On the dependence structure and quality of scrambled (<i>t</i>, <i>m</i>, <i>s</i>)-nets
Bibliographic record
Abstract
Abstract In this paper we develop a framework to study the dependence structure of scrambled ( t , m , s ) {(t,m,s)} -nets. It relies on values denoted by C b ( 𝒌 ; P n ) {C_{b}({\boldsymbol{k}};P_{n})} , which are related to how many distinct pairs of points from P n {P_{n}} lie in the same elementary 𝒌 {{\boldsymbol{k}}} -interval in base b. These values quantify the equidistribution properties of P n {P_{n}} in a more informative way than the parameter t. They also play a key role in determining if a scrambled set P ~ n {\widetilde{P}_{n}} is negative lower orthant dependent (NLOD). Indeed, this property holds if and only if C b ( 𝒌 ; P n ) ≤ 1 {C_{b}({\boldsymbol{k}};P_{n})\leq 1} for all 𝒌 ∈ ℕ s {{\boldsymbol{k}}\in\mathbb{N}^{s}} , which in turn implies that a scrambled digital ( t , m , s ) {(t,m,s)} -net in base b is NLOD if and only if t = 0 {t=0} . Through numerical examples we demonstrate that these
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 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 | 0.002 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".