Mind · Inference
LocalSpatialStateDivergence#2b5e
Classify a crowd's collective state from positions alone, by how far its local neighbourhoods depart from random
Mechanism
A model-free (zeroth-order) measure that needs only positions per frame. At random query points, drawing circles kept inside the observation area, find the k nearest agents, split the circle into four quadrants and record the local state omega = (a1, a2, a3, a4), the count per quadrant. The state space has C(k+3, 3) states. Sample many queries per frame (60) over the whole recording to get the empirical distribution P(omega). Build Q(omega) the same way from a NullModelBaseline that places the same number of agents uniformly at random in the same bounds at every frame. The JensenShannonDivergence D_JS(P, Q) then measures spatial organisation beyond chance. In fire ant colonies with k = 6, roaming scored 0.035 +/- 0.025, trailing 0.113 +/- 0.037 and aggression 0.229 +/- 0.052 (block permutation p = 0.004). k sets the spatial scale: too small is noise-dominated, too large samples too sparsely. Pushing a synthetic crowd with an attractive or repulsive force F = min(F_max, gamma / r_ij) gives a U-shaped D_JS(gamma), confirming sensitivity to order in either direction.
Invariants
- Uses positions only, with no interaction model
- Empirical and null distributions share the same k, query geometry and agent counts per frame
- Higher D_JS means more spatial structure than uniform placement
Failure modes
- Sign ambiguity: clustering and over-dispersion both raise D_JS against a uniform reference
- Choosing k by maximum regime separation on the same data, a form of MotivatedInstrumentTuning; report the full sweep
- Treats neighbourhoods as independent samples and ignores persistence and trajectories, so it can rank order but not explain mechanism
Where this came from
- Thesis Kevin Do, PhD thesis on ant collective behaviour (NCSU, 2026), Ch. 3.1.1, Eqs. 3.1-3.4, Figs. 3.1-3.3; Ch. 4.1, Fig. 4.1; Ch. 5.2
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Identity
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- Sema ID
sema:LocalSpatialStateDivergence#mh:SHA-256:2b5e93e20a335e9aff9fa14d6d8fc75b3872c759c2e7d331da7af4449062bae3- Reference
LocalSpatialStateDivergence#2b5e- Ring
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