Fault-tolerant extensions of complete multipartite networks
Why this work is in the frame
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Bibliographic record
Abstract
The authors studied the design of a fault-tolerant extension for a graph G which can survive at most m node failures, and which contains the minimum number of nodes and the fewest possible edges when the nonredundant graph (G) is a complete multipartite graph. After developing a characterization for m-fault-tolerant extensions and for optimal m-fault-tolerant extensions of a complete multipartite graph, this characterization is used to develop a procedure to construct an optimal m-fault-tolerant extension of any complete multipartite graph, for any m>or=0. The procedure is only useful when the size of the graph is relatively small, since the search time required is exponential. Several necessary conditions on any (optimal) m-fault-tolerant extension of a complete multipartite graph are proved. These conditions allow identification of some optimal m-fault-tolerant extensions of several special cases of a complete multipartite graph without performing any search.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it