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arXiv 2019年

作者： Ko, Hsin-Yu Zhang, Linfeng Santra, Biswajit Wang, Han Weinan, E. DiStasio, Robert A. Cara, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States 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 Princeton University PrincetonNJ08544 United States Department of Chemistry and Chemical Biology Cornell University IthacaNY14853 United States Department of Physics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States

A comprehensive microscopic understanding of ambient liquid water is a major challenge for ab initio simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for ab initio approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile ab initio based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model - a neural-network representation of the ab initio PES - in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H2O and D2O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects. Copyright © 2019, The Authors. All rights reserved.

关键词： Deep neural networks

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Steerable ePCA: Rotationally Invariant Exponential Family PCA

arXiv

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arXiv 2018年

作者： Zhao, Zhizhen Liu, Lydia T. Singer, Amit Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign UrbanaIL61820 United States Department of Electrical Engineering and Computer Sciences University of California at Berkeley BerkeleyCA94720 United States Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

—In photon-limited imaging, the pixel intensities are affected by photon count noise. Many applications, such as 3-D reconstruction using correlation analysis in X-ray free electron laser (XFEL) single molecule imaging, require an accurate estimation of the covariance of the underlying 2-D clean images. Accurate estimation of the covariance from low-photon count images must take into account that pixel intensities are Poisson distributed, hence the classical sample covariance estimator is sub-optimal. Moreover, in single molecule imaging, including in-plane rotated copies of all images could further improve the accuracy of covariance estimation. In this paper we introduce an efficient and accurate algorithm for covariance matrix estimation of count noise 2-D images, including their uniform planar rotations and possibly reflections. Our procedure, steerable ePCA, combines in a novel way two recently introduced innovations. The first is a methodology for principal component analysis (PCA) for Poisson distributions, and more generally, exponential family distributions, called ePCA. The second is steerable PCA, a fast and accurate procedure for including all planar rotations for PCA. The resulting principal components are invariant to the rotation and reflection of the input images. We demonstrate the efficiency and accuracy of steerable ePCA in numerical experiments involving simulated XFEL datasets and rotated Yale B face data. Copyright © 2018, The Authors. All rights reserved.

关键词： Principal component analysis

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Continuum model of irradiation-induced spinodal decomposition in the presence of dislocations

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Physical Review B 2011年第17期83卷 174106-174106页

作者： J. J. Hoyt M. Haataja Department of Materials Science and Engineering McMaster University Hamilton Ontario Canada L8S4L7 Department of Mechanical and Aerospace Engineering Princeton Institute for the Science and Technology of Materials (PRISM) Program in Applied and Computational Mathematics (PACM) Princeton University Princeton New Jersey 08544

A model of phase-separation kinetics in systems exposed to energetic particle irradiation has been extended to include the effects of mobile dislocations. It is shown that when dislocations are allowed to participate in the decomposition reaction, phase separation can occur at temperatures above the coherent spinodal, which is in agreement with several experiments on irradiated alloys. A linear stability analysis of the governing kinetic equations is performed and three regimes of microstructural evolution are identified within the parameter space of damage cascade size vs incident flux: complete phase separation, solid-solution behavior, and compositional patterning. In addition, numerical simulations of the evolving dislocation density and composition fields are performed. The numerical results provide the amplitude and wavelength of the stable patterns that can form under irradiation and elucidate the role of misfit dislocations in reducing the coherency strain due to atomic size mismatch.

关键词： PHASE transformations (Physics) THERMODYNAMICS PARTICLES (Nuclear physics) ALLOYS IRRADIATION STRAINS & stresses (Mechanics)

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Unbiased Approximations for Stationary Distributions of McKean-Vlasov SDEs

arXiv

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arXiv 2024年

作者： Awadelkarim, Elsiddig Chada, Neil K. Jasra, Ajay 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 Department of Mathematics City University of Hong Kong Hong Kong School of Data Science The Chinese University of Hong Kong Shenzhen Shenzhen China

We consider the development of unbiased estimators, to approximate the stationary distribution of Mckean-Vlasov stochastic differential equations (MVSDEs). These are an important class of processes, which frequently appear in applications such as mathematical finance, biology and opinion dynamics. Typically the stationary distribution is unknown and indeed one cannot simulate such processes exactly. As a result one commonly requires a time-discretization scheme which results in a discretization bias and a bias from not being able to simulate the associated stationary distribution. To overcome this bias, we present a new unbiased estimator taking motivation from the literature on unbiased Monte Carlo. We prove the unbiasedness of our estimator, under assumptions. In order to prove this we require developing ergodicity results of various discrete time processes, through an appropriate discretization scheme, towards the invariant measure. Numerous numerical experiments are provided, on a range of MVSDEs, to demonstrate the effectiveness of our unbiased estimator. Such examples include the Currie-Weiss model, a 3D neuroscience model and a parameter estimation problem. © 2024, CC BY-NC-SA.

关键词： Stochastic systems

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Tetratic order in the phase behavior of a hard-rectangle system

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Physical Review B 2006年第5期73卷 054109-054109页

作者： Aleksandar Donev Joshua Burton Frank H. Stillinger Salvatore Torquato Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA PRISM Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA

Previous Monte Carlo investigations by Wojciechowski et al. have found two unusual phases in two-dimensional systems of anisotropic hard particles: a tetratic phase of fourfold symmetry for hard squares [Comput. Methods Sci. Tech. 10, 235 (2004)], and a nonperiodic degenerate solid phase for hard-disk dimers [Phys. Rev. Lett. 66, 3168 (1991)]. In this work, we study a system of hard rectangles of aspect ratio two, i.e., hard-square dimers (or dominos), and demonstrate that it exhibits phases with both of these unusual properties. The liquid shows quasi-long-range tetratic order, with no nematic order. The solid phase we observe is a nonperiodic tetratic phase having the structure of a random tiling of the square lattice with dominos with the well-known degeneracy entropy 1.79kB per particle. Our simulations do not conclusively establish the thermodynamic stability of this orientationally disordered solid; however, there are strong indications that this phase is glassy. Our observations are consistent with a two-stage phase transition scenario developed by Kosterlitz and co-workers with two continuous phase transitions, the first from isotropic to tetratic liquid, and the second from tetratic liquid to solid. We obtain similar results with both a classical Monte Carlo method using true rectangles and a novel molecular dynamics algorithm employing rectangles with rounded corners.

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Reliability and efficiency of DWR-type a posteriori error estimates with smart sensitivity weight recovering

arXiv

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arXiv 2020年

作者： Endtmayer, B. Langer, U. Wick, T. Doctoral Program on Computational Mathematics Johannes Kepler University Altenbergerstr. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstr. 69 LinzA-4040 Austria Leibniz Universität Hannover Institut für Angewandte Mathematik AG Wissenschaftliches Rechnen Welfengarten 1 Hannover30167 Germany Leibniz Universität Hannover Germany

We derive efficient and reliable goal-oriented error estimations, and devise adaptive mesh procedures for the finite element method that are based on the localization of a posteriori estimates. In our previous work [SIAM J. Sci. Comput., 42(1), A371–A394, 2020], we showed efficiency and reliability for error estimators based on enriched finite element spaces. However, the solution of problems on a enriched finite element space is expensive. In the literature, it is well known that one can use some higher-order interpolation to overcome this bottleneck. Using a saturation assumption, we extend the proofs of efficiency and reliability to such higher-order interpolations. The results can be used to create a new family of algorithms, where one of them is tested on three numerical examples (Poisson problem, p-Laplace equation, Navier-Stokes benschmark), and is compared to our previous algorithm. Copyright © 2020, The Authors. All rights reserved.

关键词： Interpolation

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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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An Improved Unbiased Particle Filter

arXiv

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arXiv 2023年

作者： Jasra, Ajay Maama, Mohamed Ombao, Hernando 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 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. We assume that, for numerical reasons, one has to time-discretize the diffusion process which typically leads to filtering that is subject to discretization bias. The approach in [16] establishes that when only having access to the time discretized diffusion it is possible to remove the discretization bias with an estimator of finite variance. We improve on the method in [16] by introducing a modified estimator based on the recent work of [17]. We show that this new estimator is unbiased and has finite variance. Moreover, we conjecture and verify in numerical simulations that substantial gains are obtained. That is, for a given mean square error (MSE) and a particular class of multi-dimensional diffusion, the cost to achieve the said MSE falls. Copyright © 2023, The Authors. All rights reserved.

关键词： Mean square error

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High temperature structure detection in ferromagnets

arXiv

引用

arXiv 2018年

作者： Cao, Yuan Neykov, Matey Liu, Han Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Statistics & Data Science Carnegie Mellon University PittsburghPA United States Department of Electrical Engineering and Computer Science Northwestern University EvanstonIL United States

This paper studies structure detection problems in high temperature ferromagnetic (positive interaction only) Ising models. The goal is to distinguish whether the underlying graph is empty, i.e., the model consists of independent Rademacher variables, versus the alternative that the underlying graph contains a subgraph of a certain structure. We give matching upper and lower minimax bounds under which testing this problem is possible/impossible respectively. Our results reveal that a key quantity called graph arboricity drives the testability of the problem. On the computational front, under a conjecture of the computational hardness of sparse principal component analysis, we prove that, unless the signal is strong enough, there are no polynomial time linear tests on the sample covariance matrix which are capable of testing this problem. Copyright © 2018, The Authors. All rights reserved.

关键词： Ferromagnetism

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Anatomically adapted wavelets for integrated statistical analysis of fMRI data

Anatomically adapted wavelets for integrated statistical ana...

引用

IEEE International Symposium on Biomedical Imaging

作者： S. Görkem Özkaya Dimitri Van De Ville Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Medical Image Processing Laboratory Universita de Genève Geneve Switzerland Medical Image Processing Laboratory Ecole Polytechnique Fédérale de Lausanne Lausanne Switzerland

Wavelets have been successfully used in statistical analysis of fMRI data as a spatial transform providing a compact representation of brain activation maps. However, conventional (tensor-product) wavelet transforms assume a rectangular domain, while the essential brain activity takes place in the convoluted gray-matter layer. We use the lifting scheme to design wavelet bases for more arbitrary domains which do not have a group structure. In particular, we have considered the grey-matter cortical layer as the domain. We then applied the new transform to fMRI data using the wavelet-based SPM (WSPM) framework. Preliminary results show that the adapted wavelets have superior performance in terms of sensitivity than the standard tensor-product wavelets, while having the same control over type-I error rate (specificity).

关键词： Wavelet transforms Wavelet domain Wavelet analysis Statistical analysis Sensitivity Vectors

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