A simple formula for the coalescence dynamics in the case of a linear kernel, with application to branching in filamentous fungi
Bibliographic record
Abstract
Filamentous fungi are the world champions for colonizing their environment. They grow and branch, constantly adapting to their environmental conditions. In this paper, we propose a model for fungal branching based on the clustering of proteins on the membrane of the fungal tip. From a theoretical point of view, the model relies on finding the probability of having two big clusters in a coalescence process, in the case of a relatively small number of particles (around 50). We first derive an analytic formula for the coalescence dynamics generated by a linear kernel, based on a reduction of the infinitesimal generator. Using the same reduction, we build an approximation of the dynamics for general kernels. We then derive the coalescence kernel corresponding to our model of protein clustering on the fungal tip by computing the mean encounter time between two particles diffusing on a sphere, which represents protein diffusion on the membrane. The method, well-known as the mean first passage time theory, relies on solving a Laplace equation with mixed boundary conditions. Finally, we apply our analysis to estimate the branching probability, and show that our model is coherent with the optimization of resources controlling fungal growth observed experimentally.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".