Journal ArticleDOI
Field-theoretic approach to fluctuation effects in neural networks.
Michael A. Buice,Jack D. Cowan +1 more
TLDR
The effective spike model is constructed, which describes both neural fluctuations and response and is argued that neural activity governed by this model exhibits a dynamical phase transition which is in the universality class of directed percolation.Abstract:
A well-defined stochastic theory for neural activity, which permits the calculation of arbitrary statistical moments and equations governing them, is a potentially valuable tool for theoretical neuroscience. We produce such a theory by analyzing the dynamics of neural activity using field theoretic methods for nonequilibrium statistical processes. Assuming that neural network activity is Markovian, we construct the effective spike model, which describes both neural fluctuations and response. This analysis leads to a systematic expansion of corrections to mean field theory, which for the effective spike model is a simple version of the Wilson-Cowan equation. We argue that neural activity governed by this model exhibits a dynamical phase transition which is in the universality class of directed percolation. More general models (which may incorporate refractoriness) can exhibit other universality classes, such as dynamic isotropic percolation. Because of the extremely high connectivity in typical networks, it is expected that higher-order terms in the systematic expansion are small for experimentally accessible measurements, and thus, consistent with measurements in neocortical slice preparations, we expect mean field exponents for the transition. We provide a quantitative criterion for the relative magnitude of each term in the systematic expansion, analogous to the Ginsburg criterion. Experimental identification of dynamic universality classes in vivo is an outstanding and important question for neuroscience.read more
Citations
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Journal ArticleDOI
Neuronal avalanches imply maximum dynamic range in cortical networks at criticality
TL;DR: In this article, the authors show that cortical networks that generate neuronal avalanches benefit from a maximized dynamic range, i.e., the ability to respond to the greatest range of stimuli.
Journal ArticleDOI
Being Critical of Criticality in the Brain
John M. Beggs,Nicholas M. Timme +1 more
TL;DR: The concept of criticality is explained and substantial objections to the criticality hypothesis raised by skeptics are reviewed, and counter points are presented in dialog form.
Journal ArticleDOI
The criticality hypothesis: how local cortical networks might optimize information processing
TL;DR: In this paper, the authors review recent experiments on networks of cortical neurons, showing that they appear to be operating near the critical point in a phase transition between total randomness and boring order, and suggest that criticality may allow cortical networks to optimize information processing.
Journal ArticleDOI
Spatiotemporal dynamics of continuum neural fields
TL;DR: This work surveys recent analytical approaches to studying the spatiotemporal dynamics of continuum neural fields, an important example of spatially extended excitable systems with nonlocal interactions.
Journal ArticleDOI
Fractals in the nervous system: conceptual implications for theoretical neuroscience.
TL;DR: In this paper, the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance and drawing attention to the as yet still unresolved issues of the detailed relationships among power-law scaling, self-similarity, and self-organized criticality.
References
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Book
Quantum Field Theory and Critical Phenomena
TL;DR: In this paper, a renormalization group analysis is proposed to model the scaling behavior of a field theory in the large N limit of the ferromagnetic order at low temperature.
Journal ArticleDOI
Activity-dependent scaling of quantal amplitude in neocortical neurons
TL;DR: A new form of synaptic plasticity is described that increases or decreases the strength of all of a neuron's synaptic inputs as a function of activity, and may help to ensure that firing rates do not become saturated during developmental changes in the number and strength of synaptic inputs.
Journal ArticleDOI
Neuronal Avalanches in Neocortical Circuits
John M. Beggs,Dietmar Plenz +1 more
TL;DR: This work shows that propagation of spontaneous activity in cortical networks is described by equations that govern avalanches, and suggests that “neuronal avalanches” may be a generic property of cortical networks, and represent a mode of activity that differs profoundly from oscillatory, synchronized, or wave-like network states.
Journal ArticleDOI
The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs
William R. Softky,Christof Koch +1 more
TL;DR: It is argued that neurons that act as temporal integrators over many synaptic inputs must fire very regularly and only in the presence of either fast and strong dendritic nonlinearities or strong synchronization among individual synaptic events will the degree of predicted variability approach that of real cortical neurons.
Journal ArticleDOI
Non-equilibrium critical phenomena and phase transitions into absorbing states
TL;DR: In this article, a review of recent developments in non-equilibrium statistical physics is presented, focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail.
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