An application of an optimal statistic for characterizing relative orientations
Bibliographic record
Abstract
We present the projected Rayleigh statistic (PRS), a modification of the classic Rayleigh statistic, as a test for non-uniform relative orientation between two pseudo-vector fields. In the application here, this gives an effective way of investigating whether polarization pseudo-vectors (spin-2 quantities) are preferentially parallel or perpendicular to filaments in the interstellar medium. For example, there are other potential applications in astrophysics, e.g. when comparing small-scale orientations with larger scale shear patterns. We compare the efficiency of the PRS against histogram binning methods that have previously been used for characterizing the relative orientations of gas column density structures with the magnetic field projected on the plane of the sky. We examine data for the Vela C molecular cloud, where the column density is inferred from Herschel submillimetre observations, and the magnetic field from observations by the Balloon-borne Large-Aperture Submillimetre Telescope in the 250-, 350- and 500-μm wavelength bands. We find that the PRS has greater statistical power than approaches that bin the relative orientation angles, as it makes more efficient use of the information contained in the data. In particular, the use of the PRS to test for preferential alignment results in a higher statistical significance, in each of the four Vela C regions, with the greatest increase being by a factor 1.3 in the South-Nest region in the 250 − μ m band.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.008 | 0.043 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".