Related papers: Mean field methods for cortical network dynamics

The Bayesian view of the brain hypothesizes that the brain constructs a generative model of the world, and uses it to make inferences via Bayes' rule. Although many types of approximate inference schemes have been proposed for hierarchical…

In neural circuits, statistical connectivity rules strongly depend on neuronal type. Here we study dynamics of neural networks with cell-type specific connectivity by extending the dynamic mean field method, and find that these networks…

We study the collective dynamics of a Leaky Integrate and Fire network in which precise relative phase relationship of spikes among neurons are stored, as attractors of the dynamics, and selectively replayed at differentctime scales. Using…

Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…

We propose a cellular version of dynamical-mean field theory which gives a natural generalization of its original single-site construction and is formulated in different sets of variables. We show how non-orthogonality of the tight-binding…

A synfire chain is a simple neural network model which can propagate stable synchronous spikes called a pulse packet and widely researched. However how synfire chains coexist in one network remains to be elucidated. We have studied the…

We present an interacting branching model of neural network dynamics, incorporating key biological features such as inhibition with several types of inhibitory interactions. We establish a hierarchy of analytical mean-field approximations…

Spontaneous fluctuations and stimulus response are essential features of neural functioning but how they are connected is poorly understood. I derive fluctuation-dissipation relations (FDR) between the spontaneous spike and voltage…

The computation performed by a neuron can be formulated as a combination of dimensional reduction in stimulus space and the nonlinearity inherent in a spiking output. White noise stimulus and reverse correlation (the spike-triggered average…

Mean field limits are an important tool in the context of large-scale dynamical systems, in particular, when studying multiagent and interacting particle systems. While the continuous-time theory is well-developed, few works have considered…

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…

In this article, we are interested in the behavior of a fully connected network of $N$ neurons, where $N$ tends to infinity. We assume that the neurons follow the stochastic FitzHugh-Nagumo model, whose specificity is the non-linearity with…

We present a general information theoretic approach for identifying functional subgraphs in complex networks where the dynamics of each node are observable. We show that the uncertainty in the state of each node can be expressed as a sum of…

While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…

Functional connectivity refers to the temporal statistical relationship between spatially distinct brain regions and is usually inferred from the time series coherence/correlation in brain activity between regions of interest. In human…

Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that…

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the…

While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates.…

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…

The branching process is the minimal model for propagation dynamics, avalanches and criticality, broadly used in neuroscience. A simple extension of it, adding inhibitory nodes, induces a much-richer phenomenology, including, an…