Within the field of modeling complex objects in natural sciences, which considers systems that consist of a large number of interacting parts, a good tool for analyzing and fitting models is the theory of random evolutionary systems, considering their asymptotic properties and large deviations. In Random Evolutionary Systems we consider these systems in terms of the operators that appear in the schemes of their diffusion and the Poisson approximation. Such an approach allows us to obtain a number of limit theorems and asymptotic expansions of processes that model complex stochastic systems, both those that are autonomous and those dependent on an external random environment. In this case, various possibilities of scaling processes and their time parameters are used to obtain different limit results.

Big Mechanisms in Systems Biology: Big Data Mining, Network Modeling, and Genome-Wide Data Identification explains big mechanisms of systems biology by system identification and big data mining methods using models of biological systems. Systems biology is currently undergoing revolutionary changes in response to the integration of powerful technologies. Faced with a large volume of available literature, complicated mechanisms, small prior knowledge, few classes on the topics, and causal and mechanistic language, this is an ideal resource. This book addresses system immunity, regulation, infection, aging, evolution, and carcinogenesis, which are complicated biological systems with inconsistent findings in existing resources. These inconsistencies may reflect the underlying biology time-varying systems and signal transduction events that are often context-dependent, which raises a significant problem for mechanistic modeling since it is not clear which genes/proteins to include in models or experimental measurements. The book is a valuable resource for bioinformaticians and members of several areas of the biomedical field who are interested in an in-depth understanding on how to process and apply great amounts of biological data to improve research.