Interpolation Incorporating both spatial association and singularity
Bibliographic record
Abstract
Spatial association indexes (autocorrelation, covariance, and variogram) have been commonly used to characterize the local structure of surfaces and for data interpolation in kriging. Singularity is another index representing the scaling invariant property of measures from a multifractal point view. Spatial association and scaling invariant are two different aspects of local structure of surfaces. Both must be taken into account in data interpolation and surface construction. Kriging as one of the sophisticated mapping techniques is based on the spatial association of neighborhood values through semivariogram. Recent study of multifractal modeling has shown that the local singularity exponent involved in multifractal modeling can quantify the local scaling invariant property characterizing the concave/convex properties of the neighborhood values. The method proposed in this paper incorporates both the singularity and spatial association in data interpolation. It has been shown by a case study of As geochemical values of sediment samples from southwestern Nova Scotia, Canada, that incorporation of spatial association and singularity can improve the interpolation result significantly, especially for observed values with significant singularity.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".