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Stability Criteria for Neural Networks with Stochastic Impulsive Intensity and Impulsive Density

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Stability Criteria for Neural Networks with Stochastic Impul...

Neuromorphic Computing (ICNC), International Conference on

作者： Hao Deng Jingxin Liu Jun Peng Yingxu Wang Fei Chang School of Computer Science and Engineering Chongqing University of Science and Technology Chongqing China College of Electronic and Information Engineering Southwest University Chongqing China Center for Applied Mathematics of Guangxi Guangxi Minzu University Nanning China School of Mathematics and Physics Sciences Chongqing University of Science and Technology Chongqing China Chongqing Research Institute of Intelligent Mathematics and Autonomous AI (RI-IM·AI*) Chongqing China

ISBN: (数字)9798331508661

ISBN: (纸本)9798331508678

This paper studies stability conditions for neural networks with stochastic impulsive intensity and impulsive density. Firstly, the pth moment exponential stability conditions are given, where the impulsive intensities of impulsive neural networks are independent and identically distributed, and the impulsive sequence is defined by impulsive density. Then, taking a linear time-varying impulsive system as an example, it is shown that impulsive sequence defined by average impulsive interval is sometime insufficient in terms of stabilizing such linear time-varying systems. Finally, two examples are presented to verify that impulsive density method is more effective and universal than average impulsive interval method when dealing with time-varying systems.

关键词： Sufficient conditions Stability Neuromorphic engineering Neural networks Stability criteria Control theory Time-varying systems Numerical stability

EFFICIENT SET-THEORETIC ALGORITHMS FOR COMPUTING HIGH-ORDER FORMAN-RICCI CURVATURE ON ABSTRACT SIMPLICIAL COMPLEXES

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arXiv 2023年

作者： de Souza, Danillo Barros da Cunha, Jonatas T.S. Santos, Fernando A.N. Jost, Jürgen Rodrigues, Serafim Basque Center for Applied Mathematics Spain Universidade Federal de Pernambuco Recife Brazil Institute for Advanced Studies University of Amsterdam Oude Turfmarkt 147 Amsterdam1012 GC Netherlands Korteweg de Vries Institute for Mathematics University of Amsterdam Science Park 105-107 Amsterdam1098 XG Netherlands Max Planck Institute for Mathematics in the Sciences Leipzig and Center for Scalable Data An-alytics and Artificial Intelligence Leipzig University Germany Santa Fe Institute New Mexico United States Basque Center for Applied Mathematics Bilbao Spain

Forman-Ricci curvature (FRC) is a potent and powerful tool for analysing empirical networks, as the distribution of the curvature values can identify structural information that is not readily detected by other geometrical methods. Crucially, FRC captures higher-order structural information of clique complexes of a graph or Vietoris-Rips complexes, which is not readily accessible to alternative methods. However, existing FRC platforms are prohibitively computationally expensive. Therefore, herein we develop an efficient set-theoretic formulation for computing such high-order FRC in simplicial complexes. Significantly, our set theory representation reveals previous computational bottlenecks and also accelerates the computation of FRC. Finally, We provide a pseudo-code, a software implementation coined FastForman, as well as a benchmark comparison with alternative implementations. We envisage that FastForman will be used in Topological and Geometrical data analysis for high-dimensional complex data sets. Moreover, our development paves the way for future generalisations towards efficient computations of FRC on cell complexes. © 2023, CC BY.

关键词： Set theory

Inference on High-dimensional Single-index Models with Streaming data

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arXiv 2022年

作者： Han, Dongxiao Xie, Jinhan Liu, Jin Sun, Liuquan Huang, Jian Jiang, Bei Kong, Linglong School of Statistics and Data Science LPMC KLMDASR LEBPS Nankai University Tianjin China Department of Mathematical and Statistical Sciences University of Alberta Edmonton Canada Institute of Applied Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong

Traditional statistical methods are faced with new challenges due to streaming data. The major challenge is the rapidly growing volume and velocity of data, which makes storing such huge datasets in memory impossible. The paper presents an online inference framework for regression parameters in high-dimensional semiparametric single-index models with unknown link functions. The proposed online procedure updates only the current data batch and summary statistics of historical data instead of re-accessing the entire raw data set. At the same time, we do not need to estimate the unknown link function, which is a highly challenging task. In addition, a generalized convex loss function is used in the proposed inference procedure. To illustrate the proposed method, we use the Huber loss function and the logistic regression model's negative log-likelihood. In this study, the asymptotic normality of the proposed online debiased Lasso estimators and the bounds of the proposed online Lasso estimators are investigated. To evaluate the performance of the proposed method, extensive simulation studies have been conducted. We provide applications to Nasdaq stock prices and financial distress datasets. © 2022, CC BY-NC-SA.

关键词： Clustering algorithms

Back-n white neutron source at CSNS and its applications

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Nuclear science and Techniques 2021年第1期32卷 95-104页

作者： Jing-Yu Tang Qi An Jiang-Bo Bai Jie Bao Yu Bao Ping Cao Hao-Lei Chen Qi-Ping Chen Yong-Hao Chen Zhen Chen Zeng-Qi Cui Rui-Rui Fan Chang-Qing Feng Ke-Qing Gao Xiao-Long Gao Min-Hao Gu Chang-Cai Han Zi-Jie Han Guo-Zhu He Yong-Cheng He Yang Hong Yi-Wei Hu Han-Xiong Huang Xi-Ru Huang Hao-Yu Jiang Wei Jiang Zhi-Jie Jiang Han-Tao Jing Ling Kang Bo Li Chao Li Jia-Wen Li Qiang Li Xiao Li Yang Li Jie Liu Rong Liu Shu-Bin Liu Xing-Yan Liu Ze Long Guang-Yuan Luan Chang-Jun Ning Meng-Chen Niu Bin-Bin Qi Jie Ren Zhi-Zhou Ren Xi-Chao Ruan Zhao-Hui Song Kang Sun Zhi-Jia Sun Zhi-Xin Tan Xin-Yi Tang Bin-Bin Tian Li-Jiao Wang Peng-Cheng Wang Zhao-Hui Wang Zhong-Wei Wen Xiao-Guang Wu Xuan Wu Li-Kun Xie Xiao-Yun Yang Yi-Wei Yang Han Yi Li Yu Tao Yu Yong-Ji Yu Guo-Hui Zhang Lin-Hao Zhang Qi-Wei Zhang Xian-Peng Zhang Yu-Liang Zhang Zhi-Yong Zhang Lu-Ping Zhou Zhi-Hao Zhou Ke-Jun Zhu 无 State Key Laboratory of Particle Detection and Electronics Institute of High Energy PhysicsChinese Academy of SciencesBeijing 100049China Department of Modern Physics University of Science and Technology of ChinaHefei 230026China Institute of Nuclear Physics and Chemistry China Academy of Engineering PhysicsMianyang 621900China Key Laboratory of Nuclear Data China Institute of Atomic EnergyBeijing 102413China Institute of High Energy Physics Chinese Academy of SciencesBeijing 100049China Spallation Neutron Source Science Center Dongguan 523803China State Key Laboratory of Nuclear Physics and Technology School of PhysicsPeking UniversityBeijing 100871China Northwest Institute of Nuclear Technology Xi’an 710024China University of Chinese Academy of Sciences Beijing 100049China Department of Engineering and Applied Physics University of Science and Technology of ChinaHefei 230026China State Key Laboratory of Particle Detection and Electronics University of Science and Technology of ChinaHefei 230026China The CSNS Back-n Collaboration

Back-streaming neutrons from the spallation target of the China Spallation Neutron Source(CSNS)that emit through the incoming proton channel were exploited to build a white neutron beam facility(the so-called Back-n white neutron source),which was completed in March *** Back-n neutron beam is very intense,at approximately 29107 n/cm2/s at 55 m from the target,and has a nominal proton beam with a power of 100 kW in the CSNS-I phase and a kinetic energy of 1.6 GeV and a thick tungsten target in multiple slices with modest moderation from the cooling water through the *** addition,the excellent energy spectrum spanning from 0.5 eV to 200 MeV,and a good time resolution related tothe time-of-flight measurements make it a typical white neutron source for nuclear data measurements;its overall performance is among that of the best white neutron sources in the *** with advanced spectrometers,detectors,and application utilities,the Back-n facility can serve wide applications,with a focus on neutron-induced cross-sectional *** article presents an overview of the neutron beam characteristics,the experimental setups,and the ongoing applications at Backn.

关键词： White neutron source Nuclear data measurements Experimental setups Neutron applications

Light controlled topological plasmonics in a graphene lattice arrayed by metal nanoparticles

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Physical Review B 2023年第8期108卷 085402-085402页

作者： Lu Zhang Xi-Ming Wang Xin-Miao Qiu Zhigang Wang Jie-Yun Yan School of Science Beijing University of Posts and Telecommunications Beijing 100876 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China State Key Laboratory of Information Photonics and Optical Communications Beijing University of Posts and Telecommunications Beijing 100876 China

The implementation of topology on photonics has opened new functionalities of photonic systems, such as the topologically protected boundary photonic modes. In this study, we investigate topological plasmonics in a graphene lattice arrayed with metal nanoparticles and irradiated by a polarized light. While surface plasmon polaritons are typically excited in such systems, our study shows that the system exhibits a different photonic response with observable edge photonic modes corresponding to distinct topological states. Importantly, we show that the topological phase transition between these states can be easily achieved by controlling the polarization of the external optical field, making it more feasible in experiments than changing the structural parameters. Our system provides a controllable platform for studying topological phenomena in photonics and has potential applications in nanoscale optical devices.

关键词： Plasmonics Topological phase transition Polarization

Time-dependent probability density function for partial resetting dynamics

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arXiv 2023年

作者： Bello, Costantino Di Chechkin, Aleksei V. Hartmann, Alexander K. Palmowski, Zbigniew Metzler, Ralf University of Potsdam Institute of Physics & Astronomy Potsdam14476 Germany Faculty of Pure and Applied Mathematics Wroclaw University of Science and Technology Wroclaw50-376 Poland Akhiezer Institute for Theoretical Physics Kharkov61108 Ukraine Institute of Physics University of Oldenburg Oldenburg26129 Germany Asia Pacific Centre for Theoretical Physics Pohang37673 Korea Republic of

Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage times to a target. Recently the concept of partial resetting, in which the particle is reset to a given fraction of the current value of the process, has been established and the associated search behaviour analysed. Here we go one step further and we develop a general technique to determine the time-dependent probability density function (PDF) for Markov processes with partial resetting. We obtain an exact representation of the PDF in the case of general symmetric Lévy flights with stable index 0 Copyright © 2023, The Authors. All rights reserved.

关键词： Probability density function

A simulation study of protons heated by left/right-handed Alfvén waves generated by electromagnetic proton-proton instability

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Plasma science and Technology 2021年第12期23卷 55-62页

作者： Jiansheng YAO Yingkui ZHAO Difa YE Yi LI Lihui CHAI Jicheng SUN Institute of Applied Physics and Computational Mathematics Beijing 100088People's Republic of China CAS Key Lab of Geospace Environment School of Earth and Space SciencesUniversity of Science and Technology of ChinaHefei 230026People's Republic of China Key Laboratory of Earth and Planetary Physics Institute of Geology and GeophysicsChinese Academy of SciencesBeijing 100029People's Republic of China Key Laboratory of Polar Science Ministry of Natural ResourcesShanghai 200020People's Republic of China MNR Key Laboratory for Polar Science Polar Research Institute of ChinaShanghai 200136People's Republic of China

Most protons in the solar wind belong to one of two different populations,the less dense beam protons and the denser core *** beam protons,with a velocity of(1-2)V_(A)(V_(A)is the local Alfvén speed),always drift relative to the core protons;this kind of distribution is unstable and stimulates several kinds of wave *** this study,using a 2 D hybrid simulation model,we find that the original right-handed elliptically polarized Alfvén waves become linearly polarized,and eventually become right-handed and circularly *** that linearly polarized waves are a superposition of left-handed and right-handed waves,cyclotron resonance in the right-handed/left-handed component heats beam/core protons *** resonance between beam protons and right-handed polarized waves is stronger when the beam relative density is lower,resulting in more dramatic perpendicular heating of beam protons,whereas the situation is reversed when the beam relative density is larger.

关键词： proton/proton instability hybrid simulation Alfvén waves

Two-step flux synthesis of ultrapure transition metal dichalcogenides

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arXiv 2023年

作者： Liu, Song Liu, Yang Holtzman, Luke Nemetz Li, Baichang Holbrook, Madisen Pack, Jordan Taniguchi, Takashi Watanabe, Kenji Dean, Cory R. Pasupathy, Abhay Barmak, Katayun Rhodes, Daniel A. Hone, James Department of Mechanical Engineering Columbia University New YorkNY10027 United States Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Department of Physics Columbia University New YorkNY10027 United States National Institute for Materials Science Ibaraki Tsukuba305-0044 Japan

Two-dimensional transition metal dichalcogenides (TMDs) have attracted tremendous interest due to the unusual electronic and optoelectronic properties of isolated monolayers and the ability to assemble diverse monolayers into complex heterostructures. To understand the intrinsic properties of TMDs and fully realize their potential in applications and fundamental studies, high-purity materials are required. Here, we describe synthesis of TMD crystals using a two-step flux growth method that eliminates a major potential source of contamination. Detailed characterization of TMDs grown by this two-step method reveals charged and isovalent defects with densities an order of magnitude lower than in TMDs grown by a single-step flux technique. For WSe2, we show that increasing the Se:W ratio during growth reduces point defect density, with crystals grown at 100:1 ratio achieving charged and isovalent defect densities below 1010 cm-2 and 1011 cm-2, respectively. Initial temperature-dependent electrical transport measurements of monolayer WSe2 yield room-temperature hole mobility above 840 cm2/Vs and low-temperature disorder-limited mobility above 44,000 cm2/Vs. Electrical transport measurements of graphene-WSe2 heterostructures fabricated from the two-step flux grown WSe2 also show superior performance: higher graphene mobility, lower charged impurity density, and well-resolved integer quantum Hall states. Finally, we demonstrate that the two-step flux technique can be used to synthesize other TMDs with similar defect densities, including semiconducting 2H-MoSe2 and 2H-MoTe2, and semi-metallic Td-WTe2 and 1T’-MoTe2. © 2023, CC BY-NC-ND.

关键词： Transition metals

A nonconvex entanglement monotone determining the characteristic length of entanglement distribution in continuous-variable quantum networks

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arXiv 2024年

作者： Zhao, Yaqi Hou, Jinchuan He, Kan Piparo, Nicolò Lo Meng, Xiangyi College of Mathematics Taiyuan University of Technology Taiyuan030024 China Okinawa Institute of Science and Technology Graduate University 1919-1 Tancha Onna-son Okinawa904-0495 Japan Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute TroyNY12180 United States Network Science and Technology Center Rensselaer Polytechnic Institute TroyNY12180 United States

Quantum networks (QNs) promise to enhance the performance of various quantum technologies in the near future by distributing entangled states over long distances. The first step towards this is to develop novel entanglement measures that are both informative and computationally tractable at large scales. While numerous such entanglement measures exist for discrete-variable (DV) systems, a comprehensive exploration for experimentally preferred continuous-variable (CV) systems is lacking. Here, we introduce a class of CV entanglement measures, among which we identify a nonconvex entanglement monotone—the ratio negativity, which possesses a simple, scalable form that determines the exponential decay of optimal entanglement swapping on a chain of pure Gaussian states. This characterization opens avenues for leveraging statistical physics tools to analyze swapping-protocol-based CV QNs. Copyright © 2024, The Authors. All rights reserved.

关键词： Statistical mechanics