On Bootstrap Percolation in Living Neural Networks

Abstract

Recent experimental studies of living neural networks reveal that their global activation induced by electrical stimulation can be explained using the concept of bootstrap percolation on a directed random network. The experiment consists in activating externally an initial random fraction of the neurons and observe the process of firing until its equilibrium. The final portion of neurons that are active depends in a non linear way on the initial fraction. The main result of this paper is a theorem which enables us to find the asymptotic of final proportion of the fired neurons in the case of random directed graphs with given node degrees as the model for interacting network. This gives a rigorous mathematical proof of a phenomena observed by physicists in neural networks.

References in corpus (7)

• k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects
• Percolation in living neural networks
• The Physics of Living Neural Networks
• Remarks on Bootstrap Percolation in Metric Networks
• Rhythmogenic neuronal networks, pacemakers, and k-cores
• Quorum Percolation in Living Neural Networks
• The structure of typical clusters in large sparse random configurations

Cited by in corpus (16)

• Resilience to Contagion in Financial Networks
• Bootstrap percolation in inhomogeneous random graphs
• Sharp metastability threshold for an anisotropic bootstrap percolation model
• Bootstrap percolation on geometric inhomogeneous random graphs
• Influence Maximization for Fixed Heterogeneous Thresholds
• Metastability threshold for anisotropic bootstrap percolation in three dimensions
• Minimum stationary values of sparse random directed graphs
• Bootstrap and diffusion percolation transitions in three-dimensional lattices
• The time of bootstrap percolation with dense initial sets for all thresholds
• Bootstrap percolation in random $k$-uniform hypergraphs
• A simple proof of almost percolation on G(n;p)
• Bootstrap percolation on G(n,p) revisited
• On irreversible spread of influence in edge-weighted graphs
• The maximum time of 2-neighbour bootstrap percolation in grid graphs and some parameterized results
• On connectivity, conductance and bootstrap percolation for a random k-out, age-biased graph
• Bootstrap percolation in power-law random graphs