Related papers: Extraordinary variability and sharp transitions in…
Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at…
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 opinion dynamics on networks with a nontrivial community structure, assuming individuals can update their binary opinion as the result of the interactions with an external influence with strength $h\in [0,1]$ and with other…
Networks of strongly-coupled neurons with random connectivity exhibit chaotic, asynchronous fluctuations. In previous work, we showed that when endowed with an additional low-rank connectivity consisting of the outer product of orthogonal…
We derive some key extremal features for $k$th order Markov chains that can be used to understand how the process moves between an extreme state and the body of the process. The chains are studied given that there is an exceedance of a…
Rare event statistics for random walks on complex networks are investigated using the large deviations formalism. Within this formalism, rare events are realized as typical events in a suitably deformed path-ensemble, and their statistics…
The identification of universal properties from minimally processed data sets is one goal of machine learning techniques applied to statistical physics. Here, we study how the minimum number of variables needed to accurately describe the…
Scale-free networks with moderate edge dependence experience a phase transition between ultrasmall and small world behaviour when the power law exponent passes the critical value of three. Moreover, there are laws of large numbers for the…
We study both numerically and analytically what happens to a random graph of average connectivity "alpha" when its leaves and their neighbors are removed iteratively up to the point when no leaf remains. The remnant is made of isolated…
When real networks are considered, coupled networks with connectivity and feedback-dependency links are not rare but more general. Here we develop a mathematical framework and study numerically and analytically percolation of interacting…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…
Extreme events are unusual and rare large-amplitude fluctuations that occur can unexpectedly in nonlinear dynamical systems. Events above the extreme event threshold of the probability distribution of a nonlinear process characterize…
Ecological communities with many species can be classified into dynamical phases. In systems with all-to-all interactions, a phase where a fixed point is always reached and a dynamically-fluctuating phase have been found. The dynamics when…
Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…
Attractors of dynamical systems may be networks in phase space that can be heteroclinic (where there are dynamical connections between simple invariant sets) or excitable (where a perturbation threshold needs to be crossed to a dynamical…
The inverse problem of statistical mechanics involves finding the minimal Hamiltonian that is consistent with some observed set of correlation functions. This problem has received renewed interest in the analysis of biological networks; in…
Degree correlation is an important topological property common to many real-world networks. In this paper, the statistical measures for characterizing the degree correlation in networks are investigated analytically. We give an exact proof…
We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the…
From Physics and Biology to Seismology and Economics, the behaviour of countless systems is determined by impactful yet unlikely transitions between metastable states known as \emph{rare events}, the study of which is essential for…
Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As…