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arXiv 2024年

作者： Ruzayqat, Hamza Knio, Omar Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

This paper presents a new data assimilation (DA) scheme based on a sequential Markov Chain Monte Carlo (SMCMC) DA technique [36] which is provably convergent and has been recently used for filtering, particularly for high-dimensional non-linear, and potentially, non-Gaussian state-space models. Unlike particle filters, which can be considered exact methods and can be used for filtering non-linear, non-Gaussian models, SMCMC does not assign weights to the samples/particles, and therefore, the method does not suffer from the issue of weight-degeneracy when a relatively small number of samples is used. We design a localization approach within the SMCMC framework that focuses on regions where observations are located and restricts the transition densities included in the filtering distribution of the state to these regions. This results in immensely reducing the effective degrees of freedom and thus improving the efficiency. We test the new technique on high-dimensional (d ∼ 104 − 105) linear Gaussian model and non-linear shallow water models with Gaussian noise with real and synthetic observations. For two of the numerical examples, the observations mimic the data generated by the Surface Water and Ocean Topography (SWOT) mission led by NASA, which is a swath of ocean height observations that changes location at every assimilation time step. We also use a set of ocean drifters' real observations in which the drifters are moving according the ocean kinematics and assumed to have uncertain locations at the time of assimilation. We show that when higher accuracy is required, the proposed algorithm is superior in terms of efficiency and accuracy over competing ensemble methods and the original SMCMC *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2024, CC BY.

关键词： Markov chains

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LARGE SCALE DYNAMICS OF PRECIPITATION FRONTS IN THE TROPICAL ATMOSPHERE: A NOVEL RELAXATION LIMIT ¤

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Communications in Mathematical sciences 2004年第4期2卷 591-626页

作者： Frierson, Dargan M. W. Majda, Andrew J. Pauluis, Olivier M. Program in Applied and Computational Mathematics Princeton University Fine HallWashington Rd Princeton 08544 NJ United States Department of Mathematics and Center for Atmosphere Ocean Science Courant Institute of Mathematical Sciences New York University 251 Mercer St New York 10012 NY United States Center for Atmosphere Ocean Science Courant Institute of Mathematical Sciences New York University 251 Mercer St. New York 10012 NY United States

A simplified set of equations is derived systematically below for the interaction of large scale flow fields and precipitation in the tropical atmosphere. These equations, the Tropical Climate Model, have the form of a shallow water equation and an equation for moisture coupled through a strongly nonlinear source term. This source term, the precipitation, is of relaxation type in one region of state space for the temperature and moisture, and vanishes identically elsewhere in the state space of these variables. In addition, the equations are coupled nonlinearly to the equations for barotropic incompressible flow. Several mathematical features of this system are developed below including energy principles for solutions and their first derivatives independent of relaxation time. With these estimates, the formal infinitely fast relaxation limit converges to a novel hyperbolic free boundary problem for the motion of precipitation fronts from a large scale dynamical perspective. Elementary exact solutions of the limiting dynamics involving precipitation fronts are developed below and include three families of waves: fast drying fronts as well as slow and fast moistening fronts. The last two families of waves violate Lax's Shock Inequalities;nevertheless, numerical experiments presented below confirm their robust realizability with realistic finite relaxation times. From the viewpoint of tropical atmospheric dynamics, the theory developed here provides a new perspective on the fashion in which the prominent large scale regions of moisture in the tropics associated with deep convection can move and interact with large scale dynamics in the quasi-equilibrium approximation. © 2004 International Press

关键词： Equatorial waves Hyperbolic free boundary problems Hyperbolic pde Moisture Nonlinear relaxation equations Tropical atmospheric dynamics Tropical convection

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Antithetic Multilevel Particle Filters

arXiv

引用

arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando Applied Mathematics and Computational Science Program United States Statistics Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. This is a challenging problem which requires the use of advanced numerical schemes based upon time-discretization of the diffusion process and then the application of particle filters. Perhaps the state-of-the-art method for moderate dimensional problems is the multilevel particle filter of [12]. This is a method that combines multilevel Monte Carlo and particle filters. The approach in that article is based intrinsically upon an Euler discretization method. We develop a new particle filter based upon the antithetic truncated Milstein scheme of [10]. We show that for a class of diffusion problems, for ϵ > 0 given, that the cost to produce a mean square error (MSE) in estimation of the filter, of O(ϵ2) is O(ϵ−2 log(ϵ)2). In the case of multidimensional diffusions with non-constant diffusion coefficient, the method of [12] has a cost of O(ϵ−2.5) to achieve the same MSE. We support our theory with numerical results in several examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

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TWO-SAMPLE TEST OF COMMUNITY MEMBERSHIPS OF WEIGHTED STOCHASTIC BLOCK MODELS

arXiv

引用

arXiv 2018年

作者： Li, Yezheng Li, Hongzhe Program in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States University of Pennsylvania PhiladelphiaPA19104 United States

Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the same. A test statistic based on singular subspace distance is developed. Under the weighted stochastic block models with dense graphs, the limiting distribution of the proposed test statistic is developed. Simulation results show that the test has correct empirical type 1 errors under the dense graphs. The test also behaves as expected in empirical power, showing gradual changes when the intra-block and inter-block distributions are close and achieving 1 when the two distributions are not so close, where the closeness of the two distributions is characterized by Renyi divergence of order 1/2. The Enron email networks are used to demonstrate the proposed *** Codes 62E20, 62F03, 62H15, 91D30, 62F05 Copyright © 2018, The Authors. All rights reserved.

关键词： Clustering algorithms

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Cloaking the underlying long-range order of randomly perturbed lattices

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Physical Review E 2020年第3期101卷 032118-032118页

作者： Michael A. Klatt Jaeuk Kim Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Random, uncorrelated displacements of particles on a lattice preserve the hyperuniformity of the original lattice, that is, normalized density fluctuations vanish in the limit of infinite wavelengths. In addition to a diffuse contribution, the scattering intensity from the the resulting point pattern typically inherits the Bragg peaks (long-range order) of the original lattice. Here we demonstrate how these Bragg peaks can be hidden in the effective diffraction pattern of independent and identically distributed perturbations. All Bragg peaks vanish if and only if the sum of all probability densities of the positions of the shifted lattice points is a constant at all positions. The underlying long-range order is then “cloaked” in the sense that it cannot be reconstructed from the pair correlation function alone. On the one hand, density fluctuations increase monotonically with the strength of perturbations a, as measured by the hyperuniformity order metric Λ¯. On the other hand, the disappearance and reemergence of long-range order, depending on whether the system is cloaked as the perturbation strength increases, is manifestly captured by the τ order metric. Therefore, while the perturbation strength a may seem to be a natural choice for an order metric of perturbed lattices, the τ order metric is a superior choice. It is noteworthy that cloaked perturbed lattices allow one to easily simulate very large samples (with at least 106 particles) of disordered hyperuniform point patterns without Bragg peaks.

关键词： Classical statistical mechanics

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COVID-19 Infected Lung Computed Tomography Segmentation and Supervised Classification Approach

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Computers, Materials & Continua 2021年第7期68卷 391-407页

作者： Aqib Ali Wali Khan Mashwani Samreen Naeem Muhammad Irfan Uddin Wiyada Kumam Poom Kumam Hussam Alrabaiah Farrukh Jamal Christophe Chesneau Department of Computer Science Concordia College BahawalpurBahawalpur63100Pakistan Department of Computer Science&IT Glim Institute of Modern StudiesBahawalpur63100Pakistan Institute of Numerical Sciences Kohat University of Science&TechnologyKohat26000Pakistan Institute of Computing Kohat University of Science and TechnologyKohat26000Pakistan Program in Applied Statistics Department of Mathematics and Computer ScienceFaculty of Science and TechnologyRajamangala University of Technology ThanyaburiThanyaburi12110Thailand Departments of Mathematics Faculty of ScienceCenter of Excellence in Theoretical and Computational Science(TaCS-CoE)&KMUTT Fixed Point Research LaboratoryRoom SCL 802 Fixed Point LaboratoryScience Laboratory BuildingKing Mongkut’s University of Technology Thonburi(KMUTT)Bangkok10140Thailand Department of Medical Research China Medical University HospitalTaichung40402Taiwan College of Engineering Al Ain UniversityAl Ain64141United Arab Emirates Department of Mathematics Tafila Technical UniversityTafila66110Jordan Department of Statistics The Islamia University of BahawalpurBahawalpur63100Pakistan 11Department of MathematicsUniversitéde CaenLMNOCaen14032France

The purpose of this research is the segmentation of lungs computed tomography(CT)scan for the diagnosis of COVID-19 by using machine learning *** dataset contains data from patients who are prone to the *** contains three types of lungs CT images(Normal,Pneumonia,and COVID-19)collected from two different sources;the first one is the Radiology Department of Nishtar Hospital Multan and Civil Hospital Bahawalpur,Pakistan,and the second one is a publicly free available medical imaging database known as *** the preprocessing,a novel fuzzy c-mean automated region-growing segmentation approach is deployed to take an automated region of interest(ROIs)and acquire 52 hybrid statistical features for each ***,12 optimized statistical features are selected via the chi-square feature reduction *** the classification,five machine learning classifiers named as deep learning J4,multilayer perceptron,support vector machine,random forest,and naive Bayes are deployed to optimize the hybrid statistical features *** is observed that the deep learning J4 has promising results(sensitivity and specificity:0.987;accuracy:98.67%)among all the deployed *** a complementary study,a statistical work is devoted to the use of a new statistical model to fit the main datasets of COVID-19 collected in Pakistan.

关键词： COVID-19 machine learning fuzzy c-mean deep learning J4

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Hyper-molecules: On the representation and recovery of dynamical structures, with application to flexible macro-molecular structures in cryo-EM

arXiv

引用

arXiv 2019年

作者： Lederman, Roy R. Andén, Joakim Singer, Amit Department of Statistics and Data Science Yale University New HavenCT United States Center for Computational Mathematics Flatiron Institute New YorkNY United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Cryo-electron microscopy (cryo-EM), the subject of the 2017 Nobel Prize in Chemistry, is a technology for determining the 3-D structure of macromolecules from many noisy 2-D projections of instances of these macromolecules, whose orientations and positions are unknown. The molecular structures are not rigid objects, but flexible objects involved in dynamical processes. The different conformations are exhibited by different instances of the macromolecule observed in a cryo-EM experiment, each of which is recorded as a particle image. The range of conformations and the conformation of each particle are not known a priori;one of the great promises of cryo-EM is to map this conformation space. Remarkable progress has been made in determining rigid structures from homogeneous samples of molecules in spite of the unknown orientation of each particle image and significant progress has been made in recovering a few distinct states from mixtures of rather distinct conformations, but more complex heterogeneous samples remain a major challenge. We introduce the "hyper-molecule" framework for modeling structures across different states of heterogeneous molecules, including continuums of states. The key idea behind this framework is representing heterogeneous macromolecules as high-dimensional objects, with the additional dimensions representing the conformation space. This idea is then refined to model properties such as localized heterogeneity. In addition, we introduce an algorithmic framework for recovering such maps of heterogeneous objects from experimental data using a Bayesian formulation of the problem and Markov chain Monte Carlo (MCMC) algorithms to address the computational challenges in recovering these high dimensional hyper-molecules. We demonstrate these ideas in a prototype applied to synthetic data. Copyright © 2019, The Authors. All rights reserved.

关键词： Medical imaging

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Deep neural network for Wannier function centers

arXiv

引用

arXiv 2019年

作者： Zhang, Linfeng Chen, Mohan Wu, Xifan Wang, Han Weinan, E. Car, Roberto Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States CAPT HEDPS College of Engineering Peking University Beijing100871 China Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

We introduce a deep neural network (DNN) model that assigns the position of the centers of the electronic charge in the snapshots of a molecular dynamics trajectory. The electronic centers are uniquely specified by the unitary transformation that maps the occupied eigenstates onto maximally localized Wannier functions. In combination with deep potential molecular dynamics, a DNN approach to model the atomic potential energy surface at the ab initio density functional level of theory, the scheme makes possible to predict the dielectric properties of insulators for samples and trajectories inaccessible to direct ab initio simulation, without loss of accuracy. As an example, we report calculations of the infrared absorption spectra of light and heavy water at a dispersion inclusive hybrid functional level of theory, finding good agreement with experiment. Extensions to other spectroscopies, like Raman and sum frequency generation, are discussed. Copyright © 2019, The Authors. All rights reserved.

关键词： Quantum chemistry

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Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics

arXiv

引用

arXiv 2017年

作者： Zhang, Linfeng Han, Jiequn Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is "first principle-based" in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecular dynamics

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Structural characterization of many-particle systems on approach to hyperuniform states

arXiv

引用

arXiv 2021年

作者： Torquato, Salvatore Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The study of hyperuniform states of matter is an emerging multidisciplinary field, impinging on topics in the physical sciences, mathematics and biology. The focus of this work is the exploration of quantitative descriptors that herald when a many-particle system in d-dimensional Euclidean space Rd approaches a hyperuniform state as a function of the relevant control parameter. We establish quantitative criteria to ascertain the extent of hyperuniform and nonhyperuniform distance-scaling regimes as well as the crossover point between them in terms of the "volume" coefficient A and "surface-area" coefficient B associated with the local number variance σ2(R) for a spherical window of radius R. The larger the ratio B/A, the larger the hyperuniform scaling regime, which becomes of infinite extent in the limit B/A → ∞. To complement the known direct-space representation of the coefficient B in terms of the total correlation function h(r), we derive its corresponding Fourier representation in terms of the structure factor S(k), which is especially useful when scattering information is available experimentally or theoretically. We also demonstrate that the free-volume theory of the pressure of equilibrium packings of identical hard spheres that approach a strictly jammed state either along the stable crystal or metastable disordered branch dictates that such end states be exactly hyperuniform. Using the ratio B/A, as well as other diagnostic measures of hyperuniformity, including the hyperuniformity index H and the direct-correlation function length scale ξc, we study three different exactly solvable models as a function of the relevant control parameter, either density or temperature, with end states that are perfectly hyperuniform. Specifically, we analyze equilibrium systems of hard rods and "sticky" hard-sphere systems in arbitrary space dimension d as a function of density. We also examine low-temperature excited states of many-particle systems interacting with "steal

关键词： Temperature

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