Existence of solutions for a higher order non-local equation appearing in crack dynamics

In this paper, we prove the existence of non-negative solutions for a non-local higher order degenerate parabolic equation arising in the modeling of hydraulic fractures. The equation is similar to the well-known thin film equation, but the Laplace operator is replaced by a Dirichlet-to-Neumann operator, corresponding to the square root of the Laplace operator on a bounded domain with Neumann boundary conditions (which can also be defined using the periodic Hilbert transform). In our study, we have to deal with the usual difficulty associated to higher order equations (e.g. lack of maximum principle). However, there are important differences with, for instance, the thin film equation: First, our equation is nonlocal; Also the natural energy estimate is not as good as in the case of the thin film equation, and does not yields, for instance, boundedness and continuity of the solutions (our case is critical in dimension $1$ in that respect)

Developing capacities of community health workers in sexual and reproductive, maternal, newborn, child, and adolescent health: A mapping and review of training resources

Background: Given country demands for support in the training of community health workers (CHWs) to accelerate progress towards reaching the Millennium Development Goals in sexual and reproductive health and maternal, newborn, child, and adolescent health (SR/MNCAH), the United Nations Health Agencies conducted a synthesis of existing training resource packages for CHWs in different components of SR/MNCAH to identify gaps and opportunities and inform efforts to harmonize approaches to developing the capacity of CHWs. Methods: A mapping of training resource packages for CHWs was undertaken with documents retrieved online and from key informants. Materials were classified by health themes and analysed using agreed parameters. Ways forward were informed by a subsequent expert consultation. Results: We identified 31 relevant packages. They covered different components of the SR/MNCAH continuum in varying breadth (integrated packages) and depth (focused packages), including family planning, antenatal and childbirth care (mainly postpartum haemorrhage), newborn care, and childhood care, and HIV. There is no or limited coverage of interventions related to safe abortion, adolescent health, and gender-based violence. There is no training package addressing the range of evidence-based interventions that can be delivered by CHWs as per World Health Organization guidance. Gaps include weakness in the assessment of competencies of trainees, in supportive supervision, and in impact assessment of packages. Many packages represent individual programme efforts rather than national programme materials, which could reflect weak integration into national health systems. Conclusions: There is a wealth of training packages on SR/MNCAH for CHWs which reflects interest in strengthening the capacity of CHWs. This offers an opportunity for governments and partners to mount a synergistic response to address the gaps and ensure an evidence-based comprehensive package of interventions to be delivered by CHWs. Packages with defined competencies and methods for assessing competencies and supervision are considered best practices but remain a gap. © 2014 Tran et al

Time representation in reinforcement learning models of the basal ganglia

Reinforcement learning (RL) models have been influential in understanding many aspects of basal ganglia function, from reward prediction to action selection. Time plays an important role in these models, but there is still no theoretical consensus about what kind of time representation is used by the basal ganglia. We review several theoretical accounts and their supporting evidence. We then discuss the relationship between RL models and the timing mechanisms that have been attributed to the basal ganglia. We hypothesize that a single computational system may underlie both RL and interval timing—the perception of duration in the range of seconds to hours. This hypothesis, which extends earlier models by incorporating a time-sensitive action selection mechanism, may have important implications for understanding disorders like Parkinson's disease in which both decision making and timing are impaired

Strong solutions of the thin film equation in spherical geometry

We study existence and long-time behaviour of strong solutions for the thin film equation using a priori estimates in a weighted Sobolev space. This equation can be classified as a doubly degenerate fourth-order parabolic and it models coating flow on the outer surface of a sphere. It is shown that the strong solution asymptotically decays to the flat profile

A descriptive analysis of midwifery education, regulation and association in 73 countries: The baseline for a post-2015 pathway

© 2016 The Author(s). Background: Education, regulation and association (ERA) are the supporting pillars of an enabling environment for midwives to provide quality care. This study explores these three pillars in the 73 low- and middle-income countries who participated in the State of the World's Midwifery (SoWMy) 2014 report. It also examines the progress made since the previous report in 2011. Methods: A self-completion questionnaire collected quantitative and qualitative data on ERA characteristics and organisation in the 73 countries. The countries were grouped according to World Health Organization (WHO) regions. A descriptive analysis was conducted. Results: In 82% of the participating countries, the minimum education level requirement to start midwifery training was grade 12 or above. The average length of training was higher for direct-entry programmes at 3.1 years than for post-nursing/healthcare provider programmes at 1.9 years. The median number of supervised births that must be conducted before graduation was 33 (range 0 to 240). Fewer than half of the countries had legislation recognising midwifery as an independent profession. This legislation was particularly lacking in the Western Pacific and South-East Asia regions. In most (90%) of the participating countries, governments were reported to have a regulatory role, but some reported challenges to the role being performed effectively. Professional associations were widely available to midwives in all regions although not all were exclusive to midwives. Conclusions: Compared with the 2011 SoWMy report, there is evidence of increasing effort in low- and middle-income countries to improve midwifery education, to strengthen the profession and to follow international ERA standards and guidelines. However, not all elements are being implemented equally; some variability persists between and within regions. The education pillar showed more systematic improvement in the type of programme and length of training. The reinforcement of regulation through the development of legislation for midwifery, a recognised definition and the strengthening of midwives' associations would benefit the development of other ERA elements and the profession generally

Potential impact of midwives in preventing and reducing maternal and neonatal mortality and stillbirths: a Lives Saved Tool modelling study.

Background Strengthening the capacity of midwives to deliver high-quality maternal and newborn health services has been highlighted as a priority by global health organisations. To support low-income and middle-income countries (LMICs) in their decisions about investments in health, we aimed to estimate the potential impact of midwives on reducing maternal and neonatal deaths and stillbirths under several intervention coverage scenarios. Methods For this modelling study, we used the Lives Saved Tool to estimate the number of deaths that would be averted by 2035, if coverage of health interventions that can be delivered by professional midwives were scaled up in 88 countries that account for the vast majority of the world's maternal and neonatal deaths and stillbirths. We used four scenarios to assess the effects of increasing the coverage of midwife-delivered interventions by a modest amount (10% every 5 years), a substantial amount (25% every 5 years), and the amount needed to reach universal coverage of these interventions (ie, to 95%); and the effects of coverage attrition (a 2% decrease every 5 years). We grouped countries in three equal-sized groups according to their Human Development Index. Group A included the 30 countries with the lowest HDI, group B included 29 low-to-medium HDI countries, and group C included 29 medium-to-high HDI countries. Findings We estimated that, relative to current coverage, a substantial increase in coverage of midwife-delivered interventions could avert 41% of maternal deaths, 39% of neonatal deaths, and 26% of stillbirths, equating to 2·2 million deaths averted per year by 2035. Even a modest increase in coverage of midwife-delivered interventions could avert 22% of maternal deaths, 23% of neonatal deaths, and 14% of stillbirths, equating to 1·3 million deaths averted per year by 2035. Relative to current coverage, universal coverage of midwife-delivered interventions would avert 67% of maternal deaths, 64% of neonatal deaths, and 65% of stillbirths, allowing 4·3 million lives to be saved annually by 2035. These deaths averted would be particularly concentrated in the group B countries, which currently account for a large proportion of the world's population and have high mortality rates compared with group C. Interpretation Midwives can help to substantially reduce maternal and neonatal mortality and stillbirths in LMICs. However, to realise this potential, midwives need to have skills and competencies in line with recommendations from the International Confederation of Midwives, to be part of a team of sufficient size and skill, and to work in an enabling environment. Our study highlights the potential of midwives but there are many challenges to the achievement of this potential. If increased coverage of midwife-delivered interventions can be achieved, health systems will be better able to provide effective coverage of essential sexual, reproductive, maternal, newborn, and adolescent health interventions

Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains

The formation and propagation of singularities for Boltzmann equation in bounded domains has been an important question in numerical studies as well as in theoretical studies. Consider the nonlinear Boltzmann solution near Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We demonstrate that discontinuity is created at the non-convex part of the grazing boundary, then propagates only along the forward characteristics inside the domain before it hits on the boundary again.Comment: 39 pages, 5 Figure

Existence of weak solutions for the generalized Navier-Stokes equations with damping

In this work we consider the generalized Navier-Stokes equations with the presence of a damping term in the momentum equation. The problem studied here derives from the set of equations which govern isothermal flows of incompressible and homogeneous non-Newtonian fluids. For the generalized Navier-Stokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitz-truncation method. The existence result proved here holds for any and any sigma > 1, where q is the exponent of the diffusion term and sigma is the exponent which characterizes the damping term.MCTES, Portugal [SFRH/BSAB/1058/2010]; FCT, Portugal [PTDC/MAT/110613/2010]info:eu-repo/semantics/publishedVersio

The State of the World's Midwifery 2021 report: findings to drive global policy and practice.

The third global State of the World's Midwifery report (SoWMy 2021) provides an updated evidence base on the sexual, reproductive, maternal, newborn and adolescent health (SRMNAH) workforce. For the first time, SoWMy includes high-income countries (HICs) as well as low- and middle-income countries. This paper describes the similarities and differences between regions and income groups, and discusses the policy implications of these variations. SoWMy 2021 estimates a global shortage of 900,000 midwives, which is particularly acute in low-income countries (LICs) and in Africa. The shortage is projected to improve only slightly by 2030 unless additional investments are made. The evidence suggests that these investments would yield important returns, including: more positive birth experiences, improved health outcomes, and inclusive and equitable economic growth. Most HICs have sufficient SRMNAH workers to meet the need for essential interventions, and their education and regulatory environments tend to be strong. Upper-middle-income countries also tend to have strong policy environments. LICs and lower-middle-income countries tend to have a broader scope of practice for midwives, and many also have midwives in leadership positions within national government. Key regional variations include: major midwife shortages in Africa and South-East Asia but more promising signs of growth in South-East Asia than in Africa; a strong focus in Africa on professional midwives (rather than associate professionals: the norm in many South-East Asian countries); heavy reliance on medical doctors rather than midwives in the Americas and Eastern Mediterranean regions and parts of the Western Pacific; and a strong educational and regulatory environment in Europe but a lack of midwife leaders at national level. SoWMy 2021 provides stakeholders with the latest data and information to inform their efforts to build back better and fairer after COVID-19. This paper provides a number of policy responses to SoWMy 2021 that are tailored to different contexts, and suggests a variety of issues to consider in these contexts. These suggestions are supported by the inclusion of all countries in the report, because it is clear which countries have strong SRMNAH workforces and enabling environments and can be viewed as exemplars within regions and income groups

Timing of singleton births by onset of labour and mode of birth in NHS maternity units in England, 2005-2014: A study of linked birth registration, birth notification, and hospital episode data

BACKGROUND: Maternity care has to be available 24 hours a day, seven days a week. It is known that obstetric intervention can influence the time of birth, but no previous analysis at a national level in England has yet investigated in detail the ways in which the day and time of birth varies by onset of labour and mode of giving birth. METHOD: We linked data from birth registration, birth notification, and Maternity Hospital Episode Statistics and analysed 5,093,615 singleton births in NHS maternity units in England from 2005 to 2014. We used descriptive statistics and negative binomial regression models with harmonic terms to establish how patterns of timing of birth vary by onset of labour, mode of giving birth and gestational age. RESULTS: The timing of birth by time of day and day of the week varies considerably by onset of labour and mode of birth. Spontaneous births after spontaneous onset are more likely to occur between midnight and 6am than at other times of day, and are also slightly more likely on weekdays than at weekends and on public holidays. Elective caesarean births are concentrated onto weekday mornings. Births after induced labours are more likely to occur at hours around midnight on Tuesdays to Saturdays and on days before a public holiday period, than on Sundays, Mondays and during or just after a public holiday. CONCLUSION: The timing of births varies by onset of labour and mode of birth and these patterns have implications for midwifery and medical staffing. Further research is needed to understand the processes behind these findings