2016-Probability and Statistical Problems and Results Arising from Neural Models

Probability and Statistical Problems and Results Arising from Neural Models 
Organizer and Chair: Priscilla Greenwood (University of British Columbia) 

ANDRE LONGTIN, University of Ottawa
Fisher Information Analysis of Neural Focussing Point Processes  [PDF]
The existence of a focus in a sensory system suggests that the neural activity acquires a specific feature around the focal point. Such a feature is currently unknown. This activity should be altered when the stimulus either looms towards or recedes away from the focal point. We first develop Fisher information theory for non-Poisson firing time point process data. We find that there is a distance at which this information is maximized during looming and receding object motions. This distance is in fact chosen by certain animals to view an object. Strikingly, this maximum occurs at a bifurcation between tonic firing and bursting patterns in the neurone's dynamics where the point process becomes clustered. 
PETER ROWAT, University of California at San Diego
Firing Patterns of a Stochastic Neural Model [PDF]
Neurons in the medial entorhinal cortex exhibit an hexagonal grid-like spatial pattern of spike rates that has been proposed to represent a neural code for the navigational ability of rats and other mammals. Such a spatial pattern can be simulated from a network of neurons with both excitatory and inhibitory connections. We use a simple stochastic model of a stellate cell, with input from a simulated spatial firing field, to explore the spiking patterns produced when an influential current, Ih, is varied. 
LAWRENCE WARD, University of British Columbia
Quasicycles and Quasipatterns in the Brain? [PDF]
Quasicycles are damped oscillations sustained by noise. Similarly, quasipatterns are damped spatial patterns sustained by noise. We will describe (1) one model that exhibits quasicycles, (2) an approximation that indicates that the model's behaviour comprises a stochastic rotation process and an Ornstein-Uhlenbeck amplitude process, (3) application of the approximation to gamma-band oscillations in living brains, and (4) production of quasipatterns in spatial arrays of quasicycle oscillators.