Power spectrum and Allan variance methods for calibrating single-molecule video-tracking instruments
Bibliographic record
Abstract
Single-molecule manipulation instruments, such as optical traps and magnetic tweezers, frequently use video tracking to measure the position of a force-generating probe. The instruments are calibrated by comparing the measured probe motion to a model of Brownian motion in a harmonic potential well; the results of calibration are estimates of the probe drag, α, and spring constant, κ. Here, we present both time- and frequency-domain methods to accurately and precisely extract α and κ from the probe trajectory. In the frequency domain, we discuss methods to estimate the power spectral density (PSD) from data (including windowing and blocking), and we derive an analytical formula for the PSD which accounts both for aliasing and the filtering intrinsic to video tracking. In the time domain, we focus on the Allan variance (AV): we present a theoretical equation for the AV relevant to typical single-molecule setups and discuss the optimal manner for computing the AV from experimental data using octave-sampled overlapping bins. We show that, when using maximum-likelihood methods to fit to the data, both the PSD and AV approaches can extract α and κ in an unbiased and low-error manner, though the AV approach is simpler and more robust.
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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 | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".