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arXiv 2022年

作者： Runge, Tobias Bordis, Tabea Potanin, Alex Thüm, Thomas Schaefer, Ina Karlsruhe Institute of Technology Germany Institute of Software Engineering and Automotive Informatics TU Braunschweig Germany School for Data-Science and Computational Thinking Stellenbosch University South Africa School of Computing Australian National University Australia Institute of Software Engineering and Programming Languages University of Ulm Germany

Correctness-by-Construction (CbC) is an incremental program construction process to construct functionally correct programs. The programs are constructed stepwise along with a specification that is inherently guaranteed to be satisfied. CbC is complex to use without specialized tool support, since it needs a set of predefined refinement rules of fixed granularity which are additional rules on top of the programming language. Each refinement rule introduces a specific programming statement and developers cannot depart from these rules to construct programs. CbC allows to develop software in a structured and incremental way to ensure correctness, but the limited flexibility is a disadvantage of CbC. In this work, we compare classic CbC with CbC-Block and TraitCbC. Both approaches CbC-Block and TraitCbC, are related to CbC, but they have new language constructs that enable a more flexible software construction approach. We provide for both approaches a programming guideline, which similar to CbC, leads to well-structured programs. CbC-Block extends CbC by adding a refinement rule to insert any block of statements. Therefore, we introduce CbC-Block as an extension of CbC. TraitCbC implements correctness-by-construction on the basis of traits with specified methods. We formally introduce TraitCbC and prove soundness of the construction strategy. All three development approaches are qualitatively compared regarding their programming constructs, tool support, and usability to assess which is best suited for certain tasks and developers. © 2022, CC BY.

关键词： Formal verification

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SPECTRUM AND LIFSHITZ TAILS FOR THE ANDERSON MODEL ON THE SIERPINSKI GASKET GRAPH

arXiv

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arXiv 2024年

作者： Shou, Laura Wang, Wei Zhang, Shiwen Joint Quantum Institute Department of Physics University of Maryland College ParkMD20742 United States LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Mathematics and Statistics University of Massachusetts Lowell Southwick Hall 11 University Ave. LowellMA01854 United States

In this work, we study the Anderson model on the Sierpinski gasket graph. We first identify the almost sure spectrum of the Anderson model when the support of the random potential has no gaps. We then prove the existence of the integrated density states of the Anderson model and show that it has Lifshitz tails with Lifshitz exponent determined by the ratio of the volume growth rate and the random walk dimension of the Sierpinski gasket graph. Copyright © 2024, The Authors. All rights reserved.

关键词： Graph theory

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FPGA based Power Efficient Approximate 4:2 Compressor for Multimedia Applications

FPGA based Power Efficient Approximate 4:2 Compressor for Mu...

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International Conference on Edge computing and Applications (ICECAA)

作者： Dinesh G Arunkumar K P. Radhakrishnan Rajendra D. Jadhav Twinkle Dasari Hasamukh Lal Department of Computational Intelligence School of computing SRM Institute of Science and Technology Chennai Department of ECE Saveetha Engineering College Chennai Department of ECE Tagore Engineering college Chennai Bharati Vidyapeeth (Deemed to be University) Institute of Management Kolhapur Department of Engineering English Koneru Lakshmaiah Education Foundation Vaddeswaram Andhra Pradesh India Department of Agriculture Sciences IES University Bhopal M.P

Approximate computing plays a crucial part in error resilent and multimedia applications. This study presents the design and analysis of a 4:2 compressor that employs a Dadda multiplier to reduce output power and inaccuracy. The approximate compressors are utilized to design 8*8, 16*16,32*32 multipliers. The goal of this work is to develop a compressor with low latency, low power consumption, and fewer product stages. By reducing the number of transistors and gates the low latency compressors used to serve as multiplier design applications. The adders and product stages are to be considerable power consumption in multiplication process. The reduced compressors consume less power and it could be applicable for designers.

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Elastic Full Waveform Inversion Based on the Trust Region Strategy

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American Journal of computational Mathematics 2021年第4期11卷 241-266页

作者： Wensheng Zhang Yijun Li State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China School of Mathematical Sciences University of Chinese Academy Sciences Beijing China

In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.

关键词： Elastic Wave Equations Full-Waveform Inversion Trust Region Strate-gy Line Search Strategy Newton-Type Method Time Domain

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STRONG ERROR ANALYSIS OF EULER METHODS FOR OVERDAMPED GENERALIZED LANGEVIN EQUATIONS WITH FRACTIONAL NOISE: NONLINEAR CASE

arXiv

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arXiv 2022年

作者： Dai, Xinjie Hong, Jialin Sheng, Derui Zhou, Tau Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main difficulty lies in handling the interaction between the fractional Brownian motion and the singular kernel, which is overcome by means of the Malliavin calculus and fine estimates of several multiple singular integrals. Consequently, these two methods are proved to be strongly convergent with order nearly min{2(H + α − 1), α}, where H ∈ (1/2, 1) and α ∈ (1 − H, 1) respectively characterize the singularity levels of fractional noises and singular kernels in the underlying equation. This result improves the existing convergence order H + α − 1 of Euler methods for the nonlinear case, and gives a positive answer to the open problem raised in [4]. As an application of the theoretical findings, we further investigate the complexity of the multilevel Monte Carlo simulation based on the fast Euler method, which turns out to behave better performance than the standard Monte Carlo simulation when computing the expectation of functionals of the considered *** Codes 65C20, 65C30, 65C05, 60H07 Copyright © 2022, The Authors. All rights reserved.

关键词： Monte Carlo methods

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Amplitude Expansion Phase Field Crystal (APFC) Modeling based Efficient Dislocation Simulations using Fourier Pseudospectral Method

arXiv

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arXiv 2024年

作者： Wei, Xinyi Wang, Yangshuai Jiang, Kai Zhang, Lei School of Mathematical Sciences Institute of Natural Sciences and MOE-LSC Shanghai Jiao Tong University Shanghai200240 China Department of Mathematics Faculty of Science National University of Singapore 10 Lower Kent Ridge Road Singapore Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan411105 China

Crystalline defects play a critical role in determining the properties of crystalline solids, underscoring the need for accurate computational methods to study them. Lattice deformation in dislocation simulations, which involves changes in atomic positions, can be described either microscopically by specific atomic configurations or macroscopically by continuum elasticity, each with inherent limitations. The complex amplitude expansion of the phase field crystal (APFC) model provides a mesoscopic approach that bridges these scales. In this paper, we introduce a Fourier pseudospectral method for efficiently solving the APFC model in the context of crystalline defect simulations. This study marks the first application of the Fourier pseudospectral method to the APFC model. The method fully exploits the system’s periodicity and facilitates the implementation of periodic boundary conditions, thanks to its high accuracy and computational efficiency. Numerical experiments conducted on two-dimensional triangular lattices and three-dimensional body-centered cubic lattices for edge dislocation geometry optimization have produced strain field images that align well with by continuum elasticity predictions. The findings demonstrate the potential of the APFC model to accurately capture the complex strain fields associated with dislocations at the mesoscopic scales, a key step toward modeling more intricate crystalline defect structures and dynamics. © 2024, CC BY.

关键词： Edge dislocations

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Machine Learning-based Signal Quality Assessment for Cardiac Volume Monitoring in Electrical Impedance Tomography

arXiv

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arXiv 2023年

作者： Hyun, Chang Min Jang, Tae Jun Nam, Jeongchan Kwon, Hyeuknam Jeon, Kiwan Lee, Kyunghun School of Mathematics and Computing Computational Science and Engineering Yonsei University Seoul Korea Republic of BiLab Pangyo Korea Republic of Division of Software Yonsei University Wonju Korea Republic of National Institute for Mathematical Sciences Daejeon Korea Republic of Kyung Hee University Seoul Korea Republic of

Owing to recent advances in thoracic electrical impedance tomography, a patient's hemodynamic function can be noninvasively and continuously estimated in real-time by surveilling a cardiac volume signal associated with stroke volume and cardiac output. In clinical applications, however, a cardiac volume signal is often of low quality, mainly because of the patient's deliberate movements or inevitable motions during clinical interventions. This study aims to develop a signal quality indexing method that assesses the influence of motion artifacts on transient cardiac volume signals. The assessment is performed on each cardiac cycle to take advantage of the periodicity and regularity in cardiac volume changes. Time intervals are identified using the synchronized electrocardiography system. We apply divergent machine-learning methods, which can be sorted into discriminative-model and manifold-learning approaches. The use of machine-learning could be suitable for our real-time monitoring application that requires fast inference and automation as well as high accuracy. In the clinical environment, the proposed method can be utilized to provide immediate warnings so that clinicians can minimize confusion regarding patients' conditions, reduce clinical resource utilization, and improve the confidence level of the monitoring system. Numerous experiments using actual EIT data validate the capability of cardiac volume signals degraded by motion artifacts to be accurately and automatically assessed in real-time by machine learning. The best model achieved an accuracy of 0.95, positive and negative predictive values of 0.96 and 0.86, sensitivity of 0.98, specificity of 0.77, and AUC of 0.96. © 2023, CC BY.

关键词： Machine learning

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Three kinds of novel multi-symplectic methods for stochastic Hamiltonian partial differential equations

arXiv

引用

arXiv 2022年

作者： Hong, Jialin Hou, Baohui Li, Qiang Sun, Liying Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic Hamiltonian partial differential equations provide numerical approximations with better numerical stability, and are of vital significance for obtaining correct numerical results. In this paper, we propose three novel multi-symplectic methods for stochastic Hamiltonian partial differential equations based on the local radial basis function collocation method, the splitting technique, and the partitioned Runge–Kutta method. Concrete numerical methods are presented for nonlinear stochastic wave equations, stochastic nonlinear Schrödinger equations, stochastic Korteweg-de Vries equations and stochastic Maxwell equations. We take stochastic wave equations as examples to perform numerical experiments, which indicate the validity of the proposed methods. © 2022, CC BY.

关键词： Stochastic systems

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Three Kinds of Novel Multi-Symplectic Methods for Stochastic Hamiltonian Partial Differential Equations

SSRN

引用

SSRN 2022年

Stochastic Hamiltonian partial differential equations, which possess the multi-symplectic conservation law, are an important and fairly large class of systems. The multi-symplectic methods inheriting the geometric features of stochastic Hamiltonian partial differential equations provide numerical approximations with better numerical stability, and are of vital significance for obtaining correct numerical results. In this paper, we propose three novel multi-symplectic methods for stochastic Hamiltonian partial differential equations based on the local radial basis function collocation method, the splitting technique and the partitioned Runge-Kutta method. Concrete numerical methods are presented for nonlinear stochastic wave equations, stochastic nonlinear Schr\"odinger equations, stochastic Korteweg-de Vries equations and stochastic Maxwell equations. We take stochastic wave equations as examples to perform numerical experiments, which indicate the validity of the proposed methods. © 2022, The Authors. All rights reserved.

关键词： Stochastic systems

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Sky Sentinel: Pioneering Real-Time Facial Recognition in Intelligent Drones

Sky Sentinel: Pioneering Real-Time Facial Recognition in Int...

引用

Smart Electronics and Communication (ICOSEC), International Conference on

作者： L. Visalatchi Praveena Anjelin Malathi Eswaran Vijayalakshmi K Sathish Kumar L. Chinmay Inamdar Department of IT Dr.Umayal Ramanathan College for women Karaikudi Tamil Nadu India Department of CSE B. S. Abdur Rahman Crescent Institute of Science and Technology Kongu Engineering College Perundurai Erode Tamil Nadu India Department of Computational intelligence School of Computing College of Engineering and Technology SRM Institute of Science and Technology Kattankulathur Chennai India SCSE VIT Bhopal University Madhya Pradesh India Department of Computer Science and Engineering VIT Bhopal University Madhya Pradesh India

The goal of this article is to provide a method that makes use of a face recognition-powered unmanned aerial vehicle (UAV). The goal of this approach is to make it easier for law enforcement to identify suspects, track down missing persons, verify identities, and carry out age-based monitoring. A facial recognition system is an electronic tool that uses AI to recognise people by their faces. Identity verification often makes use of facial recognition technologies. The facial features of a picture are analysed in this procedure. This research details the steps required to design, build, and test an unmanned aerial vehicle (UAV) integrated with a camera and face recognition software. The UAV is used as a remote control for a robot equipped with Bluetooth technology. The suggested method proves it can adapt to different drone orientations. Drone camera angles in all 37 directions have an accuracy of 99.3 percent, proving this point. Recovery activities, rescue missions, occurrence inquiries, offender assessment, and crowd surveillance are just a few examples of how specialised software may aid law enforcement in their investigative work.

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