Bibliographic record
Abstract
OBJECTIVE: The use of mathematics in the study of phenomena and systems of interest to medicine has become quite popular in recent years, but not much progress has been made as a result of these efforts. The aim of this article is to identify the reasons for this failure and to suggest procedures for more successful outcomes. METHODS: We review and assess a variety of mathematical modeling procedures, from microscopic (at the level of molecular behavior) to macroscopic standpoints, from lumped-parameters to distributed-parameters approaches. Using examples that are as simple as possible, we elucidate the difference between the predictive and the explanatory powers of mathematical models, as well as the uses (and abuses) of analogy in their construction. RESULTS: Mathematical medicine is a truly interdisciplinary area that brings together medical researchers, engineers, and applied mathematicians whose vast differences in expertise and background make collaboration difficult. CONCLUSION: The lack of a common language and a common way of understanding what a mathematical model is, and what it can do, is identified as the main source of the slow progress to date, and constructive suggestions are made to improve the situation.
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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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".