Title: Homeostasis in Input-Output Networks: Structure, Classification and Applications
Abstract: Homeostasis occurs in a biological or biochemical system when some output variable remains approximately constant as some input parameters vary over some range. Recently, Golubitsky and Stewart [Homeostasis, Singularities and Networks. J. Math. Biol. 74 (2017) 387-407] introduced the notion of ‘infinitesimal homeostasis’ allowing the use of implicit differentiation and singularity theory to study homeostasis in systems of ordinary differential equations (ODEs). Generally speaking, ODEs appearing in the life sciences are encoded by ‘networks of ODEs’. Nodes (vértices) correspond to state variables and links (directed arrows) indicate which nodes are coupled to which. What distinguishes a network of ODEs from a generic system of differential equations is the capability to keep track of the output from each node individually. Hence, infinitesimal homeostasis is related to occurrence of ‘singularities’ at individual nodes. In this talk we explain a new approach to the study of the combinatorial structure and classification of homeostasis in ‘input-output networks’, that is, networks of ODES where we keep track of the output from a fixed node as well as the node(s) that depend on the external input parameters.
Bio: Bachelor in Mathematics from the University of São Paulo (1995), Master in Applied Mathematics from the University of São Paulo (1998), PhD in Applied Mathematics from the University of São Paulo (2002) and Free Professor in Applied Mathematics from the University of São Paulo (2010 ). He has experience in the areas of Applied Mathematics, Bioinformatics and Biostatistics. Mainly active in the following topics: pattern formation through symmetry breaks and synchrony breaks in dynamic systems and their applications in biomathematics; stochastic processes applied to modeling viral evolution and gene expression; bioinformatics and statistical genomics with applications in molecular biology. (Source: Lattes Curriculum)