A unified approach for the stability robustness of polynomials in a convex set
Bibliographic record
Abstract
A polynomial p(s, k) that is affine in the parameter perturbation k is considered. It is assumed that the vector k is uncertain but belongs to a convex set which contains the origin, and a polynomial is called stable if all of its roots are contained in a prespecified stability region in the complex plane. Then the stability robustness of p(s, k) can be measured by the maximal nonnegative number rho with the property that if the gauge (or the Minkowski functional) of k with respect to the convex set is less than rho , the polynomial pk is always stable. A unified approach is presented for computing the robustness measure rho . The approach imbeds the problem considered into the framework of convex analysis so that some powerful tools in convex analysis can be used. The procedure for computing rho that results from this approach is easy to implement. Various examples are included to illustrate the type of results which may be obtained.>
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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 | 0.004 | 0.010 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.002 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".