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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:A Lie algebraic classification of continuous-time
Markov models - Sumner\, J (Tasmania)
DTSTART;TZID=Europe/London:20110623T113000
DTEND;TZID=Europe/London:20110623T115000
UID:TALK31846AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/31846
DESCRIPTION:In recent work we have discussed the importance of
multiplicative closure for the Markov models used
in phylogenetics. For continuous-time Markov chai
ns\, a sufficient condition for multiplicative clo
sure of a model class is ensured by demanding that
the set of rate matrices belonging to the model c
lass form a Lie algebra. It is the case that some
Markov models do form Lie algebras (eg. JC\, F81\,
K3ST and GMM)\, and we refer to these models as `
`Lie Markov models''. Importantly\, other Markov m
odels unequivocally do not form Lie algebras (the
most conspicuous example being GTR). \nThe questio
n then naturally arises: How do we generate a full
list of Lie Markov models? To answer this questio
n in full generality seems quite difficult as the
interaction between the operations of a Lie algebr
a and the stochastic requirements of rate matrices
are somewhat at odds\, and it seems that this que
stion has not been addressed in the algebraic or s
tochastic mathematics literature. \nIn this talk\,
we will discuss how we have made signficant progr
ess in generating Lie Markov models by demanding t
hat the models have certain symmetrics under nucle
otide permutations. >From a theoretical perspectiv
e\, we show that the Lie Markov models include\, a
nd hence provide a unifying concept for\, ``group-
based'' and "equivariant" models\, whilst also gen
erating many other interesting examples. We also a
rgue that our scheme is very pleasing in the conte
xt of applied phylogenetics\, as\, for a given sym
metry of nucelotide substitution\, it provides a n
atural hierarchy of models with increasing number
of parameters. \n\nThis is joint work with Jess Fe
rnndez-Snchez and Peter Jarvis.\n\n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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