Search for: All records

PurposeThe paper aims to determine the rational homotopy type of the total space of projectivized bundles over complex projective spaces using Sullivan minimal models, providing insights into the algebraic structure of these spaces. Design/methodology/approachThe paper utilises techniques from Sullivan’s theory of minimal models to analyse the differential graded algebraic structure of projectivized bundles. It employs algebraic methods to compute the Sullivan minimal model of $P(E)$and establish relationships with the base space. FindingsThe paper determines the rational homotopy type of projectivized bundles over complex projective spaces. Of great interest is how the Chern classes of the fibre space and base space, play a critical role in determining the Sullivan model ofP(E). We also provide the homogeneous space ofP(E)whenn = 2. Finally, we prove the formality ofP(E)over a homogeneous space of equal rank. Research limitations/implicationsLimitations may include the complexity of computing minimal models for higher-dimensional bundles. Practical implicationsUnderstanding the rational homotopy type of projectivized bundles facilitates computations in algebraic topology and differential geometry, potentially aiding in applications such as topological data analysis and geometric modelling. Social implicationsWhile the direct social impact may be indirect, advancements in algebraic topology contribute to broader mathematical knowledge, which can underpin developments in science, engineering, and technology with societal benefits. Originality/valueThe paper’s originality lies in its application of Sullivan minimal models to determine the rational homotopy type of projectivized bundles over complex projective spaces, offering valuable insights into the algebraic structure of these spaces and their associated complex vector bundles. 

Abstract BackgroundIntimate partner violence (IPV) remains a global public health concern for both men and women. Spatial mapping and clustering analysis can reveal subtle patterns in IPV occurrences but are yet to be explored in Rwanda, especially at a lower small-area scale. This study seeks to examine the spatial distribution, patterns, and associated factors of IPV among men and women in Rwanda. MethodsThis was a secondary data analysis of the 2019/2020 Rwanda Demographic and Health Survey (RDHS) individual-level data set for 1947 women aged 15–49 years and 1371 men aged 15–59 years. A spatially structured additive logistic regression model was used to assess risk factors for IPV while adjusting for spatial effects. The district-level spatial model was adjusted for fixed covariate effects and was implemented using a fully Bayesian inference within the generalized additive mixed effects framework. ResultsIPV prevalence amongst women was 45.9% (95% Confidence interval (CI): 43.4–48.5%) while that for men was 18.4% (95% CI: 16.2–20.9%). Using a bivariate choropleth, IPV perpetrated against women was higher in the North-Western districts of Rwanda whereas for men it was shown to be more prevalent in the Southern districts. A few districts presented high IPV for both men and women. The spatial structured additive logistic model revealed higher odds for IPV against women mainly in the North-western districts and the spatial effects were dominated by spatially structured effects contributing 64%. Higher odds of IPV were observed for men in the Southern districts of Rwanda and spatial effects were dominated by district heterogeneity accounting for 62%. There were no statistically significant district clusters for IPV in both men or women. Women with partners who consume alcohol, and with controlling partners were at significantly higher odds of IPV while those in rich households and making financial decisions together with partners were at lower odds of experiencing IPV. ConclusionCampaigns against IPV should be strengthened, especially in the North-Western and Southern parts of Rwanda. In addition, the promotion of girl-child education and empowerment of women can potentially reduce IPV against women and girls. Furthermore, couples should be trained on making financial decisions together. In conclusion, the implementation of policies and interventions that discourage alcohol consumption and control behaviour, especially among men, should be rolled out. 

Abstract Parentage analyses via molecular markers have revealed multiple paternity within the broods of polytocous species, reshaping our understanding of animal behavior, ecology, and evolution. In a meta‐analysis of multiple paternity in bird and mammal species, we conducted a literature search and found 138 bird and 64 mammal populations with microsatellite DNA paternity results. Bird populations averaged 19.5% multiple paternity and mammals more than twice that level (46.1%). We used a Bayesian approach to construct a null model for how multiple paternity should behave at random among species, under the assumption that all mated males have equal likelihood of siring success, given mean brood size and mean number of sires. We compared the differences between the null model and the actual probabilities of multiple paternity. While a few bird populations fell close to the null model, most did not, averaging 34.0‐percentage points below null model predictions; mammals had an average probability of multiple paternity 13.6‐percentage points below the null model. Differences between bird and mammal species were also subjected to comparative phylogenetic analyses that generally confirmed our analyses that did not adjust for estimated historical relationships. Birds exhibited extremely low probabilities of multiple paternity, not only compared to mammals but also relative to other major animal taxa. The generally low probability of multiple paternity in birds might be produced by a variety of factors, including behaviors that reflect sexual selection (extreme mate guarding or unifocal female choice) and sperm competition (e.g., precedence effects favoring fertilization by early or late matings). 

Abstract BackgroundHIV/AIDS remains a major public health problem globally. The majority of people living with HIV are from Sub-Saharan Africa, particularly adolescent girls and young women (AGYW) aged 15-24 years. HIV testing is crucial as it is the gateway to HIV prevention, treatment, and care; therefore this study determined the prevalence and factors associated with self-reported HIV testing among AGYW in Rwanda. MethodsWe conducted secondary data analysis on the AGYW using data extracted from the nationally representative population-based 2019/2020 cross-sectional Rwanda Demographic and Health Survey (DHS). We described the characteristics of study participants and determined the prevalence of HIV testing and associated factors using the multivariable logistic regression model. We adjusted all our analyses for unequal sampling probabilities using survey weights. ResultsThere were a total of 5,732 AGYW, with the majority (57%) aged 15-19 years, 83% were not living with a man, 80% were from rural areas, 29% were from the East region, and 20% had a history of pregnancy. Self-reported HIV testing prevalence was 55.4% (95%CI: 53.7 to 57.0%). The odds of ever having an HIV test were significantly higher for those aged 20-24 years (aOR 2.87, 95%CI: 2.44 to 3.37); with higher education (aOR 2.41, 95%CI:1.48 to 3.93); who were rich (aOR 2.06, 95%CI:1.57 to 2.70); with access to at least one media (aOR 1.64, 95%CI: 1.14 to 2.37); who had ever been pregnant (aOR 16.12, 95%CI: 9.60 to 27.07); who ever had sex (aOR 2.40, 95%CI: 1.96 to 2.95); and those who had comprehensive HIV knowledge (aOR 1.34, 95%CI: 1.17 to 1.54). ConclusionsWe report an unmet need for HIV testing among AGYW in Rwanda. We recommend a combination of strategies to optimize access to HIV testing services, especially among the 15-19 years adolescent girls, including facility-based testing, school and community outreach, awareness campaigns on HIV testing, and home-based testing through HIV self-testing. 

BackgroundCancer remains a major public health problem, especially in Sub-Saharan Africa (SSA) where the provision of health care is poor. This scoping review mapped evidence in the literature regarding the burden of cervical, breast and prostate cancers in SSA. MethodsWe conducted this scoping review using the Arksey and O'Malley framework, with five steps: identifying the research question; searching for relevant studies; selecting studies; charting the data; and collating, summarizing, and reporting the data. We performed all the steps independently and resolved disagreements through discussion. We used Endnote software to manage references and the Rayyan software to screen studies. ResultsWe found 138 studies that met our inclusion criteria from 2,751 studies identified through the electronic databases. The majority were retrospective studies of mostly registries and patient files (n= 77, 55.8%), followed by cross-sectional studies (n= 51, 36.9%). We included studies published from 1990 to 2021, with a sharp increase from 2010 to 2021. The quality of studies was overall satisfactory. Most studies were done in South Africa (n= 20) and Nigeria (n= 17). The majority were on cervical cancer (n= 93, 67.4%), followed by breast cancer (67, 48.6%) and the least were on prostate cancer (48, 34.8%). Concerning the burden of cancer, most reported prevalence and incidence. We also found a few studies investigating mortality, disability-adjusted life years (DALYs), and years of life lost (YLL). ConclusionsWe found many retrospective record review cross-sectional studies, mainly in South Africa and Nigeria, reporting the prevalence and incidence of cervical, breast and prostate cancer in SSA. There were a few systematic and scoping reviews. There is a scarcity of cervical, breast and prostate cancer burden studies in several SSA countries. The findings in this study can inform policy on improving the public health systems and therefore reduce cancer incidence and mortality in SSA. 

Abstract Parentage analyses via microsatellite markers have revealed multiple paternity within the broods of polytocous species of mammals, reptiles, amphibians, fishes and invertebrates. The widespread phenomenon of multiple paternity may have attending relationships with such evolutionary processes as sexual selection and kin selection. However, just how much multiple paternity should a species exhibit? We developed Bayesian null models of how multiple paternity relates to brood sizes. For each of 114 species with published data on brood sizes and numbers of sires, we compared our null model estimates to published frequencies of multiple paternity. The majority of species fell close to our null model, especially among fish and invertebrate species. Some species, however, had low probabilities of multiple paternity, far from the predictions of the null model, likely due to sexual selection and environmental constraints. We suggest a major division among species’ mating systems between those with close to random mating and high levels of multiple paternity, and those with constraints that produce low levels of multiple paternity. 

Word-representable graphs were originally introduced by Kitaev and Pyatkin, motivated by work of Kitaev and Seif in algebra. Since their introduction, however, there has been a great deal of work in understanding their graph theoretical properties. In this paper, we introduce tools from partially ordered sets, Ramsey theory as well as probabilistic methods to study them. Through these, we settle a number of open problems in the field, regarding both the existence and length of word-representations for various classes of graphs. 

The rational homotopy type of a mapping space is a way to describe the structure of the space using the algebra of its homotopy groups and the differential graded algebra of its cochains. An L∞-model is a graded Lie algebra with a family of higher-order brackets satisfying the generalized Jacobi identity and antisymmetry. It can be used to study the rational homotopy type of a space. The nilpotency index of an L∞-model is useful in understanding a space's algebraic structure. In this paper, we compute the rational homotopy type of the component of some mapping spaces between projective spaces and determine the nilpotency index of corresponding L∞-models.