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Modelling the unexpected dynamics of COVID-19 in Manaus,Brazil

Infectious Disease Modelling 2024年第2期9卷 557-568页

作者： Daihai He Yael Artzy-Randrup Salihu S.Musa Tiago Gräf Felipe Naveca Lewi Stone Department of Applied Mathematics Hong Kong Polytechnic UniversityHong Kong SARChina Department of Theoretical and Computational Ecology IBEDUniversity of AmsterdamAmsterdamNetherlands Department of Genomics and Computational Biology University of Massachusetts Chan Medical SchoolWorcesterMA01605USA Department of Mathematics Aliko Dangote University of Science and TechnologyKanoNigeria Instituto Gonçalo Moniz FiocruzSalvadorBahiaBrazil Instituto Leônidas e Maria Deane FiocruzManausBrazil Mathematical Sciences School of ScienceRMIT UniversityMelbourneAustralia Biomathematics Unit School of ZoologyFaculty of Life SciencesTel Aviv UniversityTel AvivIsrael

In late March 2020,SARS-CoV-2 arrived in Manaus,Brazil,and rapidly developed into a large-scale epidemic that collapsed the local health system and resulted in extreme death *** key studies reported that∼76%of residents of Manaus were infected(attack rate AR≃76%)by October 2020,suggesting protective herd immunity had been *** this,an unexpected second wave of COVID-19 struck again in November and proved to be larger than the first,creating a catastrophe for the unprepared *** has been suggested that this could be possible if the second wave was driven by ***,it is widely reported that reinfections were at a low rate(before the emergence of Omicron),and reinfections tend to be ***,we use novel methods to model the epidemic from mortality data without considering reinfection-caused deaths and evaluate the impact of interventions to explain why the second wave *** method fits a“flexible”reproductive numberR_(0)(t)that changes over the epidemic,and it is demonstrated that the method can successfully reconstruct R_(0)(t)from simulated *** Manaus,the method finds AR≃34%by October 2020 for the first wave,which is far less than required for herd immunity yet in-line with seroprevalence *** work is complemented by a two-strain *** genomic data,the model estimates transmissibility of the new P.1 virus lineage as 1.9 times higher than that of the ***,an age class model variant that considers the high mortality rates of older adults show very similar *** models thus provide a reasonable explanation for the two-wave dynamics in Manaus without the need to rely on large reinfection rates,which until now have only been found in negligible to moderate numbers in recent surveillance efforts.

关键词： Modelling COVID-19 Reproduction number Herd immunity Reinfection

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Interface information transfer between non-matching, nonconforming interfaces using radial basis function interpolation 10

Interface information transfer between non-matching, nonconf...

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10th South African Conference on computational and applied Mechanics, SACAM 2016

作者： Bogaers, A.E.J. Kok, S. Reddy, B.D. Franz, T. Advanced Mathematical Modelling Modelling and Digital Sciences CSIR South Africa Department of Mechanical and Aeronautical Engineering University of Pretoria South Africa Department of Mathematics and Applied Mathematics University of Cape Town South Africa Centre for Research in Computational and Applied Mechanics University of Cape Town South Africa Division of Biomedical Engineering Department of Human Biology University of Cape Town South Africa Research Office University of Cape Town South Africa

ISBN: (纸本)9781868226733

In this paper we outline the use of radial basis function interpolation (RBF) to transfer information across non-matching and nonconforming interface meshes, with particular focus to partitioned fluid-structure interactions (FSI). In general, transferring information across a non-matching interface presents itself as a nontrivial problem. RBF interpolation, which requires no global connectivity information, provides an elegant means by which to negate any geometric discrepancies along the interface. The aim is to investigate the feasibility of RBF interpolation, with a strong focus on a comparison between a conservative and consistent formulation.

关键词： Interpolation

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Normalized solutions for a class of Sobolev critical Schrodinger systems

arXiv

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arXiv 2024年

作者： Li, Houwang Liu, Tianhao Zou, Wenming Beijing Institute of Mathematical Sciences and Applications Beijing100084 China Institute of Applied Physics and Computational Mathematics Beijing100088 China Department of Mathematical Sciences Tsinghua University Beijing100084 China

This paper focuses on the existence and multiplicity of normalized solutions for the following coupled Schrödinger system with Sobolev critical coupling term: (Formula presented) where N ≥ 3, a, b > 0, ω1, ω2, ν ∈ \ {0}, and the exponents p, α, β satisfy (Formula presented) The parameters λ1, λ2 ∈ will arise as Lagrange multipliers that are not prior given. This paper mainly presents several existence and multiplicity results under explicit conditions on a, b for the focusing case ω1, ω2 > 0 and attractive case ν > 0: (1) When 2 *, we prove that there exists a mountain-pass type solution, which serves as a normalized ground state. (3) When p = 2*, the existence and classification of normalized ground states are provided for and N ≥ 5, alongside a non-existence result for N = 3, 4. These results reflect the properties of the Aubin-Talenti bubble, which attains the best Sobolev embedding constant. Furthermore, we present a non-existence result for the defocusing case ω1, ω2 © 2024, CC BY.

关键词： Lagrange multipliers

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Unbiased Estimation using Underdamped Langevin Dynamics

arXiv

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arXiv 2022年

作者： Ruzayqat, Hamza 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

In this work we consider the unbiased estimation of expectations w.r.t. probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method via the underdamped Langevin dynamics, which has proven to be popular of late due to applications in statistics and machine learning. Specifically in continuous-time, the dynamics can be constructed so that as the time goes to infinity they admit the probability of interest as a stationary measure. In many cases, time-discretized versions of the underdamped Langevin dynamics are used in practice which are run only with a fixed number of iterations. We develop a novel scheme based upon doubly randomized estimation as in [17, 19], which requires access only to time-discretized versions of the dynamics. The proposed scheme aims to remove the dicretization bias and the bias resulting from running the dynamics for a finite number of iterations. We prove, under standard assumptions, that our estimator is of finite variance and either has finite expected cost, or has finite cost with a high probability. To illustrate our theoretical findings we provide numerical experiments which verify our theory, which include challenging examples from Bayesian statistics and statistical *** Codes 60J22, 65C05, 65C40, 82C31, 62G08, 35Q56 © 2022, CC BY.

关键词： Dynamics

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Unbiased Parameter Estimation for Partially Observed Diffusions

arXiv

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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

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USING REED-MULLER SEQUENCES AS DETERMINISTIC COMPRESSED SENSING MATRICES FOR IMAGE RECONSTRUCTION

USING REED-MULLER SEQUENCES AS DETERMINISTIC COMPRESSED SENS...

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IEEE International Conference on Acoustics, Speech, and Signal Processing

作者： Kangyu Ni Somantika Datta Prasun Mahanti Svetlana Roudenko Douglas Cochran School of Mathematical and Statistical Sciences Arizona State University Program in Applied and Computational Mathematics Princeton University School of Electrical Computer and Energy Engineering Arizona State University

ISBN: (纸本)9781424442959;9781424442966

An image reconstruction algorithm using compressed sensing (CS) with deterministic matrices of second-order Reed-Muller (RM) sequences is introduced. The 1D algorithm of Howard et al. using CS with RM sequences suffers significant loss in speed and accuracy when the degree of sparsity is not high, making it inviable for 2D signals. This paper describes an efficient 2D CS algorithm using RM sequences, provides medical image reconstruction examples, and compares it with the original 2D CS using noiselets. This algorithm entails several innovations that enhance its suitability for images: initial best approximation, a greedy algorithm for the nonzero locations, and a new approach in the least-squares step. These enhancements improve fidelity, execution time, and stability in the context of image reconstruction.

关键词： Compressed Sensing Reed-Muller Sequences Image Reconstruction image reconstruction Compressed sensing deterministic CONTAINMENT SPRAY carbon monosulfide Cesium matrices Redmouth disease greedy algorithm COMPRESSED conditioned stimulus

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Local Sequential MCMC for Data Assimilation with Applications in Geoscience

arXiv

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arXiv 2024年

作者： Ruzayqat, Hamza Knio, Omar 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

This paper presents a new data assimilation (DA) scheme based on a sequential Markov Chain Monte Carlo (SMCMC) DA technique [36] which is provably convergent and has been recently used for filtering, particularly for high-dimensional non-linear, and potentially, non-Gaussian state-space models. Unlike particle filters, which can be considered exact methods and can be used for filtering non-linear, non-Gaussian models, SMCMC does not assign weights to the samples/particles, and therefore, the method does not suffer from the issue of weight-degeneracy when a relatively small number of samples is used. We design a localization approach within the SMCMC framework that focuses on regions where observations are located and restricts the transition densities included in the filtering distribution of the state to these regions. This results in immensely reducing the effective degrees of freedom and thus improving the efficiency. We test the new technique on high-dimensional (d ∼ 104 − 105) linear Gaussian model and non-linear shallow water models with Gaussian noise with real and synthetic observations. For two of the numerical examples, the observations mimic the data generated by the Surface Water and Ocean Topography (SWOT) mission led by NASA, which is a swath of ocean height observations that changes location at every assimilation time step. We also use a set of ocean drifters' real observations in which the drifters are moving according the ocean kinematics and assumed to have uncertain locations at the time of assimilation. We show that when higher accuracy is required, the proposed algorithm is superior in terms of efficiency and accuracy over competing ensemble methods and the original SMCMC *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2024, CC BY.

关键词： Markov chains

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A smoothing algorithm for training max-min neural networks

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Journal of Theoretical and applied Information Technology 2012年第1期46卷 114-119页

作者： Li, Long Xu, Tian Liu, Yan Yang, Jie Department of Mathematics and Computational Science Hengyang Normal University Hengyang 421008 China Department of Applied Mathematics Dalian Polytechnic University Dalian 116034 China School of Mathematical Sciences Dalian University of Technology Dalian 116024 China

In this paper, a smoothing algorithm for training max-min neural networks is proposed. Specifically, we apply a smooth function to approximate max-min functions and use this smoothing technique twice, once to eliminate the inner min operator and once to eliminate the max operator. In place of actual network output by its approximation function, we use all partial derivatives of the approximation function with respect to weight to substitute those of the actual network output. Then, the smoothing algorithm is constructed by the gradient descent method. This algorithm can also be used to solve fuzzy relational equations. Finally, two numerical examples are provided to show the effectiveness of our smoothing algorithm for training max-min neural networks. © 2005 - 2012 JATIT & LLS. All rights reserved.

关键词： Approximation algorithms

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International Workshop on Applications of Probability and Statistics to Biology,July 11-13,2019--In Honor of Professor Minping Qian’s 80th Birthday

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Quantitative Biology 2020年第2期8卷 177-186页

作者： Minghua Deng Jianfeng Feng Hong Qian Lin Wan Fengzhu Sun Center for Quantitative Biology Peking UniversityBeijing 100871China LMAM Center for Statistical ScienceSchool of Mathematical SciencesPeking UniversityBeijing 100871China Institute of Science and Technology for Brain-inspired Intelligence Fudan UniversityShanghai 200433China School of Mathematical Sciences Fudan UniversityShanghai 200433China Centre for Computational Systems Biology Fudan UniversityShanghai 200433China Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence at Fudan University Ministry of EducationShanghai 200433China Department of Computer Science University of WarwickCoventryCV47ALUnited Kingdom Department of Applied Mathematics University of WashingtonSeattleWA 98195USA NCMIS Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Quantitative and Computational Biology Program University of Southern CaliforniaLos AngelesCA 90089USA

The International Workshop on Applications of Probability and Statistics to Biology(APSB)was successfully held in Shanghai,China,July 11-13,*** workshop was hosted by the Institute of Science and Technology for Brain-inspired Intelligence(ISTBI)at Fudan University,and in honor of the 80th birthday of *** Qian of Peking *** of the twenty eight speakers were former students or close collaborators of ***;and there were over eighty participants from all over China and United States.

关键词： Probability speakers ping

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Beta expansions: a new approach to digitally corrected A/D conversion

Beta expansions: a new approach to digitally corrected A/D c...

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IEEE International Symposium on Circuits and Systems (ISCAS)

作者： I. Daubechies R. DeVore C.S. Gunturk V.A. Vaishampayan Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics University of South Carolina Columbia SC USA Department of Mathematics Courant Institute of Mathematical Sciences New York NY USA Information Sciences Research AT and T Research Laboratories Florham Park NJ USA

We introduce a new architecture for pipelined (and also algorithmic) A/D converters that give exponentially accurate conversion using inaccurate comparators. An error analysis of a sigma-delta converter with an imperfect comparator and a constant input reveals a self-correction property that is not inherited by the successive refinement quantization algorithm that underlies both pipelined multistage A/D converters and algorithmic A/D converters. Motivated by this example, we introduce a new A/D converter, the beta converter, which has the same self-correction property as a sigma-delta converter but which exhibits higher order (exponential) accuracy with respect to the bit rate as compared to a sigma-delta converter, which exhibits only polynomial accuracy.

关键词： mathematics Delta-sigma modulation Error analysis Quantization Redundancy Error correction Voltage Sampling methods Fourier transforms Computer architecture

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