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SUMMARY:Bump attractors and waves in networks of leaky integrate-and-fire 
 neurons - Kyle Wedgwood (University of Exeter)
DTSTART:20240327T133000Z
DTEND:20240327T142000Z
UID:TALK208666@talks.cam.ac.uk
DESCRIPTION:Coauthors: Daniele Avitabile (VU Amsterdam)\, Joshua L. Davis 
 (DSTL)\nBump attractors are wandering localised patterns observed in in vi
 vo experiments of spatially-extended neurobiological networks. They are im
 portant for the brain's navigational system and speci&ensp\;c memory tasks
 . A bump attractor is characterised by a core in which neurons &ensp\;re f
 requently\, while those away from the core do not &ensp\;re. These structu
 res have been found in simulations of spiking neural networks\, but we do 
 not yet have a mathematical understanding of their existence\, because a r
 igorous analysis of the nonsmooth networks that support them is challengin
 g. We uncover a relationship between bump attractors and travelling waves 
 in a classical network of excitable\, leaky integrate-and-&ensp\;re neuron
 s. This relationship bears strong similarities to the one between complex 
 spatiotemporal patterns and waves at the onset of pipe turbulence. Waves i
 n the spiking network are determined by a &ensp\;ring set\, that is\, the 
 collection of times at which neurons reach a threshold and &ensp\;re as th
 e wave propagates. We de&ensp\;ne and study analytical properties of the v
 oltage mapping\, an operator transforming a solution's ring set into its s
 patiotemporal pro&ensp\;le. This operator allows us to construct localised
  travelling waves with an arbitrary number of spikes at the core\, and to 
 study their linear stability. A homogeneous \\laminar" state exists in the
  network\, and it is linearly stable for all values of the principal contr
 ol parameter. Su&ensp\;ciently wide disturbances to the homogeneous state 
 elicit the bump attractor. We show that one can construct waves with a see
 mingly arbitrary number of spikes at the core\; the higher the number of s
 pikes\, the slower the wave\, and the more its pro&ensp\;le resembles a st
 ationary bump. As in the&nbsp\; uid-dynamical analogy\, such waves coexist
  with the homogeneous state\, are unstable\, and the solution branches to 
 which they belong are disconnected from the laminar state\; we provide evi
 dence that the dynamics of the bump attractor displays echoes of the unsta
 ble waves\, which form its building blocks.
LOCATION:Seminar Room 1\, Newton Institute
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