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CENTRAL LIMIT THEOREM FOR TEMPORAL AVERAGE OF BACKWARD EULER-MARUYAMA METHOD

Journal of Computational Mathematics 2025年第3期43卷 588-614页

作者： Diancong Jin School of Mathematics and Statistics Hubei Key Laboratory of Engineering Modeling and Scientific ComputingHuazhong University of Science and TechnologyWuhan 430074China

This work focuses on the temporal average of the backward Euler-Maruyama(BEM)method,which is used to approximate the ergodic limit of stochastic ordinary differential equations(SODEs).We give the central limit theorem(CLT)of the temporal average of the BEM method,which characterizes its asymptotics in *** the deviation order is smaller than the optimal strong order,we directly derive the CLT of the temporal average through that of original equations and the uniform strong order of the BEM *** the case that the deviation order equals to the optimal strong order,the CLT is established via the Poisson equation associated with the generator of original *** experiments are performed to illustrate the theoretical *** main contribution of this work is to generalize the existing CLT of the temporal average of numerical methods to that for SODEs with super-linearly growing drift coefficients.

关键词： Central limit theorem Temporal average Ergodicity Backward Euler-Maruyama method

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Exploring data augmentation for Amazigh speech recognition with convolutional neural networks

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International Journal of Speech Technology 2025年第1期28卷 53-65页

作者： Boulal, Hossam Bouroumane, Farida Hamidi, Mohamed Barkani, Jamal Abarkan, Mustapha LSI Laboratory FP Taza USMBA University Taza Morocco Team of Modeling and Scientific Computing FPN UMP Nador Morocco

In the field of speech recognition, enhancing accuracy is paramount for diverse linguistic communities. Our study addresses this necessity, focusing on improving Amazigh speech recognition through the implementation of three distinct data augmentation methods: Audio Augmentation, FilterBank Augmentation, and SpecAugment. Leveraging Convolutional Neural Networks (CNNs) for speech recognition, we utilize Mel Spectrograms extracted from audio files. The study specifically targets the recognition of the initial ten Amazigh digits. We conducted experiments with a speaker-independent approach involving 42 participants. A total of 27 experiments were conducted, utilizing both original and augmented data. Among the different CNN models employed, the VGG19 model showcased significant promise. Our results demonstrate a maximum accuracy of 95.66%. Furthermore, the most notable improvement achieved through data augmentation was 4.67%. These findings signify a substantial enhancement in speech recognition accuracy, indicating the efficacy of the proposed methods. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Convolutional neural networks

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An accurate and efficient space-time Galerkin spectral method for the subdiffusion equation

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Science China Mathematics 2024年第10期67卷 2387-2408页

作者： Wei Zeng Chuanju Xu School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing Xiamen UniversityXiamen 361005China

In this paper, we design and analyze a space-time spectral method for the subdiffusion ***, we are facing two difficulties. The first is that the solutions of this equation are usually singular near the initial time. Consequently, traditional high-order numerical methods in time are inefficient. The second obstacle is that the resulting system of the space-time spectral approach is usually large and time-consuming to solve. We aim at overcoming the first difficulty by proposing a novel approach in time, which is based on variable transformation techniques. Suitable ψ-fractional Sobolev spaces and a new variational framework are introduced to establish the well-posedness of the associated variational problem. This allows us to construct our space-time spectral method using a combination of temporal generalized Jacobi polynomials(GJPs) and spatial Legendre polynomials. For the second difficulty, we propose a fast algorithm to effectively solve the resulting linear system. The fast algorithm makes use of a matrix diagonalization in space and QZ decomposition in time. Our analysis and numerical experiments show that the proposed method is exponentially convergent with respect to the polynomial degrees in both space and time directions, even though the exact solution has very limited regularity.

关键词： subdiffusion equations variable transformation Ψ-Sobolev spaces well-posedness space-time Galerkin spectral method error estimate fast algorithm

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Global Solvability for a Predator-Prey Model with Prey-Taxis and Rotational Flux Terms

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Chinese Annals of Mathematics,Series B 2024年第2期45卷 297-318页

作者： Guoqiang REN Bin LIU School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong Universityof Science and Technology

In this paper the author investigates the following predator-prey model with prey-taxis and rotational?ux terms■in a bounded domain with smooth *** presents the global existence of generalized solutions to the model... 详细信息

关键词： Predator-prey Prey-taxis Giopal existence Kotational flnux

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Enhancing amazigh ASR through convolutional neural networks and MFCC

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Multimedia Tools and Applications 2024年 1-20页

作者： Boulal, Hossam Hamidi, Mohamed Barkani, Jamal Abarkan, Mustapha LSI Laboratory FP Taza USMBA University Taza Morocco Team of modeling and scientific computing FPN UMP Nador Morocco

In this study, we developed a speech recognition system for the Amazigh language, specifically targeting the recognition of the initial ten numbers. The system employs four Convolutional Neural Network (CNN) models, including three custom-designed models and a pre-trained VGG19 model. Our experiments utilized a dataset comprising 4200 audio files recorded by 42 distinct speakers, with input features extracted as Mel Frequency Cepstral Coefficients (MFCCs). We tested three normalization methods: no normalization, Cepstral Mean and Variance Normalization (CMVN), and Min-Max normalization. While CMVN generally provided effective standardization, We achieved the highest accuracy of 97.56% using Min-Max normalization with a specific filter size in the third custom CNN model. The VGG19 model, however, showed suboptimal performance. These findings underscore the significance of selecting suitable normalization techniques and model architectures for enhancing speech recognition accuracy. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Convolutional neural networks

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Amazigh CNN speech recognition system based on Mel spectrogram feature extraction method

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International Journal of Speech Technology 2024年第1期27卷 287-296页

作者： Boulal, Hossam Hamidi, Mohamed Abarkan, Mustapha Barkani, Jamal LSI Laboratory FP Taza USMBA University Taza Morocco Team of Modeling and Scientific Computing FPN UMP Nador Morocco

The field of speech recognition makes it simpler for humans and machines to engage with speech. Number-oriented communication, such as using a registration code, mobile number, score, or account number, can benefit from speech recognition for digits. This paper presents our Amazigh automatic speech recognition (ASR) experience based on the deep learning approach. The convolutional neural network (CNN) and Mel spectrogram are exploited to evaluate audio samples and produce spectrograms as a part of the deep learning strategy. To attempt the recognition of the Amazigh numerals, we use a database that includes digits ranging from zero to nine collected from 42 native speakers in total, men and women between the ages of 20 and 40. Our experimental results show that spoken digits in Amazigh can be identified with a maximum accuracy of 93.62%, 94% Precision, and 94% Recall. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Feature extraction

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Stabilization and Blow-up in an Infinite Memory Wave Equation with Logarithmic Nonlinearity and Acoustic Boundary Conditions

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Journal of Systems Science & Complexity 2024年第4期37卷 1368-1391页

作者： PENG Qingqing ZHANG Zhifei School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

In this paper,the authors consider the stabilization and blow up of the wave equation with infinite memory,logarithmic nonlinearity and acoustic boundary *** authors discuss the existence of global solutions for the initial energy less than the depth of the potential well and investigate the energy decay estimates by introducing a Lyapunov ***,the authors establish the finite time blow up results of solutions and give the blow up time with upper bounded initial energy.

关键词： Acoustic boundary condition finite time blow-up general decay infinite memory logarithmic nonlinearity

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Adapted Runge-Kutta Methods for Nonlinear First-Order Delay BVPs with Time-variable Delay

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Acta Mathematicae Applicatae Sinica 2025年第2期41卷 400-413页

作者： Cheng-jian ZHANG Yang WANG Hao HAN School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with numerical solutions for nonlinear first-order boundary value problems(BVPs) with time-variable delay. For solving this kind of delay BVPs, by combining Runge-Kutta methods with Lagrange interpolation, a class of adapted Runge-Kutta(ARK) methods are developed. Under the suitable conditions, it is proved that ARK methods are convergent of order min{p, μ+ν +1}, where p is the consistency order of ARK methods and μ, ν are two given parameters in Lagrange interpolation. Moreover, a global stability criterion is derived for ARK methods. With some numerical experiments, the computational accuracy and global stability of ARK methods are further testified.

关键词： delay boundary value problems adapted Runge-Kutta method Lagrange interpolation error analysis global stability

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Full states pseudo-random projective synchronization of hyperchaotic system and corresponding secure communication algorithm

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Multimedia Tools and Applications 2025年第7期84卷 3527-3568页

作者： Li, Zhenbo Tang, Yezhi Xu, Feng Zhang, Yiqing School of Mathematics and Physics University of South China Hengyang421001 China Hunan Key Laboratory of Mathematical Modeling and Scientific Computing University of South China Hengyang421001 China

This paper proposes a more general and complicated synchronization scheme, termed full states pseudo-random projective synchronization (FSPRPS). In this synchronization scheme, the scaling factor is a function matrix composed of external pseudo-random sequences. It makes many existing synchronization schemes special cases of FSPRPS. Via modified active control, the proposed synchronization is realized efficiently between hyperchaotic systems. Meanwhile, based on FSPRPS, a novel secure communication algorithm who overcomes several shortcomings of many existing algorithms is constructed. In this algorithm, two systems are utilized to implement encryption. The information signal is inserted into these two systems to participate the generation of several chaotic signals. Then, the transmitted signals are masked and scrambled twice by these chaotic signals to enhance the security. In simulations, RGB color images are taken as the information signal to exhibit the feasibility and validity of the proposed algorithm. In performance analyses that followed, this algorithm is proved as huge size of key space (≥21020), high sensitivity to keys and plaintexts (PSNR is about 99.62%), excellent statistical properties (information entropy is about 7.9993), strong robustness and high processing efficiency (encryption time for a 512×512 RGB image is about 1.6 s). These all demonstrate the feasibility, robustness, high security and effectiveness of the algorithm, which can serve as an effective reference for constructing other synchronization schemes and secure communication algorithms. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

关键词： Secure communication

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Spontaneous Infection and Periodic Evolving of Domain in a Diffusive SIS Epidemic Model

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 164-191页

作者： Qiang Wen Guo-qiang Ren Bin Liu School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074China

In this paper, we consider a susceptible-infective-susceptible(SIS) reaction-diffusion epidemic model with spontaneous infection and logistic source in a periodically evolving domain. Using the iterative technique,the uniform boundedness of solution is established. In addition, the spatial-temporal risk index R0(ρ) depending on the domain evolution rate ρ(t) as well as its analytical properties are discussed. The monotonicity of R0(ρ)with respect to the diffusion coefficients of the infected dI, the spontaneous infection rate η(ρ(t)y) and interval length L is investigated under appropriate conditions. Further, the existence and asymptotic behavior of periodic endemic equilibria are explored by upper and lower solution method. Finally, some numerical simulations are presented to illustrate our analytical results. Our results provide valuable information for disease control and prevention.

关键词： diffusive SIS model spontaneous infection periodically evolving domain periodic endemic equilibrium

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