Bibliographic record
Abstract
Broadcasting is an information dissemination problem described by a group of entities, nodes, connected through an interconnection network. It finds its main application in the field of interconnection networks for parallel architecture. Broadcasting in a graph is the process of transmitting a message from one vertex, the originator, to all other vertices. We will consider the classical model in which an informed vertex informs one of its uninformed neighbours during each time unit. A broadcast graph on n vertices is a graph in which broadcasting can finish in [log2n] time units from any originator. In this paper, we will study new broadcasting properties of Knödel graphs on 2k vertices that we will denote by KG2k. KG2k is known to be a broadcast graph. KG2k may be constructed recursively. Although its different dimensions show some similarities with the dimensions of hypercube topology, KG2k is not edge transitive hence is not as symmetric as hypercube. Moreover, KG2k has the smallest diameter among all known k-regular graphs on 2k vertices. Our study shows new broadcasting properties of KG2k and how to construct new broadcast graphs by deleting some sub-graphs of KG2k. The last property is also characteristic of hypercube.
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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 | 0.001 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".