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Deep potentials for materials science

Materials Futures 2022年第2期1卷 89-115页

作者： Tongqi Wen Linfeng Zhang Han Wang Weinan E David J Srolovitz Department of Mechanical Engineering The University of Hong KongHong KongHong Kong Special Administrative Region of China DP Technology BeijingPeople’s Republic of China AI for Science Institute BeijingPeople’s Republic of China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijingPeople’s Republic of China HEDPS CAPTCollege of EngineeringPeking UniversityBeijingPeople’s Republic of China School of Mathematical Sciences Peking UniversityBeijingPeople’s Republic of China Department of Mathematics and Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJUnited States of America International Digital Economy Academy(IDEA) ShenzhenPeople’s Republic of China

To fill the gap between accurate(and expensive)ab initio calculations and efficient atomistic simulations based on empirical interatomic potentials,a new class of descriptions of atomic interactions has emerged and been widely applied;*** learning potentials(MLPs).One recently developed type of MLP is the deep potential(DP)*** this review,we provide an introduction to DP methods in computational materials *** theory underlying the DP method is presented along with a step-by-step introduction to their development and *** also review materials applications of DPs in a wide range of materials *** DP Library provides a platform for the development of DPs and a database of extant *** discuss the accuracy and efficiency of DPs compared with ab initio methods and empirical potentials.

关键词： deep potential atomistic simulation machine learning potential neural network

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Harvesting random embedding for high-frequency change-point detection in temporal complex systems

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National Science Review 2022年第4期9卷 92-104页

作者： Jia-Wen Hou Huan-Fei Ma Dake He Jie Sun Qing Nie Wei Lin Research Institute of Intelligent Complex Systems Fudan University Centre for Computational Systems Biology Institute of Science and Technology for Brain-Inspired IntelligenceFudan University School of Mathematical Sciences Soochow University Xinhua Hospital Affiliated to Shanghai Jiao Tong University School of Medicine School of Mathematical Sciences and Shanghai Center for Mathematical Sciences Fudan University Department of Mathematics Department of Developmental and Cell Biologyand NSF-Simons Center for Multiscale Cell Fate ResearchUniversity of California Shanghai Key Laboratory for Contemporary Applied Mathematics LNMS (Fudan University)and LCNBI (Fudan University) State Key Laboratory of Medical Neurobiology and MOE Frontiers Center for Brain ScienceInstitutes of Brain ScienceFudan University

Recent investigations have revealed that dynamics of complex networks and systems are crucially dependent on the temporal structures. Accurate detection of the time instant at which a system changes its internal structures has become a tremendously significant mission, beneficial to fully understanding the underlying mechanisms of evolving systems, and adequately modeling and predicting the dynamics of the systems as well. In real-world applications, due to a lack of prior knowledge on the explicit equations of evolving systems, an open challenge is how to develop a practical and model-free method to achieve the mission based merely on the time-series data recorded from real-world systems. Here, we develop such a model-free approach, named temporal change-point detection(TCD), and integrate both dynamical and statistical methods to address this important challenge in a novel way. The proposed TCD approach, basing on exploitation of spatial information of the observed time series of high dimensions, is able not only to detect the separate change points of the concerned systems without knowing, a priori, any information of the equations of the systems, but also to harvest all the change points emergent in a relatively high-frequency manner, which cannot be directly achieved by using the existing methods and *** effectiveness is comprehensively demonstrated using the data from the representative complex dynamics and real-world systems from biology to geology and even to social science.

关键词： temporal systems time series change-point detection complex dynamical systems

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DNA cyclic codes over the ring F2[u, v]/ （u^2 - 1, v^3 - v, uv - vu）

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International Journal of Biomathematics 2018年第3期11卷 247-265页

作者： Hai Q. Dinh Abhay Kumar Singh Sukhamoy Pattanayak Songsak Sriboonchitta Division of Computational Mathematics and Engineering Institute for Computational Science Ton Duc Thang University Ho Chi Minh City Vietnam Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Vietnam Department of Mathematical Sciences Kent State University 4314 Mahoning Avenue Warren Ohio 44483 USA Department of Applied Mathematics Indian Institute of Technology (ISM) Dhanbad 826004 India Faculty of Economics Chiang Mai University Chiang Mai 52000 Thailand

In this paper, our main objective is to find out the necessary and sufficient conditions for a cyclic code of arbitrary length over the ring of four elements R1 = F2 ＋ u2 （u^2 = 1） to be a reversible cyclic code. We also obtain the structure of cyclic DNA codes of odd length over the ring R = F2 [u, v]/（u^2 -1, v^3 -v, uv- vu）, which plays an important role in computational Biology. Furthermore, we establish a direct link between the elements of ring /{ and 64 codons used in the amino acids of living organisms by introducing a Gray map from R to R1. Among others, binary images of cyclic codes over R are also investigated. As applications, some cyclic DNA codes over R using the Gray map are provided.

关键词： Cyclic DNA codes reversible cyclic codes reversible-complement cyclic codes gray map.

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Generalization of Advanced Encryption Standard Based on Field of Any Characteristic

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Computers, Materials & Continua 2022年第12期73卷 6121-6138页

作者： Nabilah Abughazalah Majid Khan Noor Munir Ammar SAlanazi Iqtadar Hussain Department of Mathematical Sciences College of SciencePrincess Nourah Bint Abdulrahman UniversityP.O.Box 84428Riyadh 11671Saudi Arabia Department of Applied Mathematics&Statistics Institute of Space TechnologyIslamabadPakistan King Abdulaziz City for Science and Technology RiyadhSaudi Arabia Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar Statistical Consulting Unit College of Arts and ScienceQatar UniversityDohaQatar

Nowadays most communications are done by utilizing digital transmission *** security of this digital information transmitted through different communication systems is quite *** secrecy of digital data is one of the burning topics of the digitally developed *** exist many traditional algorithms in the literature to provide methods for robust *** most important and recent modern block cipher named the advanced encryption standard(AES)is one of the extensively utilized encryption schemes with binary *** is a succession of four fundamental steps:round key,sub-byte,shift row,and mix *** this work,we will provide an innovative methodology for extending the AES in a Galois fieldwith any characteristic *** four steps in the fundamental process with binary characteristics will be adjusted because of the new *** applying double affine transformations,we have enhanced the number of options in our suggested substitution *** reconstruction of the nonlinear confusion component and encryption structure provides robustness in the generalized *** increase in the keyspace due to the Galois field generalization implies that we have improved additional confusion abilities and broadened the current *** implementation of the proposed structure of AES for image,audio,and video encryption will provide high security for secure communication.

关键词： AES generalized AES binary field ternary function

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From atomistic to systematic coarse-grained models for molecular systems 2

From atomistic to systematic coarse-grained models for molec...

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2nd International Conference on Uncertainty Quantification in computational sciences and Engineering, UNCECOMP 2017

作者： Harmandaris, Vagelis Kalligiannaki, Evangelia Katsoulakis, Markos Plecháč, Petr Department of Mathematics and Applied Mathematics University of Crete Heraklion CreteGR-70013 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Hellas IACM/FORTH Heraklion CreteGR-70013 Greece Applied Mathematics and Computational Science CEMSE King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia Department of Mathematics and Statistics University of Massachusetts at Amherst AmherstMA01003 United States Department of Mathematical Sciences University of Delaware NewarkDE19716 United States

ISBN: (纸本)9786188284449

The development of systematic (rigorous) coarse-grained mesoscopic models for complex molecular systems is an intense research area. Here we first give an overview of methods for obtaining optimal parametrized coarse-grained models, starting from detailed atomistic representation for high dimensional molecular systems. Different methods are described based on (a) structural properties (inverse Boltzmann approaches), (b) forces (force matching), and (c) path-space information (relative entropy). Next, we present a detailed investigation concerning the application of these methods in systems under equilibrium and non-equilibrium conditions. Finally, we present results from the application of these methods to model molecular systems. © 2017 The Authors.

关键词： Coarse-grained modeling

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Deterministic guarantees for Burer–Monteiro factorizations of smooth semidefinite programs

arXiv

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arXiv 2018年

作者： Boumal, Nicolas Voroninski, Vladislav Bandeira, Afonso S. Mathematics Department Program in Applied and Computational Mathematics Princeton University Department of Mathematics Center for Data Science Courant Institute of Mathematical Sciences New York University

We consider semidefinite programs (SDPs) with equality constraints. The variable to be optimized is a positive semidefinite matrix X of size n. Following the Burer–Monteiro approach, we optimize a factor Y of size n× p instead, such that X = YY. This ensures positive semidefiniteness at no cost and can reduce the dimension of the problem if p is small, but results in a non-convex optimization problem with a quadratic cost function and quadratic equality constraints in Y. In this paper, we show that if the set of constraints on Y regularly defines a smooth manifold, then, despite non-convexity, first- and second-order necessary optimality conditions are also sufficient, provided p is large enough. For smaller values of p, we show a similar result holds for almost all (linear) cost functions. Under those conditions, a global optimum Y maps to a global optimum X = YY of the SDP. We deduce old and new consequences for SDP relaxations of the generalized eigenvector problem, the trust-region subproblem and quadratic optimization over several spheres, as well as for the Max-Cut and Orthogonal-Cut SDPs which are common relaxations in stochastic block modeling and synchronization of rotations. Copyright © 2018, The Authors. All rights reserved.

关键词： Stochastic systems

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“Pricing Dynamic Investment Fund Protection,” Hans U. Gerber and Gérard Pafumi, April 2000

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North American Actuarial Journal 2001年第1期5卷 153-157页

作者： Huang, Ya-Chun Shiu, Elias S.W. Program in Applied Mathematical and Computational Sciences University of Iowa Iowa City IA 52242-1419 United States Department of Statistics and Actuarial Science University of Iowa Iowa City IA 52242-1409 362 Schaeffer Hall United States Actuarial Science Department of Applied Mathematics Hong Kong Polytechnic University Hung Hom Hong Kong

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Total variation based denoising methods for speckle noise images

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Involve 2017年第2期10卷 327-344页

作者： Misra, Arundhati Bagchi Lockhart, Ethan Lim, Hyeona Department of Mathematical Sciences Saginaw Valley State University University Center 48710 MI United States Program in Applied Mathematics The University of Arizona Tuscon 85721 AZ United States Department of Mathematics and Statistics Mississippi State University 39762 MS United States

In this paper, we introduce a new algorithm based on total variation for denoising speckle noise images. Total variation was introduced by Rudin, Osher, and Fatemi in 1992 for regularizing images. Chambolle proposed a faster algorithm based on the duality of convex functions for minimizing the total variation, but his algorithm was built for Gaussian noise removal. Unlike Gaussian noise, which is additive, speckle noise is multiplicative. We modify the original Chambolle algorithm for speckle noise images using the first noise equation for speckle denoising, proposed by Krissian, Kikinis, Westin and Vosburgh in 2005. We apply the Chambolle algorithm to the Krissian et al. speckle denoising model to develop a faster algorithm for speckle noise images. © 2017 mathematical sciences Publishers.

关键词： anisotropic diffusion Chambolle algorithm denoising fast speckle denoising speckle noise total variation (TV) model

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Depth Separation in Norm-Bounded Infinite-Width Neural Networks 37

Depth Separation in Norm-Bounded Infinite-Width Neural Netwo...

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37th Annual Conference on Learning Theory, COLT 2024

作者： Parkinson, Suzanna Ongie, Greg Willett, Rebecca Shamir, Ohad Srebro, Nathan Committee on Computational and Applied Mathematics University of Chicago United States Department of Mathematical and Statistical Sciences Marquette University United States Department of Statistics Department of Computer Science University of Chicago United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Israel Toyota Technological Institute Chicago United States

We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared 2-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results focused on separation in terms of width, such results do not give insight into whether depth determines if it is possible to learn a network that generalizes well even when the network width is unbounded. Here, we study separation in terms of the sample complexity required for learnability. Specifically, we show that there are functions that are learnable with sample complexity polynomial in the input dimension by norm-controlled depth-3 ReLU networks, yet are not learnable with sub-exponential sample complexity by norm-controlled depth-2 ReLU networks (with any value for the norm). We also show that a similar statement in the reverse direction is not possible: any function learnable with polynomial sample complexity by a norm-controlled depth-2 ReLU network with infinite width is also learnable with polynomial sample complexity by a norm-controlled depth-3 ReLU network. © 2024 S. Parkinson, G. Ongie, R. Willett, O. Shamir & N. Srebro.

关键词： Source separation

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A new note on spectra of optimal and superoptimal preconditioned matrices

A new note on spectra of optimal and superoptimal preconditi...

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2010 International Conference on Computer Application and System Modeling, ICCASM 2010

作者： Zhang, Li-Tao Huang, Ting-Zhu Cheng, Shao-Hua Gu, Tong-Xiang Department of Mathematics and Physics Zhengzhou Institute of Aeronautical Industry Management Henan China School of Mathematical Sciences University of Electronic Science Technology of China Chengdu China Laboratory of Computationary Physics Institute of Applied Physics and Computational Mathematics Beijing China

ISBN: (纸本)9781424472369

Recently, Cheng et al. [Lin. Alg. Appl. 422 (2007): 482-485] proposed the spectral comparison of optimal preconditioner in Chan [SIAM J. Sci. Statist. Com put. 9 (1988): 766-771] and superoptimal preconditioner in Tyrtyshnikov [SIAM J. Matrix Anal. Appl. 13 (1992): 459-473]. In this paper, based on the work of Cheng et al., we further compare the spectra of optimal and superoptimal preconditioned matrices. © 2010 IEEE.

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