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Reconstruction of incidence reporting rate for SARS-CoV-2 Delta variant of COVID-19 pandemic in the US

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Infectious Disease Modelling 2024年第1期9卷 70-83页

作者： Alexandra Smirnova Mona Baroonian department of mathematics&statistics Georgia State UniversityAtlantaUSA

In recent years,advanced regularization techniques have emerged as a powerful tool aimed at stable estimation of infectious disease parameters that are crucial for future projections,prevention,and *** other system parameters,i.e.,incubation and recovery rates,the case reporting rate,Ψ,and the time-dependent effective reproduction number,R_(e)t,are directly influenced by a large number of factors making it impossible to pre-estimate these parameters in any meaningful *** this study,we propose a novel iteratively-regularized trust-region optimization algorithm,combined with SuSvIuIvRD compartmental model,for stable reconstruction ofΨand R_(e)t from reported epidemic data on vaccination percentages,incidence cases,and daily *** innovative regularization procedure exploits(and takes full advantage of)a unique structure of the Jacobian and Hessian approximation for the nonlinear observation *** proposed inversion method is thoroughly tested with synthetic and real SARS-CoV-2 Delta variant data for different regions in the United states of America from July 9,2021,to November 25,*** study shows that case reporting rate during the Delta wave of COVID-19 pandemic in the US is between 12%and 37%,with most states being in the range from 15%to 25%.This confirms earlier accounts on considerable under-reporting of COVID-19 cases due to the impact of”silent spreaders”and the limitations of testing.

关键词： Epidemiology Incidence reporting rate Compartmental model Transmission dynamic Regularization algorithm

An efficient and safe strategy for germ cell-specific automatic excision of foreign DNA in F1 hybrid transgenic silkworms

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Insect Science 2024年第1期31卷 28-46页

作者： Dingpei Long Rongpeng Liu Yang Huang Anyao Fu Yuli Zhang Zhanzhang Hao Qiang Li Hanfu Xu Zhonghuai Xiang Aichun Zhao state Key Laboratory of Resource Insects Institute of Sericulture and Systems BiologySouthwest UniversityChongqingChina department of Biology Georgia State UniversityAtlantaGeorgiaUSA Guangxi Institute of Sericulture Science NanningGuangxiChina department of mathematics and statistics Georgia State UniversityAtlantaGeorgiaUSA

The safety of transgenic technology is a major obstacle in the popularization and use of transgenic silkworms and their *** sericulture,only the first filial generation(F1)hybrid eggs produced by cross-breeding Japanese and Chinese original strains are usually used for the large-scale breeding of silkworms,but this may result in uncontrolled transgene dispersal during the popularization and application of the F1 hybrid transgenic *** address this issue,we developed a safe and efficient strategy using the GAL4/Upstream activating sequence(UAS)system,the FLP/flippase recognition target(FRT)system,and the gonad-specific expression gene promoters(RSHP1p and Nanosp)for the germ cell-specific automatic excision of foreign DNA in the F1 hybrid transgenic *** established 2 types of activator strains,R1p::GAL4-Gr and Nsp::GAL4-Gr,containing the testis-specific GAL4 gene expression cassettes driven by RSHP1p or Nanosp,respectively,and 1 type of effector strain,UAS::FLP-Rg,containing the UAS-linked FLP gene expression *** FLP recombinase-mediated sperm-specific complete excision of FRT-flanked target DNA in the F1 double-transgenic silkworms resulting from the hybridization of R1p::GAL4-Gr and UAS::FLP-Rg was 100%,whereas the complete excision efficiency resulting from the hybridization of Nsp::GAL4-Gr and UAS::FLP-Rg ranged from 13.73%to 80.3%.Additionally,we identified a gene,sw11114,that is expressed in both testis and ovary of Bombyx mori,and can be used to establish novel gonad-specific expression systems in transgenic *** strategy has the potential to fundamentally solve the safety issue in the production of F1 transgenic silkworm eggs and provides an important reference for the safety of transgenic technology in other insect species.

关键词： Bombyx mori FLP/FRT system GAL4/UAS system germ cell-specific excision safety of transgenic technology transgenic silkworm

VARIABLE STEP-SIZE BDF3 METHOD FOR ALLEN-CAHN EQUATION

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Journal of Computational mathematics 2024年第5期42卷 1380-1406页

作者： Minghua Chen Fan Yu Qingdong Zhang Zhimin Zhang School of mathematics and statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000China department of mathematics Wayne State UniversityDetroitMI 48202USA

In this work,we analyze the three-step backward differentiation formula(BDF3)method for solving the Allen-Cahn equation on variable *** BDF2 method,the discrete orthogonal convolution(DOC)kernels are positive,the stability and convergence analysis are well established in[Liao and Zhang,***.,90(2021),1207–1226]and[Chen,Yu,and Zhang,arXiv:2108.02910,2021].However,the numerical analysis for BDF3 method with variable steps seems to be highly nontrivial due to the additional degrees of freedom and the non-positivity of DOC *** developing a novel spectral norm inequality,the unconditional stability and convergence are rigorously proved under the updated step ratio restriction rk:=τk/τk−1≤1.405 for BDF3 ***,numerical experiments are performed to illustrate the theoretical *** the best of our knowledge,this is the first theoretical analysis of variable steps BDF3 method for the Allen-Cahn equation.

关键词： Variable step-size BDF3 method Allen-Cahn equation Spectral norm inequality Stability and convergence analysis

Iterative Subregion Correction Preconditioners with Adaptive Tolerance for Problems with Geometrically Localized Stiffness

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Communications on Applied mathematics and Computation 2024年第2期6卷 811-836页

作者： Michael Franco Per-Olof Persson Will Pazner department of mathematics University of CaliforniaBerkeleyBerkeleyCA 94720-3840USA Fariborz Maseeh department of mathematics and statistics Portland State UniversityPortlandOR 97201USA

We present a class of preconditioners for the linear systems resulting from a finite element or discontinuous Galerkin discretizations of advection-dominated *** preconditioners are designed to treat the case of geometrically localized stiffness,where the convergence rates of iterative methods are degraded in a localized subregion of the *** convergence may be caused by a number of factors,including the mesh size,anisotropy,highly variable coefficients,and more challenging *** approach taken in this work is to correct well-known preconditioners such as the block Jacobi and the block incomplete LU(ILU)with an adaptive inner subregion *** goal of these preconditioners is to reduce the number of costly global iterations by accelerating the convergence in the stiff region by iterating on the less expensive reduced *** tolerance for the inner iteration is adaptively chosen to minimize subregion-local work while guaranteeing global convergence *** present analysis showing that the convergence of these preconditioners,even when combined with an adaptively selected tolerance,is independent of discretization parameters(e.g.,the mesh size and diffusion coefficient)in the *** demonstrate significant performance improvements over black-box preconditioners when applied to several model convection-diffusion ***,we present performance results of several variations of iterative subregion correction preconditioners applied to the Reynolds number 2.25×10^(6)fluid flow over the NACA 0012 airfoil,as well as massively separated flow at 30°angle of attack.

关键词： Subregion correction Nested Krylov Geometrically localized stiffness

A Study of EM Algorithm as an Imputation Method: A Model-Based Simulation Study with Application to a Synthetic Compositional Data

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Open Journal of Modelling and Simulation 2024年第2期12卷 33-42页

作者： Yisa Adeniyi Abolade Yichuan Zhao department of mathematics and statistics Georgia State University Atlanta Georgia USA

Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.

关键词： Compositional Data Linear Regression Model Least Square Method Robust Least Square Method Synthetic Data Aitchison Distance Maximum Likelihood Estimation Expectation-Maximization Algorithm k-Nearest Neighbor and Mean imputation

Adaptive Sparse Grid Discontinuous Galerkin Method:Review and Software Implementation

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Communications on Applied mathematics and Computation 2024年第1期6卷 501-532页

作者： Juntao Huang Wei Guo Yingda Cheng department of mathematics and statistics Texas Tech UniversityLubbockTX79409USA department of Computational mathematics Science and EngineeringMichigan State UniversityEast LansingMI48824USA department of mathematics Michigan State UniversityEast LansingMI48824USA

This paper reviews the adaptive sparse grid discontinuous Galerkin(aSG-DG)method for computing high dimensional partial differential equations(PDEs)and its software *** C++software package called AdaM-DG,implementing the aSG-DG method,is available on GitHub at https://***/JuntaoHuang/*** package is capable of treating a large class of high dimensional linear and nonlinear *** review the essential components of the algorithm and the functionality of the software,including the multiwavelets used,assembling of bilinear operators,fast matrix-vector product for data with hierarchical *** further demonstrate the performance of the package by reporting the numerical error and the CPU cost for several benchmark tests,including linear transport equations,wave equations,and Hamilton-Jacobi(HJ)equations.

关键词： Adaptive sparse grid Discontinuous Galerkin High dimensional partial differential equation Software development

Bifurcation Analysis of a Nonlinear Vibro-Impact System with an Uncertain Parameter via OPA Method

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工程与科学中的计算机建模(英文) 2024年第1期138卷 509-524页

作者： Dongmei Huang Dang Hong Wei Li Guidong Yang Vesna Rajic School of mathematics and statistics Xidian UniversityXi’an710071China department of mathematics Changzhi UniversityChangzhi046011China department for statistics and mathematics Faculty of EconomicsUniversity of BelgradeBelgrade11000Serbia

In this paper,the bifurcation properties of the vibro-impact systems with an uncertain parameter under the impulse and harmonic excitations are ***,by means of the orthogonal polynomial approximation(OPA)method,the nonlinear damping and stiffness are expanded into the linear combination of the state *** condition for the appearance of the vibro-impact phenomenon is to be transformed based on the calculation of themean ***,the stochastic vibro-impact systemcan be turned into an equivalent high-dimensional deterministic non-smooth *** different Poincarésections are chosen to analyze the bifurcation properties and the impact numbers are identified for the periodic ***,the numerical results verify the effectiveness of the approximation method for analyzing the considered nonlinear ***,the bifurcation properties of the system with an uncertain parameter are explored through the high-dimensional deterministic *** can be found that the excitation frequency can induce period-doubling bifurcation and grazing *** the randomintensitymay result in a diffusion-based trajectory and the impact with the constraint plane,which induces the topological behavior of the non-smooth system to change *** is also found that grazing bifurcation appears in advance with increasing of the random *** stronger impulse force can result in the appearance of the diffusion phenomenon.

关键词： Orthogonal polynomial approximation vibro-impact systems non-smooth systems grazing bifurcation

Nonlinear Extrapolation Estimates of π

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Acta Mathematicae Applicatae Sinica 2024年第1期40卷 91-108页

作者： Wen-qing Xu Sha-sha Wang Da-chuan Xu Beijing Institute for Scientific and Engineering Computing Beijing University of TechnologyBeijing100124China department of mathematics and statistics California State UniversityLong BeachCalifornia90840USA department of mathematics and Physics Shijiazhuang Tiedao UniversityShijiazhuang050043China

The classical Archimedean approximation of π uses the semiperimeter or area of regular polygons inscribed in or circumscribed about a unit circle in R~2 and it is well-known that by using linear combinations of these basic estimates,modern extrapolation techniques can greatly speed up the approximation ***,when n vertices are randomly selected on the circle,the semiperimeter and area of the corresponding random inscribed and circumscribing polygons are known to converge to π almost surely as n→∞,and by further applying extrapolation processes,faster convergence rates can also be achieved through similar linear combinations of the semiperimeter and area of these random *** this paper,we further develop nonlinear extrapolation methods for approximating π through certain nonlinear functions of the semiperimeter and area of such *** focus on two types of extrapolation estimates of the forms χ_n=S_n~αA_n~β and Y_n(p)=(αS_n~p+βA_n~p)~(1/p) where α+β=1,p≠0,and Sn and An respectively represents the semiperimeter and area of a random n-gon inscribed in the unit circle in R~2,and Xn may be viewed as the limit of Y_n(p) when p→*** deriving probabilistic asymptotic expansions with carefully controlled error estimates for Xn and Y_n(p),we show that the choice α=4/3,β=-1/3 minimizes the approximation error in both cases,and their distributions are also asymptotically normal.

关键词： Archimedean polygons random polygons approximations ofπ extrapolation processes asymptotic convergence

Uncertainty Comparison Between Value-at-Risk and Expected Shortfall

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Communications in Mathematical Research 2024年第1期40卷 102-124页

作者： Qing Liu Weimin Liu Liang Peng Gengsheng Qin School of statistics Jjiangxi University of Finance and EconomicsNanchangJiangxi 330013China department of mathematics and statistics Georgia State UniversityAtlantaGA 30303USA Maurice R.Greenberg School of Risk Science Georgia State UniversityAtlantaGA 20303USA

Value-at-Risk(VaR)and expected shortfall(ES)are two key risk measures in financial risk *** these two measures has been a hot debate,and most discussions focus on risk measure *** paper uses independent data and autoregressive models with normal or t-distribution to examine the effect of the heavy tail and dependence on comparing the nonparametric inference uncertainty of these two risk *** and numerical analyses suggest that VaR at 99%level is better than ES at 97.5%level for distributions with heavier tails.

关键词： α-mixing asymptotic variance expected shortfall Value-at-Risk