Control design to shape the stationary probability density function
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Bibliographic record
Abstract
This paper extends a regulatory controller synthesis technique that was previously introduced for first-order processes to higher-order processes. The target of the design is to find a feedback control law such that the multivariate stationary probability density function (PDF) for the closed-loop process reasonably approximates a preselected target PDF. With the idea already motivated and introduced in previous work, the focus of this paper is on dealing with the various complications that arise when the process dimension is greater than one. As in the previous case, the main idea of multivariate PDF-shaping is to reduce the integral equation that governs the relationship between process dynamics and stationary PDF to a set of algebraic equations. The proposed approach relies on parameterization of the feedback control law to simplify manipulation of the integral equation. Numerical simulations with an example process are used to demonstrate application of the technique.
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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 | 0.004 | 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 | 0.000 | 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 it