Investigating a Fractional Derivative Approach to Tumour Growth and Irradiation Modelling
Bibliographic record
Abstract
Cancer is one of the foremost causes of death worldwide. Although significant strides forward are continually being made, researchers often revisit foundational questions as newer and better technol- ogy is developed. One fundamental question that piques the interest of clinicians and researchers, alike, is the optimization of cancer- and patient-speci▯c treatment schedules. Mathematical on- cology, while still in its infancy, uses mathematics, modelling, and simulation to study cancer and thus improve our understanding of the disease and its treatments. This thesis focuses on comparing ordinary and fractional di▯erential equation models of tumor growth and radiation. Patient data from the Mo▯tt Cancer Centre is used to ▯t our six candidate models. These results are analyzed to assess the usefulness of the fractional derivative for our particular application and to compare our approach to existing industry standards. Collectively, our analysis shows that mathematical modelling is an invaluable tool to the future of oncology research. iii
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".