Bibliographic record
Abstract
In this thesis we mainly give a characterization of dual frames of Gabor subspace frames. We give necessary and sufficient conditions for the existence and the uniqueness of a function h (called window) in the closed linear span of a Gabor subspace frame {EmbTnak}m,n∈Z such that the Bessel collection {EmbTnah}m,n∈Z serves as the dual frame of the original frame {EmbTnag}m,n∈Z. We solve the problem for three cases, first ab = 1, second ab = p ∈ N, and third ab = p/q, gcd(p, q) = 1. In each case, we first find the conditions for upper frame bound (known as Bessel collection). Secondly, we characterize the functions which are orthogonal to {EmbTnag}m,n∈Z in terms of the Zak transform, and then obtain necessary and sufficient conditions for lower frame bound. Here we state obtained conditions for normalized tight frame as a corollary. Finally, using all this information we solve the duality problem.
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How this classification was reachedexpand
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 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.009 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".