Recently, I have been engaged in the study of how variability can arise in neuronal firing. In particular, I have focused on the variability that would be generated through the recurrent connections within a network.? ? One project in collaboration with Stephen Coombes of Nottingham University was to examine the dynamics of localized self-sustaining bumps of activity in a discrete neural network. These bumps have been proposed as a mechanism for working memory in the pre-frontal and parietal cortices. We first showed that a model of very simple spiking neurons that were connected with recurrent local excitation and distal inhibition can support localized bumps of persistent activity like more complicated models. This simple model could then be analyzed theoretically. We showed that the network had a transition from a stable stationary bump to a wandering bump if the synaptic decay time became too short. This wandering could be mapped directly to a random walk on a lattice. Hence, purely deterministic firing could lend the appearance of stochasticity due to network connectivity.? ? Most of the past work on the dynamics of interacting neurons or oscillators have focused on the infinite system size limit where fluctuations due to the connections do not appear. However, many biological and neural networks are large but finite sized. The dynamics of such networks are not well understood. With post doctoral fellow, Michael Buice and former student Eric Hildebrand, I examined the dynamics of a large but finite size network of globally connected oscillators. The model is the weak coupling limit of a mutually connected network of any oscillator, such as a neuron, that has a tendency to synchronize due to the connections. We showed that ideas from the kinetic theory of gases and plasmas could be applied to analyze the fluctuations and correlations due to system size effects.? ? In collaboration with a group led by Mark Bodner at UCLA, we examined the firing activity statistics of neurons during a working memory task in monkeys. In general, the firing characteristics of these neurons are altered when a monkey is remembering something. However, different neurons can posses very different firing characteristics during the delay period and the activity of these neurons show very wide intra-trial and inter-trial variability. This observed variability puts strong constraints on models of working memory.
| Hildebrand, Eric J; Buice, Michael A; Chow, Carson C (2007) Kinetic theory of coupled oscillators. Phys Rev Lett 98:054101 |
| Soula, Hedi; Chow, Carson C (2007) Stochastic dynamics of a finite-size spiking neural network. Neural Comput 19:3262-92 |
| Buice, Michael A; Chow, Carson C (2007) Correlations, fluctuations, and stability of a finite-size network of coupled oscillators. Phys Rev E Stat Nonlin Soft Matter Phys 76:031118 |
| Shafi, M; Zhou, Y; Quintana, J et al. (2007) Variability in neuronal activity in primate cortex during working memory tasks. Neuroscience 146:1082-108 |
