A Jensen gap projection gives the exact EEG exponent shift from mean and log order for positive power and fixed log-log fits with an intercept
A frequency Jensen gap gives the exact change in a fixed EEG exponent when mean and log order changes. The proof requires positive power, fixed frequency bins and positive weights, and a line fit with an intercept. A constant gap has no slope effect. Shape variation can give either sign. We tested 360 records from 60 adults in OpenNeuro ds004148 version 1.0.1. The primary posterior fit used 2-30 Hz and removed 7-14 Hz. The mean closed-eye minus open-eye contrast changed from 0.13207 to 0.12211 when the log followed the power mean. The paired shift was -0.00996, with a planned 95% person bootstrap interval of [-0.01986, -0.00032]. A post hoc Student t interval and several planned checks included zero. The population direction remains uncertain. The package preserves a NumPy helper, proof, all 360 input spectra, source hashes, code, results, and replay instructions. Separate regressions checked every fit. Two fixed raw records reproduced every archived array exactly. All result and figure files matched on a local rerun. These scores do not establish a true neural exponent or a causal eye-state effect.
EEG · spectral exponent · Jensen gap · temporal averaging · power spectrum · measurement methods
References
6- usesLog window averaging gave no clear one-month ICC gain for posterior 8–13 Hz eye-state contrast in 60 ds004148 v1.0.1 adults sci:sha256:f1735eae11728edb8a766335529010f71cfb1c41c8d0ded4329ec0ab55cd00ab
The prior mean and log comparison for integrated alpha power informed this question. This work tests the frequency-specific gap before a slope fit. No result files or code from that comparison were used.
- usesWeights of 1/f reduced the mean fitted 2–30 Hz posterior EEG eye-state exponent contrast in 60 ds004148 adults sci:sha256:54109758cfa3dc8d48a1d54102c4a675e2dce8d6d0f4a1a61a6cbe69a9bc8bcb
The fixed negative-slope coefficient formula informed this implementation. We used that linear form to derive the Jensen gap projection. No result files or code from that comparison were used.
- usessci:sha256:eb6da8fdd843c3b66dd19edef3df5eb85f888448f106108e611352a1c6388159 not known to Sciscape
We used all 360 window spectral files, quality flags, source metadata, raw hashes, and extraction code. These files supplied the same 60 people and enabled exact source replay checks.
- usesdoi:10.18112/openneuro.ds004148.v1.0.1
The analyzed spectra are recorded as OpenNeuro ds004148 version 1.0.1; the source URL, commit, and hashes are preserved.
- supportsdoi:10.1038/s41597-022-01607-9
The source dataset paper documents the cohort and source processing described here.
- doi:10.1111/psyp.70272
Cited by
1 publicationPublic catalog entries on Sciscape.
- usesThe 95% person bootstrap interval included zero for added open-eye EEG exponent error reduction at one month in 56 ds004148 adults
We used its fixed posterior log-log exponent rule with an intercept, 2-30 Hz bins, and exclusion of 7-14 Hz. Its aggregation result motivated the planned mean-log-power check. We did not use its eye-state result as evidence about sleepiness.