Phil Holmes

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  Gait transitions in a phase oscillator model of an insect central pattern generator
  Zahra Aminzare, Phil Holmes

  Fast running insects employ a tripod gait with three legs in swing and three in stance, while slower walkers use a tetrapod gait with two legs in swing and four in stance. Fruit flies exhibit a tetrapod to tripod transition at intermediate speeds. We study the effect of stepping frequency on such gait transitions in a bursting neuron model where each cell represents a hemi-segmental thoracic circuit of the central pattern generator. Under phase reduction, the 24 ODE bursting neuron model becomes 6 coupled phase oscillators, each corresponding to a network driving one leg. Assuming that left and right legs maintain constant phase relations, we further reduce to a system describing ipsilateral phase differences defined on a torus. We show that bifurcations occur from multiple stable tetrapod gaits to a unique stable tripod gait as speed increases, and illustrate our results using data fitted to freely walking fruit flies.

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  Approximate symmetries in insect locomotion
  Phil Holmes
  I will describe coupled oscillator models of hexapedal locomotion and attempt to show that essentially the same central pattern generator, with appropriate parameter choices can produce the ranges of gait patterns exhibited by animals as diverse as stick insects, cockroaches and fruit flies.
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  The neural dynamics of decision making: multiple scales and a range models
  Phil Holmes
  I will describe a range of models, from cellular to cortical scales, that illuminate how we accumulate evidence and make simple decisions. Large networks composed of individual spiking neurons can capture biophysical details of synaptic transmission and neuromodulation, but their complexity renders them opaque to analysis. Employing methods of mean field and dynamical systems theory, I will argue that these high-dimensional stochastic differential equations can be approximately to simple drift-diffusion (DD) processes like those used to fit behavioral data in cognitive psychology. The DD models are analytically tractable, coincide with optimal methods from statistical decision theory, and prompt new experiments as well as questions on why we fail to optimize. If time permits, I will describe work in progress on a multi-area model of attention and descision making.
  
  The talk will draw on joint work with Fuat Balci, Rafal Bogacz, Jonathan Cohen, Philip Eckhoff, Sam Feng, Mike Schwemmer, Eric Shea-Brown, Patrick Simen, Marieke van Vugt, KongFatt Wong-Lin and Miriam Zacksenhouse.
  
  Research supported by NIMH and AFOSR.