Related papers: A scale-free method for testing the proportionalit…
The Sackin index is an important measure for the balance of phylogenetic trees. We investigate two extensions of the Sackin index to the class of galled trees and two of its subclasses (simplex galled trees and normal galled trees) where we…
We investigate the properties of the spanning trees of various real-world and model networks. The spanning tree representing the communication kernel of the original network is determined by maximizing total weight of edges, whose weights…
Tree-width has been proven to be a useful parameter to design fast and efficient algorithms for intractable problems. However, while tree-width is low on relatively sparse graphs can be arbitrary high on dense graphs. Therefore, we…
A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which…
Within the field of phylogenetics there is growing interest in measures for summarising the dissimilarity, or 'incongruence', of two or more phylogenetic trees. Many of these measures are NP-hard to compute and this has stimulated a…
Phylogenetic trees describe the evolutionary history of a group of present-day species from a common ancestor. These trees are typically reconstructed from aligned DNA sequence data. In this paper we analytically address the following…
Balanced minimum evolution is a distance-based criterion for the reconstruction of phylogenetic trees. Several algorithms exist to find the optimal tree with respect to this criterion. One approach is to minimize a certain linear functional…
We propose a novel method designed for large-scale regression problems, namely the two-stage best-scored random forest (TBRF). "Best-scored" means to select one regression tree with the best empirical performance out of a certain number of…
Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of…
The normalized stress metric measures how closely distances between vertices in a graph drawing match the graph-theoretic distances between those vertices. It is one of the most widely employed quality metrics for graph drawing, and is even…
Frequencies of $k$-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between…
Tree balance plays an important role in various research areas in phylogenetics and computer science. Typically, it is measured with the help of a balance index or imbalance index. There are more than 25 such indices available, recently…
The clustering and visualisation of high-dimensional data is a ubiquitous task in modern data science. Popular techniques include nonlinear dimensionality reduction methods like t-SNE or UMAP. These methods face the `scale-problem' of…
A rigorous methodology is proposed to study cell division data consisting in several observed genealogical trees of possibly different shapes. The procedure takes into account missing observations, data from different trees, as well as the…
We study the relation between the minimal spanning tree (MST) on many random points and the "near-minimal" tree which is optimal subject to the constraint that a proportion $\delta$ of its edges must be different from those of the MST.…
We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is…
Large tree structures are ubiquitous and real-world relational datasets often have information associated with nodes (e.g., labels or other attributes) and edges (e.g., weights or distances) that need to be communicated to the viewers. Yet,…
The ability to compare complex systems can provide new insight into the fundamental nature of the processes captured in ways that are otherwise inaccessible to observation. Here, we introduce the $n$-tangle method to directly compare two…
Motivation: While the majority of gene histories found in a clade of organisms are expected to be generated by a common process (e.g. the coalescent process), it is well-known that numerous other coexisting processes (e.g. horizontal gene…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…