Distributed Fiedler Vector Estimation With Application to Desynchronization of Harmonic Oscillator Networks
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Bibliographic record
Abstract
The Fiedler vector of a graph is the eigenvector corresponding to the algebraic connectivity, which is the second-smallest eigenvalue (counting multiple eigenvalues separately) of the corresponding Laplacian matrix. We propose a continuous-time distributed control protocol to drive the value of the state variables of a network toward the Fiedler vector, up to a scale factor. Our protocol is unbiased and robust with respect to the initial network state, but the knowledge of the algebraic connectivity is required. By means of the proposed control law, we design a local state feedback that achieves desynchronization on arbitrary undirected connected networks of diffusively coupled harmonic oscillators. We provide numerical simulations to corroborate the theoretical results.
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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 | 0.000 | 0.000 |
| 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