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SUMMARY:Interplay of random and nonnormally structured connectivity in the
  dynamics of neural networks II
DTSTART;VALUE=DATE-TIME:20130423T093000Z
DTEND;VALUE=DATE-TIME:20130423T103000Z
DTSTAMP;VALUE=DATE-TIME:20260702T205237Z
UID:indico-event-1908@indico.ific.uv.es
DESCRIPTION:Neuronal networks exhibit significant randomness in their syna
 ptic connectivity. But importantly\, alongside randomness\, the synaptic c
 onnectivity of most neural networks also features ordered structure on var
 ious levels\, depending on the network's function. Investigating the inter
 play of these two features of connectivity and their respective role in th
 e dynamics of neural networks and the computations they perform constitute
 s a general theoretical problem in neuroscience. Of particular interest ar
 e connectivity structures that can be described by a nonnormal matrix. In 
 this case the network can be described as having a hidden feedforward conn
 ectivity structure between orthogonal activity patterns\, each of which ca
 n also excite or inhibit itself. Such networks arise naturally from the se
 paration of excitatory and inhibitory neurons and yield large transient am
 plification of patterns without any dynamical slowing. This latter effect 
 has been used to explain the similarity of the fluctuating patterns of spo
 ntaneous activity in primary visual cortex (V1) to patterns of activity ev
 oked by visual stimuli.\nIn my second talk\, I will present the results of
  a recent project where as a step towards the general problems mentioned a
 bove\, I studied properties of large connectivity matrices of the form W =
  M + J\, where M (average connectivity) is an arbitrary deterministic matr
 ix which represents structure in the connectivity and is generally nonnorm
 al\, and J is a zero-mean random matrix with possibly correlated and non-u
 niformly scaled elements. Specifically\, using the Feynman diagram techniq
 ue\, we have derived a general formula for the eigenvalue distribution of 
 matrices of the above type\, generalizing the circular law for fully rando
 m matrices. Furthermore\, with the aim of studying the effect of random co
 nnectivity on the hidden feedforward structure and transient amplification
  that are of interest in the context of nonnormal connectivity matrices\, 
 we have derived general formulae for the transient evolution of the magnit
 ude and the frequency power spectrum of the linear response of firing rate
  networks to external inputs. I will present some example applications rel
 evant for neuroscience\, and in particular briefly discuss how our general
  formula for the eigenvalue distribution has been used in the study of a c
 lustered neural network with random inter-cluster connectivity by our coll
 eagues (M. Stern and L. Abbott)\, to map out the boundary between a chaoti
 c and a glassy phase of the network.\n\nhttps://indico.ific.uv.es/event/19
 08/
LOCATION:Edf. Institutos de Investigación Sala Seminarios IFIC
URL:https://indico.ific.uv.es/event/1908/
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