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We present TreeClone, a latent feature allocation model to reconstruct tumor subclones subject to phylogenetic evolution that mimics tumor evolution. Similar to most current methods, we consider data from next-generation sequencing of tumor…

In the absence of horizontal gene transfer it is possible to reconstruct the history of gene families from empirically determined orthology relations, which are equivalent to event-labeled gene trees. Knowledge of the event labels…

Designing protein sequences that fold into a target 3D structure, known as protein inverse folding, is a fundamental challenge in protein engineering. While recent deep learning methods have achieved impressive performance by recovering…

In phylogenetics, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted arbitrary acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For…

Most approaches to prediction of protein function from primary structure are based on similarity between the query sequence and sequences of known function. This approach, however, disregards the occurrence of gene duplication (paralogy) or…

This paper addresses the problem of finding a representation of a subtree distance, which is an extension of the tree metric. We show that a minimal representation is uniquely determined by a given subtree distance, and give a linear time…

The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number…

In this work, we answer an open problem in the study of phylogenetic networks. Phylogenetic trees are rooted binary trees in which all edges are directed away from the root, whereas phylogenetic networks are rooted acyclic digraphs. For the…

The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…

The structure of an evolving network contains information about its past. Extracting this information efficiently, however, is, in general, a difficult challenge. We formulate a fast and efficient method to estimate the most likely history…

Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology). Traditional Markov…

Dynamic tree data structures maintain a forest while supporting insertion and deletion of edges and a broad set of queries in $O(\log n)$ time per operation. Such data structures are at the core of many modern algorithms. Recent work has…

A phylogenetic network is a directed acyclic graph that visualises an evolutionary history containing so-called reticulations such as recombinations, hybridisations or lateral gene transfers. Here we consider the construction of a simplest…

We study the problem of constructing phylogenetic trees for a given set of species. The problem is formulated as that of finding a minimum Steiner tree on $n$ points over the Boolean hypercube of dimension $d$. It is known that an optimal…

While Generative Adversarial Networks (GANs) achieve spectacular results on unstructured data like images, there is still a gap on tabular data, data for which state of the art supervised learning still favours to a large extent decision…

The inference of new information on the relatedness of species by phylogenetic trees based on DNA data is one of the main challenges of modern biology. But despite all technological advances, DNA sequencing is still a time-consuming and…

A consensus tree is a phylogenetic tree that captures the similarity between a set of conflicting phylogenetic trees. The problem of computing a consensus tree is a major step in phylogenetic tree reconstruction. It also finds applications…

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…

Compatibility of phylogenetic trees is the most important concept underlying widely-used methods for assessing the agreement of different phylogenetic trees with overlapping taxa and combining them into common supertrees to reveal the tree…

There are several tools available to infer phylogenetic trees, which depict the evolutionary relationships among biological entities such as viral and bacterial strains in infectious outbreaks, or cancerous cells in tumor progression trees.…