Characterization of Information Channels for Asymptotic Mean\n Stationarity and Stochastic Stability of Non-stationary/Unstable Linear\n Systems
Bibliographic record
Abstract
Stabilization of non-stationary linear systems over noisy communication\nchannels is considered. Stochastically stable sources, and unstable but\nnoise-free or bounded-noise systems have been extensively studied in\ninformation theory and control theory literature since 1970s, with a renewed\ninterest in the past decade. There have also been studies on non-causal and\ncausal coding of unstable/non-stationary linear Gaussian sources. In this\npaper, tight necessary and sufficient conditions for stochastic stabilizability\nof unstable (non-stationary) possibly multi-dimensional linear systems driven\nby Gaussian noise over discrete channels (possibly with memory and feedback)\nare presented. Stochastic stability notions include recurrence, asymptotic mean\nstationarity and sample path ergodicity, and the existence of finite second\nmoments. Our constructive proof uses random-time state-dependent stochastic\ndrift criteria for stabilization of Markov chains. For asymptotic mean\nstationarity (and thus sample path ergodicity), it is sufficient that the\ncapacity of a channel is (strictly) greater than the sum of the logarithms of\nthe unstable pole magnitudes for memoryless channels and a class of channels\nwith memory. This condition is also necessary under a mild technical condition.\nSufficient conditions for the existence of finite average second moments for\nsuch systems driven by unbounded noise are provided.\n
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".