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Using polynomial truncations of the Fourier transform of the RG transformation of Dyson's hierarchical model, we show that it is possible to calculate very accurately the renormalized quantities in the symmetric phase. Numerical results…

We prove a general Fueter Theorem over real alternative *-algebras. We show that a suitable power of the Laplacian maps Dunkl-regular functions to Dunkl monogenic functions with axial symmetries. Using the embedding of hypercomplex function…

Multivariate renormalisation techniques are implemented in order to build, study and then renormalise at the poles, branched zeta functions associated with trees. For this purpose, we first prove algebraic results and develop analytic…

In 1998, B\"{o}cker and Dress gave a 1-to-1 correspondence between symbolically dated rooted trees and symbolic ultrametrics. We consider the corresponding problem for unrooted trees. More precisely, given a tree $T$ with leaf set $X$ and a…

The Block Tree (BT) is a novel compact data structure designed to compress sequence collections. It obtains compression ratios close to Lempel-Ziv and supports efficient direct access to any substring. The BT divides the text recursively…

Given a distance matrix consisting of pairwise distances between species, a distance-based phylogenetic reconstruction method returns a tree metric or equidistant tree metric (ultrametric) that best fits the data. We investigate…

Phylogenetic trees are often constructed by using a metric on the set of taxa that label the leaves of the tree. While there are a number of methods for constructing a tree using a given metric, such trees will only display the metric if it…

We consider different pentagon identities realized by the hyperbolic hypergeometric functions and investigate their degenerations to the level of complex hypergeometric functions. In particular, we show that one of the degenerations yields…

Our goal is to visualize an additional data dimension of a tree with multifaceted data through superimposition on vertical strips, which we call columns. Specifically, we extend upward drawings of unordered rooted trees where vertices have…

Reduction trees are a way of encoding a substitution procedure dictated by the relations of an algebra. We use reduction trees in the subdivision algebra to construct canonical triangulations of flow polytopes which are shellable. We…

We overcome the barrier of constructing N=4 superconformal models in one space dimension for more than three particles. The D(2,1;alpha) superalgebra of our systems is realized on the coordinates and momenta of the particles, their…

This paper presents two approaches to quantifying and visualizing variation in datasets of trees. The first approach localizes subtrees in which significant population differences are found through hypothesis testing and sparse classifiers…

We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of…

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential tree model whose state changes in time with the…

In the last years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too…

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…

Diagonalization, or eigenvalue decomposition, is very useful in many areas of applied mathematics, including signal processing and quantum physics. Matrix decomposition is also a useful tool for approximating matrices as the product of a…

Suffix trees are a fundamental data structure in stringology, but their space usage, though linear, is an important problem for its applications. We design and implement a new compressed suffix tree targeted to highly repetitive texts, such…

The problem of comparing trees representing the evolutionary histories of cancerous tumors has turned out to be crucial, since there is a variety of different methods which typically infer multiple possible trees. A departure from the…

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to…