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