Exploring complex networks via topological embedding on surfaces

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The local properties of the network are affected by the surface genus which, for example, produces significant changes in the degree distribution and in the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwoveness, changing the scaling properties from large-world-kind (small genus) to small- and ultra-small-world-kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description. Within such a framework, we study the properties of topologically-embedded graphs at high and low `temperatures' observing the formation of increasingly regular structures by cooling the system. We show that the cooling dynamics is strongly affected by the surface genus with the manifestation of a glassy-like freezing transitions occurring when the amount of topological disorder is low.Comment: 18 pages, 7 figure

Exploring complex networks via topological embedding on surfaces

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, to characterize, and to simulate networks with a broad range of properties. Any network can be embedded on a surface with sufficiently high genus and therefor

Exploring complex networks via topological embedding on surfaces

We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive because any network can be embedded on a surface with sufficiently high genus. The local properties of the network are affected by the surface genus which, for example, produces significant changes in the degree distribution and in the clustering coefficient. The global properties of the graph are also strongly affected by the surface genus which is constraining the degree of interwoveness, changing the scaling properties from large-world-kind (small genus) to small- and ultra-small-world-kind (large genus). Two elementary moves allow the exploration of all networks embeddable on a given surface and naturally introduce a tool to develop a statistical mechanics description. Within such a framework, we study the properties of topologically-embedded graphs at high and low `temperatures' observing the formation of increasingly regular structures by cooling the system. We show that the cooling dynamics is strongly affected by the surface genus with the manifestation of a glassy-like freezing transitions occurring when the amount of topological disorder is low.

Dynamical Hurst exponent as a tool to monitor unstable periods in financial time series

We investigate the use of the Hurst exponent, dynamically computed over a moving time-window, to evaluate the level of stability/instability of financial firms. Financial firms bailed-out as a consequence of the 2007-2010 credit crisis show a neat increase with time of the generalized Hurst exponent in the period preceding the unfolding of the crisis. Conversely, firms belonging to other market sectors, which suffered the least throughout the crisis, show opposite behaviors. These findings suggest the possibility of using the scaling behavior as a tool to track the level of stability of a firm. In this paper, we introduce a method to compute the generalized Hurst exponent which assigns larger weights to more recent events with respect to older ones. In this way large fluctuations in the remote past are less likely to influence the recent past. We also investigate the scaling associated with the tails of the log-returns distributions and compare this scaling with the scaling associated with the Hurst exponent, observing that the processes underlying the price dynamics of these firms are truly multi-scaling.

Conceptual outline of the knowledge graph building process.

<p>(A) Every document is split into its constituent sentences and each of them is scanned to identify expressions registered on the dictionary. In the figure, two sentences are highlighted and the matching expressions are enclosed in coloured boxes. Every one of these expressions is associated to a concept in the dictionary. (B) The concepts co-occurring in a sentence are connected pairwise. A sentence is therefore abstracted as a complete graph where the occurring concepts are the nodes and a single co-occurrence is a link. The weight of a link is increased if more instances of the same co-occurrence are present. (C) The sentence graphs are then merged in such a way that each node (concept) appears only once in the graph. In the figure it is evident that the «LAM» node (abbreviation for Lymphangioleiomyomatosis – a rare disease) appears in every graph and the «Lung» node in two of them. (D) The result of the merging is a new graph – which is no more complete – where the weight of the link is associated to the frequency of the same co-occurrence.</p

The VIP – SARCOIDOSIS path and other closely related concepts.

<p>The VIP – SARCOIDOSIS path and other closely related concepts.</p

Imatinib (GLEEVEC) – Creutzfeldt-Jakob Disease path and other closely related concepts.

<p>Imatinib (GLEEVEC) – Creutzfeldt-Jakob Disease path and other closely related concepts.</p

The CNP – SARCOIDOSIS path and other closely related concepts.

<p>The CNP – SARCOIDOSIS path and other closely related concepts.</p