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In the brain, cross-frequency coupling has been hypothesized to result from the activity of specialized microcircuits. For example, theta-gamma coupling is assumed to be generated by specialized cell pairs (PING and ING mechanisms), or…
We introduce a simple model for addressing the controversy in the study of financial systems, sometimes taken as brownian-like processes and other as critical systems with fluctuations of arbitrary magnitude. The model considers a…
The Ising model is a celebrated example of a Markov random field, introduced in statistical physics to model ferromagnetism. This is a discrete exponential family with binary outcomes, where the sufficient statistic involves a quadratic…
In random percolation one finds that the mean field regime above the upper critical dimension can simply be explained through the coexistence of infinite percolating clusters at the critical point. Because of the mapping between percolation…
We introduce a family of random matrices where correlations between matrix elements are induced via interaction-derived Boltzmann factors. Varying these yields access to different ensembles. We find a universal scaling behavior of the…
We investigate in detail a recent model of colliding mobile agents [Phys. Rev. Lett.~96, 088702], used as an alternative approach to construct evolving networks of interactions formed by the collisions governed by suitable dynamical rules.…
This article proposes a complementary theoretical framework in behavioural finance by interpreting financial markets during boom-and-bust episodes as a Le Bonian crowd. While behavioural finance has documented the limits of individual…
The "edge of chaos" phase transition in artificial neural networks is of renewed interest in light of recent evidence for criticality in brain dynamics. Statistical mechanics traditionally studied this transition with connectivity $k$ as…
We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in…
Systems that comprise many interacting dynamical networks, such as the human body with its biological networks or the global economic network consisting of regional clusters, often exhibit complicated collective dynamics. To understand the…
We show that, contrary to previous suggestions based on computer simulations or erroneous theoretical treatments, the critical points of the random-field Ising model out of equilibrium, when quasi-statically changing the applied source at…
The contact process and the slightly different susceptible-infected-susceptible model are studied on long-range connected networks in the presence of random transition rates by means of a strong disorder renormalization group method and…
Large-scale data resulting from users online interactions provide the ultimate source of information to study emergent social phenomena on the Web. From individual actions of users to observable collective behaviors, different mechanisms…
In this work we study the critical behavior of a three-state opinion model in the presence of noise. This noise represents the independent behavior, that plays the role of social temperature. Each agent on a regular D-dimensional lattice…
Emergent behavior that appears at a given level of organization may be characterized as arising from an organizationally lower level in such a way that it transcends a mere increase in the behavioral degree of complexity. It is therefore to…
This paper is concerned with a family of Reaction-Diffusion systems that we introduced in [15], and that generalizes the SIR type models from epidemiology. Such systems are now also used to describe collective behaviors.In this paper, we…
Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for…
Online platforms provide an infrastructure for social movements, leaving digital traces that can be modelled as networks to quantify how information, participation, and coordination emerge during episodes of collective action and evolve…
A general theory of innovation and progress in human society is outlined, based on the combat between two opposite forces (conservatism/inertia and speculative herding "bubble" behavior). We contend that human affairs are characterized by…
A network of coupled time-varying systems, where individual nodes are interconnected through links, is a modeling framework widely used by many disciplines. For identical nodes displaying a complex behavior known as chaos, clusters of nodes…