Evolution and stochastic dynamics in complex systems

The dissertation provides an insight on the mathematical modeling of two complex systems. Chapter 1-4 are about the biophysical model we developed for enzyme evolution. The model predicts the reaction rates as a function of the enzyme sequence. The free energies in Michaelis-Menten kinetics are represented as a function of one amino-acid contribution and two amino-acid pairs of the enzyme sequence. Our model predicts reaction-rates with high accuracy and relatively few coupling terms. The sparseness in coupling terms results in highly interpretable Michaelis-Menten energy landscapes which exhibit little non-linearity. Chapter 5-9 talk about modeling first-passage properties of random-walks on a community-structured network. The properties are exploited in developing an algorithm to partition the network into communities. On testing our algorithm on multiple artificial and real-world networks, we find that it performs better or as well as the other competitive algorithms.Ph.D.Includes bibliographical reference