New approximations for network reliability
Why this work is in the frame
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Bibliographic record
Abstract
Abstract We introduce two new methods for approximating the all‐terminal reliability of undirected graphs. First, we introduce an edge removal process: remove edges at random, one at a time, until the graph becomes disconnected. We show that the expected number of edges thus removed is equal to , where is the number of edges in the graph, and is the average of the all‐terminal reliability polynomial. Based on this process, we propose a Monte‐Carlo algorithm to quickly estimate the graph reliability (whose exact computation is NP‐hard). Moreover, we show that the distribution of the edge removal process can be used to quickly approximate the reliability polynomial. We then propose increasingly accurate asymptotics for graph reliability based solely on degree distributions of the graph. These asymptotics are tested against several real‐world networks and are shown to be accurate for sufficiently dense graphs. While the approach starts to fail for “subway‐like” networks that contain many paths of vertices of degree two, different asymptotics are derived for such networks.
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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