Related papers: Leaky Integrate-and-Fire Neuron under Poisson Stim…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
We study the problem of non-parametric Bayesian estimation of the intensity function of a Poisson point process. The observations are $n$ independent realisations of a Poisson point process on the interval $[0,T]$. We propose two related…
Neurons and other excitable systems can release energy suddenly given a small stimulus. Excitability has recently drawn increasing interest in optics, as it is key to realize all-optical artificial neurons enabling speed-of-light…
The coding properties of cells with different types of receptive fields have been studied for decades. ON-type neurons fire in response to positive fluctuations of the time-dependent stimulus, whereas OFF cells are driven by negative…
We study a stochastic process describing the continuous time evolution of the membrane potentials of finite system of neurons in the absence of external stimuli. The values of the membrane potentials evolve under the effect of {\it chemical…
It is shown that the leaky integrator, the basis for many neuronal models, possesses a negative group delay when a time-delayed recurrent inhibition is added to it. By means of this negative group delay, the leaky integrator becomes a…
We consider a bivariate diffusion process and we study the first passage time of one component through a boundary. We prove that its probability density is the unique solution of a new integral equation and we propose a numerical algorithm…
We propose stochastic, non-parametric activation functions that are fully learnable and individual to each neuron. Complexity and the risk of overfitting are controlled by placing a Gaussian process prior over these functions. The result is…
We study non-locally coupled noisy integrate-and-fire neurons with the Fokker-Planck equation. A propagating pulse state and a wavy state appear as a phase transition from an asynchronous state. We also find a solution in which traveling…
Spiking Neural Networks (SNNs) use discrete spike sequences to transmit information, which significantly mimics the information transmission of the brain. Although this binarized form of representation dramatically enhances the energy…
In spiking neural networks, neuron dynamics are described by the biologically realistic integrate-and-fire model that captures membrane potential accumulation and above-threshold firing behaviors. Among the hardware implementations of…
The dynamical responses of complex neuronal networks to external stimulus injected on a \emph{single} neuron are investigated. Stimulating the largest-degree neuron in the network, it is found that as the intensity of the stimulus…
A binding neuron (BN) whith delayed feedback is considered. The neuron is fed externally with a Poisson stream of intensity $\lambda$. The neuron's output spikes are fed into its input with time delay $\Delta$. The resulting output stream…
We study a network model of two conductance-based pacemaker neurons of differing natural frequency, coupled with either mutual excitation or inhibition, and receiving shared random inhibitory synaptic input. The networks may phase-lock…
The detection of neuronal communities is addressed with basis on two important concepts from neuroscience: facilitation of neuronal firing and nearly simultaneous beginning of activation of sets of neurons. More specifically,…
Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function…
We explore the dynamics of an integrate-and-fire neuron with an oscillatory stimulus. The frustration due to the competition between the neuron's natural firing period and that of the oscillatory rhythm, leads to a rich structure of…
Although recent neurophysiological experiments suggest that synchronous neural activity is involved in some perceptual and cognitive processes, the functional role of such coherent neuronal behavior is not well understood. As a first step…
We study the solutions of a McKean-Vlasov stochastic differential equation (SDE) driven by a Poisson process. In neuroscience, this SDE models the mean field limit of a system of $N$ interacting excitatory neurons with $N$ large. Each…
We present an approximate analytical expression for the escape rate of time-dependent driven stochastic processes with an absorbing boundary such as the driven leaky integrate-and-fire model for neural spiking. The novel approximation is…