Related papers: Analysis of a map-based neuronal model
We theoretically describe how weak signals may be efficiently transmitted throughout more than one frequency range in noisy excitable media by kind of stochastic multiresonance. This serves us here to reinterpret recent experiments in…
In real-world applications, observations are often constrained to a small fraction of a system. Such spatial subsampling can be caused by the inaccessibility or the sheer size of the system, and cannot be overcome by longer sampling.…
Mathematical modelling of the macroscopic electrical activity of the brain is highly non-trivial and requires a detailed understanding of not only the associated mathematical techniques, but also the underlying physiology and anatomy.…
We consider a model of a square-wave bursting neuron residing in the regime of tonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting. The statistical properties of the emergent bursting…
We present a novel mathematical approach to model noise in dynamical systems. We do so by considering dynamics of a chain of diffusively coupled Nagumo cells affected by noise. We show that the noise in transmembrane current can be…
The neural coding is yet to be discovered. The neuronal operational modes that arise with fixed inputs but with varying degrees of stimulation help to elucidate their coding properties. In neurons receiving {\it in vivo} stimulation, we…
Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In…
Serotonergic, noradrenergic and dopaminergic brainstem (including midbrain) neurons, often exhibit spontaneous and fairly regular spiking with frequencies of order a few Hz, though dopaminergic and noradrenergic neurons only exhibit such…
We report measurements of the brain activity of subjects engaged in behavioral exchanges with their environments. We observe brain states which are characterized by coordinated oscillation of populations of neurons that are changing rapidly…
The Non-Linear Sigma Model (NLSM) is an example of a field theory on a target space exhibiting intricate geometry. One remarkable characteristic of the NLSM is asymptotic freedom, which triggers interest in perturbative calculations. In the…
Recent advances in experimental techniques enable the simultaneous recording of activity from thousands of neurons in the brain, presenting both an opportunity and a challenge: to build meaningful, scalable models of large neural…
Humans and other animals behave as if we perform fast Bayesian inference underlying decisions and movement control given uncertain sense data. Here we show that a biophysically realistic model of the subthreshold membrane potential of a…
This work continues the analysis of complex dynamics in a class of bidimensional nonlinear hybrid dynamical systems with resets modeling neuronal voltage dynamics with adaptation and spike emission. We show that these models can generically…
Building mathematical models of brains is difficult because of the sheer complexity of the problem. One potential starting point is through basal cognition, which gives abstract representation of a range of organisms without central nervous…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Spintronic neurons which emit sharp voltage spikes are required for the realization of hardware neural networks enabling fast data processing with low-power consumption. In many neuroscience and computer science models, neurons are…
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…
Hybrid oscillator architectures that combine feedback oscillators with self-sustained negative resistance oscillators have emerged as a promising platform for artificial neuron design. In this work, we introduce a modeling and analysis…
We analyze a biophysical model of a neuron from the entorhinal cortex that includes persistent sodium and slow potassium as non-standard currents using reduction of dimension and dynamical systems techniques to determine the mechanisms for…
Models that adapt their predictions based on some given contexts, also known as in-context learning, have become ubiquitous in recent years. We propose to study the behavior of such models when data is contaminated by noise. Towards this…