Scaling behavior in probabilistic neuronal cellular automata

Abstract

We study a neural network model of interacting stochastic discrete two-state cellular automata on a regular lattice. The system is externally tuned to a critical point which varies with the degree of stochasticity (or the effective temperature). There are avalanches of neuronal activity, namely spatially and temporally contiguous sites of activity; a detailed numerical study of these activity avalanches is presented, and single, joint and marginal probability distributions are computed. At the critical point, we find that the scaling exponents for the variables are in good agreement with a mean-field theory.

Single-neuron criticality optimizes analog dendritic computation

“…In our previous models 37 38 , other parameters have been studied, but the time-length of the spikes that we introduce here proves to be a crucial factor. Such variability in the duration of the spike has been shown to shape the network dynamics 43 , and to enhance the computational capability of neuronal networks 44 . In the present model, the variable duration of dendritic spikes plays an important role in dendritic computation because it is capable of controlling the emergence of a phase transition.…”

“…While the variable-duration criterion must be satisfied to give rise to a critical neuron, it does not play such a crucial role in giving rise to a critical neuronal network 43 . The key difference between the two spatial scales is the topology: due to inhibitory signaling mechanisms during growth 61 , a dendritic tree contains no loops, whereas in neuronal networks they abound.…”

Measuring the Dynamics of Information Processing on a Local Scale in Time and Space

“…Indeed, CAs have even been used in neural network models to study criticality in avalanches of activity [75,67]. While they may not be the most realistic microscopic neural model available, it is certainly true that CAs can exhibit certain phenomena that are of particular interest in neuroscience, including avalanche behaviour (e.g.…”

“…While they may not be the most realistic microscopic neural model available, it is certainly true that CAs can exhibit certain phenomena that are of particular interest in neuroscience, including avalanche behaviour (e.g. [75,80,47,67]) and coherent propagating wave-like structures (e.g. [27,17]).…”

Unveiling causal activity of complex networks

“…For example, what fraction of the activity in such a network can be attributed to the hidden causal dynamics, and what fraction is produced by other processes, such as noise? Here we describe a new approach to this problem and demonstrate its utility on neural networks.Over the past twenty years, there have been a number of theoretical [3][4][5][6][7][8][9][10][11][12][13][14][15] and experimental [16][17][18][19][20][21][22][23][24][25][26][27][28] attempts to connect activity in living neural networks to critical avalanches like those seen in the Bak-Tang-Wiesenfeld (BTW) sandpile model [29,30]. It has been hypothesized that homeostatic mechanisms might tune the brain, a complex neural network, towards optimality associated with a critical point [31] which separates ordered ("supercritical") and disordered ("subcritical") phases, where cascades of activity are amplified or damped, respectively [15,24,27,32,33].…”