A Mathematical Model to Determine the Optimal Ratio of Researchers of Different Categories for Solving a Scientific Problem in the Military Sphere
Bibliographic record
Abstract
In the paper, the authors propose a variant of the mathematical model for justifying the optimal ratio of researchers of different categories to conduct scientific research of the highest possible quality in conditions of limited resources. The discrepancy is formulated between the quality of scientific research and the restriction on financial resources, that is, the problem of resource allocation is solved. The relationship between the quality of scientific research and the number of researchers is proposed to be reflected by the canonical parabola equation. A mathematical model is formulated that reflects the essence of the question under study. The problem is solved using the method of Lagrange multipliers. The results of the study are confirmed by a numerical experiment. Resource constraints have always existed. This is especially true now for the development of the Armed Forces of Ukraine and increasing their combat and mobilisation readiness, which result in the country's defence capability as a whole. Limited funding also takes place in military science. It is very difficult to introduce new full-time positions and divisions. Previously, the number of researchers was justified following regulatory documents when creating scientific institutions and divisions, or by analogy with similar scientific institutions. In other words, the problem was solved empirically or situationally. This scientific study concerns substantiating the number of scientific personnel in conditions of limited resources, taking into account the work that is now performed and will be performed in the future.
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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 | 0.005 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.003 | 0.002 |
| Research integrity | 0.003 | 0.003 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
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".