International School

on Informatics and Dynamics

in Complex Networks

University of Catania, 15 -19 October 2018

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Simple methods for complex brain networks
The emerging area of complex networks has led to a paradigm shift in different research communities. To improve our understanding of neural connected systems, different advanced tools derived from statistics, signal processing, information theory and statistical physics have been developed in the last decade. Here, we will focus on the comparison of brain networks (but the formalism woks well for any pair of networks). Although different estimates exist to quantify how different two networks are, an appropriate metric has not been proposed. With this framework we compare the performances of different networks distances (a topological descriptor and a kernel-based approach) with a standard and simple Euclidean metrics. We define the performance of metrics as the efficiency of distinguish two network and the time they take to capture such graph differences. We evaluate these frameworks on synthetic and real brain networks, and we show that Euclidean distance as the one that efficiently capture concrete networks differences in comparison to other proposals. We conclude that the operational use of proposed complicated methods can be justified only by showing that they out-perform well-understood traditional statistics (such as Euclidean metrics) or provide complementary information. The fact that a brain network itself may be demonstrably complex is simply not the relevant question when network differences are the aim.
Structure and Dynamics of Multilayer Networks
Complex systems are characterized by constituents -- from neurons in the brain to individuals in a social network -- which exhibit special structural organization and nonlinear dynamics. As a consequence, a complex system can not be understood by studying its units separately because their interactions lead to unexpected emerging phenomena, from collective behavior to phase transitions. Recently, we have discovered that a new level of complexity characterizes a variety of natural and artificial systems, where units interact, simultaneously, in distinct ways. For instance, this is the case of multimodal transportation systems (e.g., metro, bus and train networks) or of biological molecules, whose interactions might be of different type (e.g. physical, chemical, genetic) or functionality (e.g., regulatory, inhibitory, etc.). The unprecedented newfound wealth of multivariate data allows to categorize system's interdependency by defining distinct "layers", each one encoding a different network representation of the system. The result is a multilayer network model. Analyzing data from different domains -- including molecular biology, neuroscience, urban transport, telecommunications -- we will show that neglecting or disregarding multivariate information might lead to poor results. Conversely, multilayer models provide a suitable framework for complex data analytics, allowing to quantify the resilience of a system to perturbations (e.g., localized failures or targeted attacks), improving forecasting of spreading processes and accuracy in classification problems.
Network Analytics in the Big Data Era. Methods, Pitfalls and How to Avoid them
The New Science of Networks
Networks constitute the backbone of complex systems, from the human brain to computer communications, transport infrastructures to online social systems andmetabolic reactions to financial markets. Characterising their structure improves our understanding of the physical, biological, economic and social phenomena that shape our world. As a result, complex networks have become an essential ingredient in the background of any scientist. In this lecture I will present a brief overview of the new theory and methods of network science, of the main results found, and of some of the still open challenges. I will concentrate, in particular, on the structure and dynamics of multi-layer networks (namely multiplex networks and temporal networks) discussing cases where the presence of many layers gives rise to the emergence of novel behaviours, otherwise unobserved in single-layer networks.
Information networks, information retrieval and Internet evolution
Information networks and information aggregation. The World Wide Web as a complex network. Historical sketch of the WWW. Network metrics characterization of the WWW. The Bow-Tie structure of the web. Searching the web. The ranking of web pages. Link analysis using hubs and authorities. PageRank. General properties of information aggregation. A comment on the time evolution of search engines. The WWW as a dynamic complex system. Key aspects of social networks. The web as a private space.