Constructing Entanglement Witness Via Real Skew-Symmetric Operators

In this work, new types of EWs are introduced. They are constructed by using real skew-symmetric operators defined on a single party subsystem of a bipartite dxd system and a maximal entangled state in that system. A canonical form for these witnesses is proposed which is called canonical EW in corresponding to canonical real skew-symmetric operator. Also for each possible partition of the canonical real skew-symmetric operator corresponding EW is obtained. The method used for dxd case is extended to d1xd2 systems. It is shown that there exist Cd2xd1 distinct possibilities to construct EWs for a given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied for each type of EWs. In each step, a large class of quantum PPT states is introduced. It is shown that among them there exist entangled PPT states which are detected by the constructed witnesses. Also the idea of canonical EWs is extended to obtain other EWs with greater PPT entanglement detection power.Comment: 40 page

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

Assessing associations between the AURKAHMMR-TPX2-TUBG1 functional module and breast cancer risk in BRCA1/2 mutation carriers

While interplay between BRCA1 and AURKA-RHAMM-TPX2-TUBG1 regulates mammary epithelial polarization, common genetic variation in HMMR (gene product RHAMM) may be associated with risk of breast cancer in BRCA1 mutation carriers. Following on these observations, we further assessed the link between the AURKA-HMMR-TPX2-TUBG1 functional module and risk of breast cancer in BRCA1 or BRCA2 mutation carriers. Forty-one single nucleotide polymorphisms (SNPs) were genotyped in 15,252 BRCA1 and 8,211 BRCA2 mutation carriers and subsequently analyzed using a retrospective likelihood appr

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

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

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

Polygenic risk scores for prediction of breast cancer risk in women of African ancestry: A cross-ancestry approach

Polygenic risk scores (PRSs) are useful for predicting breast cancer risk, but the prediction accuracy of existing PRSs in women of African ancestry (AA) remains relatively low. We aim to develop optimal PRSs for the prediction of overall and estrogen receptor (ER) subtype-specific breast cancer risk in AA women. The AA dataset comprised 9235 cases and 10 184 controls from four genome-wide association study (GWAS) consortia and a GWAS study in Ghana. We randomly divided samples into training and validation sets. We built PRSs using individual-level AA data by a forward stepwise logistic regression and then developed joint PRSs that combined (1) the PRSs built in the AA training dataset and (2) a 313-variant PRS previously developed in women of European ancestry. PRSs were evaluated in the AA validation set. For overall breast cancer, the odds ratio per standard deviation of the joint PRS in the validation set was 1.34 [95% confidence interval (CI): 1.27-1.42] with the area under receiver operating characteristic curve (AUC) of 0.581. Compared with women with average risk (40th-60th PRS percentile), women in the top decile of the PRS had a 1.98-fold increased risk (95% CI: 1.63-2.39). For PRSs of ER-positive and ER-negative breast cancer, the AUCs were 0.608 and 0.576, respectively. Compared with existing methods, the proposed joint PRSs can improve prediction of breast cancer risk in AA women

Evaluating Polygenic Risk Scores for Breast Cancer in Women of African Ancestry

Background: Polygenic risk scores (PRSs) have been demonstrated to identify women of European, Asian, and Latino ancestry at elevated risk of developing breast cancer (BC). We evaluated the performance of existing PRSs trained in European ancestry populations among women of African ancestry. Methods: We assembled genotype data for women of African ancestry, including 9241 case subjects and 10 193 control subjects. We evaluated associations of 179- and 313-variant PRSs with overall and subtype-specific BC risk. PRS discriminatory accuracy was assessed using area under the receiver operating characteristic curve. We also evaluated a recalibrated PRS, replacing the index variant with variants in each region that better captured risk in women of African ancestry and estimated lifetime absolute risk of BC in African Americans by PRS category. Results: For overall BC, the odds ratio per SD of the 313-variant PRS (PRS313) was 1.27 (95% confidence interval [CI] = 1.23 to 1.31), with an area under the receiver operating characteristic curve of 0.571 (95% CI = 0.562 to 0.579). Compared with women with average risk (40th-60th PRS percentile), women in the top decile of PRS313 had a 1.54-fold increased risk (95% CI = 1.38-fold to 1.72-fold). By age 85 years, the absolute risk of overall BC was 19.6% for African American women in the top 1% of PRS313 and 6.7% for those in the lowest 1%. The recalibrated PRS did not improve BC risk prediction. Conclusion: The PRSs stratify BC risk in women of African ancestry, with attenuated performance compared with that reported in European, Asian, and Latina populations. Future work is needed to improve BC risk stratification for women of African ancestry

Cross-ancestry GWAS meta-analysis identifies six breast cancer loci in African and European ancestry women

Our study describes breast cancer risk loci using a cross-ancestry GWAS approach. We first identify variants that are associated with breast cancer at P < 0.05 from African ancestry GWAS meta-analysis (9241 cases and 10193 controls), then meta-analyze with European ancestry GWAS data (122977 cases and 105974 controls) from the Breast Cancer Association Consortium. The approach identifies four loci for overall breast cancer risk [1p13.3, 5q31.1, 15q24 (two independent signals), and 15q26.3] and two loci for estrogen receptor-negative disease (1q41 and 7q11.23) at genome-wide significance. Four of the index single nucleotide polymorphisms (SNPs) lie within introns of genes (KCNK2, C5orf56, SCAMP2, and SIN3A) and the other index SNPs are located close to GSTM4, AMPD2, CASTOR2, and RP11-168G16.2. Here we present risk loci with consistent direction of associations in African and European descendants. The study suggests that replication across multiple ancestry populations can help improve the understanding of breast cancer genetics and identify causal variants