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Dynamics and Structure: From Microtubule Networks to Population Networks
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Dynamics and Structure: From Microtubule Networks to Population Networks. |
| 개인저자 | Brooks, Heather. |
| 단체저자명 | The University of Utah. Mathematics. |
| 발행사항 | [S.l.]: The University of Utah., 2018. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2018. |
| 형태사항 | 94 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-04B. Dissertation Abstract International |
| ISBN | 9781088325483 |
| 학위논문주기 | Thesis (Ph.D.)--The University of Utah, 2018. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-04, Section: B.
Advisor: Bressloff, Paul. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | The interplay of dynamics and structure is a common theme in both mathematics and biology. In this thesis, the author develops and analyzes mathematical models that give insight into the dynamics and structure of a variety of biological applications. The author presents a variety of contributions in applications of mathematics to explore biological systems across several scales. First, she analyzes pattern formation in a partial differential equation model based on two interacting proteins that are undergoing passive and active transport, respectively. This work is inspired by a longstanding problem in identifying a biophysical mechanism for the control of synaptic density in C. elegans and leads to a novel mathematical formulation of Turing-type patterns in intracellular transport. The author also demonstrates the persistence of these patterns on growing domains, and discusses extensions for a two-dimensional model. She then presents two models that explore how stochastic processes affect intracellular dynamics. First, the author and her collaborators derive effective stochastic differential equations that describe intermittent virus trafficking. Next, she shows how ion channel fluctuations lead to subthreshold oscillations in neuron models. In the final chapter, she discusses two projects for ongoing and future work: one on modeling parasite infection on dynamic social networks, and another on the bifurcation structure of localized patterns on lattices. All of these projects, presented together, chronicle the journey of the author through her mathematical development and attempts to identify, discover, create, and communicate mathematics that inspires and excites. |
| 일반주제명 | Applied mathematics. Differential equations. Mathematical models. Biophysics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
