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| Hauptseite > Publikationsdatenbank > A Neuron Model Independent Path Integral Explored via Binary Assemblies |
| Hauptseite > Publikationsdatenbank > A Neuron Model Independent Path Integral Explored via Binary Assemblies |
| Master Thesis | FZJ-2017-08497 |
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2017
Please use a persistent id in citations: http://hdl.handle.net/2128/16654
Abstract: We present the basic exploration of a novel path integral formulation for models of biological neuronal networks that allows to keep the neuron model unspecified until quantities are explicitly calculated. This is done at the example of a binary neuron network containing an assembly, which is suited to discuss the limits of standard mean field theory and the feasibility of a path integral approach, while also being of some neuroscientific interest. Advanced theoretical approaches to the description of neuronal network activity are still in their infancy, but much needed, due to its nonlinearities, statistical nature, and nonequilibrium dynamics. There is thus now renewed interest in the transfer of mathematical tools developed in statistical physics to the theory of neural networks. We model a Hebbian cell assembly as a group of O(100) excitatory binary neurons with increased coupling embedded in a larger balanced random network. Using standard mean-field theory and simulation, the system properties and parameter dependencies are analysed, especially emergence of the high activity state, spontaneous transitions, and pairwise correlations. We then introduce the path integral formulation, applying it to a single population of binary neurons. We show the relation of the tree level approximation to mean field theory, calculate propagators and a 1-loop diagram, and generalize to multiple populations. The formulation specifically uses generic properties of neuronal networks, which allows the formal description of the systems properties before an effective neuron model is fixed. It is analytically feasible for rate, binary and, possibly, spiking neurons. The implications of the results for the assembly model and the relation of our formulation to other path integral approaches are discussed. We stress that a functional form unlocks tools to treat critical phenomena, large fluctuations, disorder and may lead eventually to effective coarse grained theories by using renormalization group methods.
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