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Complex Dynamical Systems: Definitio...

Xin, Ying.

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Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information./
Author:	Xin, Ying.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2018,
Description:	242 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-02, Section: B.
Contained By:	Dissertations Abstracts International80-02B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10954372
ISBN:	9780438238374

Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information.
Xin, Ying.

Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information. - Ann Arbor : ProQuest Dissertations & Theses, 2018 - 242 p.

Source: Dissertations Abstracts International, Volume: 80-02, Section: B.

Thesis (Ph.D.)--Ohio University, 2018.

This item must not be sold to any third party vendors.

Dynamical systems as models of complex biological systems are powerful tools that have been used to study problems in biology. This dissertation first discusses a problem in the theory of dynamical systems on the definition of topological entropy. Then dynamical systems are applied in two different fields of biology: proliferation of monolayer epithelia and the spread of infections and information. The notion of topological entropyis a measure of the complexity of a dynamical system. It can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution ϵ within T time units. It can then be formally defined as a limit of a limit superior that involves either covering numbers, or separation numbers, or spanning numbers. If covering numbers are used, the limit superior reduces to a limit. While it has been generally believed that the latter may not necessarily be the case when the definition is based on separation or spanning numbers, no actual counterexamples appear to have been previously known. Here we fill this gap in the literature by constructing such counterexamples. We then use dynamical systems to study the proliferation of epithelia. Epithelia are sheets of tightly adherent cells that line both internal and external surfaces in metazoans (multicellular animals). Mathematically, a cell in an epithelial tissue can be modeled as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. Multiple types of mathematical models have been proposed to explain this phenomenon. Among the most parsimonious of such models are topological ones that take into account only the number of sides of a given cell and the neighborhood relation between cells. The model studied here is a refinement of a previously published such model (Patel et al., PLoS Comput. Biol., 2009). While using the same modeling framework as that paper, we introduce additional options for the choice of the endpoints of the cleavage plane in the simulated development of epithelial tissues. Some of these options appear to be more biologically realistic approximations of known mechanisms that influence the cleavage plane orientation. A comparative analysis of comprehensive simulations for relevant combinations of both previously studied and our newly designed options is reported here. We compared the outcomes with the empirical distributions of the same five organisms as in (Patel et al., 2009), Drosophila (fruit fly), Hydra (closely related to jellyfish), Xenopus (clawed frog), Cucumber, and Anagallis (a flowering plant). We found that combinations of some of our new options consistently gave better fits with each of these data sets than combinations of previously studied options for choosing the cleavage plane. We also examine ODE models of epidemic spreading with a preventivebehavioral response that is triggered by awareness of the infection. Previous research on such models has mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.

ISBN: 9780438238374Subjects--Topical Terms:

1669109
Applied Mathematics.
Subjects--Index Terms:

Cell topology

Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information.
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245 1 0 $a Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2018
300 $a 242 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-02, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Just, Winfried.
502 $a Thesis (Ph.D.)--Ohio University, 2018.
506 $a This item must not be sold to any third party vendors.
506 $a This item must not be added to any third party search indexes.
520 $a Dynamical systems as models of complex biological systems are powerful tools that have been used to study problems in biology. This dissertation first discusses a problem in the theory of dynamical systems on the definition of topological entropy. Then dynamical systems are applied in two different fields of biology: proliferation of monolayer epithelia and the spread of infections and information. The notion of topological entropyis a measure of the complexity of a dynamical system. It can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution ϵ within T time units. It can then be formally defined as a limit of a limit superior that involves either covering numbers, or separation numbers, or spanning numbers. If covering numbers are used, the limit superior reduces to a limit. While it has been generally believed that the latter may not necessarily be the case when the definition is based on separation or spanning numbers, no actual counterexamples appear to have been previously known. Here we fill this gap in the literature by constructing such counterexamples. We then use dynamical systems to study the proliferation of epithelia. Epithelia are sheets of tightly adherent cells that line both internal and external surfaces in metazoans (multicellular animals). Mathematically, a cell in an epithelial tissue can be modeled as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. Multiple types of mathematical models have been proposed to explain this phenomenon. Among the most parsimonious of such models are topological ones that take into account only the number of sides of a given cell and the neighborhood relation between cells. The model studied here is a refinement of a previously published such model (Patel et al., PLoS Comput. Biol., 2009). While using the same modeling framework as that paper, we introduce additional options for the choice of the endpoints of the cleavage plane in the simulated development of epithelial tissues. Some of these options appear to be more biologically realistic approximations of known mechanisms that influence the cleavage plane orientation. A comparative analysis of comprehensive simulations for relevant combinations of both previously studied and our newly designed options is reported here. We compared the outcomes with the empirical distributions of the same five organisms as in (Patel et al., 2009), Drosophila (fruit fly), Hydra (closely related to jellyfish), Xenopus (clawed frog), Cucumber, and Anagallis (a flowering plant). We found that combinations of some of our new options consistently gave better fits with each of these data sets than combinations of previously studied options for choosing the cleavage plane. We also examine ODE models of epidemic spreading with a preventivebehavioral response that is triggered by awareness of the infection. Previous research on such models has mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.
590 $a School code: 0167.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
653 $a Cell topology
653 $a Dynamical systems
653 $a Epidemic models
653 $a Epithelial morphogenesis
653 $a Mathematical modeling
653 $a Topological entropy
690 $a 0364
690 $a 0405
710 2 $a Ohio University. $b Mathematics (Arts and Sciences). $3 3544843
773 0 $t Dissertations Abstracts International $g 80-02B.
790 $a 0167
791 $a Ph.D.
792 $a 2018
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10954372