Lines Missing Every Random Point

We prove that there is, in every direction in Euclidean space, a line that misses every computably random point. We also prove that there exist, in every direction in Euclidean space, arbitrarily long line segments missing every double exponential time random point.Comment: Added a section: "Betting in Doubly Exponential Time.

A re-examination of the life and work of A.F.G. Kerr and of his colleagues and friends

Arthur Francis George Kerr’s life is reviewed and related to a previously published account. Kerr’s collecting activity is analysed using an expanded version of the Thai Biogeography Group’s database of collections. 8,666 of the total 48,970 collections are Kerr’s and 3,178 are those of his colleagues and friends. Therefore, the total number of collections made by Kerr and his acquaintances is likely to be larger and more diverse than previously believed. Mapping of these data using GIS show that Kerr’s collecting activities focussed on particular regions of Thailand at particular times. Also large areas of the country remained unexplored by Kerr and his acquaintances: a pattern that, to some extent, persists to this day. The large, but dispersed, archive of Kerr’s photographs, maps, living collections and correspondence indicate that he was a skilled photographer (taking at least 3,000 images), cartographer (producing many hand-drawn maps) and exceptionally acute, accurate and detailed observer (filling numerous notebooks and leaving other records). It is clear that digitising these collections to form an on-line dedicated website is highly desirable to further progress on the flora of Thailand and surrounding countries and would form an unique record of the social history of early 20thC Thailand

Hormone Therapy and the Risk of Breast Cancer in BRCA1 Mutation Carriers

Background: Hormone therapy (HT) is commonly given to women to alleviate the climacteric symptoms associated with menopause. There is concern that this treatment may increase the risk of breast cancer. The potential association of HT and breast cancer risk is of particular interest to women who carry a mutation in BRCA1 because they face a high lifetime risk of breast cancer and because many of these women take HT after undergoing prophylactic surgical oophorectomy at a young age. Methods: We conducted a matched case-control study of 472 postmenopausal women with a BRCA1 mutation to examine whether or not the use of HT is associated with subsequent risk of breast cancer. Breast cancer case patients and control subjects were matched with respect to age, age at menopause, and type of menopause (surgical or natural). Odds ratios (ORs) and 95% confidence intervals (CIs) were estimated with conditional logistic regression. Statistical tests were two-sided. Results: In this group of BRCA1 mutation carriers, the adjusted OR for breast cancer associated with ever use of HT compared with never use was 0.58 (95% CI = 0.35 to 0.96; P =. 03). In analyses by type of HT, an inverse association with breast cancer risk was observed with use of estrogen only (OR = 0.51, 95% CI = 0.27 to 0.98; P =. 04); the association with use of estrogen plus progesterone was not statistically significant (OR = 0.66, 95% CI = 0.34 to 1.27; P =. 21). Conclusion: Among postmenopausal women with a BRCA1 mutation, HT use was not associated with increased risk of breast cancer; indeed, in this population, it was associated with a decreased risk

Mendelian randomisation study of height and body mass index as modifiers of ovarian cancer risk in 22,588 BRCA1 and BRCA2 mutation carriers

Item does not contain fulltextBACKGROUND: Height and body mass index (BMI) are associated with higher ovarian cancer risk in the general population, but whether such associations exist among BRCA1/2 mutation carriers is unknown. METHODS: We applied a Mendelian randomisation approach to examine height/BMI with ovarian cancer risk using the Consortium of Investigators for the Modifiers of BRCA1/2 (CIMBA) data set, comprising 14,676 BRCA1 and 7912 BRCA2 mutation carriers, with 2923 ovarian cancer cases. We created a height genetic score (height-GS) using 586 height-associated variants and a BMI genetic score (BMI-GS) using 93 BMI-associated variants. Associations were assessed using weighted Cox models. RESULTS: Observed height was not associated with ovarian cancer risk (hazard ratio [HR]: 1.07 per 10-cm increase in height, 95% confidence interval [CI]: 0.94-1.23). Height-GS showed similar results (HR = 1.02, 95% CI: 0.85-1.23). Higher BMI was significantly associated with increased risk in premenopausal women with HR = 1.25 (95% CI: 1.06-1.48) and HR = 1.59 (95% CI: 1.08-2.33) per 5-kg/m(2) increase in observed and genetically determined BMI, respectively. No association was found for postmenopausal women. Interaction between menopausal status and BMI was significant (Pinteraction < 0.05). CONCLUSION: Our observation of a positive association between BMI and ovarian cancer risk in premenopausal BRCA1/2 mutation carriers is consistent with findings in the general population

Inheritance of deleterious mutations at both BRCA1 and BRCA2 in an international sample of 32,295 women

Background: Most BRCA1 or BRCA2 mutation carriers have inherited a single (heterozygous) mutation. Transheterozygotes (TH) who have inherited deleterious mutations in both BRCA1 and BRCA2 are rare, and the consequences of transheterozygosity are poorly understood. Methods: From 32,295 female BRCA1/2 mutation carriers, we identified 93 TH (0.3 %). "Cases" were defined as TH, and "controls" were single mutations at BRCA1 (SH1) or BRCA2 (SH2). Matched SH1 "controls" carried a BRCA1 mutation found in the TH "case". Matched SH2 "controls" carried a BRCA2 mutation found in the TH "case". After matching the TH carriers with SH1 or SH2, 91 TH were matched to 9316 SH1, and 89 TH were matched to 3370 SH2. Results: The majority of TH (45.2 %) involved the three common Jewish mutations. TH were more likely than SH1 and SH2 women to have been ever diagnosed with breast cancer (BC; p = 0.002). TH were more likely to be diagnosed with ovarian cancer (OC) than SH2 (p = 0.017), but not SH1. Age at BC diagnosis was the same in TH vs. SH1 (p = 0.231), but was on average 4.5 years younger in TH than in SH2 (p < 0.001). BC in TH was more likely to be estrogen receptor (ER) positive (p = 0.010) or progesterone receptor (PR) positive (p = 0.013) than in SH1, but less likely to be ER positive (p < 0.001) or PR positive (p = 0.012) than SH2. Among 15 tumors from TH patients, there was no clear pattern of loss of heterozygosity (LOH) for BRCA1 or BRCA2 in either BC or OC. Conclusions: Our observations suggest that clinical TH phenotypes resemble SH1. However, TH breast tumor marker characteristics are phenotypically intermediate to SH1 and SH2

Cosmology with clusters of galaxies

In this Chapter I review the role that galaxy clusters play as tools to constrain cosmological parameters. I will concentrate mostly on the application of the mass function of galaxy clusters, while other methods, such as that based on the baryon fraction, are covered by other Chapters of the book. Since most of the cosmological applications of galaxy clusters rely on precise measurements of their masses, a substantial part of my Lectures concentrates on the different methods that have been applied so far to weight galaxy clusters. I provide in Section 2 a short introduction to the basics of cosmic structure formation. In Section 3 I describe the Press--Schechter (PS) formalism to derive the cosmological mass function, then discussing extensions of the PS approach and the most recent calibrations from N--body simulations. In Section 4 I review the methods to build samples of galaxy clusters at different wavelengths. Section 5 is devoted to the discussion of different methods to derive cluster masses. In Section 6 I describe the cosmological constraints, which have been obtained so far by tracing the cluster mass function with a variety of methods. Finally, I describe in Section 7 the future perspectives for cosmology with galaxy clusters and the challenges for clusters to keep playing an important role in the era of precision cosmology.Comment: 49 pages, 19 figures, Lectures for 2005 Guillermo Haro Summer School on Clusters, to appear in "Lecture notes in Physics" (Springer

Associations of common breast cancer susceptibility alleles with risk of breast cancer subtypes in BRCA1 and BRCA2 mutation carriers

Introduction: More than 70 common alleles are known to be involved in breast cancer (BC) susceptibility, and several exhibit significant heterogeneity in their associations with different BC subtypes. Although there are differences in the association patterns between BRCA1 and BRCA2 mutation carriers and the general population for several loci, no study has comprehensively evaluated the associations of all known BC susceptibility alleles with risk of BC subtypes in BRCA1 and BRCA2 carriers. Methods: We used data from 15,252 BRCA1 and 8,211 BRCA2 carriers to analyze the associations between approximately 200,000 genetic variants on the iCOGS array and risk of BC subtypes defined by estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER2) and triple-negative- (TN) status; morphologic subtypes; histological grade; and nodal involvement. Results: The estimated BC hazard ratios (HRs) for the 74 known BC alleles in BRCA1 carriers exhibited moderate correlations with the corresponding odds ratios from the general population. However, their associations with ER-positive BC in BRCA1 carriers were more consistent with the ER-positive as

Identification of independent association signals and putative functional variants for breast cancer risk through fine-scale mapping of the 12p11 locus.

BACKGROUND: Multiple recent genome-wide association studies (GWAS) have identified a single nucleotide polymorphism (SNP), rs10771399, at 12p11 that is associated with breast cancer risk. METHOD: We performed a fine-scale mapping study of a 700 kb region including 441 genotyped and more than 1300 imputed genetic variants in 48,155 cases and 43,612 controls of European descent, 6269 cases and 6624 controls of East Asian descent and 1116 cases and 932 controls of African descent in the Breast Cancer Association Consortium (BCAC; http://bcac.ccge.medschl.cam.ac.uk/ ), and in 15,252 BRCA1 mutation carriers in the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA). Stepwise regression analyses were performed to identify independent association signals. Data from the Encyclopedia of DNA Elements project (ENCODE) and the Cancer Genome Atlas (TCGA) were used for functional annotation. RESULTS: Analysis of data from European descendants found evidence for four independent association signals at 12p11, represented by rs7297051 (odds ratio (OR) = 1.09, 95 % confidence interval (CI) = 1.06-1.12; P = 3 × 10(-9)), rs805510 (OR = 1.08, 95 % CI = 1.04-1.12, P = 2 × 10(-5)), and rs1871152 (OR = 1.04, 95 % CI = 1.02-1.06; P = 2 × 10(-4)) identified in the general populations, and rs113824616 (P = 7 × 10(-5)) identified in the meta-analysis of BCAC ER-negative cases and BRCA1 mutation carriers. SNPs rs7297051, rs805510 and rs113824616 were also associated with breast cancer risk at P < 0.05 in East Asians, but none of the associations were statistically significant in African descendants. Multiple candidate functional variants are located in putative enhancer sequences. Chromatin interaction data suggested that PTHLH was the likely target gene of these enhancers. Of the six variants with the strongest evidence of potential functionality, rs11049453 was statistically significantly associated with the expression of PTHLH and its nearby gene CCDC91 at P < 0.05. CONCLUSION: This study identified four independent association signals at 12p11 and revealed potentially functional variants, providing additional insights into the underlying biological mechanism(s) for the association observed between variants at 12p11 and breast cancer risk.UK funding includes Cancer Research UK and NIH.This is the final version of the article. It first appeared from BioMed Central via http://dx.doi.org/10.1186/s13058-016-0718-

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk

Genome-Wide Association Study in BRCA1 Mutation Carriers Identifies Novel Loci Associated with Breast and Ovarian Cancer Risk

BRCA1-associated breast and ovarian cancer risks can be modified by common genetic variants. To identify further cancer risk-modifying loci, we performed a multi-stage GWAS of 11,705 BRCA1 carriers (of whom 5,920 were diagnosed with breast and 1,839 were diagnosed with ovarian cancer), with a further replication in an additional sample of 2,646 BRCA1 carriers. We identified a novel breast cancer risk modifier locus at 1q32 for BRCA1 carriers (rs2290854, P = 2.7×10-8, HR = 1.14, 95% CI: 1.09-1.20). In addition, we identified two novel ovarian cancer risk modifier loci: 17q21.31 (rs17631303, P = 1.4×10-8, HR = 1.27, 95% CI: 1.17-1.38) and 4q32.3 (rs4691139, P = 3.4×10-8, HR = 1.20, 95% CI: 1.17-1.38). The 4q32.3 locus was not associated with ovarian cancer risk in the general population or BRCA2 carriers, suggesting a BRCA1-specific associat