With normalized source mode variance at most one, a joint contrast separated site and contact covariance in two adult C. elegans input models

We tested whether a finite source covariance bound can separate common site events from separate contact events in a connectome model. We used two adult C. elegans brain maps and a fixed panel of 81 neuron labels, with 81 and 80 active targets. Separate contact noise gave unit target variance. Every nonzero source profile had norm one. Each model could use a different source covariance, with every source mode variance at most t. We proved a sharp limit from a matrix inverse and spectral decomposition. Equal target covariance first became possible at t = 9.78364 and 4.58423. Explicit positive semidefinite source matrices attained both limits. A target variance contrast attained each lower bound. Those contrasts lost separation at t = 1 after transfer to the other adult map. A joint contrast designed with both maps kept gaps of 10.82% and 9.04% of the contact baseline at t = 1. A global numerical certificate checked the joint design objective. Graph and source unit checks are preserved. Independent source reconstruction matched 907,200 matrix entries. Separate spectral checks, exact examples and 400 random cases passed. These are conditional direct linear input results. Both adult maps enter the joint design and its evaluation. Unknown gains, added target noise, membrane filters and unmeasured release properties limit biological use. The package preserves proofs, code, graph facts, source records, covariance examples, weights, figures and repeat instructions.

connectome · polyadic synapse · source covariance · variance bounds · experimental design · C. elegans · structure and function