The Application of Possibility Distribution for Solving Standard Quadratic Optimization Problems
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Bibliographic record
Abstract
A standard quadratic optimization problem (StQP) is to find optimal values of a quadratic form over the standard simplex. The concept of possibility distribution was proposed by L. A. Zadeh. This paper applies the concept of possibility distribution function to solving StQP. The application of possibility distribution function establishes that it encapsulates the constrained conditions of the standard simplex into the possibility distribution function, and the derivative of the StQP formula becomes a linear function. As a result, the computational complexity of StQP problems is reduced, and the solutions of the proposed algorithm are always over the standard simplex. This paper proves that NP-hard StQP problems are in P. Numerical examples demonstrate that StQP problems can be solved by solving a set of linear equations. Comparing with Lagrangian function method, the solutions of the new algorithm are reliable when the symmetric matrix is indefinite.
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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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.008 |
| Open science | 0.001 | 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