NETWORK DECONTAMINATION IN PRESENCE OF LOCAL IMMUNITY
Bibliographic record
Abstract
We consider the problem of decontaminating a network infected by a mobile virus. The goal is to perform the task using as small a team of antiviral agents as possible, avoiding recontamination of disinfected areas. In all the existing literature, it is assumed that the immunity level of a decontaminated site is nil; that is, a decontaminated node, in absence of an antiviral agent on site, may be re-contaminated by any infected neighbour. The network decontamination problem is studied here under a new model of immunity to recontamination: we consider the case when a decontaminated vertex, after the cleaning agent has gone, will become recontaminated only if a majority of its neighbours are infected. We study the impact that the presence of local immunity has on the number of antiviral agents necessary to decontaminate the entire network. We establish both lower and upper bounds on the number cleaners in the case of (multidimensional) toroidal meshes, graphs of vertex degree at most three (e.g., cubic graphs, binary trees, etc.), and of tree networks. In all cases the established bounds are tight. All upper-bound proofs are constructive; i.e., we exhibit decontamination protocol achieving the claimed bound. We also analyze the total number of moves performed by the agents, and establish tight bounds in some cases.
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".