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Correlation between neural spike trains increases with firing rate
Populations of neurons in the retina, olfactory system, visual and somatosensory thalamus, and several cortical regions show temporal correlation between the discharge times of their actionExpand
On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
We undertake a probabilistic analysis of the response of repetitively firing neural populations to simple pulselike stimuli. Expand
The What and Where of Adding Channel Noise to the Hodgkin-Huxley Equations
Conductance-based equations for electrically active cells form one of the most widely studied mathematical frameworks in computational biology. Expand
Impact of Network Structure and Cellular Response on Spike Time Correlations
We develop a theoretical framework that accurately predicts the structure of correlated spiking that emerges in a widely used model — recurrent networks of general integrate and fire cells. Expand
Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons.
The random transitions of ion channels between conducting and nonconducting states generate a source of internal fluctuations in a neuron, known as channel noise. The standard method for modeling theExpand
Correlation and synchrony transfer in integrate-and-fire neurons: basic properties and consequences for coding.
We study how pairs of neurons transfer correlated input currents into correlated spikes. Over rapid time scales, correlation transfer increases with both spike time variability and rate; theExpand
Direction-Selective Circuits Shape Noise to Ensure a Precise Population Code
Neural responses are noisy, and circuit structure can correlate this noise across neurons. Theoretical studies show that noise correlations can have diverse effects on population coding, but theseExpand
The Multivariate Hawkes Process in High Dimensions: Beyond Mutual Excitation
The Hawkes process is a class of point processes whose future depends on their own history. Previous theoretical work on the Hawkes process is limited to a special case in which a past event can onlyExpand
Toward closed-loop optimization of deep brain stimulation for Parkinson's disease: concepts and lessons from a computational model.
A closed-loop global optimization algorithm may identify novel DBS waveforms that could be more effective than their high-frequency counterparts. Expand
Optimal Inputs for Phase Models of Spiking Neurons
Variational methods are used to determine the optimal currents that elicit spikes in various phase reductions of neural oscillator models. We show that, for a given reduced neuron model and targetExpand