Path partitions of phylogenetic networks
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Notice bibliographique
Résumé
In phylogenetics , evolution is traditionally represented in a tree-like manner. However, phylogenetic networks can be more appropriate for representing evolutionary events such as hybridization, horizontal gene transfer, and others. In particular, the class of forest-based networks was recently introduced to represent introgression , in which genes are swapped between species. A network is forest-based if it can be obtained by adding arcs to a collection of trees, so that the endpoints of the new arcs are in different trees. This contrasts with so-called tree-based networks, which are formed by adding arcs within a single tree . We are interested in the computational complexity of recognizing forest-based networks, which was recently left as an open problem by Huber et al. It has been observed that forest-based networks coincide with directed acyclic graphs that can be partitioned into induced paths, each ending at a leaf of the original graph. Several types of path partitions have been studied in the graph theory literature, but to our best knowledge this type of ‘leaf induced path partition’ has not been directly considered before. The study of forest-based networks in terms of these partitions allows us to establish closer relationships between phylogenetics and algorithmic graph theory, and to provide answers to problems in both fields. More specifically, we show that deciding whether a network is forest-based is NP-complete, even on input networks that are tree-based, binary, and have only three leaves. This shows that partitioning a directed acyclic graph into a constant number of induced paths is NP-complete, answering a recent question of Fernau et al. We then show that the problem is polynomial-time solvable on binary networks with two leaves and on the recently introduced class of orchards, which we show to be always forest-based. Finally, for undirected graphs, we introduce unrooted forest-based networks and provide hardness results for this class as well.
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Prédiction distillée sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Apprise à partir de 10 348 étiquettes directes de Codex et de 10 348 étiquettes directes de Gemma. Le mode candidate est l'union des têtes enseignantes seuillées; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont ni des étiquettes humaines ni des étiquettes directes de modèles de pointe.
Scores Codex et Gemma par catégorie
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,000 |
| Méta-épidémiologie (sens strict) | 0,000 | 0,000 |
| Méta-épidémiologie (sens large) | 0,000 | 0,000 |
| Bibliométrie | 0,000 | 0,000 |
| Études des sciences et des technologies | 0,000 | 0,001 |
| Communication savante | 0,000 | 0,000 |
| Science ouverte | 0,000 | 0,000 |
| Intégrité de la recherche | 0,000 | 0,000 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,000 | 0,000 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découle