Related papers: Modeling of Spiking-Bursting Neural Behavior Using…
Spike Timing Dependent Plasticity is form of learning that has been demonstrated in real cortical tissue, but attempts to use it for artificial systems have not produced good results. This paper seeks to remedy this with two significant…
We propose a framework for surrogate modelling of spiking systems. These systems are often described by stiff differential equations with high-amplitude oscillations and multi-timescale dynamics, making surrogate models an attractive tool…
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…
First return maps of interspike intervals for biological neurons that generate repetitive bursts of impulses can display stereotyped structures (neuronal signatures). Such structures have been linked to the possibility of multicoding and…
A spiking neuron ``computes'' by transforming a complex dynamical input into a train of action potentials, or spikes. The computation performed by the neuron can be formulated as dimensional reduction, or feature detection, followed by a…
Common wisdom indicates that to implement a Dynamical Memory with spiking neurons two ingredients are necessary: recurrence and a neuron population. Here we shall show that the second requirement is not needed. We shall demonstrate that…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
Repeating patterns of spike sequences from a neuronal network have been proposed to be useful in the reconstruction of the network topology. Reverberations in a physiologically realistic model with various physical connection topologies…
Rapid action potential generation --- spiking --- and alternating intervals of spiking and quiescence --- bursting --- are two dynamic patterns observed in neuronal activity. In computational models of neuronal systems, the transition from…
Spiking Neural Networks (SNN) are models for "realistic" neuronal computation, which makes them somehow different in scope from "ordinary" deep-learning models widely used in AI platforms nowadays. SNNs focus on timed latency (and possibly…
The synaptic connectivity of cortex is plastic, with experience shaping the ongoing interactions between neurons. Theoretical studies of spike timing-dependent plasticity (STDP) have focused on either just pairs of neurons or large-scale…
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…
Determining how synaptic coupling within and between regions is modulated during sensory processing is an important topic in neuroscience. Electrophysiological recordings provide detailed information about neural spiking but have…
In this article, we study optimal control problems of spiking neurons whose dynamics are described by a phase model. We design minimum-power current stimuli (controls) that lead to targeted spiking times of neurons, where the cases with…
We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…
Computational models of cortical activity provide insight into the mechanisms of higher-order processing in the human brain including planning, perception and the control of movement. Activity in the cortex is ongoing even in the absence of…
Many central neurons, and in particular certain brainstem aminergic neurons exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz. A large number of ion channel types contribute to such spiking so that accurate…
Biological spiking neurons with intrinsic dynamics underlie the powerful representation and learning capabilities of the brain for processing multimodal information in complex environments. Despite recent tremendous progress in spiking…
While spike timing has been shown to carry detailed stimulus information at the sensory periphery, its possible role in network computation is less clear. Most models of computation by neural networks are based on population firing rates.…
Chimera states are spatiotemporal patterns in which coherence and incoherence coexist. We observe the coexistence of synchronous (coherent) and desynchronous (incoherent) domains in a neuronal network. The network is composed of coupled…