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Equivalences in differential and algebraic systems: theoretical and practical aspects

Tognazzi, Stefano (2019) Equivalences in differential and algebraic systems: theoretical and practical aspects. Advisor: Tribastone, Prof. Mirco. pp. 99. [IMT PhD Thesis]

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Abstract

Systems of ordinary differential equations (ODEs) are a widespread model to describe a variety of dynamical systems. When the size of these systems becomes large to find a numerical solution, model reduction is needed. Although many state aggregation notions have been developed in the literature in this dissertation we focus on backward differential equivalence (BDE) that identifies variables of ODE systems that have identical solutions whenever starting from the same initial conditions. This notion has been used effectively as a technique of reduction for chemical reaction networks. In this dissertation we aim at extending the capabilities of backward differential equivalence. We explore the following directions of research: first, we investigate the relationship between BDE and the notions of centrality on networks. Centrality measures address the task of assigning a measure of importance to each node in a network, a possible example being PageRank. Then, we study differential algebraic equations (DAEs), a widespread dynamical model that describes continuosly evolving quantities defined with differential equations, subject to constraints expressed through algebraic relationships. We investigate how we can extend the line of research on backward differential equivalence on ODEs to a notion of equivalence that relates DAEs variables that have equal solutions at all time points. Ultimately, we extend the practical capabilities of BDE on CRNs. Discovering relations between CRNs is a relevant problem in computational system biology. In this dissertation we investigate how we can combine BDE with an heuristic technique to construct a state-of-the-art algorithm to find relationships between CRNs.

Item Type: IMT PhD Thesis
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
PhD Course: Computer science and systems engineering
Identification Number: 10.6092/imtlucca/e-theses/279
Date Deposited: 14 Nov 2019 09:48
URI: http://e-theses.imtlucca.it/id/eprint/279

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