Determining All Universal Tilers

A universal tiler is a convex polyhedron whose every cross-section tiles the plane. In this paper, we introduce a certain slight-rotating operation for cross-sections of pentahedra. Based on a selected initial cross-section and by applying the slight-rotating operation suitably, we prove that a convex polyhedron is a universal tiler if and only if it is a tetrahedron or a triangular prism.Comment: 18 pages, 12 figure

Chronic Kidney Disease and GWAS: “The Proper Study of Mankind Is Man”

Genome-wide association studies (GWAS) have been applied to complex diseases such as diabetes and hypertension, successfully uncovering strong gene associations of potential pathophysiologic significance. Recently, two studies (Köttgen et al., 2010; Chambers et al., 2010) have been applied to uncover genes relevant to the pathophysiology of chronic kidney disease (CKD)

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

Fast and accurate imputation of summary statistics enhances evidence of functional enrichment

Imputation using external reference panels is a widely used approach for increasing power in GWAS and meta-analysis. Existing HMM-based imputation approaches require individual-level genotypes. Here, we develop a new method for Gaussian imputation from summary association statistics, a type of data that is becoming widely available. In simulations using 1000 Genomes (1000G) data, this method recovers 84% (54%) of the effective sample size for common (>5%) and low-frequency (1-5%) variants (increasing to 87% (60%) when summary LD information is available from target samples) versus 89% (67%) for HMM-based imputation, which cannot be applied to summary statistics. Our approach accounts for the limited sample size of the reference panel, a crucial step to eliminate false-positive associations, and is computationally very fast. As an empirical demonstration, we apply our method to 7 case-control phenotypes from the WTCCC data and a study of height in the British 1958 birth cohort (1958BC). Gaussian imputation from summary statistics recovers 95% (105%) of the effective sample size (as quantified by the ratio of $\chi^2$ association statistics) compared to HMM-based imputation from individual-level genotypes at the 227 (176) published SNPs in the WTCCC (1958BC height) data. In addition, for publicly available summary statistics from large meta-analyses of 4 lipid traits, we publicly release imputed summary statistics at 1000G SNPs, which could not have been obtained using previously published methods, and demonstrate their accuracy by masking subsets of the data. We show that 1000G imputation using our approach increases the magnitude and statistical evidence of enrichment at genic vs. non-genic loci for these traits, as compared to an analysis without 1000G imputation. Thus, imputation of summary statistics will be a valuable tool in future functional enrichment analyses.Comment: 32 pages, 4 figure

Topological Hochschild homology of Thom spectra and the free loop space

We describe the topological Hochschild homology of ring spectra that arise as Thom spectra for loop maps f: X->BF, where BF denotes the classifying space for stable spherical fibrations. To do this, we consider symmetric monoidal models of the category of spaces over BF and corresponding strong symmetric monoidal Thom spectrum functors. Our main result identifies the topological Hochschild homology as the Thom spectrum of a certain stable bundle over the free loop space L(BX). This leads to explicit calculations of the topological Hochschild homology for a large class of ring spectra, including all of the classical cobordism spectra MO, MSO, MU, etc., and the Eilenberg-Mac Lane spectra HZ/p and HZ.Comment: 58 page

Excision for simplicial sheaves on the Stein site and Gromov's Oka principle

A complex manifold $X$ satisfies the Oka-Grauert property if the inclusion \Cal O(S,X) \hookrightarrow \Cal C(S,X) is a weak equivalence for every Stein manifold $S$, where the spaces of holomorphic and continuous maps from $S$ to $X$ are given the compact-open topology. Gromov's Oka principle states that if $X$ has a spray, then it has the Oka-Grauert property. The purpose of this paper is to investigate the Oka-Grauert property using homotopical algebra. We embed the category of complex manifolds into the model category of simplicial sheaves on the site of Stein manifolds. Our main result is that the Oka-Grauert property is equivalent to $X$ representing a finite homotopy sheaf on the Stein site. This expresses the Oka-Grauert property in purely holomorphic terms, without reference to continuous maps.Comment: Version 3 contains a few very minor improvement

From scaling up to sustainability in HIV: potential lessons for moving forward

Background: In 30 years of experience in responding to the HIV epidemic, critical decisions and program characteristics for successful scale-up have been studied. Now leaders face a new challenge: sustaining large-scale HIV prevention programs. Implementers, funders, and the communities served need to assess what strategies and practices of scaling up are also relevant for sustaining delivery at scale. Methods: We reviewed white and gray literature to identify domains central to scaling-up programs and reviewed HIV case studies to identify how these domains might relate to sustaining delivery at scale. Results: We found 10 domains identified as important for successfully scaling up programs that have potential relevance for sustaining delivery at scale: fiscal support; political support; community involvement, integration, buy-in, and depth; partnerships; balancing flexibility/adaptability and standardization; supportive policy, regulatory, and legal environment; building and sustaining strong organizational capacity; transferring ownership; decentralization; and ongoing focus on sustainability. We identified one additional potential domain important for programs sustaining delivery at scale: emphasizing equity. Conclusions: Today, the public and private sector are examining their ability to generate value for populations. All stakeholders are aiming to stem the tide of the HIV epidemic. Implementers need a framework to guide the evolution of their strategies and management practices. Greater research is needed to refine the domains for policy and program implementers working to sustain HIV program delivery at scale

On Universal Tilers

A famous problem in discrete geometry is to find all monohedral plane tilers, which is still open to the best of our knowledge. This paper concerns with one of its variants that to determine all convex polyhedra whose every cross-section tiles the plane. We call such polyhedra universal tilers. We obtain that a convex polyhedron is a universal tiler only if it is a tetrahedron or a pentahedron.Comment: 10 pages, 2 figure

Clinical mentorship to improve pediatric quality of care at the health centers in rural Rwanda: a qualitative study of perceptions and acceptability of health care workers

Background: Despite evidence supporting Integrated Management of Childhood Illness (IMCI) as a strategy to improve pediatric care in countries with high child mortality, its implementation faces challenges related to lack of or poor post-didactic training supervision and gaps in necessary supporting systems. These constraints lead to health care workers’ inability to consistently translate IMCI knowledge and skills into practice. A program providing mentoring and enhanced supervision at health centers (MESH), focusing on clinical and systems improvement was implemented in rural Rwanda as a strategy to address these issues, with the ultimate goal of improving the quality of pediatric care at rural health centers. We explored perceptions of MESH from the perspective of IMCI clinical mentors, mentees, and district clinical leadership. Methods: We conducted focus group discussions with 40 health care workers from 21 MESH-supported health centers. Two FGDs in each district were carried out, including one for nurses and one for director of health centers. District medical directors and clinical mentors had individual in-depth interviews. We performed a hermeneutic analysis using Atlas.ti v5.2. Results: Study participants highlighted program components in five key areas that contributed to acceptability and impact, including: 1) Interactive, collaborative capacity-building, 2) active listening and relationships, 3) supporting not policing, 4) systems improvement, and 5) real-time feedback. Staff turn-over, stock-outs, and other facility/systems gaps were identified as barriers to MESH and IMCI implementation. Conclusion: Health care workers reported high acceptance and positive perceptions of the MESH model as an effective strategy to build their capacity, bridge the gap between knowledge and practice in pediatric care, and address facility and systems issues. This approach also improved relationships between the district supervisory team and health center-based care providers. Despite some challenges, many perceived a strong benefit on clinical performance and outcomes. This study can inform program implementers and policy makers of key components needed for developing similar health facility-based mentorship interventions and potential barriers and resistance which can be proactively addressed to ensure success