1/ <i>f</i> Noise and multifractality from bristlecone pine growth explained by the statistical convergence of random data
Bibliographic record
Abstract
Tree-ring growth records from bristlecone pines reveal an irregular pattern of fluctuations that have been linked to climatic change but otherwise have remained poorly understood. We find within these records evidence for a temporally related variance to mean power law, 1/ f noise and multifractality that empirically resembles a fractal stochastic process and could be attributed to self-organized criticality. These growth records, however, also conformed to a non-Gaussian statistical distribution (the Tweedie compound Poisson distribution) characterized by an inherent variance to mean power law, that by itself implies 1/ f noise. This distribution has a fundamental role in statistical theory as a focus of convergence for many types of random data, much like the Gaussian distribution has with the central limit theorem. The growth records were also multifractal, with the dimensional exponent of the Tweedie distribution critically balanced near the transition point between fractal stochastic processes and gamma distributed data, possibly consequent to a related convergence effect. Non-Gaussian random systems, like those related to bristlecone pine tree growth, may express 1/ f noise and multifractality through mathematical convergence effects alone, without the dynamical assumptions of self-organized criticality.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 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 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".