Abstract
The present paper provides exact mathematical expressions for the high-order moments of spiking activity in a recurrently connected network of linear Hawkes processes. It extends previous studies t...
Highlights
Immense efforts in neuroscience have been invested in measuring neuronal activity as well as the detailed connectivity between neurons
In this paper we analytically computed the statistics of neuronal activity in a recurrent network---described via moments and transposed to cumulants---from the statistics of the input neuronal population
An important contribution of our study is the description of the propagation of spiking moments in feedforward networks (Theorem 1) and recurrently connected networks (Theorem 2), which had not been explored before
Summary
Immense efforts in neuroscience have been invested in measuring neuronal activity as well as the detailed connectivity between neurons. Such studies have been too often conducted separately, despite the fact that neuronal activity and synaptic connectivity are deeply intertwined. We investigate how the spiking statistics---described via statistical moments or cumulants---propagates from an input population of neurons to an output population of recurrently connected neurons; see Figure 1A. To formalize this relationship, one needs to decide on a model for the neuronal dynamics
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