Landmarks in Binary Tree Derived Architectures.
Bibliographic record
Abstract
Let M = {v1, v2 ... vl} be an ordered set of vertices in a graph G. Then (d(u, v1), d(u, v2) ... d(u, vl)) is called the M-location of a vertex u of G. The set M is called a locating set if the vertices of G have distinct M-locations. A minimum locating set is a set M with minimum cardinality. The cardinality of a minimum locating set of G is called Location Number L(G). This concept has wide applications in motion planning and in the field of robotics. In this paper we consider networks with binary tree as an underlying structure and determine minimum locating set of such architectures.We show that the location number of an n-level X-tree lies between 2 −3 and 2 −3 + 2. We further prove that the location number of an n × n mesh of trees is greater than or equal to n/2 and less than or equal to n.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".