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Title: The jet transcendence degree of a real hypersurface and Huang-Ji-Yau Conjecture
Abstract: We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurface called {\em the jet transcendence degree}. Using this invariant, we solve in the negative the Conjecture of Huang, Ji and Yau on the algabraizability of real hypersurfaces with algebraic syzygies. | math | 0 |
Title: An equivariant generalisation of McDuff-Segal's group-completion theorem
Abstract: In this short note, we prove a G-equivariant generalisation of McDuff-Segal's group-completion theorem for finite groups G. A new complication regarding genuine equivariant localisations arises and we resolve this by isolating a simple condition on the homotopy groups of E-infinity-rings in G-spectra. We check that this condition is satisfied when our inputs are a suitable variant of E-infinity-monoids in G-spaces via the existence of multiplicative norm structures, thus giving a localisation formula for their associated G-spherical group rings. | math | 0 |
Title: Micro-macro Parareal, from ODEs to SDEs and back again
Abstract: In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver is applied as a corrector in parallel over smaller chunks of the time interval. Moreover, the coarse solver acts on a reduced state variable, which is coupled to the fine state variable through appropriate coupling operators. We first provide a contribution to the convergence analysis of the micro-macro Parareal method for multiscale linear ordinary differential equations (ODEs). Then, we extend a variant of the micro-macro Parareal algorithm for scalar stochastic differential equations (SDEs) to higher-dimensional SDEs. | math | 0 |
Title: Transversal and Paving Positroids
Abstract: In this paper, we study positroids and its overlap with two classes of matroids: transversal and paving matroids. We exhibit a new class of fundamental transversal matroids and classify the Le-diagram for rank two transversal positroids. We also establish a combinatorial description for paving positroids in terms of Le-diagrams. | math | 0 |
Title: Sharp density discrepancy for cut and project sets: An approach via lattice point counting
Abstract: Cut and project sets are obtained by taking an irrational slice of a lattice and projecting it to a lower dimensional subspace, and are fully characterised by the shape of the slice (window) and the choice of the lattice. In this context we seek to quantify fluctuations from the asymptotics for point counts. We obtain uniform upper bounds on the discrepancy depending on the diophantine properties of the lattice as well as universal lower bounds on the average of the discrepancy. In an appendix, Michael Bj\"orklund and Tobias Hartnick obtain lower bounds on the $L^2$-norm of the discrepancy also depending on the diophantine class; these lower bounds match our uniform upper bounds and both are therefore sharp. Using the sufficient criteria of Burago--Kleiner and Aliste-Prieto--Coronel--Gambaudo we find an explicit full-measure class of cut and project sets that are biLipschitz equivalent to lattices; the lower bounds on the variance indicate that this is the largest class of cut and project sets for which those sufficient criteria can apply. | math | 0 |
Title: On the Sample Complexity of Decentralized Linear Quadratic Regulator with Partially Nested Information Structure
Abstract: We study the problem of control policy design for decentralized state-feedback linear quadratic control with a partially nested information structure, when the system model is unknown. We propose a model-based learning solution, which consists of two steps. First, we estimate the unknown system model from a single system trajectory of finite length, using least squares estimation. Next, based on the estimated system model, we design a control policy that satisfies the desired information structure. We show that the suboptimality gap between our control policy and the optimal decentralized control policy (designed using accurate knowledge of the system model) scales linearly with the estimation error of the system model. Using this result, we provide an end-to-end sample complexity result for learning decentralized controllers for a linear quadratic control problem with a partially nested information structure. | math | 1 |
Title: Nonassociative $\mathrm{L}^p$-spaces and embeddings in noncommutative $\mathrm{L}^p$-spaces
Abstract: We define a notion of nonassociative $\mathrm{L}^p$-space associated to a $\mathrm{JBW}^*$-algebra (Jordan von Neumann algebra) equipped with a normal faithful state $\varphi$. In the particular case of $\mathrm{JW}^*$-algebras underlying von Neumann algebras, we connect these spaces to a complex interpolation theorem of Ricard and Xu on noncommutative $\mathrm{L}^p$-spaces. We also make the link with the nonassociative $\mathrm{L}^p$-spaces of Iochum associated to $\mathrm{JBW}$-algebras and the investigation of contractively complemented subspaces of noncommutative $\mathrm{L}^p$-spaces. More precisely, we show that our nonassociative $\mathrm{L}^p$-spaces contain isometrically the $\mathrm{L}^p$-spaces of Iochum and that all tracial nonassociative $\mathrm{L}^p$-spaces from $\mathrm{JW}^*$-factors arise as positively contractively complemented subspaces of noncommutative $\mathrm{L}^p$-spaces. | math | 0 |
Title: Three results on representations of Mackey Lie algebras
Abstract: I. Penkov and V. Serganova have recently introduced, for any non-degenerate pairing $W\otimes V\to\mathbb C$ of vector spaces, the Lie algebra $\mathfrak{gl}^M=\mathfrak{gl}^M(V,W)$ consisting of endomorphisms of $V$ whose duals preserve $W\subseteq V^*$. In their work, the category $\mathbb{T}_{\mathfrak{gl}^M}$ of $\mathfrak{gl}^M$-modules which are finite length subquotients of the tensor algebra $T(W\otimes V)$ is singled out and studied. In this note we solve three problems posed by these authors concerning the categories $\mathbb{T}_{\mathfrak{gl}^M}$. Denoting by $\mathbb{T}_{V\otimes W}$ the category with the same objects as $\mathbb{T}_{\mathfrak{gl}^M}$ but regarded as $V\otimes W$-modules, we first show that when $W$ and $V$ are paired by dual bases, the functor $\mathbb{T}_{\mathfrak{gl}^M}\to \mathbb{T}_{V\otimes W}$ taking a module to its largest weight submodule with respect to a sufficiently nice Cartan subalgebra of $V\otimes W$ is a tensor equivalence. Secondly, we prove that when $W$ and $V$ are countable-dimensional, the objects of $\mathbb{T}_{\mathrm{End}(V)}$ have finite length as $\mathfrak{gl}^M$-modules. Finally, under the same hypotheses, we compute the socle filtration of a simple object in $\mathbb{T}_{\mathrm{End}(V)}$ as a $\mathfrak{gl}^M$-module. | math | 1 |
Title: Combinatorial spectra using polynomials
Abstract: In this paper we would like to introduce some new methods for studying magic type-colorings of graphs or domination of graphs, based on combinatorial spectrum on polynomial rings. We hope that this concept will be potentially useful for the graph theorists. | math | 0 |
Title: Heisenberg uncertainty principle and its analogues in higher dimension: via Wigdersons' method
Abstract: The following question was proposed by Avi Wigderson and Yuval Wigderson: Is it possible to use the method in their paper(The uncertainty principle: variations on a theme) to prove Heisenberg uncertainty principle in higher dimension R^d, and get the correct dependence of the constant on d? We answer this question affirmatively, and also prove some generalizations of Heisenberg uncertainty principle in R^d via Wigdersons' method. | math | 0 |
Title: Height functions on Whitney umbrellas
Abstract: We study the singularities of the members of the family of height functions on Whitney umbrellas, which is also known as cross-caps, and show that the family of the height functions is a versal unfolding. Moreover, we study local intersections of a Whitney umbrella with a hyperplane through its singular point. | math | 1 |
Title: Depth-Regularized Optimization for 3D Gaussian Splatting in Few-Shot Images
Abstract: In this paper, we present a method to optimize Gaussian splatting with a limited number of images while avoiding overfitting. Representing a 3D scene by combining numerous Gaussian splats has yielded outstanding visual quality. However, it tends to overfit the training views when only a small number of images are available. To address this issue, we introduce a dense depth map as a geometry guide to mitigate overfitting. We obtained the depth map using a pre-trained monocular depth estimation model and aligning the scale and offset using sparse COLMAP feature points. The adjusted depth aids in the color-based optimization of 3D Gaussian splatting, mitigating floating artifacts, and ensuring adherence to geometric constraints. We verify the proposed method on the NeRF-LLFF dataset with varying numbers of few images. Our approach demonstrates robust geometry compared to the original method that relies solely on images. Project page: robot0321.github.io/DepthRegGS | cs | 0 |
Title: Resonances for homoclinic trapped sets
Abstract: We study semiclassical resonances generated by homoclinic trapped sets. First, under some general assumptions, we prove that there is no resonance in a region below the real axis. Then, we obtain a quantization rule and the asymptotic expansion of the resonances when there is a finite number of homoclinic trajectories. The same kind of results is proved for homoclinic sets of maximal dimension. Next, we generalize to the case of homoclinic/heteroclinic trajectories and we study the three bump case. In all these settings, the resonances may either accumulate on curves or form clouds. We also describe the corresponding resonant states. | math | 1 |
Title: The Total Matching Polytope of Complete Bipartite Graphs
Abstract: The total matching polytope generalizes the stable set polytope and the matching polytope. In this paper, we first propose new facet-defining inequalities for the total matching polytope. We then give an exponential-sized, non-redundant description in the original space and a compact description in an extended space of the total matching polytope of complete bipartite graphs. | cs | 0 |
Title: SPEER: Sentence-Level Planning of Long Clinical Summaries via Embedded Entity Retrieval
Abstract: Clinician must write a lengthy summary each time a patient is discharged from the hospital. This task is time-consuming due to the sheer number of unique clinical concepts covered in the admission. Identifying and covering salient entities is vital for the summary to be clinically useful. We fine-tune open-source LLMs (Mistral-7B-Instruct and Zephyr-7B-\b{eta}) on the task and find that they generate incomplete and unfaithful summaries. To increase entity coverage, we train a smaller, encoder-only model to predict salient entities, which are treated as content-plans to guide the LLM. To encourage the LLM to focus on specific mentions in the source notes, we propose SPEER: Sentence-level Planning via Embedded Entity Retrieval. Specifically, we mark each salient entity span with special "{{ }}" boundary tags and instruct the LLM to retrieve marked spans before generating each sentence. Sentence-level planning acts as a form of state tracking in that the model is explicitly recording the entities it uses. We fine-tune Mistral and Zephyr variants on a large-scale, diverse dataset of ~167k in-patient hospital admissions and evaluate on 3 datasets. SPEER shows gains in both coverage and faithfulness metrics over non-guided and guided baselines. | cs | 0 |
Title: Non-existence of three non-coalescing infinite geodesics with the same direction in the directed landscape
Abstract: It is believed that for metric-like models in the KPZ class the following property holds: with probability one, starting from any point, there are at most two semi-infinite geodesics with the same direction that do not coalesce. Until now, such a result was only proved for one model - exponential LPP (Coupier 11') using its inherent connection to the totally asymmetric exclusion process. We prove that the above property holds for the directed landscape, the universal scaling limit of models in the KPZ class. Our proof reduces the problem to one on line ensembles and therefore paves the way to show similar results for other metric-like models in the KPZ class. Finally, combining our result with the ones in (Busani, Seppalainen,Sorensen 22', Bhatia 23') we obtain the full qualitative geometric description of infinite geodesics in the directed landscape. | math | 0 |
Title: Minimum Coverage Sets for Training Robust Ad Hoc Teamwork Agents
Abstract: Robustly cooperating with unseen agents and human partners presents significant challenges due to the diverse cooperative conventions these partners may adopt. Existing Ad Hoc Teamwork (AHT) methods address this challenge by training an agent with a population of diverse teammate policies obtained through maximizing specific diversity metrics. However, prior heuristic-based diversity metrics do not always maximize the agent's robustness in all cooperative problems. In this work, we first propose that maximizing an AHT agent's robustness requires it to emulate policies in the minimum coverage set (MCS), the set of best-response policies to any partner policies in the environment. We then introduce the L-BRDiv algorithm that generates a set of teammate policies that, when used for AHT training, encourage agents to emulate policies from the MCS. L-BRDiv works by solving a constrained optimization problem to jointly train teammate policies for AHT training and approximating AHT agent policies that are members of the MCS. We empirically demonstrate that L-BRDiv produces more robust AHT agents than state-of-the-art methods in a broader range of two-player cooperative problems without the need for extensive hyperparameter tuning for its objectives. Our study shows that L-BRDiv outperforms the baseline methods by prioritizing discovering distinct members of the MCS instead of repeatedly finding redundant policies. | cs | 0 |
Title: Structural characterization of Cayley graphs
Abstract: We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertex-transitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle language, or just the same elementary cycle language. Under the assumption of the axiom of choice, we characterize the Cayley graphs for all group subsets as the deterministic, co-deterministic, vertex-transitive simple graphs. | cs | 1 |
Title: Preserving Image Properties Through Initializations in Diffusion Models
Abstract: Retail photography imposes specific requirements on images. For instance, images may need uniform background colors, consistent model poses, centered products, and consistent lighting. Minor deviations from these standards impact a site's aesthetic appeal, making the images unsuitable for use. We show that Stable Diffusion methods, as currently applied, do not respect these requirements. The usual practice of training the denoiser with a very noisy image and starting inference with a sample of pure noise leads to inconsistent generated images during inference. This inconsistency occurs because it is easy to tell the difference between samples of the training and inference distributions. As a result, a network trained with centered retail product images with uniform backgrounds generates images with erratic backgrounds. The problem is easily fixed by initializing inference with samples from an approximation of noisy images. However, in using such an approximation, the joint distribution of text and noisy image at inference time still slightly differs from that at training time. This discrepancy is corrected by training the network with samples from the approximate noisy image distribution. Extensive experiments on real application data show significant qualitative and quantitative improvements in performance from adopting these procedures. Finally, our procedure can interact well with other control-based methods to further enhance the controllability of diffusion-based methods. | cs | 0 |
Title: Actions, quotients and lattices of locally compact quantum groups
Abstract: We prove a number of property (T) permanence results for locally compact quantum groups under exact sequences and the presence of invariant states, analogous to their classical versions. Along the way we characterize the existence of invariant weights on quantum homogeneous spaces of quotient type, and relate invariant states for LCQG actions on von Neumann algebras to invariant vectors in canonical unitary implementations, providing an application to amenability. Finally, we introduce a notion of lattice in a locally compact quantum group, noting examples provided by Drinfeld doubles of compact quantum groups. We show that property (T) lifts from a lattice to the ambient LCQG, just as it does classically, thus obtaining new examples of non-classical, non-compact, non-discrete LCQGs with property (T). | math | 1 |
Title: Bayesian optimization for backpropagation in Monte-Carlo tree search
Abstract: In large domains, Monte-Carlo tree search (MCTS) is required to estimate the values of the states as efficiently and accurately as possible. However, the standard update rule in backpropagation assumes a stationary distribution for the returns, and particularly in min-max trees, convergence to the true value can be slow because of averaging. We present two methods, Softmax MCTS and Monotone MCTS, which generalize previous attempts to improve upon the backpropagation strategy. We demonstrate that both methods reduce to finding optimal monotone functions, which we do so by performing Bayesian optimization with a Gaussian process (GP) prior. We conduct experiments on computer Go, where the returns are given by a deep value neural network, and show that our proposed framework outperforms previous methods. | cs | 1 |
Title: Proportional 2-Choosability with a Bounded Palette
Abstract: Proportional choosability is a list coloring analogue of equitable coloring. Specifically, a $k$-assignment $L$ for a graph $G$ specifies a list $L(v)$ of $k$ available colors to each $v \in V(G)$. An $L$-coloring assigns a color to each vertex $v$ from its list $L(v)$. A proportional $L$-coloring of $G$ is a proper $L$-coloring in which each color $c \in \bigcup_{v \in V(G)} L(v)$ is used $\lfloor \eta(c)/k \rfloor$ or $\lceil \eta(c)/k \rceil$ times where $\eta(c)=\left\lvert{\{v \in V(G) : c \in L(v) \}}\right\rvert$. A graph $G$ is proportionally $k$-choosable if a proportional $L$-coloring of $G$ exists whenever $L$ is a $k$-assignment for $G$. Motivated by earlier work, we initiate the study of proportional choosability with a bounded palette by studying proportional 2-choosability with a bounded palette. In particular, when $\ell \geq 2$, a graph $G$ is said to be proportionally $(2, \ell)$-choosable if a proportional $L$-coloring of $G$ exists whenever $L$ is a $2$-assignment for $G$ satisfying $|\bigcup_{v \in V(G)} L(v)| \leq \ell$. We observe that a graph is proportionally $(2,2)$-choosable if and only if it is equitably 2-colorable. As $\ell$ gets larger, the set of proportionally $(2, \ell)$-choosable graphs gets smaller. We show that whenever $\ell \geq 5$ a graph is proportionally $(2, \ell)$-choosable if and only if it is proportionally 2-choosable. We also completely characterize the connected proportionally $(2, \ell)$-choosable graphs when $\ell = 3,4$. | math | 1 |
Title: Arithmetic progression in a finite field with prescribed norms
Abstract: Given a prime power $q$ and a positive integer $n$, let $\mathbb{F}_{q^{n}}$ represents a finite extension of degree $n$ of the finite field ${\mathbb{F}_{q}}$. In this article, we investigate the existence of $m$ elements in arithmetic progression, where every element is primitive and at least one is normal with prescribed norms. Moreover, for $n\geq6,q=3^k,m=2$ we establish that there are only $10$ possible exceptions. | math | 0 |
Title: Learning Pixel Trajectories with Multiscale Contrastive Random Walks
Abstract: A range of video modeling tasks, from optical flow to multiple object tracking, share the same fundamental challenge: establishing space-time correspondence. Yet, approaches that dominate each space differ. We take a step towards bridging this gap by extending the recent contrastive random walk formulation to much denser, pixel-level space-time graphs. The main contribution is introducing hierarchy into the search problem by computing the transition matrix between two frames in a coarse-to-fine manner, forming a multiscale contrastive random walk when extended in time. This establishes a unified technique for self-supervised learning of optical flow, keypoint tracking, and video object segmentation. Experiments demonstrate that, for each of these tasks, the unified model achieves performance competitive with strong self-supervised approaches specific to that task. Project webpage: https://jasonbian97.github.io/flowwalk | cs | 1 |
Title: Improved bounds for the bracketing number of orthants or revisiting an algorithm of Thiémard to compute bounds for the star discrepancy
Abstract: We improve the best known upper bound for the bracketing number of $d$-dimensional axis-parallel boxes anchored in $0$ (or, put differently, of lower left orthants intersected with the $d$-dimensional unit cube $[0,1]^d$). More precisely, we provide a better upper bound for the cardinality of an algorithmic bracketing cover construction due to Eric Thi\'emard, which forms the core of his algorithm to approximate the star discrepancy of arbitrary point sets from [E. Thi\'emard, An algorithm to compute bounds for the star discrepancy, J.~Complexity 17 (2001), 850 -- 880]. Moreover, the new upper bound for the bracketing number of anchored axis-parallel boxes yields an improved upper bound for the bracketing number of arbitrary axis-parallel boxes in $[0,1]^d$. In our upper bounds all constants are fully explicit. | math | 0 |
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. | math | 1 |
Title: Providing Self-Aware Systems with Reflexivity
Abstract: We propose a new type of self-aware systems inspired by ideas from higher-order theories of consciousness. First, we discussed the crucial distinction between introspection and reflexion. Then, we focus on computational reflexion as a mechanism by which a computer program can inspect its own code at every stage of the computation. Finally, we provide a formal definition and a proof-of-concept implementation of computational reflexion, viewed as an enriched form of program interpretation and a way to dynamically "augment" a computational process. | cs | 1 |
Title: Staircase symmetries in Hirzebruch surfaces
Abstract: This paper continues the investigation of staircases in the family of Hirzebruch surfaces formed by blowing up the projective plane with weight b, that was started in Bertozzi, Holm et al. in arXiv:2010.08567. We explain the symmetries underlying the structure of the set of b that admit staircases, and show how the properties of these symmetries arise from a governing Diophantine equation. We also greatly simplify the techniques needed to show that a family of steps does form a staircase by using arithmetic properties of the accumulation function. There should be analogous results about both staircases and mutations for the other rational toric domains considered, for example, by Cristofaro-Gardiner et al. in arXiv:2004.07829 and by Casals--Vianna in arXiv:2004.13232. | math | 1 |
Title: Orthogonal matroids over tracts
Abstract: We generalize Baker-Bowler's theory of matroids over tracts to orthogonal matroids, define orthogonal matroids with coefficients in tracts in terms of Wick functions, orthogonal signatures, circuit sets, and orthogonal vector sets, and establish basic properties on functoriality, duality, and minors. Our cryptomorphic definitions of orthogonal matroids over tracts provide proofs of several representation theorems for orthogonal matroids. In particular, we give a new proof that an orthogonal matroid is regular if and only if it is representable over $\mathbb{F}_2$ and $\mathbb{F}_3$, which was originally shown by Geelen, and we prove that an orthogonal matroid is representable over the sixth-root-of-unity partial field if and only if it is representable over $\mathbb{F}_3$ and $\mathbb{F}_4$. | math | 0 |
Title: Few-shot Adaptation of Multi-modal Foundation Models: A Survey
Abstract: Multi-modal (vision-language) models, such as CLIP, are replacing traditional supervised pre-training models (e.g., ImageNet-based pre-training) as the new generation of visual foundation models. These models with robust and aligned semantic representations learned from billions of internet image-text pairs and can be applied to various downstream tasks in a zero-shot manner. However, in some fine-grained domains like medical imaging and remote sensing, the performance of multi-modal foundation models often leaves much to be desired. Consequently, many researchers have begun to explore few-shot adaptation methods for these models, gradually deriving three main technical approaches: 1) prompt-based methods, 2) adapter-based methods, and 3) external knowledge-based methods. Nevertheless, this rapidly developing field has produced numerous results without a comprehensive survey to systematically organize the research progress. Therefore, in this survey, we introduce and analyze the research advancements in few-shot adaptation methods for multi-modal models, summarizing commonly used datasets and experimental setups, and comparing the results of different methods. In addition, due to the lack of reliable theoretical support for existing methods, we derive the few-shot adaptation generalization error bound for multi-modal models. The theorem reveals that the generalization error of multi-modal foundation models is constrained by three factors: domain gap, model capacity, and sample size. Based on this, we propose three possible solutions from the following aspects: 1) adaptive domain generalization, 2) adaptive model selection, and 3) adaptive knowledge utilization. | cs | 0 |
Title: Local well-posedness of a coupled Jordan-Moore-Gibson-Thompson-Pennes model of nonlinear ultrasonic heating
Abstract: In this work, we investigate a mathematical model of nonlinear ultrasonic heating based on the Jordan-Moore-Gibson-Thompson equation (JMGT) with temperature-dependent medium parameters coupled to the semilinear Pennes equation for the bioheat transfer. The equations are coupled via the temperature in the coefficients of the JMGT equation and via a nonlinear source term within the Pennes equation, which models the absorption of acoustic energy by the surrounding tissue. Using the energy method together with a fixed point argument, we prove that our model is locally well-posed, provided that the initial data are regular, small in a lower topology and the final time is short enough. | math | 0 |
Title: Nonlocal problems with critical Hardy nonlinearity
Abstract: By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical growth. | math | 1 |
Title: Covid19 Vaccine Acceptance and Deprivation in US Counties
Abstract: This report explores the central question of how socioeconomic status affects Covid19 vaccination rates in the United States, using existing open-source data. In general, a negative correlation exists between Area Deprivation Index (ADI) of a county and first dose, primary series and booster vaccination rates. Higher area deprivation correlated with polled vaccine hesitancy and lower search interest in vaccine interest, intention to vaccinate or concern about safety of vaccination. Positive correlations between ADI and certain mental health search trends were noted. No clear correlation between deprivation index and accessibility to vaccination sites were observed. In a small data sample, county level housing assistance policies and public information campaigns were noted to positively influence vaccine follow through rates. Finally, random forest, linear regression and KNN models were explored to validate the use of the above features for vaccine acceptance prediction. | cs | 0 |
Title: Representation Learning of Multivariate Time Series using Attention and Adversarial Training
Abstract: A critical factor in trustworthy machine learning is to develop robust representations of the training data. Only under this guarantee methods are legitimate to artificially generate data, for example, to counteract imbalanced datasets or provide counterfactual explanations for blackbox decision-making systems. In recent years, Generative Adversarial Networks (GANs) have shown considerable results in forming stable representations and generating realistic data. While many applications focus on generating image data, less effort has been made in generating time series data, especially multivariate signals. In this work, a Transformer-based autoencoder is proposed that is regularized using an adversarial training scheme to generate artificial multivariate time series signals. The representation is evaluated using t-SNE visualizations, Dynamic Time Warping (DTW) and Entropy scores. Our results indicate that the generated signals exhibit higher similarity to an exemplary dataset than using a convolutional network approach. | cs | 0 |
Title: C*-Algebras of one-sided subshifts over arbitrary alphabets
Abstract: We associate a C*-algebra $\widetilde{\mathcal{O}}_{\textsf{X}}$ with a subshift over an arbitrary, possibly infinite, alphabet. We show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is a full invariant for topological conjugacy of the subshifts of Ott, Tomforde, and Willis. When the alphabet is countable, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is an invariant for isometric conjugacy of subshifts with the product metric. For a suitable partial action associated with a subshift over a countable alphabet, we show that $\widetilde{\mathcal{O}}_{\textsf{X}}$ is also an invariant for continuous orbit equivalence. Additionally, we give a concrete way to compute the K-theory of $\widetilde{\mathcal{O}}_{\textsf{X}}$ and illustrate it with two examples. | math | 0 |
Title: Statistical Mechanical Analysis of Neural Network Pruning
Abstract: Deep learning architectures with a huge number of parameters are often compressed using pruning techniques to ensure computational efficiency of inference during deployment. Despite multitude of empirical advances, there is a lack of theoretical understanding of the effectiveness of different pruning methods. We inspect different pruning techniques under the statistical mechanics formulation of a teacher-student framework and derive their generalization error (GE) bounds. It has been shown that Determinantal Point Process (DPP) based node pruning method is notably superior to competing approaches when tested on real datasets. Using GE bounds in the aforementioned setup we provide theoretical guarantees for their empirical observations. Another consistent finding in literature is that sparse neural networks (edge pruned) generalize better than dense neural networks (node pruned) for a fixed number of parameters. We use our theoretical setup to prove this finding and show that even the baseline random edge pruning method performs better than the DPP node pruning method. We also validate this empirically on real datasets. | cs | 1 |
Title: Branch Prediction in Hardcaml for a RISC-V 32im CPU
Abstract: Accurate branch prediction is a critical part of high performance instruction stream processing. In this paper, I present a hardware implementation of branch prediction for a RV32IM CPU, starting with static decode stage predictions and culminating in the use of BATAGE. In addition, I detail my experience writing the RTL in Hardcaml, a hardware description library for the functional programming language OCaml. | cs | 0 |
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. | cs | 0 |
Title: Moduli spaces of orthogonal bundles over an algebraic curve
Abstract: We prove that the forgetful morphism from the moduli space of orthogonal bundles to the moduli space of vector bundles over a smooth curve is an embedding. Our proof relies on an explicit description of a set of generators for the invariants on the representation space of a quiver under the action of a product of classical groups. | math | 1 |
Title: Text mining arXiv: a look through quantitative finance papers
Abstract: This paper explores articles hosted on the arXiv preprint server with the aim to uncover valuable insights hidden in this vast collection of research. Employing text mining techniques and through the application of natural language processing methods, we examine the contents of quantitative finance papers posted in arXiv from 1997 to 2022. We extract and analyze crucial information from the entire documents, including the references, to understand the topics trends over time and to find out the most cited researchers and journals on this domain. Additionally, we compare numerous algorithms to perform topic modeling, including state-of-the-art approaches. | cs | 0 |
Title: MedSumm: A Multimodal Approach to Summarizing Code-Mixed Hindi-English Clinical Queries
Abstract: In the healthcare domain, summarizing medical questions posed by patients is critical for improving doctor-patient interactions and medical decision-making. Although medical data has grown in complexity and quantity, the current body of research in this domain has primarily concentrated on text-based methods, overlooking the integration of visual cues. Also prior works in the area of medical question summarisation have been limited to the English language. This work introduces the task of multimodal medical question summarization for codemixed input in a low-resource setting. To address this gap, we introduce the Multimodal Medical Codemixed Question Summarization MMCQS dataset, which combines Hindi-English codemixed medical queries with visual aids. This integration enriches the representation of a patient's medical condition, providing a more comprehensive perspective. We also propose a framework named MedSumm that leverages the power of LLMs and VLMs for this task. By utilizing our MMCQS dataset, we demonstrate the value of integrating visual information from images to improve the creation of medically detailed summaries. This multimodal strategy not only improves healthcare decision-making but also promotes a deeper comprehension of patient queries, paving the way for future exploration in personalized and responsive medical care. Our dataset, code, and pre-trained models will be made publicly available. | cs | 0 |
Title: Evaluating Trustworthiness of Online News Publishers via Article Classification
Abstract: The proliferation of low-quality online information in today's era has underscored the need for robust and automatic mechanisms to evaluate the trustworthiness of online news publishers. In this paper, we analyse the trustworthiness of online news media outlets by leveraging a dataset of 4033 news stories from 40 different sources. We aim to infer the trustworthiness level of the source based on the classification of individual articles' content. The trust labels are obtained from NewsGuard, a journalistic organization that evaluates news sources using well-established editorial and publishing criteria. The results indicate that the classification model is highly effective in classifying the trustworthiness levels of the news articles. This research has practical applications in alerting readers to potentially untrustworthy news sources, assisting journalistic organizations in evaluating new or unfamiliar media outlets and supporting the selection of articles for their trustworthiness assessment. | cs | 0 |
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. | math | 1 |
Title: Algebraic twists of modular forms and Hecke orbits
Abstract: We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistribution property for twisted Hecke orbits. This is done by exploiting the amplification method and the Riemann Hypothesis over finite fields, relying in particular on the ell-adic Fourier transform introduced by Deligne and studied by Katz and Laumon. | math | 1 |
Title: The Case for Bayesian Deep Learning
Abstract: The key distinguishing property of a Bayesian approach is marginalization instead of optimization, not the prior, or Bayes rule. Bayesian inference is especially compelling for deep neural networks. (1) Neural networks are typically underspecified by the data, and can represent many different but high performing models corresponding to different settings of parameters, which is exactly when marginalization will make the biggest difference for both calibration and accuracy. (2) Deep ensembles have been mistaken as competing approaches to Bayesian methods, but can be seen as approximate Bayesian marginalization. (3) The structure of neural networks gives rise to a structured prior in function space, which reflects the inductive biases of neural networks that help them generalize. (4) The observed correlation between parameters in flat regions of the loss and a diversity of solutions that provide good generalization is further conducive to Bayesian marginalization, as flat regions occupy a large volume in a high dimensional space, and each different solution will make a good contribution to a Bayesian model average. (5) Recent practical advances for Bayesian deep learning provide improvements in accuracy and calibration compared to standard training, while retaining scalability. | cs | 1 |
Title: Performance Trade-off and Joint Waveform Design for MIMO-OFDM DFRC Systems
Abstract: Dual-functional radar-communication (DFRC) has attracted considerable attention. This paper considers the frequency-selective multipath fading environment and proposes DFRC waveform design strategies based on multiple-input and multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) techniques. In the proposed waveform design strategies, the Cramer-Rao bound (CRB) of the radar system, the inter-stream interference (ISI) and the achievable rate of the communication system, are respectively considered as the performance metrics. In this paper, we focus on the performance trade-off between the radar system and the communication system, and the optimization problems are formulated. In the ISI minimization based waveform design strategy, the optimization problem is convex and can be easily solved. In the achievable rate maximization based waveform design strategy, we propose a water-filling (WF) and sequential quadratic programming (SQP) based algorithm to derive the covariance matrix and the precoding matrix. Simulation results validate the proposed DFRC waveform designs and show that the achievable rate maximization based strategy has a better performance than the ISI minimization based strategy. | cs | 0 |
Title: Extension of the Topological Abel-Jacobi Map for Cubic Threefolds
Abstract: The difference $[L_1]-[L_2]$ of a pair of skew lines on a cubic threefold defines a vanishing cycle on the cubic surface as the hyperplane section spanned by the two lines. By deforming the hyperplane, the flat translation of such vanishing cycle forms a 72-to-1 covering space $T_v$ of a Zariski open subspace of $(\mathbb P^4)^*$. Based on a lemma of Stein on the compactification of finite analytic covers, we found a compactification of $T_v$ to which the topological Abel-Jacobi map extends. Moreover, the boundary points of the compactification can be interpreted in terms of local monodromy and the singularities on cubic surfaces. We prove the associated map on fundamental groups of topological Abel-Jacobi map is surjective. | math | 0 |
Title: Predictive Multiplicity in Probabilistic Classification
Abstract: Machine learning models are often used to inform real world risk assessment tasks: predicting consumer default risk, predicting whether a person suffers from a serious illness, or predicting a person's risk to appear in court. Given multiple models that perform almost equally well for a prediction task, to what extent do predictions vary across these models? If predictions are relatively consistent for similar models, then the standard approach of choosing the model that optimizes a penalized loss suffices. But what if predictions vary significantly for similar models? In machine learning, this is referred to as predictive multiplicity i.e. the prevalence of conflicting predictions assigned by near-optimal competing models. In this paper, we present a framework for measuring predictive multiplicity in probabilistic classification (predicting the probability of a positive outcome). We introduce measures that capture the variation in risk estimates over the set of competing models, and develop optimization-based methods to compute these measures efficiently and reliably for convex empirical risk minimization problems. We demonstrate the incidence and prevalence of predictive multiplicity in real-world tasks. Further, we provide insight into how predictive multiplicity arises by analyzing the relationship between predictive multiplicity and data set characteristics (outliers, separability, and majority-minority structure). Our results emphasize the need to report predictive multiplicity more widely. | cs | 1 |
Title: Mesoscopic averaging of the two-dimensional KPZ equation
Abstract: We study the limit of a local average of the KPZ equation in dimension $d=2$ with general initial data in the subcritical regime. Our result shows that a proper spatial averaging of the KPZ equation converges in distribution to the sum of the solution to a deterministic KPZ equation and a Gaussian random variable that depends solely on the scale of averaging. This shows a unique mesoscopic averaging phenomenon that is only present in dimension two. Our work is inspired by the recent findings by Chatterjee \cite{chatterjee2021weak}. | math | 0 |
Title: Do DL models and training environments have an impact on energy consumption?
Abstract: Current research in the computer vision field mainly focuses on improving Deep Learning (DL) correctness and inference time performance. However, there is still little work on the huge carbon footprint that has training DL models. This study aims to analyze the impact of the model architecture and training environment when training greener computer vision models. We divide this goal into two research questions. First, we analyze the effects of model architecture on achieving greener models while keeping correctness at optimal levels. Second, we study the influence of the training environment on producing greener models. To investigate these relationships, we collect multiple metrics related to energy efficiency and model correctness during the models' training. Then, we outline the trade-offs between the measured energy efficiency and the models' correctness regarding model architecture, and their relationship with the training environment. We conduct this research in the context of a computer vision system for image classification. In conclusion, we show that selecting the proper model architecture and training environment can reduce energy consumption dramatically (up to 81.38%) at the cost of negligible decreases in correctness. Also, we find evidence that GPUs should scale with the models' computational complexity for better energy efficiency. | cs | 0 |
Title: Functional central limit theorems for stick-breaking priors
Abstract: We obtain the empirical strong law of large numbers, empirical Glivenko-Cantelli theorem, central limit theorem, functional central limit theorem for various nonparametric Bayesian priors which include the Dirichlet process with general stick-breaking weights, the Poisson-Dirichlet process, the normalized inverse Gaussian process, the normalized generalized gamma process, and the generalized Dirichlet process. For the Dirichlet process with general stick-breaking weights, we introduce two general conditions such that the central limit theorem and functional central limit theorem hold. Except in the case of the generalized Dirichlet process, since the finite dimensional distributions of these processes are either hard to obtain or are complicated to use even they are available, we use the method of moments to obtain the convergence results. For the generalized Dirichlet process we use its finite dimensional marginal distributions to obtain the asymptotics although the computations are highly technical. | math | 1 |
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. | cs | 0 |
Title: Sums, products and dilates on sparse graphs
Abstract: Let $A \subset \mathbb R$ and $G \subset A \times A$. We prove that, for any $\lambda \in \mathbb R \setminus \{-1,0,1\}$, \[ \max \{|A+_G A|, |A+_G \lambda A|, |A\cdot_G A|\} \gg |G|^{6/11}. \] | math | 1 |
Title: Reduction and reconstruction of SDEs via Girsanov and quasi Doob symmetries
Abstract: A reduction procedure for stochastic differential equations based on stochastic symmetries including Girsanov random transformations is proposed. In this setting, a new notion of reconstruction is given, involving the expectation values of functionals of solution to the SDE and a reconstruction theorem for general stochastic symmetries is proved. Moreover, the notable case of reduction under the closed subclass of quasi Doob transformations is presented. The theoretical results are applied to stochastic models relevant in the applications. | math | 1 |
Title: An anisotropic partial regularity criterion for the Navier-Stokes equations
Abstract: In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier--Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if $(u,p)$ is a suitable weak solution and a certain scale-invariant quantity involving only $u_3$ is small on a space-time cylinder $Q_r(x_0,t_0)$, then $u$ is regular at $(x_0,t_0)$. | math | 1 |
Title: A coordinate free characterization of certain quasidiagonal operators
Abstract: We obtain (i) a new, coordinate free, characterization of quasidiagonal operators with essential spectra contained in the unit circle by adapting the proof of a classical result in the theory of Banach spaces, (ii) an affirmative answer to some questions of Hadwin, and (iii) an alternative proof of Hadwin's characterization of the SOT, WOT and $*$-SOT closure of the unitary orbit of a given operator on a separable, infinite dimensional, complex Hilbert space. | math | 1 |
Title: Exact Computation of LTI Reach Set from Integrator Reach Set with Bounded Input
Abstract: We present a semi-analytical method for exact computation of the boundary of the reach set of a single-input controllable linear time invariant (LTI) system with given bounds on its input range. In doing so, we deduce a parametric formula for the boundary of the reach set of an integrator linear system with time-varying bounded input. This formula generalizes recent results on the geometry of an integrator reach set with time-invariant bounded input. We show that the same ideas allow for computing the volume of the LTI reach set. | math | 0 |
Title: Estimation of statistics of transitions and Hill relation for Langevin dynamics
Abstract: In molecular dynamics, statistics of transitions, such as the mean transition time, are macroscopic observables which provide important dynamical information on the underlying microscopic stochastic process. A direct estimation using simulations of microscopic trajectories over long time scales is typically computationally intractable in metastable situations. To overcome this issue, several numerical methods rely on a potential-theoretic identity, sometimes attributed to Hill in the computational statistical physics litterature, which expresses statistics of transitions in terms of the invariant measure of the sequence of configurations by which the underlying process enters metastable sets. The use of this identity then allows to replace the long time simulation problem with a rare event sampling problem, for which efficient algorithms are available. In this article, we rigorously analyse such a method for molecular systems modelled by the Langevin dynamics. Our main contributions are twofold. First, we prove the Hill relation in the fairly general context of positive Harris recurrent chains, and show that this formula applies to the Langevin dynamics. Second, we provide an explicit expression of the invariant measure involved in the Hill relation, and describe an elementary exact simulation procedure. Overall, this yields a simple and complete numerical method to estimate statistics of transitions. | math | 1 |
Title: Families of costs with zero and nonnegative MTW tensor in optimal transport
Abstract: We compute explicitly the MTW tensor (or cross curvature) for the optimal transport problem on $\mathbb{R}^n$ with a cost function of form $\mathsf{c}(x, y) = \mathsf{u}(x^{\mathfrak{t}}y)$, where $\mathsf{u}$ is a scalar function with inverse $\mathsf{s}$, $x^{\ft}y$ is a nondegenerate bilinear pairing of vectors $x, y$ belonging to an open subset of $\mathbb{R}^n$. The condition that the MTW-tensor vanishes on null vectors under the Kim-McCann metric is a fourth-order nonlinear ODE, which could be reduced to a linear ODE of the form $\mathsf{s}^{(2)} - S\mathsf{s}^{(1)} + P\mathsf{s} = 0$ with constant coefficients $P$ and $S$. The resulting inverse functions include {\it Lambert} and {\it generalized inverse hyperbolic\slash trigonometric} functions. The square Euclidean metric and $\log$-type costs are equivalent to instances of these solutions. The optimal map for the family is also explicit. For cost functions of a similar form on a hyperboloid model of the hyperbolic space and unit sphere, we also express this tensor in terms of algebraic expressions in derivatives of $\mathsf{s}$ using the Gauss-Codazzi equation, obtaining new families of strictly regular costs for these manifolds, including new families of {\it power function costs}. We analyze the $\sinh$-type hyperbolic cost, providing examples of $\mathsf{c}$-convex functions and divergence. | math | 0 |
Title: A novel efficient Multi-view traffic-related object detection framework
Abstract: With the rapid development of intelligent transportation system applications, a tremendous amount of multi-view video data has emerged to enhance vehicle perception. However, performing video analytics efficiently by exploiting the spatial-temporal redundancy from video data remains challenging. Accordingly, we propose a novel traffic-related framework named CEVAS to achieve efficient object detection using multi-view video data. Briefly, a fine-grained input filtering policy is introduced to produce a reasonable region of interest from the captured images. Also, we design a sharing object manager to manage the information of objects with spatial redundancy and share their results with other vehicles. We further derive a content-aware model selection policy to select detection methods adaptively. Experimental results show that our framework significantly reduces response latency while achieving the same detection accuracy as the state-of-the-art methods. | cs | 1 |
Title: On components of the tensor square of a Weyl module
Abstract: For a simple Lie algebra $\mathfrak{g}$ of type $A_n,B_n,C_n$ or $D_n$, we give a characterization of the set of dominant integral weights $\lambda$ such that for any rational point $\mu$ in the fundamental Weyl chamber, $2\lambda-\mu$ is a non-negative rational combination of the simple roots if and only if $V_{m\mu}\subseteq V_{m\lambda}\otimes V_{m\lambda}$ for some positive integer $m$. | math | 0 |
Title: Two-Stage Surrogate Modeling for Data-Driven Design Optimization with Application to Composite Microstructure Generation
Abstract: This paper introduces a novel two-stage machine learning-based surrogate modeling framework to address inverse problems in scientific and engineering fields. In the first stage of the proposed framework, a machine learning model termed the "learner" identifies a limited set of candidates within the input design space whose predicted outputs closely align with desired outcomes. Subsequently, in the second stage, a separate surrogate model, functioning as an "evaluator," is employed to assess the reduced candidate space generated in the first stage. This evaluation process eliminates inaccurate and uncertain solutions, guided by a user-defined coverage level. The framework's distinctive contribution is the integration of conformal inference, providing a versatile and efficient approach that can be widely applicable. To demonstrate the effectiveness of the proposed framework compared to conventional single-stage inverse problems, we conduct several benchmark tests and investigate an engineering application focused on the micromechanical modeling of fiber-reinforced composites. The results affirm the superiority of our proposed framework, as it consistently produces more reliable solutions. Therefore, the introduced framework offers a unique perspective on fostering interactions between machine learning-based surrogate models in real-world applications. | cs | 0 |
Title: The relation between Granger causality and directed information theory: a review
Abstract: This report reviews the conceptual and theoretical links between Granger causality and directed information theory. We begin with a short historical tour of Granger causality, concentrating on its closeness to information theory. The definitions of Granger causality based on prediction are recalled, and the importance of the observation set is discussed. We present the definitions based on conditional independence. The notion of instantaneous coupling is included in the definitions. The concept of Granger causality graphs is discussed. We present directed information theory from the perspective of studies of causal influences between stochastic processes. Causal conditioning appears to be the cornerstone for the relation between information theory and Granger causality. In the bivariate case, the fundamental measure is the directed information, which decomposes as the sum of the transfer entropies and a term quantifying instantaneous coupling. We show the decomposition of the mutual information into the sums of the transfer entropies and the instantaneous coupling measure, a relation known for the linear Gaussian case. We study the multivariate case, showing that the useful decomposition is blurred by instantaneous coupling. The links are further developed by studying how measures based on directed information theory naturally emerge from Granger causality inference frameworks as hypothesis testing. | cs | 1 |
Title: Location Aware Modular Biencoder for Tourism Question Answering
Abstract: Answering real-world tourism questions that seek Point-of-Interest (POI) recommendations is challenging, as it requires both spatial and non-spatial reasoning, over a large candidate pool. The traditional method of encoding each pair of question and POI becomes inefficient when the number of candidates increases, making it infeasible for real-world applications. To overcome this, we propose treating the QA task as a dense vector retrieval problem, where we encode questions and POIs separately and retrieve the most relevant POIs for a question by utilizing embedding space similarity. We use pretrained language models (PLMs) to encode textual information, and train a location encoder to capture spatial information of POIs. Experiments on a real-world tourism QA dataset demonstrate that our approach is effective, efficient, and outperforms previous methods across all metrics. Enabled by the dense retrieval architecture, we further build a global evaluation baseline, expanding the search space by 20 times compared to previous work. We also explore several factors that impact on the model's performance through follow-up experiments. Our code and model are publicly available at https://github.com/haonan-li/LAMB. | cs | 0 |
Title: Brain-Conditional Multimodal Synthesis: A Survey and Taxonomy
Abstract: In the era of Artificial Intelligence Generated Content (AIGC), conditional multimodal synthesis technologies (e.g., text-to-image, text-to-video, text-to-audio, etc) are gradually reshaping the natural content in the real world. The key to multimodal synthesis technology is to establish the mapping relationship between different modalities. Brain signals, serving as potential reflections of how the brain interprets external information, exhibit a distinctive One-to-Many correspondence with various external modalities. This correspondence makes brain signals emerge as a promising guiding condition for multimodal content synthesis. Brian-conditional multimodal synthesis refers to decoding brain signals back to perceptual experience, which is crucial for developing practical brain-computer interface systems and unraveling complex mechanisms underlying how the brain perceives and comprehends external stimuli. This survey comprehensively examines the emerging field of AIGC-based Brain-conditional Multimodal Synthesis, termed AIGC-Brain, to delineate the current landscape and future directions. To begin, related brain neuroimaging datasets, functional brain regions, and mainstream generative models are introduced as the foundation of AIGC-Brain decoding and analysis. Next, we provide a comprehensive taxonomy for AIGC-Brain decoding models and present task-specific representative work and detailed implementation strategies to facilitate comparison and in-depth analysis. Quality assessments are then introduced for both qualitative and quantitative evaluation. Finally, this survey explores insights gained, providing current challenges and outlining prospects of AIGC-Brain. Being the inaugural survey in this domain, this paper paves the way for the progress of AIGC-Brain research, offering a foundational overview to guide future work. | cs | 0 |
Title: Regularity for multi-phase problems at nearly linear growth
Abstract: Minima of the log-multiphase variational integral $$ w \mapsto \int_{\Omega} \left[|Dw|\log(1+|Dw|) + a(x)|Dw|^q + b(x)|Dw|^s\right] \, {\rm d}x\,, $$ have locally H\"older continuous gradient under sharp quantitative bounds linking the growth powers $(q,s)$ to the H\"older exponents of the modulating coefficients $a(\cdot)$ and $b(\cdot)$ respectively. | math | 0 |
Title: Existence and uniqueness of solutions to rate independent systems with history variable of integral type
Abstract: This paper investigates rate independent systems (RIS), where the dissipation functional depends not only on the rate but also on the history of the state. The latter is expressed in terms of a Volterra integral operator. We establish an existence result for the original problem and for the control thereof, without resorting to smallness assumptions. Under a smoothness condition, we prove the uniqueness of solutions to a certain class of history dependent RIS with unbounded dissipation potentials. In this context, we derive an essential estimate that opens the door to future research on the topic of optimization. | math | 0 |
Title: Wavenumber-explicit analysis for the Helmholtz $h$-BEM: error estimates and iteration counts for the Dirichlet problem
Abstract: We consider solving the exterior Dirichlet problem for the Helmholtz equation with the $h$-version of the boundary element method (BEM) using the standard second-kind combined-field integral equations. We prove a new, sharp bound on how the number of GMRES iterations must grow with the wavenumber $k$ to have the error in the iterative solution bounded independently of $k$ as $k\rightarrow \infty$ when the boundary of the obstacle is analytic and has strictly positive curvature. To our knowledge, this result is the first-ever sharp bound on how the number of GMRES iterations depends on the wavenumber for an integral equation used to solve a scattering problem. We also prove new bounds on how $h$ must decrease with $k$ to maintain $k$-independent quasi-optimality of the Galerkin solutions as $k \rightarrow \infty$ when the obstacle is nontrapping. | math | 1 |
Title: Multidimensional Sticky Brownian Motions: Tail Behaviour of the Joint Stationary Distribution
Abstract: Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary distributions of a multidimensional sticky Brownian motion, provided it is stable. We will study the large deviations principle for stationary distribution and the tail behaviour of the joint stationary distribution. | math | 1 |
Title: Distributed Multi-Object Tracking Under Limited Field of View Heterogeneous Sensors with Density Clustering
Abstract: We consider the problem of tracking multiple, unknown, and time-varying numbers of objects using a distributed network of heterogeneous sensors. In an effort to derive a formulation for practical settings, we consider limited and unknown sensor field-of-views (FoVs), sensors with limited local computational resources and communication channel capacity. The resulting distributed multi-object tracking algorithm involves solving an NP-hard multidimensional assignment problem either optimally for small-size problems or sub-optimally for general practical problems. For general problems, we propose an efficient distributed multi-object tracking algorithm that performs track-to-track fusion using a clustering-based analysis of the state space transformed into a density space to mitigate the complexity of the assignment problem. The proposed algorithm can more efficiently group local track estimates for fusion than existing approaches. To ensure we achieve globally consistent identities for tracks across a network of nodes as objects move between FoVs, we develop a graph-based algorithm to achieve label consensus and minimise track segmentation. Numerical experiments with a synthetic and a real-world trajectory dataset demonstrate that our proposed method is significantly more computationally efficient than state-of-the-art solutions, achieving similar tracking accuracy and bandwidth requirements but with improved label consistency. | cs | 0 |
Title: Towards the Atiyah-Sutcliffe conjectures for coplanar hyperbolic points
Abstract: The Atiyah-Sutcliffe normalized determinant function $D$ is a smooth complex-valued function on $C_n(H^3)$, where $C_n(H^3)$ denotes the configuration space of $n$ distinct points in hyperbolic $3$-space $H^3$. The hyperbolic version of the Atiyah-Sutcliffe conjecture $1$ (AS conjecture $1$) states that $D$ is nowhere vanishing. AS conjecture $2$ (hyperbolic version) is the stronger statement that $|D(\mathbf{x})| \geq 1$ for any $\mathbf{x} \in C_n(H^3)$. In this short article, we prove AS conjecture $2$ for hyperbolic convex coplanar quadrilaterals, that is for configurations of $4$ points in $H^2$ with none of the points in the configuration lying in the convex hull of the other three. We also obtain Y. Zhang and J. Ma's result, namely AS conjecture $1$ for non-convex quadrilaterals in $H^2$. Finally, we find an explicit lower bound for $|D|$ depending on $n$ only for the natural ``star-based'' variant of the AS problem, for convex coplanar hyperbolic configurations. The latter result holds for any $n \geq 2$. The proofs for $n=4$ make use of the symbolic library of Python. The proof of the general result follows from a general formula for the determinant. In all these cases, $D$ can be expanded as a linear combination of non-negative rational functions with positive coefficients. | math | 1 |
Title: A Distributed SDN Control Plane for Consistent Policy Updates
Abstract: Software-defined networking (SDN) is a novel paradigm that out-sources the control of packet-forwarding switches to a set of software controllers. The most fundamental task of these controllers is the correct implementation of the \emph{network policy}, i.e., the intended network behavior. In essence, such a policy specifies the rules by which packets must be forwarded across the network. This paper studies a distributed SDN control plane that enables \emph{concurrent} and \emph{robust} policy implementation. We introduce a formal model describing the interaction between the data plane and a distributed control plane (consisting of a collection of fault-prone controllers). Then we formulate the problem of \emph{consistent} composition of concurrent network policy updates (short: the \emph{CPC Problem}). To anticipate scenarios in which some conflicting policy updates must be rejected, we enable the composition via a natural \emph{transactional} interface with all-or-nothing semantics. We show that the ability of an $f$-resilient distributed control plane to process concurrent policy updates depends on the tag complexity, i. e., the number of policy labels (a.k.a. \emph{tags}) available to the controllers, and describe a CPC protocol with optimal tag complexity $f+2$. | cs | 1 |
Title: Certifying the novelty of equichordal tight fusion frames
Abstract: An equichordal tight fusion frame (ECTFF) is a finite sequence of equi-dimensional subspaces of a finite-dimensional Hilbert space that achieves equality in Conway, Hardin and Sloane's simplex bound. Every ECTFF is a type of optimal Grassmannian code, being a way to arrange a given number of members of a Grassmannian so that the minimal chordal distance between any pair of them is as large as possible. Any nontrivial ECTFF has both a Naimark complement and spatial complement which themselves are ECTFFs. It turns out that whenever the number of subspaces is at least five, taking iterated alternating Naimark and spatial complements of one ECTFF yields an infinite family of them with distinct parameters. This makes it challenging to certify the novelty of any recently discovered ECTFF: how can one guarantee that it does not arise from any previously known construction in such a Naimark-spatial way? In this paper, we propose a solution to this problem, showing that any ECTFF is a member of a Naimark-spatial family originating from either a trivial ECTFF or one with unique "minimal" parameters. In the latter case, if its minimal parameters do not match those of any previously known ECTFF, it is certifiably new. As a proof of concept, we then use these ideas to certify the novelty of some ECTFFs arising from a new method for constructing them from difference families for finite abelian groups. This method properly generalizes King's construction of ECTFFs from semiregular divisible difference sets. | math | 1 |
Title: On hypergraphs without loose cycles
Abstract: Recently, Mubayi and Wang showed that for $r\ge 4$ and $\ell \ge 3$, the number of $n$-vertex $r$-graphs that do not contain any loose cycle of length $\ell$ is at most $2^{O( n^{r-1} (\log n)^{(r-3)/(r-2)})}$. We improve this bound to $2^{O( n^{r-1} \log \log n) }$. | math | 1 |
Title: The relationship between the negative inertia index of graph $G$ and its girth $g$ and diameter $d$
Abstract: Let $G$ be a simple connected graph. We use $n(G)$, $p(G)$, and $\eta(G)$ to denote the number of negative eigenvalues, positive eigenvalues, and zero eigenvalues of the adjacency matrix $A(G)$ of $G$, respectively. In this paper, we prove that $2n(G)\geq d(G) + 1$ when $d(G)$ is odd, and $n(G) \geq \lceil \frac{g}{2}\rceil - 1$ for a graph containing cycles, where $d(G)$ and $g$ are the diameter and girth of the graph $G$, respectively. Furthermore, we characterize the extremal graphs for the cases of $2n(G) = d(G) + 1$, $n(G) = \lceil \frac{g}{2}\rceil$, and $n(G) = \lceil \frac{g}{2}\rceil - 1$. | math | 0 |
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. | cs | 1 |
Title: High order Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation
Abstract: We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward Differentiation Formulas up to order $q=5$. The development and analysis of the methods are performed in the framework of time evolving finite elements presented in C. M. Elliot and T. Ranner, IMA Journal of Numerical Analysis \textbf{41}, 1696-1845 (2021). The error estimates show through their dependence on the parameters of the equation the existence of different regimes in the behavior of the numerical solution; namely, in the diffusive regime, that is, when the diffusion parameter $\mu$ is large, the error is $O(h^{k+1}+\Delta t^{q})$, whereas in the advective regime, $\mu \ll 1$, the convergence is $O(\min (h^{k},\frac{h^{k+1} }{\Delta t})+\Delta t^{q})$. It is worth remarking that the error constant does not have exponential $\mu ^{-1}$ dependence. | math | 0 |
Title: Finite-time blowup and global-in-time unbounded solutions to a parabolic-parabolic quasilinear Keller-Segel system in higher dimensions
Abstract: In this paper we consider quasilinear Keller-Segel type systems of two kinds in higher dimensions. In the case of a nonlinear diffusion system we prove an optimal (with respect to possible nonlinear diffusions generating explosion in finite time of solutions) finite-time blowup result. In the case of a cross-diffusion system we give results which are optimal provided one assumes some proper non-decay of a nonlinear chemical sensitivity. Moreover, we show that once we do not assume the above mentioned non-decay, our result cannot be as strong as in the case of nonlinear diffusion without nonlinear cross-diffusion terms. To this end we provide an example, interesting by itself, of global-in-time unbounded solutions to the nonlinear cross-diffusion Keller-Segel system with chemical sensitivity decaying fast enough, in a range of parameters in which there is a finite-time blowup result in a corresponding case without nonlinear cross-diffusion. | math | 1 |
Title: Not Only Rewards But Also Constraints: Applications on Legged Robot Locomotion
Abstract: Several earlier studies have shown impressive control performance in complex robotic systems by designing the controller using a neural network and training it with model-free reinforcement learning. However, these outstanding controllers with natural motion style and high task performance are developed through extensive reward engineering, which is a highly laborious and time-consuming process of designing numerous reward terms and determining suitable reward coefficients. In this work, we propose a novel reinforcement learning framework for training neural network controllers for complex robotic systems consisting of both rewards and constraints. To let the engineers appropriately reflect their intent to constraints and handle them with minimal computation overhead, two constraint types and an efficient policy optimization algorithm are suggested. The learning framework is applied to train locomotion controllers for several legged robots with different morphology and physical attributes to traverse challenging terrains. Extensive simulation and real-world experiments demonstrate that performant controllers can be trained with significantly less reward engineering, by tuning only a single reward coefficient. Furthermore, a more straightforward and intuitive engineering process can be utilized, thanks to the interpretability and generalizability of constraints. The summary video is available at https://youtu.be/KAlm3yskhvM. | cs | 0 |
Title: The abstract cotangent complex and Quillen cohomology of enriched categories
Abstract: In his fundamental work, Quillen developed the theory of the cotangent complex as a universal abelian derived invariant, and used it to define and study a canonical form of cohomology, encompassing many known cohomology theories. Additional cohomology theories, such as generalized cohomology of spaces and topological Andr\'e-Quillen cohomology, can be accommodated by considering a spectral version of the cotangent complex. Recent work of Lurie established a comprehensive $\infty$-categorical analogue of the cotangent complex formalism using stabilization of $\infty$-categories. In this paper we study the spectral cotangent complex while working in Quillen's model categorical setting. Our main result gives new and explicit computations of the cotangent complex and Quillen cohomology of enriched categories. For this we make essential use of previous work, which identifies the tangent categories of operadic algebras in unstable model categories. In particular, we present the cotangent complex of an $\infty$-category as a spectrum valued functor on its twisted arrow category, and consider the associated obstruction theory in some examples of interest. | math | 1 |
Title: Distributed Hardware Accelerated Secure Joint Computation on the COPA Framework
Abstract: Performance of distributed data center applications can be improved through use of FPGA-based SmartNICs, which provide additional functionality and enable higher bandwidth communication. Until lately, however, the lack of a simple approach for customizing SmartNICs to application requirements has limited the potential benefits. Intel's Configurable Network Protocol Accelerator (COPA) provides a customizable FPGA framework that integrates both hardware and software development to improve computation and communication performance. In this first case study, we demonstrate the capabilities of the COPA framework with an application from cryptography -- secure Multi-Party Computation (MPC) -- that utilizes hardware accelerators connected directly to host memory and the COPA network. We find that using the COPA framework gives significant improvements to both computation and communication as compared to traditional implementations of MPC that use CPUs and NICs. A single MPC accelerator running on COPA enables more than 17Gbps of communication bandwidth while using only 1% of Stratix 10 resources. We show that utilizing the COPA framework enables multiple MPC accelerators running in parallel to fully saturate a 100Gbps link enabling higher performance compared to traditional NICs. | cs | 1 |
Title: Completing the Asymptotic Classification of Mostly Symmetric Short Step Walks in an Orthant
Abstract: In recent years, the techniques of analytic combinatorics in several variables (ACSV) have been applied to determine asymptotics for several families of lattice path models restricted to the orthant $\mathbb{N}^d$ and defined by step sets $\mathcal{S}\subset\{-1,0,1\}^d\setminus\{\mathbf{0}\}$. Using the theory of ACSV for smooth singular sets, Melczer and Mishna determined asymptotics for the number of walks in any model whose set of steps $\mathcal{S}$ is "highly symmetric" (symmetric over every axis). Building on this work, Melczer and Wilson determined asymptotics for all models where $\mathcal{S}$ is "mostly symmetric" (symmetric over all but one axis) *except* for models whose set of steps have a vector sum of zero but are not highly symmetric. In this paper we complete the asymptotic classification of the mostly symmetric case by analyzing a family of saddle-point-like integrals whose amplitudes are singular near their saddle points. | math | 0 |
Title: Failures and Fixes: A Study of Software System Incident Response
Abstract: This paper presents the results of a research study related to software system failures, with the goal of understanding how we might better evolve, maintain and support software systems in production. We have qualitatively analyzed thirty incidents: fifteen collected through in depth interviews with engineers, and fifteen sampled from publicly published incident reports (generally produced as part of postmortem reviews). Our analysis focused on understanding and categorizing how failures occurred, and how they were detected, investigated and mitigated. We also captured analytic insights related to the current state of the practice and associated challenges in the form of 11 key observations. For example, we observed that failures can cascade through a system leading to major outages; and that often engineers do not understand the scaling limits of systems they are supporting until those limits are exceeded. We argue that the challenges we have identified can lead to improvements to how systems are engineered and supported. | cs | 1 |
Title: Inverse questions for the large sieve
Abstract: Suppose that an infinite set $A$ occupies at most $\frac{1}{2}(p+1)$ residue classes modulo $p$, for every sufficiently large prime $p$. The squares, or more generally the integer values of any quadratic, are an example of such a set. By the large sieve inequality the number of elements of $A$ that are at most $X$ is $O(X^{1/2})$, and the quadratic examples show that this is sharp. The simplest form of the inverse large sieve problem asks whether they are the only examples. We prove a variety of results and formulate various conjectures in connection with this problem, including several improvements of the large sieve bound when the residue classes occupied by $A$ have some additive structure. Unfortunately we cannot solve the problem itself. | math | 1 |
Title: The "exponential" torsion of superelliptic Jacobians
Abstract: Let $J$ be the Jacobian of a superelliptic curve defined by the equation $y^{\ell} = f(x)$, where $f$ is a separable polynomial of degree non-divisible by $\ell$. In this article we study the "exponential" (i.e. $\ell$-power) torsion of $J$. In particular, under some mild conditions on the polynomial $f$, we determine the image of the associated $\ell$-adic representation up to the determinant. We show also that the image of the determinant is contained in an explicit $\mathbb Z_{\ell}$-lattice with a finite index. As an application, we prove the Mumford-Tate conjecture for a generic superelliptic Jacobian of the above type. | math | 0 |
Title: Regular polygraphs and the Simpson conjecture
Abstract: We prove Carlos Simpson's "semi-strictification" (or "weak unit") conjecture in the case of infinity-groupoids. More precisely, we introduce two precise versions of the conjecture, the "general" and the "regular" conjecture, involving two different notions of "non-unital categories". The "general" version involve infinity-categories where absolutely all composition operations (horizontal, vertical and whiskering) are defined and compatible, the "regular" version involve infinity-categories where all the composition operations corresponding to "regular" pasting diagram are defined and compatible. In both case we construct (weak) model structures on these categories such that fibrant objects have weak units and weak inverse. We prove the regular version of the conjecture using the original strategy of Kapranov and Voevodsky, together with our previous work on polygraphs. The general version cannot be proved by these methods and is still open. In order to do this we also study some subtle property of the combinatorics of polygraphs, and we construct a new counting function for polygraphs, inspired by previous work of Makkai. | math | 1 |
Title: Sharp phase transition for random loop models on trees
Abstract: We investigate the random loop model on the $d$-ary tree. For $d \geq 3$, we establish a (locally) sharp phase transition for the existence of infinite loops. Moreover, we derive rigorous bounds that in principle allow to determine the value of the critical parameter with arbitrary precision. Additionally, we prove the existence of an asymptotic expansion for the critical parameter in terms of $d^{-1}$. The corresponding coefficients can be determined in a schematic way and we calculated them up to order $6$. | math | 1 |
Title: Hörmander properties of discrete time Markov processes
Abstract: We present an abstract framework for establishing smoothing properties within a specific class of inhomogeneous discrete-time Markov processes. These properties, in turn, serve as a basis for demonstrating the existence of a density function for our process or more precisely for a regularized version of it. They can also be exploited to show its total variation convergence towards the solution of a Stochastic Differential Equation as the time step between two observations of our discrete time Markov process tends to zero. The distinctive feature of our methodology lies in the exploration of smoothing properties under a local weak H\"ormander type condition satisfied by the discrete-time Markov process. Our H\"ormander property is demonstrated to align with the standard local weak H\"ormander associated to the Stochastic Differential Equation which is the total variation limit of our discrete time Markov process. | math | 0 |
Title: Dynamic Mode Decomposition of Control-Affine Nonlinear Systems using Discrete Control Liouville Operators
Abstract: Representation of nonlinear dynamical systems as infinite-dimensional linear operators over Hilbert spaces enables analysis of nonlinear systems via pseudo-spectral operator analysis. In this paper, we provide a novel representation for discrete-time control-affine nonlinear dynamical systems as linear operators acting on a Hilbert space. We also demonstrate that this representation can be used to predict the behavior of the closed-loop system given a known feedback law using recorded snapshots of the system state resulting from arbitrary, potentially open-loop control inputs. We thereby extend the predictive capabilities of dynamic mode decomposition to discrete-time nonlinear systems that are affine in control. We validate the method using two numerical experiments by predicting the response of a controlled Duffing oscillator to a known feedback law, as well as demonstrating the advantage of the developed method relative to existing techniques in the literature. | math | 0 |
Title: Learning to Prompt with Text Only Supervision for Vision-Language Models
Abstract: Foundational vision-language models such as CLIP are becoming a new paradigm in vision, due to their excellent generalization abilities. However, adapting these models for downstream tasks while maintaining their generalization remains a challenge. In literature, one branch of methods adapts CLIP by learning prompts using visual information. While effective, most of these works require labeled data which is not practical, and often struggle to generalize towards new datasets due to over-fitting on the source data. An alternative approach resorts to training-free methods by generating class descriptions from large language models (LLMs) and perform prompt ensembling. However, these methods often generate class specific prompts that cannot be transferred to other classes, which incur higher costs by generating LLM descriptions for each class separately. In this work, we propose to combine the strengths of these both streams of methods by learning prompts using only text data derived from LLMs. As supervised training of prompts is not trivial due to absence of images, we develop a training approach that allows prompts to extract rich contextual knowledge from LLM data. Moreover, with LLM contextual data mapped within the learned prompts, it enables zero-shot transfer of prompts to new classes and datasets potentially cutting the LLM prompt engineering cost. To the best of our knowledge, this is the first work that learns generalized prompts using text only data. We perform extensive evaluations on 4 benchmarks where our method improves over prior ensembling works while being competitive to those utilizing labeled images. Our code and pre-trained models are available at https://github.com/muzairkhattak/ProText. | cs | 0 |
Title: Xorshift1024*, Xorshift1024+, Xorshift128+ and Xoroshiro128+ Fail Statistical Tests for Linearity
Abstract: L'Ecuyer & Simard's Big Crush statistical test suite has revealed statistical flaws in many popular random number generators including Marsaglia's Xorshift generators. Vigna recently proposed some 64-bit variations on the Xorshift scheme that are further scrambled (i.e., Xorshift1024*, Xorshift1024+, Xorshift128+, Xoroshiro128+). Unlike their unscrambled counterparts, they pass Big Crush when interleaving blocks of 32 bits for each 64-bit word (most significant, least significant, most significant, least significant, etc.). We report that these scrambled generators systematically fail Big Crush---specifically the linear-complexity and matrix-rank tests that detect linearity---when taking the 32 lowest-order bits in reverse order from each 64-bit word. | cs | 1 |
Title: Logic of temporal attribute implications
Abstract: We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point characterization, investigate closure properties of model classes, present an axiomatization and prove its completeness, and investigate alternative axiomatizations and normalized proofs. We investigate decidability and complexity issues of the logic and prove that the entailment problem is NP-hard and belongs to EXPSPACE. We show that by restricting to predictive formulas, the entailment problem is decidable in pseudo-linear time. | cs | 1 |
Title: The Art of Deception: Robust Backdoor Attack using Dynamic Stacking of Triggers
Abstract: The area of Machine Learning as a Service (MLaaS) is experiencing increased implementation due to recent advancements in the AI (Artificial Intelligence) industry. However, this spike has prompted concerns regarding AI defense mechanisms, specifically regarding potential covert attacks from third-party providers that cannot be entirely trusted. Recent research has uncovered that auditory backdoors may use certain modifications as their initiating mechanism. DynamicTrigger is introduced as a methodology for carrying out dynamic backdoor attacks that use cleverly designed tweaks to ensure that corrupted samples are indistinguishable from clean. By utilizing fluctuating signal sampling rates and masking speaker identities through dynamic sound triggers (such as the clapping of hands), it is possible to deceive speech recognition systems (ASR). Our empirical testing demonstrates that DynamicTrigger is both potent and stealthy, achieving impressive success rates during covert attacks while maintaining exceptional accuracy with non-poisoned datasets. | cs | 0 |
Title: Nuclei instance segmentation and classification in histopathology images with StarDist
Abstract: Instance segmentation and classification of nuclei is an important task in computational pathology. We show that StarDist, a deep learning nuclei segmentation method originally developed for fluorescence microscopy, can be extended and successfully applied to histopathology images. This is substantiated by conducting experiments on the Lizard dataset, and through entering the Colon Nuclei Identification and Counting (CoNIC) challenge 2022, where our approach achieved the first spot on the leaderboard for the segmentation and classification task for both the preliminary and final test phase. | cs | 1 |
Title: Twisted Rokhlin property for mapping class groups
Abstract: In this paper, generalising the idea of the Rokhlin property, we explore the concept of the twisted Rokhlin property of topological groups. A topological group is said to exhibit the twisted Rokhlin property if, for each automorphism $\phi$ of the group, there exists a $\phi$-twisted conjugacy class that is dense in the group. We provide a complete classification of connected orientable infinite-type surfaces without boundaries whose mapping class groups possess the twisted Rokhlin property. Additionally, we prove that the mapping class groups of the remaining surfaces do not admit any dense $\phi$-twisted conjugacy class for any automorphism $\phi$. This supplements the recent work of Lanier and Vlamis on the Rokhlin property of big mapping class groups. We also prove that the mapping class group of each connected orientable infinite-type surface without boundary possesses the $R_\infty$-property. | math | 0 |
Title: Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption
Abstract: This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system \begin{eqnarray*} \begin{array}{llc} u_t=\Delta u-\chi\nabla\cdot (u\nabla v)+\kappa u-\mu u^2,\\ v_t=\Delta v-uv, \end{array} \end{eqnarray*} in $N$-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large $\mu$ and prove that for any $\mu>0$ there exists a weak solution. Moreover, in the case of $\kappa>0$ convergence to the constant equilibrium $(\frac{\kappa}{\mu},0)$ is shown. | math | 1 |
Title: Design and Implementation Considerations for a Virtual File System Using an Inode Data Structure
Abstract: Virtual file systems are a tool to centralize and mobilize a file system that could otherwise be complex and consist of multiple hierarchies, hard disks, and more. In this paper, we discuss the design of Unix-based file systems and how this type of file system layout using inode data structures and a disk emulator can be implemented as a single-file virtual file system in Linux. We explore the ways that virtual file systems are vulnerable to security attacks and introduce straightforward solutions that can be implemented to help prevent or mitigate the consequences of such attacks. | cs | 0 |
Title: The Rank of the Odd Normal Out
Abstract: Say we have a collection of independent random variables $X_0, ... , X_n$, where $X_0 \sim \mathcal{N}(\mu_0, \sigma_0^2)$, but $X_i \sim \mathcal{N}(\mu, \sigma^2)$, for $1 \leq i \leq n$. We characterize the distribution of $R_0 := 1 + \sum_{i=1}^{n} \mathbf{1}\{X_i \leq X_0\}$, the rank of the random variable whose distribution potentially differs from that of the others -- the odd normal out. We show that $R_0 - 1$ is approximately beta-binomial, an approximation that becomes equality as $\sigma/\sigma_0$ or $(\mu-\mu_0)/\sigma_0$ become large or small. The intra-class correlation of the approximating beta-binomial depends on $\Pr(X_1 \leq X_0)$ and $\Pr(X_1 \leq X_0, X_2 \leq X_0)$. Our approach relies on the conjugacy of the beta distribution for the binomial: $\Phi((X_0-\mu)/\sigma)$ is approximately $\mathrm{Beta}(\alpha(\sigma/\sigma_0, (\mu-\mu_0)/\sigma_0), \beta(\sigma/\sigma_0, (\mu-\mu_0)/\sigma_0))$ for functions $\alpha, \beta > 0$. We study the distributions of the in-normal ranks. Throughout, simulations corroborate the formulae we derive. | math | 0 |
Title: Stochastic PDEs involving a bilaplacian operator
Abstract: In this article, we study the existence and uniqueness problem for linear Stochastic PDEs involving a bilaplacian operator. Our results on the existence and uniqueness are obtained through an application of a Monotonicity inequality, which we also prove here. As an application of these results, we also obtain a probabilistic representation of the solution for a linear PDE involving the bilaplacian operator. | math | 0 |
Title: On Probabilistic Completeness of Probabilistic Cell Decomposition
Abstract: Probabilistic Cell Decomposition (PCD) is a probabilistic path planning method combining the concepts of approximate cell decomposition with probabilistic sampling. It has been shown that the use of lazy evaluation techniques and supervised sampling in important areas result in a high performance path planning method. Even if it was postulated before that PCD is probabilistically complete, we present a detailed proof of probabilistic completeness here for the first time. | cs | 1 |