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Cryptography: Recent research trends of encrypting mathematics

Materials Today: Proceedings 2022年 56卷 3247-3253页

作者： Kikani, Ria Jatin Verma, Kirti Navalakhe, Rachna Shrivastava, Gourav Shrivastava, Vineeta Department of Information Technology Silver Oak College of Engineering and Technology GTU Gujarat India Department of Engineering Mathematics Lakshmi Narain College of Technology MP Bhopal India Department of Applied Mathematics and Computational Science Shri G.S. Institute of Technology and Science MP Indore India Department of Computer Science and Engineering SAGE University MP Bhopal India Department of Computer Science and Engineering Lakshmi Narain College of Technology MP Bhopal India

In today's world where technology and mathematics are progressing hand in hand there are so many things to be considered and thought of when it comes to network security. Cryptography plays a prominent and an important role when it comes to securing the system from unwanted hazardous attacks. As the Internet has made great strides in different domains it has impacted the human life in several ways and hence data security has become the question of the hour. In such a scenario cryptography plays a big role as it ensures that the data transmitted is received as it is without any alteration or modification. However, we have discussed the algorithms and various methods required in order to maintain the security. In the subsequent sections we shall be discussing about theoretical computer science, cryptography attacks, algorithms and its application in everyday life. © 2021

关键词： Cryptography

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Low-rank generalized alternating direction implicit iteration method for solving matrix equations

arXiv

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arXiv 2024年

作者： Zhang, Juan Xun, Wenlu Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education Hunan Key Laboratory for Computation and Simulation in Science and Engineering School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China School of Mathematics and Computational Science Xiangtan University Hunan Xiangtan China

This paper presents an effective low-rank generalized alternating direction implicit iteration (R-GADI) method for solving large-scale sparse and stable Lyapunov matrix equations and continuous-time algebraic Riccati matrix equations. The method is based on generalized alternating direction implicit iteration (GADI), which exploits the low-rank property of matrices and utilizes the Cholesky factorization approach for solving. The advantage of the new algorithm lies in its direct and efficient low-rank formulation, which is a variant of the Cholesky decomposition in the Lyapunov GADI method, saving storage space and making it computationally effective. When solving the continuous-time algebraic Riccati matrix equation, the Riccati equation is first simplified to a Lyapunov equation using the Newton method, and then the R-GADI method is employed for computation. Additionally, we analyze the convergence of the R-GADI method and prove its consistency with the convergence of the GADI method. Finally, the effectiveness of the new algorithm is demonstrated through corresponding numerical experiments. Copyright © 2024, The Authors. All rights reserved.

关键词： Riccati equations

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When are dynamical systems learned from time series data statistically accurate? 38

When are dynamical systems learned from time series data sta...

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38th Conference on Neural Information Processing Systems, NeurIPS 2024

作者： Park, Jeongjin Yang, Nicole Tianjiao Chandramoorthy, Nisha School of Computational Science and Engineering Georgia Institute of Technology AtlantaGA30332 United States Department of Mathematics Emory University AtlantaGA30322 United States Department of Statistics The University of Chicago ChicagoIL60637 United States

Conventional notions of generalization often fail to describe the ability of learned models to capture meaningful information from dynamical data. A neural network that learns complex dynamics with a small test error may still fail to reproduce its physical behavior, including associated statistical moments and Lyapunov exponents. To address this gap, we propose an ergodic theoretic approach to generalization of complex dynamical models learned from time series data. Our main contribution is to define and analyze generalization of a broad suite of neural representations of classes of ergodic systems, including chaotic systems, in a way that captures emulating underlying invariant, physical measures. Our results provide theoretical justification for why regression methods for generators of dynamical systems (Neural ODEs) fail to generalize, and why their statistical accuracy improves upon adding Jacobian information during training. We verify our results on a number of ergodic chaotic systems and neural network parameterizations, including MLPs, ResNets, Fourier Neural layers, and RNNs. © 2024 Neural information processing systems foundation. All rights reserved.

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Generalization Error Estimates of Machine Learning Methods for Solving High Dimensional Schrödinger Eigenvalue Problems

arXiv

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arXiv 2024年

作者： Yu, Hao Guo, Yixiao Ming, Pingbing LSEC 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

We propose a machine learning method for computing eigenvalues and eigenfunctions of the Schrödinger operator on a d-dimensional hypercube with Dirichlet boundary conditions. The cut-off function technique is employed to construct trial functions that precisely satisfy the homogeneous boundary conditions. This approach eliminates the error caused by the standard boundary penalty method, improves the overall accuracy of the method, as demonstrated by the typical numerical examples. Under the assumption that the eigenfunctions belong to a spectral Barron space, we derive an explicit convergence rate of the generalization error of the proposed method, which does not suffer from the curse of dimensionality. We verify the assumption by proving a new regularity shift result for the eigenfunctions when the potential function belongs to an appropriate spectral Barron space. Moreover, we extend the generalization error bound to the normalized penalty method, which is widely used in practice. Copyright © 2024, The Authors. All rights reserved.

关键词： Boundary conditions

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A Diffuse-Interface Lattice Boltzmann Method for the Dendritic Growth with Thermosolutal Convection

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Communications in computational Physics 2023年第4期33卷 1164-1188页

作者： Chengjie Zhan Zhenhua Chai Baochang Shi Ping Jiang Shaoning Geng Dongke Sun School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan430074P.R.China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and TechnologyWuhan 430074P.R.China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan430074P.R.China The State Key Laboratory of Digital Manufacturing Equipment and Technology School of Mechanical Science and EngineeringHuazhong University of Science and TechnologyWuhan 430074P.R.China School of Mechanical Engineering Southeast UniversityNanjing 211189P.R.China

In this work,we proposed a diffuse-interface model for the dendritic growth with thermosolutal *** this model,the sharp boundary between the fluid and solid dendrite is firstly replaced by a thin but nonzero thickness diffuse interface,which is described by the order parameter,and the diffuse-interface based governing equations for the dendritic growth are *** solve the model for the dendritic growth with thermosolutal convection,we also developed a diffuse-interface multirelaxation-time lattice Boltzmann(LB)*** this method,the order parameter in the phase-field equation is combined into the force caused by the fluid-solid interaction,and the treatment on the complex fluid-solid interface can be *** addition,four LB models are designed for the phase-field equation,concentration equation,temperature equation and the Navier-Stokes equations in a unified ***,we performed some simulations of the dendritic growth to test the present diffuse-interface LB method,and found that the numerical results are in good agreements with some previous works.

关键词： Dendritic growth diffuse interface lattice Boltzmann method phase-field method.

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Neural Cryptography with Fog computing Network for Health Monitoring Using IoMT

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Computer Systems science & engineering 2023年第1期44卷 945-959页

作者： G.Ravikumar K.Venkatachalam Mohammed A.AlZain Mehedi Masud Mohamed Abouhawwash Department of Computer Science and Engineering Coimbatore Institute of Engineering and TechnologyCoimbatore641109India Department of Applied Cybernetics Faculty of ScienceUniversity of Hradec Králové50003Hradec KrálovéCzech Republic Department of Information Technology College of Computers and Information TechnologyTaif UniversityP.O.Box 11099Taif21944Saudi Arabia Department of Computer Science College of Computers and Information TechnologyTaif UniversityP.O.Box 11099Taif21944Saudi Arabia Department of Mathematics Faculty of ScienceMansoura UniversityMansoura35516Egypt Department of Computational Mathematics Scienceand Engineering(CMSE)Michigan State UniversityEast LansingMI48824USA

Sleep apnea syndrome(SAS)is a breathing disorder while a person is *** traditional method for examining SAS is Polysomnography(PSG).The standard procedure of PSG requires complete overnight observation in a *** typically provides accurate results,but it is expensive and time ***,for people with Sleep apnea(SA),available beds and laboratories are ***,it may produce inaccurate ***,this paper proposes the Internet of Medical Things(IoMT)framework with a machine learning concept of fully connected neural network(FCNN)with k-near-est neighbor(k-NN)*** paper describes smart monitoring of a patient’s sleeping habit and diagnosis of SA using FCNN-KNN+average square error(ASE).For diagnosing SA,the Oxygen saturation(SpO2)sensor device is popularly used for monitoring the heart rate and blood oxygen *** diagnosis information is securely stored in the IoMT fog computing *** can care-fully monitor the SA patient remotely on the basis of sensor values,which are efficiently stored in the fog computing *** proposed technique takes less than 0.2 s with an accuracy of 95%,which is higher than existing models.

关键词： Sleep apnea polysomnography IOMT fog node security neural network KNN signature encryption sensor

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FINITE ELEMENT ERROR ESTIMATES FOR THE NONLINEAR SCHRÖDINGER-POISSON MODEL

arXiv

引用

arXiv 2023年

作者： Cui, Tao Lu, Wenhao Pan, Naiyan Zheng, Weiying LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Science University of Chinese Academy of Sciences Beijing100190 China

In this paper, we study a priori error estimates for the finite element approximation of the nonlinear Schrödinger-Poisson model. The electron density is defined by an infinite series over all eigenvalues of the Hamiltonian operator. To establish the error estimate, we present a unified theory of error estimates for a class of nonlinear problems. The theory is based on three conditions: 1) the original problem has a solution u which is the fixed point of a compact operator A, 2) A is Fréchet-differentiable at u and I − A′[u] has a bounded inverse in a neighborhood of u, and 3) there exists an operator Ah which converges to A in the neighborhood of u. The theory states that Ah has a fixed point uh which solves the approximate problem. It also gives the error estimate between u and uh, without assumptions on the well-posedness of the approximate problem. We apply the unified theory to the finite element approximation of the Schrödinger-Poisson model and obtain optimal error estimate between the numerical solution and the exact solution. Numerical experiments are presented to verify the convergence rates of numerical *** Codes 65M60, 65L15, 37L65 Copyright © 2023, The Authors. All rights reserved.

关键词： Approximation theory

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MONOLITHIC MULTIGRID FOR REDUCED MAGNETOHYDRODYNAMIC EQUATIONS

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Journal of computational mathematics 2021年第3期39卷 453-470页

作者： Xiaodi Zhang Weiying Zheng LSEC NCMISInstitute of Computational Mathermatics and Scientific ComputingAcademy of Mathematics and Systerns ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Science University of Chinese Academy of SciencesBeijing 100049China

In this paper,the monolithic multigrid method is investigated for reduced magnetohydrodynamic *** propose a diagonal Braess-Sarazin smoother for the finite element discrete system and prove the uniform convergence of the MMG method with respect to mesh sizes.A multigrid-preconditioned FGMRES method is proposed to solve the magnetohydrodynamic *** turns out to be robust for relatively large physical *** extensive numerical experiments,we demonstrate the optimality of the monolithic multigrid method with respect to the number of degrees of freedom.

关键词： Monolithic multigrid Magnetohydrodynamic equations Diagonal Braess-Sarazin smoother Finite element method

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A Survey Analysis on Dental Caries Detection from RVG Images Using Deep Learning 1

引用

8th International Conference on Emerging Research in computing, Information, Communication and Applications, ERCICA 2023

作者： Nageswari, P. Pareek, Piyush Kumar Suresh Kumar, A. Aditya, Pai H. Guru Prasad, M.S. Kandasamy, Manivel Department of Mathematics Mahendra Institute of Technology Tamil Nadu Namakkal637503 India Computer Science and Engineering NITTE Meenakshi Institute of Technology Bangalore560064 India Karnataka Bengaluru562112 India Unitedworld School of Computational Intelligence Karnavati University Gujarat Gandhinagar382422 India

ISBN: (数字)9789819976331

ISBN: (纸本)9789819976324

A rapid developing area of study in the healthcare industry is medical imaging. Medical imaging is crucial for the early identification, diagnosis, and treatment of disorders. Ultrasound, magnetic resonance, computed tomography, X-rays, and other imaging techniques fall under this category. Dental caries is one of the most common conditions affecting people of all ages globally. Using radiovisiography (RVG) or dental X-ray images, it could be challenging to spot dental caries in its early stages. Practically, all medical fields use deep learning to predict or identify certain diseases. This research work has proposed and investigated a customized convolution neural network (CCNN) for caries detection from dental X-ray images. Few datasets are available for dental image processing. A total of 1300 X-ray images, 500 intra-oral photographic images, and 150 OPG images were collected from two medical practitioners with ground truth and used as a dataset for dental disease detection and image segmentation. This research work has demonstrated that image enhancement techniques play an important role in improving the quality of dental radiograph images. This research work explores different image augmentation techniques, which contribute to increasing the size of the dataset and improving accuracy. Image segmentation plays an important role in further classification and dental disease detection. Various deep learning models, including AlexNet, EfficientNetB0 and B7, Inception3, VGG-16, and the proposed CCNN model, are used to train the dataset. With more accuracy, a comparison between the deep learning model and the suggested CCNN model has been conducted. © 2024, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

关键词： Image enhancement

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Applying Graph Neural Networks to ERP Systems with a Focus on Business Centric Development 1

Applying Graph Neural Networks to ERP Systems with a Focus o...

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1st International Conference on Software, Systems and Information Technology, SSITCON 2024

作者： Umanesan, R. Harshavardhana, C.N. Somashekar, P. Siva Kota Reddy, P. Dhiliphan Kumar, M. Singh, Ramanjeet Vel Tech Rangarajan Dr. Sagunthala R&d Institute of Science and Technology School of Computing Department of Computer Science and Engineering Chennai India Government First Grade College for Women Department of Mathematics Holenarasipura India Department of Mathematics Mysuru India Jss Science and Technology University Department of Mathematics Mysuru India Department of Management Studies Madurai India Chandigarh University Gharuan Mohali India

ISBN: (纸本)9798350352931

Software for enterprise resource planning (ERP) has grown in popularity as a means to streamline corporate processes that are critical for survival in the modern, globalized marketplace. In order to cater to the specific needs of their global customer base in terms of both price and availability, suppliers in the textile industry are under increasing pressure to enhance their manufacturing management practices. This task is becoming more dependent on the careful selection and usage of information technology. Preprocessing, feature extraction, and training are the three phases that make up this method. Time difference relevance and K-L distance are components of preprocessing. The feature selection approach employs Kernel Principal Component Analysis for the factor extraction phase. An GNN was used for the model's training. The proposed technique outperforms CNN and SVM with an average accuracy of 9 2. 1 6percent. © 2024 IEEE.

关键词： Textile industry

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