The aim of this volume is to make a connection among advanced mathematical tools and application to real problems. There are many different mathematical structures analyzed in the book and all of them are in important applications, like statistics and biology, neural networks and financial markets, asymptotic methods for partial differential equations and the problem of tsunami propagation. Plasma physics has been given a new approach, using focal points in analogy to the theory of tsunami waves.

Di usion-reaction processes are ubiquitous in nature: they border and bridge diverse research areas such as physics, chemistry, biology and sociology. This book addresses systems where the transport properties of the reactants largely control the kinetics of the process. In this context, the need to account for the role played by the underlying, possibly complex, topology as well as by many-body effects prompts us to go over standard reaction-diffusion equations and to develop proper techniques able to work out the interplay between such features. Applications considered span a vast range of interdisciplinary fields and the systems analyzed can be as different as diffusion of charge carriers, virus spreading within a population, chemical reactions, or marketing strategies.