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)

Multidimensional Quasi-Monte Carlo Malliavin Greeks

We investigate the use of Malliavin calculus in order to calculate the Greeks of multidimensional complex path-dependent options by simulation. For this purpose, we extend the formulas employed by Montero and Kohatsu-Higa to the multidimensional case. The multidimensional setting shows the convenience of the Malliavin Calculus approach over different techniques that have been previously proposed. Indeed, these techniques may be computationally expensive and do not provide flexibility for variance reduction. In contrast, the Malliavin approach exhibits a higher flexibility by providing a class of functions that return the same expected value (the Greek) with different accuracies. This versatility for variance reduction is not possible without the use of the generalized integral by part formula of Malliavin Calculus. In the multidimensional context, we find convenient formulas that permit to improve the localization technique, introduced in Fourni\'e et al and reduce both the computational cost and the variance. Moreover, we show that the parameters employed for variance reduction can be obtained \textit{on the flight} in the simulation. We illustrate the efficiency of the proposed procedures, coupled with the enhanced version of Quasi-Monte Carlo simulations as discussed in Sabino, for the numerical estimation of the Deltas of call, digital Asian-style and Exotic basket options with a fixed and a floating strike price in a multidimensional Black-Scholes market.Comment: 22 pages, 6 figure

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

Quality care during labour and birth: a multi-country analysis of health system bottlenecks and potential solutions

BACKGROUND: Good outcomes during pregnancy and childbirth are related to availability, utilisation and effective implementation of essential interventions for labour and childbirth. The majority of the estimated 289,000 maternal deaths, 2.8 million neonatal deaths and 2.6 million stillbirths every year could be prevented by improving access to and scaling up quality care during labour and birth. METHODS: The bottleneck analysis tool was applied in 12 countries in Africa and Asia as part of the Every Newborn Action Plan process. Country workshops engaged technical experts to complete the survey tool, which is designed to synthesise and grade health system "bottlenecks", factors that hinder the scale up, of maternal-newborn intervention packages. We used quantitative and qualitative methods to analyse the bottleneck data, combined with literature review, to present priority bottlenecks and actions relevant to different health system building blocks for skilled birth attendance and basic and comprehensive emergency obstetric care. RESULTS: Across 12 countries the most critical bottlenecks identified by workshop participants for skilled birth attendance were health financing (10 out of 12 countries) and health workforce (9 out of 12 countries). Health service delivery bottlenecks were found to be the most critical for both basic and comprehensive emergency obstetric care (9 out of 12 countries); health financing was identified as having critical bottlenecks for comprehensive emergency obstetric care (9 out of 12 countries). Solutions to address health financing bottlenecks included strengthening national financing mechanisms and removing financial barriers to care seeking. For addressing health workforce bottlenecks, improved human resource planning is needed, including task shifting and improving training quality. For health service delivery, proposed solutions included improving quality of care and establishing public private partnerships. CONCLUSIONS: Progress towards the 2030 targets for ending preventable maternal and newborn deaths is dependent on improving quality of care during birth and the immediate postnatal period. Strengthening national health systems to improve maternal and newborn health, as a cornerstone of universal health coverage, will only be possible by addressing specific health system bottlenecks during labour and birth, including those within health workforce, health financing and health service delivery

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

Strengthening the emergency healthcare system for mothers and children in The Gambia

A system to improve the management of emergencies during pregnancy, childbirth, infancy and childhood in a region of The Gambia (Brikama) with a population of approximately 250,000 has been developed

Systematic review of effect of community-level interventions to reduce maternal mortality

<p>Abstract</p> <p>Background</p> <p>The objective was to provide a systematic review of the effectiveness of community-level interventions to reduce maternal mortality.</p> <p>Methods</p> <p>We searched published papers using Medline, Embase, Cochrane library, CINAHL, BNI, CAB ABSTRACTS, IBSS, Web of Science, LILACS and African Index Medicus from inception or at least 1982 to June 2006; searched unpublished works using National Research Register website, metaRegister and the WHO International Trial Registry portal. We hand searched major references.</p> <p>Selection criteria were maternity or childbearing age women, comparative study designs with concurrent controls, community-level interventions and maternal death as an outcome. We carried out study selection, data abstraction and quality assessment independently in duplicate.</p> <p>Results</p> <p>We found five cluster randomised controlled trials (RCT) and eight cohort studies of community-level interventions. We summarised results as odds ratios (OR) and confidence intervals (CI), combined using the Peto method for meta-analysis. Two high quality cluster RCTs, aimed at improving perinatal care practices, showed a reduction in maternal mortality reaching statistical significance (OR 0.62, 95% CI 0.39 to 0.98). Three equivalence RCTs of minimal goal-oriented versus usual antenatal care showed no difference in maternal mortality (1.09, 95% CI 0.53 to 2.25). The cohort studies were of low quality and did not contribute further evidence.</p> <p>Conclusion</p> <p>Community-level interventions of improved perinatal care practices can bring about a reduction in maternal mortality. This challenges the view that investment in such interventions is not worthwhile. Programmes to improve maternal mortality should be evaluated using randomised controlled techniques to generate further evidence.</p