Related papers: Dyadic groups, dyadic trees and symmetries in long…
Trees corresponding to $\Lambda$- and $\Xi$-$n$-coalescents can be both quite similar and fundamentally different compared to bifurcating tree models based on Kingman's $n$-coalescent. This has consequences for inference of a well-fitting…
Phylogenetic networks are a generalization of phylogenetic trees that are used in biology to represent reticulate or non-treelike evolution. Recently, several algorithms have been developed which aim to construct phylogenetic networks from…
Phylogenomics is a new field which applies to tools in phylogenetics to genome data. Due to a new technology and increasing amount of data, we face new challenges to analyze them over a space of phylogenetic trees. Because a space of…
Cancers follow a clonal Darwinian evolution, with fitter subclones replacing more quiescent cells, ultimately giving rise to macroscopic disease. High-throughput genomics provides the opportunity to investigate these processes and determine…
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…
Machine learning methods can detect complex relationships between variables, but usually do not exploit domain knowledge. This is a limitation because in many scientific disciplines, such as systems biology, domain knowledge is available in…
The amount of completely sequenced chloroplast genomes increases rapidly every day, leading to the possibility to build large scale phylogenetic trees of plant species. Considering a subset of close plant species defined according to their…
Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting…
To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…
An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set $X$ of species from a…
The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…
One of humanity's earliest mathematical inquiries might have involved the geometric patterns in plants. The arrangement of leaves on a branch, seeds in a sunflower, and spines on a cactus exhibit repeated spirals, which appear with an…
We develop the theory of ``branch algebras'', which are infinite-dimensional associative algebras that are isomorphic, up to taking subrings of finite codimension, to a matrix ring over themselves. The main examples come from groups acting…
The Watson-Crick complementary properties of DNA make DNA a useful tool for the self-assembly of various target complexes. Concepts from graph theory can be used to model the self-assembling process in which the vertices of the graph…
The mitosis process of an eukaryotic cell can be represented by the structure constants of an evolution algebra. Any isotopism of the latter corresponds to a mutation of genotypes of the former. This paper uses Computational Algebraic…
We study the problem of visualizing phylogenetic networks, which are extensions of the Tree of Life in biology. We use a space filling visualization method, called DAGmaps, in order to obtain clear visualizations using limited space. In…
This paper examines the effect of mimicking discontinuous heredity caused by carrying more than one chromosome in some living organisms cells in Evolutionary Multi-Objective Optimization algorithms. In this representation, the phenotype may…
In this paper we have established relations of the genetic tables with magic and bimagic squares. Connections with Hamming distances, binomial coefficients are established. The idea of Gray code is applied. Shannon entropy of magic squares…
Epigenetic Tracking is a mathematical model of biological cells, originally conceived to study embryonic development. Computer simulations proved the capacity of the model to generate complex 3-dimensional cellular structures, and the…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…