This book concerns the use of concepts from statistical physics in the description of financial systems. The authors illustrate the scaling concepts used in probability theory, critical phenomena, and fully developed turbulent fluids. These concepts are then applied to financial time series. The authors also present a stochastic model that displays several of the statistical properties observed in empirical data. Statistical physics concepts such as stochastic dynamics, short- and long-range correlations, self-similarity and scaling permit an understanding of the global behaviour of economic systems without first having to work out a detailed microscopic description of the system. Physicists will find the application of statistical physics concepts to economic systems interesting. Economists and workers in the financial world will find useful the presentation of empirical analysis methods and well-formulated theoretical tools that might help describe systems composed of a huge number of interacting subsystems.

Many complex systems present an intrinsic bipartite nature and are described and modeled in terms of networks. Bipartite networks are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set and the heterogeneity makes it very difficult to discriminate preferential links between the elements from randomly occurring links reflecting system heterogeneity. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis, which takes into account system heterogeneity. We apply our method to a biological, an economic and a social complex system. Our method is able to detect network structures which are informative about the organization and specialization of the investigated systems. Specifically, our method (i) identifies the preferential relationships between the elements, (ii) highlights the clustered structure of systems, and (iii) defines and classifies links according to the type of statistically validated relationships between the connected nodes.

By analyzing a database of a questionnaire answered by a large majority of candidates and elected in a parliamentary election, we quantitatively verify that female candidates on average present political profiles which are more compassionate and more concerned with social welfare issues than male candidates and the voting procedure acts as a process of information aggregation. Our results show that information aggregation proceeds with at least two distinct paths. In the first case candidates characterize themselves with a political profile aiming to describe the profile of the majority of voters. This is typically the case of candidates of political parties which are competing for the center of the various political dimensions. In the second case, candidates choose a political profile manifesting a clear difference from opposite political profiles endorsed by candidates of a political party positioned at the opposite extreme of some political dimension.