Mixtures of multiplicative cascade models in geochemistry
Why this work is in the frame
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Bibliographic record
Abstract
Abstract. Multifractal modeling of geochemical map data can help to explain the nature of frequency distributions of element concentration values for small rock samples and their spatial covariance structure. Useful frequency distribution models are the lognormal and Pareto distributions which plot as straight lines on logarithmic probability and log-log paper, respectively. The model of de Wijs is a simple multiplicative cascade resulting in discrete logbinomial distribution that closely approximates the lognormal. In this model, smaller blocks resulting from dividing larger blocks into parts have concentration values with constant ratios that are scale-independent. The approach can be modified by adopting random variables for these ratios. Other modifications include a single cascade model with ratio parameters that depend on magnitude of concentration value. The Turcotte model, which is another variant of the model of de Wijs, results in a Pareto distribution. Often a single straight line on logarithmic probability or log-log paper does not provide a good fit to observed data and two or more distributions should be fitted. For example, geochemical background and anomalies (extremely high values) have separate frequency distributions for concentration values and for local singularity coefficients. Mixtures of distributions can be simulated by adding the results of separate cascade models. Regardless of properties of background, an unbiased estimate can be obtained of the parameter of the Pareto distribution characterizing anomalies in the upper tail of the element concentration frequency distribution or lower tail of the local singularity distribution. Computer simulation experiments and practical examples are used to illustrate the approach.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it