Related papers: Absence of Breakdown of the Poisson Hypothesis I. …
We present an example of a highly connected closed network of servers, where the time correlations do not go to zero in the infinite volume limit. This phenomenon is similar to the continuous symmetry breaking at low temperatures in…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
We study the contact process on a class of evolving scale-free networks, where each node updates its connections at independent random times. We give a rigorous mathematical proof that there is a transition between a phase where for all…
We study the collective behavior of an Ising system on a small-world network with the interaction $J(r) \propto r^{-\alpha}$, where $r$ represents the Euclidean distance between two nodes. In the case of $\alpha = 0$ corresponding to the…
We consider the relationship between the temperature at which averaged energy landscape properties change sharply ($T_{o}$), and the breakdown of mean-field treatments of the dynamics of supercooled liquids. First, we show that the solution…
We study the mean-field limit of a generic class of dynamic co-evolving latent space networks motivated by the social and opinion dynamics literature. Such models include $n$ agents, whose opinions are given by latent stochastic processes,…
Herein, we consider a voting model for information cascades on several types of networks -- a random graph, the Barab\'{a}si-Albert(BA) model, and lattice networks -- by using one parameter $\omega$; $\omega=1,0, -1$ respectively correspond…
Folding of RNA is subject to a competition between entropy, relevant at high temperatures, and the random, or random looking, sequence, determining the low- temperature phase. It is known from numerical simulations that for random as well…
We develop a theoretical approach to percolation in random clustered networks. We find that, although clustering in scale-free networks can strongly affect some percolation properties, such as the size and the resilience of the giant…
We study the evolution of structural disorder under cooling in supercooled liquids, focusing on covalent networks. We introduce a model for the energy of networks that incorporates weak non-covalent interactions. We show that at…
The edges in networks are not only binary, either present or absent, but also take weighted values in many scenarios (e.g., the number of emails between two users). The covariate-$p_0$ model has been proposed to model binary directed…
Based on the theory of hypernetwork and WeChat online social relations, the paper proposes an evolving hypernetwork model with the competitiveness and the age of nodes. In the model, nodes arrive at the system in accordance with Poisson…
In this paper we introduce and investigate the statistical mechanics of hierarchical neural networks: First, we approach these systems \`a la Mattis, by thinking at the Dyson model as a single-pattern hierarchical neural network and we…
Small-world networks are highly clustered networks with small distances among the nodes. There are many biological neural networks that present this kind of connections. There are no special weightings in the connections of most existing…
We develop a mean-field theory for the totally asymmetric simple exclusion process (TASEP) with open boundaries, in order to investigate the so-called dynamical transition. The latter phenomenon appears as a singularity in the relaxation…
Coherent, large scale dynamics in many nonequilibrium physical, biological, or information transport networks are driven by small-scale local energy input. Here, we introduce and explore an analytically tractable nonlinear model for…
We present high-accuracy quasi-stationary (QS) simulations of the contact process in quenched networks, built using the configuration model with both structural and natural cutoffs. The critical behavior is analyzed in the framework of the…
This article provides a characterization of stability for switched nonlinear systems under average dwell-time constraints, in terms of necessary and sufficient conditions involving multiple Lyapunov functions. Earlier converse results focus…
We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice Z^d. Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated…
We present a simple model of communication in networks with hierarchical branching. We analyze the behavior of the model from the viewpoint of critical systems under different situations. For certain values of the parameters, a continuous…