Simulation of coalescence with stratified sampling
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Bibliographic record
Abstract
We analyze a stratified strategy for numerical integration and for simulation of coalescence. We use random points which are more evenly distributed in the unit cube than usual pseudo-random numbers. They are constructed so that only one point of the set lies in specific sub-intervals of the cube. This property leads to an improved convergence rate for the variance, when they are used for integrating indicator functions. A bound for the variance is proved and assessed through a numerical experiment. We also devise a Monte Carlo algorithm for the simulation of the coagulation equation. We start with an initial population of particles whose sizes are sampled from some initial distribution, and these sizes evolve according to the coalescence dynamics; the random numbers used are the stratified points described above. The results of some numerical experiments show a smaller variance, when compared to a Monte Carlo simulation using plain random samples.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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