Bibliographic record
Abstract
This appendix gives some definitions of fundamental mathematical concepts that are used in AI, but are traditionally taught in other courses. It also introduces some notation and data structures that are used in various parts of the book. Discrete Mathematics The mathematical concepts we build on include: sets A set has elements (members). We write s ∈ S if s is an element of set S . The elements in a set define the set, so that two sets are equal if they have the same elements. tuples An n -tuple is an ordered grouping of n elements, written 〈 x 1 , …, x n 〉. A 2-tuple is a pair , and a 3-tuple is a triple . Two n -tuples are equal if they have the same members in the corresponding positions. If S is a set, S n is the set of n -tuples 〈 x 1 , …, x n 〉 where x i is a member of S . S 1 × S 2 × ··· × S n is the set of n -tuples 〈 x 1 , …, x n 〉 where each x i is in S i . relations A relation is a set of n-tuples. The tuples in the relation are said to be true of the relation. functions A function , or mapping , f from set D , the domain of f , into set R , the range of f , written f : D → R , is a subset of D × R such that for every d ∈ D there is a unique r ∈ R such that 〈 d, r 〉 ∈ f .
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 | 0.003 | 0.010 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.005 | 0.007 |
| Science and technology studies | 0.003 | 0.003 |
| Scholarly communication | 0.005 | 0.007 |
| Open science | 0.004 | 0.003 |
| Research integrity | 0.002 | 0.008 |
| Insufficient payload (model declined to judge) | 0.074 | 0.056 |
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".