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An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other…
The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce branching process methods to their study. This approach…
Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…
Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks, to distinguish different networks, and to see when one…
We present analytical results for the distribution of shortest path lengths (DSPL) in a network growth model which evolves by node duplication (ND). The model captures essential properties of the structure and growth dynamics of social…
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 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…
Transition points mark qualitative changes in the macroscopic properties of large complex systems. Explosive transitions, exhibiting properties of both continuous and discontinuous phase transitions, have recently been uncovered in network…
Phylogenetic networks provide a more general description of evolutionary relationships than rooted phylogenetic trees. One way to produce a phylogenetic network is to randomly place $k$ arcs between the edges of a rooted binary phylogenetic…
Using a simple model with link removals as well as link additions, we show that an evolving network is scale free with a degree exponent in the range of (2, 4]. We then establish a relation between the network evolution and a set of…
Phylogenetic networks are a generalization of phylogenetic trees to leaf-labeled directed acyclic graphs that represent ancestral relationships between species whose past includes non-tree-like events such as hybridization and horizontal…
Learning vector representations for programs is a critical step in applying deep learning techniques for program understanding tasks. Various neural network models are proposed to learn from tree-structured program representations, e.g.,…
Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network…
We consider propagation models that describe the spreading of an attribute, called "damage", through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a…
Phylogenetic trees and networks are graphs used to model evolutionary relationships, with trees representing strictly branching histories and networks allowing for events in which lineages merge, called reticulation events. While the…
Phylogenetic networks are a generalization of phylogenetic trees that allow for representation of reticulate evolution. Recently, a space of unrooted phylogenetic networks was introduced, where such a network is a connected graph in which…
It was recently shown that a large class of phylogenetic networks, the `labellable' networks, is in bijection with the set of `expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks…
Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…
Phylogenetic networks are an important way to represent evolutionary histories that involve reticulations such as hybridization or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain…
Inference of phylogenetic networks is of increasing interest in the genomic era. However, the extent to which phylogenetic networks are identifiable from various types of data remains poorly understood, despite its crucial role in…