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Featured researches published by Lester Caudill.


Inverse Problems | 1998

Stability and Reconstruction for an Inverse Problem for the Heat Equation

Kurt Bryan; Lester Caudill

We examine the inverse problem of determining the shape of some unknown portion of the boundary of a region from measurements of the Cauchy data for solutions to the heat equation on . By suitably linearizing the inverse problem we obtain uniqueness and continuous dependence results. We propose an algorithm for recovering estimates of the unknown portion of the surface and use the insight gained from a detailed analysis of the inverse problem to regularize the inversion. Several computational examples are presented.


Inverse Problems | 2005

Reconstruction of an unknown boundary portion from Cauchy data in n dimensions

Kurt Bryan; Lester Caudill

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples.


CBE- Life Sciences Education | 2010

Impact of Interdisciplinary Undergraduate Research in Mathematics and Biology on the Development of a New Course Integrating Five STEM Disciplines

Lester Caudill; April Hill; Kathy Hoke; Ovidiu Lipan

Funded by innovative programs at the National Science Foundation and the Howard Hughes Medical Institute, University of Richmond faculty in biology, chemistry, mathematics, physics, and computer science teamed up to offer first- and second-year students the opportunity to contribute to vibrant, interdisciplinary research projects. The result was not only good science but also good science that motivated and informed course development. Here, we describe four recent undergraduate research projects involving students and faculty in biology, physics, mathematics, and computer science and how each contributed in significant ways to the conception and implementation of our new Integrated Quantitative Science course, a course for first-year students that integrates the material in the first course of the major in each of biology, chemistry, mathematics, computer science, and physics.


Bulletin of Mathematical Biology | 2013

A Single-Parameter Model of the Immune Response to Bacterial Invasion

Lester Caudill

The human immune response to bacterial pathogens is a remarkably complex process, involving many different cell types, chemical signals, and extensive lines of communication. Mathematical models of this system have become increasingly high-dimensional and complicated, as researchers seek to capture many of the major dynamics. In this paper, we argue that, in some important instances, preference should be given to low-dimensional models of immune response, as opposed to their high-dimensional counterparts. One such model is analyzed and shown to reflect many of the key phenomenological properties of the immune response in humans. Notably, this model includes a single parameter that, when combined with a single set of reference parameter values, may be used to quantify the overall immunocompetence of individual hosts.


Current Treatment Options in Infectious Diseases | 2016

The Role of Mathematical Modeling in Designing and Evaluating Antimicrobial Stewardship Programs

Lester Caudill; Joanna R. Wares

Opinion statementAntimicrobial agent effectiveness continues to be threatened by the rise and spread of pathogen strains that exhibit drug resistance. This challenge is most acute in healthcare facilities where the well-established connection between resistance and suboptimal antimicrobial use has prompted the creation of antimicrobial stewardship programs (ASPs). Mathematical models offer tremendous potential for serving as an alternative to controlled human experimentation for assessing the effectiveness of ASPs. Models can simulate controlled randomized experiments between groups of virtual patients, some treated with the ASP measure under investigation, and some without. By removing the limitations inherent in human experimentation, including health risks, study cohort size, possible number of replicates, and effective study duration, model simulations can provide valuable information to inform decisions regarding the design of new ASPs, as well as evaluation and improvement of existing ASPs. To date, the potential of mathematical modeling methods in evaluating ASPs is largely untapped and much work remains to be done to leverage this potential.


Bulletin of Mathematical Biology | 2018

A Mathematical Model of the Inflammatory Response to Pathogen Challenge

Lester Caudill; Fiona Lynch

The human body’s immune response to bacterial challenge, even when successful in controlling the infection, can result in negative consequences for the host, including reduced functionality of associated tissues. We present and analyze a low-dimensional mathematical model of this immune response to pathogen invasion, incorporating the coordinated actions of active immune cells, and both pro- and anti-inflammatory cytokines. The model simulates both the positive (pathogen reduction) and negative (local tissue dysfunction) effects of the immune response and includes the important role of immunologic memory in the process of a return to stasis. This differential equation-based model is sufficiently general to be applicable to a wide range of human tissues and organs.


Electronic Journal of Differential Equations, Conference 01 C-1 | 1996

Uniqueness for a Boundary Identification Problem in Thermal Imaging

Kurt Bryan; Lester Caudill


The journal of college science teaching | 2012

Challenging Disciplinary Boundaries in the First Year: A New Introductory Integrated Science Course for STEM Majors.

Lisa Gentile; Lester Caudill; Mirela Fetea; April Hill; Kathy Hoke; Barry Lawson; Ovidiu Lipan; Michael Kerckhove; Carol A. Parish; Krista J Stenger; Doug Szajda


winter simulation conference | 2013

A hybrid agent-based and differential equations model for simulating antibiotic resistance in a hospital ward

Lester Caudill; Barry Lawson


Proceedings of the ASME Design Engineering Technical Conferences | 1995

Stability and Resolution in Thermal Imaging

Lester Caudill; Kurt Bryan

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Kurt Bryan

Rose-Hulman Institute of Technology

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April Hill

University of Richmond

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Doug Szajda

University of Richmond

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Fiona Lynch

University of Richmond

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