Sufficient codition for extendibility and two-dimensional power spectrum estimation
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Bibliographic record
Abstract
A sufficient condition for the extendibility of two-dimensional (2-d) quadratically symmetric autocorrelation samples is derived based on matrix decomposition approaches. This condition is very simple to test because it boils down to a positive definiteness checking of a set of Toeplitz form matrices. It is shown by means of examples that this sufficient condition can be very useful, in some cases, by making the tedious extendibility test unnecessary. This paper also presents a method which can approximate with small error a given quadratically symmetric autocorrelation function (a.c.f) over a square with a new a.c.f that is guaranteed to be extendible. This method is also based on a matrix decomposition approach and employs an iterative gradient algorithm. Its implications to the estimation of a 2-d power spectrum is demonstrated.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it