Ephaptic Dependence Detectors: Theory and Simulations

This paper documents a focused investigation intowhether an ephaptic-perceptron-inspired framework can be usedas a detector of statistical dependence between two input streams.The project began with an information-theoretic hypothesisgrounded in entropy inequalities for mixed random variablesand progressed through a sequence of simulation studies inMATLAB. We first examined whether disagreement betweenentropy-based channel preference and the current ephaptic perceptronimplementation could serve as a dependence signal. Thathypothesis was evaluated on synthetic data with known groundtruth and on real wearable acceleration recordings. We thentested a direct theorem-driven criterion based on the inequalityH(Z) ≥ max{H(A),H(B)} for a mixed output Z formed fromtwo binary streams. The direct criterion produced no violationson either independent or dependent synthetic data and no violationson real data, demonstrating that it is a one-way consistencycheck rather than a practical detector. Finally, we generalizedthe mixing rule from a one-parameter convex form to a twoparameterform Z = λ1A+λ2B and evaluated features derivedfrom the entropy gap surface. The minimum gap feature achievedmodest but statistically significant above-chance detection onsynthetic data, with balanced accuracy 0.584 and permutationp-value 0.0017, while mean and variance features remained atchance. Across all experiments, mutual information remainedthe strongest and most interpretable dependence indicator, whileephaptic gap features emerged as weak but potentially usefulauxiliary cues.