Discrete and continuous cosine transform generalized to Lie groups SU(3) and G(2)
Bibliographic record
Abstract
In the paper we complete the development and description of the four variants of two-dimensional generalization of the cosine transform started in [Patera and Zaratsyan, J. Math Phys. 46, 053514 (2005)]. Each variant is based on a compact semisimple Lie group G of rank 2. Here, the groups are SU(3) and G(2). The cosines are generalized as the corresponding C-functions of the Lie group. A C-function is the contribution to an irreducible character from one orbit of the appropriate Weyl group. An explicit description is provided for expansions of functions given on the fundamental region F of the two compact simple Lie groups into series of C-functions. The fundamental region F is an equilateral triangle for SU(3) and half of such a triangle for G(2). Expansion coefficients are calculated using orthogonality of C-functions on F. Discrete expansions are set up on a grid FM⊂F. The grid is defined group theoretically for all positive integers M. It consists of points in F that represent conjugacy classes of elements of the finite maximal Abelian subgroup of G generated by its elements of order M. The C-functions are orthogonal on such a grid; hence, coefficients of discrete expansions are calculated independently of the continuous expansions. Processing digital data, sampled on triangular lattices, is the motivating application here.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".