Related papers: Weighted Food Webs Make Computing Phylogenetic Div…
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…
The classical, ubiquitous, predecessor problem is to construct a data structure for a set of integers that supports fast predecessor queries. Its generalization to weighted trees, a.k.a. the weighted ancestor problem, has been extensively…
For many taxa, the current high rates of extinction are likely to result in a significant loss of biodiversity. The evolutionary heritage of biodiversity is frequently quantified by a measure called phylogenetic diversity (PD). We predict…
Unrooted phylogenetic networks are graphs used to represent evolutionary relationships. Accurately reconstructing such networks is of great relevance for evolutionary biology. It has recently been conjectured that all phylogenetic networks…
The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…
In Francis and Steel (2015), it was shown that there exists non-trivial networks on $4$ leaves upon which the distance metric affords a metric on a tree which is not the base tree of the network. In this paper we extend this result in two…
Inspired by scientific collaboration networks, especially our empirical analysis of the network of econophysicists, an evolutionary model for weighted networks is proposed. Both degree-driven and weight-driven models are considered.…
Phylogenetic networks are important for the study of evolution. The number of methods to find such networks is increasing, but most such methods can only reconstruct small networks. To find bigger networks, one can attempt to combine small…
We consider the classic problem of Network Reliability. A network is given together with a source vertex, one or more target vertices, and probabilities assigned to each of the edges. Each edge appears in the network with its associated…
Phylogenomics, even more so than traditional phylogenetics, needs to represent the uncertainty in evolutionary trees due to systematic error. Here we illustrate the analysis of genome-scale alignments of yeast, using robust measures of the…
Phylogenetic networks provide a framework for representing evolutionary histories involving reticulate events such as hybridization or horizontal gene transfer. A central problem is to infer such networks from local structural information.…
The method of flexi-Weighted Least Squares on evolutionary trees uses simple polynomial or exponential functions of the evolutionary distance in place of model-based variances. This has the advantage that unexpected deviations from…
Evolutionary computation methods have been successfully applied to neural networks since two decades ago, while those methods cannot scale well to the modern deep neural networks due to the complicated architectures and large quantities of…
In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. The question of how many sequence sites are required to recover this evolutionary…
The weighted ancestor problem on a rooted node-weighted tree $T$ is a generalization of the classic predecessor problem: construct a data structure for a set of integers that supports fast predecessor queries. Both problems are known to…
The Fair Proportion of a species in a phylogenetic tree is a very simple measure that has been used to assess its value relative to the overall phylogenetic diversity represented by the tree. It has recently been proved by Fuchs and Jin to…
Ultametrics are an important class of distances used in applications such as phylogenetics, clustering and classification theory. Ultrametrics are essentially distances that can be represented by an edge-weighted rooted tree so that all of…
Tree containment problem is a fundamental problem in phylogenetic study, as it is used to verify a network model. It asks whether a given network contain a subtree that resembles a binary tree. The problem is NP-complete in general, even in…
Phylogenetic networks allow modeling reticulate evolution, capturing events such as hybridization and horizontal gene transfer. A fundamental computational problem in this context is the Tree Containment problem, which asks whether a given…
Latent space models for network data characterize each node through a vector of latent features whose pairwise similarities define the edge probabilities among the pairs of nodes. Although this formulation has led to successful…