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pro vyhledávání: '"Bienvenu, François"'
Autor:
Bienvenu, François
Models of random phylogenetic networks have been used since the inception of the field, but the introduction and rigorous study of mathematically tractable models is a much more recent topic that has gained momentum in the last 5 years. This manuscri
Externí odkaz:
http://arxiv.org/abs/2410.13574
In recent years, there has been an effort to extend the classical notion of phylogenetic balance, originally defined in the context of trees, to networks. One of the most natural ways to do this is with the so-called $B_2$ index. In this paper, we st
Externí odkaz:
http://arxiv.org/abs/2407.19454
Autor:
Bienvenu, François, Steel, Mike
Publikováno v:
Bull. Math. Biol. 86, 94 (2024)
In a recent paper, the question of determining the fraction of binary trees that contain a fixed pattern known as the snowflake was posed. We show that this fraction goes to 1, providing two very different proofs: a purely combinatorial one that is q
Externí odkaz:
http://arxiv.org/abs/2402.04499
Autor:
Bienvenu, François, Duchamps, Jean-Jil
Publikováno v:
Electron. J. Probab. 29:1-48 (2024)
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages correlates neg
Externí odkaz:
http://arxiv.org/abs/2211.02407
Publikováno v:
Journal of Mathematical Biology 83:52 (2021)
Measures of phylogenetic balance, such as the Colless and Sackin indices, play an important role in phylogenetics. Unfortunately, these indices are specifically designed for phylogenetic trees, and do not extend naturally to phylogenetic networks (wh
Externí odkaz:
http://arxiv.org/abs/2010.08079
Publikováno v:
Random Structures & Algorithms, 60(4):653-689 (2022)
Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical properties,
Externí odkaz:
http://arxiv.org/abs/2007.09701
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Publikováno v:
Random Structures & Algorithms, 59(2):155-188 (2021)
Starting from any graph on $\{1, \ldots, n\}$, consider the Markov chain where at each time-step a uniformly chosen vertex is disconnected from all of its neighbors and reconnected to another uniformly chosen vertex. This Markov chain has a stationar
Externí odkaz:
http://arxiv.org/abs/1906.08806
Autor:
Bienvenu, François
Publikováno v:
Combinatorics, Probability and Computing, 28(6):811-815 (2019)
Consider any fixed graph whose edges have been randomly and independently oriented, and write $\{S \leadsto i\}$ to indicate that there is an oriented path going from a vertex $s \in S$ to vertex $i$. Narayanan (2016) proved that for any set $S$ and
Externí odkaz:
http://arxiv.org/abs/1711.08815
Publikováno v:
Stochastic Processes and their Applications 129(6):2010-2048 (2019)
We introduce a new random graph model motivated by biological questions relating to speciation. This random graph is defined as the stationary distribution of a Markov chain on the space of graphs on $\{1, \ldots, n\}$. The dynamics of this Markov ch
Externí odkaz:
http://arxiv.org/abs/1706.01015