Bibliographic record
Abstract
Introduction The difference between semirings and rings is the lack of additive inverses in semirings. The most common examples of semirings which are not rings are the non-negative integers ℤ + , the non-negative rationals ℚ + and the non-negative reals ℝ + with usual addition and multiplication. There are classical examples of non-numerical semirings as well. One of the first examples appeared in the work of Dedekind in connection with the algebra of ideals of a commutative ring (one can add and multiply ideals but it is not possible to subtract them). Later Vandiver proposed the class of semirings as the best class of algebraic structures which includes both rings and bounded distributive lattices. Boolean algebras, max-algebras, tropical semirings and fuzzy scalars are other important examples of semirings. See the monographs for more details. During the last few decades, matrices with entries from various semirings have attracted the attention of many researchers working both in theoretical and applied mathematics. It should be emphasized that the majority of examples of semirings arise in various applications of algebra. To illustrate an application of semirings, we present a situation that arises constantly in parallel computations. To make this situation more apparent, we give its ‘real life’ analogue. Let us consider k seaports. A ship with certain goods arrives at the i -th port at the moment x i , i = 1, …, k . Also there are l airports with a airplane in each airport.
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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.001 | 0.001 |
| 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".