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Full-Text Articles in Physical Sciences and Mathematics
A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill
A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill
Department of Math & Statistics Faculty Publications
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 values, …
Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan
Stability And Resolution In Thermal Imaging, Lester Caudill, Kurt Bryan
Department of Math & Statistics Faculty Publications
This paper examines an inverse problem which arises in thermal imaging. We investigate the problem of detecting and imaging corrosion in a material sample by applying a heat flux and measuring the induced temperature on the sample's exterior boundary. The goal is to identify the profile of some inaccessible portion of the boundary. We study the case in which one has data at every point on the boundary of the region, as well as the case in which only finitely many measurements are available. An inversion procedure is developed and used to study the stability of the inverse problem for …