Growth on multiple interactive-essential resources in a self-cycling\n fermentor: An impulsive differential equations approach
Bibliographic record
Abstract
We introduce a model of the growth of a single microorganism in a\nself-cycling fermentor in which an arbitrary number of resources are limiting,\nand impulses are triggered when the concentration of one specific substrate\nreaches a predetermined level. The model is in the form of a system of\nimpulsive differential equations. We consider the operation of the reactor to\nbe successful if it cycles indefinitely without human intervention and derive\nconditions for this to occur. In this case, the system of impulsive\ndifferential equations has a periodic solution. We show that success is\nequivalent to the convergence of solutions to this periodic solution. We\nprovide conditions that ensure that a periodic solution exists. When it exists,\nit is unique and attracting. However, we also show that whether a solution\nconverges to this periodic solution, and hence whether the model predicts that\nthe reactor operates successfully, is initial condition dependent. The analysis\nis illustrated with numerical examples.\n
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.001 |
| 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".