Modeling of birth-death and diffusion processes in biological complex environments

Vitali, Silvia (2018) Modeling of birth-death and diffusion processes in biological complex environments, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Fisica, 30 Ciclo. DOI 10.6092/unibo/amsdottorato/8579.
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Abstract

This thesis is centered on the theory of stochastic processes and their applications in biological systems characterized by a complex environment. Three case studies have been modeled by the use of the three fundamental tools of stochastic processes: the master equation (ME), the stochastic differential equation (SDE) and the partial differential equation (PDE). The principal approach here applied to deal with complexity is the characterization of the system by means of probability distributions describing each a parameter of the model or the introduction of fractional order derivatives to include non-local and memory effects maintaining the linearity in the equations. In Chapter 1 we briefly review the theory of stochastic processes. In Chapter 2 we derive a birth-death process master equation to test if Long Interspersed Elements (LINEs) can be modeled according to the neutral theory of biodiversity. In Chapter 3 we derive a model of anomalous diffusion based on a Langevin approach in which anomalous behavior arise in the asymptotic intermediate state as a consequence of the heterogeneity of the system, from the superposition of Ornstein-Uhlenback processes. In Chapter 4 we propose an extension of the cable equation, used to describe anomalous diffusion phenomena as the signal conduction in spiny dendrites, by introducing a Caputo time fractional derivative.

Abstract
Tipologia del documento
Tesi di dottorato
Autore
Vitali, Silvia
Supervisore
Co-supervisore
Dottorato di ricerca
Ciclo
30
Coordinatore
Settore disciplinare
Settore concorsuale
Parole chiave
Fractional calculus; anomalous diffusion; Langevin equation; Transposable elements; master equation; dendrites; birth-death process; ecological model; evolution.
URN:NBN
DOI
10.6092/unibo/amsdottorato/8579
Data di discussione
20 Aprile 2018
URI

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