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arXiv 2021年

作者： Yang, Yijun Wang, Shujun Zhu, Lei Yu, Lequan Robotics and Autonomous Systems Thrust The Hong Kong University of Science and Technology Guangzhou China Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom Department of Electronic and Computer Engineering The Hong Kong University of Science and Technology Hong Kong Department of Statistics and Actuarial Science The University of Hong Kong Hong Kong

Modern deep neural networks struggle to transfer knowledge and generalize across diverse domains when deployed to real-world applications. Currently, domain generalization (DG) is introduced to learn a universal representation from multiple domains to improve the network generalization ability on unseen domains. However, previous DG methods only focus on the data-level consistency scheme without considering the synergistic regularization among different consistency schemes. In this paper, we present a novel Hierarchical Consistency framework for Domain Generalization (HCDG) by integrating Extrinsic Consistency and Intrinsic Consistency synergistically. Particularly, for the Extrinsic Consistency, we leverage the knowledge across multiple source domains to enforce data-level consistency. To better enhance such consistency, we design a novel Amplitude Gaussian-mixing strategy into Fourier-based data augmentation called DomainUp. For the Intrinsic Consistency, we perform task-level consistency for the same instance under the dual-task scenario. We evaluate the proposed HCDG framework on two medical image segmentation tasks, i.e., optic cup/disc segmentation on fundus images and prostate MRI segmentation. Extensive experimental results manifest the effectiveness and versatility of our HCDG framework. © 2021, CC BY.

关键词： Deep neural networks

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Sufficient Conditions of the Ergodicity of Queueing Systems with Absolute Priority

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Moscow University computational mathematics and Cybernetics 2020年第1期44卷 37-43页

作者： Mistryukov, A. V. Ushakov, V. G. Department of Computational Mathematics and Cybernetics Moscow State University Moscow Russia Federal Research Center of Computer Science and Conrol Russian Academy of Sciences Moscow Russia

The familiar results on ergodicity of priority queueing systems were obtained under the assumption that the input streams of requests of all priorities are Poisson. This assumption is weakened by finding the sufficient conditions of ergodicity of queueing systems with two classes of priorities, where the stream of requests of higher priority is hyperexponential, and the one of lower priority is reccurent. Systems with different types of absolute priority are investigated. To obtain the sought ergodicity conditions, relations are determined that link the sequential values of waiting times of each priority.

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Smooth and Enhanced Smooth Quadrature-Inspired Generalized Choquet Integral

SSRN

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SSRN 2023年

作者： Karczmarek, Pawel Gregosiewicz, Adam Lagodowski, Zbigniew A. Dolecki, Michal Galka, Lukasz Powroznik, Pawel Pedrycz, Witold Department of Computational Intelligence Lublin University of Technology ul. Nadbystrzycka 36B Lublin20-618 Poland Department of Mathematics Lublin University of Technology ul. Nadbystrzycka 36B Lublin20-618 Poland Department of Computer Science Lublin University of Technology ul. Nadbystrzycka 36B Lublin20-618 Poland Department of Electrical & Computer Engineering University of Alberta EdmontonT6R 2V4 AB Canada Systems Research Institute Polish Academy of Sciences Warsaw Poland

In this study, we propose and thoroughly analyze a new concept of aggregation operator based on the generalization of Choquet integral (CI). This approach is based on an application of quadrature formulae to calculate the Choquet integral values. However, we use a novel modification of this method based on a so called smoothing operation. In this manner, the value obtained is more precise and allows to preserve the key features of Choquet integral which can be effectively utilized in a process of aggregation of classifiers, or, in a more general form, in the information fusion processes. Numerical experiments series demonstrate the efficiency of our approach. Moreover, mathematical properties of newly constructed operators are thoroughly discussed. © 2023, The Authors. All rights reserved.

关键词： Classification (of information)

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Minkowski Functionals of Large-Scale Structure as a Probe of Modified Gravity

arXiv

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arXiv 2023年

作者： Jiang, Aoxiang Liu, Wei Fang, Wenjuan Li, Baojiu Barrera-Hinojosa, Cristian Zhang, Yufei CAS Key Laboratory for Research in Galaxies and Cosmology Department of Astronomy University of Science and Technology of China Anhui Hefei230026 China School of Astronomy and Space Sciences University of Science and Technology of China Anhui Hefei230026 China Institute for Computational Cosmology Department of Physics Durham University South Road DurhamDH1 3LE United Kingdom Instituto de Física y Astronomía Universidad de Valparaíso Gran Bretaña 1111 Valparaíso Chile Department of Computer Science Durham University South Road DurhamDH1 3LE United Kingdom College of Mathematics and Physics Leshan Normal University Leshan614000 China

In this study, we explore the potential of utilizing the four Minkowski functionals, which can fully describe the morphological properties of the large-scale structures, as a robust tool for investigating the modified gravity, particularly on non-linear and quasi-linear scales. With the assistance of the N-body simulation, we employ the Minkowski functionals to probe the Hu-Sawicki f(R) gravity model. The focus is on understanding the morphorlogical properties extracted by the Minkowski functionals and their sensitivity to modified gravity. Our analysis involves a comprehensive examination of the cosmic variance arising from finite simulation volumes. By systematically varying smoothing scales and redshifts, we quantify the information encoded in the Minkowski functionals measured from the dark-matter density field. The goal is to assess the capacity of the Minkowksi functionals to constrain the model and explore potential improvements through their combination. Additionally, we investigate the impact of using biased tracers such as dark matter halos and the halo occupation distribution galaxies on the modified gravity signatures within the Minkowksi functionals of the LSS. Furthermore, we evaluate the influence of the redshift space distortion on the observed results. In summary, our study suggests that the Minkowski functionals of the large-scale structures hold promise as a stringent tool for constraining modified gravity and offer valuable insights into the morphological features of the cosmic web. Copyright © 2023, The Authors. All rights reserved.

关键词： Gravitation

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Binomial coefficients in a row of Pascal’s triangle from extension of power of eleven: Newton’s unfinished work

arXiv

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arXiv 2020年

作者： Islam, Md. Shariful Islam, Md. Robiul Hossan, Md. Shorif Kibria, Md. Hasan Department of Mathematics University of Dhaka Bangladesh Department of Applied Mathematics University of Dhaka Bangladesh Department of Computer Science and Engineering Green University of Bangladesh Dhaka Bangladesh

The aim of this paper is to find a general formula to generate any row of Pascal’s triangle as an extension of the concept of (11)n. In this study, the visualization of each row of Pascal’s triangle has been presented by extending the concept of the power of 11 to the power of 101, 1001, 10001, and so on. We briefly discuss how our proposed concept works for any n by inserting an appropriate number of zeros between 1 and 1 (eleven), that is the concept of (11)n has been extended to (1Θ1)n, where Θ represents the number of zeros. We have proposed a formula for obtaining the value of Θ. The proposed concept has been verified with Pascal’s triangle and matched successfully. Finally, Pascal’s triangle for a large n has been presented considering the 51st row as an *** Codes 01-08, 11-03. © 2020, CC BY.

关键词： Number theory

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Strain energy density as a Gaussian process and its utilization in stochastic finite element analysis: application to planar soft tissues

arXiv

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arXiv 2022年

作者： Aggarwal, Ankush Jensen, Bjørn Sand Pant, Sanjay Lee, Chung-Hao Glasgow Computational Engineering Centre James Watt School of Engineering University of Glasgow GlasgowG12 8LT United Kingdom School of Computing Science University of Glasgow GlasgowG12 8LT United Kingdom Department of Applied Mathematics and Computer Science Technical University of Denmark Kgs. Lyngby2800 Denmark Zienkiewicz Centre for Computational Engineering Swansea University SwanseaSA1 8EP United Kingdom School of Aerospace and Mechanical Engineering The University of Oklahoma NormanOK73019 United States

Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar, hyperelastic and incompressible soft tissues. The strain energy density of soft tissues is modeled as a GP, which can be regressed to experimental stress-strain data obtained from biaxial experiments. Moreover, the GP model can be weakly constrained to be convex. A key advantage of a GP-based model is that, in addition to the mean value, it provides a probability density (i.e. associated uncertainty) for the strain energy density. To simulate the effect of this uncertainty, a non-intrusive stochastic finite element analysis (SFEA) framework is proposed. The proposed framework is verified against an artificial dataset based on the Gasser–Ogden–Holzapfel model and applied to a real experimental dataset of a porcine aortic valve leaflet tissue. Results show that the proposed framework can be trained with limited experimental data and fits the data better than several existing models. The SFEA framework provides a straightforward way of using the experimental data and quantifying the resulting uncertainty in simulation-based predictions. © 2022, CC BY.

关键词： Machine learning

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Exploring Koopman Operator Based Surrogate Models—Accelerating the Analysis of Critical Pedestrian Densities 13th

Exploring Koopman Operator Based Surrogate Models—Accelerat...

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13th Conference on Traffic and Granular Flow, TGF 2019

作者： Lehmberg, Daniel Dietrich, Felix Kevrekidis, Ioannis G. Bungartz, Hans-Joachim Köster, Gerta Department of Computer Science and Mathematics Munich University of Applied Sciences Munich Germany Department of Informatics Technical University of Munich Garching Germany Whiting School of Engineering Johns Hopkins University Baltimore United States Princeton University Princeton United States

ISBN: (纸本)9783030559724

We apply the Koopman operator framework to pedestrian dynamics. In an example scenario, we generate crowd density time series data with a microscopic pedestrian simulator. We then approximate the Koopman operator in matrix form through Extended Dynamic Mode Decomposition, using Geometric Harmonics on the data as a dictionary. The Koopman matrix is integrated into a surrogate model, which allows to approximate crowd density time series data to be generated, independently from the original microscopic simulator. The evaluation of the constructed surrogate model is orders of magnitude faster, and enables us to use methods that require many model evaluations. © 2020, Springer Nature Switzerland AG.

关键词： Dynamic mode decomposition

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Local Number Fluctuations in Hyperuniform and Nonhyperuniform Systems: Higher-Order Moments and Distribution Functions

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Physical Review X 2021年第2期11卷 021028-021028页

作者： Salvatore Torquato Jaeuk Kim Michael A. Klatt Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 91058 Erlangen Germany

The local number variance σ2(R) associated with a spherical sampling window of radius R enables a classification of many-particle systems in d-dimensional Euclidean space Rd according to the degree to which large-scale density fluctuations are suppressed, resulting in a demarcation between hyperuniform and nonhyperuniform phyla. To more completely characterize density fluctuations, we carry out an extensive study of higher-order moments or cumulants, including the skewness γ1(R), excess kurtosis γ2(R), and the corresponding probability distribution function P[N(R)] of a large family of models across the first three space dimensions, including both hyperuniform and nonhyperuniform systems with varying degrees of short- and long-range order. To carry out this comprehensive program, we derive new theoretical results that apply to general point processes, and we conduct high-precision numerical studies. Specifically, we derive explicit closed-form integral expressions for γ1(R) and γ2(R) that encode structural information up to three-body and four-body correlation functions, respectively. We also derive rigorous bounds on γ1(R), γ2(R), and P[N(R)] for general point processes and corresponding exact results for general packings of identical spheres. High-quality simulation data for γ1(R), γ2(R), and P[N(R)] are generated for each model. We also ascertain the proximity of P[N(R)] to the normal distribution via a novel Gaussian “distance” metric l2(R). Among all models, the convergence to a central limit theorem (CLT) is generally fastest for the disordered hyperuniform processes in two or higher dimensions such that γ1(R)∼l2(R)∼R−(d+1)/2 and γ2(R)∼R−(d+1) for large R. The convergence to a CLT is slower for standard nonhyperuniform models and slowest for the “antihyperuniform” model studied here. We prove that one-dimensional hyperuniform systems of class I or any d-dimensional lattice cannot obey a CLT. Remarkably, we discover a type of universality in that, for all of ou

关键词： Exotic phases of matter Fluctuations & noise Nonequilibrium statistical mechanics Surface & interfacial phenomena

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On a Cyclometric Modification of the Chua System

On a Cyclometric Modification of the Chua System

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International IEEE Conference and Workshop: Óbuda on Electrical and Power Engineering (CANDO-EPE)

作者： Bálint Nagy Antal Joós Attila Kovari Department of Mathematics Institute of Computer Engineering University of Dunaujvaros Dunaujvaros Hungary Department of Natural Sciences Kandó Kálmán Faculty of Electrical Engineering Institute of Electrophysics Obuda University Budapest Hungary Department of Applied Quantitative Methods Faculty of Finance and Accountancy Budapest Business University Budapest Hungary Kandó Kálmán Faculty of Electrical Engineering Institute of Electronics and Communication Systems Obuda University Budapest Hungary Faculty of Computer Science Institute of Digital Technology Eszterházy Károly Catholic University Eger Hungary Department of Natural Sciences Institute of Engineering University of Dunaújváros Dunaujvaros Hungary GAMF Faculty of Engineering and Computer Science John Von Neumann University Kecskemét Hungary

Chaos is not only a unique chapter in the theory of dynamical systems but also a useful one with many applications in the field of communications. In this work a cyclometric modification of the well-known example of chaotic systems, the modified differential equations describing the behavior of the Chua-circuit is investigated. The results obtained can be applied in the encryption methods of the implementation of different communication channels like machine-machine or cognitive one.

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Finding an approximate global optimum of characteristic objects preferences by using simulated annealing 12th

Finding an approximate global optimum of characteristic obje...

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12th KES International Conference on Intelligent Decision Technologies, KES-IDT 2020

作者： Więckowski, Jakub Kizielewicz, Bartlomiej Kolodziejczyk, Joanna Research Team on Intelligent Decision Support Systems Faculty of Computer Science and Information Technology Department of Artificial Intelligence and Applied Mathematics West Pomeranian University of Technology in Szczecin Ul. Żolnierska 49 Szczecin71-210 Poland

ISBN: (纸本)9789811559242

Random processes are increasingly becoming a topic of consideration in many areas where decision-making is an important factor. The random factor affects the difficulty of determining input parameters. The selection of these parameters can be a key element in achieving the correct results. Stochastic optimization methods can be used to solve this problem. In this article, the simulated annealing method was used to obtain an optimal solution, which then, in combination with the COMET method, provided satisfactory results by determining the relationship between the preferences of the initial alternatives and newly identified alternatives. The purpose of this study was to systematize the knowledge of effective selection of input parameters for stochastic methods. The obtained solution indicates how to select a grid to an unknown problem and how to select a step in the simulated annealing method to achieve more precise results. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2020.

关键词： Simulated annealing

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