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We compare the phylogenetic tensors for various trees and networks for two, three and four taxa. If the probability spaces between one tree or network and another are not identical then there will be phylogenetic tensors that could have…
'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support…
The C-Orientation problem asks whether it is possible to orient an undirected graph to a directed phylogenetic network of a desired network class C. This problem arises, for example, when visualising evolutionary data, as popular methods…
A graph is a $k$-leaf power of a tree $T$ if its vertices are leaves of $T$ and two vertices are adjacent in $T$ if and only if their distance in $T$ is at most $k$. Then $T$ is a $k$-leaf root of $G$. This notion was introduced by…
For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter.…
This paper studies the relationship between undirected (unrooted) and directed (rooted) phylogenetic networks. We describe a polynomial-time algorithm for deciding whether an undirected nonbinary phylogenetic network, given the locations of…
Rapid developments in genetics and biology have led to phylogenetic methods becoming an important direction in the study of cancer and viral evolution. Although our understanding of gene biology and biochemistry has increased and is…
This paper presents methods to compare high order networks, defined as weighted complete hypergraphs collecting relationship functions between elements of tuples. They can be considered as generalizations of conventional networks where only…
The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been…
We fully characterize a large class of feedforward neural networks in terms of truncation maps. As an application, we show how a ReLU neural network can implement a feature map which separates concentric data.
A directed phylogenetic network is tree-child if every non-leaf vertex has a child that is not a reticulation. As a class of directed phylogenetic networks, tree-child networks are very useful from a computational perspective. For example,…
We show a first-order asymptotics result for the number of galled networks with $n$ leaves. This is the first class of phylogenetic networks of {\it large} size for which an asymptotic counting result of such strength can be obtained. In…
Since Darwin, species trees have been used as a simplified description of the relationships which summarize the complicated network $N$ of reality. Recent evidence of hybridization and lateral gene transfer, however, suggest that there are…
Pathways are integral to systems biology. Their classical representation has proven useful but is inconsistent in the meaning assigned to each arrow (or edge) and inadvertently implies the isolation of one pathway from another. Conversely,…
Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree…
Recently there has been considerable interest in the problem of finding a phylogenetic network with a minimum number of reticulation vertices which displays a given set of phylogenetic trees, that is, a network with minimum hybrid number.…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
In the context of reconstructing phylogenetic networks from a collection of phylogenetic trees, several characterisations and subsequently algorithms have been established to reconstruct a phylogenetic network that collectively embeds all…
Are biological networks different from other large complex networks? Both large biological and non-biological networks exhibit power-law graphs (number of nodes with degree k, N(k) ~ k-b) yet the exponents, b, fall into different ranges.…
Phylogenetic trees summarize evolutionary relationships between organisms, and tools to analyze collections of phylogenetic trees enable contrasts between different genes' ancestry. The BHV metric space has enabled the analysis of…