Two C. elegans pharynx response matrices had minimum completion rank two at a Laplace rate of 1 per second
We tested whether a narrow neuronal route limits fitted response diversity. We kept all 302 neuron slots and all positive neuronal links in two C. elegans whole-animal maps. RIPL and RIPR gave a two-cell separator in both maps. A shared scalar linear model thus bounds crossing transfer rank by two at each regular Laplace rate. In one fixed wild-type atlas, 37 outward and 25 inward kernels passed q < 0.05 and had at least three finite stored amplitudes. At a Laplace rate of 1 per second, one-channel fits needed uniform magnitude allowances of 3.576215 outward and 1.206225 inward. Four-entry products gave lower bounds, and complete fits attained them. Exact rational factors gave rank-two completions of all 62 binary64 values. Unknown entries stayed free. A time-domain cancellation check kept both bounds. Neither detected mask had a complete three-by-three panel. A panel selected by coverage gave a target for better matched-state measurements. Full-graph controls showed that pooling states can increase rank. The result describes fixed pooled functions, not a physiological channel count. Joint kernel errors and animal identifiers were not available. We preserve code, 9,303 graph facts, exact certificates, provenance, all results, figures, and repeat instructions. A full raw-source rebuild matched 32 numerical and figure files byte for byte. An offline matrix replay matched 27 files.
C. elegans · connectome · pharynx · signal propagation · matrix completion · transfer rank · missing data · linear systems · structure and function
References
9- usesdoi:10.1038/s41586-023-06683-4
Supplies the measured neural signal atlas and the interpretation of its fitted transfer kernels.
- usesdoi:10.17605/OSF.IO/E2SYT
Original signal atlas data repository. The package records the exact WormNeuroAtlas commit and source file hashes.
- usesdoi:10.1098/rstb.1986.0056
Supplies anatomy for the pinned White whole export.
- usesdoi:10.1038/s41586-019-1352-7
Supplies the whole-animal anatomy. We use the July 2020 corrected hermaphrodite workbook.
- supportsdoi:10.1002/cne.24932
Describes the pharyngeal nervous system and its neuronal routes through RIP.
- supportsdoi:10.1007/BF02551379
Gives prior graph theory for transfer rank and vertex-disjoint paths. We do not claim a new separator-rank theorem.
- supportsdoi:10.1109/TAC.2018.2867336
Gives related prior theory for identification of dynamic networks from partial node measurements.
- usesMagnitude reciprocity required a factor of 2.05 at 1 per second in 106 fitted C. elegans kernel pairs sci:sha256:da3cc12411ba6896e11db51061c273e0c8017109b89d9955b527ae76729b4fc4
Uses its export audit, analytic kernel-transform method, and loop-based cell-factor test as a starting point. This work tests rank across a neuronal boundary, instead of reciprocal transfer.
- supportsAt Laplace rates of 0.2 and 1 per second, removing four of 106 C. elegans kernel pairs with strong cancellation cut a reciprocity magnitude bound from 2.60 to 1.39 sci:sha256:d6592a9b70ebda3478fcb41c88b82653f072e54539897371fe9c9f1777827f8b
Shows why cancellation and pooled fitted functions need separate checks. We add a time-domain cancellation filter and full-graph state-pooling rank controls.
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