Convexity, Jensen's inequality and benefits of noisy mechanical ventilation
Bibliographic record
Abstract
Mechanical ventilators breathe for you when you cannot or when your lungs are too sick to do their job. Most ventilators monotonously deliver the same-sized breaths, like clockwork; however, healthy people do not breathe this way. This has led to the development of a biologically variable ventilator--one that incorporates noise. There are indications that such a noisy ventilator may be beneficial for patients with very sick lungs. In this paper we use a probabilistic argument, based on Jensen's inequality, to identify the circumstances in which the addition of noise may be beneficial and, equally important, the circumstances in which it may not be beneficial. Using the local convexity of the relationship between airway pressure and tidal volume in the lung, we show that the addition of noise at low volume or low pressure results in higher mean volume (at the same mean pressure) or lower mean pressure (at the same mean volume). The consequence is enhanced gas exchange or less stress on the lungs, both clinically desirable. The argument has implications for other life support devices, such as cardiopulmonary bypass pumps. This paper illustrates the benefits of research that takes place at the interface between mathematics and medicine.
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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 | 0.004 | 0.025 |
| 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 | 0.004 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".