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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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Uniqueness of weak solutions to the primitive equations in some anisotropic spaces

引用

Journal of Differential Equations 2025年 444卷

作者： Tim Binz Yoshiki Iida Program in Applied and Computational Mathematics Princeton University Fine Hall Washington Road Princeton 08544 NJ the United States of America Department of Pure and Applied Mathematics Graduate School of Fundamental Science and Engineering Waseda University Okubo 3-4-1 Shinjuku-ku Tokyo 169-8555 Japan

We consider the both 3D and 2D viscous primitive equations for ocean in the isothermal setting. While strong global well-posedness of the viscous primitive equations for large data in H 1 has already proved, the uniqueness of the weak solutions of Leray–Hope type for given initial data in L 2 remains an outstanding open problem. In this paper, we establish a new conditional uniqueness result for weak solutions to the primitive equations, that is, if a weak solution belongs some scaling invariant function spaces, and satisfies some additional assumptions, then the weak solution is unique. In particular, our result can be obtained as different one from z -weak solutions framework by adopting some anisotropic approaches with the homogeneous toroidal Besov spaces. As an application of the proof, we establish the energy equality for weak solutions in the uniqueness class given in the main theorem.

关键词： 35Q86 35K59 86A05 86A10 35Q35 Primitive equations Conditional uniqueness Anisotropic spaces Besov spaces Scaling invariance

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Unbiased Estimation Using a Class of Diffusion Processes

SSRN

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SSRN 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas 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 Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d ∈ N0. This latter process is constructed such that, starting at X0 = 0, one has X1 ∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 15] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(Ε2), for arbitrary Ε > 0, the associated cost is O(Ε−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(Ε2), the associated cost is, with high probability, O(Ε−2|log(Ε)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse problems. © 2022, The Authors. All rights reserved.

关键词： Diffusion

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Global and local reduced models for interacting, heterogeneous agents

arXiv

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arXiv 2021年

作者： Thiem, Thomas N. Kemeth, Felix P. Bertalan, Tom Laing, Carlo R. Kevrekidis, Ioannis G. Department of Chemical and Biological Engineering Princeton University United States Department of Chemical and Biomolecular Engineering Whiting School of Engineering Johns Hopkins University United States Department of Mechanical Engineering Massachusetts Institute of Technology United States School of Natural and Computational Sciences Massey University New Zealand Department of Applied Mathematics and Statistics Johns Hopkins University United States

Large collections of coupled, heterogeneous agents can manifest complex dynamical behavior presenting difficulties for simulation and analysis. However, if the collective dynamics lie on a low-dimensional manifold then the original agent-based model may be approximated with a simplified surrogate model on and near the low-dimensional space where the dynamics live. Analytically identifying such simplified models can be challenging or impossible, but here we present a data-driven coarse-graining methodology for discovering such reduced models. We consider two types of reduced models: globally-based models which use global information and predict dynamics using information from the whole ensemble, and locally-based models that use local information, that is, information from just a subset of agents close (close in heterogeneity space, not physical space) to an agent, to predict the dynamics of an agent. For both approaches we are able to learn laws governing the behavior of the reduced system on the low-dimensional manifold directly from time series of states from the agent-based system. These laws take the form of either a system of ordinary differential equations (ODEs), for the globally-based approach, or a partial differential equation (PDE) in the locally-based case. For each technique we employ a specialized artificial neural network integrator that has been templated on an Euler time stepper (i.e. a ResNet) to learn the laws of the reduced model. As part of our methodology, we utilize the proper orthogonal decomposition (POD) to identify the low-dimensional space of the dynamics. Our globally-based technique uses the resulting POD basis to define a set of coordinates for the agent states in this space, and then seeks to learn the time evolution of these coordinates as a system of ODEs. For the locally-based technique, we propose a methodology for learning a partial differential equation representation of the agents;the PDE law depends on the state variables and

关键词： Dynamics

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Sensitivity Analysis of Wind Energy Resources with Bayesian non-Gaussian and nonstationary Functional ANOVA

arXiv

引用

arXiv 2021年

作者： Zhang, Jiachen Crippa, Paola Genton, Marc G. Castruccio, Stefano Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Civid and Environmental Engineering and Geoscience University of Notre Dame United States Statistics Program King Abdullah University of Science and Technology Saudi Arabia

The transition from non-renewable to renewable energies represents a global societal challenge, and developing a sustainable energy portfolio is an especially daunting task for developing countries where little to no information is available regarding the abundance of renewable resources such as wind. Weather model simulations are key to obtain such information when observational data are scarce and sparse over a country as large and geographically diverse as Saudi Arabia. However, output from such models is uncertain, as it depends on inputs such as the parametrization of the physical processes and the spatial resolution of the simulated domain. In such situations, a sensitivity analysis must be performed and the input may have a spatially heterogeneous influence of wind. In this work, we propose a latent Gaussian functional analysis of variance (ANOVA) model that relies on a nonstationary Gaussian Markov random field approximation of a continuous latent process. The proposed approach is able to capture the local sensitivity of Gaussian and non-Gaussian wind characteristics such as speed and threshold exceedances over a large simulation domain, and a continuous underlying process also allows us to assess the effect of different spatial resolutions. Our results indicate that (1) the non-local planetary boundary layer scheme and high spatial resolution are both instrumental in capturing wind speed and energy (especially over complex mountainous terrain), and (2) the impact of planetary boundary layer scheme and resolution on Saudi Arabia’s planned wind farms is small (at most 1.4%). Thus, our results lend support for the construction of these wind farms in the next decade. © 2021, CC BY-NC-ND.

关键词： Sensitivity analysis

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Local viscoelastic properties and shear stress propagation in bulk and confined polymer melts and low-molecular weight liquids

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Physical Review Research 2024年第2期6卷 023161-023161页

作者： Alireza F. Behbahani Petra Bačová Patrycja Polińska Craig Burkhart Manolis Doxastakis Vagelis Harmandaris Institut für Physik Johannes Gutenberg-Universität Mainz Staudingerweg 7 D-55099 Mainz Germany Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas Heraklion GR-71110 Greece Departamento de Ciencia de los Materiales e Ingeniería Metalúrgica y Química Inorgánica Facultad de Ciencias IMEYMAT Campus Universitario Río San Pedro s/n. Puerto Real Cádiz 11510 Spain Goodyear S.A. Avenue Gordon Smith Colmar-Berg L-7750 Luxembourg The Goodyear Tire & Rubber Company 142 Goodyear Boulevard Akron Ohio 44305 USA Department of Chemical and Biomolecular Engineering University of Tennessee Knoxville Tennessee 37996 USA Computation-based Science and Technology Research Center The Cyprus Institute Nicosia 2121 Cyprus Department of Mathematics and Applied Mathematics University of Crete Heraklion GR-71110 Greece

Through the analysis of the spatial correlations of local stress, we detect the propagation of long-ranged liquid-elasticity-mediated shear stress waves in polymeric and low-molecular weight liquids. The propagation of shear waves is effectively planar; i.e., σαβ propagates in the αβ plane. The autocorrelation functions of the local stress of a region are affected by both the relaxation of stress in that region and the propagation of stress from the region to the rest of the sample. However, due to the planar propagation of shear waves, the transfer of σαβ from those slices of the simulation box that are periodic in the αβ plane is negligible. This allows direct probing of the position-dependent local stress relaxation modulus of liquid in the vicinity of a confining surface.

关键词： Confinement Non-Newtonian fluids Physisorption Polymer behavior Polymer conformation & topology Rheological properties

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Understanding viscoelastic flow instabilities: Oldroyd-B and beyond

arXiv

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arXiv 2022年

作者： Sánchez, Hugo A. Castillo Jovanović, Mihailo R. Kumar, Satish Morozov, Alexander Shankar, V. Subramanian, Ganesh Wilson, Helen J. Department Of Applied Mathematics And Statistics Institute Of Mathematics And Computational Sciences University Of Sao Paulo Brazil Ming Hsieh Department Of Electrical And Computer Engineering University Of Southern California Los AngelesCA90089 United States Department Of Chemical Engineering And Materials Science University Of Minnesota MinneapolisMN55455 United States SUPA School Of Physics And Astronomy The University Of Edinburgh EdinburghEH9 3FD United Kingdom Department Of Chemical Engineering Indian Institute Of Technology Kanpur208016 India Engineering Mechanics Unit Jawaharlal Nehru Center For Advanced Scientific Research Bangalore560064 India Mathematics Department University College London Gower Street LondonWC1E 6BT United Kingdom

The Oldroyd-B model has been used extensively to predict a host of instabilities in shearing flows of viscoelastic fluids, often realized experimentally using polymer solutions. The present review, written on the occasion of the birth centenary of James Oldroyd, provides an overview of instabilities found across major classes of shearing flows. These comprise (i) the canonical rectilinear shearing flows including plane Couette, plane and pipe Poiseuille flows;(ii) viscometric shearing flows with curved streamlines such as those in the TaylorCouette, cone-and-plate and parallel-plate geometries;(iii) non-viscometric shearing flows with an underlying extensional flow topology such as the flow in a cross-slot device;and (iv) multilayer shearing flows. While the underlying focus in all these cases is on results obtained using the Oldroyd-B model, we also discuss their relation to the actual instability, and as to how the shortcomings of the Oldroyd-B model may be overcome by the use of more realistic constitutive models. All the three commonly used tools of stability analysis, viz., modal linear stability, nonmodal stability, and weakly nonlinear stability analyses are discussed, with supporting evidence from experiments and numerical simulations as appropriate. Despite only accounting for a shear-rate-independent viscosity and first normal stress coefficient, the Oldroyd-B model is able to qualitatively predict the majority of instabilities in the aforementioned shearing flows. The review also highlights, where appropriate, open questions in the area of viscoelastic stability. © 2022, CC BY.

关键词： Stability

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Hyperuniformity of maximally random jammed packings of hyperspheres across spatial dimensions

arXiv

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arXiv 2023年

作者： Maher, Charles Emmett Jiao, Yang Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The maximally random jammed (MRJ) state is the most random (i.e., disordered) configuration of strictly jammed (mechanically rigid) nonoverlapping objects. MRJ packings are hyperuniform, meaning their long-wavelength density fluctuations are anomalously suppressed compared to typical disordered systems, i.e., their structure factors S(k) tend to zero as the wave number |k| tends to zero. Here, we show that generating high-quality strictly jammed states for Euclidean space dimensions d = 3, 4, and 5 is of paramount importance in ensuring hyperuniformity and extracting precise values of the hyperuniformity exponent α > 0 for MRJ states, defined by the power-law behavior of S(k) ∼ |k|α in the limit |k| → 0. Moreover, we show that for fixed d it is more difficult to ensure jamming as the particle number N increases, which results in packings that are nonhyperuniform. Free-volume theory arguments suggest that the ideal MRJ state does not contain rattlers, which act as defects in numerically generated packings. As d increases, we find that the fraction of rattlers decreases substantially. Our analysis of the largest truly jammed packings suggests that the ideal MRJ packings for all dimensions d ≥ 3 are hyperuniform with α = d − 2, implying the packings become more hyperuniform as d increases. The differences in α between MRJ packings and recently proposed Manna-class random close packed (RCP) states, which were reported to have α = 0.25 in d = 3 and be nonhyperuniform (α = 0) for d = 4 and d = 5, demonstrate the vivid distinctions between the large-scale structure of RCP and MRJ states in these dimensions. Our paper clarifies the importance of the link between true jamming and hyperuniformity and motivates the development of an algorithm to produce rattler-free three-dimensional MRJ packings. © 2023, CC BY.

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The Role of Heterogeneity in Autonomous Perimeter Defense Problems

arXiv

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arXiv 2022年

作者： Adler, Aviv Mickelin, Oscar Ramachandran, K. Sukhatme, Gaurav S. Karaman, Sertac Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Computer Science University of Southern California Los AngelesCA90089 United States Department of Aeronautics and Astronautics Massachusetts Institute of Technology CambridgeMA02139 United States

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamic programming

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An immersed peridynamics model of fluid-structure interaction accounting for material damage and failure

arXiv

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arXiv 2022年

作者： Kim, Keon Ho Bhalla, Amneet P.S. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering San Diego State University San DiegoCA United States Departments of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States

This paper develops and benchmarks an immersed peridynamics method to simulate the deformation, damage, and failure of hyperelastic materials within a fluid-structure interaction framework. The immersed peridynamics method describes an incompressible structure immersed in a viscous incompressible fluid. It expresses the momentum equation and incompressibility constraint in Eulerian form, and it describes the structural motion and resultant forces in Lagrangian form. Coupling between Eulerian and Lagrangian variables is achieved by integral transforms with Dirac delta function kernels, as in standard immersed boundary methods. The major difference between our approach and conventional immersed boundary methods is that we use peridynamics, instead of classical continuum mechanics, to determine the structural forces. We focus on non-ordinary state-based peridynamic material descriptions that allow us to use a constitutive correspondence framework that can leverage well-characterized nonlinear constitutive models of soft materials. The convergence and accuracy of our approach are compared to both conventional and immersed finite element methods using widely used benchmark problems of nonlinear incompressible elasticity. We demonstrate that the immersed peridynamics method yields comparable accuracy with similar numbers of structural degrees of freedom for several choices of the size of the peridynamic horizon. We also demonstrate that the method can generate grid-converged simulations of fluid-driven material damage growth, crack formation and propagation, and rupture under large deformations. © 2022, CC BY-SA.

关键词： Continuum mechanics

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