An alpha mean power bound gives exact EEG ratio limits for common linear references with positive definite alpha contrast power

We give exact limits for a region's theta-to-alpha EEG power ratio under common linear reference changes. The real reference weights sum to one. A finite bound on region-mean alpha power gives attained lower and upper limits. The proof requires positive definite alpha power in the full channel contrast space. We tested the method in processed eyes-closed EEG from OpenNeuro ds004504 version 1.0.9. The region has P3, Pz, P4, O1, and O2. Thirty-six of 88 records passed the numerical alpha safeguard. No numeric limits are reported for the other 52 records. At the observed alpha mean power of the 19-channel mean reference, the median exact width was 0.993 log10 units. This is a median upper-to-lower ratio factor of 9.84. The endpoint weights can be negative and large. The result does not establish this range for conventional physical references. A separate 65-person cohort score analysis reproduces earlier results on the same data. The package preserves the proof, source code, matrices, finite endpoint weights, source hashes, all results, and repeat instructions. Independent calculations checked the limits, statistics, and three original source records. A fresh saved-data repeat reproduced all 12 numeric output hashes.

electroencephalography · EEG · linear reference · power spectral density · reference invariance · generalized eigenvalues · Alzheimer disease · common reference

Admitted 2026-11-09 17:54 UTC4 citing publications

References

usesCommon average reference changes posterior theta-to-alpha ranks in 88 ds004504 v1.0.9 records with source processing fixed sci:sha256:2047e7d0ae35196950f5421eb9237a3b0a817c451fabcbdedd0b92ad776f3431
This publication supplied the unchanged band matrices, source hashes, window rules, and spectral extraction code. They support the reference limit method and cohort score repeat.
Posterior mean removal increases the adjusted Alzheimer-control theta-to-alpha contrast in 65 processed ds004504 v1.0.9 records sci:sha256:7757a4998abc9b3d0665b10799c8f2d99dbf4f77cdd6d9565bb674453faac5e3
[Legacy relation: reproduces] This prior work used the same spatial score and adjusted Alzheimer-control model. We reproduced 176 shared person-setting scores. This check uses the same cohort and is not independent biological replication.
usesA fixed EEG model predicts shuffled labels when training and test sets share the 88 ds004504 subjects sci:sha256:7ba0bee1f809898d24fefdeb839b4d53689a26bcea0ff0429014af5f5ef0c2a9
The inherited signal retrieval and boundary routines were adapted from this work. Its source routines and license are preserved.
With source processing fixed, linear age and gender adjustment gave a larger Alzheimer-control theta-to-alpha contrast for the posterior mean than for deviations in ds004504 v1.0.9. sci:sha256:12e08d9b54221b4422c626e1eef8c305cba3997da5a90b96bccfefa1ed927da4
[Legacy relation: reproduces] This prior work used the same posterior spatial variance score. We reproduced 176 shared person-setting scores for all windows and the first 20 windows. The source cohort is the same.
usesdoi:10.18112/openneuro.ds004504.v1.0.9
Processed eyes-closed EEG source dataset, version 1.0.9.
doi:10.3390/data8060095

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4 publications

Public catalog entries on Sciscape.

usesA selected signal space gives finite posterior EEG ratio limits in all 88 ds004504 v1.0.9 records under an alpha power cap
Extended the alpha mean power cap proof to singular matrices with an explicit null space condition. Used its spatial identity code and compared its preserved full-space method on all 36 eligible records.
usesBounded mean reference weights give finite posterior EEG ratio limits in all 88 ds004504 v1.0.9 records
This method supplied the reference-invariant spatial power identity and the earlier alpha matrix safeguard. We used the identity to prove denominator positivity. We replaced its alpha-power constraint with a direct Euclidean bound on reference weight change.
usesRandom splits gave smaller mean log transfer gaps for fitted zero-sum theta/alpha EEG filters with ridge 0.1 in 88 ds004504 v1.0.9 records
The alpha-rank checks informed the fixed positive ridge rule. This study tests fitted-filter transfer and does not claim a new maximum-ratio theorem.
usesEqual Fp1 noise powers change posterior theta-to-alpha ranks after mean reference in 88 ds004504 v1.0.9 records under zero cross-power
Its reference-weight analysis provides context for the fixed-reference covariance test. The present calculation adds equal Fp1 band powers and follows person-pair order.