Related papers: Mean field methods for cortical network dynamics
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
The brain's activity is characterized by the interaction of a very large number of neurons that are strongly affected by noise. However, signals often arise at macroscopic scales integrating the effect of many neurons into a reliable…
The optical conductivity contains relevant information on the properties of correlated electron systems. In infinite dimensions, where dynamical mean field theory becomes exact, vertex corrections can be neglected and the conductivity…
Heterogeneity of firing rate statistics is known to have severe consequences on neural coding. Recent experimental recordings in weakly electric fish indicate that the distribution-width of superficial pyramidal cell firing rates (trial-…
A general expansion scheme based on the concept of linked cluster expansion from the theory of classical spin systems is constructed for models of interacting electrons. It is shown that with a suitable variational formulation of mean-field…
Dynamical balance of excitation and inhibition is usually invoked to explain the irregular low firing activity observed in the cortex. We propose a robust nonlinear balancing mechanism for a random network of spiking neurons, which works…
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…
Neural dynamics is determined by the transmission of discrete synaptic pulses (synaptic shot-noise) among neurons. However, the neural responses are usually obtained within the diffusion approximation modeling synaptic inputs as continuous…
Recurrent neural networks have gained widespread use in modeling sequence data across various domains. While many successful recurrent architectures employ a notion of gating, the exact mechanism that enables such remarkable performance is…
We consider finite systems of $N$ interacting neurons described by non-linear Hawkes processes in a mean field frame. Neurons are described by their membrane potential. They spike randomly, at a rate depending on their potential. In between…
We investigate a network of integrate-and-fire neurons characterized by a distribution of spiking frequencies. Upon increasing the coupling strength, the model exhibits a transition from an asynchronous regime to a nontrivial collective…
Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…
We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…
Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous…
We consider pulse-coupled Leaky Integrate-and-Fire neural networks with randomly distributed synaptic couplings. This random dilution induces fluctuations in the evolution of the macroscopic variables and deterministic chaos at the…
Neurons in the intact brain receive a continuous and irregular synaptic bombardment from excitatory and inhibitory pre-synaptic neurons, which determines the firing activity of the stimulated neuron. In order to investigate the influence of…
When inhibitory neurons constitute about 40% of neurons they could have an important antinociceptive role, as they would easily regulate the level of activity of other neurons. We consider a simple network of cortical spiking neurons with…
In neural circuits, synaptic strengths influence neuronal activity by shaping network dynamics, and neuronal activity influences synaptic strengths through activity-dependent plasticity. Motivated by this fact, we study a recurrent-network…
Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations…
It is frequently hypothesized that cortical networks operate close to a critical point. Advantages of criticality include rich dynamics well-suited for computation and critical slowing down, which may offer a mechanism for dynamic memory.…