Random Fields and Stochastic Geometry (09w5040)
Bibliographic record
Abstract
The main topics of this workshop lay at the point where Probability meets Geometry, specifically the study of the random geometry and topology generated by smooth random functions. While these problems have their roots in various applications of image and shape analysis in a wide variety of disciplines, their main mathematical content lies in probability theory. It is there that recent major advances led us to holding a workshop in this general area at this particular time. Specifically, over the last few years, a minor revolution, which was born in Jonathan Taylor’s McGill Ph.D. thesis, has been taking place regarding the way the sample path properties of smooth multi-parameter stochastic processes, or random fields, have been studied. While the setting is primarily in the world of Gaussian random fields, the basic results also extend out into the non-Gaussian world. The approach is based on treating parameter spaces, where possible, as Riemannian manifolds with metrics induced by the fields. These results involve an intruiging blend of probability and geometry, and although the revolution has, primarily, been taking place at the level of theoretical mathematics, it has already had an impact on applications of random field theory in applied settings as wide apart as astrophysics and medical imaging. The interface between random field theory and stochastic geometry has been at the centre of this activity, which is why most of the participants in the workshop came from the areas of this interface. However, it
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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 | 0.003 | 0.007 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.007 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.163 | 0.050 |
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".