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

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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Publisher's Note: “Reacting and non-reacting, three-dimensional shear layers with spanwise stretching” [Phys. Fluids 34, 123602 (2022)]

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Physics of Fluids 2023年第1期35卷

作者： Jonathan L. Palafoutas William A. Sirignano 1Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA 2Department of Mechanical and Aerospace Engineering University of California Irvine Irvine California 92697 USA

This article was published online on 2 December 2022 with errors throughout the paper. All the derivative terms had the wrong denominator; the denominators were

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On a Dynamic Variant of the Iteratively Regularized Gauss-Newton Method with Sequential Data

arXiv

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arXiv 2022年

作者： Chada, Neil K. Iglesias, Marco A. Lu, Shuai Werner, Frank Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal23955 Saudi Arabia School of Mathematical Sciences University of Nottingham NottinghamNG72RD United Kingdom School of Mathematical Sciences Fudan University Shanghai200433 China Institut für Mathematik University of Wuerzburg Emil–Fischer–Str. 30 Würzburg97074 Germany

For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed inverse problems can only be used with a single instance of the observed data, in this work we propose a new framework that enables existing algorithms to invert multiple instances of data in a sequential fashion. Specifically we will work with the well-known iteratively regularized Gauss–Newton method (IRGNM), a variational methodology for solving nonlinear inverse problems. We develop a theory of convergence analysis for a proposed dynamic IRGNM algorithm in the presence of Gaussian white noise. We combine this algorithm with the classical IRGNM to deliver a practical (hybrid) algorithm that can invert data sequentially while producing fast estimates. Our work includes the proof of well-definedness of the proposed iterative scheme, as well as various error bounds that rely on standard assumptions for nonlinear inverse problems. We use several numerical experiments to verify our theoretical findings, and to highlight the benefits of incorporating sequential data. The context of the numerical experiments comprises various parameter identification problems including a Darcy flow PDE, and that of electrical impedance tomography. © 2022, CC BY-NC-SA.

关键词： Inverse problems

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Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability

arXiv

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arXiv 2021年

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

Time-dependent interphase diffusion processes in multiphase heterogeneous media arise ubiquitously in physics, chemistry and biology. Examples of heterogeneous media include composites, geological media, gels, foams and cell aggregates. The recently developed concept of spreadability, S(t), provides a direct link between time-dependent diffusive transport and the microstructure of two-phase media across length scales [Torquato, S., Phys. Rev. E., 104 054102 (2021)]. To investigate the capability of S(t) to probe microstructures of real heterogeneous media, we explicitly compute S(t) for well-known two-dimensional and three-dimensional idealized model structures that span across nonhyperuniform and hyperuniform classes. Among the former class, we study fully penetrable spheres and equilibrium hard spheres, and in the latter class, we examine sphere packings derived from "perfect glasses", uniformly randomized lattices (URL), disordered stealthy hyperuniform point processes and Bravais lattices. Hyperuniform media are characterized by an anomalous suppression of volume fraction fluctuations at large length scales compared to that of any nonhyperuniform medium. We further confirm that the small-, intermediate- and long-time behaviors of S(t) sensitively capture the small-, intermediate- and large-scale characteristics of the models. In instances in which the spectral density (Equation presented)V (k) has a power-law form B|k|α in the limit |k| → 0, the long-time spreadability provides a simple means to extract the value of the coefficients α and B that is robust against noise in (Equation presented)V (k) at small wavenumbers. For typical nonhyperuniform media, the intermediate-time spreadability is slower for models with larger values of the coefficient B = (Equation presented)V (0). Interestingly, the excess spreadability S(∞) - S(t) for URL packings has nearly exponential decay at small to intermediate t, but transforms to a power-law decay at large t, and the time f

关键词： Diffusion

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Artificial neural network approach to large-eddy simulation of compressible isotropic turbulence

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Physical Review E 2019年第5期99卷 053113-053113页

作者： Chenyue Xie Jianchun Wang Ke Li Chao Ma The Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

A subgrid-scale (SGS) model for large-eddy simulation (LES) of compressible isotropic turbulence is constructed by using a data-driven framework. An artificial neural network (ANN) based on local stencil geometry is employed to predict the unclosed SGS terms. The input features are based on the first-order and second-order derivatives of filtered velocity and temperature which appear in the second-order Taylor approximation of the SGS stress and heat flux. It is shown that the proposed ANN-7 model performs better than the gradient model in the a priori test. The correlation coefficient is larger and the relative error is smaller for ANN-7 model as compared to those of the gradient model in the a priori test. In an a posteriori analysis, the performance of ANN-7 model shows advantage over the dynamic Smagorinsky model and dynamic mixed model in the prediction of spectra and structure functions of velocity and temperature, and instantaneous flow structures. Artificial neural network is a promising tool for understanding the physical fundamentals of SGS unclosed terms with further improvement.

关键词： Compressible flows Turbulence

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ON THE STABILITY OF POSITIVE SEMIGROUPS

arXiv

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arXiv 2021年

作者： Del Moral, Pierre Horton, Emma Jasra, Ajay Centre de Recherche Inria Bordeaux Sud-Ouest Talence 33405 France Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science & Technology Building 1 Thuwal23955-6900 Saudi Arabia

The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V -norm contraction methods, associated to functionally weighted Banach spaces for Markov semigroups, to positive semigroups. This methodology is applied to a general class of positive and possibly time-inhomogeneous bounded integral semigroups and their normalised versions. The spectral theorems that we develop are an extension of Perron-Frobenius and Krein-Rutman theorems for positive operators to a class of time-varying positive semigroups. In the context of time-homogeneous models, the regularity conditions discussed in the present article appear to be necessary and sufficient condition for the existence of leading eigenvalues. We review and illustrate the impact of these results in the context of positive semigroups arising in transport theory, physics, mathematical biology and signal processing. Copyright © 2021, The Authors. All rights reserved.

关键词： Banach spaces

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On the Parameter Combinations that Matter and on Those that do Not

arXiv

引用

arXiv 2021年

作者： Evangelou, Nikolaos Wichrowski, Noah J. Kevrekidis, George A. Dietrich, Felix Kooshkbaghi, Mahdi McFann, Sarah Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Johns Hopkins University United States Department of Applied Mathematics and Statistics Johns Hopkins University United States Department of Mathematics and Statistics University of Massachusetts Amherst United States Department of Informatics Technical University of Munich Germany The Program in Applied and Computational Mathematics Princeton University United States Department of Chemical and Biological Engineering Princeton University United States Lewis-Sigler Institute for Integrative Genomics Princeton University United States

We present a data-driven approach to characterizing nonidentifiability of a model’s parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal combinations of parameters required to characterize the output behavior of a chemical system: a set of effective parameters for the model. Furthermore, we introduce and use a Conformal Autoencoder Neural Network technique, as well as a kernel-based Jointly Smooth Function technique, to disentangle the redundant parameter combinations that do not affect the output behavior from the ones that do. We discuss the interpretability of our data-driven effective parameters, and demonstrate the utility of the approach both for behavior prediction and parameter estimation. In the latter task, it becomes important to describe level sets in parameter space that are consistent with a particular output behavior. We validate our approach on a model of multisite phosphorylation, where a reduced set of effective parameters (nonlinear combinations of the physical ones) has previously been established *** Codes 37E99 (Primary), 68T07 (Secondary) Copyright © 2021, The Authors. All rights reserved.

关键词： Parameter estimation

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DP Compress: a Model Compression Scheme for Generating Efficient Deep Potential Models

arXiv

引用

arXiv 2021年

作者： Lu, Denghui Jiang, Wanrun Chen, Yixiao Zhang, Linfeng Jia, Weile Wang, Han Chen, Mohan HEDPS CAPT College of Engineering Peking University Beijing100871 China Songshan Lake Materials Laboratory Guangdong Dongguan523808 China Institute of Physics Chinese Academy of Sciences Beijing100190 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Beijing Institute of Big Data Research Beijing100871 China Institute of Computing Technology Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning based PES model. This scheme, we call DP Compress, is an efficient post-processing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster, and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, H2O, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online. Copyright © 2021, The Authors. All rights reserved.

关键词： Molecular dynamics

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Analysis of Multilevel Replicator Dynamics for General Two-Strategy Social Dilemmas

arXiv

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arXiv 2019年

作者： Cooney, Daniel B. Program in Applied and Computational Mathematics Princeton University

Here we consider a game-theoretic model of multilevel selection in which individuals compete based on their payoff and groups also compete based on the average payoff of group members. Our focus is on multilevel social dilemmas: games in which individuals are best off cheating, while groups of individuals do best when composed of many cooperators. We analyze the dynamics of the two-level replicator dynamics, a nonlocal hyperbolic PDE describing deterministic birth-death dynamics for both individuals and groups. While past work on such multilevel dynamics has restricted attention to scenarios with exactly solvable within-group dynamics, we use comparison principles and an invariant property of the tail of the population distribution to extend our analysis to all possible two-player, two-strategy social dilemmas. In the Stag-Hunt and similar games with coordination thresholds, we show that any amount of between-group competition allows for fixation of cooperation in the population. For the Prisoners’ Dilemma and Hawk-Dove game, we characterize the threshold level of between-group selection dividing a regime in which the population converges to a delta function at the equilibrium of the within-group dynamics from a regime in which between-group competition facilitates the existence of steady-state densities supporting greater levels of cooperation. In particular, we see that the threshold selection strength and average payoff at steady state depend on a tug-of-war between the individual-level incentive to be a defector in a many-cooperator group and the group-level incentive to have many cooperators over many defectors. We also find that lower-level selection casts a long shadow: if groups are best off with a mix of cooperators and defectors, then there will always be fewer cooperators than optimal at steady state, even in the limit of infinitely strong competition between groups. Copyright © 2019, The Authors. All rights reserved.

关键词： Dynamics

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Towards a mathematical understanding of neural network-based machine learning: What we know and what we don't

arXiv

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arXiv 2020年

作者： Weinan, E. Ma, Chao Wojtowytsch, Stephan Wu, Lei Department of Mathematics Princeton University United States Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Stanford University United States Beijing Institute of Big Data Research China

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