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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling
The Analysis Of Neural Heterogeneity Through Mathematical And Statistical Methods, Kyle Wendling
Theses and Dissertations
Diversity of intrinsic neural attributes and network connections is known to exist in many areas of the brain and is thought to significantly affect neural coding. Recent theoretical and experimental work has argued that in uncoupled networks, coding is most accurate at intermediate levels of heterogeneity. I explore this phenomenon through two distinct approaches: a theoretical mathematical modeling approach and a data-driven statistical modeling approach.
Through the mathematical approach, I examine firing rate heterogeneity in a feedforward network of stochastic neural oscillators utilizing a high-dimensional model. The firing rate heterogeneity stems from two sources: intrinsic (different individual cells) and network …
An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper
An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper
Theses and Dissertations
Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.
First, we create a …