T-theory

T-theory

T-theory is a branch of discrete mathematics dealing with analysis of trees and discrete metric spaces.

General history

As per Andreas Dress, T-theory originated from a question raised by Manfred Eigen, a recipient of the Nobel Prize in Chemistry, in the late seventies. He was trying to fit twenty distinct t-RNA modecules of the "E. Coli" bacterium into a tree.

One of the most important concepts of T-theory is the tight span of a metric space. If "X" is a metric space, the tight span "T(X)" of "X" is, up to isomorphism, the unique minimal injective metric space that contains "X". John Isbell was the first to discover the tight span in 1964, which he called the injective envelope. Dress independently constructed the same construct, which he called the tight span.

Application areas

* Phylogenetic analysis, which is used to create phylogenetic trees.
* Online algorithms - "k"-server problem

Recent developments

* Bernd Sturmfels, Professor of Mathematics and Computer Science at Berkeley, and Josephine Yu classified six-point metrics using T-theory.

References

* cite journal
author= Hans-Jurgen Bandelt and Andreas Dress
title= A canonical decomposition theory for metrics on a finite set
journal= Advances in Mathematics
year= 1992 | volume= 92 | pages= 47–105
doi= 10.1016/0001-8708(92)90061-O
* cite journal
author=A. Dress, V. Moulton and W. Terhalle
title=T-theory: An Overview
journal=European Journal of Combinatorics
year=1996
volume=17
issue=2–3
pages=161–175
doi=10.1006/eujc.1996.0015
* cite journal
author=John Isbell
title=Six theorems about metric spaces
journal=Comment. Math. Helv.
year=1964
volume=39
pages=65–74
doi=10.1007/BF02566944
* cite journal
author=Bernd Sturmfels and Josephine Yu
title=Classification of Six-Point Metrics
journal=The Electronic Journal of Combinatorics
year=2004
volume=11


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