Related papers: Statistical Physics approach to dendritic computat…
A dynamical mean-field approximation (DMA) previously proposed by the present author [H. Hasegawa, Phys. Rev E {\bf 67}, 041903 (2003)] has been extended to ensembles described by a general noisy spiking neuron model. Ensembles of $N$-unit…
This paper models the dynamics of a large set of interacting neurons within the framework of statistical field theory. We use a method initially developed in the context of statistical field theory [44] and later adapted to complex systems…
Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in the wave coordinate frame. Nonequilibrium dynamics are more…
Consider a large number $n$ of neurons, each being connected to approximately $N$ other ones, chosen at random. When a neuron spikes, which occurs randomly at some rate depending on its electric potential, its potential is set to a minimum…
Entanglement phase transitions in quantum chaotic systems subject to projective measurements and in random tensor networks have emerged as a new class of critical points separating phases with different entanglement scaling. We propose a…
We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…
Questions about information encoded by the brain demand statistical frameworks for inferring relationships between neural firing and features of the world. The landmark discovery of grid cells demonstrates that neurons can represent spatial…
Neural computations emerge from myriads of neuronal interactions occurring in intricate spiking networks. Due to the inherent complexity of neural models, relating the spiking activity of a network to its structure requires simplifying…
When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate h, the interplay between creation and annihilation of excitable waves leads to an average activity F. It has recently been…
Describing the collective dynamics of large neural populations using low-dimensional models for averaged variables has long been an attractive task in theoretical neuroscience. Recently developed reduction methods make it possible to derive…
The Poisson Nernst-Planck equations for charge concentration and electric potential in a ball is a model of electro-diffusion of ions in the head of a neuronal dendritic spine. We study the relaxation and the steady state when an initial…
Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity…
Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled…
The structure of the axon-dendrite connections of neurons of the brain creates a rich spatial structure in which provided various combinations of signals surrounding neurons. Structure of dendritic trees and shape of dendritic spines allow…
We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network…
An exact low-dimensional system of mean-field equations for an infinite-size network of pulse coupled integrate-and-fire neurons with a bimodal distribution of an excitability parameter is derived. Bifurcation analysis of these equations…
We investigate the stimulus-dependent tuning properties of a noisy ionic conductance model for intrinsic subthreshold oscillations in membrane potential and associated spike generation. On depolarization by an applied current, the model…
This article investigates the emergence of phase synchronization in a network of randomly connected neurons by chemical synapses. The study uses the classic Hodgkin-Huxley model to simulate the neuronal dynamics under the action of a train…
For a class of excitatory spiking neuron models with delayed feedback fed with a Poisson stochastic process, it is proven that the stream of output interspike intervals cannot be presented as a Markov process of any order. Keywords: spiking…
We present a theoretical study aiming at model fitting for sensory neurons. Conventional neural network training approaches are not applicable to this problem due to lack of continuous data. Although the stimulus can be considered as a…