Weight distributions in the fruit-fly and the mouse connectomes

By the growing number of available structural connectome data, the distributions of the synaptic weights can be determined which provides a hint at the learning mechanisms at play, both in the global and local level. In this work, we show a numerical analysis of this on the occasion of the latest large connectomes, the mouse visual cortex and the fruit-fly optical lobe, which, while evolutionarily distant share similar motion processing strategies. In general, it is found that the local node strengths can follow heavy-tailed distributions that decay faster than a power-law (PL), if we shuffle the weights among the nodes randomly. To understand this deviation from the global PL behavior, we propose a mechanism that can explain this difference which may resolve the ubiquitous contradicting observation of lognormal (LN) and PL tails related to critical behavior. We also show that synaptic weights of edges of fully proofread connectomes considered here, emanating from source and terminating at the sink nodes (broadcasters/integrators), respectively, exhibit PL tailed distributions, with exponents smaller than 3, so they are scale-free.