ESOLID—a system for exact boundary evaluation

We present a system, ESOLID, that performs exact boundary evaluation of low-degree curved solids in reasonable amounts of time. ESOLID performs accurate Boolean operations using exact representations and exact computations throughout. The demands of exact computation require a different set of algorithms and efficiency improvements than those found in a traditional inexact floating point based modeler. We describe the system architecture, representations, and issues in implementing the algorithms. We also describe a number of techniques that increase the efficiency of the system based on lazy evaluation, use of floating point filters, arbitrary floating point arithmetic with error bounds, and lower dimensional formulation of subproblems. ESOLID has been used for boundary evaluation of many complex solids. These include both synthetic datasets and parts of a Bradley Fighting Vehicle designed using the BRL-CAD solid modeling system. It is shown that ESOLID can correctly evaluate the boundary of solids that are very hard to compute using a fixed-precision floating point modeler. In terms of performance, it is about an order of magnitude slower as compared to a floating point boundary evaluation system on most cases

A HYBRID APPROACH FOR DETERMINANT SIGNS OF MODERATE-SIZED MATRICES

Many geometric computations have at their core the evaluation of the sign of the determinant of a matrix. A fast, failsafe determinant sign operation is often a key part of a robust implementation. While linear problems from 3D computational geometry usually require determinants no larger than six, non-linear problems involving algebraic curves and surfaces produce larger matrices. Furthermore, the matrix entries often exceed machine precision, while existing approaches focus on machine-precision matrices. In this paper, we describe a practical hybrid method for computing the sign of the determinant of matrices of order up to 60. The stages include a floating-point filter based on the singular value decomposition of a matrix, an adaptive-precision implementation of Gaussian elimination, and a standard modular arithmetic determinant algorithm. We demonstrate our method on a number of examples encountered while solving polynomial systems

Aquilegia, Vol. 37 No. 3, Summer 2013, Newsletter of the Colorado Native Plant Society

https://epublications.regis.edu/aquilegia/1143/thumbnail.jp

Parent-of-origin-specific allelic associations among 106 genomic loci for age at menarche.

Age at menarche is a marker of timing of puberty in females. It varies widely between individuals, is a heritable trait and is associated with risks for obesity, type 2 diabetes, cardiovascular disease, breast cancer and all-cause mortality. Studies of rare human disorders of puberty and animal models point to a complex hypothalamic-pituitary-hormonal regulation, but the mechanisms that determine pubertal timing and underlie its links to disease risk remain unclear. Here, using genome-wide and custom-genotyping arrays in up to 182,416 women of European descent from 57 studies, we found robust evidence (P < 5 × 10(-8)) for 123 signals at 106 genomic loci associated with age at menarche. Many loci were associated with other pubertal traits in both sexes, and there was substantial overlap with genes implicated in body mass index and various diseases, including rare disorders of puberty. Menarche signals were enriched in imprinted regions, with three loci (DLK1-WDR25, MKRN3-MAGEL2 and KCNK9) demonstrating parent-of-origin-specific associations concordant with known parental expression patterns. Pathway analyses implicated nuclear hormone receptors, particularly retinoic acid and γ-aminobutyric acid-B2 receptor signalling, among novel mechanisms that regulate pubertal timing in humans. Our findings suggest a genetic architecture involving at least hundreds of common variants in the coordinated timing of the pubertal transition

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe

Genome-Wide Meta-Analyses of Breast, Ovarian, and Prostate Cancer Association Studies Identify Multiple New Susceptibility Loci Shared by at Least Two Cancer Types.

UNLABELLED: Breast, ovarian, and prostate cancers are hormone-related and may have a shared genetic basis, but this has not been investigated systematically by genome-wide association (GWA) studies. Meta-analyses combining the largest GWA meta-analysis data sets for these cancers totaling 112,349 cases and 116,421 controls of European ancestry, all together and in pairs, identified at P < 10(-8) seven new cross-cancer loci: three associated with susceptibility to all three cancers (rs17041869/2q13/BCL2L11; rs7937840/11q12/INCENP; rs1469713/19p13/GATAD2A), two breast and ovarian cancer risk loci (rs200182588/9q31/SMC2; rs8037137/15q26/RCCD1), and two breast and prostate cancer risk loci (rs5013329/1p34/NSUN4; rs9375701/6q23/L3MBTL3). Index variants in five additional regions previously associated with only one cancer also showed clear association with a second cancer type. Cell-type-specific expression quantitative trait locus and enhancer-gene interaction annotations suggested target genes with potential cross-cancer roles at the new loci. Pathway analysis revealed significant enrichment of death receptor signaling genes near loci with P < 10(-5) in the three-cancer meta-analysis. SIGNIFICANCE: We demonstrate that combining large-scale GWA meta-analysis findings across cancer types can identify completely new risk loci common to breast, ovarian, and prostate cancers. We show that the identification of such cross-cancer risk loci has the potential to shed new light on the shared biology underlying these hormone-related cancers. Cancer Discov; 6(9); 1052-67. ©2016 AACR.This article is highlighted in the In This Issue feature, p. 932.The Breast Cancer Association Consortium (BCAC), the Prostate Cancer Association Group to Investigate Cancer Associated Alterations in the Genome (PRACTICAL), and the Ovarian Cancer Association Consortium (OCAC) that contributed breast, prostate, and ovarian cancer data analyzed in this study were in part funded by Cancer Research UK [C1287/A10118 and C1287/A12014 for BCAC; C5047/A7357, C1287/A10118, C5047/A3354, C5047/A10692, and C16913/A6135 for PRACTICAL; and C490/A6187, C490/A10119, C490/A10124, C536/A13086, and C536/A6689 for OCAC]. Funding for the Collaborative Oncological Gene-environment Study (COGS) infrastructure came from: the European Community's Seventh Framework Programme under grant agreement number 223175 (HEALTH-F2-2009-223175), Cancer Research UK (C1287/A10118, C1287/A 10710, C12292/A11174, C1281/A12014, C5047/A8384, C5047/A15007, C5047/A10692, and C8197/A16565), the US National Institutes of Health (CA128978) and the Post-Cancer GWAS Genetic Associations and Mechanisms in Oncology (GAME-ON) initiative (1U19 CA148537, 1U19 CA148065, and 1U19 CA148112), the US Department of Defence (W81XWH-10-1-0341), the Canadian Institutes of Health Research (CIHR) for the CIHR Team in Familial Risks of Breast Cancer, Komen Foundation for the Cure, the Breast Cancer Research Foundation, and the Ovarian Cancer Research Fund [with donations by the family and friends of Kathryn Sladek Smith (PPD/RPCI.07)]. Additional financial support for contributing studies is documented under Supplementary Financial Support.This is the author accepted manuscript. The final version is available from the American Association for Cancer Research via http://dx.doi.org/10.1158/2159-8290.CD-15-122

Relationships between motivational, demographic, and academic variables and course grade in developmental mathematics among students at North Central State College

2014 Summer.To assist North Central State College with the identification of students who are not likely to receive a grade of A, B, or C in their Pre-Algebra course, a regression equation was developed. The variables used in the analysis were representative of previous academic performance, depth and breadth of developmental education needs, recency of math education, motivational scores from the College Student Inventory Form B™ (CSI-B), and self-reported demographic data such as the number of hours planned to work. The overall accuracy of the success prediction, both yes and no, would have been 62% had the model been used with the students in the historical sample. This was supported by a logistic regression model which produced similar results. The development of student success plans based upon the model at the individual and section levels, implementation of other assessments to learn more about the relationships between self-efficacy, resilience and grit, and a review of the Mathway for each major provided the College with implications for advising and student success practices. Implications for future research included the addition of other variables, further study of males to determine variables that matter most to their success prediction, and determination of the value of other motivational assessments like Grit Scales and their associations to course grade

Accurate Computation of the Medial Axis of a Polyhedron

: We present an accurate and efficient algorithm to compute the internal Voronoi region and medial axis of a 3-D polyhedron. It uses exact arithmetic and representations for accurate computation of the medial axis. The sheets, seams, and junctions of the medial axis are represented as trimmed quadric surfaces, algebraic space curves, and algebraic numbers, respectively. The algorithm works by recursively finding neighboring junctions along the axis. It utilizes discretization of space and linear programming to speed up the search step. We also present a new algorithm for analysis of the topology of an algebraic plane curve, which is the core of our medial axis algorithm. To speed up the computation, wehave designed specialized algorithms for fast computation on implicit geometric structures. These include lazy evaluation based on multivariate Sturm sequences, fast resultant computation, curve topology analysis, and floating-point filters. The algorithm has been implemented and we highl..