Bibliographic record
Abstract
筆者らは昨年12月の数理研研究集会で、拡張Hensel構成をMoses-Yun補間式ではなく初期因子のGröbner基底を使うことで高速化する考えを発表した。その時点では単なるアイデアだったが、2段階で研究が進展し、従変数の個数が少ない場合には十分高速な算法が出来上がった。研究成果は進展に応じて2論文として、国際会議CASC2016とSYNASC2016で発表された。特に後者では、Gröbner基底の簡単かつ新しい定理を基に、" minimal因子 "分離に対する分割征服算法が考案され、著しい高速化が達成された。また、" maximal 因子"分離に対しては、主変数の次数の低いHensel因子から順に構成する算法とHensel因子の歪みを矯正する算法が考案された。前者は拡張Hensel構成の解析関数への適用を可能にするものである。
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 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.009 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.011 | 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".