211 research outputs found
Polyhedral Covers of Tree Space
The phylogenetic tree space, introduced by Billera, Holmes, and Vogtmann, is
a cone over a simplicial complex. In this short article, we construct this
complex from local gluings of classical polytopes, the associahedron and the
permutohedron. Its homotopy is also reinterpreted and calculated based on
polytope data.Comment: 8 pages, 9 figure
Diagonalizing the genome II: toward possible applications
In a previous paper, we showed that the orientable cover of the moduli space
of real genus zero algebraic curves with marked points is a compact aspherical
manifold tiled by associahedra, which resolves the singularities of the space
of phylogenetic trees. In this draft of a sequel, we construct a related
(stacky) resolution of a space of real quadratic forms, and suggest, perhaps
without much justification, that systems of oscillators parametrized by such
objects may may provide useful models in genomics.Comment: 11 pages, 3 figure
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