Ruijsenaars' hypergeometric function and the modular double of U_q(sl(2,C))

Simultaneous eigenfunctions of two Askey-Wilson second order difference operators are constructed as formal matrix coefficients of the principal series representation of the modular double of the quantized universal enveloping algebra U_q(sl(2,C)). These eigenfunctions are shown to be equal to Ruijsenaars' hypergeometric function under a proper parameter correspondence.Comment: Replaced to synchronize formula numbers with the published version. 25 page

Fourier spectra from exoplanets with polar caps and ocean glint

The weak orbital-phase dependent reflection signal of an exoplanet contains information on the planet surface, such as the distribution of continents and oceans on terrestrial planets. This light curve is usually studied in the time domain, but because the signal from a stationary surface is (quasi)periodic, analysis of the Fourier series may provide an alternative, complementary approach. We study Fourier spectra from reflected light curves for geometrically simple configurations. Depending on its atmospheric properties, a rotating planet in the habitable zone could have circular polar ice caps. Tidally locked planets, on the other hand, may have symmetric circular oceans facing the star. These cases are interesting because the high-albedo contrast at the sharp edges of the ice-sheets and the glint from the host star in the ocean may produce recognizable light curves with orbital periodicity, which could also be interpreted in the Fourier domain. We derive a simple general expression for the Fourier coefficients of a quasiperiodic light curve in terms of the albedo map of a Lambertian planet surface. Analytic expressions for light curves and their spectra are calculated for idealized situations, and dependence of spectral peaks on the key parameters inclination, obliquity, and cap size is studied.Comment: 15 pages, 2 tables, 13 figure

Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions

We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometrical properties of this polytope. The most general functions we describe in this way are sums of two very-well-poised _10φ_9's and their Nassrallah-Rahman type integral representation

Mice and more

A report on the Mouse Initiatives V meeting 'Genomics of Complex Systems in Biomedical Research', The Jackson Laboratory, Bar Harbor, USA, 30 July-2 August 2003

Limits of elliptic hypergeometric biorthogonal functions

The purpose of this article is to bring structure to (basic) hypergeometric biorthogonal systems, in particular to the q-Askey scheme of basic hypergeometric orthogonal polynomials. We aim to achieve this by looking at the limits as p->0 of the elliptic hypergeometric biorthogonal functions from Spiridonov, with parameters which depend in varying ways on p. As a result we get 38 systems of biorthogonal functions with for each system at least one explicit measure for the bilinear form. Amongst these we indeed recover the q-Askey scheme. Each system consists of (basic hypergeometric) rational functions or polynomials.Comment: 27 pages. This is a self-contained article which can also be seen as part 1 of a 3 part series on limits of (multivariate) elliptic hypergeometric biorthogonal functions and their measure

The alliance of genome resources: transforming comparative genomics.

Comparing genomic and biological characteristics across multiple species is essential to using model systems to investigate the molecular and cellular mechanisms underlying human biology and disease and to translate mechanistic insights from studies in model organisms for clinical applications. Building a scalable knowledge commons platform that supports cross-species comparison of rich, expertly curated knowledge regarding gene function, phenotype, and disease associations available for model organisms and humans is the primary mission of the Alliance of Genome Resources (the Alliance). The Alliance is a consortium of seven model organism knowledgebases (mouse, rat, yeast, nematode, zebrafish, frog, fruit fly) and the Gene Ontology resource. The Alliance uses a common set of gene ortholog assertions as the basis for comparing biological annotations across the organisms represented in the Alliance. The major types of knowledge associated with genes that are represented in the Alliance database currently include gene function, phenotypic alleles and variants, human disease associations, pathways, gene expression, and both protein-protein and genetic interactions. The Alliance has enhanced the ability of researchers to easily compare biological annotations for common data types across model organisms and human through the implementation of shared programmatic access mechanisms, data-specific web pages with a unified look and feel , and interactive user interfaces specifically designed to support comparative biology. The modular infrastructure developed by the Alliance allows the resource to serve as an extensible knowledge commons capable of expanding to accommodate additional model organisms

Limits of multivariate elliptic beta integrals and related bilinear forms

In this article we consider the elliptic Selberg integral, which is a BC_n symmetric multivariate extension of the elliptic beta integral. We categorize the limits that are obtained as p → 0, for given behavior of the parameters as p → 0. This article is therefore the multivariate version of our earlier paper "Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions". The integrand of the elliptic Selberg integral is the measure for the BC_n symmetric biorthogonal functions introduced by the second author, so we also consider the limits of the associated bilinear form. We also provide the limits for the discrete version of this bilinear form, which is related to a multivariate extension of the Frenkel-Turaev summation