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Articles 1 - 8 of 8
Full-Text Articles in Physical Sciences and Mathematics
Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang
Stability Analysis And Application Of A Mathematical Cholera Model, Shu Liao, Jim Wang
Mathematics & Statistics Faculty Publications
In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.
Analysis Of Biological Features Associated With Meiotic Recombination Hot And Cold Spots In Saccharomyces Cerevisiae, Loren Hansen, Nak-Kyeong Kim, Leonardo Mariño-Ramírez, David Landsman
Analysis Of Biological Features Associated With Meiotic Recombination Hot And Cold Spots In Saccharomyces Cerevisiae, Loren Hansen, Nak-Kyeong Kim, Leonardo Mariño-Ramírez, David Landsman
Mathematics & Statistics Faculty Publications
Meiotic recombination is not distributed uniformly throughout the genome. There are regions of high and low recombination rates called hot and cold spots, respectively. The recombination rate parallels the frequency of DNA double-strand breaks (DSBs) that initiate meiotic recombination. The aim is to identify biological features associated with DSB frequency. We constructed vectors representing various chromatin and sequence-based features for 1179 DSB hot spots and 1028 DSB cold spots. Using a feature selection approach, we have identified five features that distinguish hot from cold spots in Saccharomyces cerevisiae with high accuracy, namely the histone marks H3K4me3, H3K14ac, H3K36me3, and H3K79me3; …
Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko
Acceleration Techniques By Post-Processing Of Numerical Solutions Of The Hammerstein Equation, Khomsan Neamprem, Hideaki Kaneko
Mathematics & Statistics Faculty Publications
No abstract provided.
Mesoscopic Methods In Engineering And Science, Chuguang Zheng, Jiding Lu, Zhaoli Guo, Li-Shi Luo, Manfred Krafczyk
Mesoscopic Methods In Engineering And Science, Chuguang Zheng, Jiding Lu, Zhaoli Guo, Li-Shi Luo, Manfred Krafczyk
Mathematics & Statistics Faculty Publications
Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the macroscopic dynamics …
Putting The X In Biology: A Review Of The Mathematics Of Life, John Adam
Putting The X In Biology: A Review Of The Mathematics Of Life, John Adam
Mathematics & Statistics Faculty Publications
(First Paragraph) Charles Darwin's 1859 work On the Origin of the Species contained no equations. But that does not mean mathematics has no role to play in the science of life; in fact, the field of biomathematics is burgeoning and has been for several decades. Ian Stewart's new book does an admirable job of unfolding the mathematics undergirding so much of the research being carried out today in the many fields that comprise the subject of biology. Stewart sets the context by noting five great revolutions that have changed the way scientists think about life. These five revolutions are: (i) …
Numerics Of The Lattice Boltzmann Method: Effects Of Collision Models On The Lattice Boltzmann Simulations, Li-Shi Luo, Wei Liao, Xingwang Chen, Yan Peng, Wei Zhang
Numerics Of The Lattice Boltzmann Method: Effects Of Collision Models On The Lattice Boltzmann Simulations, Li-Shi Luo, Wei Liao, Xingwang Chen, Yan Peng, Wei Zhang
Mathematics & Statistics Faculty Publications
We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxation-time (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of …
Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Stability, Charles B. Harris, Richard D. Noren
Uniform L1 Behavior Of A Time Discretization Method For A Volterra Integrodifferential Equation With Convex Kernel; Stability, Charles B. Harris, Richard D. Noren
Mathematics & Statistics Faculty Publications
We study stability of a numerical method in which the backward Euler method is combined with order one convolution quadrature for approximating the integral term of the linear Volterra integrodifferential equation u'(t) + ∫0 β (t - s)Au(s) ds = 0, t ≥ 0, u(0) = u0, which arises in the theory of linear viscoelasticity. Here A is a positive self-adjoint densely defined linear operator in a real Hilbert space, and β (t) is locally integrable, nonnegative, nonincreasing, convex, and -β'(t) is convex. We establish stability of the method under these hypotheses on β(t). Thus, …
Weighted Scores Method For Regression Models With Dependent Data, Aristidis K. Nikoloulopoulos, Harry Joe, N. Rao Chaganty
Weighted Scores Method For Regression Models With Dependent Data, Aristidis K. Nikoloulopoulos, Harry Joe, N. Rao Chaganty
Mathematics & Statistics Faculty Publications
There are copula-based statistical models in the literature for regression with dependent data such as clustered and longitudinal overdispersed counts, for which parameter estimation and inference are straightforward. For situations where the main interest is in the regression and other univariate parameters and not the dependence, we propose a "weighted scores method", which is based on weighting score functions of the univariate margins. The weight matrices are obtained initially fitting a discretized multivariate normal distribution, which admits a wide range of dependence. The general methodology is applied to negative binomial regression models. Asymptotic and small-sample efficiency calculations show that our …