Characterization of Decentralized and Quotient Fixed Modes via Graph Theory
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Bibliographic record
Abstract
This paper deals with the decentralized control of systems with distinct modes. A simple graph-theoretic approach is first proposed to identify those modes of the system which cannot be moved by means of a linear time-invariant decentralized controller. To this end, the system is transformed into its Jordan state-space representation. Then, a matrix is computed, which has the same order as the transfer function matrix of the system. A bipartite graph is constructed from the computed matrix. Now, the problem of characterizing the decentralized fixed modes of the system reduces to verifying if this graph has a complete bipartite subgraph with a certain property. Analogously, a graph-theoretic method is presented to compute the modes of the system which are fixed with respect to any general (nonlinear and time-varying) decentralized controller. The proposed approaches are quite simpler than the existing ones, which often require calculating the rank of several matrices.
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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 | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.005 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.005 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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