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Friday, January 5 — Session 6: Neuron Models and Neural Networks
8:30-9:10 am	Anna Lin Duke University
9:10-9:30 am	Kresimir Josic University of Houston Email: josic@math.uh.edu authors: Brent Doiron (NYU), Jaime de la Rocha (NYU), Eric Shea-Brown (NYU), Kresimir Josic* (University of Houston) How do correlations propagate in a neuronal network? There  is  strong  evidence  that the  spike  responses  of distinct cortical neurons are  correlated during sensory processing. I will  address the question  of how  neurons transform  correlations in their   inputs  into   correlations  between   their   outputs  (spike trains).  In particular,  I  will present  experimental and  numerical evidence  that suggests  that  the susceptibility  to a  synchronizing input increases with the rate of the neurons' response. Analysis  of leaky  integrate  and fire  (LIF)  neurons confirms  this expectation.  The   mechanism  underlying  this   covariation  can  be explained using a simple caricature  of a threshold system. Finally, I will discuss  the impact of  this result on information  processing in neuronal networks.
9:30-9:50 am	Andrey Shilnikov Department of Mathematics and Statistics, Georgia State University Email: ashilnikov@gsu.edu Complex homoclinic bifurcations of periodic orbits for onset on bursting in a neuron model Bursting activity has been reported in many different neurons and associated with a variety of functions of the nervous system. Our study is focused on determining the biophysical and bifurcational mechanisms underlying the origin and evolution of bursting activity via reduction to a family of onto Poincare mappings. We show that at transformations bursting undergoes complex homoclinic bifurcations of a saddle periodic orbit setting the threshold between quiescent and tonic spiking phases.
9:50-10:30 am	Armen Stepayants Department of Physics & Center for Interdisciplinary Research on Complex Systems, Northeastern University Designing artificial neural networks with biologically inspired dynamic properties. Analysis   of   neuron  morphology   reveals   features  of   synaptic connectivity  that are common  to many  cortical circuits.  While most local neurons  have the  potential for being  interconnected, cortical connectivity remains sparse. The  probability for nearby neurons to be in synaptic  contact is on  the order of  10% and decays  rapidly with increasing   distance   between   neurons.   In   addition,   cortical connectivity  is predominantly  excitatory with  only about  15-20% of inhibitory  neurons and  inhibitory synapses.  To explore  the reasons behind such  design we build  robust recurrent networks  of excitatory and  inhibitory neurons  that have  specified dynamic  properties. The results show how artificial  networks benefit from sparse connectivity and small fraction of inhibitory synapses.

 

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