###### Ran Darshan

Neuronal activity exhibits significant temporal variability. This irregularity of *in vivo *spiking patterns has long appeared paradoxical in view of the large number of synaptic afferents to the neurons that should, a priori, average out temporal fluctuations in the input to the neurons. A general solution to this problem is the *balance hypothesis* (van Vreeswijk and Sompolinsky 1996) which posits that excitatory as well as inhibitory couplings strengths scale as 1/sqrt(𝐾), where K is the degree of the connectivity graph of the network. A remarkable theoretical result is that in this *balanced regime*, highly irregular firing emerges from the collective network dynamics and is, in general, chaotic with high dimensions of the attractors. Combined with many experimental results obtained in recent years, these theoretical results support the idea that the balanced regime is a fundamental mode of operation of local cortical networks. In my talk I will briefly review the theory of the balanced regime and describe my recent work, where I developed a theory of spatial correlations across neurons in networks of networks operating in that regime. In this work, I established the general structural conditions under which such recurrent networks can settle into a dynamical state where correlations are highly robust and spatially modulated. The work thus provides new insights on the emergence of correlations in local cortical circuits, where topography and structure are widespread. If times allows, I will elaborate on my recent paper (Darshan et al. 2016), were I applied the theory to explain how spatiotemporal patterns of neural activity emerge in the songbird neural circuit, which drives exploratory behavior during song learning.

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###### Ran Darshan

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Neuronal activity exhibits significant temporal variability. This irregularity of *in vivo *spiking patterns has long appeared paradoxical in view of the large number of synaptic afferents to the neurons that should, a priori, average out temporal fluctuations in the input to the neurons. A general solution to this problem is the *balance hypothesis* (van Vreeswijk and Sompolinsky 1996) which posits that excitatory as well as inhibitory couplings strengths scale as 1/sqrt(𝐾), where K is the degree of the connectivity graph of the network. A remarkable theoretical result is that in this *balanced regime*, highly irregular firing emerges from the collective network dynamics and is, in general, chaotic with high dimensions of the attractors. Combined with many experimental results obtained in recent years, these theoretical results support the idea that the balanced regime is a fundamental mode of operation of local cortical networks. In my talk I will briefly review the theory of the balanced regime and describe my recent work, where I developed a theory of spatial correlations across neurons in networks of networks operating in that regime. In this work, I established the general structural conditions under which such recurrent networks can settle into a dynamical state where correlations are highly robust and spatially modulated. The work thus provides new insights on the emergence of correlations in local cortical circuits, where topography and structure are widespread. If times allows, I will elaborate on my recent paper (Darshan et al. 2016), were I applied the theory to explain how spatiotemporal patterns of neural activity emerge in the songbird neural circuit, which drives exploratory behavior during song learning.