Roger Lui - Academia.edu (original) (raw)

Papers by Roger Lui

Research paper thumbnail of A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability

Journal of Mathematical Chemistry, 2010

In this paper we develop a reduction method for multiple time scale stochastic reaction networks.... more In this paper we develop a reduction method for multiple time scale stochastic reaction networks. When the transition-rate matrix between different states of the species is available, we obtain systems of reduced equations, whose solutions can successively approximate, to any degree of accuracy, the exact probability that the reaction system be in any particular state. For the case when the transition-rate matrix is not available, one needs to rely on the chemical master equation. For this case, we obtain a corresponding reduced master equation with first-order accuracy. We illustrate the accuracy and efficiency of both approaches by simulating several motivating examples and comparing the results of our simulations with the results obtained by the exact method. Our examples include both linear and nonlinear reaction networks as well as a three time scale stochastic reaction-diffusion model arising from gene expression.

Research paper thumbnail of An integro-differential equation arising from an electrochemistry model

Google, Inc. (search). SIGN IN SIGN UP. An integro-differential equation arising from an electroc... more Google, Inc. (search). SIGN IN SIGN UP. An integro-differential equation arising from an electrochemistry model. Authors: YS Choi, Roger Lui, Published in: · Journal. Quarterly of Applied Mathematics archive. Volume LV Issue 4, Dec. ...

Research paper thumbnail of Global Spatio-temporal Patterns of Influenza in the Post-pandemic Era

Scientific reports, 2015

We study the global spatio-temporal patterns of influenza dynamics. This is achieved by analysing... more We study the global spatio-temporal patterns of influenza dynamics. This is achieved by analysing and modelling weekly laboratory confirmed cases of influenza A and B from 138 countries between January 2006 and January 2015. The data were obtained from FluNet, the surveillance network compiled by the the World Health Organization. We report a pattern of skip-and-resurgence behavior between the years 2011 and 2013 for influenza H1N1pdm, the strain responsible for the 2009 pandemic, in Europe and Eastern Asia. In particular, the expected H1N1pdm epidemic outbreak in 2011/12 failed to occur (or "skipped") in many countries across the globe, although an outbreak occurred in the following year. We also report a pattern of well-synchronized wave of H1N1pdm in early 2011 in the Northern Hemisphere countries, and a pattern of replacement of strain H1N1pre by H1N1pdm between the 2009 and 2012 influenza seasons. Using both a statistical and a mechanistic mathematical model, and thro...

Research paper thumbnail of One-dimensional viscoelastic cell motility models

Mathematical biosciences, 2011

In this paper we consider a class of one-dimensional cell motility models with increasing complex... more In this paper we consider a class of one-dimensional cell motility models with increasing complexities beginning with a kinematic model and ending with a model based on viscoelastic theory. In many of these models, we establish the existence of traveling cell solutions and show numerically that the solutions of the time-dependent problem converge to the traveling cell solutions as t → ∞. As a result, we are able to predict the eventual length and speed of the cell.

Research paper thumbnail of Linearized stability of traveling cell solutions arising from a moving boundary problem

Proceedings of the American Mathematical Society, 2007

Abstract. In 2003, Mogilner and Verzi proposed a one-dimensional model on the crawling movement o... more Abstract. In 2003, Mogilner and Verzi proposed a one-dimensional model on the crawling movement of a nematode sperm cell. Under certain conditions, the model can be reduced to a moving boundary problem for a single equation involving the length density of the ...

Research paper thumbnail of Existence of traveling wave solutions for a one-dimensional cell motility model

Taiwanese Journal of Mathematics, 2004

In this paper, we extend the existence of traveling wave result in [1] to the case where the rate... more In this paper, we extend the existence of traveling wave result in [1] to the case where the rate of disassembly of free polymers is non-zero. Mathematical methods used include dynamical system techniques and global bifurcation theory.

Research paper thumbnail of Patterns for four-allele population genetics model

Theoretical Population Biology, 2012

In this paper, we find and classify all existing patterns for a single-locus four-allele populati... more In this paper, we find and classify all existing patterns for a single-locus four-allele population genetics models in continuous time. An existing pattern for a k-allele model means a set of all coexisting asymptotically stable equilibria with respect to the flow defined by the system of equations ṗ(i)=p(i)(r(i)-r),i=1,…,k, where p(i) and r(i) are the frequency and marginal fitness of allele A(i), respectively, and r is the mean fitness of the population. It is well known that for the two-allele model there are only three existing patterns, depending on the relative fitness between the homozygotes and the heterozygote. For the three-allele model there are 14 existing patterns, and we shall show in this paper that for the four-allele model there are 117 existing patterns. We also describe the domains of attraction for coexisting asymptotically stable equilibria. The problem of finding existing patterns has been studied in the past, and it is an important problem because the results can be used to predict the long-term genetic makeup of a population. It should be pointed out that this continuous-time model is only an approximation to the corresponding discrete-time model. However, the set of equilibria and their stability properties are the same for the two models.

Research paper thumbnail of Stacked Fronts for Cooperative Systems with Equal Diffusion Coefficients

SIAM Journal on Mathematical Analysis, 2011

Research paper thumbnail of Existence of Travelling Wave Solutions for a Bistable Evolutionary Ecology Model

SIAM Journal on Mathematical Analysis, 1992

Research paper thumbnail of Existence and Stability of Traveling Wave Solutions for a Population Genetic Model via Singular Perturbations

SIAM Journal on Applied Mathematics, 1994

Using singular perturbation methods, the existence and stability of traveling wave solutions for ... more Using singular perturbation methods, the existence and stability of traveling wave solutions for a density-dependent selection migration model in population genetics is proved. Single locus and two alleles are assumed, and it is also assumed that the fitnesses of the ...

Research paper thumbnail of One-dimensional reduced semiconductor equations for an asymmetric two-piece doping function

Nonlinearity, 2002

In this paper, we prove the existence and uniqueness of the solutions of the one-dimensional stea... more In this paper, we prove the existence and uniqueness of the solutions of the one-dimensional steady-state reduced semiconductor equations for the voltage-driven case using a two-piece doping function that jumps from-α to β.

Research paper thumbnail of Moving boundary problem for a one-dimensional crawling nematode sperm cell model

Nonlinear Analysis: Real World Applications, 2005

This paper is a continuation of the authors' investigation of the crawling nematode sperm ce... more This paper is a continuation of the authors' investigation of the crawling nematode sperm cell model proposed by Mogilner and Verzi in 2003 (J. Stat. Phys. 110 (2003) 1169). In the earlier papers (J. Math. Biol. 49 (2004) 310 and J. Math. 8 (2004) 399), the first and last ...

Research paper thumbnail of Uniqueness of steady-states and asymptotic behavior of solutions of a liquid junction model with insulation

Nonlinear Analysis: Real World Applications, 2002

Research paper thumbnail of Electrokinetic remediation of contaminated soil

Nonlinear Analysis: Theory, Methods & Applications, 1997

Google, Inc. (search). ...

Research paper thumbnail of A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability

Journal of Mathematical Chemistry, 2010

In this paper we develop a reduction method for multiple time scale stochastic reaction networks.... more In this paper we develop a reduction method for multiple time scale stochastic reaction networks. When the transition-rate matrix between different states of the species is available, we obtain systems of reduced equations, whose solutions can successively approximate, to any degree of accuracy, the exact probability that the reaction system be in any particular state. For the case when the transition-rate matrix is not available, one needs to rely on the chemical master equation. For this case, we obtain a corresponding reduced master equation with first-order accuracy. We illustrate the accuracy and efficiency of both approaches by simulating several motivating examples and comparing the results of our simulations with the results obtained by the exact method. Our examples include both linear and nonlinear reaction networks as well as a three time scale stochastic reaction-diffusion model arising from gene expression.

Research paper thumbnail of Traveling wave solutions from microscopic to macroscopic chemotaxis models

Journal of Mathematical Biology, 2010

In this paper, we study the existence and nonexistence of traveling wave solutions for the one-di... more In this paper, we study the existence and nonexistence of traveling wave solutions for the one-dimensional microscopic and macroscopic chemotaxis models. The microscopic model is based on the velocity jump process of Othmer et al. (SIAM J Appl Math 57:1044-1081). The macroscopic model, which can be shown to be the parabolic limit of the microscopic model, is the classical Keller-Segel model, (Keller and Segel in J Theor Biol 30:225-234; 377-380, 1971). In both models, the chemosensitivity function is given by the derivative of a potential function, (v), which must be unbounded below at some point for the existence of traveling wave solutions. Thus, we consider two examples:

Research paper thumbnail of Traveling wave solutions for a one-dimensional crawling nematode sperm cell model

Journal of Mathematical Biology, 2004

In this paper, we proved that the one-dimensional crawling nematode sperm cell model proposed by ... more In this paper, we proved that the one-dimensional crawling nematode sperm cell model proposed by supports traveling wave solutions if there is no disassembly of unbundled filaments in the cell. Uniqueness of traveling wave is established under additional assumptions and numerical examples are also given in the paper. Mathematical methods used include dynamical system techniques, implicit function theorem and global bifurcation theory.

Research paper thumbnail of Some remarks about the wave speed and travelling wave solutions of a nonlinear integral operator

Journal of Mathematical Biology, 1984

In this paper, we extend the existence of travelling wave solutions of a nonlinear operator in th... more In this paper, we extend the existence of travelling wave solutions of a nonlinear operator in the inferior case to higher dimensions and establish the uniqueness of that solution. In addition we determine the sign of the wave speed in a special case.

Research paper thumbnail of Existence of steady-state solutions to predator-prey equations in a heterogeneous environment

Journal of Mathematical Analysis and Applications, 1987

Research paper thumbnail of Vapor Leak Detection for an Underground Storage Tank System

Journal of Environmental Engineering, 2006

... written by Brian Lehtinen and Michael Pyzocha between September 2002 and April 2003 under the... more ... written by Brian Lehtinen and Michael Pyzocha between September 2002 and April 2003 under the supervision of Professor Roger Lui. ... They would also like to thank Professor Yi Hua Ma and Professor David Olinger of the Mechanical Engineering Department at Worcester ...

Research paper thumbnail of A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability

Journal of Mathematical Chemistry, 2010

In this paper we develop a reduction method for multiple time scale stochastic reaction networks.... more In this paper we develop a reduction method for multiple time scale stochastic reaction networks. When the transition-rate matrix between different states of the species is available, we obtain systems of reduced equations, whose solutions can successively approximate, to any degree of accuracy, the exact probability that the reaction system be in any particular state. For the case when the transition-rate matrix is not available, one needs to rely on the chemical master equation. For this case, we obtain a corresponding reduced master equation with first-order accuracy. We illustrate the accuracy and efficiency of both approaches by simulating several motivating examples and comparing the results of our simulations with the results obtained by the exact method. Our examples include both linear and nonlinear reaction networks as well as a three time scale stochastic reaction-diffusion model arising from gene expression.

Research paper thumbnail of An integro-differential equation arising from an electrochemistry model

Google, Inc. (search). SIGN IN SIGN UP. An integro-differential equation arising from an electroc... more Google, Inc. (search). SIGN IN SIGN UP. An integro-differential equation arising from an electrochemistry model. Authors: YS Choi, Roger Lui, Published in: · Journal. Quarterly of Applied Mathematics archive. Volume LV Issue 4, Dec. ...

Research paper thumbnail of Global Spatio-temporal Patterns of Influenza in the Post-pandemic Era

Scientific reports, 2015

We study the global spatio-temporal patterns of influenza dynamics. This is achieved by analysing... more We study the global spatio-temporal patterns of influenza dynamics. This is achieved by analysing and modelling weekly laboratory confirmed cases of influenza A and B from 138 countries between January 2006 and January 2015. The data were obtained from FluNet, the surveillance network compiled by the the World Health Organization. We report a pattern of skip-and-resurgence behavior between the years 2011 and 2013 for influenza H1N1pdm, the strain responsible for the 2009 pandemic, in Europe and Eastern Asia. In particular, the expected H1N1pdm epidemic outbreak in 2011/12 failed to occur (or "skipped") in many countries across the globe, although an outbreak occurred in the following year. We also report a pattern of well-synchronized wave of H1N1pdm in early 2011 in the Northern Hemisphere countries, and a pattern of replacement of strain H1N1pre by H1N1pdm between the 2009 and 2012 influenza seasons. Using both a statistical and a mechanistic mathematical model, and thro...

Research paper thumbnail of One-dimensional viscoelastic cell motility models

Mathematical biosciences, 2011

In this paper we consider a class of one-dimensional cell motility models with increasing complex... more In this paper we consider a class of one-dimensional cell motility models with increasing complexities beginning with a kinematic model and ending with a model based on viscoelastic theory. In many of these models, we establish the existence of traveling cell solutions and show numerically that the solutions of the time-dependent problem converge to the traveling cell solutions as t → ∞. As a result, we are able to predict the eventual length and speed of the cell.

Research paper thumbnail of Linearized stability of traveling cell solutions arising from a moving boundary problem

Proceedings of the American Mathematical Society, 2007

Abstract. In 2003, Mogilner and Verzi proposed a one-dimensional model on the crawling movement o... more Abstract. In 2003, Mogilner and Verzi proposed a one-dimensional model on the crawling movement of a nematode sperm cell. Under certain conditions, the model can be reduced to a moving boundary problem for a single equation involving the length density of the ...

Research paper thumbnail of Existence of traveling wave solutions for a one-dimensional cell motility model

Taiwanese Journal of Mathematics, 2004

In this paper, we extend the existence of traveling wave result in [1] to the case where the rate... more In this paper, we extend the existence of traveling wave result in [1] to the case where the rate of disassembly of free polymers is non-zero. Mathematical methods used include dynamical system techniques and global bifurcation theory.

Research paper thumbnail of Patterns for four-allele population genetics model

Theoretical Population Biology, 2012

In this paper, we find and classify all existing patterns for a single-locus four-allele populati... more In this paper, we find and classify all existing patterns for a single-locus four-allele population genetics models in continuous time. An existing pattern for a k-allele model means a set of all coexisting asymptotically stable equilibria with respect to the flow defined by the system of equations ṗ(i)=p(i)(r(i)-r),i=1,…,k, where p(i) and r(i) are the frequency and marginal fitness of allele A(i), respectively, and r is the mean fitness of the population. It is well known that for the two-allele model there are only three existing patterns, depending on the relative fitness between the homozygotes and the heterozygote. For the three-allele model there are 14 existing patterns, and we shall show in this paper that for the four-allele model there are 117 existing patterns. We also describe the domains of attraction for coexisting asymptotically stable equilibria. The problem of finding existing patterns has been studied in the past, and it is an important problem because the results can be used to predict the long-term genetic makeup of a population. It should be pointed out that this continuous-time model is only an approximation to the corresponding discrete-time model. However, the set of equilibria and their stability properties are the same for the two models.

Research paper thumbnail of Stacked Fronts for Cooperative Systems with Equal Diffusion Coefficients

SIAM Journal on Mathematical Analysis, 2011

Research paper thumbnail of Existence of Travelling Wave Solutions for a Bistable Evolutionary Ecology Model

SIAM Journal on Mathematical Analysis, 1992

Research paper thumbnail of Existence and Stability of Traveling Wave Solutions for a Population Genetic Model via Singular Perturbations

SIAM Journal on Applied Mathematics, 1994

Using singular perturbation methods, the existence and stability of traveling wave solutions for ... more Using singular perturbation methods, the existence and stability of traveling wave solutions for a density-dependent selection migration model in population genetics is proved. Single locus and two alleles are assumed, and it is also assumed that the fitnesses of the ...

Research paper thumbnail of One-dimensional reduced semiconductor equations for an asymmetric two-piece doping function

Nonlinearity, 2002

In this paper, we prove the existence and uniqueness of the solutions of the one-dimensional stea... more In this paper, we prove the existence and uniqueness of the solutions of the one-dimensional steady-state reduced semiconductor equations for the voltage-driven case using a two-piece doping function that jumps from-α to β.

Research paper thumbnail of Moving boundary problem for a one-dimensional crawling nematode sperm cell model

Nonlinear Analysis: Real World Applications, 2005

This paper is a continuation of the authors' investigation of the crawling nematode sperm ce... more This paper is a continuation of the authors' investigation of the crawling nematode sperm cell model proposed by Mogilner and Verzi in 2003 (J. Stat. Phys. 110 (2003) 1169). In the earlier papers (J. Math. Biol. 49 (2004) 310 and J. Math. 8 (2004) 399), the first and last ...

Research paper thumbnail of Uniqueness of steady-states and asymptotic behavior of solutions of a liquid junction model with insulation

Nonlinear Analysis: Real World Applications, 2002

Research paper thumbnail of Electrokinetic remediation of contaminated soil

Nonlinear Analysis: Theory, Methods & Applications, 1997

Google, Inc. (search). ...

Research paper thumbnail of A reduction method for multiple time scale stochastic reaction networks with non-unique equilibrium probability

Journal of Mathematical Chemistry, 2010

In this paper we develop a reduction method for multiple time scale stochastic reaction networks.... more In this paper we develop a reduction method for multiple time scale stochastic reaction networks. When the transition-rate matrix between different states of the species is available, we obtain systems of reduced equations, whose solutions can successively approximate, to any degree of accuracy, the exact probability that the reaction system be in any particular state. For the case when the transition-rate matrix is not available, one needs to rely on the chemical master equation. For this case, we obtain a corresponding reduced master equation with first-order accuracy. We illustrate the accuracy and efficiency of both approaches by simulating several motivating examples and comparing the results of our simulations with the results obtained by the exact method. Our examples include both linear and nonlinear reaction networks as well as a three time scale stochastic reaction-diffusion model arising from gene expression.

Research paper thumbnail of Traveling wave solutions from microscopic to macroscopic chemotaxis models

Journal of Mathematical Biology, 2010

In this paper, we study the existence and nonexistence of traveling wave solutions for the one-di... more In this paper, we study the existence and nonexistence of traveling wave solutions for the one-dimensional microscopic and macroscopic chemotaxis models. The microscopic model is based on the velocity jump process of Othmer et al. (SIAM J Appl Math 57:1044-1081). The macroscopic model, which can be shown to be the parabolic limit of the microscopic model, is the classical Keller-Segel model, (Keller and Segel in J Theor Biol 30:225-234; 377-380, 1971). In both models, the chemosensitivity function is given by the derivative of a potential function, (v), which must be unbounded below at some point for the existence of traveling wave solutions. Thus, we consider two examples:

Research paper thumbnail of Traveling wave solutions for a one-dimensional crawling nematode sperm cell model

Journal of Mathematical Biology, 2004

In this paper, we proved that the one-dimensional crawling nematode sperm cell model proposed by ... more In this paper, we proved that the one-dimensional crawling nematode sperm cell model proposed by supports traveling wave solutions if there is no disassembly of unbundled filaments in the cell. Uniqueness of traveling wave is established under additional assumptions and numerical examples are also given in the paper. Mathematical methods used include dynamical system techniques, implicit function theorem and global bifurcation theory.

Research paper thumbnail of Some remarks about the wave speed and travelling wave solutions of a nonlinear integral operator

Journal of Mathematical Biology, 1984

In this paper, we extend the existence of travelling wave solutions of a nonlinear operator in th... more In this paper, we extend the existence of travelling wave solutions of a nonlinear operator in the inferior case to higher dimensions and establish the uniqueness of that solution. In addition we determine the sign of the wave speed in a special case.

Research paper thumbnail of Existence of steady-state solutions to predator-prey equations in a heterogeneous environment

Journal of Mathematical Analysis and Applications, 1987

Research paper thumbnail of Vapor Leak Detection for an Underground Storage Tank System

Journal of Environmental Engineering, 2006

... written by Brian Lehtinen and Michael Pyzocha between September 2002 and April 2003 under the... more ... written by Brian Lehtinen and Michael Pyzocha between September 2002 and April 2003 under the supervision of Professor Roger Lui. ... They would also like to thank Professor Yi Hua Ma and Professor David Olinger of the Mechanical Engineering Department at Worcester ...