Maintaining Intruder Detection Capability in a Rectangular Domain with Sensors
Bibliographic record
Abstract
In order to detect intruders that attempt to pass through a rectangular domain, sensors are placed at nodes of a regular spaced grid laid out over the rectangle. An intruder that steps within the sensing range of a sensor will be detected. It is desired that we prevent potential attacks in either one dimension or two dimensions. A one-dimensional attack succeeds when an intruder enters from the top North side and exits out the bottom South side of the domain without being detected. Preventing attacks in two dimensions requires that we simultaneously prevent the intruder from either entering North and exiting South or entering East left side and exiting West right side undetected. Initially, all of the sensors are working properly and the domain is fully protected, i.e., attacks will be detected, in both dimensions assuming the grid points are such that neighboring sensors have overlapping sensing ranges and include all four boundaries of the domain. Over time, the sensors may fail and we are left with a subset of working sensors. Under these conditions we wish to 1 determine if one or two-dimensional attack detection still persists and 2 if not, restore protection by adding the least number of sensors required to ensure detection in either one or two dimensions. Ideally, the set of currently working sensors would provide some amount of fault-tolerance. In particular, it would be advantageous if for a given k, the set of sensors maintains protection in one or two dimensions even if upi¾źto k of the sensors fail. This leads to the problems of 1 deciding if a subset of the sensors provides protection with upi¾źto k faults and 2 if not, finding the minimum number of grid points to add sensors to in order to achieve k fault-tolerance. In this paper, we provide algorithms for deciding if a set sensors provides k-fault tolerant protection against attacks in both one and two dimensions, for optimally restoring k-fault tolerant protection in one dimension and for restoring protection in two dimensions optimally for $$k=0$$ and approximately otherwise.
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How this classification was reachedexpand
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 | 0.001 | 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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".