Related papers: Percolation in living neural networks
Robustness of two coupled networks system has been studied only for dependency coupling (S. Buldyrev et. al., Nature, 2010) and only for connectivity coupling (E. A. Leicht and R. M. D'Souza, arxiv:09070894). Here we study, using a…
Percolation theory can be used to describe the structural properties of complex networks using the generating function formulation. This mapping assumes that the network is locally tree-like and does not contain short-range loops between…
We study the problem of wireless network resilience to node failures from a percolation-based perspective. In practical wireless networks, it is often the case that the failure probability of a node depends on its degree (number of…
We compare phase transition and critical phenomena of bond percolation on Euclidean lattices, nonamenable graphs, and complex networks. On a Euclidean lattice, percolation shows a phase transition between the nonpercolating phase and…
In this study, we investigate bond percolation in networks that have the Poisson degree distribution and a nearest-neighbor degree-degree correlation. Previous numerical studies on percolation critical behaviors of degree-correlated…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
We explore the interplay between the topological relevance of a neuron and its dynamical traces in experimental cultured neuronal networks. We monitor the growth and development of these networks to characterise the evolution of their…
Deep neural networks exhibit empirical neural scaling laws, with error decreasing as a power law with increasing model or data size, across a wide variety of architectures, tasks, and datasets. This universality suggests that scaling laws…
Methods for determining the percolation threshold usually study the behavior of network ensembles and are often restricted to a particular type of probabilistic node/link removal strategy. We propose a network-specific method to determine…
Percolation is an emblematic model to assess the robustness of interconnected systems when some of their components are corrupted. It is usually investigated in simple scenarios, such as the removal of the system's units in random order, or…
We investigate the following vertex percolation process. Starting with a random regular graph of constant degree, delete each vertex independently with probability p, where p=n^{-alpha} and alpha=alpha(n) is bounded away from 0. We show…
Percolation is a fundamental concept that brought new understanding on the robustness properties of complex systems. Here we consider percolation on weakly interacting networks, that is, network layers coupled together by much less…
Networks composed from both connectivity and dependency links were found to be more vulnerable compared to classical networks with only connectivity links. Their percolation transition is usually of a first order compared to the second…
A perturbative method is developed for calculating the effects of recurrent synaptic interactions between neurons embedded in a network. A series expansion is constructed that converges for networks with noisy membrane potential and weak…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
We present exact analysis of the physical properties of bimodal networks specified by the two peak degree distribution fully incorporating the degree-degree correlation between node connection. The structure of the correlated bimodal…
Weak multiplex percolation generalizes percolation to multi-layer networks, represented as networks with a common set of nodes linked by multiple types (colors) of edges. We report a novel discontinuous phase transition in this problem.…
Many real-world networks are coupled together to maintain their normal functions. Here we study the robustness of multiplex networks with interdependent and interconnected links under k-core percolation, where a node fails when it connects…
The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on…
Many biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability. In balanced networks, strong excitatory synaptic inputs are canceled by strong inhibitory inputs…