Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions
Bibliographic record
Abstract
Abstract. The concepts and models of multifractals have been employed in various fields in the geosciences to characterize singular fields caused by nonlinear geoprocesses. Several indices involved in multifractal models, i.e., asymmetry, multifractality, and range of singularity, are commonly used to characterize nonlinear properties of multifractal fields. An understanding of how these indices are related to the processes involved in the generation of multifractal fields is essential for multifractal modeling. In this paper, a five-parameter binomial multiplicative cascade model is proposed based on the anisotropic partition processes. Each partition divides the unit set (1-D length or 2-D area) into h equal subsets (segments or subareas) and m1 of them receive d1 (> 0) and m2 receive d2 (> 0) proportion of the mass in the previous subset, respectively, where m1+m2 ≤ h. The model is demonstrated via several examples published in the literature with asymmetrical fractal dimension spectra. This model demonstrates the various properties of asymmetrical multifractal distributions and multifractal indices with explicit functions, thus providing insight into and an understanding of the properties of asymmetrical binomial multifractal distributions.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
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".