Scale-adjusted metrics of scientific collaboration
Bibliographic record
Abstract
Scientific collaboration is increasing on nearly all fronts. In most fields of inquiry, the proportions of multiple authors', multiple institutions', and multiple countries' papers have increased regularly since the birth of scientific journals. Two questions that are frequently asked are: how does collaboration compare from one place to the other, and how does the intensity of collaboration between partners compare in systems with multiple players? For obvious reasons, absolute numbers do not reveal much, but it has been known since the 1970s that the percentages of collaboration present an inverse relationship relative to the number of papers. This paper presents scale-independent methods to examine how frequently collaboration occurs as a function of size. In addition to these scale-adjusted statistics, which are based on the use of the Katz normalization method, this paper proposes a new method to compute a scale-adjusted preference index of collaboration between entities of various sizes. Examples are provided for the world, the European Research Area (ERA), and the US states, as well as for Canadian universities.
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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 | 0.008 | 0.067 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.013 | 0.014 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".