Related papers: Survival probability of random networks
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation…
We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its…
Recently several authors have proposed stochastic evolutionary models for the growth of the web graph and other networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to…
In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…
In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the…
We define a general model of stochastically-evolving graphs, namely the \emph{Edge-Uniform Stochastically-Evolving Graphs}. In this model, each possible edge of an underlying general static graph evolves independently being either alive or…
Synfire chains are thought to underlie precisely-timed sequences of spikes observed in various brain regions and across species. How they are formed is not understood. Here we analyze self-organization of synfire chains through the…
We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking…
The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the…
This work shows that dynamical features typical of full random matrices can be observed also in the simple finite one-dimensional (1D) noninteracting Anderson model with nearest neighbor couplings. In the thermodynamic limit, all…
We study the dynamics and trapping of excitations for a dimer with an energy off-set $\Delta$ coupled to an external environment. Using a Lindblad quantum master equation approach, we calculate the survival probability $\Pi(t)$ of the…
We study the effective resistance of small-world resistor networks. Utilizing recent analytic results for the propagator of the Edwards-Wilkinson process on small-world networks, we obtain the asymptotic behavior of the disorder-averaged…
We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barab\'asi-Albert (BA),…
Recently, it became possible to experimentally generate and characterize a very thin silica system on a substrate which can be basically described as a 2D random network. The key structural properties, in particular related to the ring…
We study the statistical and dynamic properties of the systems characterized by an ultrametric space of states and translationary non-invariant symmetric transition matrices of the Parisi type subjected to "locally constant" randomization.…
We assess the performance of a recently proposed renormalized adiabatic local density approximation (rALDA) for \textit{ab initio} calculations of electronic correlation energies in solids and molecules. The method is an extension of the…
We systematically analyze optimization dynamics in deep neural networks (DNNs) trained with stochastic gradient descent (SGD) and study the effect of learning rate $\eta$, depth $d$, and width $w$ of the neural network. By analyzing the…
In this paper we present a numerical study of a mathematical model of spiking neurons introduced by Ferrari et al. in an article entitled Phase transition forinfinite systems of spiking neurons. In this model we have a countable number of…
We investigate the extent to which the probabilistic properties of a chaotic scattering system with dissipation can be understood from the properties of the dissipation-free system. For large energies $E$, a fully chaotic scattering leads…
We develop a statistical theory of networks. A network is a set of vertices and links given by its adjacency matrix $\c$, and the relevant statistical ensembles are defined in terms of a partition function $Z=\sum_{\c} \exp {[}-\beta \H(\c)…