Hybrid system modelling and simulation with Dirac deltas
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
For a wide variety of problems, creating detailed continuous models of physical systems is impractical. Hybrid models can abstract away short transient behaviour in order to simplify the study of such systems. For example, when modelling a bouncing ball, the bounce can be abstracted as a discontinuous change of the velocity. Impulsive differential equations can be used to model and simulate hybrid systems such as the bouncing ball. In this approach, the force acted on the ball by the floor is abstracted as an impulse. Current simulators cannot handle such approximations well due to the limitations of machine precision.In this paper, we present two approaches for the simulation of impulses: symbolic and numerical. Our contribution is a theoretically founded description of both approaches in a Causal Block Diagram simulator, and an analysis of the conditions for which a symbolic approach is better than a numerical one.
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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 | 0.001 | 0.000 |
| 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 it