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Analyzing the dynamics of COVID-19 transmission in select regions of the Philippines: A modeling approach to assess the impact of various tiers of community quarantines

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Heliyon 2024年第21期10卷 e39330页

作者： Mata, May Anne E. Escosio, Rey Audie S. Rosero, El Veena Grace A. Viernes, Jhunas Paul T. Anonuevo, Loreniel E. Hernandez, Bryan S. Addawe, Joel M. Addawe, Rizavel C. Pilar-Arceo, Carlene P.C. Mendoza, Victoria May P. de los Reyes, Aurelio A. Mindanao Center for Disease Watch and Analytics (DiWA) University of the Philippines Mindanao Tugbok District Davao City 8000 Philippines Interdisciplinary Applied Modeling (IAM) Laboratory University of the Philippines Mindanao Tugbok District Davao City 8000 Philippines Department of Mathematics Physics and Computer Science University of the Philippines Mindanao Tugbok District Davao City 8000 Philippines University of the Philippines Resilience Institute University of the Philippines Diliman Quezon City 1101 Philippines Institute of Mathematics University of the Philippines Diliman Quezon City 1101 Philippines Faculdade de Ciências Universidade de Lisboa Lisbon 1749-016 Portugal BioISI—Biosystems & Integrative Sciences Institute Faculdade de Ciências Universidade de Lisboa Lisbon 1749-016 Portugal Department of Mathematics and Computer Science University of the Philippines Baguio Baguio City 2600 Philippines Mapúa Malayan Colleges Mindanao Davao City 8000 Philippines Mathematics Department Caraga State University Ampayon Butuan City 8600 Philippines

The COVID-19 pandemic has significantly impacted communities worldwide, and effective management strategies are critical to reduce transmission rates and minimize the impact of the disease. In this study, we modeled and analyzed the COVID-19 transmission dynamics and derived relevant epidemiological values for three regions of the Philippines, namely, the National Capital Region (NCR), Davao City, and Baguio City, under different community quarantine implementations. The unique features and differences of these regions-of-interest were accounted for in simulating the disease spread and in estimating key epidemiological parameters fitted to the reported COVID-19 cases. Results support the robustness of the model formulated and provides insights into the effect of the government's implemented intervention protocols. With a forecasting feature, this modeling framework is beneficial for science-based decision support, policy making, and assessment for recent and future pandemics wherever regions-of-interest. © 2024 The Author(s)

关键词： Community quarantine Compartmental model Coronavirus Population factor SEIR Time-varying reproduction number

The quenching-activation behavior of the gradient descent dynamics for two-layer neural network models

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arXiv 2020年

作者： Ma, Chao Wu, Lei Weinan, E. Department of Mathematics Princeton University Program in Applied and Computational Mathematics Princeton University Institute of Big Data Research

A numerical and phenomenological study of the gradient descent (GD) algorithm for training two-layer neural network models is carried out for different parameter regimes when the target function can be accurately approximated by a relatively small number of neurons. It is found that for Xavier-like initialization, there are two distinctive phases in the dynamic behavior of GD in the under-parametrized regime: An early phase in which the GD dynamics follows closely that of the corresponding random feature model and the neurons are effectively quenched, followed by a late phase in which the neurons are divided into two groups: a group of a few "activated" neurons that dominate the dynamics and a group of background (or "quenched") neurons that support the continued activation and deactivation process. This neural network-like behavior is continued into the mildly over-parametrized regime, where it undergoes a transition to a random feature-like behavior. The quenching-activation process seems to provide a clear mechanism for "implicit regularization". This is qualitatively different from the dynamics associated with the "mean-field" scaling where all neurons participate equally and there does not appear to be qualitative changes when the network parameters are changed. Copyright © 2020, The Authors. All rights reserved.

关键词： Gradient methods

Evolution of interface singularities in shallow water equations with variable bottom topography

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arXiv 2022年

作者： Camassa, R. D’Onofrio, R. Falqui, G. Ortenzi, Giovanni Pedroni, M. University of North Carolina at Chapel Hill Carolina Center for Interdisciplinary Applied Mathematics Department of Mathematics Chapel HillNC27599 United States Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca Via Roberto Cozzi 55 MilanoI-20125 Italy I-24044 Italy INFN Sezione di Milano-Bicocca Piazza della Scienza 3 Milano20126 Italy

Wave front propagation with non-trivial bottom topography is studied within the formalism of hyperbolic long wave models. Evolution of non-smooth initial data is examined, and in particular the splitting of singular points and their short time behaviour is described. In the opposite limit of longer times, the local analysis of wavefronts is used to estimate the gradient catastrophe formation and how this is influenced by the topography. The limiting cases when the free surface intersects the bottom boundary, belonging to the so-called "physical" and "non-physical" vacuum classes, are examined. Solutions expressed by power series in the spatial variable lead to a hierarchy of ordinary differential equations for the time-dependent series coefficients, which are shown to reveal basic differences between the two vacuum cases: for non-physical vacuums, the equations of the hierarchy are recursive and linear past the first two pairs, while for physical vacuums the hierarchy is non-recursive, fully coupled and nonlinear. The former case may admit solutions that are free of singularities for nonzero time intervals, while the latter is shown to develop non-standard velocity shocks instantaneously. Polynomial bottom topographies simplify the hierarchy, as they contribute only a finite number of inhomogeneous forcing terms to the equations in the recursion relations. However, we show that truncation to finite dimensional systems and polynomial solutions is in general only possible for the case of a quadratic bottom profile. In this case the system’s evolution can reduce to, and is completely described by, a low dimensional dynamical system for the time-dependent coefficients. This system encapsulates all the nonlinear properties of the solution for general power series initial data, and in particular governs the loss of regularity in finite times at the dry point. For the special case of parabolic bottom topographies, an exact, self-similar solution class is introduced and stu

关键词： Wavefronts

Simulating Cardiac Fluid Dynamics in the Human Heart

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arXiv 2023年

作者： Davey, Marshall Puelz, Charles Rossi, Simone Smith, Margaret Anne Wells, David R. Sturgeon, Gregory M. Segars, W. Paul Vavalle, John P. Peskin, Charles S. Griffith, Boyce E. University of North Carolina Chapel HillNC United States Department of Pediatrics-Cardiology Baylor College of Medicine Texas Children’s Hospital HoustonTX United States Department of Mathematics University North Carolina Chapel HillNC United States Department of Radiology Duke University Medical Center DurhamNC United States Division of Cardiology Department of Medicine University of North Carolina School of Medicine Chapel HillNC United States Courant Institute of Mathematical Sciences New York University New YorkNY United States Departments of Mathematics 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 School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

Cardiac fluid dynamics fundamentally involves interactions between complex blood flows and the structural deformations of the muscular heart walls and the thin, flexible valve leaflets. There has been longstanding scientific, engineering, and medical interest in creating mathematical models of the heart that capture, explain, and predict these fluid-structure interactions. However, existing computational models that account for interactions among the blood, the actively contracting myocardium, and the cardiac valves are limited in their abilities to predict valve performance, resolve fine-scale flow features, or use realistic descriptions of tissue biomechanics. Here we introduce and benchmark a comprehensive mathematical model of cardiac fluid dynamics in the human heart. A unique feature of our model is that it incorporates biomechanically detailed descriptions of all major cardiac structures that are calibrated using tensile tests of human tissue specimens to reflect the heart’s microstructure. Further, it is the first fluid-structure interaction model of the heart that provides anatomically and physiologically detailed representations of all four cardiac valves. We demonstrate that this integrative model generates physiologic dynamics, including realistic pressure-volume loops that automatically capture isovolumetric contraction and relaxation, and predicts fine-scale flow features. None of these outputs are prescribed;instead, they emerge from interactions within our comprehensive description of cardiac physiology. Such models can serve as tools for predicting the impacts of medical devices or clinical interventions. They also can serve as platforms for mechanistic studies of cardiac pathophysiology and dysfunction, including congenital defects, cardiomyopathies, and heart failure, that are difficult or impossible to perform in patients. Copyright © 2023, The Authors. All rights reserved.

关键词： Heart

DIFFUSION CURVATURE FOR ESTIMATING LOCAL CURVATURE IN HIGH DIMENSIONAL DATA

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arXiv 2022年

作者： Bhaskar, Dhananjay MacDonald, Kincaid Fasina, Oluwadamilola Thomas, Dawson Rieck, Bastian Adelstein, Ian Krishnaswamy, Smita Department of Genetics Yale School of Medicine New HavenCT United States Department of Mathematics Yale University New HavenCT United States Program for Applied Mathematics Yale University New HavenCT United States Department of Physics Yale University New HavenCT United States Institute of AI for Health Helmholtz Pioneer Campus Munich Germany Department of Computer Science Yale University New HavenCT United States Program for Computational Biology and Bioinformatics Yale University New HavenCT United States

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes. © 2022, CC BY.

关键词： Geometry

Consistent lifting relations for the initialization of total-energy double-distribution-function kinetic models

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Physical Review E 2023年第6期108卷 065301-065301页

作者： Yiming Qi (岐亦铭) Lian-Ping Wang (王连平) Zhaoli Guo (郭照立) Shiyi Chen (陈十一) State Key Laboratory for Turbulence and Complex Systems College of engineering Peking University Beijing 100871 China Guangdong Provincial Key Laboratory of Turbulence Research and Applications Center for Complex Flows and Soft Matter Research and Department of Mechanics and Aerospace Engineering Southern University of Science and Technology Shenzhen Guangdong 518055 China Institute of Interdisciplinary Research for Mathematics and Applied Science Huazhong University of Science and Technology Wuhan Hubei 430074 China Eastern Institute for Advanced Study Eastern Institute of Technology Ningbo Zhejiang 315200 China

A lifting relation connecting the distribution function explicitly with the hydrodynamic variables is necessary for the Boltzmann equation-based mesoscopic approaches in order to correctly initialize a nonuniform hydrodynamic flow. We derive two lifting relations for Guo et al.'s total-energy double-distribution-function (DDF) kinetic model [Z. L. Guo et al., Phys. Rev. E 75, 036704 (2007)], one from the Hermite expansion of the conserved and nonconserved moments, and the second from the O(τ) Chapman-Enskog (CE) approximation of the Maxwellian exponential equilibrium. While both forms are consistent to the compressible Navier-Stokes-Fourier system theoretically, we stress that the latter may introduce numerical oscillations under the recently optimized discrete velocity models [Y. M. Qi et al., Phys. Fluids 34, 116101 (2022)], namely a 27 discrete velocity model of the seventh-order Gauss-Hermite quadrature (GHQ) accuracy (D3V27A7) for the velocity field combined with a 13 discrete velocity model of the fifth-order GHQ accuracy (D3V13A5) for the total energy. It is shown that the Hermite-expansion–based lifting relation can be alternatively derived from the latter approach using the truncated Hermite-polynomial equilibrium. Additionally, a relationship between the order of CE expansions and the truncated order of Hermite equilibria is developed to determine the minimal order of a Hermite equilibria required to recover any multiple-timescale macroscopic system. Next, three-dimensional compressible Taylor-Green vortex flows with different initial conditions and Ma numbers are simulated to demonstrate the effectiveness and potential issues of these lifting relations. The Hermite-expansion–based lifting relation works well in all cases, while the Chapman-Enskog-expansion–based lifting relation may produce numerical oscillations and a theoretical model is developed to predict such oscillations. Furthermore, the corresponding lifting relations for Qi et al.'s total energy

关键词： Three-dimensional turbulence Turbulence simulations Direct numerical simulations Lattice-Boltzmann methods

Normalized solutions for nonlinear Schrödinger systems with special mass-mixed terms: The linear couple case

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arXiv 2021年

作者： Chen, Zhen Zhong, Xuexiu Zou, Wenming Department of Mathematical Sciences Tsinghua University Beijing100084 China South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal University Guangzhou510631 China

In this paper, we prove the existence of positive solutions (λ1, λ2, u, v) ∈ 2 × H1(N, 2) to the following coupled Schrödinger system (Equation presented), satisfying the normalization constraints (Equation presented). The parameters µ1, µ2, β > 0 are prescribed and the masses a, b > 0. Here 2 + 4/N ∗, where 2∗ = 2N/N-2 if N ≥ 3 and 2∗ = +∞ if N = 2. So that the terms µ1|u|p−2u,µ2|v|q−2v are of the so-called mass supercritical, while the linear couple terms βv, βu are of mass subcritical. An essential novelty is that this is the first try to deal with the linear couples in the normalized solution frame with mass mixed terms, which are big nuisances due to the lack of compactness of the embedding H1(N) → L2(N), even working in the radial subspace. For the Sobolev subcritical case, we can obtain the existence of positive ground state solution for any given a, b > 0 and β > 0, provided 2 ⩽ N ⩽ 4. For the Sobolev critical case with N = 3, 4, it can be viewed as a counterpart of the Brezis-Nirenberg critical semilinear elliptic problem for the system case in the context of normalized solutions. Under some suitable assumptions, we obtain the existence or non-existence of positive normalized ground state *** Codes 35J50, 35B08, 35Q55, 35J20 Copyright © 2021, The Authors. All rights reserved.

关键词： Ground state

A new deduce of the strict binding inequality and its application: Ground state normalized solution to Schrödinger equations with potential

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arXiv 2021年

作者： Zhong, Xuexiu Zou, Wenming South China Research Center for Applied Mathematics and Interdisciplinary Studies South China Normal University Guangzhou510631 China Department of Mathematical Sciences Tsinghua University Beijing100084 China

In the present paper, we prove the existence of solutions (λ, u) ∈ R × H1(RN ) to the following elliptic equations with potential −∆u + (V (x) + λ)u = g(u) in RN, satisfying the normalization constraint ∫ N u2 = a > 0, which is deduced by searching for solitary wave solution to the time-dependent nonlinear Schrödinger equations. Besides the importance in the applications, not negligible reasons of our interest for such problems with potential V (x) are their stimulating and challenging mathematical difficulties. We develop an interesting way basing on iteration and give a new proof of the so-called "sub-additive inequality", which can simply the standard process in the traditional sense. Under some very relax assumption on the potential V (x) and some other suitable assumptions on g, we can obtain the existence of ground state solution for prescribed a > *** Codes 35Q55, 35Q51, 35B09, 35C08, 35J20 Copyright © 2021, The Authors. All rights reserved.

关键词： Ground state

Fast principal component analysis for cryo-electron microscopy images

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Biological imaging 2023年 3卷 e2-e2页

作者： Nicholas F Marshall Oscar Mickelin Yunpeng Shi Amit Singer Department of Mathematics Oregon State University Corvallis Oregon 97331 USA. Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA. Department of Mathematics Princeton University Princeton New Jersey 08544 USA.

Principal component analysis (PCA) plays an important role in the analysis of cryo-electron microscopy (cryo-EM) images for various tasks such as classification, denoising, compression, and ab initio modeling. We introduce a fast method for estimating a compressed representation of the 2-D covariance matrix of noisy cryo-EM projection images affected by radial point spread functions that enables fast PCA computation. Our method is based on a new algorithm for expanding images in the Fourier-Bessel basis (the harmonics on the disk), which provides a convenient way to handle the effect of the contrast transfer functions. For images of size × , our method has time complexity ( + ) and space complexity ( + ). In contrast to previous work, these complexities are independent of the number of different contrast transfer functions of the images. We demonstrate our approach on synthetic and experimental data and show acceleration by factors of up to two orders of magnitude.

关键词： Covariance estimation Fourier–Bessel cryo-EM denoising principal component analysis single particle reconstruction