Orthogonal Range Reporting and Rectangle Stabbing for Fat Rectangles

In this paper we study two geometric data structure problems in the special case when input objects or queries are fat rectangles. We show that in this case a significant improvement compared to the general case can be achieved. We describe data structures that answer two- and three-dimensional orthogonal range reporting queries in the case when the query range is a \emph{fat} rectangle. Our two-dimensional data structure uses $O(n)$ words and supports queries in $O(\log\log U +k)$ time, where $n$ is the number of points in the data structure, $U$ is the size of the universe and $k$ is the number of points in the query range. Our three-dimensional data structure needs $O(n\log^{\varepsilon}U)$ words of space and answers queries in $O(\log \log U + k)$ time. We also consider the rectangle stabbing problem on a set of three-dimensional fat rectangles. Our data structure uses $O(n)$ space and answers stabbing queries in $O(\log U\log\log U +k)$ time.Comment: extended version of a WADS'19 pape

Genetic determinants of daytime napping and effects on cardiometabolic health

This is the final version. Available from Nature Research via the DOI in this record. Summary GWAS statistics are publicly available at The Sleep Disorder Knowledge Portal webpage: http://sleepdisordergenetics.org/.Daytime napping is a common, heritable behavior, but its genetic basis and causal relationship with cardiometabolic health remain unclear. Here, we perform a genome-wide association study of self-reported daytime napping in the UK Biobank (n = 452,633) and identify 123 loci of which 61 replicate in the 23andMe research cohort (n = 541,333). Findings include missense variants in established drug targets for sleep disorders (HCRTR1, HCRTR2), genes with roles in arousal (TRPC6, PNOC), and genes suggesting an obesity-hypersomnolence pathway (PNOC, PATJ). Association signals are concordant with accelerometer-measured daytime inactivity duration and 33 loci colocalize with loci for other sleep phenotypes. Cluster analysis identifies three distinct clusters of nap-promoting mechanisms with heterogeneous associations with cardiometabolic outcomes. Mendelian randomization shows potential causal links between more frequent daytime napping and higher blood pressure and waist circumference.National Institute of HealthNational Institute of HealthNational Institute of HealthNational Institute of HealthNational Institute of HealthMGH Research Scholar Fund, Academy of FinlandMedical Research CouncilSpanish Government of Investigation, Development and InnovationSeneca FoundationNIDDKInstrumentarium Science FoundationYrjö Jahnsson Foundatio

The Parkinson’s Disease Mendelian Randomization Research Portal

Mendelian randomization is a method for exploring observational associations to find evidence of causality. To apply Mendelian randomization between risk factors/phenotypic traits (exposures) and PD in a large, unbiased manner, and to create a public resource for research. We observed evidence for causal associations between 12 exposures and risk of PD. Of these, nine were effects related to increasing adiposity and decreasing risk of PD. The remaining top three exposures that affected PD risk were tea drinking, time spent watching television, and forced vital capacity, but these may have been biased and were less convincing. Other exposures at nominal statistical significance included inverse effects of smoking and alcohol. We present a new platform which offers Mendelian randomization analyses for a total of 5,839 genome-wide association studies versus the largest PD genome-wide association studies available (https://pdgenetics.shinyapps.io/MRportal/). Alongside, we report further evidence to support a causal role for adiposity on lowering the risk of PD. © 2019 The Authors. Movement Disorders published by Wiley Periodicals, Inc. on behalf of International Parkinson and Movement Disorder Society.AJN reports grants from Parkinson’s UK, Barts Charity, Leonard Wolfson Experimental Neurology Centre, UCL Movement Disorders Centre and the Virginia Kieley Benefaction; honoraria or consultancy fees from Britannia, Global Kinetics Corporation, Profile Pharmaceuticals, Guide point, Biogen and Roche. KH and DAH are employees of 23andMe and hold stock or stock options in 23andMe. DAL reports grants from the Medical Research Council, numerous charitable funders,Medtronic and Roche. ZG-O reports consultancy fees from Inceptions Sciences,Idorsia, Denali, Lysosomal Therapeutics inc. HM reports reports consultancy from Biogen, UCB, Abbvie, Denali, Biohaven; lecture fees/honoraria from Biogen, UCB,C4X Discovery, GE-Healthcare, Welcome Trust, Movement Disorders Society; Research Grants from Parkinson’s UK, Cure Parkinson’s Trust, PSP Association, CBD Solutions, Drake Foundation, Medical Research Council. Dr Morris is a co-applicanton a patent application related to C9ORF72 (PCT/GB2012/052140)

Common Variant Burden Contributes to the Familial Aggregation of Migraine in 1,589 Families

© 2018 Elsevier Inc. Complex traits, including migraine, often aggregate in families, but the underlying genetic architecture behind this is not well understood. The aggregation could be explained by rare, penetrant variants that segregate according to Mendelian inheritance or by the sufficient polygenic accumulation of common variants, each with an individually small effect, or a combination of the two hypotheses. In 8,319 individuals across 1,589 migraine families, we calculated migraine polygenic risk scores (PRS) and found a significantly higher common variant burden in familial cases (n = 5,317, OR = 1.76, 95% CI = 1.71–1.81, p = 1.7 × 10−109) compared to population cases from the FINRISK cohort (n = 1,101, OR = 1.32, 95% CI = 1.25–1.38, p = 7.2 × 10−17). The PRS explained 1.6% of the phenotypic variance in the population cases and 3.5% in the familial cases (including 2.9% for migraine without aura, 5.5% for migraine with typical aura, and 8.2% for hemiplegic migraine). The results demonstrate a significant contribution of common polygenic variation to the familial aggregation of migraine. Gormley et al. use polygenic risk scores to show that common variation, captured by genome-wide association studies, in combination contributes to the aggregation of migraine in families. The results may have similar implications for other complex traits in general

Orthogonal range reporting and rectangle stabbing for fat rectangles

In this paper we study two geometric data structure problems in the special case when input objects or queries are fat rectangles. We show that in this case a significant improvement compared to the general case can be achieved. We describe data structures that answer two- and three-dimensional orthogonal range reporting queries in the case when the query range is a fat rectangle. Our two-dimensional data structure uses O(n) words and supports queries in O(log log U+ k) time, where n is the number of points in the data structure, U is the size of the universe and k is the number of points in the query range. Our three-dimensional data structure needs O(nlog εU) words of space and answers queries in O(log log U+ k) time. We also consider the rectangle stabbing problem on a set of three-dimensional fat rectangles. Our data structure uses O(n) space and answers stabbing queries in O(log Ulog log U+ k) time

Computational geometry and its Application to Computer Graphics

This paper gives a basic introduction into some of the techniques and data structures developed in computational geometry with emphasis on their use in computer graphics applications. Due to the limited space only global ideas are outlined and no details are presented. References are added, in particular in a subsection "Further Reading" at the end of each section, for those that are interested in learning more about the topics treate