41,247 research outputs found
Langlands duality for finite-dimensional representations of quantum affine algebras
We describe a correspondence (or duality) between the q-characters of
finite-dimensional representations of a quantum affine algebra and its
Langlands dual in the spirit of q-alg/9708006 and 0809.4453. We prove this
duality for the Kirillov-Reshetikhin modules and their irreducible tensor
products. In the course of the proof we introduce and construct "interpolating
(q,t)-characters" depending on two parameters which interpolate between the
q-characters of a quantum affine algebra and its Langlands dual.Comment: 40 pages; several results and comments added. Accepted for
publication in Letters in Mathematical Physic
A MOSAIC of methods: Improving ortholog detection through integration of algorithmic diversity
Ortholog detection (OD) is a critical step for comparative genomic analysis
of protein-coding sequences. In this paper, we begin with a comprehensive
comparison of four popular, methodologically diverse OD methods: MultiParanoid,
Blat, Multiz, and OMA. In head-to-head comparisons, these methods are shown to
significantly outperform one another 12-30% of the time. This high
complementarity motivates the presentation of the first tool for integrating
methodologically diverse OD methods. We term this program MOSAIC, or Multiple
Orthologous Sequence Analysis and Integration by Cluster optimization. Relative
to component and competing methods, we demonstrate that MOSAIC more than
quintuples the number of alignments for which all species are present, while
simultaneously maintaining or improving functional-, phylogenetic-, and
sequence identity-based measures of ortholog quality. Further, we demonstrate
that this improvement in alignment quality yields 40-280% more confidently
aligned sites. Combined, these factors translate to higher estimated levels of
overall conservation, while at the same time allowing for the detection of up
to 180% more positively selected sites. MOSAIC is available as python package.
MOSAIC alignments, source code, and full documentation are available at
http://pythonhosted.org/bio-MOSAIC
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