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The phase-resetting curve (PRC) of a neural oscillator describes the effect of a perturbation on its periodic motion and is therefore useful to study how the neuron responds to stimuli and whether it phase locks to other neurons in a network. Combining theory, computer simulations and electrophysiological experiments we present a simple method for(More)
We demonstrate that two key theoretical objects used widely in computational neuroscience, the phase-resetting curve (PRC) from dynamics and the spike triggered average (STA) from statistical analysis, are closely related when neurons fire in a nearly regular manner and the stimulus is sufficiently small. We prove that the STA due to injected noisy current(More)
Oscillations are a common feature of odor-evoked and spontaneous activity in the olfactory system in vivo and in vitro and are thought to play an important role in information processing and memory in a variety of brain areas. Theoretical and experimental studies have described several mechanisms by which oscillations can be generated and synchronized.(More)
We have investigated the effect of the phase response curve on the dynamics of oscillators driven by noise in two limit cases that are especially relevant for neuroscience. Using the finite element method to solve the Fokker-Planck equation we have studied (i) the impact of noise on the regularity of the oscillations quantified as the coefficient of(More)
The transient oscillatory model of odor identity encoding seeks to explain how odorants with spatially overlapped patterns of input into primary olfactory networks can be discriminated. This model provides several testable predictions about the distributed nature of network oscillations and how they control spike timing. To test these predictions, 16(More)
The brain is noisy. Neurons receive tens of thousands of highly fluctuating inputs and generate spike trains that appear highly irregular. Much of this activity is spontaneous - uncoupled to overt stimuli or motor outputs - leading to questions about the functional impact of this noise. Although noise is most often thought of as disrupting patterned(More)
Genetic disorders arising from copy number variations in the ERK (extracellular signal-regulated kinase) MAP (mitogen-activated protein) kinases or mutations in their upstream regulators that result in neuro-cardio-facial-cutaneous syndromes are associated with developmental abnormalities, cognitive deficits, and autism. We developed murine models of these(More)
Markov chains provide realistic models of numerous stochastic processes in nature. We demonstrate that in any Markov chain, the change in occupation number in state A is correlated to the change in occupation number in state B if and only if A and B are directly connected. This implies that if we are only interested in state A, fluctuations in B may be(More)
We have combined neurophysiologic recording, statistical analysis, and computational modeling to investigate the dynamics of the respiratory network in the brainstem. Using a multielectrode array, we recorded ensembles of respiratory neurons in perfused in situ rat preparations that produce spontaneous breathing patterns, focusing on inspiratory pre-motor(More)
Combining computer simulations and electrophysiological experiments we have studied the effect of noise on the responses of olfactory neurons. In particular, we first investigated the reliability of mitral cell responses and found, as previously observed in other neural systems, that, in the presence of background noise, mitral cells reliably respond to(More)