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Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds
Identifying Important Parameters In The Inflammatory Process With A Mathematical Model Of Immune Cell Influx And Macrophage Polarization, Marcella Torres, Jing Wang, Paul J. Yannie, Shobha Ghosh, Rebecca A. Segal, Angela M. Reynolds
Department of Math & Statistics Faculty Publications
In an inflammatory setting, macrophages can be polarized to an inflammatory M1 phenotype or to an anti-inflammatory M2 phenotype, as well as existing on a spectrum between these two extremes. Dysfunction of this phenotypic switch can result in a population imbalance that leads to chronic wounds or disease due to unresolved inflammation. Therapeutic interventions that target macrophages have therefore been proposed and implemented in diseases that feature chronic inflammation such as diabetes mellitus and atherosclerosis. We have developed a model for the sequential influx of immune cells in the peritoneal cavity in response to a bacterial stimulus that includes macrophage …
Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam
Critical Fault-Detecting Time Evaluation In Software With Discrete Compound Poisson Models, Min-Hsiung Hsieh, Shuen-Lin Jeng, Paul Kvam
Department of Math & Statistics Faculty Publications
Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure …
Mean Value Theorems For Riemannian Manifolds Via The Obstacle Problem, Brian Benson, Ivan Blank, Jeremy Lecrone
Mean Value Theorems For Riemannian Manifolds Via The Obstacle Problem, Brian Benson, Ivan Blank, Jeremy Lecrone
Department of Math & Statistics Faculty Publications
We develop some of the basic theory for the obstacle problem on Riemannian manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all within the integral.
Perturbed Obstacle Problems In Lipschitz Domains: Linear Stability And Nondegeneracy In Measure, Ivan Blank, Jeremy Lecrone
Perturbed Obstacle Problems In Lipschitz Domains: Linear Stability And Nondegeneracy In Measure, Ivan Blank, Jeremy Lecrone
Department of Math & Statistics Faculty Publications
We consider the classical obstacle problem on bounded, connected Lipschitz domains D⊂Rn. We derive quantitative bounds on the changes to contact sets under general perturbations to both the right-hand side and the boundary data for obstacle problems. In particular, we show that the Lebesgue measure of the symmetric difference between two contact sets is linearly comparable to the L1-norm of perturbations in the data.