Two-parameter nonsmooth grazing bifurcations of limit cycles: classification and open problems

This paper proposes a strategy for the classification of codimension-two grazing bifurcations of limit cycles in piecewise smooth systems of ordinary differential equations. Such nonsmooth transitions (C-bifurcations) occur when the cycle interacts with a discontinuity boundary of phase space in a non-generic way. Several such codimension-one events have recently been identified, causing for example period-adding or sudden onset of chaos. Here, the focus is on codimension-two grazings that are local in the sense that the dynamics can be fully described by an appropriate Poincaré map from a neighbourhood of the grazing point (or points) of the critical cycle to itself. It is proposed that codimension-two grazing bifurcations can be divided into three distinct types: either the grazing point is degenerate, or the the grazing cycle is itself degenerate (e.g. non-hyperbolic) or we have the simultaneous occurrence of two grazing events. A careful distinction is drawn between their occurrence in systems with discontinuous states, discontinuous vector fields, or that have discontinuity in some derivative of the vector field. Examples of each kind of bifurcation are presented, mostly derived from mechanical applications. For each example, where possible, principal bifurcation curves characteristic to the codimension-two scenario are presented and general features of the dynamics discussed. Many avenues for future research are opened.

Rise and Fall of a Multi-sheet Intrusive Complex, Elba Island, Italy

Elba Island intrusive complex: multisheet laccoliths, sheeted pluton, mafic dyke swarm. Laccolith magma fed from dykes and emplaced in crustal discontinuities (traps). Pluton growth by downward stacking of three magma pulses. Laccoliths and plutons: different outcomes of similar processes in different conditions. Emplacement of excess magma in a short time led to massive gravity slide

Addressing Inequity to Achieve the Maternal and Child Health Millennium Development Goals: Looking Beyond Averages.

Inequity in access to and use of child and maternal health interventions is impeding progress towards the maternal and child health Millennium Development Goals. This study explores the potential health gains and equity impact if a set of priority interventions for mothers and under fives were scaled up to reach national universal coverage targets for MDGs in Tanzania. We used the Lives Saved Tool (LiST) to estimate potential reductions in maternal and child mortality and the number of lives saved across wealth quintiles and between rural and urban settings. High impact maternal and child health interventions were modelled for a five-year scale up, by linking intervention coverage, effectiveness and cause of mortality using data from Tanzania. Concentration curves were drawn and the concentration index estimated to measure the equity impact of the scale up. In the poorest population quintiles in Tanzania, the lives of more than twice as many mothers and under-fives were likely to be saved, compared to the richest quintile. Scaling up coverage to equal levels across quintiles would reduce inequality in maternal and child mortality from a pro rich concentration index of -0.11 (maternal) and -0.12 (children) to a more equitable concentration index of -0,03 and -0.03 respectively. In rural areas, there would likely be an eight times greater reduction in maternal deaths than in urban areas and a five times greater reduction in child deaths than in urban areas. Scaling up priority maternal and child health interventions to equal levels would potentially save far more lives in the poorest populations, and would accelerate equitable progress towards maternal and child health MDGs

A multidisciplinary systematic literature review on frailty: Overview of the methodology used by the Canadian Initiative on Frailty and Aging

<p>Abstract</p> <p>Background</p> <p>Over the past two decades, there has been a substantial growth in the body of literature on frailty in older persons. However, there is no consensus on its definition or the criteria used to identify frailty. In response to this lack of consensus, the Canadian Initiative on Frailty and Aging carried out a set of systematic reviews of the literature in ten areas of frailty research: biological basis; social basis; prevalence; risk factors; impact; identification; prevention and management; environment and technology; health services; health and social policy. This paper describes the methodology that was developed for the systematic reviews.</p> <p>Methods</p> <p>A Central Coordination Group (CCG) was responsible for developing the methodology. This involved the development of search strategies and keywords, article selection processes, quality assessment tools, and guidelines for the synthesis of results. Each review was conducted by two experts in the content area, with the assistance of methodologists and statisticians from the CCG.</p> <p>Results</p> <p>Conducting a series of systematic literature reviews involving a range of disciplines on a concept that does not have a universally accepted definition posed several conceptual and methodological challenges. The most important conceptual challenge was determining what would qualify as literature on frailty. The methodological challenges arose from our goal of structuring a consistent methodology for reviewing literature from diverse fields of research. At the outset, certain methodological guidelines were deemed essential to ensure the validity of all the reviews. Nevertheless, it was equally important to permit flexibility in the application of the proposed methodology to capture the essence of frailty research within the given fields.</p> <p>Conclusion</p> <p>The results of these reviews allowed us to establish the status of current knowledge on frailty and promote collaboration between disciplines. Conducting systematic literature reviews in health science that involve multiple disciplines is a mechanism to facilitate interdisciplinary collaboration and a more integrated understanding of health. This initiative highlighted the need for further methodological development in the performance of multidisciplinary systematic reviews.</p

Regulation of mammary gland branching morphogenesis by the extracellular matrix and its remodeling enzymes.

A considerable body of research indicates that mammary gland branching morphogenesis is dependent, in part, on the extracellular matrix (ECM), ECM-receptors, such as integrins and other ECM receptors, and ECM-degrading enzymes, including matrix metalloproteinases (MMPs) and their inhibitors, tissue inhibitors of metalloproteinases (TIMPs). There is some evidence that these ECM cues affect one or more of the following processes: cell survival, polarity, proliferation, differentiation, adhesion, and migration. Both three-dimensional culture models and genetic manipulations of the mouse mammary gland have been used to study the signaling pathways that affect these processes. However, the precise mechanisms of ECM-directed mammary morphogenesis are not well understood. Mammary morphogenesis involves epithelial 'invasion' of adipose tissue, a process akin to invasion by breast cancer cells, although the former is a highly regulated developmental process. How these morphogenic pathways are integrated in the normal gland and how they become dysregulated and subverted in the progression of breast cancer also remain largely unanswered questions

Occupation and skin cancer: the results of the HELIOS-I multicenter case-control study

<p>Abstract</p> <p>Background</p> <p>Non-melanoma skin cancer (NMSC) is the most frequent tumour among Caucasian populations worldwide. Among the risk factors associated with this tumour, there are host-related factors and several environmental agents. A greater likelihood of high exposure to physical agents (with the exception of solar radiation) and chemical agents depends on the work setting. Our objective is to evaluate the role of occupational exposures in NMSC, with special emphasis on risk factors other than solar radiation and skin type.</p> <p>Methods</p> <p>We analysed 1585 cases (1333 basal cell carcinoma (BCC) and 183 squamous cell carcinoma (SCC)) and 1507 controls drawn from the Helios-I multicenter study. Odds ratios (OR) and 95% confidence intervals (CI) were estimated using logistic regression mixed models.</p> <p>Results</p> <p>For NMSC as a whole (both <it>histological types</it>), miners and quarrymen, secondary education teachers, and masons registered excess risk, regardless of exposure to solar radiation and skin type (OR 7.04, 95% CI 2.44–20.31; OR 1.75, 95% CI 1.05–2.89 and OR 1.54, 95% CI 1.04–2.27, respectively). Frequency of BCC proved higher among railway engine drivers and firemen (OR 4.55; 95% CI 0.96–21.57), specialised farmers (OR 1.65; 95% CI 1.05–2.59) and salesmen (OR 3.02; 95% CI 1.05–2.86), in addition to miners and quarrymen and secondary education teachers (OR 7.96; 95% CI 2.72–23.23 and OR 1.76; 95% CI 1.05–2.94 respectively). The occupations that registered a higher risk of <it>SCC (though not of BCC</it>) were those involving direct contact with livestock, construction workers not elsewhere classified (OR 2.95, 95% CI 1.12–7.74), stationary engine and related equipment operators not elsewhere classified (OR 5.31, 95% CI 1.13–21.04) and masons (OR 2.55, 95% CI 1.36–4.78).</p> <p>Conclusion</p> <p>Exposure to hazardous air pollutants, arsenic, ionizing radiations and burns may explain a good part of the associations observed in this study. The Helios study affords an excellent opportunity for further in-depth study of physical and chemical agents and NMSC based on matrices of occupational exposure.</p

Brane-World Gravity

The observable universe could be a 1+3-surface (the "brane") embedded in a 1+3+\textit{d}-dimensional spacetime (the "bulk"), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the \textit{d} extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak ($\sim$ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1+10-dimensional M theory encompasses the known 1+9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity "leaks" into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review analyzes the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall--Sundrum models. We also cover the simplest brane-world models in which 4-dimensional gravity on the brane is modified at \emph{low} energies -- the 5-dimensional Dvali--Gabadadze--Porrati models. Then we discuss co-dimension two branes in 6-dimensional models.Comment: A major update of Living Reviews in Relativity 7:7 (2004) "Brane-World Gravity", 119 pages, 28 figures, the update contains new material on RS perturbations, including full numerical solutions of gravitational waves and scalar perturbations, on DGP models, and also on 6D models. A published version in Living Reviews in Relativit

Gravitational Waves from Gravitational Collapse

Gravitational wave emission from the gravitational collapse of massive stars has been studied for more than three decades. Current state of the art numerical investigations of collapse include those that use progenitors with realistic angular momentum profiles, properly treat microphysics issues, account for general relativity, and examine non--axisymmetric effects in three dimensions. Such simulations predict that gravitational waves from various phenomena associated with gravitational collapse could be detectable with advanced ground--based and future space--based interferometric observatories.Comment: 68 pages including 13 figures; revised version accepted for publication in Living Reviews in Relativity (http://www.livingreviews.org

'How to know what you need to do': a cross-country comparison of maternal health guidelines in Burkina Faso, Ghana and Tanzania

Initiatives to raise the quality of care provided to mothers need to be given priority in Sub Saharan Africa (SSA). The promotion of clinical practice guidelines (CPGs) is a common strategy, but their implementation is often challenging, limiting their potential impact. Through a cross-country perspective, this study explored CPGs for maternal health in Burkina Faso, Ghana, and Tanzania. The objectives were to compare factors related to CPG use including their content compared with World Health Organization (WHO) guidelines, their format, and their development processes. Perceptions of their availability and use in practice were also explored. The overall purpose was to further the understanding of how to increase CPGs' potential to improve quality of care for mothers in SSA. The study was a multiple case study design consisting of cross-country comparisons using document review and key informant interviews. A conceptual framework to aid analysis and discussion of results was developed, including selected domains related to guidelines' implementability and use by health workers in practice in terms of usability, applicability, and adaptability. The study revealed few significant differences in content between the national guidelines for maternal health and WHO recommendations. There were, however, marked variations in the format of CPGs between the three countries. Apart from the Ghanaian and one of the Tanzanian CPGs, the levels of both usability and applicability were assessed as low or medium. In all three countries, the use of CPGs by health workers in practice was perceived to be limited. Our cross-country study suggests that it is not poor quality of content or lack of evidence base that constitute the major barrier for CPGs to positively impact on quality improvement in maternal care in SSA. It rather emphasises the need to prioritise the format of guidelines to increase their usability and applicability and to consider these attributes together with implementation strategies as integral to their development processes