is fixed. The analysis is carried out on a special family of rectilinear Cartesian grids for the RK collocation method with a designated kernel with finite support. We assume the Lam\'{e} parameters satisfy $\lambda \geq \mu$ to avoid adding extra constraints on the nonlocal kernel. Finally, numerical experiments are conducted to validate the theoretical results.


Title: Ergodicity of skew products over linearly recurrent IETs
Abstract: We prove that the skew product over a linearly recurrent interval exchange transformation defined by almost any real-valued, mean-zero linear combination of characteristic functions of intervals is ergodic with respect to Lebesgue measure.


Title: A Simple Generalization of a Result for Random Matrices with Independent Sub-Gaussian Rows
Abstract: In this short note, we give a very simple but useful generalization of a result of Vershynin (Theorem 5.39 of [1]) for a random matrix with independent sub-Gaussian rows. We also explain with an example where our generalization is useful.


Title: Exponential sums, twisted multiplicativity and moments
Abstract: We study averages over squarefree moduli of the size of exponential sums with polynomial phases. We prove upper bounds on various moments of such sums, and obtain evidence of un-correlation of exponential sums associated to different suitably unrelated and generic polynomials. The proofs combine analytic arguments with the algebraic interpretation of exponential sums and their monodromy groups.


Title: State Space Decomposition and Subgoal Creation for Transfer in Deep Reinforcement Learning
Abstract: Typical reinforcement learning (RL) agents learn to complete tasks specified by reward functions tailored to their domain. As such, the policies they learn do not generalize even to similar domains. To address this issue, we develop a framework through which a deep RL agent learns to generalize policies from smaller, simpler domains to more complex ones using a recurrent attention mechanism. The task is presented to the agent as an image and an instruction specifying the goal. This meta-controller guides the agent towards its goal by designing a sequence of smaller subtasks on the part of the state space within the attention, effectively decomposing it. As a baseline, we consider a setup without attention as well. Our experiments show that the meta-controller learns to create subgoals within the attention.


Title: Hilbert space operators with compatible off-diagonal corners
Abstract: Given a complex, separable Hilbert space $\mathcal{H}$, we characterize those operators for which $\| P T (I-P) \| = \| (I-P) T P \|$ for all orthogonal projections $P$ on $\mathcal{H}$. When $\mathcal{H}$ is finite-dimensional, we also obtain a complete characterization of those operators for which $\mathrm{rank}\, (I-P) T P = \mathrm{rank}\, P T (I-P)$ for all orthogonal projections $P$. When $\mathcal{H}$ is infinite-dimensional, we show that any operator with the latter property is normal, and its spectrum is contained in either a line or a circle in the complex plane.


Title: Decomposable and atomic projection maps
Abstract: It is shown that a trace invariant projection map, i.e. a positive unital idempotent map, of a finite dimensional C*-algebra into itself is non-decomposable if and only if it is atomic, or equivalently not the sum of a 2-positive and a 2-copositive map. In particular projections onto spin factors of dimension greater than 6 are atomic.


Title: The Stanley Conjecture Revisited
Abstract: In the seminal work of Stanley, several conjectures were made on the structure of Littlewood-Richardson coefficients for the multiplication of Jack symmetric functions. Motivated by recent results of Alexandersson and the present author, we postulate that a certain 'windowing' property holds for all such Jack L-R coefficients. This property provides a vast set of relations between these coefficients and allows for their direct computation in certain novel cases. We demonstrate compatibility between our windowing conjecture and the conjectures of Stanley, with the hope of illuminating the structures within.


Title: Towards Higher Spectral Efficiency: Rate-2 Full-Diversity Complex Space-Time Block Codes
Abstract: The upcoming 5G networks demand high-speed and high spectral-efficiency communications to keep up with the proliferating traffic demands. To this end, Massive multiple-input multiple-output (MIMO) techniques have gained significant traction owing to its ability to achieve these without increasing bandwidth or density of base stations. The preexisting space-time block code (STBC) designs cannot achieve a rate of more than 1 for more than two transmit antennas while preserving the orthogonality and full diversity conditions. In this paper, we present Jagannath codes - a novel complex modulation STBC, that achieves a very high rate of 2 for three and four transmit antennas. The presented designs achieve full diversity and overcome the previously achieved rates with the three and four antenna MIMO systems. We present a detailed account of the code construction of the proposed designs, orthogonality and full diversity analysis, transceiver model and conditional maximum likelihood (ML) decoding. In an effort to showcase the improvement achieved with the presented designs, we compare the rates and delays of some of the known STBCs with the proposed designs. The effective spectral efficiency and coding gain of the presented designs are compared to the Asymmetric Coordinate Interleaved design (ACIOD) and Jafarkhani code. We presented an effective spectral efficiency improvement by a factor of 2 with the proposed Jagannath codes. Owing to the full diversity of the presented designs, we demonstrate significant coding gains (6 dB and 12 dB) with the proposed designs.


Title: Equivariant Morse theory for Lie algebra actions on Riemannian foliations
Abstract: Consider the transverse isometric action of a finite dimensional Lie algebra g on a Riemannian foliation. This paper studies the equivariant Morse-Bott theory on the leaf space of the Riemannian foliations in this setting. Among other things, we establish a foliated version of the Morse-Bott lemma for a g-invariant basic Morse-Bott function, and a foliated version of the usual handle presentation theorem. In the non-equivariant case, we apply these results to present a new proof of the Morse inequalities on Riemannian foliations. In the equivariant case, we apply these results to study Hamiltonian action of an abelian Lie algebra on a presymplectic manifold whose underlying foliation is also Riemannian, and extend the Kirwan surjectivity and injectivity theorem in equivariant symplectic geometry to this situation. Among other things, this implies the Kirwan surjectivity and injectivity hold for Hamiltonian torus actions on symplectic orbifolds.


Title: Multiplicity of normalized solutions for the fractional Schrödinger equation with potentials
Abstract: We get multiplicity of normalized solutions for the fractional Schr\"{o}dinger equation $$ (-\Delta)^su+V(\varepsilon x)u=\lambda u+h(\varepsilon x)f(u)\quad \mbox{in $\mathbb{R}^N$}, \qquad\int_{\mathbb{R}^N}|u|^2dx=a, $$ where $(-\Delta)^s$ is the fractional Laplacian, $s\in(0,1)$, $a,\varepsilon>0$, $\lambda\in\mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier, $V,h:\mathbb{R}^N\rightarrow[0,+\infty)$ are bounded and continuous, and $f$ is continuous function with $L^2$-subcritical growth. We prove that the numbers of normalized solutions are at least the numbers of global maximum points of $h$ when $\varepsilon$ is small enough.


Title: Modeling multiple taxis: tumor invasion with phenotypic heterogeneity, haptotaxis, and unilateral interspecies repellence
Abstract: We provide a short review of existing models with multiple taxis performed by (at least) one species and consider a new mathematical model for tumor invasion featuring two mutually exclusive cell phenotypes (migrating and proliferating). The migrating cells perform nonlinear diffusion and two types of taxis in response to non-diffusing cues: away from proliferating cells and up the gradient of surrounding tissue. Transitions between the two cell subpopulations are influenced by subcellular (receptor binding) dynamics, thus conferring the setting a multiscale character. We prove global existence of weak solutions to a simplified model version and perform numerical simulations for the full setting under several phenotype switching and motility scenarios. We also compare (via simulations) this model with the corresponding haptotaxis-chemotaxis one featuring indirect chemorepellent production and provide a discussion about possible model extensions and mathematical challenges.


Title: Chromatic symmetric function of graphs from Borcherds algebras
Abstract: Let $\mathfrak g$ be a Borcherds algebra with the associated graph $G$. We prove that the chromatic symmetric function of $G$ can be recovered from the Weyl denominator identity of $\mathfrak g$ and this gives a Lie theoretic proof of Stanley's expression for chromatic symmetric function in terms of power sum symmetric function. Also, this gives an expression for chromatic symmetric function of $G$ in terms of root multiplicities of $\lie g$. The absolute value of the linear coefficient of the chromatic polynomial of $G$ is known as the chromatic discriminant of $G$. As an application of our main theorem, we prove that graphs with different chromatic discriminants are distinguished by their chromatic symmetric functions. Also, we find a connection between the Weyl denominators and the $G$-elementary symmetric functions. Using this connection, we give a Lie theoretic proof of non-negativity of coefficients of $G$-power sum symmetric functions.


Title: Directional flow in perivascular networks: Mixed finite elements for reduced-dimensional models on graphs
Abstract: The flow of cerebrospinal fluid through the perivascular spaces of the brain is believed to play a crucial role in eliminating toxic waste proteins. While the driving forces of this flow have been enigmatic, experiments have shown that arterial wall motion is central. In this work, we present a network model for simulating pulsatile fluid flow in perivascular networks. We establish the well-posedness of this model in the primal and dual mixed variational settings, and show how it can be discretized using mixed finite elements. Further, we utilize this model to investigate fundamental questions concerning the physical mechanisms governing perivascular fluid flow. Notably, our findings reveal that arterial pulsations can induce directional flow in branching perivascular networks.


Title: Projections, Embeddings and Stability
Abstract: In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and practical implications; the theory applies even if the boundary operator is rank deficient, or near rank deficient. If desired, the pseudoinverse can be implemented directly using standard tools like Matlab. We also introduce a new and simplified version of the semidiscrete approximation of the linear PDE system, which completely avoids taking the time derivative of the boundary data. The stability results are valid for general, nondiagonal summation-by-parts norms. Another key result is the extension of summation-by-parts operators to multi-domains by means of carefully crafted embedding operators. No extra numerical boundary conditions are required at the grid interfaces. The aforementioned pseudoinverse allows for a compact representation of these multi-block operators, which preserves all relevant properties of the single-block operators. The embedding operators can be constructed for multiple space dimensions. Numerical results for the two-dimensional Maxwell's equations are presented, and they show very good agreement with theory.


Title: On the maximum of the weighted binomial sum $(1+a)^{-r}\sum_{i=0}^{r}\binom{m}{i}a^{i}$
Abstract: Recently, Glasby and Paseman considered the following sequence of binomial sums $\{2^{-r}\sum_{i=0}^{r}\binom{m}{i}\}_{r=0}^{m}$ and showed that this sequence is unimodal and attains its maximum value at $r=\lfloor\frac{m}{3}\rfloor+1$ for $m\in\mathbb{Z}_{\geq0}\setminus\{0,3,6,9,12\}$. They also analyzed the asymptotic behavior of the maximum value of the sequence as $m$ approaches infinity. In the present work, we generalize their results by considering the sequence $\{(1+a)^{-r}\sum_{i=0}^{r}\binom{m}{i}a^{i}\}_{r=0}^{m}$ for integers $a \geq 1$. We also consider a family of discrete probability distributions that naturally arises from this sequence.


Title: An Adaptive Incremental Gradient Method With Support for Non-Euclidean Norms
Abstract: Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some large-scale optimization tasks. To overcome the problem, we propose and analyze several novel adaptive variants of the popular SAGA algorithm. Eventually, we design a variant of Barzilai-Borwein step-size which is tailored for the incremental gradient method to ensure memory efficiency and fast convergence. We establish its convergence guarantees under general settings that allow non-Euclidean norms in the definition of smoothness and the composite objectives, which cover a broad range of applications in machine learning. We improve the analysis of SAGA to support non-Euclidean norms, which fills the void of existing work. Numerical experiments on standard datasets demonstrate a competitive performance of the proposed algorithm compared with existing variance-reduced methods and their adaptive variants.


Title: Efficient Scenario Generation for Chance-constrained Economic Dispatch Considering Ambient Wind Conditions
Abstract: Scenario generation is an effective data-driven method for solving chance-constrained optimization while ensuring desired risk guarantees with a finite number of samples. Crucial challenges in deploying this technique in the real world arise due to the absence of appropriate risk-tuning models tailored for the desired application. In this paper, we focus on designing efficient scenario generation schemes for economic dispatch in power systems. We propose a novel scenario generation method based on filtering scenarios using ambient wind conditions. These filtered scenarios are deployed incrementally in order to meet desired risk levels while using minimum resources. In order to study the performance of the proposed scheme, we illustrate the procedure on case studies performed for both 24-bus and 118-bus systems with real-world wind power forecasting data. Numerical results suggest that the proposed filter-and-increment scenario generation model leads to a precise and efficient solution for the chance-constrained economic dispatch problem.


Title: Inductive Synthesis of Finite-State Controllers for POMDPs
Abstract: We present a novel learning framework to obtain finite-state controllers (FSCs) for partially observable Markov decision processes and illustrate its applicability for indefinite-horizon specifications. Our framework builds on oracle-guided inductive synthesis to explore a design space compactly representing available FSCs. The inductive synthesis approach consists of two stages: The outer stage determines the design space, i.e., the set of FSC candidates, while the inner stage efficiently explores the design space. This framework is easily generalisable and shows promising results when compared to existing approaches. Experiments indicate that our technique is (i) competitive to state-of-the-art belief-based approaches for indefinite-horizon properties, (ii) yields smaller FSCs than existing methods for several models, and (iii) naturally treats multi-objective specifications.


Title: Graph Neural Networks for Tabular Data Learning: A Survey with Taxonomy and Directions
Abstract: In this survey, we dive into Tabular Data Learning (TDL) using Graph Neural Networks (GNNs), a domain where deep learning-based approaches have increasingly shown superior performance in both classification and regression tasks compared to traditional methods. The survey highlights a critical gap in deep neural TDL methods: the underrepresentation of latent correlations among data instances and feature values. GNNs, with their innate capability to model intricate relationships and interactions between diverse elements of tabular data, have garnered significant interest and application across various TDL domains. Our survey provides a systematic review of the methods involved in designing and implementing GNNs for TDL (GNN4TDL). It encompasses a detailed investigation into the foundational aspects and an overview of GNN-based TDL methods, offering insights into their evolving landscape. We present a comprehensive taxonomy focused on constructing graph structures and representation learning within GNN-based TDL methods. In addition, the survey examines various training plans, emphasizing the integration of auxiliary tasks to enhance the effectiveness of instance representations. A critical part of our discussion is dedicated to the practical application of GNNs across a spectrum of GNN4TDL scenarios, demonstrating their versatility and impact. Lastly, we discuss the limitations and propose future research directions, aiming to spur advancements in GNN4TDL. This survey serves as a resource for researchers and practitioners, offering a thorough understanding of GNNs' role in revolutionizing TDL and pointing towards future innovations in this promising area.


Title: Multimodal Sampling via Approximate Symmetries
Abstract: Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accelerate the samplings significantly. However, the distributions from most applications do not have exact symmetries. This paper considers the distributions with approximate symmetries. We first construct an exactly symmetric reference distribution from the target one by averaging over the group orbit associated with the approximate symmetry. Next, we can apply the multilevel Monte Carlo methods by constructing a continuation path between the reference and target distributions. We discuss how to implement these steps with annealed importance sampling and tempered transitions. Compared with traditional multilevel methods, the proposed approach can be more effective since the reference and target distributions are much closer. Numerical results of the Ising models are presented to illustrate the efficiency of the proposed method.


Title: Detection and Discovery of Misinformation Sources using Attributed Webgraphs
Abstract: Website reliability labels underpin almost all research in misinformation detection. However, misinformation sources often exhibit transient behavior, which makes many such labeled lists obsolete over time. We demonstrate that Search Engine Optimization (SEO) attributes provide strong signals for predicting news site reliability. We introduce a novel attributed webgraph dataset with labeled news domains and their connections to outlinking and backlinking domains. We demonstrate the success of graph neural networks in detecting news site reliability using these attributed webgraphs, and show that our baseline news site reliability classifier outperforms current SoTA methods on the PoliticalNews dataset, achieving an F1 score of 0.96. Finally, we introduce and evaluate a novel graph-based algorithm for discovering previously unknown misinformation news sources.


Title: On Newton polytopes of Lagrangian augmentations
Abstract: This note explores the use of Newton polytopes in the study of Lagrangian fillings of Legendrian submanifolds. In particular, we show that Newton polytopes associated to augmented values of Reeb chords can distinguish infinitely many distinct Lagrangian fillings, both for Legendrian links and higher-dimensional Legendrian spheres. The computations we perform work in finite characteristic, which significantly simplifies arguments and also allows us to show that there exist Legendrian links with infinitely many non-orientable exact Lagrangian fillings.


Title: Investigation of the Sense of Agency in Social Cognition, based on frameworks of Predictive Coding and Active Inference: A simulation study on multimodal imitative interaction
Abstract: When agents interact socially with different intentions, conflicts are difficult to avoid. Although how agents can resolve such problems autonomously has not been determined, dynamic characteristics of agency may shed light on underlying mechanisms. The current study focused on the sense of agency (SoA), a specific aspect of agency referring to congruence between the agent's intention in acting and the outcome. Employing predictive coding and active inference as theoretical frameworks of perception and action generation, we hypothesize that regulation of complexity in the evidence lower bound of an agent's model should affect the strength of the agent's SoA and should have a critical impact on social interactions. We built a computational model of imitative interaction between a robot and a human via visuo-proprioceptive sensation with a variational Bayes recurrent neural network, and simulated the model in the form of pseudo-imitative interaction using recorded human body movement data. A key feature of the model is that each modality's complexity can be regulated differently with a hyperparameter assigned to each module. We first searched for an optimal setting that endows the model with appropriate coordination of multimodal sensation. This revealed that the vision module's complexity should be more tightly regulated than that of the proprioception module. Using the optimally trained model, we examined how changing the tightness of complexity regulation after training affects the strength of the SoA during interactions. The results showed that with looser regulation, an agent tends to act more egocentrically, without adapting to the other. In contrast, with tighter regulation, the agent tends to follow the other by adjusting its intention. We conclude that the tightness of complexity regulation crucially affects the strength of the SoA and the dynamics of interactions between agents.


Title: Legendrians with vanishing Shelukhin-Chekanov-Hofer metric
Abstract: We show that the Legendrian lift of an exact, displaceable Lagrangian has vanishing Shelukhin-Chekanov-Hofer pseudo-metric by lifting an argument due to Sikorav to the contactization. In particular, this proves the existence of such Legendrians, providing counterexamples to a conjecture of Rosen and Zhang.


Title: Deep Learning Based Superposition Coded Modulation for Hierarchical Semantic Communications over Broadcast Channels
Abstract: We consider multi-user semantic communications over broadcast channels. While most existing works consider that each receiver requires either the same or independent semantic information, this paper explores the scenario where the semantic information desired by different receivers is different but correlated. In particular, we investigate semantic communications over Gaussian broadcast channels where the transmitter has a common observable source but the receivers wish to recover hierarchical semantic information in adaptation to their channel conditions. Inspired by the capacity achieving property of superposition codes, we propose a deep learning based superposition coded modulation (DeepSCM) scheme. Specifically, the hierarchical semantic information is first extracted and encoded into basic and enhanced feature vectors. A linear minimum mean square error (LMMSE) decorrelator is then developed to obtain a refinement from the enhanced features that is uncorrelated with the basic features. Finally, the basic features and their refinement are superposed for broadcasting after probabilistic modulation. Experiments are conducted for two-receiver image semantic broadcasting with coarse and fine classification as hierarchical semantic tasks. DeepSCM outperforms the benchmarking coded-modulation scheme without a superposition structure, especially with large channel disparity and high order modulation. It also approaches the performance upperbound as if there were only one receiver.


Title: Identifiability of Covariance Kernels in the Gaussian Process Regression Model
Abstract: Gaussian process regression (GPR) model is a popular nonparametric regression model. In GPR, features of the regression function such as varying degrees of smoothness and periodicities are modeled through combining various covarinace kernels, which are supposed to model certain effects. The covariance kernels have unknown parameters which are estimated by the EM-algorithm or Markov Chain Monte Carlo. The estimated parameters are keys to the inference of the features of the regression functions, but identifiability of these parameters has not been investigated. In this paper, we prove identifiability of covariance kernel parameters in two radial basis mixed kernel GPR and radial basis and periodic mixed kernel GPR. We also provide some examples about non-identifiable cases in such mixed kernel GPRs.


Title: On the shape factor of interaction laws for a non-local approximation of the Sobolev norm and the total variation
Abstract: We consider the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge to a multiple of the Sobolev norm or the total variation, depending on a summability exponent, but the exact values of the constants are unknown in many cases. We describe a new approach to the Gamma-convergence result that leads in some special cases to the exact value of the constants, and to the existence of smooth recovery families.


Title: Local limit theorem for time-inhomogeneous functions of Markov processes
Abstract: In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear dynamical systems.


Title: Hot Streaks on Social Media
Abstract: Measuring the impact and success of human performance is common in various disciplines, including art, science, and sports. Quantifying impact also plays a key role on social media, where impact is usually defined as the reach of a user's content as captured by metrics such as the number of views, likes, retweets, or shares. In this paper, we study entire careers of Twitter users to understand properties of impact. We show that user impact tends to have certain characteristics: First, impact is clustered in time, such that the most impactful tweets of a user appear close to each other. Second, users commonly have 'hot streaks' of impact, i.e., extended periods of high-impact tweets. Third, impact tends to gradually build up before, and fall off after, a user's most impactful tweet. We attempt to explain these characteristics using various properties measured on social media, including the user's network, content, activity, and experience, and find that changes in impact are associated with significant changes in these properties. Our findings open interesting avenues for future research on virality and influence on social media.


Title: Grassroots Social Networking: Where Members Own and Control their Personal Information and Social Graph
Abstract: Offering an architecture for social networking in which the members are in control of their personal information and social graph is an open challenge. Here we present a grassroots architecture for serverless, permissionless, peer-to-peer social networks termed Grassroots Social Networking that aims to address this challenge. The architecture is geared for roaming (address-changing) agents communicating over an unreliable network, e.g., smartphones communicating via UDP. The architecture incorporates (i) a decentralized social graph, where each member controls, maintains and stores only their local neighborhood in the graph; (ii) member-created feeds, with authors and followers who create and store the feeds; and (iii) a grassroots dissemination protocol, in which communication among members occurs only along the edges of the social graph. The architecture realizes these components using the blocklace data structure -- a distributed partially-ordered counterpart of the replicated totally-ordered blockchain. We provide two example Grassroots Social Networking protocols -- Twitter-like and WhatsApp-like -- and address their security (safety, liveness and privacy), spam/bot/deep-fake resistance, and implementation, demonstrating how server-based social networks could be supplanted by a grassroots architecture.


Title: Dynamic Packet Scheduler Optimization in Wireless Relay Networks
Abstract: In this work, we investigate the optimal dynamic packet scheduling policy in a wireless relay network (WRN). We model this network by two sets of parallel queues, that represent the subscriber stations (SS) and the relay stations (RS), with random link connectivity. An optimal policy minimizes, in stochastic ordering sense, the process of cost function of the SS and RS queue sizes. We prove that, in a system with symmetrical connectivity and arrival distributions, a policy that tries to balance the lengths of all the system queues, at every time slot, is optimal. We use stochastic dominance and coupling arguments in our proof. We also provide a low-overhead algorithm for optimal policy implementation.


Title: Stable cohomology of congruence subgroups
Abstract: We describe the $\mathbb{F}_p$-cohomology of the congruence subgroups $SL_n(\mathbb{Z}, p^m)$ in degrees $* < p$, for all large enough $n$, establishing a formula proposed by F. Calegari. Along the way, we also establish a formula for the stable cohomology of $SL_n(\mathbb{Z}/p)$ with certain twisted coefficients.


Title: On the Ideal Number of Groups for Isometric Gradient Propagation
Abstract: Recently, various normalization layers have been proposed to stabilize the training of deep neural networks. Among them, group normalization is a generalization of layer normalization and instance normalization by allowing a degree of freedom in the number of groups it uses. However, to determine the optimal number of groups, trial-and-error-based hyperparameter tuning is required, and such experiments are time-consuming. In this study, we discuss a reasonable method for setting the number of groups. First, we find that the number of groups influences the gradient behavior of the group normalization layer. Based on this observation, we derive the ideal number of groups, which calibrates the gradient scale to facilitate gradient descent optimization. Our proposed number of groups is theoretically grounded, architecture-aware, and can provide a proper value in a layer-wise manner for all layers. The proposed method exhibited improved performance over existing methods in numerous neural network architectures, tasks, and datasets.


Title: Local behavior for solutions to anisotropic weighted quasilinear degenerate parabolic equations
Abstract: This paper aims to study the local behavior of solutions to a class of anisotropic weighted quasilinear degenerate parabolic equations with the weights comprising two power-type weights of different dimensions. We first capture the asymptotic behavior of the solution near the singular or degenerate point of the weights. In particular, we find an explicit upper bound on the decay rate exponent determined by the structures of the equations and weights, which can be achieved under certain condition and meanwhile reflects the damage effect of the weights on the regularity of the solution. Furthermore, we prove the local H\"{o}lder regularity of solutions to non-homogeneous parabolic $p$-Laplace equations with single power-type weights.


Title: Radio Network Lower Bounds Made Easy
Abstract: Theoreticians have studied distributed algorithms in the radio network model for close to three decades. A significant fraction of this work focuses on lower bounds for basic communication problems such as wake-up (symmetry breaking among an unknown set of nodes) and broadcast (message dissemination through an unknown network topology). In this paper, we introduce a new technique for proving this type of bound, based on reduction from a probabilistic hitting game, that simplifies and strengthens much of this existing work. In more detail, in this single paper we prove new expected time and high probability lower bounds for wake-up and global broadcast in single and multichannel versions of the radio network model both with and without collision detection. In doing so, we are able to reproduce results that previously spanned a half-dozen papers published over a period of twenty-five years. In addition to simplifying these existing results, our technique, in many places, also improves the state of the art: of the eight bounds we prove, four strictly strengthen the best known previous result (in terms of time complexity and/or generality of the algorithm class for which it holds), and three provide the first known non-trivial bound for the case in question. The fact that the same technique can easily generate this diverse collection of lower bounds indicates a surprising unity underlying communication tasks in the radio network model---revealing that deep down, below the specifics of the problem definition and model assumptions, communication in this setting reduces to finding efficient strategies for a simple game.


Title: Cost Minimization in Multi-cloud Systems with Runtime Microservice Re-orchestration
Abstract: Multi-cloud systems facilitate a cost-efficient and geographically-distributed deployment of microservice-based applications by temporary leasing virtual nodes with diverse pricing models. To preserve the cost-efficiency of multi-cloud deployments, it is essential to redeploy microservices onto the available nodes according to a dynamic resource configuration, which is often performed to better accommodate workload variations. However, this approach leads to frequent service disruption since applications are continuously shutdown and redeployed in order to apply the new resource assignment. To overcome this issue, we propose a re-orchestration scheme that migrates microservice at runtime based on a rolling update scheduling logic. Specifically, we propose an integer linear optimization problem that minimizes the cost associated to multi-cloud virtual nodes and that ensures that delay-sensitive microservices are co-located on the same regional cluster. The resulting rescheduling order guarantees no service disruption by repacking microservices between the available nodes without the need to turn off the outdated microservice instance before redeploying the updated version. In addition, we propose a two-step heuristic scheme that effectively approximates the optimal solution at the expense of close-to-zero service disruption and QoS violation probability. Results show that proposed schemes achieve better performance in terms of cost mitigation, low service disruption and low QoS violation probability compared to baseline schemes replicating Kubernetes scheduler functionalities.


Title: Connected sums and directed systems in knot Floer homologies
Abstract: We prove a number of fundamental properties about instanton knot Floer homology. Our arguments rely on general properties of sutured Floer theories and apply also in the Heegaard Floer and monopole Floer settings, where many of our results were already known. Our main result is the connected sum formula for instanton knot Floer homology. An extension of this result proves the oriented skein exact triangle for the minus version of instanton knot Floer homology. Finally, we derive a new model of the minus version of instanton knot Floer homology, which takes the form of a free, finitely generated chain complex over a polynomial ring, as opposed to a direct limit. This construction is new to all of the Floer theories. We explore these results also in the context of Heegaard Floer theory as well.


Title: On Completely Edge-Independent Spanning Trees in Locally Twisted Cubes
Abstract: A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if any two of them are pairwisely edge-disjoint, they are called completely edge-independent spanning trees (CEISTs for short). CEISTs can facilitate many network functionalities, and constructing CEISTs as maximally allowed as possible in a given network is a worthy undertaking. In this paper, we establish the maximal number of CEISTs in the locally twisted cube network, and propose an algorithm to construct $\lfloor \frac{n}{2} \rfloor$ CEISTs in $LTQ_n$, the $n$-dimensional locally twisted cube. The proposed algorithm has been actually implemented, and we present the outputs. Network broadcasting in the $LTQ_n$ was simulated using $\lfloor\frac{n}{2}\rfloor$ CEISTs, and the performance compared with broadcasting using a single tree.


Title: Evaluating LLMs on Document-Based QA: Exact Answer Selection and Numerical Extraction using Cogtale dataset
Abstract: Document-based Question-Answering (QA) tasks are crucial for precise information retrieval. While some existing work focus on evaluating large language models performance on retrieving and answering questions from documents, assessing the LLMs performance on QA types that require exact answer selection from predefined options and numerical extraction is yet to be fully assessed. In this paper, we specifically focus on this underexplored context and conduct empirical analysis of LLMs (GPT-4 and GPT-3.5) on question types, including single-choice, yes-no, multiple-choice, and number extraction questions from documents in zero-shot setting. We use the CogTale dataset for evaluation, which provide human expert-tagged responses, offering a robust benchmark for precision and factual grounding. We found that LLMs, particularly GPT-4, can precisely answer many single-choice and yes-no questions given relevant context, demonstrating their efficacy in information retrieval tasks. However, their performance diminishes when confronted with multiple-choice and number extraction formats, lowering the overall performance of the model on this task, indicating that these models may not yet be sufficiently reliable for the task. This limits the applications of LLMs on applications demanding precise information extraction from documents, such as meta-analysis tasks. These findings hinge on the assumption that the retrievers furnish pertinent context necessary for accurate responses, emphasizing the need for further research. Our work offers a framework for ongoing dataset evaluation, ensuring that LLM applications for information retrieval and document analysis continue to meet evolving standards.


Title: Enriched Annotations for Tumor Attribute Classification from Pathology Reports with Limited Labeled Data
Abstract: Precision medicine has the potential to revolutionize healthcare, but much of the data for patients is locked away in unstructured free-text, limiting research and delivery of effective personalized treatments. Generating large annotated datasets for information extraction from clinical notes is often challenging and expensive due to the high level of expertise needed for high quality annotations. To enable natural language processing for small dataset sizes, we develop a novel enriched hierarchical annotation scheme and algorithm, Supervised Line Attention (SLA), and apply this algorithm to predicting categorical tumor attributes from kidney and colon cancer pathology reports from the University of California San Francisco (UCSF). Whereas previous work only annotated document level labels, we in addition ask the annotators to enrich the traditional label by asking them to also highlight the relevant line or potentially lines for the final label, which leads to a 20% increase of annotation time required per document. With the enriched annotations, we develop a simple and interpretable machine learning algorithm that first predicts the relevant lines in the document and then predicts the tumor attribute. Our results show across the small dataset sizes of 32, 64, 128, and 186 labeled documents per cancer, SLA only requires half the number of labeled documents as state-of-the-art methods to achieve similar or better micro-f1 and macro-f1 scores for the vast majority of comparisons that we made. Accounting for the increased annotation time, this leads to a 40% reduction in total annotation time over the state of the art.


Title: Atomistic modelling of near-crack-tip plasticity
Abstract: An atomistic model of near-crack-tip plasticity on a square lattice under anti-plane shear kinematics is formulated and studied. The model is based upon a new geometric and functional framework of a lattice manifold complex, which ensures that the crack surface is fully taken into account, while preserving the crucial notion of duality. As a result, existence of locally stable equilibrium configurations containing both a crack opening and dislocations is established. Notably, with the boundary in the form of a crack surface accounted for, no minimum separation between a dislocation core and the crack surface or the crack tip is required. The work presented here constitutes a foundation for several further studies aiming to put the phenomenon of near-crack-tip plasticity on a rigorous footing.


Title: A study in sums of products
Abstract: We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic number theory.


Title: The Impact of Distance on Performance and Scalability of Distributed Database Systems in Hybrid Clouds
Abstract: The increasing need for managing big data has led the emergence of advanced database management systems. There has been increased efforts aimed at evaluating the performance and scalability of NoSQL and Relational databases hosted by either private or public cloud datacenters. However, there has been little work on evaluating the performance and scalability of these databases in hybrid clouds, where the distance between private and public cloud datacenters can be one of the key factors that can affect their performance. Hence, in this paper, we present a detailed evaluation of throughput, scalability, and VMs size vs. VMs number for six modern databases in a hybrid cloud, consisting of a private cloud in Adelaide and Azure based datacenter in Sydney, Mumbai, and Virginia regions. Based on results, as the distance between private and public clouds increases, the throughput performance of most databases reduces. Second, MongoDB obtains the best throughput performance, followed by MySQL C luster, whilst Cassandra exposes the most fluctuation in through performance. Third, vertical scalability improves the throughput of databases more than the horizontal scalability. Forth, exploiting bigger VMs rather than more VMs with less cores can increase throughput performance for Cassandra, Riak, and Redis.


Title: Gradient Methods Never Overfit On Separable Data
Abstract: A line of recent works established that when training linear predictors over separable data, using gradient methods and exponentially-tailed losses, the predictors asymptotically converge in direction to the max-margin predictor. As a consequence, the predictors asymptotically do not overfit. However, this does not address the question of whether overfitting might occur non-asymptotically, after some bounded number of iterations. In this paper, we formally show that standard gradient methods (in particular, gradient flow, gradient descent and stochastic gradient descent) never overfit on separable data: If we run these methods for $T$ iterations on a dataset of size $m$, both the empirical risk and the generalization error decrease at an essentially optimal rate of $\tilde{\mathcal{O}}(1/\gamma^2 T)$ up till $T\approx m$, at which point the generalization error remains fixed at an essentially optimal level of $\tilde{\mathcal{O}}(1/\gamma^2 m)$ regardless of how large $T$ is. Along the way, we present non-asymptotic bounds on the number of margin violations over the dataset, and prove their tightness.


Title: A-infinity algebras, modules and functor categories
Abstract: In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis. Finally, starting from an idea of V. Lyubashenko's, we give a conceptual construction of A-infinity functor categories using a suitable closed monoidal category of cocategories. In particular, this yields a natural construction of the bialgebra structure on the bar construction of the Hochschild complex of an associative algebra.


Title: Byzantine-Resilient Gradient Coding through Local Gradient Computations
Abstract: We consider gradient coding in the presence of an adversary controlling so-called malicious workers trying to corrupt the computations. Previous works propose the use of MDS codes to treat the responses from malicious workers as errors and correct them using the error-correction properties of the code. This comes at the expense of increasing the replication, i.e., the number of workers each partial gradient is computed by. In this work, we propose a way to reduce the replication to $s+1$ instead of $2s+1$ in the presence of $s$ malicious workers. Our method detects erroneous inputs from the malicious workers, transforming them into erasures. This comes at the expense of $s$ additional local computations at the main node and additional rounds of light communication between the main node and the workers. We define a general framework and give fundamental limits for fractional repetition data allocations. Our scheme is optimal in terms of replication and local computation and incurs a communication cost that is asymptotically, in the size of the dataset, a multiplicative factor away from the derived bound. We furthermore show how additional redundancy can be exploited to reduce the number of local computations and communication cost, or, alternatively, tolerate straggling workers.


Title: Proof of Halin's normal spanning tree conjecture
Abstract: Halin conjectured 20 years ago that a graph has a normal spanning tree if and only if every minor of it has countable colouring number. We prove Halin's conjecture. This implies a forbidden minor characterisation for the property of having a normal spanning tree.


Title: A determinantal formula for orthosymplectic Schur functions
Abstract: We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J. Algebraic Combin., 2003) for general linear Lie superalgebras. Our proof uses the Jacobi--Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent. Math., 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J. Combin. Theory Ser. A, 2016).


Title: Dimension-Minimality and Primality of Counter Nets
Abstract: A $k$-Counter Net ($k$-CN) is a finite-state automaton equipped with $k$ integer counters that are not allowed to become negative, but do not have explicit zero tests. This language-recognition model can be thought of as labelled vector addition systems with states, some of which are accepting. Certain decision problems for $k$-CNs become easier, or indeed decidable, when the dimension $k$ is small. Yet, little is known about the effect that the dimension $k$ has on the class of languages recognised by $k$-CNs. Specifically, it would be useful if we could simplify algorithmic reasoning by reducing the dimension of a given CN. To this end, we introduce the notion of dimension-primality for $k$-CN, whereby a $k$-CN is prime if it recognises a language that cannot be decomposed into a finite intersection of languages recognised by $d$-CNs, for some $d<k$. We show that primality is undecidable. We also study two related notions: dimension-minimality (where we seek a single language-equivalent $d$-CN of lower dimension) and language regularity. Additionally, we explore the trade-offs in expressiveness between dimension and non-determinism for CN.


Title: An Edge-Cloud Collaboration Framework for Generative AI Service Provision with Synergetic Big Cloud Model and Small Edge Models
Abstract: Generative artificial intelligence (GenAI) offers various services to users through content creation, which is believed to be one of the most important components in future networks. However, training and deploying big artificial intelligence models (BAIMs) introduces substantial computational and communication overhead.This poses a critical challenge to centralized approaches, due to the need of high-performance computing infrastructure and the reliability, secrecy and timeliness issues in long-distance access of cloud services. Therefore, there is an urging need to decentralize the services, partly moving them from the cloud to the edge and establishing native GenAI services to enable private, timely, and personalized experiences. In this paper, we propose a brand-new bottom-up BAIM architecture with synergetic big cloud model and small edge models, and design a distributed training framework and a task-oriented deployment scheme for efficient provision of native GenAI services. The proposed framework can facilitate collaborative intelligence, enhance adaptability, gather edge knowledge and alleviate edge-cloud burden. The effectiveness of the proposed framework is demonstrated through an image generation use case. Finally, we outline fundamental research directions to fully exploit the collaborative potential of edge and cloud for native GenAI and BAIM applications.


Title: Popularity of patterns over $d$-equivalence classes of words and permutations
Abstract: Two same length words are $d$-equivalent if they have same descent set and same underlying alphabet. In particular, two same length permutations are $d$-equivalent if they have same descent set. The popularity of a pattern in a set of words is the overall number of copies of the pattern within the words of the set. We show the far-from-trivial fact that two patterns are $d$-equivalent if and only if they are equipopular over any $d$-equivalence class, and this equipopularity does not follow obviously from a trivial equidistribution.


Title: Probabilistic Galois Theory in Function Fields
Abstract: We study the irreducibility and Galois group of random polynomials over function fields. We prove that a random polynomial $f=y^n+\sum_{i=0}^{n-1}a_i(x)y^i\in\mathbb F_q[x][y]$ with i.i.d coefficients $a_i$ taking values in the set $\{a(x)\in\mathbb{F}_q[x]: \mathrm{deg}\, a\leq d\}$ with uniform probability, is irreducible with probability tending to $1-\frac{1}{q^d}$ as $n\to\infty$, where $d$ and $q$ are fixed. We also prove that with the same probability, the Galois group of this random polynomial contains the alternating group $A_n$. Moreover, we prove that if we assume a version of the polynomial Chowla conjecture over $\mathbb{F}_q[x]$, then the Galois group of this polynomial is actually equal to the symmetric group $S_n$ with probability tending to $1-\frac{1}{q^d}$. We also study the other possible Galois groups occurring with positive limit probability. Finally, we study the same problems with $n$ fixed and $d\to\infty$.


Title: Autonomous Driving Implementation in an Experimental Environment
Abstract: Autonomous systems require identifying the environment and it has a long way to go before putting it safely into practice. In autonomous driving systems, the detection of obstacles and traffic lights are of importance as well as lane tracking. In this study, an autonomous driving system is developed and tested in the experimental environment designed for this purpose. In this system, a model vehicle having a camera is used to trace the lanes and avoid obstacles to experimentally study autonomous driving behavior. Convolutional Neural Network models were trained for Lane tracking. For the vehicle to avoid obstacles, corner detection, optical flow, focus of expansion, time to collision, balance calculation, and decision mechanism were created, respectively.


Title: Detecting Hostile Posts using Relational Graph Convolutional Network
Abstract: This work is based on the submission to the competition Hindi Constraint conducted by AAAI@2021 for detection of hostile posts in Hindi on social media platforms. Here, a model is presented for detection and classification of hostile posts and further classify into fake, offensive, hate and defamation using Relational Graph Convolutional Networks. Unlike other existing work, our approach is focused on using semantic meaning along with contextutal information for better classification. The results from AAAI@2021 indicates that the proposed model is performing at par with Google's XLM-RoBERTa on the given dataset. Our best submission with RGCN achieves an F1 score of 0.97 (7th Rank) on coarse-grained evaluation and achieved best performance on identifying fake posts. Among all submissions to the challenge, our classification system with XLM-Roberta secured 2nd rank on fine-grained classification.


Title: On transfer maps in the algebraic $K$-theory of spaces
Abstract: We show that the Waldhausen trace map $\mathrm{Tr}_X \colon A(X) \to QX_+$, which defines a natural splitting map from the algebraic $K$-theory of spaces to stable homotopy, is natural up to \emph{weak} homotopy with respect to transfer maps in algebraic $K$-theory and Becker-Gottlieb transfer maps respectively.


Title: The Natural Selection of Conservative Science
Abstract: Social epistemologists have argued that high risk, high reward science has an important role to play in scientific communities. Recently, though, it has also been argued that various scientific fields seem to be trending towards conservatism -- the increasing production of what Kuhn (1970) would have called `normal science'. This paper will explore a possible explanation for this sort of trend: that the process by which scientific research groups form, grow, and dissolve might be inherently hostile to high risk science. In particular, I employ a paradigm developed by Smaldino and McElreath (2016) that treats a scientific community as a population undergoing selection. As will become clear, perhaps counter-intuitively this sort of process in some ways promotes high risk, high reward science. But, as I will point out, high risk high reward science is, in general, the sort of thing that is hard to repeat. While more conservative scientists will be able to train students capable of continuing their successful projects, and so create thriving lineages, successful risky science may not be the sort of thing one can easily pass on. In such cases, the structure of scientific communities selects against high risk, high rewards projects. More generally, this paper makes clear that there are at least two processes to consider in thinking about how incentives shape scientific communities -- the process by which individual scientists make choices about their careers and research, and the selective process governing the formation of new research groups.


Title: Image classification and retrieval with random depthwise signed convolutional neural networks
Abstract: We propose a random convolutional neural network to generate a feature space in which we study image classification and retrieval performance. Put briefly we apply random convolutional blocks followed by global average pooling to generate a new feature, and we repeat this k times to produce a k-dimensional feature space. This can be interpreted as partitioning the space of image patches with random hyperplanes which we formalize as a random depthwise convolutional neural network. In the network's final layer we perform image classification and retrieval with the linear support vector machine and k-nearest neighbor classifiers and study other empirical properties. We show that the ratio of image pixel distribution similarity across classes to within classes is higher in our network's final layer compared to the input space. When we apply the linear support vector machine for image classification we see that the accuracy is higher than if we were to train just the final layer of VGG16, ResNet18, and DenseNet40 with random weights. In the same setting we compare it to an unsupervised feature learning method and find our accuracy to be comparable on CIFAR10 but higher on CIFAR100 and STL10. We see that the accuracy is not far behind that of trained networks, particularly in the top-k setting. For example the top-2 accuracy of our network is near 90% on both CIFAR10 and a 10-class mini ImageNet, and 85% on STL10. We find that k-nearest neighbor gives a comparable precision on the Corel Princeton Image Similarity Benchmark than if we were to use the final layer of trained networks. As with other networks we find that our network fails to a black box attack even though we lack a gradient and use the sign activation. We highlight sensitivity of our network to background as a potential pitfall and an advantage. Overall our work pushes the boundary of what can be achieved with random weights.


Title: Approximating the Shapley Value without Marginal Contributions
Abstract: The Shapley value, which is arguably the most popular approach for assigning a meaningful contribution value to players in a cooperative game, has recently been used intensively in explainable artificial intelligence. Its meaningfulness is due to axiomatic properties that only the Shapley value satisfies, which, however, comes at the expense of an exact computation growing exponentially with the number of agents. Accordingly, a number of works are devoted to the efficient approximation of the Shapley value, most of them revolve around the notion of an agent's marginal contribution. In this paper, we propose with SVARM and Stratified SVARM two parameter-free and domain-independent approximation algorithms based on a representation of the Shapley value detached from the notion of marginal contribution. We prove unmatched theoretical guarantees regarding their approximation quality and provide empirical results including synthetic games as well as common explainability use cases comparing ourselves with state-of-the-art methods.


Title: ALOHA Receivers: a Network Calculus Approach for Analyzing Coded Multiple Access with SIC
Abstract: Motivated by the need to hide the complexity of the physical layer from performance analysis in a layer 2 protocol, a class of abstract receivers, called Poisson receivers, was recently proposed in [1] as a probabilistic framework for providing differentiated services in uplink transmissions in 5G networks. In this paper, we further propose a deterministic framework of ALOHA receivers that can be incorporated into the probabilistic framework of Poisson receivers for analyzing coded multiple access with successive interference cancellation. An ALOHA receiver is characterized by a success function of the number of packets that can be successfully received. Inspired by the theory of network calculus, we derive various algebraic properties for several operations on success functions and use them to prove various closure properties of ALOHA receivers, including (i) ALOHA receivers in tandem, (ii) cooperative ALOHA receivers, (iii) ALOHA receivers with traffic multiplexing, and (iv) ALOHA receivers with packet coding. By conducting extensive simulations, we show that our theoretical results match extremely well with the simulation results.