Marco Pettini

Quantifying networks complexity from information geometry viewpoint

We consider a Gaussian statistical model whose parameter space is given by the variances of random variables. Underlying this model we identify networks by interpreting random variables as sitting on vertices and their correlations as weighted edges among vertices. We then associate to the parameter space a statistical manifold endowed with a Riemannian metric structure (that of Fisher-Rao). Going on, in analogy with the microcanonical definition of entropy in Statistical Mechanics, we introduce an entropic measure of networks complexity. We prove that it is invariant under networks isomorphism. Above all, considering networks as simplicial complexes, we evaluate this entropy on simplexes and find that it monotonically increases with their dimension.

Characterisation of the Idiotypic Immune Network Through Persistent Entropy

In the present work we intend to investigate how to detect the behaviour of the immune system reaction to an external stimulus in terms of phase transitions. The immune model considered follows Jerne’s idiotypic network theory. We considered two graph complexity measures—the connectivity entropy and the approximate von Neumann entropy—and one entropy for topological spaces, the so-called persistent entropy. The simplicial complex is obtained enriching the graph structure of the weighted idiotypic network, and it is formally analyzed by persistent homology and persistent entropy. We obtained numerical evidences that approximate von Neumann entropy and persistent entropy detect the activation of the immune system. In addition, persistent entropy allows also to identify the antibodies involved in the immune memory.

Beam?plasma instability and fast particles: the Lynden-Bell approach

Beam–plasma instability, i.e., the response of plasma bulk to the injection of supra-thermal charged-particle beams, can be appropriately characterized by a long-range interaction system. This physical system hosts a number of very interesting phenomena and, in particular, the emergence of long-lived quasi-stationary states. We characterize the self-consistent distribution functions of such out-of-equilibrium states by means of the Lynden-Bell theory. The prediction of this theory, based on the statistical mechanics of the Vlasov equation, are checked against the outcomes of numerical simulations of the discrete system. Moreover, a phenomenological study of the effective resonance band for the system response is also addressed. A threshold value is found in the initial spread of beam-particle momenta. This threshold allows discrimination between the resonant and non-resonant regimes. The analysis of the thermalization of a few percent of the beam population characterized by large initial momenta (with respect to the main part of the beam itself) is also performed and it confirms and deepens our understanding of the physical meaning of the mentioned threshold.

Random walk of passive tracers among randomly moving obstacles

BackgroundThis study is mainly motivated by the need of understanding how the diffusion behavior of a biomolecule (or even of a larger object) is affected by other moving macromolecules, organelles, and so on, inside a living cell, whence the possibility of understanding whether or not a randomly walking biomolecule is also subject to a long-range force field driving it to its target.MethodBy means of the Continuous Time Random Walk (CTRW) technique the topic of random walk in random environment is here considered in the case of a passively diffusing particle among randomly moving and interacting obstacles.ResultsThe relevant physical quantity which is worked out is the diffusion coefficient of the passive tracer which is computed as a function of the average inter-obstacles distance.ConclusionsThe results reported here suggest that if a biomolecule, let us call it a test molecule, moves towards its target in the presence of other independently interacting molecules, its motion can be considerably slowed down.

Catching homologies by geometric entropy

Abstract A geometric entropy is defined in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. As such it can be a good candidate for measuring networks complexity. Here we investigate its ability to single out topological features of networks proceeding in a bottom-up manner: first we consider small size networks by analytical methods and then large size networks by numerical techniques. Two different classes of networks, the random graphs and the scale-free networks, are investigated computing their Betti numbers and then showing the capability of geometric entropy of detecting homologies.

Collective behavior of oscillating electric dipoles

We investigate the dynamics of a population of identical biomolecules mimicked as electric dipoles with random orientations and positions in space and oscillating with their intrinsic frequencies. The biomolecules, beyond being coupled among themselves via the dipolar interaction, are also driven by a common external energy supply. A collective mode emerges by decreasing the average distance among the molecules as testified by the emergence of a clear peak in the power spectrum of the total dipole moment. This is due to a coherent vibration of the most part of the molecules at a frequency definitely larger than their own frequencies corresponding to a partial cluster synchronization of the biomolecules. These results can be verified experimentally via spectroscopic investigations of the strength of the intermolecular electrodynamic interactions, thus being able to test the possible biological relevance of the observed macroscopic mode.

Investigation of Brownian diffusion and long-distance electrodynamic interactions of biomolecules

The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is shown that when the particles are uniformly distributed throughout the accessible space, the self-diffusion coefficient is always lowered by the considered interparticle interactions, irrespective of their attractive or repulsive character. Transitional phenomena are observed for Coulomb-electrostatic (repulsive) and dipole-electrodynamic (attractive) interactions considered both separately and in competition. The outcomes reported in this paper clearly indicate a feasible experimental method to probe the activation of resonant electrodynamic interactions among biomolecules.