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

ON STABILITY OF QUANTUM STOCHASTIC DIFFERENTIAL EQUATION

The long run behaviour of solutions of Lipschitzian quantum stochastic differential equation (QSDE) with non-instantaneous impulse is studied. This is achieved by imposing some conditions on the coefficients associated with the map P. Using the fixed point approach, we show that a solution exists under the given conditions and subsequently establish Ulam's type stability. We present some examples to further justify its application

Primary osteogenic sarcoma of the breast

BACKGROUND: Primary extra-osseous osteogenic sarcomas have been reported in many tissues of the body but their occurrence in the breast is extremely rare. It can arise as a result of osseous metaplasia in a pre-existing benign or malignant neoplasm of the breast or as non-phylloides sarcoma from the soft tissue of a previously normal breast. CASE PRESENTATION: A 40 year-old Nigerian woman was clinically diagnosed to have carcinoma of the left breast. The histology report of core-needle biopsy of the mass showed a malignant neoplasm comprising islands of chondroblastic and osteoblastic stromal cells. This report changed the diagnosis from carcinoma to osteogenic sarcoma of the breast. She had a left modified radical mastectomy, however there was significant post surgery skin deficit. A latissimus dorsi musculocutaneous flap was used to cover the anterior chest wall defect. Sections from the mastectomy specimen confirmed the diagnosis of osteogenic sarcoma. She died six months after mastectomy. CONCLUSION: A diagnosis of osteogenic sarcoma of the breast was made based on histology report and after excluding an osteogenic sarcoma arising from underlying ribs and sternum. This is the second documented case of primary osteogenic sarcoma of the breast coming from Nigeri

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

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

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 \u3c 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

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

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