Related papers: Ultrametrics in the genetic code and the genome
We study the dynamics of genetic code evolution. The model of Vetsigian et al. [1] and Vetsigian [2] uses the mechanism of horizontal gene transfer to demonstrate convergence of the genetic code to a near universal solution. We reproduce…
Phrase structure trees have a hierarchical structure. In many subjects, most notably in Taxonomy such tree structures have been studied using ultrametrics. Here syntactical hierarchical phrase trees are subject to a similar analysis, which…
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity, is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
Genome rearrangement distances are an established method in genome comparison. Works in this area may include various rearrangement operations representing large-scale mutations, gene orientation information, the number of nucleotides in…
A simple and surprisingly accurate description of spectral diffusion in deeply frozen globular proteins is constructed directly using the concept of ultrametricity of protein dynamics. Earlier the similar concept has been used for…
A genetic algorithm is suitable for exploring large search spaces as it finds an approximate solution. Because of this advantage, genetic algorithm is effective in exploring vast and unknown space such as molecular search space. Though the…
Geometric graphs appear in many real-world data sets, such as road networks, sensor networks, and molecules. We investigate the notion of distance between embedded graphs and present a metric to measure the distance between two geometric…
Genome rearrangements are events where large blocks of DNA exchange places during evolution. The analysis of these events is a promising tool for understanding evolutionary genomics, providing data for phylogenetic reconstruction based on…
We live in a period where bio-informatics is rapidly expanding, a significant quantity of genomic data has been produced as a result of the advancement of high-throughput genome sequencing technology, raising concerns about the costs…
Advancements in genomic research such as high-throughput sequencing techniques have driven modern genomic studies into "big data" disciplines. This data explosion is constantly challenging conventional methods used in genomics. In parallel…
The log-det distance between two aligned DNA sequences was introduced as a tool for statistically consistent inference of a gene tree under simple non-mixture models of sequence evolution. Here we prove that the log-det distance, coupled…
A field with an absolute value function is a basic type of metric space, which includes the real and complex numbers with their standard metrics, and ultrametrics on fields like the p-adic numbers. Here we try to give some perspectives of…
We consider random binary trees that appear as the output of certain standard algorithms for sorting and searching if the input is random. We introduce the subtree size metric on search trees and show that the resulting metric spaces…
As the amount and complexity of genetic information increases it is necessary that we explore some efficient ways of handling these data. This study takes the "divide and conquer" approach for analyzing high dimensional genomic data. Our…
It is known that PQ-symmetric maps on the boundary characterize the quasi-isometry type of visual hyperbolic spaces, in particular, of geodesically complete \br-trees. We define a map on pairs of PQ-symmetric ultrametric spaces which…
We design a heuristic method, a genetic algorithm, for the computation of an upper bound of the minimum distance of a linear code over a finite field. By the use of the row reduced echelon form, we obtain a permutation encoding of the…
We discuss the similarity of the degeneration structure of the genetic code with a pure number theoretic -- ``divisors code.'' The most interesting thing about our observation is not that there is a connection between number theory and the…
DNA codes have many applications, such as in data storage, DNA computing, etc. Good DNA codes have large sizes and satisfy some certain constraints. In this paper, we present a new construction method for reversible DNA codes. We show that…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…