Related papers: Percolation in living neural networks
We analyze the properties of Degree-Ordered Percolation (DOP), a model in which the nodes of a network are occupied in degree-descending order. This rule is the opposite of the much studied degree-ascending protocol, used to investigate…
We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with…
Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting…
Generally, the threshold of percolation in complex networks depends on the underlying structural characterization. However, what topological property plays a predominant role is still unknown, despite the speculation of some authors that…
Spreading of either information or matter can often be treated as a network problem. It can be of great importance to be able to estimate the likelihood that spreading through a network reaches essentially the entire network while still not…
We provide arguments for the property of the degree-degree correlations of giant components formed by the percolation process on uncorrelated random networks. Using the generating functions, we derive a general expression for the…
During the past two decades, percolation has long served as a basic paradigm for network resilience, community formation and so on in complex systems. While the percolation transition is known as one of the most robust continuous…
The goal of is to study how increased variability in the degree distribution impacts the global connectivity properties of a large network. We approach this question by modeling the network as a uniform random graph with a given degree…
Directed and heterogeneous hypergraphs capture directional higher-order interactions with intrinsically asymmetric functional dependencies among nodes. As a result, damage to certain nodes can suppress entire hyperedges, whereas failure of…
The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…
We investigate percolation transitions in a nonlocal network model numerically. In this model, each node has an exclusive partner and a link is forbidden between two nodes whose $r$-neighbors share any exclusive pair. The $r$-neighbor of a…
We consider neighbor-induced damage percolation, a model describing systems where the inactivation of some elements may damage their neighboring active ones, making them unusable. We present an exact solution for the size of the giant…
In this paper, we study the order of the largest connected component of a random graph having two sources of randomness: first, the graph is chosen randomly from all graphs with a given degree sequence, and then bond percolation is applied.…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
We reconsider the problem of percolation on an equilibrium random network with degree-degree correlations between nearest-neighboring vertices focusing on critical singularities at a percolation threshold. We obtain criteria for…
We introduce techniques for exploring the functionality of a neural network and extracting simple, human-readable approximations to its performance. By performing gradient ascent on the input space of the network, we are able to produce…
We study the behavior of algebraic connectivity in a weighted graph that is subject to site percolation, random deletion of the vertices. Using a refined concentration inequality for random matrices we show in our main theorem that the…
Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…