Spectral analysis on infinite Sierpinski fractafolds

A fractafold, a space that is locally modeled on a specified fractal, is the fractal equivalent of a manifold. For compact fractafolds based on the Sierpinski gasket, it was shown by the first author how to compute the discrete spectrum of the Laplacian in terms of the spectrum of a finite graph Laplacian. A similar problem was solved by the second author for the case of infinite blowups of a Sierpinski gasket, where spectrum is pure point of infinite multiplicity. Both works used the method of spectral decimations to obtain explicit description of the eigenvalues and eigenfunctions. In this paper we combine the ideas from these earlier works to obtain a description of the spectral resolution of the Laplacian for noncompact fractafolds. Our main abstract results enable us to obtain a completely explicit description of the spectral resolution of the fractafold Laplacian. For some specific examples we turn the spectral resolution into a "Plancherel formula". We also present such a formula for the graph Laplacian on the 3-regular tree, which appears to be a new result of independent interest. In the end we discuss periodic fractafolds and fractal fields

Acceptability of evidence-based neonatal care practices in rural Uganda – implications for programming

<p>Abstract</p> <p>Background</p> <p>Although evidence-based interventions to reach the Millennium Development Goals for Maternal and Neonatal mortality reduction exist, they have not yet been operationalised and scaled up in Sub-Saharan African cultural and health systems. A key concern is whether these internationally recommended practices are acceptable and will be demanded by the target community. We explored the acceptability of these interventions in two rural districts of Uganda.</p> <p>Methods</p> <p>We conducted 10 focus group discussions consisting of mothers, fathers, grand parents and child minders (older children who take care of other children). We also did 10 key informant interviews with health workers and traditional birth attendants.</p> <p>Results</p> <p>Most maternal and newborn recommended practices are acceptable to both the community and to health service providers. However, health system and community barriers were prevalent and will need to be overcome for better neonatal outcomes. Pregnant women did not comprehend the importance of attending antenatal care early or more than once unless they felt ill. Women prefer to deliver in health facilities but most do not do so because they cannot afford the cost of drugs and supplies which are demanded in a situation of poverty and limited male support. Postnatal care is non-existent. For the newborn, delayed bathing and putting nothing on the umbilical cord were neither acceptable to parents nor to health providers, requiring negotiation of alternative practices.</p> <p>Conclusion</p> <p>The recommended maternal-newborn practices are generally acceptable to the community and health service providers, but often are not practiced due to health systems and community barriers. Communities associate the need for antenatal care attendance with feeling ill, and postnatal care is non-existent in this region. Health promotion programs to improve newborn care must prioritize postnatal care, and take into account the local socio-cultural situation and health systems barriers including the financial burden. Male involvement and promotion of waiting shelters at selected health units should be considered in order to increase access to supervised deliveries. Scale-up of the evidence based practices for maternal-neonatal health in Sub-Saharan Africa should follow rapid appraisal and adaptation of intervention packages to address the local health system and socio-cultural situation.</p

Socioeconomic and physical distance to the maternity hospital as predictors for place of delivery: an observation study from Nepal

BACKGROUND: Although the debate on the safety and women's right of choice to a home delivery vs. hospital delivery continues in the developed countries, an undesirable outcome of home delivery, such as high maternal and perinatal mortality, is documented in developing countries. The objective was to study whether socio-economic factors, distance to maternity hospital, ethnicity, type and size of family, obstetric history and antenatal care received in present pregnancy affected the choice between home and hospital delivery in a developing country. METHODS: This cross-sectional study was done during June, 2001 to January 2002 in an administratively and geographically well-defined territory with a population of 88,547, stretching from urban to adjacent rural part of Kathmandu and Dhading Districts of Nepal with maximum of 5 hrs of distance from Maternity hospital. There were no intermediate level of private or government hospital or maternity homes in the study area. Interviews were carried out on 308 women who delivered within 45 days of the date of the interview with a pre-tested structured questionnaire. RESULTS: A distance of more than one hour to the maternity hospital (OR = 7.9), low amenity score status (OR = 4.4), low education (OR = 2.9), multi-parity (OR = 2.4), and not seeking antenatal care in the present pregnancy (OR = 4.6) were statistically significantly associated with an increased risk of home delivery. Ethnicity, obstetric history, age of mother, ritual observance of menarche, type and size of family and who is head of household were not statistically significantly associated with the place of delivery. CONCLUSIONS: The socio-economic standing of the household was a stronger predictor of place of delivery compared to ethnicity, the internal family structure such as type and size of family, head of household, or observation of ritual days by the mother of an important event like menarche. The results suggested that mothers, who were in the low-socio-economic scale, delivered at home more frequently in a developing country like Nepal

Can environmental or occupational hazards alter the sex ratio at birth? A systematic review

More than 100 studies have examined whether environmental or occupational exposures of parents affect the sex ratio of their offspring at birth. For this review, we searched Medline and Web of Science using the terms ‘sex ratio at birth’ and ‘sex ratio and exposure’ for all dates, and reviewed bibliographies of relevant studies to find additional articles. This review focuses on exposures that have been the subject of at least four studies including polychlorinated biphenyls (PCBs), dioxins, pesticides, lead and other metals, radiation, boron, and g-forces. For paternal exposures, only dioxins and PCBs were consistently associated with sex ratios higher or lower than the expected 1.06. Dioxins were associated with a decreased proportion of male births, whereas PCBs were associated with an increased proportion of male births. There was limited evidence for a decrease in the proportion of male births after paternal exposure to DBCP, lead, methylmercury, non-ionizing radiation, ionizing radiation treatment for childhood cancer, boron, or g-forces. Few studies have found higher or lower sex ratios associated with maternal exposures. Studies in humans and animals have found a reduction in the number of male births associated with lower male fertility, but the mechanism by which environmental hazards might change the sex ratio has not yet been established

Spherical functions and harmonic analysis on free groups

Let F,, r &gt; 1, be a free group with r generators. In this paper, we study a principal series and a complementary series of irreducible unitary representations of F,, which are defined through the action of F, on its Poisson boundary, relative to a simple random walk. We show that the regular representation of F, can be written as a direct integral of the representations of the principal series and that the resulting harmonic analysis on the free group bears a close resemblance with the harmonic analysis of SL(2, IR)