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 systems in the real world, ranging from technological ones such as the Internet and World Wide Web, biological networks such as that of connections of the nervous systems, food webs or  protein interactions, infrastructural systems such as networks of roads, airports or the power-grid, to patterns of social and professional relationships such as friendship, sex partners, network of Hollywood actors, co-authorship networks and many more. Recent years have witnessed a substantial amount of interest within the scientific community in the properties of these networks. The emergence of the internet in particular, coupled with the widespread availability of inexpensive computing resources has facilitated studies ranging from large scale empirical analysis of networks in the real world, to the development of theoretical models and tools to explore the various properties of these systems. The study of networks is broadly interdisciplinary and central developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology and the social sciences. This book brings together a collection of cutting-edge research in the field from a diverse array of researchers ranging from physicists to social scientists and presents them in a coherent fashion, highlighting the strong interconnections between the different areas. Topics included are social networks and social media, opinion and innovation diffusion, biological and health-related networks, language networks, as well as network theory, community detection, or growth models for Complex Networks.

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 in four parts: (a) a historical part, written by Vittorio Capecchi which helps us understand the changes in the relationship between mathematics and sociology by analyzing the mathematical models of Paul F. Lazarsfeld, the model of simulation and artificial societies, models of artificial neural network and considering all the changes in scientific paradigms considered; (b) a part coordinated by Pier Luigi Contucci on mathematical models that consider the relationship between the mathematical models that come from physics and linguistics to arrive at the study of society and those which are born within sociology and economics; (c) a part coordinated by Massimo Buscema analyzing models of artificial neural networks; (d) a part coordinated by Bruno D'Amore which considers the relationship between mathematics and art. The title of the book "Mathematics and Society" was chosen because the mathematical applications exposed in the book allow you to address two major issues: (a) the general theme of technological innovation and quality of life (among the essays are on display mathematical applications to the problems of combating pollution and crime, applications to mathematical problems of immigration, mathematical applications to the problems of medical diagnosis, etc.) (b) the general theme of technical innovation and creativity, for example the art and mathematics section which connects to the theme of creative cities. The book is very original because it is not addressed only to those who are passionate about mathematical applications in social science but also to those who, in different societies, are: (a) involved in technological innovation to improve the quality of life; (b) involved in the wider distribution of technological innovation in different areas of creativity (as in the project "Creative Cities Network" of UNESCO).

A network is a mathematical object consisting of a set of pointsthat are connected to each other in somefashion by lines. It turns out thissimple descriptioncorresponds to a bewildering array of systems in the real world, ranging from technological ones such as the Internet and WorldWide Web, biological networks such as that of connections of thenervous systems, food webs or protein interactions, infrastructural systems such as networks of roads, airports or the power-grid, to patterns of social and professional relationships such as friendship, sex partners, network ofHollywood actors, co-authorship networks and many more.

Recent years have witnessed a substantial amount of interest within thescientific community in the properties of these networks. The emergenceof the internet in particular, coupled with the widespread availability ofinexpensive computing resources has facilitated studies ranging fromlarge scale empirical analysis of networks in the real world, to the developmentof theoretical models and tools to explore the various properties of these systems.The study of networks is broadly interdisciplinary and central developments haveoccurred in many fields, including mathematics, physics, computer and informationsciences, biology and the social sciences.

This book brings together a collectionof cutting-edge research in the field from adiversearray of researchers ranging fromphysicists to social scientists and presents them in acoherent fashion, highlighting thestrong interconnections between the different areas. Topicsincluded are social networks and social media, opinion and innovation diffusion, biological and health-related networks, language networks, as well as network theory, community detection, or growth models for Complex Networks."

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 in four parts: (a) a historical part, written by Vittorio Capecchi which helps us understand the changes in the relationship between mathematics and sociology by analyzing the mathematical models of Paul F. Lazarsfeld, the model of simulation and artificial societies, models of artificial neural network and considering all the changes in scientific paradigms considered; (b) a part coordinated by Pier Luigi Contucci on mathematical models that consider the relationship between the mathematical models that come from physics and linguistics to arrive at the study of society and those which are born within sociology and economics; (c) a part coordinated by Massimo Buscema analyzing models of artificial neural networks; (d) a part coordinated by Bruno D'Amore which considers the relationship between mathematics and art.

The title of the book "Mathematics and Society" was chosen because the mathematical applications exposed in the book allow you to address two major issues: (a) the general theme of technological innovation and quality of life (among the essays are on display mathematical applications to the problems of combating pollution and crime, applications to mathematical problems of immigration, mathematical applications to the problems of medical diagnosis, etc.) (b) the general theme of technical innovation and creativity, for example the art and mathematics section which connects to the theme of creative cities.

The book is very original because it is not addressed only to those who are passionate about mathematical applications in social science but also to those who, in different societies, are: (a) involved in technological innovation to improve the quality of life; (b) involved in the wider distribution of technological innovation in different areas of creativity (as in the project "Creative Cities Network" of UNESCO).

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 defined, and it appears obvious that the civic organisation and politics itself should take the opportunities the "digital revolution" offers. Institutional inertia, nevertheless, causes large delays in updating and adapting. Therefore, the balance between participation and delegated representation is now facing a crisis. A thorough understanding of the factors involved in participation is a first step towards providing solutions. Using the Internet to fill the gap and build a digital democracy provides an opportunity, along with several risks that need to be carefully analysed. It needs to be implemented using a fully inter- and trans-disciplinary perspective. The six contributions included in this State-of-the Art Survey present research in the field of social sciences as well as mathematics and computer science and aim at contributing to a better understanding of the potential and dangers of digital democracy, helping readers go beyond the misunderstandings, the misconceptions,and the conceptual and practical abuses that the very notion of democracy is undergoing during this age of technological revolution and social turmoils.

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 description with a physical insight of spin glass models. Topics covered include the physical origins of those models and their treatment with replica theory; mathematical properties like correlation inequalities and their use in the thermodynamic limit theory; main exact solutions of the mean field models and their probabilistic structures; and the theory of the structural properties of the spin glass phase such as stochastic stability and the overlap identities. Finally, a detailed account is given of the recent numerical simulation results and properties, including overlap equivalence, ultrametricity and decay of correlations. The book is ideal for mathematical physicists and probabilists working in disordered systems.