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Correlation-aware probabilistic data summarization for large-scale multi-block scientific data visualization

computational Visual Media 2023年第3期9卷 513-529页

作者： Yang Yang Kecheng Lu Yu Wu Yunhai Wang Yi Cao Institute of Applied Physics and Computational Mathematics Beijing 100094China School of Computer Science and Technology Shandong UniversityQingdao 266237China

In this paper,we propose a correlationaware probabilistic data summarization technique to efficiently analyze and visualize large-scale multi-block volume data generated by massively parallel scientific *** core of our technique is correlation modeling of distribution representations of adjacent data blocks using copula functions and accurate data value estimation by combining numerical information,spatial location,and correlation distribution using Bayes’*** effectively preserves statistical properties without merging data blocks in different parallel computing nodes and repartitioning them,thus significantly reducing the computational ***,this enables reconstruction of the original data more accurately than existing *** demonstrate the effectiveness of our technique using six datasets,with the largest having one billion grid *** experimental results show that our approach reduces the data storage cost by approximately one order of magnitude compared to state-of-the-art methods while providing a higher reconstruction accuracy at a lower computational cost.

关键词： correlation-awareness large-scale data multi-block methods probabilistic data summarization

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Asymmetry and Condition Number of an Elliptic-Parabolic System for Biological Network Formation

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应用数学与计算数学学报 2025年第1期7卷 78-94页

作者： Clarissa Astuto Daniele Boffi Jan Haskovec Peter Markowich Giovanni Russo Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics"F.Casorati" University of Pavia27100 PaviaItaly Applied Mathematics and Computational Sciences Department King Abdullah University of Science and Technology4700 ThuwalSaudi Arabia Department of Mathematics University of Vienna1090 ViennaAustria Department of Mathematics and Computer Science University of Catania95125 CataniaItaly

We present results of numerical simulations of the tensor-valued elliptic-parabolic PDE model for biological network *** numerical method is based on a nonlinear finite difference scheme on a uniform Cartesian grid in a two-dimensional(2D)*** focus is on the impact of different discretization methods and choices of regularization parameters on the symmetry of the numerical *** particular,we show that using the symmetric alternating direction implicit(ADI)method for time discretization helps preserve the symmetry of the solution,compared to the(non-symmetric)ADI ***,we study the effect of the regularization by the isotropic background perme-ability r＞0,showing that the increased condition number of the elliptic problem due to decreasing value of r leads to loss of *** show that in this case,neither the use of the symmetric ADI method preserves the symmetry of the ***,we perform the numerical error analysis of our method making use of the Wasserstein distance.

关键词： Bionetwork formation Cai-Hu model Leaf venation Asymmetry Conditioning number Finite-difference scheme Semi-implicit Symmetric alternating direction implicit(ADI) Wasserstein distance

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Single-Timescale Multi-Sequence Stochastic Approximation Without Fixed Point Smoothness: Theories and Applications

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IEEE Transactions on Signal Processing 2025年 73卷 1939-1953页

作者： Huang, Yue Wu, Zhaoxian Ma, Shiqian Ling, Qing Sun Yat-Sen University School of Computer Science and Engineering Guangdong Provincial Key Laboratory of Computational Science Guangzhou510006 China Rice University Department of Computational Applied Mathematics and Operations Research Houston77251 United States Pazhou Lab Guangzhou510275 China

Stochastic approximation (SA) that involves multiple coupled sequences, also known as multiple-sequence SA (MSSA), finds diverse applications in the fields of signal processing and machine learning. However, existing theoretical understandings of MSSA are limited: the multi-timescale analysis implies a slow convergence rate, whereas the single-timescale analysis relies on a stringent fixed point smoothness assumption. In this paper, we establish tighter single-timescale analysis for MSSA, without assuming smoothness of the fixed points. Our theoretical findings reveal that, when all involved operators are strongly monotone, MSSA converges at a rate of O˜(K−1), where K denotes the total number of iterations. When all involved operators are strongly monotone except for the main one, MSSA converges at a rate of O(K− 1/2 ). These rates align with the ones established for single-sequence SA. Applying our novel theoretical findings to bilevel optimization and communication-efficient distributed learning offers relaxed assumptions and/or simpler algorithms with performance guarantees, as validated by numerical experiments. © 1991-2012 IEEE.

关键词： Approximation theory

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Convergence analysis of a Legendre spectral collocation method for nonlinear Fredholm integral equations in multidimensions

Convergence analysis of a Legendre spectral collocation meth...

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作者： Zaky, Mahmoud A. Hendy, Ahmed S. Department of Applied Mathematics National Research Centre Cairo Egypt Department of Mathematics Faculty of Science Benha University Benha Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and Mathematics Ural Federal University Yekaterinburg Russia

It is a very challenging task to solve a nonlinear integral equation in multidimensions. The main purpose of this paper is to develop and analyze a spectral collocation method for a class of nonlinear Fredholm integral equations of the second kind in multidimensions. The proposed spectral collocation method is based on a multivariate Legendre approximation in the frequency space. It is shown by both theory and numerics that the proposed spectral collocation scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations. © 2020 John Wiley & Sons, Ltd.

关键词： Fredholm integral equations

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Firefly Algorithm Approach for Recovering the Mathematical Structure of One-Dimensional Chaotic Maps from Time Series Data 3

Firefly Algorithm Approach for Recovering the Mathematical S...

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3rd International Conference on computer Technologies, ICCTech 2024

作者： Galvez, Akemi Fister, Iztok Fister, Iztok Iglesias, Andres University of Cantabria Dept. of Applied Mathematics & Computational Sciences Santander Spain University of Maribor Faculty of Electrical Engineering & Computer Science Maribor Slovenia

ISBN: (纸本)9798350395419

Uncovering the mathematical structure of unknown chaotic systems from limited time series data poses a significant challenge in the field of dynamical systems, with broad applications across various domains. In this paper, we propose a swarm intelligence approach to tackle this issue, specifically focusing on one-dimensional discrete maps. Our approach leverages the firefly algorithm, a popular nature-inspired metaheuristic, known for its optimization capabilities. We assess the performance of the method by applying it to two illustrative examples of time series derived from one-dimensional maps: the Hénon map and the Burger map. The results show that this approach is promising for recovering the equations of motion of one-dimensional chaotic maps, even in situations where no additional information is available beyond the provided data points. © 2024 IEEE.

关键词： Time series

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Schur Nets: effectively exploiting local structure for equivariance in higher order graph neural networks 24

Schur Nets: effectively exploiting local structure for equiv...

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Proceedings of the 38th International Conference on Neural Information Processing Systems

作者： Qingqi Zhang Ruize Xu Risi Kondor Computational and Applied Mathematics University of Chicago Department of Computer Science University of Chicago Computational and Applied Mathematics and Department of Computer Science and Department of Statistics University of Chicago

ISBN: (纸本)9798331314385

Recent works have shown that extending the message passing paradigm to subgraphs communicating with other subgraphs, especially via higher order messages, can boost the expressivity of graph neural networks. In such architectures, to faithfully account for local structure such as cycles, the local operations must be equivariant to the automorphism group of the local environment. However, enumerating the automorphism groups of all subgraphs of interest and finding appropriate equivariant operations for each one of them separately is generally not feasible. In this paper we propose a solution to this problem based on spectral graph theory that bypasses having to determine the automorphism group entirely and constructs a basis for equivariant operations directly from the graph Laplacian. We show that this approach can boost the performance of GNNs on some standard benchmarks.

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Approximating reproduction numbers: a general numerical method for age-structured models

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Mathematical Biosciences and Engineering 2024年第4期21卷 5360-5393页

作者： De Reggi, Simone Scarabel, Francesca Vermiglio, Rossana Department of Mathematics Computer Science and Physics University of Udine via delle Scienze 206 Udine33100 Italy Department of Applied Mathematics University of Leeds Woodhouse LeedsLS2 9JT United Kingdom CDLab – Computational Dynamics Laboratory University of Udine Italy

In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of the birth and transition processes, we propose an equivalent formulation for the age-integrated state within the extended space framework. Then, we discretize the birth and transition operators via pseudospectral collocation. We discuss applications to epidemic models with continuous and piecewise continuous rates, with different interpretations of the age variable (e.g., demographic age, infection age and disease age) and the transmission terms (e.g., horizontal and vertical transmission). The tests illustrate that the method can compute different reproduction numbers, including the basic and type reproduction numbers as special cases. c 2024 the Author(s), licensee AIMS Press.

关键词： Numerical methods

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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

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应用数学与计算数学学报 2025年第1期7卷 3-39页

作者： Hendrik Ranocha Andrew R.Winters Hugo Guillermo Castro Lisandro Dalcin Michael Schlottke-Lakemper Gregor J.Gassner Matteo Parsani Applied Mathematics University of HamburgBundesstr.5520146 HamburgGermany Department of Mathematics Applied Mathematics Linköping UniversityLinköpingSweden Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Applied and Computational Mathematics RWTH Aachen UniversityAachenGermany High-Performance Computing Center Stuttgart University of StuttgartStuttgartGermany Department of Mathematics and Computer Science University of CologneCologneGermany Center for Data and Simulation Science University of CologneCologneGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Physical Science and Engineering Division(PSE) King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.

关键词： Explicit Runge-Kutta(RK)methods Step size control Compressible fluid dynamics Adaptivity in space and time Shock capturing

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Depth Separation in Norm-Bounded Infinite-Width Neural Networks 37

Depth Separation in Norm-Bounded Infinite-Width Neural Netwo...

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37th Annual Conference on Learning Theory, COLT 2024

作者： Parkinson, Suzanna Ongie, Greg Willett, Rebecca Shamir, Ohad Srebro, Nathan Committee on Computational and Applied Mathematics University of Chicago United States Department of Mathematical and Statistical Sciences Marquette University United States Department of Statistics Department of Computer Science University of Chicago United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Israel Toyota Technological Institute Chicago United States

We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared 2-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results focused on separation in terms of width, such results do not give insight into whether depth determines if it is possible to learn a network that generalizes well even when the network width is unbounded. Here, we study separation in terms of the sample complexity required for learnability. Specifically, we show that there are functions that are learnable with sample complexity polynomial in the input dimension by norm-controlled depth-3 ReLU networks, yet are not learnable with sub-exponential sample complexity by norm-controlled depth-2 ReLU networks (with any value for the norm). We also show that a similar statement in the reverse direction is not possible: any function learnable with polynomial sample complexity by a norm-controlled depth-2 ReLU network with infinite width is also learnable with polynomial sample complexity by a norm-controlled depth-3 ReLU network. © 2024 S. Parkinson, G. Ongie, R. Willett, O. Shamir & N. Srebro.

关键词： Source separation

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IoDseC++: authenticated key exchange protocol for cloud-enable internet of drone communication

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Journal of Ambient Intelligence and Humanized Computing 2023年第7期14卷 9529-9542页

作者： Amin, Ruhul Jayaswal, Sakshita Sureshkumar, Venkatasamy Rathore, Balram Jha, Ananya Abdussami, Mohammad Department of Computer Science and Engineering IIIT Naya raipur Sector 24 Chhattisgarh Naya Raipur493661 India Department of Applied Mathematics and Computational Sciences PSG College of Technology Tamilnadu Coimbatore641004 India

In recent times, sensor node or smart camera can be embedded in the drones for the collection of important data with the help of Internet Technology. Several security threats/vulnerabilities may hamper the system while collecting data. Hence, strong protection against security attacks is essential in drone based data collection system. In this work, we have considered a drone based cloud enable architecture for collecting and sharing information. The aim of this paper is to design a lightweight security protocol which will provide secure communication and mutual authentication among the entities. The proposed protocol establishes temporary session key for each session in order to make the complete system security attacks free. We have simulated the proposed protocol for measuring security strength using Scyther simulation whose results show all the claimed parameters are private during protocol run. It also ensures the correctness of mutual authentication. The informal analysis confirms strong protection on all security threats related to proposed architecture. The performance analysis has also made which shows that the protocol is lightweight and achieves better efficiency in comparison with related published works. © 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

关键词： Drones

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