Related papers: Using the tangle: a consistent construction of phy…
A recurring theme in the least squares approach to phylogenetics has been the discovery of elegant combinatorial formulas for the least squares estimates of edge lengths. These formulas have proved useful for the development of efficient…
We address the question of finding the community structure of a complex network. In an earlier effort [H. Zhou, {\em Phys. Rev. E} (2003)], the concept of network random walking is introduced and a distance measure defined. Here we…
Computing the Fr\'{e}chet distance for surfaces is a surprisingly hard problem and the only known algorithm is limited to computing it between flat surfaces. We adapt this algorithm to create one for computing the Fr\'{e}chet distance for a…
We study the evolution of networks through `triplets' - three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order…
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
In the field of topological data analysis, persistence modules are used to express geometrical features of data sets. The matching distance $d_\mathcal{M}$ measures the difference between $2$-parameter persistence modules by taking the…
The problem of optimizing distributed database includes: fragmentation and positioning data. Several different approaches and algorithms have been proposed to solve this problem. In this paper, we propose an algorithm that builds the…
Most of major algorithms for phylogenetic tree reconstruction assume that sequences in the analyzed set either do not have any offspring, or that parent sequences can maximally mutate into just two descendants. The graph resulting from such…
Several structural learning algorithms for staged tree models, an asymmetric extension of Bayesian networks, have been defined. However, they do not scale efficiently as the number of variables considered increases. Here we introduce the…
Evolutionary histories for species that cross with one another or exchange genetic material can be represented by leaf-labelled, directed graphs called phylogenetic networks. A major challenge in the burgeoning area of phylogenetic networks…
An ordered labeled tree is a tree in which the nodes are labeled and the left-to-right order among siblings is relevant. The edit distance between two ordered labeled trees is the minimum cost of changing one tree into the other through a…
The Neighbor-Joining algorithm is a popular distance-based phylogenetic method that computes a tree metric from a dissimilarity map arising from biological data. Realizing dissimilarity maps as points in Euclidean space, the algorithm…
Most phylogenetic analyses result in a sample of trees, but summarizing and visualizing these samples can be challenging. Consensus trees often provide limited information about a sample, and so methods such as consensus networks,…
The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral…
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
Clustering is a fundamental problem in machine learning where distance-based approaches have dominated the field for many decades. This set of problems is often tackled by partitioning the data into K clusters where the number of clusters…
Pathogen genome data offers valuable structure for spatial models, but its utility is limited by incomplete sequencing coverage. We propose a probabilistic framework for inferring genetic distances between unsequenced cases and known…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
Phylogenetic reconciliation seeks to explain host-symbiont co-evolution by mapping parasite trees onto host trees through events such as cospeciation, duplication, host switching, and loss. Finding an optimal reconciliation that ensures…
Given the amino acid sequence of a protein, researchers often infer its structure and function by finding homologous, or evolutionarily-related, proteins of known structure and function. Since structure is typically more conserved than…