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Single trial analyses of ensemble activity in alert animals demonstrate that cortical circuits dynamics evolve through temporal sequences of metastable states. Metastability has been studied for its potential role in sensory coding, memory…
In this report trial-to-trial variations in the synchronized responses of neural networks are offered as evidence for excitation-inhibition ratio being a dynamic variable over time scales of minutes. Synchronized network responses to…
We show that the unavoidable increase in neuronal response latency to ongoing stimulation serves as a nonuniform gradual stretching of neuronal circuit delay loops and emerges as an essential mechanism in the formation of various types of…
In this paper we study the hydrodynamic limit for a stochastic process describing the time evolution of the membrane potentials of a system of neurons with spatial dependency. We do not impose on the neurons mean-field type interactions.…
In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. A Spike-Timing Dependent Plasticity (STDP) rule is a…
Accurately modelling the dynamics of complex systems and discovering their governing differential equations are critical tasks for accelerating scientific discovery. Using noisy, synthetic data from two damped oscillatory systems, we…
Neural Ordinary Differential Equations (ODEs) represent a significant advancement at the intersection of machine learning and dynamical systems, offering a continuous-time analog to discrete neural networks. Despite their promise, deploying…
We study a stochastic system of interacting neurons and its metastable properties. The system consists of $N$ neurons, each spiking randomly with rate depending on its membrane potential. At its spiking time, the neuron potential is reset…
The voltage-conductance kinetic model for the collective behavior of neurons has been studied by scientists and mathematicians for two decades, but the rigorous analysis of its solution structure has been only partially obtained in spite of…
Recurrently connected neuron populations play key roles in sensory perception and memory storage across various brain regions. While these populations are often assumed to encode information through firing rates, this method becomes…
The circuits comprising superconducting optoelectronic synapses, dendrites, and neurons are described by numerically cumbersome and formally opaque coupled differential equations. Reference 1 showed that a phenomenological model of…
The activity of ensembles of simultaneously recorded neurons can be represented as a set of points in the space of firing rates. Even though the dimension of this space is equal to the ensemble size, neural activity can be effectively…
Neuromorphic computing is a brainlike information processing paradigm that requires adaptive learning mechanisms. A spiking neuro-evolutionary system is used for this purpose; plastic resistive memories are implemented as synapses in…
Stochastic point processes with refractoriness appear frequently in the quantitative analysis of physical and biological systems, such as the generation of action potentials by nerve cells, the release and reuptake of vesicles at a synapse,…
Spike-timing-dependent plasticity(STDP) is a biological process in which the precise order and timing of neuronal spikes affect the degree of synaptic modification. While there have been numerous research focusing on the role of STDP in…
Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability…
Robot-assisted therapy can deliver high-dose, task-specific training after neurologic injury, but most systems act primarily at the limb level-engaging the impaired neural circuits only indirectly-which remains a key barrier to truly…
Motivation: Modeling biological signaling networks using ordinary differential equations (ODEs) has proven to be a powerful technique for generating insight into cellular dynamics, but it typically requires estimating rate parameters based…
Optogenetics is a new tool to study neuronal circuits that have been genetically modified to allow stimulation by flashes of light. We study recordings from single neurons within neural circuits under optogenetic stimulation. The data from…
Networks of stochastic spiking neurons are interesting models in the area of Theoretical Neuroscience, presenting both continuous and discontinuous phase transitions. Here we study fully connected networks analytically, numerically and by…