We study a network by inducing a topology capable of reflecting its key properties; e.g., RNA structures can be considered as contact graphs and are viewed as triangulations of orientable surfaces. Here the topological space is induced by passing from a simple graph to a fatgraph which allows us to categorize structures by genus. A topology can also be induced by specifying certain complexes within the network and we currently work on formalizing this in the graphical homology framework.
RNA plays a central role within living cells by facilitating a variety of biochemical tasks. RNA acts as a messenger linking DNA and proteins and furthermore catalyzes reactions just as proteins. Consequently, RNA embodies both genotypic legislative and phenotypic executive functions. We study the dynamics of evolving RNA populations in the context of genotypic neutrality, i.e. phenotypically equivalent RNA sequences form vast extended neutral networks that facilitate evolution.
We study the relationship between networks of interacting entities and the dynamics they generate. These phase spaces are obtained by certain sequential updates; the system itself specifies which update orders are of relevance; e.g., we study systems of viral outbreaks, where we model the shockwave of infected entities at a given time using trees. It is important to characterize locality in the system and how interactions amongst entities can be expressed.
|Cotiso Andrei Bura||Graduate Research Assistant|