Partitioning Problems Arising From Independent Shifted-Geometric and Exponential Samples With Unequal Intensities
Bibliographic record
Abstract
Two problems dealing with the random skewed splitting of some population into J different types are considered. In a first discrete setup, the sizes of the sub-populations come from independent shifted-geometric with unequal characteristics. Various J → ∞ asymptotics of the induced occupancies are investigated: the total population size, the number of unfilled types, the index of consecutive filled types, the maximum number of individuals in some state and the index of the type(s) achieving this maximum. Equivalently, this problem is amenable to the classical one of assigning indistinguishable particles (Bosons) at J sites, in some random allocation problem. In a second parallel setup in the continuum, we consider a large population of say J ‘stars’, the intensities of which have independent exponential distributions with unequal inverse temperatures. Stars are being observed only if their intensities exceed some threshold value. Depending on the choice of the inverse temperatures, we investigate the energy partitioning among stars, the total energy emitted by the observed stars, the number of the observable stars and the energy and index of the star emitting the most.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
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 | 0.001 |
| 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) | 0.000 | 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 teacher head, 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".