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Title: Fully Automated Image De-fencing using Conditional Generative Adversarial Networks
Abstract: Image de-fencing is one of the important aspects of recreational photography in which the objective is to remove the fence texture present in an image and generate an aesthetically pleasing version of the same image without the fence texture. In this paper, we aim to develop an automated and effective technique for fence removal and image reconstruction using conditional Generative Adversarial Networks (cGANs). These networks have been successfully applied in several domains of Computer Vision focusing on image generation and rendering. Our initial approach is based on a two-stage architecture involving two cGANs that generate the fence mask and the inpainted image, respectively. Training of these networks is carried out independently and, during evaluation, the input image is passed through the two generators in succession to obtain the de-fenced image. The results obtained from this approach are satisfactory, but the response time is long since the image has to pass through two sets of convolution layers. To reduce the response time, we propose a second approach involving only a single cGAN architecture that is trained using the ground-truth of fenced de-fenced image pairs along with the edge map of the fenced image produced by the Canny Filter. Incorporation of the edge map helps the network to precisely detect the edges present in the input image, and also imparts it an ability to carry out high quality de-fencing in an efficient manner, even in the presence of a fewer number of layers as compared to the two-stage network. Qualitative and quantitative experimental results reported in the manuscript reveal that the de-fenced images generated by the single-stage de-fencing network have similar visual quality to those produced by the two-stage network. Comparative performance analysis also emphasizes the effectiveness of our approach over state-of-the-art image de-fencing techniques. | cs | 1 |
Title: Stanley decompositions of modules of covariants
Abstract: For a complex reductive group $H$ with finite-dimensional representations $W$ and $U$, the module of covariants for $W$ of type $U$ is the space of all $H$-equivariant polynomial functions $W \longrightarrow U$. In this paper, we take $H$ to be one of the classical groups $\operatorname{GL}(V)$, $\operatorname{Sp}(V)$, or $\operatorname{O}(V)$ arising in Howe's dual pair setting, where $W$ is a direct sum of copies of $V$ and $V^*$. Our main result is a uniform combinatorial model for Stanley decompositions of the modules of covariants, using visualizations that we call jellyfish. Our decompositions allow us to interpret the Hilbert series as a positive combination of rational expressions which have concrete combinatorial interpretations in terms of lattice paths; significantly, this interpretation does not depend on the Cohen-Macaulay property. As a corollary, we recover a major result of Nishiyama-Ochiai-Taniguchi (2001) regarding the Bernstein degree of unitary highest weight $(\mathfrak{g},K)$-modules. We also extend our methods to compute the Hilbert series of the invariant rings for the groups $\operatorname{SL}(V)$ and $\operatorname{SO}(V)$, as well as the Wallach representations of type ADE. | math | 0 |
Title: Optimal Placement of Dynamic Var Sources by Using Empirical Controllability Covariance
Abstract: In this paper, the empirical controllability covariance (ECC), which is calculated around the considered operating condition of a power system, is applied to quantify the degree of controllability of system voltages under specific dynamic var source locations. An optimal dynamic var source placement method addressing fault-induced delayed voltage recovery (FIDVR) issues is further formulated as an optimization problem that maximizes the determinant of ECC. The optimization problem is effectively solved by the NOMAD solver, which implements the Mesh Adaptive Direct Search algorithm. The proposed method is tested on an NPCC 140-bus system and the results show that the proposed method with fault specified ECC can solve the FIDVR issue caused by the most severe contingency with fewer dynamic var sources than the Voltage Sensitivity Index (VSI) based method. The proposed method with fault unspecified ECC does not depend on the settings of the contingency and can address more FIDVR issues than VSI method when placing the same number of SVCs under different fault durations. It is also shown that the proposed method can help mitigate voltage collapse. | math | 1 |
Title: DEM: A Method for Certifying Deep Neural Network Classifier Outputs in Aerospace
Abstract: Software development in the aerospace domain requires adhering to strict, high-quality standards. While there exist regulatory guidelines for commercial software in this domain (e.g., ARP-4754 and DO-178), these do not apply to software with deep neural network (DNN) components. Consequently, it is unclear how to allow aerospace systems to benefit from the deep learning revolution. Our work here seeks to address this challenge with a novel, output-centric approach for DNN certification. Our method employs statistical verification techniques, and has the key advantage of being able to flag specific inputs for which the DNN's output may be unreliable - so that they may be later inspected by a human expert. To achieve this, our method conducts a statistical analysis of the DNN's predictions for other, nearby inputs, in order to detect inconsistencies. This is in contrast to existing techniques, which typically attempt to certify the entire DNN, as opposed to individual outputs. Our method uses the DNN as a black-box, and makes no assumptions about its topology. We hope that this work constitutes another step towards integrating DNNs in safety-critical applications - especially in the aerospace domain, where high standards of quality and reliability are crucial. | cs | 0 |
Title: Towards a Formal Modelling, Analysis, and Verification of a Clone Node Attack Detection Scheme in the Internet of Things
Abstract: In a clone node attack, an attacker attempted to physically capture the devices to gather sensitive information to conduct various insider attacks. Several solutions for detecting clone node attacks on IoT networks have been presented in the viewpoints above. These solutions are focused on specific system designs, processes, and feature sets and act as a high-level abstraction of underlying system architectures based on a few performance requirements. However, critical features like formal analysis, modelling, and verification are frequently overlooked in existing proposed solutions aimed at verifying the correctness and robustness of systems in order to ensure that no problematic scenarios or anomalies exist. This paper presents a formal analysis, modelling, and verification of our existing proposed clone node attack detection scheme in IoT. Firstly, we modelled the architectural components of the proposed scheme using High-Level Petri Nets (HLPNs) and then mapped them using their specified functionalities. Secondly, we defined and analysed the behavioural properties of the proposed scheme using Z specification language. Furthermore, we used the Satisfiability Modulo Theories Library (SMT-Lib) and the Z3 Solver to validate and demonstrate the overall functionality of the proposed scheme. Finally, in addition to modelling and analysis, this work employs Coloured Petri Nets (CPNs), which combine Petri Nets with a high-level programming language, making them more suitable for large-scale system modelling. To perform the simulations in CPN, we used both timed and untimed models, where timed models are used to evaluate performance, and untimed models are used to validate logical validity. | cs | 1 |
Title: Stable determination of the initial data in an IBVP for the wave equation outside a non-trapping obstacle
Abstract: We establish a double logarithmic stability inequality for the problem of determining the initial data in an IBVP for the wave equation outside a non-trapping obstacle from two localized measurements. | math | 0 |
Title: Hopf algebras with enough quotients
Abstract: A family of algebra maps $H\to A_i$ whose common domain is a Hopf algebra is said to be jointly inner faithful if it does not factor simultaneously through a proper Hopf quotient of $H$. We show that tensor and free products of jointly inner faithful maps of Hopf algebras are again jointly inner faithful, generalizing a number of results in the literature on torus generation of compact quantum groups. | math | 1 |
Title: On two open questions for extension bundles
Abstract: In this paper we give positive answers for two open questions on extension bundles over weighted projective lines, raised by Kussin, Lenzing and Meltzer in the paper ``Triangle singularities, ADE-chains and weighted projective lines''. | math | 0 |
Title: CLASS-M: Adaptive stain separation-based contrastive learning with pseudo-labeling for histopathological image classification
Abstract: Histopathological image classification is an important task in medical image analysis. Recent approaches generally rely on weakly supervised learning due to the ease of acquiring case-level labels from pathology reports. However, patch-level classification is preferable in applications where only a limited number of cases are available or when local prediction accuracy is critical. On the other hand, acquiring extensive datasets with localized labels for training is not feasible. In this paper, we propose a semi-supervised patch-level histopathological image classification model, named CLASS-M, that does not require extensively labeled datasets. CLASS-M is formed by two main parts: a contrastive learning module that uses separated Hematoxylin and Eosin images generated through an adaptive stain separation process, and a module with pseudo-labels using MixUp. We compare our model with other state-of-the-art models on two clear cell renal cell carcinoma datasets. We demonstrate that our CLASS-M model has the best performance on both datasets. Our code is available at github.com/BzhangURU/Paper_CLASS-M/tree/main | cs | 0 |
Title: A noncommutative Davis' decomposition for martingales
Abstract: We prove an analogue of the classical Davis' decomposition for martingales in noncommutative L_p-spaces, involving the square functions. We also determine the dual space of the noncommutative conditioned Hardy space \h_1. We further extend this latter result to the case 1<p<2. | math | 1 |
Title: A two-stage stochastic programming model for electric substation flood mitigation prior to an imminent hurricane
Abstract: We present a stochastic programming model for informing the deployment of ad hoc flood mitigation measures to protect electrical substations prior to an imminent and uncertain hurricane. The first stage captures the deployment of a fixed number of mitigation resources, and the second stage captures grid operation in response to a contingency. The primary objective is to minimize expected load shed. We develop methods for simulating flooding induced by extreme rainfall and construct two geographically realistic case studies, one based on Tropical Storm Imelda and the other on Hurricane Harvey. Applying our model to those case studies, we investigate the effect of the mitigation budget on the optimal objective value and solutions. Our results highlight the sensitivity of the optimal mitigation to the budget, a consequence of those decisions being discrete. We additionally assess the value of having better mitigation options and the spatial features of the optimal mitigation. | math | 0 |
Title: Improving the Deployment of Recycling Classification through Efficient Hyper-Parameter Analysis
Abstract: The paradigm of automated waste classification has recently seen a shift in the domain of interest from conventional image processing techniques to powerful computer vision algorithms known as convolutional neural networks (CNN). Historically, CNNs have demonstrated a strong dependency on powerful hardware for real-time classification, yet the need for deployment on weaker embedded devices is greater than ever. The work in this paper proposes a methodology for reconstructing and tuning conventional image classification models, using EfficientNets, to decrease their parameterisation with no trade-off in model accuracy and develops a pipeline through TensorRT for accelerating such models to run at real-time on an NVIDIA Jetson Nano embedded device. The train-deployment discrepancy, relating how poor data augmentation leads to a discrepancy in model accuracy between training and deployment, is often neglected in many papers and thus the work is extended by analysing and evaluating the impact real world perturbations had on model accuracy once deployed. The scope of the work concerns developing a more efficient variant of WasteNet, a collaborative recycling classification model. The newly developed model scores a test-set accuracy of 95.8% with a real world accuracy of 95%, a 14% increase over the original. Our acceleration pipeline boosted model throughput by 750% to 24 inferences per second on the Jetson Nano and real-time latency of the system was verified through servomotor latency analysis. | cs | 1 |
Title: Normal operators for momentum ray transforms, I: The inversion formula
Abstract: The momentum ray transform $I_m^k$ integrates a rank $m$ symmetric tensor field $f$ on $\mathbb R^n$ over lines with the weight $t^k$, $I_m^kf(x,\xi)=\int_{-\infty}^\infty t^k\langle f(x+t\xi),\xi^m\rangle\,\mathrm{d}t$. We compute the normal operator $N_m^k=(I_m^k){}^*I_m^k$ and present an inversion formula recovering a rank $m$ tensor field $f$ from the data $(N_m^0f,\dots,N_m^mf)$. | math | 0 |
Title: On Classes of Fredholm Type Operators
Abstract: Given an idempotent $p$ in a Banach algebra and following the study in \cite{P50} of p-invertibility, we consider here left p-invertibility, right p-invertibility and p-invertibility in the Calkin Algebra $\mathcal{C}(X),$ where $X$ is a Banach space. Then we define and study left and right generalized Drazin invertibility and we characterize left and right Drazin invertible elements in the Calkin algebra. Globally, this leads to define and characterize the classes of P-Fredholm, pseudo B-Fredholm and weak B-Fredholm operators. | math | 0 |
Title: Strategic Bidding Wars in On-chain Auctions
Abstract: The Ethereum block-building process has changed significantly since the emergence of Proposer-Builder Separation. Validators access blocks through a marketplace, where block builders bid for the right to construct the block and earn MEV (Maximal Extractable Value) rewards in an on-chain competition, known as the MEV-boost auction. While more than 90% of blocks are currently built via MEV-Boost, trade-offs between builders' strategic behaviors and auction design remain poorly understood. In this paper we address this gap. We introduce a game-theoretic model for MEV-Boost auctions and use simulations to study different builders' bidding strategies observed in practice. We study various strategic interactions and auction setups and evaluate how the interplay between critical elements such as access to MEV opportunities and improved connectivity to relays impact bidding performance. Our results demonstrate the importance of latency on the effectiveness of builders' strategies and the overall auction outcome from the proposer's perspective. | cs | 0 |
Title: The Weyl law for algebraic tori
Abstract: We give an asymptotic evaluation for the number of automorphic characters of an algebraic torus $T$ with bounded analytic conductor. The analytic conductor which we use is defined via the local Langlands correspondence for tori by choosing a finite dimensional complex algebraic representation of the $L$-group of $T$. Our results therefore fit into a general framework of counting automorphic representations on reductive groups by analytic conductor. | math | 1 |
Title: Space reduction techniques for the $3$-wise Kemeny problem
Abstract: Kemeny's rule is one of the most studied and well-known voting schemes with various important applications in computational social choice and biology. Recently, Kemeny's rule was generalized via a set-wise approach by Gilbert et. al. This paradigm presents interesting advantages in comparison with Kemeny's rule since not only pairwise comparisons but also the discordance between the winners of subsets of three alternatives are also taken into account in the definition of the $3$-wise Kendall-tau distance between two rankings. In spite of the NP-hardness of the 3-wise Kemeny problem which consists of computing the set of $3$-wise consensus rankings, namely rankings whose total $3$-wise Kendall-tau distance to a given voting profile is minimized, we establish in this paper several generalizations of the Major Order Theorems, as obtained by Milosz and Hamel for Kemeny's rule, for the $3$-wise Kemeny voting schemes to achieve a substantial search space reduction by efficiently determining in polynomial time the relative orders of pairs of alternatives. Essentially, our theorems quantify precisely the nontrivial property that if the preference for an alternative over another one in an election is strong enough, not only in the head-to-head competition but even when taking into account one or two more alternatives, then the relative order of these two alternatives in all $3$-wise consensus rankings must be as expected. As an application, we also obtain an improvement of the Major Order Theorems for Kememy's rule. Moreover, we show that the well-known $3/4$-majority rule of Betzler et al. for Kemeny's rule is only valid in general for elections with no more than $5$ alternatives with respect to the $3$-wise Kemeny scheme. Several simulations and tests of our algorithms on real-world and uniform data are provided. | cs | 0 |
Title: A Deep Dive on the Impact of COVID-19 in Software Development
Abstract: Context: COVID-19 pandemic has impacted different business sectors around the world. Objective. This study investigates the impact of COVID-19 on software projects and software development professionals. Method: We conducted a mining software repository study based on 100 GitHub projects developed in Java using ten different metrics. Next, we surveyed 279 software development professionals for better understanding the impact of COVID-19 on daily activities and wellbeing. Results: We identified 12 observations related to productivity, code quality, and wellbeing. Conclusions: Our findings highlight that the impact of COVID-19 is not binary (reduce productivity vs. increase productivity) but rather a spectrum. For many of our observations, substantial proportions of respondents have differing opinions from each other. We believe that more research is needed to uncover specific conditions that cause certain outcomes to be more prevalent. | cs | 1 |
Title: Scalable network reconstruction in subquadratic time
Abstract: Network reconstruction consists in determining the unobserved pairwise couplings between $N$ nodes given only observational data on the resulting behavior that is conditioned on those couplings -- typically a time-series or independent samples from a graphical model. A major obstacle to the scalability of algorithms proposed for this problem is a seemingly unavoidable quadratic complexity of $O(N^2)$, corresponding to the requirement of each possible pairwise coupling being contemplated at least once, despite the fact that most networks of interest are sparse, with a number of non-zero couplings that is only $O(N)$. Here we present a general algorithm applicable to a broad range of reconstruction problems that achieves its result in subquadratic time, with a data-dependent complexity loosely upper bounded by $O(N^{3/2}\log N)$, but with a more typical log-linear complexity of $O(N\log^2N)$. Our algorithm relies on a stochastic second neighbor search that produces the best edge candidates with high probability, thus bypassing an exhaustive quadratic search. In practice, our algorithm achieves a performance that is many orders of magnitude faster than the quadratic baseline, allows for easy parallelization, and thus enables the reconstruction of networks with hundreds of thousands and even millions of nodes and edges. | cs | 0 |
Title: Second-order Approximation of Exponential Random Graph Models
Abstract: Exponential random graph models (ERGMs) are flexible probability models allowing edge dependency. However, it is known that, to a first-order approximation, many ERGMs behave like Erd\"os-R\'enyi random graphs, where edges are independent. In this paper, to distinguish ERGMs from Erd\"os-R\'enyi random graphs, we consider second-order approximations of ERGMs using two-stars and triangles. We prove that the second-order approximation indeed achieves second-order accuracy in the triangle-free case. The new approximation is formally obtained by Hoeffding decomposition and rigorously justified using Stein's method. | math | 0 |
Title: An analysis of training and generalization errors in shallow and deep networks
Abstract: This paper is motivated by an open problem around deep networks, namely, the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we analyze this phenomenon in the case of regression problems when each unit evaluates a periodic activation function. We argue that the minimal expected value of the square loss is inappropriate to measure the generalization error in approximation of compositional functions in order to take full advantage of the compositional structure. Instead, we measure the generalization error in the sense of maximum loss, and sometimes, as a pointwise error. We give estimates on exactly how many parameters ensure both zero training error as well as a good generalization error. We prove that a solution of a regularization problem is guaranteed to yield a good training error as well as a good generalization error and estimate how much error to expect at which test data. | cs | 1 |
Title: Edge-Linear First-Order Dependency Parsing with Undirected Minimum Spanning Tree Inference
Abstract: The run time complexity of state-of-the-art inference algorithms in graph-based dependency parsing is super-linear in the number of input words (n). Recently, pruning algorithms for these models have shown to cut a large portion of the graph edges, with minimal damage to the resulting parse trees. Solving the inference problem in run time complexity determined solely by the number of edges (m) is hence of obvious importance. We propose such an inference algorithm for first-order models, which encodes the problem as a minimum spanning tree (MST) problem in an undirected graph. This allows us to utilize state-of-the-art undirected MST algorithms whose run time is O(m) at expectation and with a very high probability. A directed parse tree is then inferred from the undirected MST and is subsequently improved with respect to the directed parsing model through local greedy updates, both steps running in O(n) time. In experiments with 18 languages, a variant of the first-order MSTParser (McDonald et al., 2005b) that employs our algorithm performs very similarly to the original parser that runs an O(n^2) directed MST inference. | cs | 1 |
Title: Symmetry and asymmetry between positive and negative square energies of graphs
Abstract: The positive and negative square energies of a graph, $s^+(G)$ and $s^-(G)$, are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively. The first results on square energies revealed symmetry between $s^+(G)$ and $s^-(G)$. This paper reviews examples of asymmetry between these parameters, for example using large random graphs and the ratios $s^+/s^-$ and $s^-/s^+$, as well as new examples of symmetry. We answer some questions previously asked about $s^{+}$ and $s^{-}$ and suggest several further avenues of research. | math | 0 |
Title: Generalized domination structure in cubic graphs
Abstract: In this paper, we consider generalized domination structure in graphs, which stipulates the structure of a minimum dominating set. Two cycles of length 0 mod 3 intersecting with one path are the constituents of the domination structure and by taking every three vertices on the cycles we can obtain a minimum dominating set. For a cubic graph, we construct generalized domination structure by adding edges in a certain way. We prove that the minimum dominating set of a cubic graph is determined in polynomial time. | math | 1 |
Title: Adaptive Belief Discretization for POMDP Planning
Abstract: Partially Observable Markov Decision Processes (POMDP) is a widely used model to represent the interaction of an environment and an agent, under state uncertainty. Since the agent does not observe the environment state, its uncertainty is typically represented through a probabilistic belief. While the set of possible beliefs is infinite, making exact planning intractable, the belief space's complexity (and hence planning complexity) is characterized by its covering number. Many POMDP solvers uniformly discretize the belief space and give the planning error in terms of the (typically unknown) covering number. We instead propose an adaptive belief discretization scheme, and give its associated planning error. We furthermore characterize the covering number with respect to the POMDP parameters. This allows us to specify the exact memory requirements on the planner, needed to bound the value function error. We then propose a novel, computationally efficient solver using this scheme. We demonstrate that our algorithm is highly competitive with the state of the art in a variety of scenarios. | cs | 1 |
Title: On perturbations of singular complex analytic curves
Abstract: Suppose $V$ is a singular complex analytic curve inside $\mathbb{C}^{2}$. We investigate when a singular or non-singular complex analytic curve $W$ inside $\mathbb{C}^{2}$ with sufficiently small Hausdorff distance $d_{H}(V, W)$ from $V$ must intersect $V$. We obtain a sufficient condition on $W$ which when satisfied gives an affirmative answer to our question. More precisely, we show the intersection is non-empty for any such $W$ that admits at most one non-normal crossing type discriminant point associated with some proper projection. As an application, we prove a special case of the higher-dimensional analog, and also a holomorphic multifunction analog of a result by Lyubich-Peters. | math | 0 |
Title: On the maximum of the weighted binomial sum $(1+a)^{-r}\sum_{i=0}^{r}\binom{m}{i}a^{i}$
Abstract: Recently, Glasby and Paseman considered the following sequence of binomial sums $\{2^{-r}\sum_{i=0}^{r}\binom{m}{i}\}_{r=0}^{m}$ and showed that this sequence is unimodal and attains its maximum value at $r=\lfloor\frac{m}{3}\rfloor+1$ for $m\in\mathbb{Z}_{\geq0}\setminus\{0,3,6,9,12\}$. They also analyzed the asymptotic behavior of the maximum value of the sequence as $m$ approaches infinity. In the present work, we generalize their results by considering the sequence $\{(1+a)^{-r}\sum_{i=0}^{r}\binom{m}{i}a^{i}\}_{r=0}^{m}$ for integers $a \geq 1$. We also consider a family of discrete probability distributions that naturally arises from this sequence. | math | 0 |
Title: Short Squeeze in DeFi Lending Market: Decentralization in Jeopardy?
Abstract: Anxiety levels in the Aave community spiked in November 2022 as Avi Eisenberg performed an attack on Aave. Eisenberg attempted to short the CRV token by using funds borrowed on the protocol to artificially deflate the value of CRV. While the attack was ultimately unsuccessful, it left the Aave community scared and even raised question marks regarding the feasibility of large lending platforms under decentralized governance. In this work, we analyze Avi Eisenberg's actions and show how he was able to artificially lower the price of CRV by selling large quantities of borrowed CRV for stablecoins on both decentralized and centralized exchanges. Despite the failure of his attack, it still led to irretrievable debt worth more than 1.5 Mio USD at the time and, thereby, quadrupled the protocol's irretrievable debt. Furthermore, we highlight that his attack was enabled by the vast proportion of CRV available to borrow as well as Aave's lending protocol design hindering rapid intervention. We stress Eisenberg's attack exposes a predicament of large DeFi lending protocols: limit the scope or compromise on 'decentralization'. | cs | 1 |
Title: Normalized solutions to the Chern-Simons-Schrödinger system: the supercritical case
Abstract: We are concerned with the existence of normalized solutions for a class of generalized Chern-Simons-Schr\"{o}dinger type problems with supercritical exponential growth $$ -\Delta u +\lambda u+A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u),\quad \partial_1A_2-\partial_2A_1=-\frac{1}{2}|u|^2,\quad \partial_1A_1+\partial_2A_2=0,\quad \partial_1A_0=A_2|u|^2,\quad \partial_2A_0=-A_1|u|^2,\quad \int_{\mathbb{R}^2}|u|^2dx=a^2, $$ where $a\neq0$, $\lambda\in \mathbb{R}$ is known as the Lagrange multiplier and $f\in C^1(\mathbb{R})$ denotes the nonlinearity that fulfills the supercritical exponential growth in the Trudinger-Moser sense at infinity. Under suitable assumptions, combining the constrained minimization approach together with the homotopy stable family and elliptic regularity theory, we obtain that the problem has at least a ground state solution. | math | 0 |
Title: Image of Lie polynomial of degree $2$ evaluated on Nilpotent Lie algebra
Abstract: We delineate the image of multilinear Lie polynomial of degree $2$ evaluated on $L$ where $L$ is a finite-dimensional nilpotent Lie algebra over field $k$ with $\dim L' \leq 4$. | math | 1 |
Title: Synchrony and Anti-synchrony in Weighted Networks
Abstract: We consider weighted coupled cell networks, that is networks where the interactions between any two cells have an associated weight that is a real valued number. Weighted networks are ubiquitous in real-world applications. We consider a dynamical systems perspective by associating to each network a set of continuous dynamical systems, the ones that respect the graph structure of the network. For weighted networks it is natural for the admissible coupled cell systems to have an additive input structure. We present a characterization of the synchrony subspaces and the anti-synchrony subspaces for a weighted network depending on the restrictions that are imposed to their admissible input-additive coupled cell systems. These subspaces are flow-invariant by those systems and are generalized polydiagonal subspaces, that is, are characterized by conditions on the cell coordinates of the types $x_i = x_j$ and/or $x_k = -x_l$ and/or $x_m=0$. The existence and identification of the synchrony and anti-synchony subspaces for a weighted network are deeply relevant from the applications and dynamics point of view. Our characterization of the synchrony and anti-synchrony subspaces of a weighted network follows from our results where we give necessary and sufficient conditions for a generalized polydiagonal to be left invariant by the adjacency matrix and/or the Laplacian matrix of the network. | math | 1 |
Title: In Lieu of Privacy: Anonymous Contact Tracing
Abstract: We present Tracer Tokens, a hardware token of privacy-preserving contact tracing utilizing Exposure Notification \cite{GAEN} protocol. Through subnetworks, we show that any disease spread by proximity can be traced such as seasonal flu, cold, regional strains of COVID-19, or Tuberculosis. Further, we show this protocol to notify $n^n$ users in parallel, providing a speed of information unmatched by current contact tracing methods. | cs | 1 |
Title: Channel Estimation for FAS-assisted Multiuser mmWave Systems
Abstract: This letter investigates the challenge of channel estimation in a multiuser millimeter-wave (mmWave) time-division duplexing (TDD) system. In this system, the base station (BS) employs a multi-antenna uniform linear array (ULA), while each mobile user is equipped with a fluid antenna system (FAS). Accurate channel state information (CSI) plays a crucial role in the precise placement of antennas in FAS. Traditional channel estimation methods designed for fixed-antenna systems are inadequate due to the high dimensionality of FAS. To address this issue, we propose a low-sample-size sparse channel reconstruction (L3SCR) method, capitalizing on the sparse propagation paths characteristic of mmWave channels. In this approach, each fluid antenna only needs to switch and measure the channel at a few specific locations. By observing this reduced-dimensional data, we can effectively extract angular and gain information related to the sparse channel, enabling us to reconstruct the full CSI. Simulation results demonstrate that our proposed method allows us to obtain precise CSI with minimal hardware switching and pilot overhead. As a result, the system sum-rate approaches the upper bound achievable with perfect CSI. | cs | 0 |
Title: Modulus representation of the Riemann xi-function and equivalent inequalities for the Riemann hypothesis
Abstract: We derive a representation of the modulus of the Riemann xi-function and present purely analytical inequalities which are equivalent to the Riemann hypothesis. We also discuss polynomial approximations of the inequalities. | math | 0 |
Title: IoT in the Era of Generative AI: Vision and Challenges
Abstract: Equipped with sensing, networking, and computing capabilities, Internet of Things (IoT) such as smartphones, wearables, smart speakers, and household robots have been seamlessly weaved into our daily lives. Recent advancements in Generative AI exemplified by GPT, LLaMA, DALL-E, and Stable Difussion hold immense promise to push IoT to the next level. In this article, we share our vision and views on the benefits that Generative AI brings to IoT, and discuss some of the most important applications of Generative AI in IoT-related domains. Fully harnessing Generative AI in IoT is a complex challenge. We identify some of the most critical challenges including high resource demands of the Generative AI models, prompt engineering, on-device inference, offloading, on-device fine-tuning, federated learning, security, as well as development tools and benchmarks, and discuss current gaps as well as promising opportunities on enabling Generative AI for IoT. We hope this article can inspire new research on IoT in the era of Generative AI. | cs | 0 |
Title: On Model Compression for Neural Networks: Framework, Algorithm, and Convergence Guarantee
Abstract: Model compression is a crucial part of deploying neural networks (NNs), especially when the memory and storage of computing devices are limited in many applications. This paper focuses on two model compression techniques: low-rank approximation and weight pruning in neural networks, which are very popular nowadays. However, training NN with low-rank approximation and weight pruning always suffers significant accuracy loss and convergence issues. In this paper, a holistic framework is proposed for model compression from a novel perspective of nonconvex optimization by designing an appropriate objective function. Then, we introduce NN-BCD, a block coordinate descent (BCD) algorithm to solve the nonconvex optimization. One advantage of our algorithm is that an efficient iteration scheme can be derived with closed-form, which is gradient-free. Therefore, our algorithm will not suffer from vanishing/exploding gradient problems. Furthermore, with the Kurdyka-{\L}ojasiewicz (K{\L}) property of our objective function, we show that our algorithm globally converges to a critical point at the rate of O(1/k), where k denotes the number of iterations. Lastly, extensive experiments with tensor train decomposition and weight pruning demonstrate the efficiency and superior performance of the proposed framework. Our code implementation is available at https://github.com/ChenyangLi-97/NN-BCD | cs | 0 |
Title: The Lyapunov spectrum as the Newton-Raphson method for countable Markov interval maps
Abstract: We consider MRL maps (Markov-Renyi-L\"uroth), a class of interval maps with infinitely many branches that can have parabolic fixed points. We prove that for every MRL map $T$, the Lyapunov spectrum can be expressed in terms of the Legendre transform of the topological pressure of $-t\log|T'|$, generalizing previous results in the area. We also show that the Lyapunov spectrum coincides with a function directly related to the Newton-Raphson method applied to the topological pressure of $-t\log|T'|$. | math | 0 |
Title: Entropy and the Kullback-Leibler Divergence for Bayesian Networks: Computational Complexity and Efficient Implementation
Abstract: Bayesian networks (BNs) are a foundational model in machine learning and causal inference. Their graphical structure can handle high-dimensional problems, divide them into a sparse collection of smaller ones, underlies Judea Pearl's causality, and determines their explainability and interpretability. Despite their popularity, there are almost no resources in the literature on how to compute Shannon's entropy and the Kullback-Leibler (KL) divergence for BNs under their most common distributional assumptions. In this paper, we provide computationally efficient algorithms for both by leveraging BNs' graphical structure, and we illustrate them with a complete set of numerical examples. In the process, we show it is possible to reduce the computational complexity of KL from cubic to quadratic for Gaussian BNs. | cs | 0 |
Title: Zero-one law for directional transience of one dimensional excited random walks
Abstract: The probability that a one dimensional excited random walk in stationary ergodic and elliptic cookie environment is transient to the right (left) is either zero or one. This solves a problem posed by Kosygina and Zerner [8]. | math | 1 |
Title: Better and Simpler Lower Bounds for Differentially Private Statistical Estimation
Abstract: We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the covariance of a Gaussian up to spectral error $\alpha$ requires $\tilde{\Omega}\left(\frac{d^{3/2}}{\alpha \varepsilon} + \frac{d}{\alpha^2}\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\alpha \le O\left(\frac{1}{\sqrt{d}}\right)$, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded $k$th moments requires $\tilde{\Omega}\left(\frac{d}{\alpha^{k/(k-1)} \varepsilon} + \frac{d}{\alpha^2}\right)$ samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of $k = 2$. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples. | math | 0 |
Title: Limit Theorems for the Fractional Non-homogeneous Poisson Process
Abstract: The fractional non-homogeneous Poisson process was introduced by a time-change of the non-homogeneous Poisson process with the inverse $\alpha$-stable subordinator. We propose a similar definition for the (non-homogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional non-homogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe's theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation. | math | 1 |
Title: Euler's Theorem for Regular CW-Complexes
Abstract: For strongly connected, pure $n$-dimensional regular CW-complexes, we show that {\it evenness} (each $(n{-}1)$-cell is contained in an even number of $n$-cells) is equivalent to generalizations of both cycle decomposition and traversability. | math | 0 |
Title: On the Law of Large Numbers and Convergence Rates for the Discrete Fourier Transform of Random Fields
Abstract: We study the Marcinkiewicz-Zygmund strong law of large numbers for the cubic partial sums of the discrete Fourier transform of random fields. We establish Marcinkiewicz-Zygmund types rate of convergence for the discrete Fourier transform of random fields under weaker conditions than identical distribution. | math | 0 |
Title: Strong universality, recurrence, and analytic P-ideals in dynamical systems
Abstract: Given a dynamical system $(X,T)$ and a family $\mathsf{I}\subseteq \mathcal{P}(\omega)$ of "small" sets of nonnegative integers, a point $x \in X$ is said to be $\mathsf{I}$-strong universal if for each $y \in X$ there exists a subsequence $(T^nx: n \in A)$ of its orbit which is convergent to $y$ and, in addition, the set of indexes $A$ is "not small," that is, $A\notin \mathsf{I}$. An analoguous definition is given for $\mathsf{I}$-strong recurrence. In this work, we provide several structural properties and relationships between $\mathsf{I}$-strong universality, $\mathsf{I}$-strong recurrence, and the corresponding ordinary notions of $\mathsf{I}$-universality and $\mathsf{I}$-recurrence. As applications, we provide sufficient conditions which ensure the equivalence between the above notions and the property that each nonempty open set contains some cluster point of some orbit. In addition, we show that if $T$ is a homomorphism on a Fr\'{e}chet space $X$ and there exists a dense set of vectors with null orbit, then for each $y \in X$ the set of all vectors $x \in X$ such that $\lim_{n \in A}T^nx=y$ for some $A\subseteq \omega$ with nonzero upper asymptotic density is either empty or comeager. In the special case of linear dynamical systems on Banach spaces with a dense set of uniformly recurrent vectors, we obtain that $T$ is upper frequently hypercyclic if and only if there exists a hypercyclic vector $x \in X$ for which $\lim_{n \in A}T^nx=0$ for some $A\subseteq \omega$ with nonzero upper asymptotic density. | math | 0 |
Title: Phase transitions of McKean-Vlasov SDEs in Multi-well Landscapes
Abstract: Phase transitions and critical behaviour of a class of MV-SDEs, whose concomitant non-local Fokker-Planck equation includes the Granular Media equation with quadratic interaction potential as a special case, is studied. By careful analysis of an implicit auxiliary integral equation, it is shown for a wide class of potentials that below a certain `critical threshold' there are exactly as many stationary measures as extrema of the potential, while above another the stationary measure is unique, and consequently phase transition(s) between. For symmetric bistable potentials, these critical thresholds are proven to be equal and a strictly increasing function of the aggregation parameter. Additionally, a simple condition is provided for symmetric multi-well potentials with an arbitrary number of extrema to demonstrate analogous behaviour. This answers, with considerably more generality, a conjecture of Tugaut [Stochastics, 86:2, 257-284]. To the best of our knowledge many of these results are novel. Others simplify the proofs of known results whilst greatly increasing their applicability. | math | 0 |
Title: On the Ramsey number of the double star
Abstract: The double star $S(m_1,m_2)$ is obtained from joining the centres of a star with $m_1$ leaves and a star with $m_2$ leaves. We give a short proof of a new upper bound on the two-colour Ramsey number of $S(m_1,m_2)$, for positive $m_1,m_2$ fulfilling $(\sqrt 5+1)m_2/2 < m_1 < 3m_2$. Our result implies that for all positive $m$, the Ramsey number of the double star $S(2m,m)$ is at most $4.275m$. | math | 0 |
Title: Asynchronous Downlink Massive MIMO Networks: A Stochastic Geometry Approach
Abstract: Massive multiple-input multiple-output (MIMO) is recognized as a promising technology for the next generation of wireless networks because of its potential to increase the spectral efficiency. In initial studies of massive MIMO, the system has been considered to be perfectly synchronized throughout the entire cells. However, perfect synchronization may be hard to attain in practice. Therefore, we study a massive MIMO system whose cells are not synchronous to each other, while transmissions in a cell are still synchronous. We analyze an asynchronous downlink massive MIMO system in terms of the coverage probability and the ergodic rate by means of the stochastic geometry tool. For comparison, we also obtain the results for the synchronous systems. In addition, we investigate the effect of the uplink power control and the number of pilot symbols on the downlink ergodic rate, and we observe that there is an optimal value for the number of pilot symbols maximizing the downlink ergodic rate of a cell. Our results also indicate that, compared to the cases with synchronous transmission, the downlink ergodic rate is more sensitive to the uplink power control in the asynchronous mode. | cs | 1 |
Title: Constructing Thick $B_h$-sets
Abstract: A subset $A$ of a commutative semigroup $X$ is called a $B_h$ set in $X$ if the only solutions to $a_1+\dots+a_h = b_1 + \cdots +b_h$ (with $a_i,b_i \in A$) are the trivial solutions $\{a_1,\dots,a_h\} = \{b_1,\dots,b_h\}$ (as multisets). With $h=2$ and $X={\mathbb Z}$, these sets are also known as Sidon sets, Golomb Rulers, and Babcock sets. In this work, we generalize constructions of Bose-Chowla and Singer and give the resultant bounds on the diameter of a $k$ element $B_h$ set in $\mathbb Z$ for small $k$. We conclude with a list of open problems. | math | 0 |
Title: MindOpt Adapter for CPLEX Benchmarking Performance Analysis
Abstract: This report provides a comprehensive analysis of the performance of MindOpt Adapter for CPLEX 12.9 in benchmark testing. CPLEX, recognized as a robust Mixed Integer Programming (MIP) solver, has faced some scrutiny regarding its performance on MIPLIB 2017 when configured to default settings. MindOpt Adapter aims to enhance CPLEX's performance by automatically applying improved configurations for solving optimization problems. Our testing demonstrates that MindOpt Adapter for CPLEX yields successfully solved 230 of the 240 problems in the MIPLIB 2017 benchmark set. This performance surpasses all the other solvers in terms of the number of problems solved and the geometric mean of running times. The report provides a comparison of the benchmark results against the outcomes achieved by CPLEX under its default configuration. | cs | 0 |
Title: Detecting Unseen Falls from Wearable Devices using Channel-wise Ensemble of Autoencoders
Abstract: A fall is an abnormal activity that occurs rarely, so it is hard to collect real data for falls. It is, therefore, difficult to use supervised learning methods to automatically detect falls. Another challenge in using machine learning methods to automatically detect falls is the choice of engineered features. In this paper, we propose to use an ensemble of autoencoders to extract features from different channels of wearable sensor data trained only on normal activities. We show that the traditional approach of choosing a threshold as the maximum of the reconstruction error on the training normal data is not the right way to identify unseen falls. We propose two methods for automatic tightening of reconstruction error from only the normal activities for better identification of unseen falls. We present our results on two activity recognition datasets and show the efficacy of our proposed method against traditional autoencoder models and two standard one-class classification methods. | cs | 1 |
Title: Learning Traffic Speed Dynamics from Visualizations
Abstract: Space-time visualizations of macroscopic or microscopic traffic variables is a qualitative tool used by traffic engineers to understand and analyze different aspects of road traffic dynamics. We present a deep learning method to learn the macroscopic traffic speed dynamics from these space-time visualizations, and demonstrate its application in the framework of traffic state estimation. Compared to existing estimation approaches, our approach allows a finer estimation resolution, eliminates the dependence on the initial conditions, and is agnostic to external factors such as traffic demand, road inhomogeneities and driving behaviors. Our model respects causality in traffic dynamics, which improves the robustness of estimation. We present the high-resolution traffic speed fields estimated for several freeway sections using the data obtained from the Next Generation Simulation Program (NGSIM) and German Highway (HighD) datasets. We further demonstrate the quality and utility of the estimation by inferring vehicle trajectories from the estimated speed fields, and discuss the benefits of deep neural network models in approximating the traffic dynamics. | cs | 1 |
Title: A localization-delocalization transition for nonhomogeneous random matrices
Abstract: We consider $N\times N$ self-adjoint Gaussian random matrices defined by an arbitrary deterministic sparsity pattern with $d$ nonzero entries per row. We show that such random matrices exhibit a canonical localization-delocalization transition near the edge of the spectrum: when $d\gg\log N$ the random matrix possesses a delocalized approximate top eigenvector, while when $d\ll\log N$ any approximate top eigenvector is localized. The key feature of this phenomenon is that it is universal with respect to the sparsity pattern, in contrast to the delocalization properties of exact eigenvectors which are sensitive to the specific sparsity pattern of the random matrix. | math | 0 |
Title: Full instability of boundary layers with the Navier boundary condition
Abstract: We consider the problem of the stability of the Navier-Stokes equations in $\mathbb{T}\times \mathbb{R}_+$ near shear flows which are linearly unstable for the Euler equation. In \cite{greniernguyen}, the authors prove an $L^{\infty}$ instability result for the no-slip boundary condition which also denies the validity of the Prandtl boundary layer expansion. In this paper, we generalise this result to a Navier slip boundary condition with viscosity dependent slip length: $\partial_y u =\nu^{-\gamma}u$ at $y=0$, where $\gamma >1/2$. This range includes the physical slip rate $\gamma=1$. | math | 0 |
Title: Spectral-based Graph Neutral Networks for Complementary Item Recommendation
Abstract: Modeling complementary relationships greatly helps recommender systems to accurately and promptly recommend the subsequent items when one item is purchased. Unlike traditional similar relationships, items with complementary relationships may be purchased successively (such as iPhone and Airpods Pro), and they not only share relevance but also exhibit dissimilarity. Since the two attributes are opposites, modeling complementary relationships is challenging. Previous attempts to exploit these relationships have either ignored or oversimplified the dissimilarity attribute, resulting in ineffective modeling and an inability to balance the two attributes. Since Graph Neural Networks (GNNs) can capture the relevance and dissimilarity between nodes in the spectral domain, we can leverage spectral-based GNNs to effectively understand and model complementary relationships. In this study, we present a novel approach called Spectral-based Complementary Graph Neural Networks (SComGNN) that utilizes the spectral properties of complementary item graphs. We make the first observation that complementary relationships consist of low-frequency and mid-frequency components, corresponding to the relevance and dissimilarity attributes, respectively. Based on this spectral observation, we design spectral graph convolutional networks with low-pass and mid-pass filters to capture the low-frequency and mid-frequency components. Additionally, we propose a two-stage attention mechanism to adaptively integrate and balance the two attributes. Experimental results on four e-commerce datasets demonstrate the effectiveness of our model, with SComGNN significantly outperforming existing baseline models. | cs | 0 |
Title: Attackers reveal their arsenal: An investigation of adversarial techniques in CTI reports
Abstract: Context: Cybersecurity vendors often publish cyber threat intelligence (CTI) reports, referring to the written artifacts on technical and forensic analysis of the techniques used by the malware in APT attacks. Objective: The goal of this research is to inform cybersecurity practitioners about how adversaries form cyberattacks through an analysis of adversarial techniques documented in cyberthreat intelligence reports. Dataset: We use 594 adversarial techniques cataloged in MITRE ATT\&CK. We systematically construct a set of 667 CTI reports that MITRE ATT\&CK used as citations in the descriptions of the cataloged adversarial techniques. Methodology: We analyze the frequency and trend of adversarial techniques, followed by a qualitative analysis of the implementation of techniques. Next, we perform association rule mining to identify pairs of techniques recurring in APT attacks. We then perform qualitative analysis to identify the underlying relations among the techniques in the recurring pairs. Findings: The set of 667 CTI reports documents 10,370 techniques in total, and we identify 19 prevalent techniques accounting for 37.3\% of documented techniques. We also identify 425 statistically significant recurring pairs and seven types of relations among the techniques in these pairs. The top three among the seven relationships suggest that techniques used by the malware inter-relate with one another in terms of (a) abusing or affecting the same system assets, (b) executing in sequences, and (c) overlapping in their implementations. Overall, the study quantifies how adversaries leverage techniques through malware in APT attacks based on publicly reported documents. We advocate organizations prioritize their defense against the identified prevalent techniques and actively hunt for potential malicious intrusion based on the identified pairs of techniques. | cs | 0 |
Title: Efficient Scenario Generation for Chance-constrained Economic Dispatch Considering Ambient Wind Conditions
Abstract: Scenario generation is an effective data-driven method for solving chance-constrained optimization while ensuring desired risk guarantees with a finite number of samples. Crucial challenges in deploying this technique in the real world arise due to the absence of appropriate risk-tuning models tailored for the desired application. In this paper, we focus on designing efficient scenario generation schemes for economic dispatch in power systems. We propose a novel scenario generation method based on filtering scenarios using ambient wind conditions. These filtered scenarios are deployed incrementally in order to meet desired risk levels while using minimum resources. In order to study the performance of the proposed scheme, we illustrate the procedure on case studies performed for both 24-bus and 118-bus systems with real-world wind power forecasting data. Numerical results suggest that the proposed filter-and-increment scenario generation model leads to a precise and efficient solution for the chance-constrained economic dispatch problem. | math | 0 |
Title: Simplicial $*$-modules and mild actions
Abstract: We develop an analogue of the theory of $*$-modules in the world of simplicial sets, based on actions of a certain simplicial monoid $E\mathcal M$ originally appearing in the construction of global algebraic $K$-theory. As our main results, we show that strictly commutative monoids with respect to a certain box product on these simplicial $*$-modules yield models of equivariantly and globally coherently commutative monoids, and we give a characterization of simplicial $*$-modules in terms of a certain mildness condition on the $E\mathcal M$-action, relaxing the notion of tameness previously investigated by Sagave-Schwede and the first author. | math | 0 |
Title: Computation of Infinitesimals for a Group Action on a Multispace of One Independent Variable
Abstract: This paper expands upon the work of Peter Olver's paper [Appl. Algebra Engrg. Comm. Comput. 11 (2001), 417-436], wherein Olver uses a moving frames approach to examine the action of a group on a curve within a generalization of jet space known as multispace. Here we seek to further study group actions on the multispace of curves by computing the infinitesimals for a given action. For the most part, we proceed formally, and produce in the multispace a recursion relation that closely mimics the previously known prolongation recursion relations for infinitesimals of a group action on jet space. | math | 0 |
Title: Fractional non-homogeneous counting process
Abstract: A new fractional non-homogeneous counting process has been introduced and developed using the Kilbas and Saigo three-parameter generalization of the Mittag-Leffler function. The probability distribution function of this process reproduces for certain set of the fractality parameters the famous Poisson and fractional Poisson probability distributions as well as the probability distribution function of a counting process displaying stretched exponential interarrival times distribution. Applications of the developed fractional non-homogeneous counting process cover fractional compound process, the generalization of combinatorial polynomials and numbers, statistics of the fractional non-homogeneous counting process and a new representation of the Kilbas and Saigo function. | math | 0 |
Title: Maximum Likelihood With a Time Varying Parameter
Abstract: We consider the problem of tracking an unknown time varying parameter that characterizes the probabilistic evolution of a sequence of independent observations. To this aim, we propose a stochastic gradient descent-based recursive scheme in which the log-likelihood of the observations acts as time varying gain function. We prove convergence in mean-square error in a suitable neighbourhood of the unknown time varying parameter and illustrate the details of our findings in the case where data are generated from distributions belonging to the exponential family. | math | 1 |
Title: On dual quaternions, dual split quaternions and Cartan-Schouten metrics on perfect Lie groups
Abstract: We discuss Cartan-Schouten metrics (Riemannian or pseudo-Riemannian metrics that are parallel with respect to the Cartan-Schouten canonical connection) on perfect Lie groups. Applications are foreseen in Information Geometry. Throughout this work, the tangent bundle TG and the cotangent bundle T*G of a Lie group G, are always endowed with their Lie group structures induced by the right trivialization. We show that TG and T*G are isomorphic if G possesses a biinvariant Riemannian or pseudo-Riemannian metric. We also show that, if on a perfect Lie group, there exists a Cartan-Schouten metric, then it must be biinvariant. We compute all such metrics on the cotangent bundles of simple Lie groups. We further show the following. Endowed with their canonical Lie group structures, the set of unit dual quaternions is isomorphic to TSU(2), the set of unit dual split quaternions is isomorphic to T*SL(2,R). The group SE(3) of special rigid displacements of the Euclidean 3-space is isomorphic to T*SO(3). The group SE(2,1) of special rigid displacements of the Minkowski 3-space is isomorphic to T*SO(2,1). Some results on SE(3) by N. Miolane and X. Pennec, and M. Zefran, V. Kumar and C. Croke, are generalized to SE(2,1) and to T*G, for any simple Lie group G. | math | 0 |
Title: The Zassenhaus variety of a reductive Lie algebra in positive characteristic
Abstract: Let g be the Lie algebra of a connected reductive group G over an algebraically closed field k of characteristic p>0. Let $Z$ be the centre of the universal enveloping algebra U=U(g) of g. Its maximal spectrum is called the Zassenhaus variety of g. We show that, under certain mild assumptions on G, the field of fractions Frac(Z) of Z is G-equivariantly isomorphic to the function field of the dual space g* with twisted G-action. In particular Frac(Z) is rational. This confirms a conjecture J. Alev. Furthermore we show that Z is a unique factorisation domain, confirming a conjecture of A. Braun and C. Hajarnavis. Recently, A. Premet used the above result about Frac(Z), a result of Colliot-Thelene, Kunyavskii, Popov and Reichstein and reduction mod p arguments to show that the Gelfand-Kirillov conjecture cannot hold for simple complex Lie algebras that are not of type A, C or G_2. | math | 1 |
Title: Optimal Hardy-weights for the $(p,A)$-Laplacian with a potential term
Abstract: We construct new optimal $L^p$ Hardy-type inequalities for elliptic Schr\"odinger-type operators | math | 1 |
Title: LMBot: Distilling Graph Knowledge into Language Model for Graph-less Deployment in Twitter Bot Detection
Abstract: As malicious actors employ increasingly advanced and widespread bots to disseminate misinformation and manipulate public opinion, the detection of Twitter bots has become a crucial task. Though graph-based Twitter bot detection methods achieve state-of-the-art performance, we find that their inference depends on the neighbor users multi-hop away from the targets, and fetching neighbors is time-consuming and may introduce bias. At the same time, we find that after finetuning on Twitter bot detection, pretrained language models achieve competitive performance and do not require a graph structure during deployment. Inspired by this finding, we propose a novel bot detection framework LMBot that distills the knowledge of graph neural networks (GNNs) into language models (LMs) for graph-less deployment in Twitter bot detection to combat the challenge of data dependency. Moreover, LMBot is compatible with graph-based and graph-less datasets. Specifically, we first represent each user as a textual sequence and feed them into the LM for domain adaptation. For graph-based datasets, the output of LMs provides input features for the GNN, enabling it to optimize for bot detection and distill knowledge back to the LM in an iterative, mutually enhancing process. Armed with the LM, we can perform graph-less inference, which resolves the graph data dependency and sampling bias issues. For datasets without graph structure, we simply replace the GNN with an MLP, which has also shown strong performance. Our experiments demonstrate that LMBot achieves state-of-the-art performance on four Twitter bot detection benchmarks. Extensive studies also show that LMBot is more robust, versatile, and efficient compared to graph-based Twitter bot detection methods. | cs | 0 |
Title: GIT-Mol: A Multi-modal Large Language Model for Molecular Science with Graph, Image, and Text
Abstract: Large language models have made significant strides in natural language processing, enabling innovative applications in molecular science by processing textual representations of molecules. However, most existing language models cannot capture the rich information with complex molecular structures or images. In this paper, we introduce GIT-Mol, a multi-modal large language model that integrates the Graph, Image, and Text information. To facilitate the integration of multi-modal molecular data, we propose GIT-Former, a novel architecture that is capable of aligning all modalities into a unified latent space. We achieve a 5%-10% accuracy increase in properties prediction and a 20.2% boost in molecule generation validity compared to the baselines. With the any-to-language molecular translation strategy, our model has the potential to perform more downstream tasks, such as compound name recognition and chemical reaction prediction. | cs | 0 |
Title: A note on Laguerre truncated polynomials and quadrature formula
Abstract: In this contribution we deal with Gaussian quadrature rules based on orthogonal polynomials associated with a weight function $w(x)= x^{\alpha} e^{-x}$ supported on an interval $(0,z)$, $z>0.$ The modified Chebyshev algorithm is used in order to test the accuracy in the computation of the coefficients of the three-term recurrence relation, the zeros and weights, as well as the dependence on the parameter $z.$ | math | 0 |
Title: Optimal Decomposition and Recombination of Isostatic Geometric Constraint Systems for Designing Layered Materials
Abstract: Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint systems, we describe an O(n^3) algorithm for a broad class of constraint systems that are isostatic or underconstrained. The algorithm achieves optimality by using the new notion of a canonical DR-plan that also meets various desirable, previously studied criteria. In addition, we leverage recent results on Cayley configuration spaces to show that the indecomposable systems---that are solved at the nodes of the optimal DR-plan by recombining solutions to child systems---can be minimally modified to become decomposable and have a small DR-plan, leading to efficient realization algorithms. We show formal connections to well-known problems such as completion of underconstrained systems. Well suited to these methods are classes of constraint systems that can be used to efficiently model, design and analyze quasi-uniform (aperiodic) and self-similar, layered material structures. We formally illustrate by modeling silica bilayers as body-hyperpin systems and cross-linking microfibrils as pinned line-incidence systems. A software implementation of our algorithms and videos demonstrating the software are publicly available online (visit http://cise.ufl.edu/~tbaker/drp/index.html.) | cs | 1 |
Title: The bridge number of satellite knots, links, and spatial graphs in the 3-sphere and lens spaces
Abstract: Let $T$ be a satellite knot, link, or spatial graph in a 3-manifold $M$ that is either $S^3$ or a lens space. Let $b_0$ and $b_1$ denote genus 0 and genus 1 bridge number, respectively. Suppose that $T$ has a companion knot $K$ and wrapping number $\omega$ with respect to $K$. When $K$ is not a torus knot, we show that $b_1(T)\geq \omega b_1(K)$. There are previously known counter-examples if $K$ is a torus knot. Along the way, we generalize and give a new proof of Schubert's result that $b_0(T) \geq \omega b_0(K)$. We also prove versions of the theorem applicable to when $T$ is a ``lensed satellite'' or when there is a torus separating components of $T$. | math | 0 |
Title: Towards Seamless Serverless Computing Across an Edge-Cloud Continuum
Abstract: Serverless computing has emerged as an attractive paradigm due to the efficiency of development and the ease of deployment without managing any underlying infrastructure. Nevertheless, serverless computing approaches face numerous challenges to unlock their full potential in hybrid environments. To gain a deeper understanding and firsthand knowledge of serverless computing in edge-cloud deployments, we review the current state of open-source serverless platforms and compare them based on predefined requirements. We then design and implement a serverless computing platform with a novel edge orchestration technique that seamlessly deploys serverless functions across the edge and cloud environments on top of the Knative serverless platform. Moreover, we propose an offloading strategy for edge environments and four different functions for experimentation and showcase the performance benefits of our solution. Our results demonstrate that such an approach can efficiently utilize both cloud and edge resources by dynamically offloading functions from the edge to the cloud during high activity, while reducing the overall application latency and increasing request throughput compared to an edge-only deployment. | cs | 0 |
Title: An Adaptive Incremental Gradient Method With Support for Non-Euclidean Norms
Abstract: Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some large-scale optimization tasks. To overcome the problem, we propose and analyze several novel adaptive variants of the popular SAGA algorithm. Eventually, we design a variant of Barzilai-Borwein step-size which is tailored for the incremental gradient method to ensure memory efficiency and fast convergence. We establish its convergence guarantees under general settings that allow non-Euclidean norms in the definition of smoothness and the composite objectives, which cover a broad range of applications in machine learning. We improve the analysis of SAGA to support non-Euclidean norms, which fills the void of existing work. Numerical experiments on standard datasets demonstrate a competitive performance of the proposed algorithm compared with existing variance-reduced methods and their adaptive variants. | math | 1 |
Title: Comparison of Syntactic Parsers on Biomedical Texts
Abstract: Syntactic parsing is an important step in the automated text analysis which aims at information extraction. Quality of the syntactic parsing determines to a large extent the recall and precision of the text mining results. In this paper we evaluate the performance of several popular syntactic parsers in application to the biomedical text mining. | cs | 1 |
Title: Sorting Can Exponentially Speed Up Pure Dynamic Programming
Abstract: Many discrete minimization problems, including various versions of the shortest path problem, can be efficiently solved by dynamic programming (DP) algorithms that are "pure" in that they only perform basic operations, as min, max, +, but no conditional branchings via if-then-else in their recursion equations. It is known that any pure (min,+) DP algorithm solving the minimum weight spanning tree problem on undirected n-vertex graphs must perform at least $2^{\Omega(\sqrt{n})}$ operations. We show that this problem can be solved by a pure (min,max,+) DP algorithm performing only $O(n^3)$ operations. The algorithm is essentially a (min,max) algorithm: addition operations are only used to output the final values. The presence of both min and max operations means that now DP algorithms can sort: this explains the title of the paper. | cs | 1 |
Title: Manipulating Trajectory Prediction with Backdoors
Abstract: Autonomous vehicles ought to predict the surrounding agents' trajectories to allow safe maneuvers in uncertain and complex traffic situations. As companies increasingly apply trajectory prediction in the real world, security becomes a relevant concern. In this paper, we focus on backdoors - a security threat acknowledged in other fields but so far overlooked for trajectory prediction. To this end, we describe and investigate four triggers that could affect trajectory prediction. We then show that these triggers (for example, a braking vehicle), when correlated with a desired output (for example, a curve) during training, cause the desired output of a state-of-the-art trajectory prediction model. In other words, the model has good benign performance but is vulnerable to backdoors. This is the case even if the trigger maneuver is performed by a non-casual agent behind the target vehicle. As a side-effect, our analysis reveals interesting limitations within trajectory prediction models. Finally, we evaluate a range of defenses against backdoors. While some, like simple offroad checks, do not enable detection for all triggers, clustering is a promising candidate to support manual inspection to find backdoors. | cs | 0 |
Title: Some results and a conjecture on certain subclasses of graphs according to the relations among certain energies, degrees and conjugate degrees of graphs
Abstract: Let $G$ be a simple graph of order $n$ with degree sequence $(d)=(d_1,d_2,\ldots,d_n)$ and conjugate degree sequence $(d^*)=(d_1^*,d_2^*,\ldots,d_n^*)$. In \cite{AkbariGhorbaniKoolenObudi2010,DasMojallalGutman2017} it was proven that $\mathcal{E}(G)\leq \sum_{i=1}^{n} \sqrt{d_i}$ and $\sum_{i=1}^{n} \sqrt{d_i^*} \leq LEL(G) \leq IE(G) \leq \sum_{i=1}^{n} \sqrt{d_i}$, where $\mathcal{E}(G)$, $LEL(G)$ and $IE(G)$ are the energy, the Laplacian-energy-like invariant and the incidence energy of $G$, respectively, and in \cite{DasMojallalGutman2017} it was concluded that the class of all connected simple graphs of order $n$ can be dividend into four subclasses according to the position of $\mathcal{E}(G)$ in the order relations above. Then, they proposed a problem about characterizing all graphs in each subclass. In this paper, we attack this problem. First, we count the number of graphs of order $n$ in each of four subclasses for every $1\leq n \leq 8$ using a Sage code. Second, we present a conjecture on the ratio of the number of graphs in each subclass to the number of all graphs of order $n$ as $n$ approaches the infinity. Finally, as a first partial solution to the problem, we determine subclasses to which a path, a complete graph and a cycle graph of order $n\geq 1$ belong. | math | 1 |
Title: Local-in-time strong solutions of the homogeneous Landau-Coulomb equation with $L^p$ initial datum
Abstract: We consider the homogeneous Landau equation with Coulomb potential and general initial data $f_{in} \in L^p$, where $p$ is arbitrarily close to $3/2$. We show the local-in-time existence and uniqueness of smooth solutions for such initial data. The constraint $p > 3/2$ has appeared in several related works and appears to be the minimal integrability assumption achievable with current techniques. We adapt recent ODE methods and conditional regularity results appearing in [arXiv:2303.02281] to deduce new short time $L^p \to L^\infty$ smoothing estimates. These estimates enable us to construct local-in-time smooth solutions for large $L^p$ initial data, and allow us to show directly conditional regularity results for solutions verifying \emph{unweighted} Prodi-Serrin type conditions. As a consequence, we obtain additional stability and uniqueness results for the solutions we construct. | math | 0 |
Title: Electromechanical phase-field fracture modelling of piezoresistive CNT-based composites
Abstract: We present a novel computational framework to simulate the electromechanical response of self-sensing carbon nanotube (CNT)-based composites experiencing fracture. The computational framework combines electrical-deformation-fracture finite element modelling with a mixed micromechanics formulation. The latter is used to estimate the constitutive properties of CNT-based composites, including the elastic tensor, fracture energy, electrical conductivity, and linear piezoresistive coefficients. These properties are inputted into a coupled electro-structural finite element model, which simulates the evolution of cracks based upon phase-field fracture. The coupled physical problem is solved in a monolithic manner, exploiting the robustness and efficiency of a quasi-Newton algorithm. 2D and 3D boundary value problems are simulated to illustrate the potential of the modelling framework in assessing the influence of defects on the electromechanical response of meso- and macro-scale smart structures. Case studies aim at shedding light into the interplay between fracture and the electromechanical material response and include parametric analyses, validation against experiments and the simulation of complex cracking conditions (multiple defects, crack merging). The presented numerical results showcase the efficiency and robustness of the computational framework, as well as its ability to model a large variety of structural configurations and damage patterns. The deformation-electrical-fracture finite element code developed is made freely available to download. | cs | 1 |
Title: On upper bounds on expectations of gOSs based on DFR and DFRA distributions
Abstract: We focus on the problem of establishing the optimal upper bounds on generalized order statistics which are based on the underlying cdf belonging to the family of distributions with decreasing failure rate and decreasing failure rate on the average. This issue has been previously considered by Bieniek [Projection bounds on expectations of generalized order statistics from DFR and DFRA families, Statistics, 2006; 40: 339--351], who established upper nonnegative mean-variance bounds with use of the projections of the compositions of density functions of the uniform generalized order statistic and the exponential distribution function onto the properly chosen convex cones. In this paper we obtain possibly negative upper bounds, by improving the zero bounds obtained by Bieniek for some particular cases of gOSs. We express the bounds in the scale units generated by the central absolute moments of arbitrary orders. We also describe the attainability conditions. | math | 1 |
Title: Phase transition and diffusion among socially interacting self-propelled agents
Abstract: We consider a hydrodynamic model of swarming behavior derived from the kinetic description of a particle system combining a noisy Cucker-Smale consensus force and self-propulsion. In the large self-propulsion force limit, we provide evidence of a phase transition from disordered to ordered motion which manifests itself as a change of type of the limit model (from hyperbolic to diffusive) at the crossing of a critical noise intensity. In the hyperbolic regime, the resulting model, referred to as the `Self-Organized Hydrodynamics (SOH)', consists of a system of compressible Euler equations with a speed constraint. We show that the range of SOH models obtained by this limit is restricted. To waive this restriction, we compute the Navier-Stokes diffusive corrections to the hydrodynamic model. Adding these diffusive corrections, the limit of a large propulsion force yields unrestricted SOH models and offers an alternative to the derivation of the SOH using kinetic models with speed constraints. | math | 1 |
Title: Universality for bounded degree spanning trees in randomly perturbed graphs
Abstract: We solve a problem of Krivelevich, Kwan and Sudakov [SIAM Journal on Discrete Mathematics 31 (2017), 155-171] concerning the threshold for the containment of all bounded degree spanning trees in the model of randomly perturbed dense graphs. More precisely, we show that, if we start with a dense graph $G_\alpha$ on $n$ vertices with $\delta(G_\alpha)\ge \alpha n$ for $\alpha>0$ and we add to it the binomial random graph $G(n,C/n)$, then with high probability the graph $G_\alpha\cup G(n,C/n)$ contains copies of all spanning trees with maximum degree at most $\Delta$ simultaneously, where $C$ depends only on $\alpha$ and $\Delta$. | math | 1 |
Title: On wormholes in the moduli space of surfaces
Abstract: We study a certain wormholing phenomenon that takes place in the Koll\'ar--Shepherd-Barron--Alexeev (KSBA) compactification of the moduli space of surfaces of general type. It occurs because of the appearance of particular extremal P-resolutions in surfaces on the KSBA boundary. We state a general wormhole conjecture, and we prove it for a wide range of cases. At the end, we discuss some topological properties and open questions. | math | 1 |
Title: Model order reduction and sensitivity analysis for complex heat transfer simulations inside the human eyeball
Abstract: Heat transfer in the human eyeball, a complex organ, is significantly influenced by various pathophysiological and external parameters. Particularly, heat transfer critically affects fluid behavior within the eye and ocular drug delivery processes. Overcoming the challenges of experimental analysis, this study introduces a comprehensive three-dimensional mathematical and computational model to simulate the heat transfer in a realistic geometry. Our work includes an extensive sensitivity analysis to address uncertainties and delineate the impact of different variables on heat distribution in ocular tissues. To manage the model's complexity, we employed a very fast model reduction technique with certified sharp error bounds, ensuring computational efficiency without compromising accuracy. Our results demonstrate remarkable consistency with experimental observations and align closely with existing numerical findings in the literature. Crucially, our findings underscore the significant role of blood flowand environmental conditions, particularly in the eye's internal tissues. Clinically, this model offers a promising tool for examining the temperature-related effects of various therapeutic interventions on the eye. Such insights are invaluable for optimizing treatment strategies in ophthalmology. | math | 0 |
Title: Normal operators with highly incompatible off-diagonal corners
Abstract: Let $\mathcal{H}$ be a complex, separable Hilbert space, and $\mathcal{B}(\mathcal{H})$ denote the set of all bounded linear operators on $\mathcal{H}$. Given an orthogonal projection $P \in \mathcal{B}(\mathcal{H})$ and an operator $D \in \mathcal{B}(\mathcal{H})$, we may write $D=\begin{bmatrix} D_1& D_2 D_3 & D_4 \end{bmatrix}$ relative to the decomposition $\mathcal{H} = \mathrm{ran}\, P \oplus \mathrm{ran}\, (I-P)$. In this paper we study the question: for which non-negative integers $j, k$ can we find a normal operator $D$ and an orthogonal projection $P$ such that $\mathrm{rank}\, D_2 = j$ and $\mathrm{rank}\, D_3 = k$? Complete results are obtained in the case where $\mathrm{dim}\, \mathcal{H} < \infty$, and partial results are obtained in the infinite-dimensional setting. | math | 1 |
Title: Architectural Design for Secure Smart Contract Development
Abstract: As time progresses, the need for more secure applications grows exponentially. The different types of sensitive information that is being transferred virtually has sparked a rise in systems that leverage blockchain. Different sectors are beginning to use this disruptive technology to evaluate the risks and benefits. Sectors like finance, medicine, higher education, and wireless communication have research regarding blockchain. Futhermore, the need for security standards in this area of research is pivotal. In recent past, several attacks on blockchain infrastructures have resulted in hundreds of millions dollars lost and sensitive information compromised. Some of these attacks include DAO attacks, bZx attacks, and Parity Multisignature Wallet Double Attacks which targeted vulnerabilities within smart contracts on the Ethereum network. These attacks exposed the weaknesses of current smart contract development practices which has led to the increase in distrust and adoption of systems that leverage blockchain for its functionality. In this paper, I identify common software vulnerabilities and attacks on blockchain infrastructures, thoroughly detail the smart contract development process and propose a model for ensuring a stronger security standard for future systems leveraging smart contracts. The purpose for proposing a model is to promote trust among end users in the system which is a foundational element for blockchain adoption in the future. | cs | 0 |
Title: A multipartite analogue of Dilworth's Theorem
Abstract: We prove that every partially ordered set on $n$ elements contains $k$ subsets $A_{1},A_{2},\dots,A_{k}$ such that either each of these subsets has size $\Omega(n/k^{5})$ and, for every $i<j$, every element in $A_{i}$ is less than or equal to every element in $A_{j}$, or each of these subsets has size $\Omega(n/(k^{2}\log n))$ and, for every $i \not = j$, every element in $A_{i}$ is incomparable with every element in $A_{j}$ for $i\ne j$. This answers a question of the first author from 2006. As a corollary, we prove for each positive integer $h$ there is $C_h$ such that for any $h$ partial orders $<_{1},<_{2},\dots,<_{h}$ on a set of $n$ elements, there exists $k$ subsets $A_{1},A_{2},\dots,A_{k}$ each of size at least $n/(k\log n)^{C_{h}}$ such that for each partial order $<_{\ell}$, either $a_{1}<_{\ell}a_{2}<_{\ell}\dots<_{\ell}a_{k}$ for any tuple of elements $(a_1,a_2,\dots,a_k) \in A_1\times A_2\times \dots \times A_k$, or $a_{1}>_{\ell}a_{2}>_{\ell}\dots>_{\ell}a_{k}$ for any $(a_1,a_2,\dots,a_k) \in A_1\times A_2\times \dots \times A_k$, or $a_i$ is incomparable with $a_j$ for any $i\ne j$, $a_i\in A_i$ and $a_j\in A_j$. This improves on a 2009 result of Pach and the first author motivated by problems in discrete geometry. | math | 0 |
Title: A complete characterization of spectra of the Randic matrix of level-wise regular trees
Abstract: Let $G$ be a simple finite connected graph with vertex set $V(G) = \{v_1,v_2,\ldots,v_n\}$. Denote the degree of vertex $v_i$ by $d_i$ for all $1 \leq i \leq n$. The Randi\'c matrix of $G$, denoted by $R(G) = [r_{i,j}]$, is the $n \times n$ matrix whose $(i,j)$-entry $r_{i,j}$ is $r_{i,j} = 1/\sqrt{d_id_j}$ if $v_i$ and $v_j$ are adjacent in $G$ and 0 otherwise. A tree is a connected acyclic graph. A level-wise regular tree is a tree rooted at one vertex $r$ or two (adjacent) vertices $r$ and $r'$ in which all vertices with the minimum distance $i$ from $r$ or $r'$ have the same degree $m_i$ for $0 \leq i \leq h$, where $h$ is the height of $T$. In this paper, we give a complete characterization of the eigenvalues with their multiplicity of the Randi\'c matrix of level-wise regular trees. We prove that the eigenvalues of the Randi\'c matrix of a level-wise regular tree are the eigenvalues of the particular tridiagonal matrices, which are formed using the degree sequence $(m_0,m_1,\ldots,m_{h-1})$ of level-wise regular trees. | math | 0 |
Title: Grassroots Social Networking: Where Members Own and Control their Personal Information and Social Graph
Abstract: Offering an architecture for social networking in which the members are in control of their personal information and social graph is an open challenge. Here we present a grassroots architecture for serverless, permissionless, peer-to-peer social networks termed Grassroots Social Networking that aims to address this challenge. The architecture is geared for roaming (address-changing) agents communicating over an unreliable network, e.g., smartphones communicating via UDP. The architecture incorporates (i) a decentralized social graph, where each member controls, maintains and stores only their local neighborhood in the graph; (ii) member-created feeds, with authors and followers who create and store the feeds; and (iii) a grassroots dissemination protocol, in which communication among members occurs only along the edges of the social graph. The architecture realizes these components using the blocklace data structure -- a distributed partially-ordered counterpart of the replicated totally-ordered blockchain. We provide two example Grassroots Social Networking protocols -- Twitter-like and WhatsApp-like -- and address their security (safety, liveness and privacy), spam/bot/deep-fake resistance, and implementation, demonstrating how server-based social networks could be supplanted by a grassroots architecture. | cs | 0 |
Title: The homology of the partition algebras
Abstract: We show that the homology of the partition algebras, interpreted as appropriate Tor-groups, is isomorphic to that of the symmetric groups in a range of degrees that increases with the number of nodes. Furthermore, we show that when the defining parameter $\delta$ of the partition algebra is invertible, the homology of the partition algebra is in fact isomorphic to the homology of the symmetric group in all degrees. These results parallel those obtained for the Brauer algebras in the authors' earlier work, but with significant differences and difficulties in the inductive resolution and high acyclicity arguments required to prove them. Our results join the growing literature on homological stability for algebras, which now encompasses the Temperley-Lieb, Brauer and partition algebras, as well as the Iwahori-Hecke algebras of types A and B. | math | 0 |
Title: Minimum Sobolev norm interpolation of derivative data
Abstract: We study the problem of reconstructing a function on a manifold satisfying some mild conditions, given data on the values and some derivatives of the function at arbitrary points on the manifold. While the problem of finding a polynomial of two variables with total degree $\le n$ given the values of the polynomial and some of its derivatives at exactly the same number of points as the dimension of the polynomial space is sometimes impossible, we show that such a problem always has a solution in a very general situation if the degree of the polynomials is sufficiently large. We give estimates on how large the degree should be, and give explicit constructions for such a polynomial even in a far more general case. As the number of sampling points at which the data is available increases, our polynomials converge to the target function on the set where the sampling points are dense. Numerical examples in single and double precision show that this method is stable and of high-order. | math | 1 |
Title: Evaluating LLMs on Document-Based QA: Exact Answer Selection and Numerical Extraction using Cogtale dataset
Abstract: Document-based Question-Answering (QA) tasks are crucial for precise information retrieval. While some existing work focus on evaluating large language models performance on retrieving and answering questions from documents, assessing the LLMs performance on QA types that require exact answer selection from predefined options and numerical extraction is yet to be fully assessed. In this paper, we specifically focus on this underexplored context and conduct empirical analysis of LLMs (GPT-4 and GPT-3.5) on question types, including single-choice, yes-no, multiple-choice, and number extraction questions from documents in zero-shot setting. We use the CogTale dataset for evaluation, which provide human expert-tagged responses, offering a robust benchmark for precision and factual grounding. We found that LLMs, particularly GPT-4, can precisely answer many single-choice and yes-no questions given relevant context, demonstrating their efficacy in information retrieval tasks. However, their performance diminishes when confronted with multiple-choice and number extraction formats, lowering the overall performance of the model on this task, indicating that these models may not yet be sufficiently reliable for the task. This limits the applications of LLMs on applications demanding precise information extraction from documents, such as meta-analysis tasks. These findings hinge on the assumption that the retrievers furnish pertinent context necessary for accurate responses, emphasizing the need for further research. Our work offers a framework for ongoing dataset evaluation, ensuring that LLM applications for information retrieval and document analysis continue to meet evolving standards. | cs | 0 |
Title: Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation
Abstract: We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the universal function approximation capability of ESN, it is shown that the reconstruction problem can be formulated as a fixed-point problem, in which the trajectory of the dynamical system is a fixed point of the ESN. An under-relaxed fixed-point iteration is proposed to reconstruct the nonlinear dynamics from a sparse observation. The proposed fixed-point ESN is tested against both univariate and multivariate chaotic dynamical systems by randomly removing up to 95% of the data. It is shown that the fixed-point ESN is able to reconstruct the complex dynamics from only 5 ~ 10% of the data. For a relatively simple non-chaotic dynamical system, the numerical experiments on a forced van der Pol oscillator show that it is possible to reconstruct the nonlinear dynamics from only 1~2% of the data. | cs | 1 |
Title: Embedding 1-Planar Graphs in Ten Pages
Abstract: Every planar graph has a 4-page book embedding and this bound is tight. We show that every 1-planar graph, which is a graph that admits a drawing with at most one crossing per edge, has a 10-page book embedding. In addition, four pages are sometimes necessary and always sufficient if the planar skeleton, obtained from a 1-planar drawing by removing all crossed edges, has a Hamiltonian cycle. | cs | 0 |
Title: Efficient Communication in Federated Learning Using Floating-Point Lossy Compression
Abstract: In the expanding realm of machine learning (ML) within edge computing, the efficient exchange of information in federated learning (FL) environments is paramount. FL's decentralized nature often leads to significant communication bottlenecks, particularly in settings where resources are limited. Traditional data compression techniques, such as quantization and pruning, provide partial solutions but can compromise model performance or necessitate costly retraining. Our paper addresses this issue through \textit{FedSZ}, a novel lossy compression-based FL framework. \textit{FedSZ} is designed to minimize the size of local model updates without impacting model performance. Our framework features a compression pipeline integrating data partitioning, lossy and lossless model parameters, metadata compression, and efficient serialization. We conduct a thorough evaluation of \textit{FedSZ} utilizing a variety of lossy compressors, among which SZ2 emerged as the most effective, consistently performing well across diverse neural network architectures, including AlexNet, MobileNetV2, and ResNet50, and datasets such as CIFAR-10, Caltech101, and FMNIST. A relative error bound of 1E-2 balances compression and data integrity, achieving compression ratios ranging from $5.55\mbox{--}12.61\times$. Furthermore, we observed that the runtime overhead introduced by \textit{FedSZ} is minimal, at less than $4.7\%$, compared to a significant reduction in network transfer times, which we noted to exceed $13.3\times$ reduction or saving of over $100$s in edge networks operating at 10Mbps. Our findings firmly establish the efficacy of \textit{FedSZ}, offering valuable insights for achieving an optimal balance between communication efficiency and model performance in FL settings, particularly in edge computing environments. | cs | 0 |
Title: Robustness Evaluation of Regression Tasks with Skewed Domain Preferences
Abstract: In natural phenomena, data distributions often deviate from normality. One can think of cataclysms as a self-explanatory example: events that occur almost never, and at the same time are many standard deviations away from the common outcome. In many scientific contexts it is exactly these tail events that researchers are most interested in anticipating, so that adequate measures can be taken to prevent or attenuate a major impact on society. Despite such efforts, we have yet to provide definite answers to crucial issues in evaluating predictive solutions in domains such as weather, pollution, health. In this paper, we deal with two encapsulated problems simultaneously. First, assessing the performance of regression models when non-uniform preferences apply - not all values are equally relevant concerning the accuracy of their prediction, and there's a particular interest in the most extreme values. Second, assessing the robustness of models when dealing with uncertainty regarding the actual underlying distribution of values relevant for such problems. We show how different levels of relevance associated with target values may impact experimental conclusions, and demonstrate the practical utility of the proposed methods. | cs | 1 |
Title: Synthetic Data in AI: Challenges, Applications, and Ethical Implications
Abstract: In the rapidly evolving field of artificial intelligence, the creation and utilization of synthetic datasets have become increasingly significant. This report delves into the multifaceted aspects of synthetic data, particularly emphasizing the challenges and potential biases these datasets may harbor. It explores the methodologies behind synthetic data generation, spanning traditional statistical models to advanced deep learning techniques, and examines their applications across diverse domains. The report also critically addresses the ethical considerations and legal implications associated with synthetic datasets, highlighting the urgent need for mechanisms to ensure fairness, mitigate biases, and uphold ethical standards in AI development. | cs | 0 |
Title: On the Uniqueness of Bayesian Coarse Correlated Equilibria in Standard First-Price and All-Pay Auctions
Abstract: In first-price and all-pay auctions under the standard symmetric independent private-values model, we show that the unique Bayesian Coarse Correlated Equilibrium with symmetric, differentiable and strictly increasing bidding strategies is the unique strict Bayesian Nash Equilibrium. Interestingly, this result does not require assumptions on the prior distribution. The proof is based on a dual bound of the infinite-dimensional linear program. Numerical experiments without restrictions on bidding strategies show that for first-price auctions and discretisations up to 21 of the type and bid space, increasing discretisation sizes actually increase the concentration of Bayesian Coarse Correlated Equilibrium over the Bayesian Nash Equilibrium, so long as the prior c.d.f. is concave. Such a concentration is also observed for all-pay auctions, independent of the prior distribution. Overall, our results imply that the equilibria of these important class of auctions are indeed learnable. | cs | 0 |
Title: Inductive Synthesis of Finite-State Controllers for POMDPs
Abstract: We present a novel learning framework to obtain finite-state controllers (FSCs) for partially observable Markov decision processes and illustrate its applicability for indefinite-horizon specifications. Our framework builds on oracle-guided inductive synthesis to explore a design space compactly representing available FSCs. The inductive synthesis approach consists of two stages: The outer stage determines the design space, i.e., the set of FSC candidates, while the inner stage efficiently explores the design space. This framework is easily generalisable and shows promising results when compared to existing approaches. Experiments indicate that our technique is (i) competitive to state-of-the-art belief-based approaches for indefinite-horizon properties, (ii) yields smaller FSCs than existing methods for several models, and (iii) naturally treats multi-objective specifications. | cs | 1 |
Title: Self-similar solutions with fat tails for Smoluchowski's coagulation equation with singular kernels
Abstract: We show the existence of self-similar solutions with fat tails for Smoluchowski's coagulation equation for homogeneous kernels satisfying $C_1 \left(x^{-a}y^{b}+x^{b}y^{-a}\right)\leq K\left(x,y\right)\leq C_2\left(x^{-a}y^{b}+x^{b}y^{-a}\right)$ with $a>0$ and $b<1$. This covers especially the case of Smoluchowski's classical kernel $K(x,y)=(x^{1/3} + y^{1/3})(x^{-1/3} + y^{-1/3})$. For the proof of existence we first consider some regularized kernel $K_{\epsilon}$ for which we construct a sequence of solutions $h_{\epsilon}$. In a second step we pass to the limit $\epsilon\to 0$ to obtain a solution for the original kernel $K$. The main difficulty is to establish a uniform lower bound on $h_{\epsilon}$. The basic idea for this is to consider the time-dependent problem and choosing a special test function that solves the dual problem. | math | 1 |
Title: Inequalities about the area bounded by three cevian lines of a triangle
Abstract: In the paper we prove generalization of Schl\"omilch's and Zetel's theorems about concurrent lines in a triangle. This generalization is obtained as a corollary of sharp geometric inequality about the ratio of triangular areas which is proved using discrete variant of H\"older's inequality. Also a new sharp refinement of J.F. Rigby's inequality, which itself generalized M\"obius theorem about the areas of triangles formed by cevians of a triangle, is proved. | math | 0 |
Title: b-articulation points and b-bridges in strongly biconnected directed graphs
Abstract: A directed graph $G=(V,E)$ is called strongly biconnected if $G$ is strongly connected and the underlying graph of $G$ is biconnected. This class of directed graphs was first introduced by Wu and Grumbach. Let $G=(V,E)$ be a strongly biconnected directed graph. An edge $e\in E$ is a b-bridge if the subgraph $G\setminus \left\lbrace e\right\rbrace =(V,E\setminus \left\lbrace e\right\rbrace) $ is not strongly biconnected. A vertex $w\in V$ is a b-articulation point if $G\setminus \left\lbrace w\right\rbrace$ is not strongly biconnected, where $G\setminus \left\lbrace w\right\rbrace$ is the subgraph obtained from $G$ by removing $w$. In this paper we study b-articulation points and b-bridges. | cs | 1 |
Title: Gradient Methods Never Overfit On Separable Data
Abstract: A line of recent works established that when training linear predictors over separable data, using gradient methods and exponentially-tailed losses, the predictors asymptotically converge in direction to the max-margin predictor. As a consequence, the predictors asymptotically do not overfit. However, this does not address the question of whether overfitting might occur non-asymptotically, after some bounded number of iterations. In this paper, we formally show that standard gradient methods (in particular, gradient flow, gradient descent and stochastic gradient descent) never overfit on separable data: If we run these methods for $T$ iterations on a dataset of size $m$, both the empirical risk and the generalization error decrease at an essentially optimal rate of $\tilde{\mathcal{O}}(1/\gamma^2 T)$ up till $T\approx m$, at which point the generalization error remains fixed at an essentially optimal level of $\tilde{\mathcal{O}}(1/\gamma^2 m)$ regardless of how large $T$ is. Along the way, we present non-asymptotic bounds on the number of margin violations over the dataset, and prove their tightness. | cs | 1 |