Symmetric canonical quincunx tight framelets with high vanishing moments and smoothness
Bibliographic record
Abstract
In this paper, we propose an approach to construct a family of two-dimensional compactly supported real-valued quincunx tight framelets { ϕ ; ψ 1 , ψ 2 , ψ 3 } \{\phi ; \psi _1,\psi _2,\psi _3\} in L 2 ( R 2 ) L_2(\mathbb {R}^2) with symmetry property and arbitrarily high orders of vanishing moments. Such quincunx tight framelets are associated with quincunx tight framelet filter banks { a ; b 1 , b 2 , b 3 } \{a;b_1,b_2,b_3\} having increasing orders of vanishing moments, possessing symmetry property, and enjoying the additional double canonical properties: \[ b 1 ( k 1 , k 2 ) a m p ; = ( − 1 ) 1 + k 1 + k 2 a ( 1 − k 1 , − k 2 ) , b 3
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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 source (direct Gemma or distilled Codex), 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".