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Field theory for biophysical neural networks
Siwei Qiu,Carson C. Chow +1 more
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Here, it is shown how ideas from quantum field theory can be used to construct an effective reduced theory, which may be analyzed with lattice computations.Abstract:
The human brain is a complex system composed of a network of hundreds of billions of discrete neurons that are coupled through time dependent synapses. Simulating the entire brain is a daunting challenge. Here, we show how ideas from quantum field theory can be used to construct an effective reduced theory, which may be analyzed with lattice computations. We give some examples of how the formalism can be applied to biophysically plausible neural network models.read more
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Ghosts of bump attractors in stochastic neural fields: Bottlenecks and extinction
TL;DR: In this paper, the authors study the dynamics of stationary bumps in neural field equations near a saddle-node bifurcation and derive a quadratic amplitude equation that describes the slow evolution of the even mode (bump contractions).
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Ghosts of bump attractors in stochastic neural fields: Bottlenecks and extinction
TL;DR: A quadratic amplitude equation is derived that describes the slow evolution of the even mode (bump contractions) as it depends on the distance from the bifurcation, which can be analyzed to reveal bump extinction time both below and above the saddle-node.
References
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A. L. Hodgkin,A. F. Huxley +1 more
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Effective Action for Composite Operators
TL;DR: In this paper, a Rayleigh-Ritz procedure is introduced which replaces arbitrary variations with parametric variations, and previously unsolved nonlinear equations become solvable algebraic equations in the Rayleigh Ritz approximation.
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Type i membranes, phase resetting curves, and synchrony
TL;DR: It is shown in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation and the differences between synapses that act rapidly and those that act slowly are shown.
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Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma
J. A. Connor,Charles F. Stevens +1 more
TL;DR: Membrane parameters of an isolated neural cell body have been determined by voltage clamp analysis and data are expressed as membrane ion‐specific conductances, leak conductance, and capacitance.