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40th International Symposium on computational Geometry, SoCG 2024

作者： Bhore, Sujoy Nöllenburg, Martin Tóth, Csaba D. Wulms, Jules Department of Computer Science and Engineering Indian Institute of Technology Bombay Mumbai India Institute of Logic and Computation Algorithms and Complexity Group TU Wien Austria Department of Mathematics California State University Northridge Los AngelesCA United States Department of Computer Science Tufts University MedfordMA United States Department of Mathematics and Computer Science TU Eindhoven Netherlands

ISBN: (纸本)9783959773164

A fundamental question is whether one can maintain a maximum independent set (MIS) in polylogarithmic update time for a dynamic collection of geometric objects in Euclidean space. For a set of intervals, it is known that no dynamic algorithm can maintain an exact MIS in sublinear update time. Therefore, the typical objective is to explore the trade-off between update time and solution size. Substantial efforts have been made in recent years to understand this question for various families of geometric objects, such as intervals, hypercubes, hyperrectangles, and fat objects. We present the first fully dynamic approximation algorithm for disks of arbitrary radii in the plane that maintains a constant-factor approximate MIS in polylogarithmic expected amortized update time. Moreover, for a fully dynamic set of n unit disks in the plane, we show that a 12-approximate MIS can be maintained with worst-case update time O(log n), and optimal output-sensitive reporting. This result generalizes to fat objects of comparable sizes in any fixed dimension d, where the approximation ratio depends on the dimension and the fatness parameter. Further, we note that, even for a dynamic set of disks of unit radius in the plane, it is impossible to maintain O(1 + Ε)-approximate MIS in truly sublinear update time, under standard complexity assumptions. Our results build on two recent technical tools: (i) The MIX algorithm by Cardinal et al. (ESA 2021) that can smoothly transition from one independent set to another;hence it suffices to maintain a family of independent sets where the largest one is an O(1)-approximate MIS. (ii) A dynamic nearest/farthest neighbor data structure for disks by Kaplan et al. (DCG 2020) and Liu (SICOMP 2022), which generalizes the dynamic convex hull data structure by Chan (JACM 2010), and quickly yields a "replacement" disk (if any) when a disk in one of our independent sets is deleted. © Sujoy Bhore, Martin Nöllenburg, Csaba D. Tóth, and Jules Wulms.

关键词： Data structures

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A Bicriterion Concentration Inequality and Prophet Inequalities for k-Fold Matroid Unions 16

A Bicriterion Concentration Inequality and Prophet Inequalit...

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16th Innovations in Theoretical computer science Conference, ITCS 2025

作者： Alon, Noga Gravin, Nick Pollner, Tristan Rubinstein, Aviad Wang, Hongao Weinberg, S. Matthew Zhang, Qianfan Department of Mathematics Princeton University NJ United States Schools of Mathematics and Computer Science Tel Aviv University Tel Aviv Israel Key Laboratory of Interdisciplinary Research of Computation and Economics Shanghai University of Finance and Economics China Department of Management Science and Engineering Stanford University CA United States Department of Computer Science Stanford University CA United States Department of Computer Science Purdue University West LafayetteIN United States Department of Computer Science Princeton University NJ United States

ISBN: (纸本)9783959773614

We investigate prophet inequalities with competitive ratios approaching 1, seeking to generalize k-uniform matroids. We first show that large girth does not suffice: for all k, there exists a matroid of girth ≥ k and a prophet inequality instance on that matroid whose optimal competitive ratio is12. Next, we show k-fold matroid unions do suffice: we provide a prophet inequality with competitive ratio (Formula presented) for any k-fold matroid union. Our prophet inequality follows from an online contention resolution scheme. The key technical ingredient in our online contention resolution scheme is a novel bicriterion concentration inequality for arbitrary monotone 1-Lipschitz functions over independent items which may be of independent interest. Applied to our particular setting, our bicriterion concentration inequality yields "Chernoff-strength" concentration for a 1-Lipschitz function that is not (approximately) self-bounding. © Noga Alon, Nick Gravin, Tristan Pollner, Aviad Rubinstein, Hongao Wang, S. Matthew Weinberg, and Qianfan Zhang.

关键词： Choquet integral

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A Case-Based-Reasoning Analysis of the COMPAS Dataset 37

A Case-Based-Reasoning Analysis of the COMPAS Dataset

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37th Annual Conference on Legal Knowledge and Information Systems, JURIX 2024

作者： van Woerkom, Wijnand Grossi, Davide Prakken, Henry Verheij, Bart Department of Information and Computing Sciences Utrecht University Netherlands Bernoulli Institute for Mathematics Computer Science and Artificial Intelligence University of Groningen Netherlands Amsterdam Center for Law and Economics University of Amsterdam Netherlands Institute for Logic Language and Computation University of Amsterdam Netherlands

ISBN: (纸本)9781643685625

In this paper we build on a formal model of reasoning with dimensions to analyze data from the COMPAS program—a widely used and studied tool for predicting recidivism. We extend the underlying theory of the model by introducing a notion of consistency and apply it to assess whether COMPAS follows this principle in its risk assessments and supervision level recommendations. Our analysis yields three key findings. First, the program’s risk score assignments appear highly inconsistent, but we argue this is due to important input features missing from the dataset. Second, the program’s recommended supervision levels do exhibit a high degree of consistency. Third, we uncover errors in the dataset related to the conversion of raw scores to decile scores. These findings cast doubts on previous studies conducted on the COMPAS dataset, and demonstrate the need for evaluation studies like ours. © 2024 The Authors.

关键词： case-based reasoning COMPAS dataset consistency analysis explainable artificial intelligence

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Quantum Nonlocality: Multicopy Resource Interconvertibility and Their Asymptotic Inequivalence

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Physical Review Letters 2024年第25期132卷 250205-250205页

作者： Subhendu B. Ghosh Snehasish Roy Chowdhury Guruprasad Kar Arup Roy Tamal Guha Manik Banik Physics and Applied Mathematics Unit Department of Physics A B N Seal College Cooch Behar West Bengal 736101 India QICI Quantum Information and Computation Initiative Department of Computer Science Department of Physics of Complex Systems

Quantum nonlocality, pioneered in Bell’s seminal work and subsequently verified through a series of experiments, has drawn substantial attention due to its practical applications in various protocols. Evaluating and comparing the extent of nonlocality within distinct quantum correlations holds significant practical relevance. Within the resource theoretic framework this can be achieved by assessing the interconversion rate among different nonlocal correlations under free local operations and shared randomness. In this study we, however, present instances of quantum nonlocal correlations that are incomparable in the strongest sense. Specifically, when starting with an arbitrary many copies of one nonlocal correlation, it becomes impossible to obtain even a single copy of the other correlation, and this incomparability holds in both directions. Such incomparable quantum correlations can be obtained even in the simplest Bell scenario, which involves two parties, each having two dichotomic measurements setups. Notably, there exist an uncountable number of such incomparable correlations. Our result challenges the notion of a “unique gold coin,” often referred to as the “maximally resourceful state,” within the framework of the resource theory of quantum nonlocality. To this end, we provide examples of isotropic quantum correlations that cannot be distilled up to the Tsirelson point, and thus partially answer a long-standing open question in nonlocality distillation.

关键词： Quantum correlations, foundations & formalism Quantum foundations Resource theories

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Improving Prediction Quality of Face Image Preference Using Combinatorial Fusion Algorithm 16th

Improving Prediction Quality of Face Image Preference Using...

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16th International Conference on Brain Informatics, BI 2023

作者： Zhang, Zihan Schweikert, Christina Shimojo, Shinsuke Hsu, D. Frank Laboratory of Informatics and Data Mining Department of Computer and Information Science Fordham University YorkNY10023 United States Division of Computer Science Mathematics and Science St. John’s University QueensNY11439 United States Division of Biology and Biological Engineering/Computation and Neural Systems California Institute of Technology PasadenaCA91125 United States

ISBN: (纸本)9783031430749

When two face images are shown to a subject, the subject’s preference choice is influenced by many factors. Although it is a challenging task, one way to detect a subject’s preference is to analyze the eye movement gaze cascade in the recorded video sequence together with a set of extracted attributes (features). Combinatorial fusion algorithm (CFA) is a new information fusion and machine learning paradigm for combining multiple scoring systems using rank-score characteristic (RSC) function and cognitive diversity (CD). In this paper, we apply CFA in the analysis of the eye movement gaze cascade sequence. In particular, we characterize each of the attributes and measure the diversity between two attributes using RSC function and CD respectively. The novelty of the combinatorial fusion approach is the new paradigm of incorporating both score function and rank function as well as using both score combination and rank combination. In addition, our results demonstrate that weighted rank combination has some advantage over weighted score combination when the weight is measured using diversity strength. Since diversity strength depends only on cognitive diversity between two attributes but not on any specific sequence in the eye movement gaze cascade, our result facilitates learning and modeling in an unsupervised manner. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Information fusion

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Dimension-independent learning rates for high-dimensional classification problems

arXiv

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arXiv 2024年

作者： Lerma-Pineda, Andres Felipe Petersen, Philipp Frieder, Simon Lukasiewicz, Thomas Department of Computer Science University of Oxford United Kingdom Department of Mathematics University of Vienna Austria Institute of Logic and Computation Vienna University of Technology Vienna Austria

MSC Codes 68T05, 62C20, 41A25, 41A46We study the problem of approximating and estimating classification functions that have their decision boundary in the RBV2 space. Functions of RBV2 type arise naturally as solutions of regularized neural network learning problems and neural networks can approximate these functions without the curse of dimensionality. We modify existing results to show that every RBV2 function can be approximated by a neural network with bounded weights. Thereafter, we prove the existence of a neural network with bounded weights approximating a classification function. And we leverage these bounds to quantify the estimation rates. Finally, we present a numerical study that analyzes the effect of different regularity conditions on the decision boundaries. © 2024, CC BY.

关键词： Deep neural networks

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GRADIENT-FREE TRAINING OF RECURRENT NEURAL NETWORKS

arXiv

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arXiv 2024年

作者： Bolager, Erik Lien Cukarska, Ana Burak, Iryna Monfared, Zahra Dietrich, Felix School of Computation Information and Technology Germany Munich Data Science Institute Technical University of Munich Germany Germany Department of Mathematics and Computer Science Heidelberg University Germany

Recurrent neural networks are a successful neural architecture for many time-dependent problems, including time series analysis, forecasting, and modeling of dynamical systems. Training such networks with backpropagation through time is a notoriously difficult problem because their loss gradients tend to explode or vanish. In this contribution, we introduce a computational approach to construct all weights and biases of a recurrent neural network without using gradient-based methods. The approach is based on a combination of random feature networks and Koopman operator theory for dynamical systems. The hidden parameters of a single recurrent block are sampled at random, while the outer weights are constructed using extended dynamic mode decomposition. This approach alleviates all problems with backpropagation commonly related to recurrent networks. The connection to Koopman operator theory also allows us to start using results in this area to analyze recurrent neural networks. In computational experiments on time series, forecasting for chaotic dynamical systems, and control problems, as well as on weather data, we observe that the training time and forecasting accuracy of the recurrent neural networks we construct are improved when compared to commonly used gradient-based methods. Copyright © 2024, The Authors. All rights reserved.

关键词： Recurrent neural networks

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Holes in Convex and Simple Drawings 32

Holes in Convex and Simple Drawings

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32nd International Symposium on Graph Drawing and Network Visualization, GD 2024

作者： Bergold, Helena Orthaber, Joachim Scheucher, Manfred Schröder, Felix Institute of Computer Science Freie Universität Berlin Germany TUM School of Computation Information and Technology Technische Universität München Germany Institute of Software Technology Graz University of Technology Austria Institut Für Mathematik Technische Universität Berlin Germany Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Prague Czech Republic Institute of Mathematics Technische Universität Berlin Germany

ISBN: (纸本)9783959773430

Gons and holes in point sets have been extensively studied in the literature. For simple drawings of the complete graph a generalization of the Erdos-Szekeres theorem is known and empty triangles have been investigated. We introduce a notion of k-holes for simple drawings and study their existence with respect to the convexity hierarchy. We present a family of simple drawings without 4-holes and prove a generalization of Gerken's empty hexagon theorem for convex drawings. A crucial intermediate step will be the structural investigation of pseudolinear subdrawings in convex drawings. © Helena Bergold, Joachim Orthaber, Manfred Scheucher, and Felix Schröder.

关键词： Geometry

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ON HIGH-ORDER/LOW-ORDER AND MICRO-MACRO METHODS FOR IMPLICIT TIME-STEPPING OF THE BGK MODEL

arXiv

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arXiv 2024年

作者： Hauck, Cory D. Laiu, M. Paul Schnake, Stefan R. Mathematics in Computation Section Computer Science and Mathematics Division Oak Ridge National Laboratory Oak RidgeTN37831 United States Mathematics Department University of Tennessee KnoxvilleTN37996 United States

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the BGK equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. The accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near *** Codes 65M60, 65B99, 35Q31 Copyright © 2024, The Authors. All rights reserved.

关键词： Phase space methods

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The Peridigm Meshfree Peridynamics Code

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Journal of Peridynamics and Nonlocal Modeling 2024年第1期6卷 118-148页

作者： Littlewood, David J. Parks, Michael L. Foster, John T. Mitchell, John A. Diehl, Patrick Center for Computing Research Sandia National Laboratories Albuquerque NM United States Hildebrand Department of Petroleum and Geosystems Engineering University of Texas at Austin Austin TX United States Center of Computation & Technology and Department of Physics and Astronomy Louisiana State University Baton Rouge LA United States Computer Science and Mathematics Division Oak Ridge National Laboratory Oak Ridge TN United States

Peridigm is a meshfree peridynamics code written in C++ for use on large-scale parallel computers. It was originally developed at Sandia National Laboratories and is currently managed as an open-source, community driven software project. Its primary features include bond-based, state-based, and non-ordinary state-based constitutive models, bond failure laws, contact, and support for explicit and implicit time integration. To date, Peridigm has been used primarily by methods developers focused on solid mechanics and material failure. Peridigm utilizes foundational software components from Sandia’s Trilinos project and was designed for extensibility. This paper provides an overview of the solution methods implemented in Peridigm, a discussion of its software infrastructure, and demonstrates the use of Peridigm for the solution of several example problems. © 2023, The Author(s).

关键词： Meshfree methods Open source software Peridynamics

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