MatrixBandwidth.jl: Fast algorithms for matrix bandwidth minimization and recognition
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The bandwidth of an matrix is the minimum non-negative integer {0, 1, , -1} such that , = 0 whenever | -| > .Reordering the rows and columns of a matrix to reduce its bandwidth has many practical applications in engineering and scientific computing: it can improve performance when solving linear systems, approximating partial differential equations, optimizing circuit layout, and more (Mafteiu-Scai, 2014).There are two variants of this problem: minimization, which involves finding a permutation matrix such that the bandwidth of T is minimized, and recognition, which entails determining whether there exists a permutation matrix such that the bandwidth of T is less than or equal to some fixed non-negative integer (an optimal permutation that fully minimizes the bandwidth of is not required).Accordingly, MatrixBandwidth.jloffers fast algorithms for matrix bandwidth minimization and recognition.Julia's (Bezanson et al., 2017) combination of easy syntax and high performance, along with its rapidly growing ecosystem for scientific computing, made it the ideal language of choice for this project.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 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