Related papers: Numerical Frequency Transfer Function Analysis of …

There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the…

We present a novel formulation for biochemical reaction networks in the context of signal transduction. The model consists of input-output transfer functions, which are derived from differential equations, using stable equilibria. We select…

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…

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…

Probability density function of output interspike intervals is found in exact form for leaky integrate and fire neuron stimulated with Poisson stream. The diffusion approximation is not exploited.

The statistics of the output activity of a neuron during its stimulation by the stream of input impulses that forms the stochastic Poisson process is studied. The leaky integrate-and-fire neuron is considered as a neuron model. A new…

We studied the impact of a dynamical threshold on the f-I curve-the relationship between the input and the firing rate of a neuron-in the presence of background synaptic inputs. First, we found that, while the leaky integrate-and-fire model…

The behaviour of neurons under the influence of periodic external input has been modelled very successfully by circle maps. The aim of this note is to extend certain aspects of this analysis to a much more general class of forcing…

Neuronal dynamics are fundamentally constrained by the underlying structural network architecture, yet much of the details of this synaptic connectivity are still unknown even in neuronal cultures in vitro. Here we extend a previous…

The adaptive leaky integrate-and-fire (ALIF) model is fundamental within computational neuroscience and has been instrumental in studying our brains $\textit{in silico}$. Due to the sequential nature of simulating these neural models, a…

Providing an analytical treatment to the stochastic feature of neurons' dynamics is one of the current biggest challenges in mathematical biology. The noisy leaky integrate-and-fire model and its associated Fokker-Planck equation are…

We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between…

We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…

Spiking neural network (SNN) is interesting due to its strong bio-plausibility and high energy efficiency. However, its performance is falling far behind conventional deep neural networks (DNNs). In this paper, considering a general class…

Correlated electrical activity in neurons is a prominent characteristic of cortical microcircuits. Despite a growing amount of evidence concerning both spike-count and subthreshold membrane potential pairwise correlations, little is known…

Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…

Artificial neural networks (ANNs) have been extensively used for the description of problems arising from biological systems and for constructing neuromorphic computing models. The third generation of ANNs, namely, spiking neural networks…

We consider a fully-connected network of leaky integrate-and-fire neurons with spike-timing-dependent plasticity. The plasticity is controlled by a parameter representing the expected weight of a synapse between neurons that are firing…

Spiking Neural Networks (SNNs) are valued for their ability to process spatio-temporal information efficiently, offering biological plausibility, low energy consumption, and compatibility with neuromorphic hardware. However, the commonly…

Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with…