D-Stability and Structured Singular Values Analysis and Applications to Economic Models
Bibliographic record
Abstract
The stability analysis of transportation and economic models plays a fundamental role in understanding dynamic systems. The term stability means the ability of a system under consideration to return to an equilibrium state subject to perturbations. The analysis on D-stability extends the concept of stability by ensuring that the system is stable under a predefined set of various uncertainties. The computation of structured singular values plays a critical role in analyzing the dynamical system’s robustness and performance. For transportation models, structured singular value analysis helps evaluate traffic demand fluctuations. On the other hand, in economic systems, structured singular values aid in understanding the impacts of interest rates or supply chain disruptions on the performance and stability of the system. This article discusses the interplay between stability analysis, D-stability analysis, and structured singular values, and then emphasizes their applications to transportation and economic models. The aim is to study how one can ensure a robust and resilient system design. Through practical and numerical examples, the study illustrates how these concepts may set up a mathematical foundation for advancing robust modeling practices in dynamic and uncertain environments.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".