Bibliographic record
Abstract
There has been a lot of research on ellipse fitting and measuring ellipticity of a set of points. However, when the shape is primarily hyperbolic or parabolic, there are no existing methods to measure such properties. This paper describes the first known methods of measuring conicity, hyperbolicity and parabolicity of a set of points. After finding the best conic fit, we measure the corresponding ellipticity (using a known method), hyperbolicity or parabolicity value with respect to that best fit. We are interested in measures which rely exclusively on shape boundary points. They should also be calculated very quickly, be invariant to rotation, scaling and translation. The evaluation of fits transforms the point data into polar representation where the radius in this representation is equal to the difference of distances from each point to both foci (for hyperbolas), and the sum of distances from each point to the focus and a line parallel to the directrix line (for parabolas). The linearity of the polar representation will correspond to the quality of the fit for the original data. The conicity measure is tested on a set of 45 shapes. 1
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 | 0.004 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.006 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.003 | 0.005 |
| Open science | 0.001 | 0.004 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".