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Graduate Thesis of Luis M. Gómez

Gómez, Luis M.ProgramPhD in Applied Sciences with mention in Mathematical Engineering, Universidad de Concepción
Enrollment Year2009
Senior Year2015
Thesis TitleDynamics of discrete networks with deterministic updates schedules. Application to genetic regulatory networks

Thesis Summary:

Boolean networks have been used as models of gene regulation networks and other biological networks, as well as other types of distributed dynamical systems. A key element in these models is the update scheme, which indicates the order in which the states must be updated. Equivalence classes of deterministic update schemes can be defined according to the tag associated with the network (update digraph), where elements in the same equivalence class have the same dynamic behavior. In this doctoral thesis, we study the relationship between the update digraph and the dynamic properties of the associated network. More precisely, we study the problem of determining necessary and sufficient conditions for the preservation of boundary cycles of Boolean networks iterated under non-equivalent update schemes. We show that the related complexity problems lie in the class of NP-hard problems and we prove that the information provided by the update digraphs is not sufficient to determine if two Boolean networks share boundary cycles. At the same time, we treat the inverse problem with the update schemes, which consists of, given a Boolean network and a dynamic characteristic (for example a limit cycle), to determine if there is an update scheme such that the network iterated with this Scheme has this characteristic in its dynamic behavior. These types of problems usually arise in the reconstruction of networks based on observed data of their dynamics. We study the relationship between the algorithmic complexity of these types of problems and the structure of the interaction digraph and the type of activation functions of the networks. In addition, we give some classes of networks in which these problems are polynomial.

Thesis Director(s) Julio Aracena
Thesis Project Approval Date2011, October 21
Thesis Defense Date2015, January 06
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ISI Publications from the Thesis

Julio ARACENA, Luis GOMEZ, Lilian SALINAS: Limit cycles and update digraphs in Boolean networks. Discrete Applied Mathematics, vol. 161, 1-2, pp. 1-12, (2013).

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