Related papers: Weber's law implies neural discharge more regular …

The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an exponentially decaying threshold to model the neuronal…

We study a network of spiking neurons with heterogeneous excitabilities connected via inhibitory delayed pulses. For globally coupled systems the increase of the inhibitory coupling reduces the number of firing neurons by following a Winner…

We derive a synaptic weight update rule for learning temporally precise spike train to spike train transformations in multilayer feedforward networks of spiking neurons. The framework, aimed at seamlessly generalizing error backpropagation…

Neurons communicate with downstream systems via sparse and incredibly brief electrical pulses, or spikes. Using these events, they control various targets such as neuromuscular units, neurosecretory systems, and other neurons in connected…

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…

Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing…

A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…

Power laws arise in a variety of phenomena ranging from matter undergoing phase transition to the distribution of word frequencies in the English language. Usually, their presence is only apparent when data is abundant, and accurately…

This article presents a biological neural network model driven by inhomogeneous Poisson processes accounting for the intrinsic randomness of synapses. The main novelty is the introduction of local interactions: each firing neuron triggers…

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…

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…

This article contains two main theoretical results on neural spike train models. The first assumes that the spike train is modeled as a counting or point process on the real line where the conditional intensity function is a product of a…

In spiking neural networks an action potential could in principle trigger subsequent spikes in the neighbourhood of the initial neuron. A successful spike is that which trigger subsequent spikes giving rise to cascading behaviour within the…

A fundamental inequality governing the spike activity of peripheral neurons is derived and tested against auditory data. This inequality states that the steady-state firing rate must lie between the arithmetic and geometric means of the…

In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…

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 address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…

We determine the large size limit of a network of interacting Hawkes Processes on an adaptive network. The flipping of the node variables is taken to have an intensity given by the mean-field of the afferent edges and nodes. The flipping of…

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…

We study the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and L\"ocherbach (2016) in a diffusive scaling. The system consists of $N$ neurons, each spiking randomly with rate depending on its…