Related papers: An integrate-and-fire model to generate spike trai…
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…
Neurons subject to a common non-stationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations…
Stochastic integrate-and-fire (IF) neuron models have found widespread applications in computational neuroscience. Here we present results on the white-noise-driven perfect, leaky, and quadratic IF models, focusing on the spectral…
The statistical analysis of neuronal spike trains by models of point processes often relies on the assumption of constant process parameters. However, it is a well-known problem that the parameters of empirical spike trains can be highly…
This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is…
In spiking neural networks, the information is conveyed by the spike times, that depend on the intrinsic dynamics of each neuron, the input they receive and on the connections between neurons. In this article we study the Markovian nature…
Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…
The instantaneous state of a neural network consists of both the degree of excitation of each neuron, the network is composed of, and positions of impulses in communication lines between neurons. In neurophysiological experiments, the…
The instantaneous state of a neural network consists of both the degree of excitation of each neuron the network is composed of and positions of impulses in communication lines between the neurons. In neurophysiological experiments, the…
We model the dynamics of the leaky integrate-fire neuron under periodic stimulation as a Markov process with respect to the stimulus phase. This avoids the unrealistic assumption of a stimulus reset after each spike made in earlier work and…
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…
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 consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not at this precise moment. The system evolves as…
Spike generation in neurons produces a temporal point process, whose statistics is governed by intrinsic phenomena and the external incoming inputs to be coded. In particular, spike-evoked adaptation currents support a slow temporal process…
Analytical expressions are put forward to investigate the forced spiking activity of abstract neuron models such as the driven leaky integrate-and-fire (LIF) model. The method is valid in a wide parameter regime beyond the restraining…
A fundamental problem in neuroscience is to characterize the dynamics of spiking from the neurons in a circuit that is involved in learning about a stimulus or a contingency. A key limitation of current methods to analyze neural spiking…
Randomly-connected networks of integrate-and-fire (IF) neurons are known to display asynchronous irregular (AI) activity states, which resemble the discharge activity recorded in the cerebral cortex of awake animals. However, it is not…
Numerical investigations have been made of responses of a Hodgkin-Huxley (HH) neuron to spike-train inputs whose interspike interval (ISI) is modulated by deterministic, semi-deterministic (chaotic) and stochastic signals. As deterministic…
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…
We present a first-order non-homogeneous Markov model for the interspike-interval density of a continuously stimulated spiking neuron. The model allows the conditional interspike-interval density and the stationary interspike-interval…