A new approach to node-failure protection with span-protecting p-cycles
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Bibliographic record
Abstract
Recent work has revealed a new, relatively simple and possibly cost-effective, approach to achieve combined protection of optical networks against both node and span failures. The resulting network designs use only a single set of p-cycle structures that have the same or only slightly more capacity than a corresponding optimal set of p-cycles for span protection. The new principle is based on a generalization of how nodes in a BLSR-ring or p-cycle (to date) derive survivability through loop-back at the nearest two neighbour-nodes on the same ring. The generalization views any combination of node failure and an affected transiting path from the standpoint of the two-hop segment defined by the failure node, and the nodes immediately adjacent on the affected path. We then ask whether these nodes are found together within the same p-cycle as the failure node, or another p-cycle entirely. In any case where they are, we show that the transiting path affected by the node failure is inherently restorable by ordinary p-cycle switching actions whether the respective two-hop segment is on-cycle, straddling, or partially on-cycle and partially straddling. We explain the principle and characterize its effectiveness in terms of network-wide single node failure restorability (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-node</sub> ) in networks designed only for minimum spare capacity, networks designed for enhanced R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-node</sub> (at min capacity) and networks designed strictly for R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-node</sub> = 1.
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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