Related papers: Survival probability of random networks

We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…

We study large $N\times N$ power-law random band matrices $H=(H_{ij})$ with centered complex Gaussian entries, where the variances satisfy a power-law decay $\mathbb{E}|H_{ij}|^2\propto (|i-j|/W+1)^{-1-\alpha}$, for some exponent…

We demonstrate the oscillatory decay of the survival probability of the stochastic dynamics $d\x_\eps=\mb{a}(\x_\eps)\, dt +\sqrt{2\eps}\,\mb{b}(\x_\eps)\,d\w$, which is activated by small noise over the boundary of the domain of attraction…

We propose a simple model of the evolution of a social network which involves local search and volatility (random decay of links). The model captures the crucial role the network plays for information diffusion. This is responsible for a…

Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…

Using coherent states as initial states, we investigate the quantum dynamics of the Lipkin-Meshkov-Glick (LMG) and Dicke models in the semi-classical limit. They are representative models of bounded systems with one- and two-degrees of…

In this report trial-to-trial variations in the synchronized responses of neural networks are offered as evidence for excitation-inhibition ratio being a dynamic variable over time scales of minutes. Synchronized network responses to…

We present a theoretical study of the survival probability of a state initially prepared in the one-particle sector of a multi-qubit system. The motivation for our work is the ongoing laboratory development of multi-qubit platforms based on…

We consider events over the probability space generated by the degree sequences of multiple independent Erd\H{o}s-R\'enyi random graphs, and consider an approximation probability space where such degree sequences are deemed to be sequences…

The maximum entropy production (MEP) principle is a hypothetical law of physics which dictates that complex systems, far from equilibrium, evolve into an ordered dissipative structure (DS) which generates as much entropy per second as…

Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…

In the reaction-diffusion process $A+B \to \varnothing$ on random scale-free (SF) networks with the degree exponent $\gamma$, the particle density decays with time in a power law with an exponent $\alpha$ when initial densities of each…

Recently it was shown (I.A.Gruzberg, A. Kl\"umper, W. Nuding and A. Sedrakyan, Phys.Rev.B 95, 125414 (2017)) that taking into account random positions of scattering nodes in the network model with $U(1)$ phase disorder yields a localization…

The spectral evolution model aims to characterize the growth of large networks (i.e., how they evolve as new edges are established) in terms of the eigenvalue decomposition of the adjacency matrices. It assumes that, while eigenvectors…

For large fully connected neuron networks, we study the dynamics of homogenous assemblies of interacting neurons described by time elapsed models. Under general assumptions on the firing rate which include the ones made in previous works…

We present a stochastic model for a social network, where new actors may join the network, existing actors may become inactive and, at a later stage, reactivate themselves. Our model captures the evolution of the network, assuming that…

It has been reported in the literature that the survival probability $P(t)$ near an exceptional point where two eigenstates coalesce should generally exhibit an evolution $P(t) \sim t^2 e^{-\Gamma t}$, in which $\Gamma$ is the decay rate of…

We study complex networks under random matrix theory (RMT) framework. Using nearest-neighbor and next-nearest-neighbor spacing distributions we analyze the eigenvalues of adjacency matrix of various model networks, namely, random,…

Barab\'asi-Albert's `Scale Free' model is the starting point for much of the accepted theory of the evolution of real world communication networks. Careful comparison of the theory with a wide range of real world networks, however,…

We investigate mechanisms of the typically observed recoverable prevalence in epidemic spreading. Assuming the time-independent connectivity correlations, we analyze the dynamics of spreading on linearly growing scale-free (SF) networks,…