A Half-Size Singularity Test Matrix for Fast and Reliable Passivity Assessment of Rational Models
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Bibliographic record
Abstract
One major difficulty in the rational modeling of linear systems is that the obtained model can be nonpassive, thereby leading to unstable simulations. The model's passivity properties are usually assessed by computing the eigenvalues of a Hamiltonian matrix, which is derived from the model parameters. The purely imaginary eigenvalues represent crossover frequencies where the model's conductance matrix is singular, allowing to pinpoint frequency intervals of passivity violations. Unfortunately, the eigenvalue computation time can be excessive for large models. Also, the test applies only to symmetrical models, and the testing is made difficult by numerical noise in the extracted eigenvalues. In this paper a new (non-Hamiltonian) half-size singularity test matrix is derived for use with admittance parameter state-space models, which overcomes these shortcomings. It gives a computational speedup by a factor of eight; it is applicable to both symmetric and unsymmetrical models; and it produces noiseless eigenvalues for reliable passivity assessment.
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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