A statistical model of false negative and false positive detection of phase singularities
Bibliographic record
Abstract
The complexity of cardiac fibrillation dynamics can be assessed by analyzing the distribution of phase singularities (PSs) observed using mapping systems. Interelectrode distance, however, limits the accuracy of PS detection. To investigate in a theoretical framework the PS false negative and false positive rates in relation to the characteristics of the mapping system and fibrillation dynamics, we propose a statistical model of phase maps with controllable number and locations of PSs. In this model, phase maps are generated from randomly distributed PSs with physiologically-plausible directions of rotation. Noise and distortion of the phase are added. PSs are detected using topological charge contour integrals on regular grids of varying resolutions. Over 100 × 106 realizations of the random field process are used to estimate average false negative and false positive rates using a Monte-Carlo approach. The false detection rates are shown to depend on the average distance between neighboring PSs expressed in units of interelectrode distance, following approximately a power law with exponents in the range of 1.14 to 2 for false negatives and around 2.8 for false positives. In the presence of noise or distortion of phase, false detection rates at high resolution tend to a non-zero noise-dependent lower bound. This model provides an easy-to-implement tool for benchmarking PS detection algorithms over a broad range of configurations with multiple PSs.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".