A fractional-order dynamical approach to vector equilibrium problems with partial order induced by a polyhedral cone
Bibliographic record
Abstract
In this paper, we propose a specific dynamical model for solving a class of vector equilibrium problems with partial order induced by a polyhedral cone which is generated by some matrix.Unlike the traditional dynamical models, it particularly possesses the feature of fractional-order system.The so-called Mittag-Leffler stability of the dynamical system is studied, which verifies the convergence to the solution of the corresponding vector equilibrium problems.This result is established by applying the techniques involving Caputo fractional derivatives, Lipschitz-type continuity, and strong pseudomonotonicity assumptions with partial ordering based on a polyhedral cone.Numerical implementations are demonstrated to illustrate the proposed approach.In addition, a real-world application to the general framework of vector network equilibrium models based on polyhedral cone ordering is presented.
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How this classification was reachedexpand
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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".