Pre-registered spectral and certified mixing analysis of the male Drosophila central nervous system connectome
Abstract
We report a pre-registered test of five hypotheses about the synapse-flow random walk on the connectome of the male Drosophila central nervous system (166,700 neurons, 124 million synapses), in which a walker moves to a postsynaptic partner in proportion to synapse number. The hypotheses concern the spectral gap and its dependence on the neck connective, the localisation of the leading modes of an input-normalised signed map, the certified mixing depth measured by the Dobrushin coefficient, its robustness to per-synapse detection confidence, and the dependence of the signed spectrum on the neurotransmitter sign convention. After public registration and a code freeze, each was tested once. Two held: the two-neuron photoreceptor modes that lead the signed spectrum are an artefact of normalising by very small inputs, removed by an input floor at the median, and they do not depend on the sign convention. Three failed: at a threshold of five synapses per connection the spectral gap is an order of magnitude smaller than predicted (|λ2| = 0.9965) and the chain is certifiably far from mixed after 128 steps, and at no confidence level tested was the mixing depth certifiably robust. Exploratory analyses trace the slow mode to eleven neurons of the cord, seven of them mesothoracic efferent neurons, that become nearly closed once weak connections are dropped, find a similar boundary set in the lamina of the FlyWire female brain, show that null models preserving cell-type wiring reproduce the slow modes, and show that exact chains built from the confidence data change the depth profile after 32 steps by at most 0.017 at the pre-registered confidence level, far less than the worst-case certificate allows. Random-walk summaries of connectomes are dominated by nearly closed sets at the edges of the reconstruction unless these are treated explicitly.
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BibTeX
@misc{kopel2026preregistered,
title = {{Pre-registered spectral and certified mixing analysis of the male Drosophila central nervous system connectome}},
author = {Eran Kopel},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33054},
eprint = {2609.33054},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33054},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Pre-registered spectral and certified mixing analysis of the male Drosophila central nervous system connectome
AU - Eran Kopel
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33054
UR - https://arxiv.org/abs/2609.33054
AB - We report a pre-registered test of five hypotheses about the synapse-flow random walk on the connectome of the male Drosophila central nervous system (166,700 neurons, 124 million synapses), in which a walker moves to a postsynaptic partner in proportion to synapse number. The hypotheses concern the spectral gap and its dependence on the neck connective, the localisation of the leading modes of an input-normalised signed map, the certified mixing depth measured by the Dobrushin coefficient, its robustness to per-synapse detection confidence, and the dependence of the signed spectrum on the neurotransmitter sign convention. After public registration and a code freeze, each was tested once. Two held: the two-neuron photoreceptor modes that lead the signed spectrum are an artefact of normalising by very small inputs, removed by an input floor at the median, and they do not depend on the sign convention. Three failed: at a threshold of five synapses per connection the spectral gap is an order of magnitude smaller than predicted (|λ_2| = 0.9965) and the chain is certifiably far from mixed after 128 steps, and at no confidence level tested was the mixing depth certifiably robust. Exploratory analyses trace the slow mode to eleven neurons of the cord, seven of them mesothoracic efferent neurons, that become nearly closed once weak connections are dropped, find a similar boundary set in the lamina of the FlyWire female brain, show that null models preserving cell-type wiring reproduce the slow modes, and show that exact chains built from the confidence data change the depth profile after 32 steps by at most 0.017 at the pre-registered confidence level, far less than the worst-case certificate allows. Random-walk summaries of connectomes are dominated by nearly closed sets at the edges of the reconstruction unless these are treated explicitly.
ER -