The notion of stability in mathematics, biology, ecology and environmental sustainability
Bibliographic record
Abstract
Abstract: The term “stability ” has many different meanings and its interpretation and application in various sciences is not absolutely identical. Historically, stability has been first formally defined in mathematical form by Lyapunov to describe equilibrium behaviour of the solar system. Lyapunov stability considers the behaviour of a system solution if its initial state is in the neighbourhood of an equilibrium point. Conceptually, it states that the equilibrium point is stable if all solutions originating in its neighbourhood forever remain “close enough ” to equilibrium. Due to its precise definition and well-established mathematical technique, Lyapunov stability has found a widespread application outside its original context, particularly to analyse solutions of mathematical models of biological communities in order to determine conditions they must satisfy to be stable. Research of this kind has been a dominating trend and, in words of Justus (2006), set much of the agenda of twentieth century mathematical ecology. There are, however, intrinsic features of the ecological systems that distinguish them from physical systems and limit a mechanical application of mathematical technique of stability study. An ecosystem is comprised of living (biotic) components and their non-living (abiotic) factors. A biotic part of an ecosystem (i.e., plants, animals and micro-organisms) is organized in hierarchical structures according to their role in the energetic and metabolic processes called trophic levels.
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".