Related papers: Fast {\large\it Cl-}type inhibitory neuron with de…
Correlations in spike-train ensembles can seriously impair the encoding of information by their spatio-temporal structure. An inevitable source of correlation in finite neural networks is common presynaptic input to pairs of neurons. Recent…
We consider a class of stochastic impulse control problems of general stochastic processes i.e. not necessarily Markovian. Under fairly general conditions we establish existence of an optimal impulse control. We also prove existence of…
We examine the effects of stochastic input currents on the firing behavior of two excitable neurons coupled with fast excitatory synapses. In such cells (models), typified by the quadratic integrate and fire model, mutual synaptic coupling…
We describe a new, computationally simple method for analyzing the dynamics of neuronal spike trains driven by external stimuli. The goal of our method is to test the predictions of simple spike-generating models against extracellularly…
We model the ligand-receptor molecular communication channel with a discrete-time Markov model, and show how to obtain the capacity of this channel. We show that the capacity-achieving input distribution is iid; further, unusually for a…
Large sparse circuits of spiking neurons exhibit a balanced state of highly irregular activity under a wide range of conditions. It occurs likewise in sparsely connected random networks that receive excitatory external inputs and recurrent…
This paper exploits the fact that the variability in the inter-spike intervals, in the spike train issuing from a neuron, carries substantial information regarding the input to the neuron. A framework for neuronal information processing is…
Spike-train responses of single Hodgkin-Huxley (HH) and integrate-and-fire (IF) neurons with and without the refractory period, are calculated and compared. The HH and IF neurons are assumed to receive spike-train inputs with the constant…
If interspike intervals are dependent the instantaneous firing rate does not catch important features of spike trains. In this case the conditional instantaneous rate plays the role of the instantaneous firing rate for the case of samples…
We provide rigorous and exact results characterizing the statistics of spike trains in a network of leaky integrate and fire neurons, where time is discrete and where neurons are submitted to noise, without restriction on the synaptic…
We demonstrate deterministic extensive chaos in the dynamics of large sparse networks of theta neurons in the balanced state. The analysis is based on numerically exact calculations of the full spectrum of Lyapunov exponents, the entropy…
Networks of fast-spiking interneurons are crucial for the generation of neural oscillations in the brain. Here we study the synchronous behavior of interneuronal networks that are coupled by delayed inhibitory and fast electrical synapses.…
We study a purely inhibitory neural network model where neurons are represented by their state of inhibition. The study we present here is partially based on the work of Cottrell \cite{Cot} and Fricker et al. \cite{FRST}. The spiking rate…
We study mean-field descriptions for spatially-extended networks of linear (leaky) and quadratic integrate-and-fire neurons with stochastic spiking times. We consider large-population limits of continuous-time Galves-L\"ocherbach (GL)…
Neural responses are highly variable, and some portion of this variability arises from fluctuations in modulatory factors that alter their gain, such as adaptation, attention, arousal, expected or actual reward, emotion, and local metabolic…
We consider a linear Gaussian noise channel used with delayed feedback. The channel noise is assumed to be a ARMA (autoregressive and/or moving average) process. We reformulate the Gaussian noise channel into an intersymbol interference…
Many properties of perceptual decision making are well-modeled by deep neural networks. However, such architectures typically treat decisions as instantaneous readouts, overlooking the temporal dynamics of the decision process. We present…
Neurons fire irregularly on multiple timescales when stimulated with a periodic pulse train. This raises two questions: Does this irregularity imply significant intrinsic stochasticity? Can existing neuron models be readily extended to…
Synchronized oscillations in networks of inhibitory and excitatory coupled bursting neurons are common in a variety of neural systems from central pattern generators to human brain circuits. One example of the latter is the subcortical…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…