19,858 research outputs found
Algebraic Unimodular Counting
We study algebraic algorithms for expressing the number of non-negative
integer solutions to a unimodular system of linear equations as a function of
the right hand side. Our methods include Todd classes of toric varieties via
Gr\"obner bases, and rational generating functions as in Barvinok's algorithm.
We report polyhedral and computational results for two special cases: counting
contingency tables and Kostant's partition function.Comment: 21 page
Not all simplicial polytopes are weakly vertex-decomposable
In 1980 Provan and Billera defined the notion of weak -decomposability for
pure simplicial complexes. They showed the diameter of a weakly
-decomposable simplicial complex is bounded above by a polynomial
function of the number of -faces in and its dimension. For weakly
0-decomposable complexes, this bound is linear in the number of vertices and
the dimension. In this paper we exhibit the first examples of non-weakly
0-decomposable simplicial polytopes
Stellar Populations in Spiral Galaxies
We report preliminary results of the characterization of bulge and inner disk
stellar populations for 8 nearby spiral galaxies using Gemini/GMOS. The
long-slit spectra extend out to 1-2 disk scale lengths with S/N/Ang > 50. Two
different model fitting techniques, absorption-line indices and full spectral
synthesis, are found to weigh age, metallicity, and abundance ratios
differently, but with careful attention to the data/model matching (resolution
and flux calibration), we are able constrain real signatures of age and
metallicity gradients in star-forming galaxies.Comment: 4 pages, 3 figures. To appear in the proceedings for IAUS 241
"Stellar Populations as Building Blocks of Galaxies", Eds. R.F. Peletier and
A. Vazdeki
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