Algorithms for Reticulate Networks of Multiple Phylogenetic Trees
Bibliographic record
Abstract
A reticulate network N of multiple phylogenetic trees may have vertices with two or more parents (called reticulation vertices). There are two ways to define the reticulation number of N. One is to define it as the number of reticulation vertices in N; in this case, a reticulate network with the smallest reticulation number is called an optimal type-I reticulate network of the trees. The other is to define it as the total number of parents of reticulation vertices in N minus the number of reticulation vertices in N; in this case, a reticulate network with the smallest reticulation number is called an optimal type-II reticulate network of the trees. In this paper, we present a fast algorithm for constructing one or all optimal type-I reticulate networks of multiple phylogenetic trees. We then use the algorithm together with other ideas to obtain an algorithm for estimating a lower bound on the reticulation number of an optimal type-II reticulate network of the input trees. To our knowledge, these are the first fast algorithms for the problems. Our experimental data shows that our algorithms can construct optimal type-I reticulate networks rapidly and can compute better lower bounds for optimal type-II reticulate networks within much shorter time than the previously best program.
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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 | 0.002 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.006 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".