Gino Del Ferraro

Anergy in self-directed B lymphocytes: A statistical mechanics perspective.

Self-directed lymphocytes may evade clonal deletion at ontogenesis but still remain harmless due to a mechanism called clonal anergy. For B-lymphocytes, two major explanations for anergy developed over the last decades: according to Varela theory, anergy stems from a proper orchestration of the whole B-repertoire, such that self-reactive clones, due to intensive feed-back from other clones, display strong inertia when mounting a response. Conversely, according to the model of cognate response, self-reacting cells are not stimulated by helper lymphocytes and the absence of such signaling yields anergy. Through statistical mechanics we show that helpers do not prompt activation of a sub-group of B-cells: remarkably, the latter are just those broadly interacting in the idiotypic network. Hence Varela theory can finally be reabsorbed into the prevailing framework of the cognate response model. Further, we show how the B-repertoire architecture may emerge, where highly connected clones are self-directed as a natural consequence of ontogenetic learning.

Perturbative Large Deviation Analysis of Non-Equilibrium Dynamics

Macroscopic fluctuation theory has shown that a wide class of non-equilibrium stochastic dynamical systems obey a large deviation principle, but except for a few one-dimensional examples these larg ...

A Cavity Master Equation for the continuous time dynamics of discrete spins models

We present an alternate method to close the master equation representing the continuous time dynamics of interacting Ising spins. The method makes use of the theory of random point processes to derive a master equation for local conditional probabilities. We analytically test our solution studying two known cases, the dynamics of the mean-field ferromagnet and the dynamics of the one-dimensional Ising system. We present numerical results comparing our predictions with Monte Carlo simulations in three different models on random graphs with finite connectivity: the Ising ferromagnet, the random field Ising model, and the Viana-Bray spin-glass model.

Causal analysis, Correlation-Response, and Dynamic cavity

The purpose of this note is to point out analogies between causal analysis in statistics and the correlation-response theory in statistical physics. It is further shown that for some systems the dynamic cavity offers a way to compute the stationary state of a non- equilibrium process effectively, which could then be taken an alternative starting point of causal analysis.

On one-step replica symmetry breaking in the Edwards-Anderson spin glass model

We consider a one-step replica symmetry breaking description of the Edwards–Anderson spin glass model in 2D. The ingredients of this description are a Kikuchi approximation to the free energy and a second-level statistical model built on the extremal points of the Kikuchi approximation, which are also fixed points of a generalized belief propagation (GBP) scheme. We show that a generalized free energy can be constructed where these extremal points are exponentially weighted by their Kikuchi free energy and a Parisi parameter y, and that the Kikuchi approximation of this generalized free energy leads to second-level, one-step replica symmetry breaking (1RSB), GBP equations. We then proceed analogously to the Bethe approximation case for tree-like graphs, where it has been shown that 1RSB belief propagation equations admit a survey propagation solution. We discuss when and how the one-step-replica symmetry breaking GBP equations that we obtain also allow a simpler class of solutions which can be interpreted as a class of generalized survey propagation equations for the single instance graph case.