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Evaluating COVID-19 Surveillance Testing Strategies at Colorado School of Mines: A Stochastic Modeling Approach

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arXiv 2024年

作者： Albrecht, Laura Leiderman, Karin Sindi, Suzanne S. Nychka, Douglas Applied Mathematics and Statistics Department Colorado School of Mines GoldenCO United States Mathematics Department University of North Carolina Chapel Hill Chapel HillNC United States UNC Blood Research Center University of North Carolina Chapel Hill Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel Hill Chapel HillNC United States Department of Applied Mathematics University of California Merced MercedCA United States

This study introduces a stochastic model of COVID-19 transmission tailored to the Colorado School of Mines campus and evaluates surveillance testing strategies within a university context. Enhancing the conventional SEIR framework with stochastic transitions, our model accounts for the unique characteristics of disease spread in a residential college, including specific states for testing, quarantine, and isolation. Employing an approximate Bayesian computation (ABC) method for parameter estimation, we navigate the complexities inherent in stochastic models, enabling an accurate fit of the model with the campus case data. We then studied our model under the estimated parameters to evaluate the efficacy of different testing policies that could be implemented on a university campus. This framework not only advances understanding of COVID-19 dynamics on the Mines campus but serves as a blueprint for comparable settings, providing insights for informed strategies against infectious diseases. © 2024, CC BY.

关键词： COVID-19

Unbiased Parameter Estimation for Partially Observed Diffusions

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arXiv 2023年

作者： Awadelkarim, Elsiddig Jasra, Ajay Ruzayqat, Hamza 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

In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting log-likelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically out-perform existing unbiased *** Codes 60J22, 62M05, 65C40, 62M20 © 2023, CC BY.

关键词： Parameter estimation

Existence and Stability of Nonequilibrium Steady States of Nernst-Planck-Navier-Stokes Systems

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arXiv 2022年

作者： Constantin, Peter Ignatova, Mihaela Lee, Fizay-Noah Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Temple University PhiladelphiaPA19122 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

MSC Codes 35Q30, 35Q35, 35Q92We consider the Nernst-Planck-Navier-Stokes system in a bounded domain of Rd, d = 2, 3 with general nonequilibrium Dirichlet boundary conditions for the ionic concentrations. We prove the existence of smooth steady state solutions and present a sufficient condition in terms of only the boundary data that guarantees that these solutions have nonzero fluid velocity. We show that time evolving solutions are ultimately bounded uniformly, independently of their initial size. In addition, we consider one dimensional steady states with steady nonzero currents and show that they are globally nonlinearly stable as solutions in a three dimensional periodic strip, if the currents are sufficiently weak. © 2022, CC BY.

关键词： Navier Stokes equations

Robust and conservative dynamical low-rank methods for the Vlasov equation via a novel macro-micro decomposition

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arXiv 2023年

作者： Coughlin, Jack Hu, Jingwei Shumlak, Uri Department of Applied Mathematics University of Washington SeattleWA98195 United States Aerospace and Energetics Research Program University of Washington SeattleWA98195 United States

Dynamical low-rank (DLR) approximation has gained interest in recent years as a viable solution to the curse of dimensionality in the numerical solution of kinetic equations including the Boltzmann and Vlasov equations. These methods include the projector-splitting and Basis-update & Galerkin (BUG) DLR integrators, and have shown promise at greatly improving the computational efficiency of kinetic solutions. However, this often comes at the cost of conservation of charge, current and energy. In this work we show how a novel macro-micro decomposition may be used to separate the distribution function into two components, one of which carries the conserved quantities, and the other of which is orthogonal to them. We apply DLR approximation to the latter, and thereby achieve a clean and extensible approach to a conservative DLR scheme which retains the computational advantages of the base scheme. Moreover, our approach requires no change to the mechanics of the DLR approximation, so it is compatible with both the BUG family of integrators and the projector-splitting integrator which we use here. We describe a first-order integrator which can exactly conserve charge and either current or energy, as well as an integrator which exactly conserves charge and energy and exhibits second-order accuracy on our test problems. To highlight the flexibility of the proposed macro-micro decomposition, we implement a pair of velocity space discretizations, and verify the claimed accuracy and conservation properties on a suite of plasma benchmark *** Codes 35Q61, 35Q83, 65M06, 65M70 Copyright © 2023, The Authors. All rights reserved.

关键词： Vlasov equation

CA-PCA: Manifold Dimension Estimation, Adapted for Curvature

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arXiv 2023年

作者： Gilbert, Anna C. O’Neill, Kevin Applied Mathematics Program Yale University New HavenCT United States Flatiron Institute New YorkNY United States The MITRE Corporation United States

The success of algorithms in the analysis of high-dimensional data is often attributed to the manifold hypothesis, which supposes that this data lie on or near a manifold of much lower dimension. It is often useful to determine or estimate the dimension of this manifold before performing dimension reduction, for instance. Existing methods for dimension estimation are calibrated using a flat unit ball. In this paper, we develop CA-PCA, a version of local PCA based instead on a calibration of a quadratic embedding, acknowledging the curvature of the underlying manifold. Numerous careful experiments show that this adaptation improves the estimator in a wide range of *** Codes 62H25, 62R30 © 2023, CC BY.

关键词： Principal component analysis

Unified Variational Approach Description of Ground-State Phases of the Two-Dimensional Electron Gas

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Physical Review Letters 2024年第26期133卷 266504-266504页

作者： Conor Smith Yixiao Chen (陈一潇) Ryan Levy Yubo Yang (杨煜波) Miguel A. Morales Shiwei Zhang Center for Computational Quantum Physics Flatiron Institute New York New York 10010 USA Department of Electrical and Computer Engineering University of New Mexico Albuquerque New Mexico 87131 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different Ansätze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs=37±1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.

关键词： Wave functions

On Runge–Kutta methods of order 10

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arXiv 2025年

作者： Stepanov, Misha Department of Mathematics and Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

关键词： Runge Kutta methods

ON THE GLOBAL WELL-POSEDNESS AND GEVREY REGULARITY OF SOME ELECTRODIFFUSION MODELS

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arXiv 2022年

作者： Abdo, Elie Lee, Fizay-Noah Wang, Weinan Department of Mathematics Temple University PhiladelphiaPA19122 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics University of Arizona TucsonAZ85712 United States

We consider the Nernst-Planck equations describing the nonlinear time evolution of multiple ionic concentrations in a two-dimensional incompressible fluid. The velocity of the fluid evolves according to either the Euler or Darcy’s equations, both forced nonlinearly by the electric forces generated by the presence of charged ions. We address the global well-posedness and Gevrey regularity of the resulting electrodiffusion models in the periodic setting. © 2022, CC BY.

关键词： Nonlinear equations

Inferring System and Optimal Control Parameters of Closed-Loop Systems from Partial Observations

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Inferring System and Optimal Control Parameters of Closed-Lo...

IEEE Conference on Decision and Control

作者： Victor Geadah Juncal Arbelaiz Harrison Ritz Nathaniel D. Daw Jonathan D. Cohen Jonathan W. Pillow Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mechanical and Aerospace Engineering Princeton University Princeton NJ USA Princeton Neuroscience Institute Princeton University Princeton NJ USA

ISBN: (数字)9798350316339

ISBN: (纸本)9798350316346

We consider the joint problem of system identification and inverse optimal control for discrete-time stochastic Linear Quadratic Regulators. We analyze finite and infinite time horizons in a partially observed setting, where the state is observed noisily. To recover closed-loop system parameters, we develop inference methods based on probabilistic statespace model (SSM) techniques. First, we show that the system parameters exhibit non-identifiability in the infinite-horizon from closed-loop measurements, and we provide exact and numerical methods to disentangle the parameters. Second, to improve parameter identifiability, we show that we can further enhance recovery by either (1) incorporating additional partial measurements of the control signals or (2) moving to the finitehorizon setting. We further illustrate the performance of our methodology through numerical examples.

关键词： Regulators Optimal control Stochastic processes Probabilistic logic System identification Numerical models Closed loop systems