Reliability analysis of the uncertain fractional‐order dynamic system with state constraint
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Bibliographic record
Abstract
Uncertain fractional‐order differential equations driven by the Liu process are of significance to depict the heredity and memory features of uncertain dynamical systems. This paper primarily analyses the reliability of the uncertain fractional‐order dynamic system with a state constraint. First, consider the possibility that the real dynamical system is actually limited; the state constraint is absorbed to the ordinary uncertain fractional‐order dynamical system. The concept of reliability of uncertain system is presented innovatively, which are ulteriorly formulated through the existing first‐hitting time theorem. Second, based on the proposed reliability and under a given sufficient condition, a novel uncertain fractional‐order dynamic system with a state constraint is modeled mathematically; corresponding minimum operation ability of the uncertain system is also given. Lastly, the uncertain fractional‐order dynamic system with a state constraint is applied to different physical and financial dynamical models. Analytic expressions of reliability indexes are derived to demonstrate the reasonableness of our model. Meanwhile, expected time response and American barrier option prices are calculated by using the predictor–corrector scheme. The sensitivity analysis is also presented for the numerical examples.
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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 | 0.011 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.004 |
| Science and technology studies | 0.000 | 0.001 |
| 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