Metric and topological entropy bounds on state estimation for stochastic non-linear systems
Bibliographic record
Abstract
This paper studies state estimation over noisy channels for stochastic non-linear systems. We consider three estimation objectives, a strong and a weak form of almost sure stability of the estimation error as well as quadratic stability in expectation. For all three objectives, we derive lower bounds on the smallest channel capacity Coabove which the objective can be achieved with an arbitrarily small error. Lower bounds are obtained via a dynamical systems (through a novel construction of a dynamical system), an information-theoretic and a random dynamical systems approach. The first two approaches show that for a large class of systems, such as additive noise systems, Co = ∞, i.e., the estimation objectives cannot be achieved via channels of finite capacity. The random dynamical systems approach is shown to be operationally non-adequate for the problem, since it yields finite lower bounds Co under mild assumptions. Finally, we prove that a memoryless noisy channel in general constitutes no obstruction to asymptotic almost sure state estimation with arbitrarily small errors, when there is no noise in the system.
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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 | 0.005 | 0.041 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.003 | 0.008 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.002 | 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".