Displacement, velocity, acceleration, and energy of a dynamical system derived from a damped harmonic oscillator extracted from video frames
Bibliographic record
Abstract
This dissertation reflects applying external forces to a harmonic oscillatory system based on the digital-image-based harmonic oscillator equation. This leads to solving partial differential equations (PDEs) since we consider video frame picture elements fr(x, y) in each equation. By solving each equation subject to an external applied force, we can extract motion waveforms from video frames (fr’s) showing a moving object with sinusoidal oscillations about an equilibrium point (e.g., up and down movements of a biker in motion). A frame fr waveform emanates from a harmonic oscillator. After solving the PDE equation which results video frame pixels fr(x, y), we can compute other quantities including velocity, acceleration, and energy of the harmonic oscillator system. In fact, role of fr(x, y) in the digital-image-based harmonic oscillator equation that is the equation of motion of the oscillator is identical to the displacement of the system. As a result, the main component to computing the quantities of the oscillator is fr(x, y). By taking the derivatives of fr(x, y), we obtain the velocity, acceleration, and energy of the system and then investigate their features. A specific focus belongs to the energy of the oscillatory system. The main reason for this concentration is that the fluctuations in energy suggest a varying distribution of forces across the image. Higher energy regions likely represent important features of the object in the digital image, such as fluctuating edges, textures, and so on.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 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".