Related papers: Mean field theory for a balanced hypercolumn model…
A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population.…
Mean-field models provide a link between microscopic neuronal activity and macroscopic brain dynamics. Their derivation depends on simplifying assumptions, such as all-to-all connectivity, limiting their biological realism. To overcome…
We consider a threshold-crossing spiking process as a simple model for the activity within a population of neurons. Assuming that these neurons are driven by a common fluctuating input with Gaussian statistics, we evaluate the…
The theory of Balanced Neural Networks is a very popular explanation for the high degree of variability and stochasticity in the brain's activity. Roughly speaking, it entails that typical neurons receive many excitatory and inhibitory…
Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…
We consider a network of randomly coupled rate-based neurons influenced by external and internal noise. We derive a second-order stochastic mean-field model for the network dynamics and use it to analyze the stability and bifurcations in…
Population rate or activity equations are the foundation of a common approach to modeling for neural networks. These equations provide mean field dynamics for the firing rate or activity of neurons within a network given some connectivity.…
Recent studies have suggested that the cognitive process of the human brain is realized as probabilistic inference and can be further modeled by probabilistic graphical models like Markov random fields. Nevertheless, it remains unclear how…
A mean field feedback artificial neural network algorithm is developed and explored for the set covering problem. A convenient encoding of the inequality constraints is achieved by means of a multilinear penalty function. An approximate…
Travelling waves of neural firing activity are observed in brain tissue as a part of various sensory, motor and cognitive processes. They represent an object of major interest in the study of excitable networks, with analysis conducted in…
Computational models of cortical activity provide insight into the mechanisms of higher-order processing in the human brain including planning, perception and the control of movement. Activity in the cortex is ongoing even in the absence of…
Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for…
Massively parallel recordings of spiking activity in cortical networks show that covariances vary widely across pairs of neurons. Their low average is well understood, but an explanation for the wide distribution in relation to the static…
A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the…
The response time of physical computational elements is finite, and neurons are no exception. In hierarchical models of cortical networks each layer thus introduces a response lag. This inherent property of physical dynamical systems…
We study finite-size fluctuations in a network of spiking deterministic neurons coupled with non-uniform synaptic coupling. We generalize a previously developed theory of finite size effects for uniform globally coupled neurons. In the…
Mesoscopic models of finite-size neuronal populations are crucial to understand the dynamics of neural networks in the brain, especially their fluctuations and response to stimuli. However, current theories to derive such models are based…
A spin version of dynamical mean-field theory is extended for magnetically ordered states in the Heisenberg model. The self-consistency equations are solved with high numerical accuracy by means of the continuous-time quantum Monte Carlo…
Research has shown that neurons within the brain are selective to certain stimuli. For example, the fusiform face area (FFA) region is known by neuroscientists to selectively activate when people see faces over non-face objects. However,…
We propose and analyse a procedure for using a standard activity-based neuron network model and firing data to compute the effective connection strengths between neurons in a network. We assume a Heaviside response function, that the…