Browsing Faculty Works, Department of Mathematics by Title
Now showing items 114133 of 224

Mathematical Models of EAntigen Mediated Immune Tolerance and Activation following Prenatal HBV Infection
(PLOS, 20120702)We develop mathematical models for the role of hepatitis B eantigen in creating immunological tolerance during hepatitis B virus infection and propose mechanisms for hepatitis B eantigen clearance, subsequent emergence ... 
Maximality Theorems on the Sum of Two Maximal Monotone Operators and Application to Variational Inequality Problems
(Hindawi, 20160811)Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let and be maximal monotone operators. The maximality of the sum of two maximal monotone operators has been an ... 
Model Reduction by Rational Interpolation
(Siam, 20160701)The last two decades have seen major developments in interpolatory methods for model reduction of largescale linear dynamical systems. Advances of note include the ability to produce (locally) optimal reduced models at ... 
Model Reduction for DAEs with an Application to Flow Control
(SpringerVerlag Berlin, 20150101) 
Model Reduction for Systems with Inhomogeneous Initial Conditions
We consider the model reduction problem for linear timeinvariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable ... 
Model reduction of descriptor systems by interpolatory projection methods
(Siam Publications, 2013)In this paper, we investigate an interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that directly applying the subspace conditions from the ... 
Modeling stochasticity and variability in gene regulatory networks
(20120606)Modeling stochasticity in gene regulatory networks is an important and complex problem in molecular systems biology. To elucidate intrinsic noise, several modeling strategies such as the Gillespie algorithm have been used ... 
Modeling Superparamagnetic Particles in Blood Flow for Applications in Magnetic Drug Targeting
(MDPI, 20170604)Magnetic drug targeting is a technique that involves the binding of medicine to magnetizable particles to allow for more specific transport to the target location. This has recently come to light as a method of drug delivery ... 
Modeling the Mechanisms by Which HIV Associated Immunosuppression Influences HPV Persistence at the Oral Mucosa
(PLOS, 20170106)Human immunodeficiency virus (HIV)infected patients are at an increased risk of coinfection with human papilloma virus (HPV), and subsequent malignancies such as oral cancer. To determine the role of HIVassociated immune ... 
Multiscale immunoepidemiological modeling of withinhost and betweenhost HIV dynamics: systematic review of mathematical models
(PeerJ, 20170928)Objective The objective of this study is to conduct a systematic review of multiscale HIV immunoepidemiological models to improve our understanding of the synergistic impact between the HIV viralimmune dynamics at the ... 
multiplescales spacetime analysis of a randomly perturbed onedimensional waveequation
(AIP Publishing, 197710)An initial value problem for one_dimensional wave propagation is considered; the medium is assumed to be randomly perturbed as a function of both space and time. The stochastic perturbation theory of Papanicolaou and Keller ... 
Multiscale Coupling of Transcranial Direct Current Stimulation to Neuron Electrodynamics: Modeling the Influence of the Transcranial Electric Field on Neuronal Depolarization
(Hindawi Publishing Corporation, 20141023)Transcranial direct current stimulation (tDCS) continues to demonstrate success as a medical intervention for neurodegenerative diseases, psychological conditions, and traumatic brain injury recovery. One aspect of tDCS ... 
Multistate Model Builder (MSMB): a flexible editor for compact biochemical models
(Biomed Central Ltd, 20140404)Background Building models of molecular regulatory networks is challenging not just because of the intrinsic difficulty of describing complex biological processes. Writing a model is a creative effort that calls for more ... 
A Network of SCOP Hidden Markov Models and Its Analysis
(20110523)Background The Structural Classification of Proteins (SCOP) database uses a large number of hidden Markov models (HMMs) to represent families and superfamilies composed of proteins that presumably share the same evolutionary ... 
A New Topological Degree Theory for Perturbations of Demicontinuous Operators and Applications to Nonlinear Equations with Nonmonotone Nonlinearities
(Hindawi, 20161018)Let 𝑋 be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇 : 𝑋 ⊇ 𝐷(𝑇)→ 2𝑋∗ be maximal monotone of type 𝚪𝜙 𝑑 (i.e., there exist 𝑑 ≥ 0 and a nondecreasing ... 
Noncoercive Perturbed Densely Defined Operators and Application to Parabolic Problems
(Hindawi, 20150809)Let 𝑋 be a real locally uniformly convex reflexive separable Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇: 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be maximal monotone and 𝑆 : 𝑋 ⊇ 𝐷(𝑆) → 𝑋∗ quasibounded generalized ... 
Nonlinear Integral Inequalities in Two Independent Variables and Their Applications
(Hindawi Publishing Corporation, 20071105)This paper generalizes results of Cheung and Ma (2005) to more general inequalities with more than one distinct nonlinear term. From our results, some results of Cheung and Ma ( 2005) can be deduced as some special cases. ... 
Nonlinear integral inequalities with delay for discontinuous functions and their applications
(20130911)This paper investigates integral inequalities with delay for discontinuous functions involving two nonlinear terms. We do not require the classes ℘ and ȷ in Gallo and Piccirillo’s paper (Bound. Value Probl. 2009:808124, ... 
NONLINEAR PARAMETRIC INVERSION USING INTERPOLATORY MODEL REDUCTION
(Siam Publications, 20150101)