Martedi' 13 novembre alle 9,30 in Aula Buzano (Politecnico di Torino,
DISMA) il prof
Badal Joshi (California State University San Marcos)
terrà un seminario dal titolo
Graphical symmetries of reaction networks and their stationary measures
Abstract: Reaction networks are used to model chemical reactions,
biochemical reactions, interacting populations in ecology, genetics and
infectious disease dynamics among many other systems. Depending on the
system scale, three most commonly used models are continuous-time Markov
chain (CTMC), stochastic differential equations and ordinary differential
equations (ODE). With increased data and scientific focus shifting towards
biochemistry which often involves populations as small as few tens of
molecules, CTMC models have seen dramatic increase in relevance. The
long-term dynamics of a continuous-time Markov chain model are described by
its stationary distribution. In general, the explicit form of the
stationary distribution is impossible to obtain even for very small
networks. However, when the network has some natural symmetries, we can
obtain the explicit stationary distribution and it can be connected with
the equilibria of the corresponding ODE system. We will discuss the
symmetries of reaction balance, complex balance, reaction vector balance,
and cycle balance and their properties in both the deterministic (ODE)
setting and stochastic (CTMC) setting. We will also discuss the relations
between the various forms of balance and the connection with existence and
form of the stationary distribution.
Cordialmente,
Enrico Bibbona
Probability, Statistics and Optimization group
Department of Mathematical Sciences "G. L Lagrange"
Politecnico di Torino