We are deligthed to launch our 2020 seminars series welcoming Prof. Andrea Gabrielli, from the Engineering Department of the University Roma Tre. Prof. Gabrielli’s talk will be held at the Dept. of Computer Science, Università degli Studi di Torino, on Feb. 20th, 2020, at 3:30 pm in Aula B (floor ‘R’).

Find below more information about the talk and the speaker.

## Grand canonical ensemble of heterogeneous weighted networks

**Abstract**

In the last years the formulation of statistical ensembles of binary and weighted random graphs satisfying some arbitrary constraints has attracted much attention in phys/math communities for its two-fold potential application [1, 2]: (i) The construction of appropriate null models for the statistical validation of high order properties of real networks; (ii) the reconstruction of the statistical properties of real network starting for partial accessible information. The cornerstone of the statistical physics of complex networks is the idea that the links, and not the nodes, are the effective particles of the system. Here we formulate a mapping between weighted networks and lattice gasses, making the conceptual step forward of interpreting weighted links as particles with a generalised coordinate [3]. This leads to the definition of the grand canonical ensemble of weighted complex networks. We derive exact expressions for the partition function and thermodynamic quantities, both in the cases of global and local (i.e., node-specific) constraints on density and mean energy of particles. We further show that, when modeling real cases of networks, the binary and weighted statistics of the ensemble can be disentangled, leading to a simplified framework for a range of practical applications. **References **

[1] T. Squartini, G. Caldarelli, G. Cimini, A. Gabrielli, D, Garlaschelli, Phys. Reports **757**, 1-47 (2018).

[2] G. Cimini, T. Squartini, F. Saracco, D. Garlaschelli, A. Gabrielli, G. Caldarelli, Nature Review Physics **1**, 58-71 (2019).

[3] A. Gabrielli, R. Mastrandrea, G. Caldarelli, G. Cimini, Phys. Rev. E **99**, 030301(R) (2019)

**Andrea Gabrielli** is Associate Professor in Physics at the Engineering Department of the University Roma Tre of Rome. Previously he was permanent researcher at the Institute of Complex Systems (ISC) of the Italian CNR from 2004 to 2019. He worked in the last 25 years in statistical physics, fractal growth phenomena, percolation, self-organized criticality, application of statistical physics to cosmological and gravitational problems. His main present interest focuses on the applications of complex networks and stochastic processes to economy and brain science. More in detail his present scientific activity deals with:

1) Applications of complex network theory to socio-economic networks and analysis of fMRI data about brain function;

2) Statistical physics of extended gravitational and long range interacting systems;

3) Stochastic processes with multiplicative noise, turbulence and the relation with long range interactions;

4) Theory of anomalous diffusion in NMR experiments in organic and inorganic complex media.

Further info at his official home page.

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