Related papers: On Bootstrap Percolation in Living Neural Networks

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…

This article is a mini-review about electrical current flows in networks from the perspective of statistical physics. We briefly discuss analytical methods to solve the conductance of an arbitrary resistor network. We then turn to basic…

We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…

Bootstrap percolation is a well-known model to study the spreading of rumors, new products or innovations on social networks. The empirical studies show that community structure is ubiquitous among various social networks. Thus, studying…

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation…

K-core and bootstrap percolation are widely studied models that have been used to represent and understand diverse deactivation and activation processes in natural and social systems. Since these models are considerably similar, it has been…

Almost all network research has been focused on the properties of a single network that does not interact and depends on other networks. In reality, many real-world networks interact with other networks. Here we develop an analytical…

Global integration of information in the brain results from complex interactions of segregated brain networks. Identifying the most influential neuronal populations that efficiently bind these networks is a fundamental problem of systems…

Perceptions and actions, thoughts and memories result from coordinated activity in hundreds or even thousands of neurons in the brain. It is an old dream of the physics community to provide a statistical mechanics description for these and…

This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…

Elements of neural networks, both biological and artificial, can be described by their selectivity for specific cognitive features. Understanding these features is important for understanding the inner workings of neural networks. For a…

Traditional percolation theory assumes static microscopic rules, limiting its ability to describe real-world complex systems where macroscopic order actively regulates local interactions. Here, we introduce feedback percolation, an unified…

The mathematical theory of pattern formation in electrically coupled networks of excitable neurons forced by small noise is presented in this work. Using the Freidlin-Wentzell large deviation theory for randomly perturbed dynamical systems…

An artificial neuron is modelled as a weighted summation followed by an activation function which determines its output. A wide variety of activation functions such as rectified linear units (ReLU), leaky-ReLU, Swish, MISH, etc. have been…

Recently it has been shown analytically that electric currents in a random diode network are distributed in a multifractal manner [O. Stenull and H. K. Janssen, Europhys. Lett. 55, 691 (2001)]. In the present work we investigate the…

We develop a general theory for percolation in directed random networks with arbitrary two point correlations and bidirectional edges, that is, edges pointing in both directions simultaneously. These two ingredients alter the previously…

We investigate the dynamics of a network consisting of an array of identical cortical units with nearest neighbor interactions under periodic arousal. Each unit consists of two interconnected populations of neurons tuned to a state in which…

Most networks of interest do not live in isolation. Instead they form components of larger systems in which multiple networks with distinct topologies coexist and where elements distributed amongst different networks may interact directly.…

Cortical neurons are characterized by irregular firing and a broad distribution of rates. The balanced state model explains these observations with a cancellation of mean excitatory and inhibitory currents, which makes fluctuations drive…

While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates.…