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Derivatives of Intersection Local Time for Two Independent Symmetricα-stable Processes

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1273-1292页

作者： Huan ZHOU Guang Jun SHEN Qian YU Department of Mathematics Anhui Normal UniversityWuhu 241002P.R.China Department of Mathematics Nanjing University of Aeronautics and AstronauticsNanjing 211106P.R.China key laboratory of mathematical modelling and high performance computing of air vehicles(NUAA) MIITNanjing 211106P.R.China

In this paper,we consider the derivatives of intersection local time for two independent d-dimensional symmetricα-stable processes X^(α) and X^(α)with respective indices α and α.We first study the sufficient condition for the existence of the derivatives,which makes us obtain the exponential integrability and H?lder *** we show that this condition is also necessary for the existence of derivatives of intersection local time at the ***,we also study the power variation of the derivatives.

关键词： Symmetric stable processes intersection local time exponential integrability power variation

An oscillation-free Hermite WENO scheme for hyperbolic conservation laws

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Science China Mathematics 2024年第2期67卷 431-454页

作者： Zhuang Zhao Jianxian Qiu School of mathematical Sciences and Institute of Natural Sciences Shanghai Jiao Tong UniversityShanghai 200240China School of mathematical Sciences and Fujian Provincial key laboratory of mathematical Modeling and high-performance Scientific computing Xiamen UniversityXiamen 361005China

In this paper, the sixth-order oscillation-free Hermite weighted essentially non-oscillatory (OFHWENO) scheme is proposed for hyperbolic conservation laws on structured meshes, where the zeroth- andfirst-order moments are the variables for the governing equations. The main difference from other HWENOschemes existing in the literature is that we add high-order numerical damping terms in the first-order momentequations to control spurious oscillations for the OF-HWENO scheme. The OF-HWENO scheme not only canachieve the designed optimal numerical order, but also can be easily implemented as we use only one set ofstencils in the reconstruction procedure and the same reconstructed polynomials are applied for the zeroth- andfirst-order moment equations. In order to obtain the adaptive order resolution when facing discontinuities, atransition polynomial is added in the reconstruction, where the associated linear weights can also be any positivenumbers as long as their summation equals one. In addition, the OF-HWENO scheme still keeps compactnessas only immediate neighbor values are needed in the space discretization. Some benchmark numerical tests areperformed to illustrate the high-order accuracy, high resolution and robustness of the proposed scheme.

关键词： Hermite WENO scheme hyperbolic conservation laws oscillation-free adaptive order discontinuous Galerkin method

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

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Communications on Applied Mathematics and Computation 2024年第1期6卷 605-624页

作者： Feng Zheng Jianxian Qiu College of Mathematics and Statistics Fujian Normal UniversityFuzhou350117FujianChina School of mathematical Sciences and Fujian Provincial key laboratory of mathematical Modeling&high-performance Scientific computing Xiamen UniversityXiamen361005FujianChina

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation *** can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary ***,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO *** numerical tests are performed to verify the high resolution and high accuracy of the scheme.

关键词： Finite volume Dimension by dimension HWENO Hyperbolic conservation laws

Software Vulnerability Mining and Analysis Based on Deep Learning

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Computers, Materials & Continua 2024年第8期80卷 3263-3287页

作者： Shibin Zhao Junhu Zhu Jianshan Peng State key laboratory of mathematical Engineering and Advanced computing Zhengzhou450001China

In recent years,the rapid development of computer software has led to numerous security problems,particularly software *** flaws can cause significant harm to users’privacy and *** security defect detection technology relies on manual or professional reasoning,leading to missed detection and high false detection *** intelligence technology has led to the development of neural network models based on machine learning or deep learning to intelligently mine holes,reducing missed alarms and false ***,this project aims to study Java source code defect detection methods for defects like null pointer reference exception,XSS(Transform),and Structured Query Language(SQL)***,the project uses open-source Javalang to translate the Java source code,conducts a deep search on the AST to obtain the empty syntax feature library,and converts the Java source code into a dependency *** feature vector is then used as the learning target for the neural *** types of Convolutional Neural Networks(CNN),Long Short-Term Memory(LSTM),Bi-directional Long Short-Term Memory(BiLSTM),and Attention Mechanism+Bidirectional LSTM,are used to investigate various code defects,including blank pointer reference exception,XSS,and SQL injection *** results show that the attention mechanism in two-dimensional BLSTM is the most effective for object recognition,verifying the correctness of the method.

关键词： Vulnerability mining software security deep learning static analysis

Solving the subset sum problem by the quantum Ising model with variational quantum optimization based on conditional values at risk

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Science China(Physics,Mechanics & Astronomy) 2024年第8期67卷 43-55页

作者： Qilin Zheng Miaomiao Yu Pingyu Zhu Yan Wang Weihong Luo Ping Xu Institute for Quantum Information and State key laboratory of high performance computing College of Computer Science and TechnologyNational University of Defense TechnologyChangsha 410073China Hefei National laboratory Hefei 230088China

The subset sum problem is a combinatorial optimization problem,and its complexity belongs to the nondeterministic polynomial time complete(NP-Complete)*** problem is widely used in encryption,planning or scheduling,and integer *** accurate search algorithm with polynomial time complexity has not been found,which makes it challenging to be solved on classical *** effectively solve this problem,we translate it into the quantum Ising model and solve it with a variational quantum optimization method based on conditional values at *** proposed model needs only n qubits to encode 2ndimensional search space,which can effectively save the encoding quantum *** model inherits the advantages of variational quantum algorithms and can obtain good performance at shallow circuit depths while being robust to noise,and it is convenient to be deployed in the Noisy Intermediate Scale Quantum *** investigate the effects of the scalability,the variational ansatz type,the variational depth,and noise on the ***,we also discuss the performance of the model under different conditional values at *** computer simulation,the scale can reach more than nine *** selecting the noise type,we construct simulators with different QVs and study the performance of the model with *** addition,we deploy the model on a superconducting quantum computer of the Origin Quantum Technology Company and successfully solve the subset sum *** model provides a new perspective for solving the subset sum problem.

关键词： subset sum problem quantum Ising model conditional values at risk variational quantum optimization

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Bioinspired sensing-memory-computing integrated vision systems: biomimetic mechanisms, design principles, and applications

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Science China(Information Sciences) 2024年第5期67卷 5-27页

作者： Yujie HUANG Yinlong TAN Yan KANG Yabo CHEN Yuhua TANG Tian JIANG Institute for Quantum Information and State key laboratory of high performance computing College of Computer National University of Defense Technology College of Advanced Interdisciplinary Studies National University of Defense Technology Institute for Quantum Science and Technology College of ScienceNational University of Defense Technology

With the explosion of sensory data in the Internet of Things(Io T) era, conventional machine vision systems are becoming increasingly difficult to meet the requirements of high efficiency, low energy consumption, and low latency due to their inherent shortcomings of separate sensing, memory, and computing units. Inspired by the retina and neuromorphic computing, the sensing-memory-computing integrated vision system(SMCVS) that features low power consumption, low latency, and high parallelism has been considered a promising technology to surpass the von Neumann architecture and realize strong artificial ***, novel materials like two-dimensional semiconductors and quantum dots with novel optoelectronic performance provide hardware carriers for implementing integrated sensing-memory-computing architectures,attracting considerable attention. This paper reviews the recent research progress in bioinspired vision systems in terms of biomimetic mechanisms, design principles, computational architectures, and ***, the biomimetic mechanisms are illustrated to guide the design of high-performance artificial visual perception systems. Then the research progress of optoelectronic-synapse-based bioinspired vision systems in the device principles and applications including image filtering, color recognition, visual adaptation, and motion detection are summarized. Finally, the challenges and future developing directions of the SMCVS are provided regarding bionic application, architecture design, and device fabrication.

关键词： sensing-memory-computing architecture neuromorphic computing retinomorphic device image recognition visual system

The quantum Ising model for perfect matching and solving it with variational quantum eigensolver

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Science China(Information Sciences) 2024年第9期67卷 306-320页

作者： Qilin ZHENG Pingyu ZHU Chao WU Miaomiao YU Weihong LUO Ping XU Institute for Quantum Information and State key laboratory of high performance computing College of Computer Science and Technology National University of Defense Technology Hefei National laboratory

Obtaining all perfect matchings of a graph is a tough problem in graph theory, and its complexity belongs to the #P-Complete class. The problem is closely related to combinatorics, marriage matching problems, dense subgraphs, the Gaussian boson sampling, chemical molecular structures, and dimer *** this paper, we propose a quadratic unconstrained binary optimization formula of the perfect matching problem and translate it into the quantum Ising model. We can obtain all perfect matchings by mapping them to the ground state of the quantum Ising Hamiltonian and solving it with the variational quantum eigensolver. Adjusting the model's parameters can also achieve the maximum or minimum weighted perfect matching. The experimental results on a superconducting quantum computer of the Origin Quantum computing Technology Company show that our model can encode 2~n dimensional optimization space with only O（n） qubits consumption and achieve a high success probability of the ground state corresponding to all perfect matchings. In addition, the further simulation results show that the model can support a scale of more than 14 qubits, effectively resist the adverse effects of noise, and obtain a high success probability at a shallow variational depth. This method can be extended to other combinatorial optimization problems.

关键词： perfect matching Ising model quantum Hamiltonian variational quantum eigensolver quadratic unconstrained binary optimization

Credit assignment for trained neural networks based on Koopman operator theory

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Frontiers of Computer Science 2024年第1期18卷 251-253页

作者： Zhen LIANG Changyuan ZHAO Wanwei LIU Bai XUE Wenjing YANG Zhengbin PANG Institute for Quantum Information&State key laboratory of high performance computing National University of Defense TechnologyChangsha 410000China Institute of Software Chinese Academy of SciencesBeijing 100190China College of Computer Science and Technology National University of Defense TechnologyChangsha 410000China

1 Introduction Artificial neural networks(ANNs,also NNs)have recently emerged as leading candidate models for deep learning,popularly used in various areas[1–3].Behind the enormous success,ANNs are generally with complicated structures,there being an intricate data flow through multiple linear or nonlinear components between the input layer and the output ***,it is pressing to evaluate how much a specific component contributes to the final output,termed the Credit Assignment Problem(CAP)[4]in this paper.

关键词： layer. assignment operator

Thermal conductivity of GeTe crystals based on machine learning potentials

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Chinese Physics B 2024年第4期33卷 104-107页

作者：张健张昊春李伟峰张刚 School of Energy Science and Engineering Harbin Institute of TechnologyHarbin 150001China Institute of high performance computing Agency for ScienceTechnology and ResearchSingapore 138632Singapore School of Physics&State key laboratory of Crystal Materials Shandong UniversityJinan 250100China

GeTe has attracted extensive research interest for thermoelectric *** this paper,we first train a neuroevolution potential(NEP)based on a dataset constructed by ab initio molecular dynamics,with the Gaussian approximation potential(GAP)as a *** phonon density of states is then calculated by two machine learning potentials and compared with density functional theory results,with the GAP potential having higher ***,the thermal conductivity of a GeTe crystal at 300 K is calculated by the equilibrium molecular dynamics method using both machine learning potentials,and both of them are in good agreement with the experimental results;however,the calculation speed when using the NEP potential is about 500 times faster than when using the GAP ***,the lattice thermal conductivity in the range of 300 K-600 K is calculated using the NEP *** lattice thermal conductivity decreases as the temperature increases due to the phonon anharmonic *** study provides a theoretical tool for the study of the thermal conductivity of GeTe.

关键词： machine learning potentials thermal conductivity molecular dynamics