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Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…
We study the critical behavior and the out-of-equilibrium dynamics of a two-dimensional Ising model with non-static interactions. In our model, bonds are dynamically changing according to a majority rule depending on the set of closest…
The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in…
A system defined by two coupled Ising models, with a bimodal random field acting in one of them, is investigated. The interactions among variables of each Ising system are infinite-ranged, a limit where mean field becomes exact. This model…
Non-equilibrium systems lack an explicit characterisation of their steady state like the Boltzmann distribution for equilibrium systems. This has drastic consequences for the inference of parameters of a model when its dynamics lacks…
Whether an idea, information, infection, or innovation diffuses throughout a society depends not only on the structure of the network of interactions, but also on the timing of those interactions. Recent studies have shown that diffusion…
We study a dynamical Ising model of agents' opinions (buy or sell) with coupling coefficients reassessed continuously in time according to how past external news (magnetic field) have explained realized market returns. By combining herding,…
The character of critical behavior in physical systems depends on the range of interactions. In the limit of infinite range of the interactions, systems will exhibit mean-field critical behavior, i.e., critical behavior not affected by…
Recently research on bubble and its burst attract much interest of researchers in various field such as economics and physics. Economists have been regarding bubble as a disorder in prices. However, this research strategy has overlooked an…
Neurons in the brain are wired into adaptive networks that exhibit a range of collective dynamics. Oscillations, for example, are paradigmatic synchronous patterns of neural activity with a defined temporal scale. Neuronal avalanches, in…
We develop a model for point processes on the real line, where the intensity can be locally unbounded without inducing an explosion. In contrast to an orderly point process, for which the probability of observing more than one event over a…
"Noise-induced volatility" refers to a phenomenon of increased level of fluctuations in the collective dynamics of bistable units in the presence of a rapidly varying external signal, and intermediate noise levels. The archetypical…
Recent work emphasizes that the maximum entropy principle provides a bridge between statistical mechanics models for collective behavior in neural networks and experiments on networks of real neurons. Most of this work has focused on…
We introduce a new model that mimics the strong and sudden effects induced by conformity in tightly interacting human societies. Such effects range from mere crowd phenomena to dramatic political turmoil. The model is a modified version of…
The interplay between causal mechanisms and emerging collective behaviors is a central aspect of understanding, controlling, and predicting complex networked systems. In our work, we investigate the relationship between higher-order…
We present a neuronal network model inspired by the Ising model, where each neuron is a binary spin ($s_i = \pm1$) interacting with its neighbors on a 2D lattice. Updates are asynchronous and follow Metropolis dynamics, with a…
In the era of social media, every day billions of individuals produce content in socio-technical systems resulting in a deluge of information. However, human attention is a limited resource and it is increasingly challenging to consume the…
Background: We study mechanisms underlying the collective emotional behavior of Bloggers by using the agent-based modeling and the parameters inferred from the related empirical data. Methodology/Principal Findings: A bipartite network of…
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…
We investigate large changes, bursts, of the continuous stochastic signals, when the exponent of multiplicativity is higher than one. Earlier we have proposed a general nonlinear stochastic model which can be transformed into Bessel process…