Related papers: Systematic fluctuation expansion for neural networ…
The neural dynamics generating sensory, motor, and cognitive functions are commonly understood through field theories for neural population activity. Classic neural field theories are derived from highly simplified models of individual…
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…
Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time…
Recent experimental advances are producing an avalanche of data on both neural connectivity and neural activity. To take full advantage of these two emerging datasets we need a framework that links them, revealing how collective neural…
Finite-sized populations of spiking elements are fundamental to brain function, but also used in many areas of physics. Here we present a theory of the dynamics of finite-sized populations of spiking units, based on a quasi-renewal…
Firing rate fluctuations in neural populations are observed experimentally over multiple time scales, in single neurons, across trials when elicited by stimuli, and across populations. In this work, we examine how firing rate fluctuations…
A population of firing neurons is expected to carry information not only by mean firing rate but also by fluctuation and synchrony among neurons. In order to examine this possibility, we have studied responses of neuronal ensembles to three…
The collective dynamics of neural populations are often characterized in terms of correlations in the spike activity of different neurons. Open questions surround the basic nature of these correlations. In particular, what leads to…
This paper studies a stochastic neural field model that is extended from our previous paper [14]. The neural field model consists of many heterogeneous local populations of neurons. Rigorous results on the stochastic stability are proved,…
Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise.…
Mean field theory is a device to analyze the collective behavior of a dynamical system comprising many interacting particles. The theory allows to reduce the behavior of the system to the properties of a handful of parameters. In neural…
Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
Comprehensive and predictive simulation of coupled reaction networks has long been a goal of biology and other fields. Currently, metabolic network models that utilize enzyme mass action kinetics have predictive power but are limited in…
In this note, we develop semi-analytical techniques to obtain the full correlational structure of a stochastic network of nonlinear neurons described by rate variables. Under the assumption that pairs of membrane potentials are jointly…
Perturbation experiments are carried out by contact process and its mean-field version. Here, the mortality rate is increased or decreased suddenly. It is known that the fluctuation enhancement (FE) occurs after the perturbation, where FE…
Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in…
The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the…
In this paper we investigate the normal and the large fluctuations of additive functionals associated with a stochastic process under a general non-Poissonian resetting mechanism. Cumulative functionals of regenerative processes are very…