In a general sense, Physics studies the laws of the Universe. This broad perspective can be reduced to say that Physics is concerned in the way in which objects move, that is everything which is subjected to the rules of *Mechanics*. Nowadays, we know at least four different types of Mechanics which are called: Classical, Quantum, Relativistic and Statistical. Each Mechanic applies under a certain regime. Classical Mechanics deals with everyday objects, Quantum Mechanics with very small particles (like electrons), Relativistic Mechanics with very fast particles (whose velocity is close to the speed of light) and Statistical Mechanics with a big number of elements (of the order of the Avogadro's number). The theoretical description of these four Mechanics relies on the Hamiltonian formalism. Moreover, they can be used together, for instance, when the particles are very little and fast, Relativistic Quantum Mechanics is taken into account.

When many agents are interacting together, they can give rise to peculiar behaviours which can't be reduced to the sum of the characteristics of the single elements making up the system. Such properties emerge as a collective behaviour of all the particles. These are called

Nowadays, the research trends in Statistical Mechanics can be divided in two branches: Non-equilibrium and Equilibrium. In the first case, the time evolution of the system is of main interest. Here, the most important quantity is the

My research interests focus on both branches of Statistical Mechanics. In the following, you can find a brief description on the problems I'm working on.

Consider a weighted combination of two lattices (in the case of the picture they are two fully connected graph). If you link the spins of each party of variables in a ferromagnetic or disorder way, you obtain a bipartite spin system. These kind of models present remarkable behaviour, with particular reference to the free energy which gives rise to a degenerate self-consistence equation. The model can be studied also outside the fully connected interaction between the parties, using, for instance, a Bernoulli distributed bond dilution. Moreover, it can be shown that an analogical neural network can be mapped into a bipartite model, widening, in this way, the possible applications of these kind of systems.

J. Phys. A: Math. Theor. 44 245002

EPJB (2013) 86:332

J. Stat. Mech. (2011) P02027

Take a chain in which each site can accommodate any number of particles. The probability of transition between the sites can depend on many parameters and the various models are classified with respect to them. This family of models is often called in the literature as

JSP (2014) 154:432-465

JSP (2003) 113:389-410

J. Phys. A: Math. Theor. 47 095001

Consider a network where we associate to each edge a dichotomic variable, i.e. +1 or -1. In this way, we can build a signed adjacency matrix. Allowing the nodes (which in SM are usually called spins) to take +1 or -1 as well, it is interesting to determine the node configuration which maximizes the quadratic form associated to the graph. This can be achieved using many different techniques from Algebra, like spectral analysis, or Physics, like the Ginzburg-Landau functional. In SM this problem can be understood as finding the minimum of the free energy of a disordered system. An important version of this problem is obtained when some values of the nodes are fixed a priori. This simple variation implies the breakdown of standard techniques and requires developing new optimization strategies.

Journal of Complex Networks, 3 (3):469-506

Information and Inference: A Journal of the IMA, 1 (1), pp. 2167

ACM Transactions on Sensor Networks, 8 (3), pp. 1-42