Smooth Piecewise Algebraic Approximation as Applied to Large-Scale 2D Scattered Geodetic Data Fitting
Bibliographic record
Abstract
We have developed an efficient method, Smooth Piecewise Algebraic Approximation (hereafter SPAA), to automatically compute a smooth approximation of large-scale functional scattered 2D observation points and tilt between them. The area of study is divided into patches and piecewise algebraic surfaces are fitted to the data. When the surfaces are approximated, a set of constraints is imposed in such a way that the resulting function is continuous only in the zero and first derivatives everywhere in the region, which results in a very short computation time. In other word, the surfaces are fitted simultaneously, using the constraints as set-conditions which the parameters of the surfaces must also satisfy. This method does not require a triangulation or quadrangulation of the data points and as such, it is very well suited for extremely large datasets.This method has been successfully applied to the monthly mean sea level and re-levelling data in Canada to thereby compile a map of Vertical Crustal Movements (VCM) in the region. The VCM model obtained using this method accommodates different kinds of scattered geodetic data, while yielding the optimum approximation to them. Enforcing the continuity and smoothness throughout the surfaces, the VCM model of Canada highlights the long wavelength temporal variations of the crust in the region, mainly due to Post Glacial Rebound (PGR). As a result, using the method of SPAA, a more physically meaningful VCM is modelled.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".