Related papers: The complexity of dynamics in small neural circuit…
Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality depends on the emerging collective dynamics of the network. Synchrony of oscillations is one of the most…
In a first step towards the comprehension of neural activity, one should focus on the stability of the various dynamical states. Even the characterization of idealized regimes, such as a perfectly periodic spiking activity, reveals…
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…
Mean field theory has been successfully used to analyze deep neural networks (DNN) in the infinite size limit. Given the finite size of realistic DNN, we utilize the large deviation theory and path integral analysis to study the deviation…
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 are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…
Neural field equations are used to describe the spatiotemporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under…
We address the inverse problem of reconstructing both the structure and dynamics of a network from mean-field measurements, which are linear combinations of node states. This setting arises in applications where only a few aggregated…
This paper introduces a class of stochastic models of interacting neurons with emergent dynamics similar to those seen in local cortical populations, and compares them to very simple reduced models driven by the same mean excitatory and…
We here unify the field theoretical approach to neuronal networks with large deviations theory. For a prototypical random recurrent network model with continuous-valued units, we show that the effective action is identical to the rate…
In this work, we propose a nonlinear stochastic model of a network of stochastic spiking neurons. We heuristically derive the mean-field limit of this system. We then design a Monte Carlo method for the simulation of the microscopic system,…
Random networks with complex topology are common in Nature, describing systems as diverse as the world wide web or social and business networks. Recently, it has been demonstrated that most large networks for which topological information…
Deciphering the underpinnings of the dynamical processes leading to information transmission, processing, and storing in the brain is a crucial challenge in neuroscience. An inspiring but speculative theoretical idea is that such dynamics…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…
Starting from a spectral expansion of the Fokker-Plank equation for the membrane potential density in a network of spiking neurons, a low-dimensional dynamics of the collective firing rate is derived. As a result a $n$-order ordinary…
Synaptic interactions structure the phase space of the dynamics of neural circuits and constrain neural computation. Understanding how requires methods that handle those discrete interactions, yet few exist. Recently, it was discovered that…
We investigate numerically the collective dynamical behavior of pulse-coupled non-leaky integrate-and-fire-neurons that are arranged on a two-dimensional small-world network. To ensure ongoing activity, we impose a probability for…
Neural activity exhibits a vast range of timescales that can be several fold larger than the membrane time constant of individual neurons. Two types of mechanisms have been proposed to explain this conundrum. One possibility is that large…
Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space…
The collective dynamics of a network of excitable nodes changes dramatically when inhibitory nodes are introduced. We consider inhibitory nodes which may be activated just like excitatory nodes but, upon activating, decrease the probability…