Binary matrix decompositions without tongue-and-groove underdosage for radiation therapy planning
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Bibliographic record
Abstract
In the present paper we consider a particular case of the segmentation problem arising in the elaboration of radiation therapy plans. This problem consists in decomposing an integer matrix A into a nonnegative integer linear combination of some particular binary matrices called segments which represent fields that are deliverable with a multileaf collimator. For the radiation therapy context, it is desirable to find a decomposition that minimizes the beam-on time, that is the sum of the coefficients of the decomposition. Here we investigate a variant of this minimization problem with an additional constraint on the segments, called the tongue-and-groove constraint. Although this minimization problem under the condition that the used segments have to respect the tongue-and-groove constraint has already been studied, the complexity of it is still unknown. Here we prove that in the particular case where A is a binary matrix this problem is polynomially solvable. We provide a polynomial procedure that finds such a decomposition with minimal beam-on time. Furthermore, we show that the beam-on time of an optimal decomposition (but not the segmentation itself) can be found by determining the chromatic number of a related perfect graph.
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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 | 0.001 | 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 | 0.001 | 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