On Farthest-Point Information in Networks.
Bibliographic record
Abstract
Consider the continuum of points along the edges of a network, an embedded undirected graph with positive edge weights. Distance between these points can be measured as shortest path distance along the edges of the network. We introduce two new concepts to capture farthest-point information in this metric space. The first, eccentricity diagrams, are used to encode the distance towards farthest points for any point on the network compactly. With this, we can solve the minimum eccentricity feed-link problem, i.e., the problem to extend a network by one new point minimizing the largest network distance towards the new point. The second, network farthest-point diagrams, provide an implicit description of the sets of farthest points. A network farthest-point diagram is, in principle, a compressed farthest-point network Voronoi link diagram generated by the entire continuum of uncountably many points on the network at hand. We provide construction algorithms for data structures that allow for queries for the distance to farthest points as well as their location from any point on a network in optimal time. Thus, we establish first bounds on construction times and storage requirements of such data structures.
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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 | 0.003 | 0.034 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.004 | 0.007 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.020 |
| Open science | 0.003 | 0.007 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.007 | 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".