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We investigate the in-distribution generalization of machine learning algorithms. We depart from traditional complexity-based approaches by analyzing information-theoretic bounds that quantify the dependence between a learning algorithm and…
We give a survey of the known results on mixing time of Glauber dynamics for the Ising model on the square lattice and present a technique that makes exact sampling of the Ising model at all temperatures possible in polynomial time. At high…
In order to figure out and to forecast the emergence phenomena of social systems, we propose several probabilistic models for the analysis of financial markets, especially around a crisis. We first attempt to visualize the collective…
Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as Pseudo-likelihood maximization (PLM), are biased. Using the…
Unlike the classical kinetic theory of rarefied gases, where microscopic interactions among gas molecules are described as binary collisions, the modelling of socio-economic phenomena in a multi-agent system naturally requires to consider,…
We analyse the spin-flip dynamics in kinetic Ising chains with Kimball-Deker-Haake (KDH) transition rates, and evaluate exactly the evolution of global quantities like magnetisation and its fluctuations, and the two-time susceptibilities…
In the framework of abstract linear inverse problems in infinitedimensional Hilbert space we discuss generic convergence behaviours of approximate solutions determined by means of general projection methods, namely outside the standard…
We present a general expression for the values of the average kinetic energy and of the temperature of kinetic decoupling of a WIMP, valid for any cosmological model. We show an example of the usage of our solution when the Hubble rate has…
A metric is introduced on the two dimensional space of parameters describing the Ising model on a Bethe lattice of co-ordination number q. The geometry associated with this metric is analysed and it is shown that the Gaussian curvature…
The Ising model doesn't have a strictly defined dynamics, only a spectrum. There are different ways to equip it with a time dependence e.g. the Glauber or the Kawasaki dynamics, which are both stochastic, but it means there is a master…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
We study the ordering kinetics of a generalization of the voter model with long-range interactions, the $p$-voter model, in one dimension. It is defined in terms of boolean variables $S_{i}$, agents or spins, located on sites $i$ of a…
The simulation of evacuation of pedestrians from skyscraper is a situation where the symmetry analysis method and equations of fluid dynamics finds to be very useful. When applied, they strongly reduce the number of free parameters used in…
We study phase separation in two dimensions in the scaling limit below criticality. The general form of the magnetization profile as the volume goes to infinity is determined exactly within the field theoretical framework which explicitly…
We study the coevolution of a generalized Glauber dynamics for Ising spins, with tunable threshold, and of the graph topology where the dynamics takes place. This simple coevolution dynamics generates a rich phase diagram in the space of…
We show that an high temperature expansion at fixed order parameter can be derived for the quantum Ising model. The basic point is to consider a statistical generating functional associated to the local spin state. The probability at…
Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…
In this work, the probability of an event under some joint distribution is bounded by measuring it with the product of the marginals instead (which is typically easier to analyze) together with a measure of the dependence between the two…
We introduce and analyze a natural class of nonlinear dynamics for spin systems such as the Ising model. This class of dynamics is based on the framework of mass action kinetics, which models the evolution of systems of entities under…
Long-range synchrony from short-range interactions is a familiar pattern in biological and physical systems, many of which share a common set of ``universal'' properties at the point of synchronization. Common biological systems of coupled…