Non-Euclidean geometry in nature

I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random graphs. For these systems I discuss the following interlinked questions: (i) the optimal embedding of plants leaves in the three-dimensional space, (ii) the spectral statistics of sparse random matrix ensembles.Comment: 52 pages, 21 figures, last section is rewritten, a reference to chaotic Hamiltonian systems is adde

Extraction and Analysis of Facebook Friendship Relations

Online Social Networks (OSNs) are a unique Web and social phenomenon, affecting tastes and behaviors of their users and helping them to maintain/create friendships. It is interesting to analyze the growth and evolution of Online Social Networks both from the point of view of marketing and other of new services and from a scientific viewpoint, since their structure and evolution may share similarities with real-life social networks. In social sciences, several techniques for analyzing (online) social networks have been developed, to evaluate quantitative properties (e.g., defining metrics and measures of structural characteristics of the networks) or qualitative aspects (e.g., studying the attachment model for the network evolution, the binary trust relationships, and the link prediction problem).\ud However, OSN analysis poses novel challenges both to Computer and Social scientists. We present our long-term research effort in analyzing Facebook, the largest and arguably most successful OSN today: it gathers more than 500 million users. Access to data about Facebook users and their friendship relations, is restricted; thus, we acquired the necessary information directly from the front-end of the Web site, in order to reconstruct a sub-graph representing anonymous interconnections among a significant subset of users. We describe our ad-hoc, privacy-compliant crawler for Facebook data extraction. To minimize bias, we adopt two different graph mining techniques: breadth-first search (BFS) and rejection sampling. To analyze the structural properties of samples consisting of millions of nodes, we developed a specific tool for analyzing quantitative and qualitative properties of social networks, adopting and improving existing Social Network Analysis (SNA) techniques and algorithms

Spatial projection of input-ouput tables for small areas

Studies on regional economy have achieved a huge expansion in the last decades. In particular, from an input-ouput optic many efforts have been devoted to carring out a suitable methodology, which enable us to cover the overall and exhaustive knowledge of the economic reality of one region. Given that a input-output table (IOT) gathers both intersectorial relationships and the final demand of the economy, it allows us to provide a reliable picture of one economy in a certain moment of time. Nonetheless, the elaboration of a IOT is a complex task, which needs many human and economic resources. Thus, most of the tables elaborated using direct methods have as a benchmark frame either a country or a region, although it is difficult to find matrices related to smaller geografic spaces like, for instance, counties. So, if we attempt to perform a deeper study of both spaces, it would be of great help if we could dispose of estimation methods, which enable us to make tables with less information, i.e, indirect (semidirect) methods of estimation. Let´s say that the economy of a region is determined by the relations among productive structures of their counties, therefore a previous knowledge of these productive structures can be interesting. The basic aim of this work consists of estimating a TIO for each one of the eight Asturian Counties in 1995, since this is the last period in which we possess published information relative to regional accounts. To this end, a technique focused on mathematical theory of the information: cross entropy, will be employed. Such a technique has lately been applied to the construction of regional tables, largely for two reasons: one, flexibility as regards the information it needs; the other, to produce some rather suitable empiric results. From the tables estimates by this method we will be able to know the characteristics of economic structures of the counties. To achieve this scope, tools related to the graph theory, have been applied. Their application in input-output analisis has a great potential to provide a simple vision of the relations between the different sectors, as well as being able to integrate matters as important as the relative positions of the sectors, their orientation or paths in which drive the economic influence inside the corresponding structure.

Systemic risk assessment through high order clustering coefficient

In this article we propose a novel measure of systemic risk in the context of financial networks. To this aim, we provide a definition of systemic risk which is based on the structure, developed at different levels, of clustered neighbours around the nodes of the network. The proposed measure incorporates the generalized concept of clustering coefficient of order $l$ of a node $i$ introduced in Cerqueti et al. (2018). Its properties are also explored in terms of systemic risk assessment. Empirical experiments on the time-varying global banking network show the effectiveness of the presented systemic risk measure and provide insights on how systemic risk has changed over the last years, also in the light of the recent financial crisis and the subsequent more stringent regulation for globally systemically important banks.Comment: Submitte