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This book offers a unified perspective on the study of complex systems for scholars of various disciplines, including mathematics, physics, computer science, biology, economics and social science. The contributions, written by leading scientists, cover a broad set of topics, including new approaches to data science, the connection between scaling limits and conformal field theories, and new ideas on the Legendre duality approach in statistical mechanics of disordered systems. The volume moreover explores results on extreme values of correlated random variables and their connection with the Riemann zeta functions, the relation between diffusion phenomena and complex systems, and the Brownian web, which appears as the universal scaling limit of several probabilistic models. Written for researchers from a broad range of scientific fields, this text examines a selection of recent developments in complex systems from a rigorous perspective.

"Presenting and developing the theory of spin glasses as a prototype for complex systems, this book is a rigorous and up-to-date introduction to their properties. The book combines a mathematical desc

The book shows a very original organization addressing in a non traditional way, but with a systematic approach, to who has an interest in using mathematics in the social sciences.The book is divided

Digital democracy is a hot topic nowadays, its relevance growing along with the impact of computational platforms on our(political) life. Communication is the basal fabric on which society is def

A network is a mathematical object consisting of a set of points that are connected to each other in some fashion by lines. It turns out this simple description corresponds to a bewildering array of s