Modeling trajectories using functional linear differential equations
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.
Bibliographic record
Abstract
We are motivated by a study that seeks to better understand the dynamic relationship between muscle activation and paw position during locomotion. For each gait cycle in this experiment, activation in the biceps and triceps is measured continuously and in parallel with paw position as a mouse trotted on a treadmill. We propose an innovative general regression method that draws from both ordinary differential equations and functional data analysis to model the relationship between these functional inputs and responses as a dynamical system that evolves over time. Specifically, our model addresses gaps in both literatures and borrows strength across curves estimating ODE parameters across all curves simultaneously rather than separately modeling each functional observation. Our approach compares favorably to related functional data methods in simulations and in cross-validated predictive accuracy of paw position in the gait data. In the analysis of the gait cycles, we find that paw speed and position are dynamically influenced by inputs from the biceps and triceps muscles and that the effect of muscle activation persists beyond the activation itself.
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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 | 0.000 | 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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 it