- T-theory
T-theory is a branch of
discrete mathematics dealing with analysis of trees and discretemetric spaces .General history
As per
Andreas Dress , T-theory originated from a question raised byManfred Eigen , a recipient of theNobel 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 minimalinjective 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 tree s.
*Online algorithm s - "k"-server problemRecent 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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