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We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
Variability in neural responses is an ubiquitous phenomenon in neurons, usually modeled with stochastic differential equations. In particular, stochastic integrate-and-fire models are widely used to simplify theoretical studies. The…
Neurons communicate with downstream systems via sparse and incredibly brief electrical pulses, or spikes. Using these events, they control various targets such as neuromuscular units, neurosecretory systems, and other neurons in connected…
Population-wide oscillations are ubiquitously observed in mesoscopic signals of cortical activity. In these network states a global oscillatory cycle modulates the propensity of neurons to fire. Synchronous activation of neurons has been…
Recent analyses combining advanced theoretical techniques and high-quality data from thousands of simultaneously recorded neurons provide strong support for the hypothesis that neural dynamics operate near the edge of instability across…
An important idea in neural information processing is the communication-through-coherence hypothesis, according to which communication between two brain regions is effective only if they are phase-locked. Also of importance is neuronal…
How the information microscopically processed by individual neurons is integrated and used in organizing the behavior of an animal is a central question in neuroscience. The coherence of neuronal dynamics over different scales has been…
The highly irregular spiking activity of cortical neurons and behavioral variability suggest that the brain could operate in a fundamentally probabilistic way. Mimicking how the brain implements and learns probabilistic computation could be…
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…
Cortical circuits exhibit high levels of response diversity, even across apparently uniform neuronal populations. While emerging data-driven approaches exploit this heterogeneity to infer effective models of cortical circuit computation…
A steadily increasing body of evidence suggests that the brain performs probabilistic inference to interpret and respond to sensory input and that trial-to-trial variability in neural activity plays an important role. The neural sampling…
Synchronized brain rhythms, associated with diverse cognitive functions, have been observed in electrical recordings of brain activity. Neural synchronization may be well described by using the population-averaged global potential $V_G$ in…
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…
Recent studies have shown how spiking networks can learn complex functionality through error-correcting plasticity, but the resulting structures and dynamics remain poorly studied. To elucidate how these models may link to observed dynamics…
In the last century, most sensorimotor studies of cortical neurons relied on average firing rates. Rate coding is efficient for fast sensorimotor processing that occurs within a few seconds. Much less is known about the neural mechanisms…
We study the effect of intrinsic heterogeneity on the activity of a population of leaky integrate-and-fire neurons. By rescaling the dynamical equation, we derive mathematical relations between multiple neuronal parameters and a fluctuating…
Neuronal heterogeneity, characterized by the presence of a multitude of spiking neuronal patterns, is a widespread phenomenon throughout the nervous system. In particular, the brain exhibits strong variability among inhibitory neurons.…
Neural oscillations are universal phenomena and can be observed at different levels of neural systems, from single neuron to macroscopic brain. The frequency of those oscillations are related to the brain functions. However, little is know…
Synaptic connections in neuronal circuits are modulated by pre- and post-synaptic spiking activity. Heuristic models of this process of synaptic plasticity can provide excellent fits to results from in-vitro experiments in which pre- and…
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…