Bibliographic record
Abstract
In this paper, we study batch codes, which wereintroduced by Ishai, Kushilevitz, Ostrovsky and Sahai in [4].A batch code specifies a method to distribute adatabase of $n$ items among $m$ devices (servers)in such a way that any $k$ itemscan be retrieved by reading at most $t$ items from each of the servers. It is of interest to devise batch codes thatminimize the total storage, denoted by $N$, over all $m$ servers.We restrict out attention to batch codesin which every server stores a subset ofthe items. This is purely a combinatorial problem, sowe call this kind of batch code a ''combinatorial batch code''.We only study the special case $t=1$, where,for various parameter situations, we are able to presentbatch codes that are optimal with respect to the storagerequirement, $N$. We also study uniform codes, where every item isstored in precisely $c$ of the $m$ servers (such a codeis said to have rate $1/c$). Interesting new resultsare presented in the cases $c = 2, k-2$ and $k-1$. In addition,we obtain improved existence results for arbitraryfixed $c$ using the probabilistic method.
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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 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.010 | 0.002 |
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".