Methods Based on Rational Function Approximation of Green's Function Spectra
Bibliographic record
Abstract
In this chapter, the authors describe the rational function fitting method (RFFM) and spectral differential equation approximation method (SDEAM), which shift the burden of numerical computations from the evaluation of the slowly converging and highly oscillating Sommerfeld integrals to the approximation of their integrands with rational functions, which enable use of standard identities allowing for analytic evaluation of these integrals. The vector fitting-based RFFM requires availability of the analytic solution of the one-dimensional boundary value problems for the spectra of vector potential components. SDEAM solutions both for the vector potential Green's function components in the traditional formulation and mixed-potential Green's function components discussed can be performed with high-order discontinuous Galerkin method. By analogy with planar layered medium, casting of the Green's function spectrum into the pole-residual form allows to evaluate space domain Green's function in spherical layered medium in closed-form as well Okhmatovski and Cangellaris.
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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 | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.003 |
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".