Linear Stochastic Graphon Systems with Q-Space Noise
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Bibliographic record
Abstract
The modelling and control of systems on large complex networks is intractable in general. One approach is to use graphon theory which provides limit objects for infinite sequences of graphs permitting one to approximate arbitrarily large networks by infinite dimensional operators. Such a formulation was initiated in the work of Gao and Caines (2020, 2021) extending classical linear system control theory to the control of systems on large networks. This paper introduces infinite dimensional stochastic processes called Q-space noise into this framework. First, Brownian motions in Hilbert spaces are defined. Second, stochastic dynamical systems on large graphs using Q-space noise processes are shown to converge in the graph limit in expectation. Third, state-to-state and linear-quadratic control of these systems is formulated and the limit approximations are established. Finally, the behavior of these approximations is illustrated numerically.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| 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