Proof of a result relating to orthogonal scaling functions series expansions
Bibliographic record
Abstract
In Zarowski the projection error behaviour of the scaling function series expansion was considered, and a closed form expression (which is valid when /spl phi/(t) satisfies certain moment constraints) for the error /spl epsiv/(t)=x(t)-a(t)(a(t) is the projection of x(t) onto subspace V/sub L/ of L/sup 2/(R)) was given in Zarowski (2000) for x(t)={ts,t/spl ges/0; 0,t<0 with s/spl isin/{0,1,2,...}. However, a proof of the validity of the stated expression for /spl epsiv/(t) was not given except for a few special values of s. In this paper we give a proof which is valid for all s/spl isin/{0,1,2,...}. Some miscellaneous facts about /spl epsiv/(t) are also presented.
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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 | 0.001 |
| 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 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".