We show that numerical approximations of Kolmogorov complexity (K) of graphs and networks capture some group-theoretic and topological properties of empirical networks, ranging from metabolic to social networks, and of small synthetic networks that we have produced. That K and the size of the...

We study the evolution of asexual microorganisms with small mutation rate in fluctuating environments, and develop techniques that allow us to expand the formal solution of the evolution equations to first order in the mutation rate. Our method can be applied to both discrete time and continuous...

Mapping sequences onto biopolymer structures is characterized by redundancy since the numbers of sequences exceed the numbers of structures. The degree of Redundancy depends on the notion of structure. Two classes of biopolymers, RNA molecules and proteins are considered in detail. A general...

We describe statistical inference in continuous time Markov processes of DNA sequences related by a phylogenetic tree. The maximum likelihood estimator can be found by the expectation maximization (EM) algorithm and an expression for the information matrix is also derived. We provide explicit...

There is an intrinsic relationship between the molecular evolution in primordial period and genomic or proteomic properties of contemporary species. The genomic data may help us understand the driving force of evolution of life at a molecular level. In the absence of evidence, numerous problems...

Recent papers have promoted the view that model-based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested...

Fitness landscapes are an important concept in molecular evolution since evolutionary adaptation as well as {\it in vitro} selection of biomolecules can be viewed as a hill-climbing-like process. Global features of landscapes can be described by statistical measures such as correlation functions...

Evolution has created the complexity of the animate world and deciphering the language of evolution is the key toward understanding nature. The dynamics of evolution is simplified by considering it as a superposition of three less sophisticated processes: population dynamics, population support...

RNA and protein molecules were found to be both templates for replication and specific catalysts for biochemical reactions. RNA molecules, although very difficult to obtain via plausible synthetic pathways under prebiotic conditions, are the only candidates for early replicons. Only they are...