Browsing by Subject "WEIGHTS"

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  • Orponen, Tuomas (2019)
    Let mu be Radon measures on R, with mu nonatomic and nu doubling, and write mu = mu(a) + mu(s) for the Lebesgue decomposition of mu relative to nu. For an interval I subset of R, define alpha(mu,nu) (I) := W-1 (mu(I), nu(I)), the Wasserstein distance of normalised blow-ups of mu and nu restricted to I. Let S nu be the square function S-nu(2) (mu) = Sigma alpha(2)(mu,nu)(I) chi(1), where D is the family of dyadic intervals of side-length at most 1. I prove that S-nu(mu) is finite mu(a) almost everywhere and infinite mu(s) almost everywhere. I also prove a version of the result for a nondyadic variant of the square function S-nu(mu). The results answer the simplest "n = d = 1" case of a problem of J. Azzam, G. David and T. Toro.
  • Hay, Simon I.; Abajobir, Amanuel Alemu; Abate, Kalkidan Hassen; Abbafati, Cristiana; Abbas, Kaja M.; Abd-Allah, Foad; Abdulle, Abdishakur M.; Abebo, Teshome Abuka; Abera, Semaw Ferede; Aboyans, Victor; Abu-Raddad, Laith J.; Ackerman, Ilana N.; Adedeji, Isaac A.; Adetokunboh, Olatunji; Afshin, Ashkan; Aggarwal, Rakesh; Agrawal, Sutapa; Agrawal, Anurag; Kiadaliri, Aliasghar Ahmad; Ahmed, Muktar Beshir; Aichour, Amani Nidhal; Aichour, Ibtihel; Aichour, Miloud Taki Eddine; Aiyar, Sneha; Akinyemiju, Tomi F.; Akseer, Nadia; Al Lami, Faris Hasan; Alahdab, Fares; Al-Aly, Ziyad; Alam, Khurshid; Alam, Noore; Alam, Tahiya; Alasfoor, Deena; Alene, Kefyalew Addis; Ali, Raghib; Alizadeh-Navaei, Reza; Alkaabi, Juma M.; Alkerwi, Ala'a; Alla, Francois; Allebeck, Peter; Allen, Christine; Al-Maskari, Fatma; AlMazroa, Mohammad AbdulAziz; Al-Raddadi, Rajaa; Alsharif, Ubai; Kivimaki, Mika; Lallukka, Tea; Meretoja, Atte; Meretoja, Tuomo J.; Weiderpass, Elisabete; GBD 2016 DALYs HALE Collaborators (2017)
    Background Measurement of changes in health across locations is useful to compare and contrast changing epidemiological patterns against health system performance and identify specific needs for resource allocation in research, policy development, and programme decision making. Using the Global Burden of Diseases, Injuries, and Risk Factors Study 2016, we drew from two widely used summary measures to monitor such changes in population health: disability-adjusted life-years (DALYs) and healthy life expectancy (HALE). We used these measures to track trends and benchmark progress compared with expected trends on the basis of the Socio-demographic Index (SDI). Methods We used results from the Global Burden of Diseases, Injuries, and Risk Factors Study 2016 for all-cause mortality, cause-specific mortality, and non-fatal disease burden to derive HALE and DALYs by sex for 195 countries and territories from 1990 to 2016. We calculated DALYs by summing years of life lost and years of life lived with disability for each location, age group, sex, and year. We estimated HALE using age-specific death rates and years of life lived with disability per capita. We explored how DALYs and HALE differed from expected trends when compared with the SDI: the geometric mean of income per person, educational attainment in the population older than age 15 years, and total fertility rate. Findings The highest globally observed HALE at birth for both women and men was in Singapore, at 75.2 years (95% uncertainty interval 71.9-78.6) for females and 72.0 years (68.8-75.1) for males. The lowest for females was in the Central African Republic (45.6 years [42.0-49.5]) and for males was in Lesotho (41.5 years [39.0-44.0]). From 1990 to 2016, global HALE increased by an average of 6.24 years (5.97-6.48) for both sexes combined. Global HALE increased by 6.04 years (5.74-6.27) for males and 6.49 years (6.08-6.77) for females, whereas HALE at age 65 years increased by 1.78 years (1.61-1.93) for males and 1.96 years (1.69-2.13) for females. Total global DALYs remained largely unchanged from 1990 to 2016 (-2.3% [-5.9 to 0.9]), with decreases in communicable, maternal, neonatal, and nutritional (CMNN) disease DALYs offset by increased DALYs due to non-communicable diseases (NCDs). The exemplars, calculated as the five lowest ratios of observed to expected age-standardised DALY rates in 2016, were Nicaragua, Costa Rica, the Maldives, Peru, and Israel. The leading three causes of DALYs globally were ischaemic heart disease, cerebrovascular disease, and lower respiratory infections, comprising 16.1% of all DALYs. Total DALYs and age-standardised DALY rates due to most CMNN causes decreased from 1990 to 2016. Conversely, the total DALY burden rose for most NCDs; however, age-standardised DALY rates due to NCDs declined globally. Interpretation At a global level, DALYs and HALE continue to show improvements. At the same time, we observe that many populations are facing growing functional health loss. Rising SDI was associated with increases in cumulative years of life lived with disability and decreases in CMNN DALYs offset by increased NCD DALYs. Relative compression of morbidity highlights the importance of continued health interventions, which has changed in most locations in pace with the gross domestic product per person, education, and family planning. The analysis of DALYs and HALE and their relationship to SDI represents a robust framework with which to benchmark location-specific health performance. Country-specific drivers of disease burden, particularly for causes with higher-than-expected DALYs, should inform health policies, health system improvement initiatives, targeted prevention efforts, and development assistance for health, including financial and research investments for all countries, regardless of their level of sociodemographic development. The presence of countries that substantially outperform others suggests the need for increased scrutiny for proven examples of best practices, which can help to extend gains, whereas the presence of underperforming countries suggests the need for devotion of extra attention to health systems that need more robust support. Copyright (C) The Author(s). Published by Elsevier Ltd. This is an Open Access article under the CC BY 4.0 license.
  • GBD 2017 DALYs & HALE Coll (2018)
    Background How long one lives, how many years of life are spent in good and poor health, and how the population's state of health and leading causes of disability change over time all have implications for policy, planning, and provision of services. We comparatively assessed the patterns and trends of healthy life expectancy (HALE), which quantifies the number of years of life expected to be lived in good health, and the complementary measure of disability-adjusted life years (DALYs), a composite measure of disease burden capturing both premature mortality and prevalence and severity of ill health, for 359 diseases and injuries for 195 countries and territories over the past 28 years. Methods We used data for age-specific mortality rates, years of life lost (YLLs) due to premature mortality, and years lived with disability (YLDs) from the Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2017 to calculate HALE and DALYs from 1990 to 2017. We calculated HALE using age-specific mortality rates and YLDs per capita for each location, age, sex, and year. We calculated DALYs for 359 causes as the sum of YLLs and YLDs. We assessed how observed HALE and DALYs differed by country and sex from expected trends based on Sociodemographic Index (SDI). We also analysed HALE by decomposing years of life gained into years spent in good health and in poor health, between 1990 and 2017, and extra years lived by females compared with males. Findings Globally, from 1990 to 2017, life expectancy at birth increased by 7.4 years (95% uncertainty interval 74-7.8), from 65.6 years (65.3-65- 8) in 1990 to 73.0 years (72.7-73.3) in 2017. The increase in years of life varied from 5.1 years (5.0-5.3) in high SDI countries to 12.0 years (11.3-12.8) in low SDI countries. Of the additional years of life expected at birth, 26.3% (20.1-33.1) were expected to be spent in poor health in high SDI countries compared with 11.7% (8.8-15.1) in low-middle SDI countries. HALE at birth increased by 6.3 years (5.9-6.7), from 57.0 years (54.6-59.1) in 1990 to 63.3 years (60.5-65.7) in 2017. The increase varied from 3.8 years (3.4-4.1) in high SDI countries to 10.5 years (9.8-11.2) in low SDI countries. Even larger variations in HALE than these were observed between countries, ranging from 1.0 year (0.4-1.7) in Saint Vincent and the Grenadines (62.4 years [59.9-64.7] in 1990 to 63.5 years [60.9-65.8] in 2017) to 23.7 years (21.9-25.6) in Eritrea (30.7 years [28.9-32.2] in 1990 to 54.4 years [51.5-57.1] in 2017). In most countries, the increase in HALE was smaller than the increase in overall life expectancy, indicating more years lived in poor health. In 180 of 195 countries and territories, females were expected to live longer than males in 2017, with extra years lived varying from 1.4 years (0.6-2.3) in Algeria to 11.9 years (10.9-12.9) in Ukraine. Of the extra years gained, the proportion spent in poor health varied largely across countries, with less than 20% of additional years spent in poor health in Bosnia and Herzegovina, Burundi, and Slovakia, whereas in Bahrain all the extra years were spent in poor health. In 2017, the highest estimate of HALE at birth was in Singapore for both females (75.8 years [72.4-78.7]) and males (72.6 years [69 " 8-75.0]) and the lowest estimates were in Central African Republic (47.0 years [43.7-50.2] for females and 42.8 years [40.1-45.6] for males). Globally, in 2017, the five leading causes of DALYs were neonatal disorders, ischaemic heart disease, stroke, lower respiratory infections, and chronic obstructive pulmonary disease. Between 1990 and 2017, age-standardised DALY rates decreased by 41.3% (38.8-43.5) for communicable diseases and by 49"8% (47.9-51.6) for neonatal disorders. For non-communicable diseases, global DALYs increased by 40.1% (36.8-43.0), although age-standardised DALY rates decreased by 18.1% (16.0-20.2). Interpretation With increasing life expectancy in most countries, the question of whether the additional years of life gained are spent in good health or poor health has been increasingly relevant because of the potential policy implications, such as health-care provisions and extending retirement ages. In some locations, a large proportion of those additional years are spent in poor health. Large inequalities in HALE and disease burden exist across countries in different SDI quintiles and between sexes. The burden of disabling conditions has serious implications for health system planning and health-related expenditures. Despite the progress made in reducing the burden of communicable diseases and neonatal disorders in low S DI countries, the speed of this progress could be increased by scaling up proven interventions. The global trends among non-communicable diseases indicate that more effort is needed to maximise HALE, such as risk prevention and attention to upstream determinants of health. Copyright (C) 2018 The Author(s). Published by Elsevier Ltd.
  • Holman, Sean; Uhlmann, Gunther (2018)
    We study the microlocal properties of the geodesic X-ray transform X on a manifold with boundary allowing the presence of conjugate points. Assuming that there are no self-intersecting geodesics and all conjugate pairs are nonsingular we show that the normal operator N = X-t o X can be decomposed as the sum of a pseudodifferential operator of order -1 and a sum of Fourier integral operators. We also apply this decomposition to prove inversion of X is only mildly ill-posed when all conjugate points are of order 1, and a certain graph condition is satisfied, in dimension three or higher.
  • Chung, Francis J.; Ola, Petri; Salo, Mikko; Tzou, Leo (2018)
    In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim-Uhlmann and Kenig-Sjostrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system. (C) 2017 Elsevier Masson SAS. All rights reserved.