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The Necessary and Sufficient Conditions of Exponential Stability for Heat and Wave Equations with Memory

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Journal of Systems science & Complexity 2024年第3期37卷 1037-1051页

作者： LI Lingfei ZHANG Xiaoyi ZHOU Xiuxiang school of science Northeast Electric Power UniversityJilin 132012China school of mathematics and Statistics Lingnan Normal UniversityZhanjiang 524048China

This paper is addressed to a study of the stability of heat and wave equations with *** necessary and sufficient conditions of the exponential stability are investigated by the theory of Laplace transform. The results show that the stability depends on the decay rate and the coefficient of the kernel functions of the memory. Besides, the feedback stabilization of the heat equation is obtained by constructing finite dimensional controller according to unstable eigenvalues. This stabilizing procedure is easy to operate and can be applicable for other parabolic equations with memory.

关键词： Memory stability stabilization

BSTFNet:An Encrypted Malicious Traffic Classification Method Integrating Global Semantic and Spatiotemporal Features

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Computers, Materials & Continua 2024年第3期78卷 3929-3951页

作者： Hong Huang Xingxing Zhang Ye Lu Ze Li Shaohua Zhou school of Computer science and Engineering Sichuan University of Science&EngineeringYibin644002China school of mathematics and Statistics Sichuan University of Science&EngineeringYibin644002China

While encryption technology safeguards the security of network communications,malicious traffic also uses encryption protocols to obscure its malicious *** address the issues of traditional machine learning methods relying on expert experience and the insufficient representation capabilities of existing deep learning methods for encrypted malicious traffic,we propose an encrypted malicious traffic classification method that integrates global semantic features with local spatiotemporal features,called BERT-based Spatio-Temporal Features Network(BSTFNet).At the packet-level granularity,the model captures the global semantic features of packets through the attention mechanism of the Bidirectional Encoder Representations from Transformers(BERT)*** the byte-level granularity,we initially employ the Bidirectional Gated Recurrent Unit(BiGRU)model to extract temporal features from bytes,followed by the utilization of the Text Convolutional Neural Network(TextCNN)model with multi-sized convolution kernels to extract local multi-receptive field spatial *** fusion of features from both granularities serves as the ultimate multidimensional representation of malicious *** approach achieves accuracy and F1-score of 99.3.%and 99.40%,respectively,on the publicly available USTC-TFC2016 dataset,and effectively reduces sample confusion within the Neris and Virut *** experimental results demonstrate that our method has outstanding representation and classification capabilities for encrypted malicious traffic.

关键词： Encrypted malicious traffic classification bidirectional encoder representations from transformers text convolutional neural network bidirectional gated recurrent unit

Recent Advances on Deep Learning for Sign Language Recognition

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Computer Modeling in Engineering & sciences 2024年第6期139卷 2399-2450页

作者： Yanqiong Zhang Xianwei Jiang school of mathematics and Information science Nanjing Normal University of Special EducationNanjing210038China

Sign language,a visual-gestural language used by the deaf and hard-of-hearing community,plays a crucial role in facilitating communication and promoting *** language recognition(SLR),the process of automatically recognizing and interpreting sign language gestures,has gained significant attention in recent years due to its potential to bridge the communication gap between the hearing impaired and the hearing *** emergence and continuous development of deep learning techniques have provided inspiration and momentum for advancing *** paper presents a comprehensive and up-to-date analysis of the advancements,challenges,and opportunities in deep learning-based sign language recognition,focusing on the past five years of *** explore various aspects of SLR,including sign data acquisition technologies,sign language datasets,evaluation methods,and different types of neural *** Neural Networks(CNN)and Recurrent Neural Networks(RNN)have shown promising results in fingerspelling and isolated sign ***,the continuous nature of sign language poses challenges,leading to the exploration of advanced neural network models such as the Transformer model for continuous sign language recognition(CSLR).Despite significant advancements,several challenges remain in the field of *** challenges include expanding sign language datasets,achieving user independence in recognition systems,exploring different input modalities,effectively fusing features,modeling co-articulation,and improving semantic and syntactic ***,developing lightweight network architectures for mobile applications is crucial for practical *** addressing these challenges,we can further advance the field of deep learning for sign language recognition and improve communication for the hearing-impaired community.

关键词： Sign language recognition deep learning artificial intelligence computer vision gesture recognition

FNNWV: farthest-nearest neighbor-based weighted voting for class-imbalanced crowdsourcing

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science China(Information sciences) 2024年第10期67卷 172-188页

作者： Wenjun ZHANG Liangxiao JIANG Ziqi CHEN Chaoqun LI school of Computer science China University of Geosciences Key Laboratory of Artificial Intelligence Ministry of Education school of mathematics and Physics China University of Geosciences

In crowdsourcing scenarios, we can hire crowd workers to label crowdsourced tasks and then use label integration algorithms to infer the integrated label for each instance in the tasks. As more and more label integration algorithms are proposed, the performance of inference based only on the information of the inferred instance gradually converges. Recent algorithms attempt to exploit the information of the inferred instance's nearest neighbors to infer and achieve good performance. However, when crowdsourced tasks are class-imbalanced, negative instances are more easily to occur in the nearest neighbors because negative instances are the majority, and thus recent algorithms are more easily biased toward the negative class. To this end, in this paper, we propose a novel label integration algorithm called farthest-nearest neighbor-based weighted voting(FNNWV) for class-imbalanced crowdsourcing. Specifically, FNNWV considers the nearest neighbors to be more similar to the inferred instance and thus uses them to vote ayes in weighted voting. Yet at the same time, FNNWV considers the farthest neighbors to be more different from the inferred instance and thus uses them to vote nays in weighted voting. Since negative instances are easier to occur in both the nearest neighbors and the farthest neighbors, FNNWV weakens the effect of negative instances by voting ayes and nays. The experimental results on 22 simulated and one real-world crowdsourced datasets show that FNNWV significantly outperforms all the other state-of-the-art competitors.

关键词： crowdsourcing label integration nearest neighbor farthest neighbor weighted voting

Asymptotic Inference in the Random Coefficient Autoregressive Model with Time-functional Variance Noises

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 320-346页

作者： En-wen ZHU Zi-wei DENG Han-jun ZHANG Jun CAO Xiao-hui LIU Department of mathematics and Statistics Changsha University of Science and TechnologyChangsha 410114China school of mathematics and Computational science Xiangtan UniversityXiangtan 411105China school of Statistics and Data science and Key Laboratory of Data Science in Finance and EconomicsJiangxi University of Finance and EconomicsNanchang 330013China

This paper considers the random coefficient autoregressive model with time-functional variance noises,hereafter the RCA-TFV *** first establish the consistency and asymptotic normality of the conditional least squares estimator for the constant *** semiparametric least squares estimator for the variance of the random coefficient and the nonparametric estimator for the variance function are constructed,and their asymptotic results are reported.A simulation study is presented along with an analysis of real data to assess the performance of our method in finite samples.

关键词： random coefficient autoregressive model time-functional variance conditional least squares semiparametric least squares

Second-order error analysis of the averaged L1 scheme L1 for time-fractional initial-value and subdiffusion problems

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science China mathematics 2024年第7期67卷 1641-1664页

作者： Jinye Shen Fanhai Zeng Martin Stynes school of mathematics Southwestern University of Finance and EconomicsChengdu611130China school of mathematics Shandong UniversityJinan250100China Applied and Computational mathematics Division Beijing Computational Science Research CenterBeijing100193China

Fractional initial-value problems(IVPs) and time-fractional initial-boundary value problems(IBVPs), each with a Caputo temporal derivative of order α ∈(0, 1), are considered. An averaged variant of the well-known L1 scheme is proved to be O(N^(-2)) convergent for IVPs on suitably graded meshes with N points, thereby improving the O(N^(-(2-α))) convergence rate of the standard L1 scheme. The analysis relies on a delicate decomposition of the temporal truncation error that yields a sharp dependence of the order of convergence on the degree of mesh grading used. This averaged L1 scheme can be combined with a finite difference or piecewise linear finite element discretization in space for IBVPs, and under a restriction on the temporal mesh width, one gets again O(N^(-2)) convergence in time, together with O(h^(2)) convergence in space,where h is the spatial mesh width. Numerical experiments support our results.

关键词： time-fractional subdiffusion averaged L1 scheme

Mean-square exponential stability of stochastic Volterra systems in infinite dimensions

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science China(Information sciences) 2024年第10期67卷 298-314页

作者： Lin FU Shiguo PENG Feiqi DENG Quanxin ZHU school of Automation Guangdong University of Technology school of Automation science and Engineering South China University of Technology Key Laboratory of Computing and Stochastic mathematics(Ministry of Education) School of Mathematics and StatisticsHunan Normal University

Over the past decade, the study of stability theory in integro-differential systems has grown significantly owing to their relevance in solving physical and engineering problems, such as viscoelasticity and thermo-viscoelasticity in materials with memory properties. This paper concentrates on a class of infinite-dimensional stochastic integro-differential systems. We establish the well-posedness of the system and identify mild solutions to the system and an abstract stochastic Cauchy problem. This identification is identified by employing a semigroup approach combined with Yosida approximation. We derive sufficient conditions that ensure the mean-square exponential stability of mild solutions to the system boils down to the boundedness of a certain function and a norm estimate for the stochastic part. These conditions are implemented through the semigroup approach and the composition operator method. Illustrative examples are provided and the obtained theoretical results are validated by numerical simulations.

关键词： stochastic integro-differential equations mean-square exponential stability stochastic distributed parameter systems Hardy space composition operators

TOEPLITZ OPERATORS BETWEEN WEIGHTED BERGMAN SPACES OVER THE HALF-PLANE

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Acta Mathematica Scientia 2024年第5期44卷 1707-1720页

作者： Lixia FENG Yan LI Zhiyu WANG Liankuo ZHAO school of mathematics and Computer science Shanxi Normal UniversityTaiyuan030031China

In this paper,by characterizing Carleson measures,we investigate a class of bounded Toeplitz operator between weighted Bergman spaces with Békolléweights over the half-plane for all index choices.

关键词： weighted Bergman spaces Békolléweights Carleson measure Toeplitz operators

Global Phase Portraits of Uniform Isochronous Centers System of Degree Six with Polynomial Commutator

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 577-599页

作者： Li-na GUO Ai-yong CHEN Shuai-feng ZHAO school of mathematics and Statistics Henan University of Science and TechnologyLuoyang 471023China Department of mathematics Hunan First Normal UniversityChangsha 410205China school of Mechatronics Engineering Henan University of Science and TechnologyLuoyang 471023China

This paper studies the global phase portraits of uniform isochronous centers system of degree six with polynomial *** systems have the form x=-y+xf(x,y),y=x+yf(x,y),where f(x,y)=a_(1)x+a_(2)xy+a_(3.xy^(2)+a_(4)xy^(3.+a_(5)xy^(4)=xσ(y),and any zero of 1+a_(1)y+a_(2)y^(2)+a_(3.y^(3.+a_(4)y^(4)+a_(5)y^(5),y=y is an invariant straight *** last,all global phase portraits are drawn on the Poincare disk.

关键词： global phase portraits uniform isochronous center polynomial commutator invariant straight lines