Maximum number of fixed points and cycle structure in Boolean networks

Type of event: 
UCN@Sophia Labex seminar
Julio Aracena
Speaker's affiliation: 
Université de Concepción, Chili
Tue, 2016-12-06 14:00 - 15:00
EURECOM, Room 101
Refreshments/coffee will be served after the talk. The UCN@Sophia labex seminar is sponsored by the labex UCN@Sophia.




A Boolean network is a system of a finite set of interacting Boolean variables, which evolve, in a discrete time, according to a predefined rule. They have applications in many areas, including the modeling of neural and gene networks, social systems, and in information theory, for the network coding problem. Among the many dynamical properties that can be studied, fixed points are of special interest, since they correspond to stable states of the system and often have a strong meaning.  For instance, some network coding solvability problems with binary alphabet can be reduced to problems of fixed points in Boolean networks.

In this talk I will show some results about how the structure of the interaction graph of a Boolean network can determine the maximum number of fixed points of the network. In particular, I will exhibit some optimal upper bounds on the number of fixed points in terms of the cycle structure of the interaction graph for certain families of networks.



Short bio: 


Julio Aracena Lucero a obtenu son diplôme d'ingénieur mathématicien en 1997 à l'Université du Chili, et son doctorat en mathématiques appliquées à l'Université de Grenoble et à l'Université du Chili en 2001. Il est reconnu pour ses travaux sur les systèmes dynamiques discrets. Sa thématique principale porte sur les relations entre le graphe d'interaction de ces systèmes et leurs comportements limites. Il a, en particulier, établi une borne fondamentale sur le nombre de points fixes d'un système dynamique discret qui ne dépend que de la structure des cycles de son graphe d'interaction. Il a rejoint en 2004 le Département d'Ingénierie Mathématique de la Université de Concepción, Chili. Il a été nommé full professor en janvier de  2016. Il est actuellement en séjour sabbatique de six mois dans l'équipe MDSC-I3S financé par le Labex UCN@Sophia et l'Université de Nice


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