Toward a kinetic-based probabilistic time geography
Bibliographic record
Abstract
Time geography represents a powerful framework for the quantitative analysis of individual movement. Time geography effectively delineates the space–time boundaries of possible individual movement by characterizing movement constraints. The goal of this paper is to synchronize two new ideas, probabilistic time geography and kinetic-based time geography, to develop a more realistic set of movement constraints that consider movement probabilities related to object kinetics. Using random-walk theory, the existing probabilistic time geography model characterizes movement probabilities for the space–time cone using a normal distribution. The normal distribution has a symmetric probability density function and is an appropriate model in the absence of skewness – which we relate to an object’s initial velocity. Moving away from a symmetric distribution for movement probabilities, we propose the use of the skew-normal distribution to model kinetic-based movement probabilities, where the degree and direction of skewness is related to movement direction and speed. Following a description of our model, we use a set of case-studies to demonstrate the skew-normal model: a random walk, a correlated random walk, wildlife data, cyclist data, and athlete movement data. Our results show that for objects characterized by random movement behavior, the existing model performs well, but for object movement with kinetic properties (e.g., athletes), the proposed model provides a substantial improvement. Future work will look to extend the proposed probabilistic framework to the space–time prism.
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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 | 0.018 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.004 | 0.010 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".