A double bounded key identity for Goellnitz's (big) partition theorem

Given integers i,j,k,L,M, we establish a new double bounded q-series identity from which the three parameter (i,j,k) key identity of Alladi-Andrews-Gordon for Goellnitz's (big) theorem follows if L, M tend to infinity. When L = M, the identity yields a strong refinement of Goellnitz's theorem with a bound on the parts given by L. This is the first time a bounded version of Goellnitz's (big) theorem has been proved. This leads to new bounded versions of Jacobi's triple product identity for theta functions and other fundamental identities.Comment: 17 pages, to appear in Proceedings of Gainesville 1999 Conference on Symbolic Computation

Evidence of Widespread Selection on Standing Variation in Europe at Height-Associated SNPs

Strong signatures of positive selection at newly arising genetic variants are well-documented in humans, but this form of selection may not be widespread in recent human evolution. Because many human traits are highly polygenic and partly determined by common, ancient genetic variation, an alternative model for rapid genetic adaptation has been proposed: weak selection acting on many pre-existing (standing) genetic variants, or polygenic adaptation. By studying height, a classic polygenic trait, we demonstrate the first human signature of widespread selection on standing variation. We show that frequencies of alleles associated with increased height, both at known loci and genome-wide, are systematically elevated in Northern Europeans compared with Southern Europeans $(p<4.3×10^{−4})$. This pattern mirrors intra-European height differences and is not confounded by ancestry or other ascertainment biases. The systematic frequency differences are consistent with the presence of widespread weak selection (selection coefficients $~10^{−3}–10^{−5}$ per allele) rather than genetic drift alone $(p<10^{−15})$

Brown representability for space-valued functors

In this paper we prove two theorems which resemble the classical cohomological and homological Brown representability theorems. The main difference is that our results classify small contravariant functors from spaces to spaces up to weak equivalence of functors. In more detail, we show that every small contravariant functor from spaces to spaces which takes coproducts to products up to homotopy and takes homotopy pushouts to homotopy pullbacks is naturally weekly equivalent to a representable functor. The second representability theorem states: every contravariant continuous functor from the category of finite simplicial sets to simplicial sets taking homotopy pushouts to homotopy pullbacks is equivalent to the restriction of a representable functor. This theorem may be considered as a contravariant analog of Goodwillie's classification of linear functors.Comment: 19 pages, final version, accepted by the Israel Journal of Mathematic

q-Newton binomial: from Euler to Gauss

A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter

Genetic, environmental and stochastic factors in monozygotic twin discordance with a focus on epigenetic differences

PMCID: PMC3566971This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

DG-algebras and derived A-infinity algebras

A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and show that any dga A over an arbitrary commutative ground ring k is equivalent to a minimal derived A-infinity algebra. Such a minimal derived A-infinity algebra model for A is a k-projective resolution of the homology algebra of A together with a family of maps satisfying appropriate relations. As in the case of A-infinity algebras, it is possible to recover the dga up to quasi-isomorphism from a minimal derived A-infinity algebra model. Hence the structure we are describing provides a complete description of the quasi-isomorphism type of the dga.Comment: v3: 27 pages. Minor corrections, to appear in Crelle's Journa

Outcome Assessment of a Dedicated HIV Positive Health Care Worker Clinic at a Central Hospital in Malawi: A Retrospective Observational Study

BACKGROUND: Malawi has one of the world's lowest densities of Health Care Workers (HCW) per capita. This study evaluates outcomes of a dedicated HCW HIV clinic in Malawi, created at Zomba Central Hospital in January 2007. METHODS AND FINDINGS: Retrospective cohort data was analyzed comparing HCW clinic patient baseline characteristics and treatment outcomes at 18 months after inception, against those attending the general HIV clinic. In-depth interviews and focus group discussions were conducted to explore perceptions of patients and caregivers regarding program value, level of awareness and barriers for uptake amongst HCW. 306 patients were enrolled on antiretroviral therapy (ART) in the HCW HIV clinic, 6784 in the general clinic. Significantly (p<0.01) more HCW clients were initiated on ART on the basis of CD4 as opposed to WHO Stage 3/4 (36% vs.23%). Significantly fewer HCW clients defaulted (6% vs.17%), and died (4% vs.12%). The dedicated HCW HIV clinic was perceived as important and convenient in terms of reduced waiting times, and prompt and high quality care. Improved confidentiality was an appreciated quality of the HCW clinic however barriers included fear of being recognized. CONCLUSIONS/SIGNIFICANCE: Outcomes at the HCW clinic appear better compared to the general HIV clinic. The strategy of dedicated clinics to care for health providers is a means of HIV impact mitigation within human resource constrained health systems in high prevalence settings

ParaHaplo 2.0: a program package for haplotype-estimation and haplotype-based whole-genome association study using parallel computing

<p>Abstract</p> <p>Background</p> <p>The use of haplotype-based association tests can improve the power of genome-wide association studies. Since the observed genotypes are unordered pairs of alleles, haplotype phase must be inferred. However, estimating haplotype phase is time consuming. When millions of single-nucleotide polymorphisms (SNPs) are analyzed in genome-wide association study, faster methods for haplotype estimation are required.</p> <p>Methods</p> <p>We developed a program package for parallel computation of haplotype estimation. Our program package, ParaHaplo 2.0, is intended for use in workstation clusters using the Intel Message Passing Interface (MPI). We compared the performance of our algorithm to that of the regular permutation test on both Japanese in Tokyo, Japan and Han Chinese in Beijing, China of the HapMap dataset.</p> <p>Results</p> <p>Parallel version of ParaHaplo 2.0 can estimate haplotypes 100 times faster than a non-parallel version of the ParaHaplo.</p> <p>Conclusion</p> <p>ParaHaplo 2.0 is an invaluable tool for conducting haplotype-based genome-wide association studies (GWAS). The need for fast haplotype estimation using parallel computing will become increasingly important as the data sizes of such projects continue to increase. The executable binaries and program sources of ParaHaplo are available at the following address: <url>http://en.sourceforge.jp/projects/parallelgwas/releases/</url></p