Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lie Markov Models   Recent work has discussed the importance of multiplicative closure for the
Markov models used in phylogenetics. For continuous-time Markov chains, a
sufficient condition for multiplicative closure of a model class is ensured by
demanding that the set of rate-matrices belonging to the model class form a Lie
algebra. It is the case that some well-known Markov models do form Lie algebras
and we refer to such models as "Lie Markov models". However it is also the case
that some other well-known Markov models unequivocally do not form Lie
algebras. In this paper, we will discuss how to generate Lie Markov models by
demanding that the models have certain symmetries under nucleotide
permutations. We show that the Lie Markov models include, and hence provide a
unifying concept for, "group-based" and "equivariant" models. For each of two,
three and four character states, the full list of Lie Markov models with
maximal symmetry is presented and shown to include interesting examples that
are neither group-based nor equivariant. We also argue that our scheme is
pleasing in the context of applied phylogenetics, as, for a given symmetry of
nucleotide substitution, it provides a natural hierarchy of models with
increasing number of parameters.

15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org