Asymmetric autocatalytic reactions and their stationary distribution
Bibliographic record
Abstract
Abstract We consider a general class of autocatalytic reactions, which has been shown to display stochastic switching behaviour (discreteness-induced transitions (DITs)) in some parameter regimes. This behaviour was shown to occur either when the overall species count is low or when the rate of inflow and outflow of species is relatively much smaller than the rate of autocatalytic reactions. The long-term behaviour of this class was analysed in Bibbona et al. (Bibbona et al. 2020 J. R. Soc. Interface17, 20200243 (doi:10.1098/rsif.2020.0243)) with an analytic formula for the stationary distribution in the symmetric case. We focus on the case of asymmetric autocatalytic reactions and provide a formula for an approximate stationary distribution of the model. We show this distribution has different properties corresponding to the distinct behaviour of the process in the three parameter regimes; in the DIT regime, the formula provides the fraction of time spent at each of the stable points.
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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 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| 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".