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Record W3203886902 · doi:10.1364/josab.439879

Stochastic systems: tutorial

2021· article· en· W3203886902 on OpenAlex
C. J. McKinstrie, Trevor J. Stirling, Amr S. Helmy

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.
fundA Canadian funder is recorded on the work.

Bibliographic record

VenueJournal of the Optical Society of America B · 2021
Typearticle
Languageen
FieldEngineering
TopicAdvanced Control Systems Optimization
Canadian institutionsUniversity of Toronto
FundersNatural Sciences and Engineering Research Council of Canada
KeywordsComputer science

Abstract

fetched live from OpenAlex

In this tutorial, three examples of stochastic systems are considered: a strongly damped oscillator, a weakly damped oscillator and an undamped oscillator (integrator) driven by noise. The evolution of these systems is characterized by the temporal correlation functions and spectral densities of their displacements, which are determined and discussed. Damped oscillators reach steady stochastic states. Their correlations are decreasing functions of the difference between the sample times, and their spectra have peaks near their resonance frequencies. An undamped oscillator never reaches a steady state. Its energy increases with time, and its spectrum is sharply peaked at low frequencies. The required mathematical methods and physical concepts are explained on a just-in-time basis, and some theoretical pitfalls are mentioned. The insights one gains from studies of oscillators can be applied to a wide variety of physical systems, such as atom and semiconductor lasers, which will be discussed in a subsequent tutorial.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Simulation or modeling · Consensus signal: Simulation or modeling
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.949
Threshold uncertainty score0.253

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.005
GPT teacher head0.202
Teacher spread0.197 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it