Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations

The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results

Stability, Boundedness, and Existence of Periodic Solutions to Certain Third-Order Delay Differential Equations with Multiple Deviating Arguments

The behaviour of solutions for certain third-order nonlinear differential equations with multiple deviating arguments is considered. By employing Lyapunov’s second method, a complete Lyapunov functional is constructed and used to establish sufficient conditions that guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results not only are new but also include many outstanding results in the literature. Finally, the correctness and effectiveness of the results are justified with examples

Genetic variants in microRNA and microRNA biogenesis pathway genes and breast cancer risk among women of African ancestry

MicroRNAs (miRNA) regulate breast biology by binding to specific RNA sequences, leading to RNA degradation and inhibition of translation of their target genes. While germline genetic variations may disrupt some of these interactions between miRNAs and their targets, studies assessing the relationship between genetic variations in the miRNA network and breast cancer risk are still limited, particularly among women of African ancestry

Parity and breastfeeding are protective against breast cancer in Nigerian women

As the relation between reproductive factors and breast cancer risk has not been systematically studied in indigenous women of sub-Saharan Africa, we examined this in a case–control study in Nigeria. In-person interviews were conducted using structured questionnaires to collect detailed reproductive history in 819 breast cancer cases and 569 community controls between 1998 and 2006. Logistic regression was used to estimate odds ratios (ORs) and 95% confidence intervals (CI). Compared with women with menarcheal age <17 years, the adjusted OR for women with menarcheal age ⩾17 years was 0.72 (95% CI: 0.54–0.95, P=0.02). Parity was negatively associated with risk (P-trend=0.02) but age at first live birth was not significant (P=0.16). Importantly, breast cancer risk decreased by 7% for every 12 months of breastfeeding (P-trend=0.005). It is worth noting that the distribution of reproductive risk factors changed significantly from early to late birth cohorts in the direction of increasing breast cancer incidence. Our findings also highlight the heterogeneity of breast cancer aetiology across populations, and indicate the need for further studies among indigenous sub-Saharan women

Genome-wide association studies in women of African ancestry identified 3q26.21 as a novel susceptibility locus for oestrogen receptor negative breast cancer

Multiple breast cancer loci have been identified in previous genome-wide association studies, but they were mainly conducted in populations of European ancestry. Women of African ancestry are more likely to have young-onset and oestrogen receptor (ER) negative breast cancer for reasons that are unknown and understudied. To identify genetic risk factors for breast cancer in women of African descent, we conducted a meta-analysis of two genome-wide association studies of breast cancer; one study consists of 1,657 cases and 2,029 controls genotyped with Illumina's HumanOmni2.5 BeadChip and the other study included 3,016 cases and 2,745 controls genotyped using Illumina Human1M-Duo BeadChip. The top 18,376 single nucleotide polymorphisms (SNP) from the meta-analysis were replicated in the third study that consists of 1,984 African Americans cases and 2,939 controls. We found that SNP rs13074711, 26.5 Kb upstream of TNFSF10 at 3q26.21, was significantly associated with risk of oestrogen receptor (ER)-negative breast cancer (odds ratio [OR]=1.29, 95% CI: 1.18-1.40; P = 1.8 × 10 (-) (8)). Functional annotations suggest that the TNFSF10 gene may be involved in breast cancer aetiology, but further functional experiments are needed. In addition, we confirmed SNP rs10069690 was the best indicator for ER-negative breast cancer at 5p15.33 (OR = 1.30; P = 2.4 × 10 (-) (10)) and identified rs12998806 as the best indicator for ER-positive breast cancer at 2q35 (OR = 1.34; P = 2.2 × 10 (-) (8)) for women of African ancestry. These findings demonstrated additional susceptibility alleles for breast cancer can be revealed in diverse populations and have important public health implications in building race/ethnicity-specific risk prediction model for breast cancer

Characterizing Genetic Susceptibility to Breast Cancer in Women of African Ancestry

Background: Genome-wide association studies have identified approximately 100 common genetic variants associated with breast cancer risk, the majority of which were discovered in women of European ancestry. Because of different patterns of linkage disequilibrium, many of these genetic markers may not represent signals in populations of African ancestry. Methods: We tested 74 breast cancer risk variants and conducted fine-mapping of these susceptibility regions in 6,522 breast cancer cases and 7,643 controls of African ancestry from three genetic consortia (AABC, AMBER, and ROOT). Results: Fifty-four of the 74 variants (73%) were found to have ORs that were directionally consistent with those previously reported, of which 12 were nominally statistically significant ( P < 0.05). Through fine-mapping, in six regions ( 3p24, 12p11, 14q13, 16q12/FTO, 16q23, 19p13 ), we observed seven markers that better represent the underlying risk variant for overall breast cancer or breast cancer subtypes, whereas in another two regions ( 11q13, 16q12/TOX3 ), we identified suggestive evidence of signals that are independent of the reported index variant. Overlapping chromatin features and regulatory elements suggest that many of the risk alleles lie in regions with biological functionality. Conclusions: Through fine-mapping of known susceptibility regions, we have revealed alleles that better characterize breast cancer risk in women of African ancestry. Impact: The risk alleles identified represent genetic markers for modeling and stratifying breast cancer risk in women of African ancestry. Cancer Epidemiol Biomarkers Prev; 26(7); 1-11. ©2017 AACR

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

Maroon Archaeology Beyond the Americas: A View From Kenya

Archaeological research on Maroons—that is, runaway slaves—has been largely confined to the Americas. This essay advocates a more global approach. It specifically uses two runaway slave communities in 19th-century coastal Kenya to rethink prominent interpretive themes in the field, including “Africanisms,” Maroons’ connections to indigenous groups, and Maroon group cohesion and identity. This article’s analysis demonstrates that the comparisons enabled by a more globalized perspective benefit the field. Instead of eliding historical and cultural context, these comparisons support the development of more localized and historically specific understandings of individual runaway slave communities both in Kenya and throughout the New World

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