Eigenfunctions of the Laplacian and associated Ruelle operator

Let $\Gamma$ be a co-compact Fuchsian group of isometries on the Poincar\'e disk \DD and $\Delta$ the corresponding hyperbolic Laplace operator. Any smooth eigenfunction $f$ of $\Delta$, equivariant by $\Gamma$ with real eigenvalue $\lambda=-s(1-s)$, where $s={1/2}+ it$, admits an integral representation by a distribution \dd_{f,s} (the Helgason distribution) which is equivariant by $\Gamma$ and supported at infinity \partial\DD=\SS^1. The geodesic flow on the compact surface \DD/\Gamma is conjugate to a suspension over a natural extension of a piecewise analytic map T:\SS^1\to\SS^1, the so-called Bowen-Series transformation. Let $\ll_s$ be the complex Ruelle transfer operator associated to the jacobian $-s\ln |T'|$. M. Pollicott showed that \dd_{f,s} is an eigenfunction of the dual operator $\ll_s^*$ for the eigenvalue 1. Here we show the existence of a (nonzero) piecewise real analytic eigenfunction $\psi_{f,s}$ of $\ll_s$ for the eigenvalue 1, given by an integral formula \psi_{f,s} (\xi)=\int \frac{J(\xi,\eta)}{|\xi-\eta|^{2s}} \dd_{f,s} (d\eta), \noindent where $J(\xi,\eta)$ is a $\{0,1\}$-valued piecewise constant function whose definition depends upon the geometry of the Dirichlet fundamental domain representing the surface \DD/\Gamma

European cancer mortality predictions for the year 2019 with focus on breast cancer

Background We predicted cancer mortality figures in the European Union (EU) for the year 2017 using most recent available data, with a focus on lung cancer. Materials and methods We retrieved cancer death certification data and population figures from the World Health Organisation and Eurostat databases. Age-standardized (world standard population) rates were computed for France, Germany, Italy, Poland, Spain, the UK and the EU overall in 1970–2012. We obtained estimates for 2017 by implementing a joinpoint regression model. Results The predicted number of cancer deaths for 2017 in the EU is 1 373 500, compared with 1 333 400 in 2012 (+3%). Cancer mortality rates are predicted to decline in both sexes, reaching 131.8/100 000 men (−8.2% when compared with 2012) and 84.5/100 000 women (−3.6%). Mortality rates for all selected cancer sites are predicted to decline, except pancreatic cancer in both sexes and lung cancer in women. In men, pancreatic cancer rate is stable, in women it increases by 3.5%. Lung cancer mortality rate in women is predicted to rise to 14.6/100 000 in 2017 (+5.1% since 2012, corresponding to 92 300 predicted deaths), compared with 14.0/100 000 for breast cancer, corresponding to 92 600 predicted deaths. Only younger (25–44) women have favourable lung cancer trends, and rates at this age group are predicted to be similar in women (1.4/100 000) and men (1.2/100 000). In men lung cancer rates are predicted to decline by 10.7% since 2012, and falls are observed in all age groups. Conclusion European cancer mortality projections for 2017 confirm the overall downward trend in rates, with a stronger pattern in men. This is mainly due to different smoking prevalence trends in different generations of men and women. Lung cancer rates in young European women are comparable to those in men, confirming that smoking has the same impact on lung cancer in the two sexes

European cancer mortality predictions for the year 2020 with a focus on prostate cancer

Background: Current cancer mortality figures are important for disease management and resource allocation. We estimated mortality counts and rates for 2020 in the European Union (EU) and for its six most populous countries. Materials and methods: We obtained cancer death certification and population data from the World Health Organization and Eurostat databases for 1970-2015. We estimated projections to 2020 for 10 major cancer sites plus all neoplasms and calculated the number of avoided deaths over 1989-2020. Results: Total cancer mortality rates in the EU are predicted to decline reaching 130.1/100 000 men (-5.4% since 2015) and 82.2 in women (-4.1%) in 2020. The predicted number of deaths will increase by 4.7% reaching 1 428 800 in 2020. In women, the upward lung cancer trend is predicted to continue with a rate in 2020 of 15.1/100 000 (higher than that for breast cancer, 13.5) while in men we predicted further falls. Pancreatic cancer rates are also increasing in women (+1.2%) but decreasing in men (-1.9%). In the EU, the prostate cancer predicted rate is 10.0/100 000, declining by 7.1% since 2015; decreases for this neoplasm are 3c8% at age 45-64, 14% at 65-74 and 75-84, and 6% at 85 and over. Poland is the only country with an increasing prostate cancer trend (+18%). Mortality rates for other cancers are predicted to decline further. Over 1989-2020, we estimated over 5 million avoided total cancer deaths and over 400 000 for prostate cancer. Conclusion: Cancer mortality predictions for 2020 in the EU are favourable with a greater decline in men. The number of deaths continue to rise due to population ageing. Due to the persistent amount of predicted lung (and other tobacco-related) cancer deaths, tobacco control remains a public health priority, especially for women. Favourable trends for prostate cancer are largely attributable to continuing therapeutic improvements along with early diagnosis

reply to the letter to the editor european cancer mortality predictions for the year 2019 with focus on breast cancer by malvezzi m et al by marsden and hamoda on behalf of the british menopause society medical advisory council

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Cancer mortality predictions for 2017 in Latin America.

From most recent available data, we predicted cancer mortality statistics in selected Latin American countries for the year 2017, with focus on lung cancer. We obtained death certification data from the World Health Organization and population data from the Pan American Health Organization database for all neoplasms and selected cancer sites. We derived figures for Argentina, Brazil, Chile, Colombia, Cuba, Mexico and Venezuela. Using a logarithmic Poisson count data joinpoint model, we estimated number of deaths and age-standardized (world population) mortality rates in 2017. Total cancer mortality rates are predicted to decline in all countries. The highest mortality rates for 2017 are in Cuba, i.e. 132.3/100 000 men and 93.3/100 000 women. Mexico had the lowest predicted rates, 64.7/100 000 men and 60.6/100 000 women. In contrast, the total number of cancer deaths is expected to rise due to population ageing and growth. Men showed declines in lung cancer trends in all countries and age groups considered, while only Colombian and Mexican women had downward trends. Stomach and (cervix) uteri rates are predicted to continue their declines, though mortality from these neoplasms remains comparatively high. Colorectal, breast and prostate cancer rates were predicted to decline moderately, as well as leukaemias. There was no clear pattern for pancreatic cancer. Between 1990 and 2017 about 420 000 cancer deaths were avoided in 5 of the 7 countries, no progress was observed in Brazil and Cuba. Cancer mortality rates for 2017 in seven selected Latin American countries are predicted to decline, though there was appreciable variability across countries. Mortality from major cancers-including lung and prostate-and all cancers remains comparatively high in Cuba, indicating the need for improved prevention and management

Cancer mortality in the elderly in 11 countries worldwide, 1970-2015

BACKGROUND: Population ageing results in an increasing cancer burden in the elderly. We aimed to evaluate time-trends in cancermortality for adults aged 65 and over for 17 major cancer-types and all cancer combined in 11 countries worldwide over the period 1970-2015. MATERIALS AND METHODS: We obtained cancer death certification and population figures from the WHO and PAHO databases. We computed age-standardized (world standard population) rates for individuals aged 65 and over, and applied joinpoint regression models. RESULTS: Age-standardized mortality rates for all cancers combined showed a heterogeneous, but widespread decline. Lung cancermortality rates have been decreasing among men, and increasing among women. Pancreatic cancer had unfavourable trends in all countriesfor both sexes. Despite variability across countries, other tobacco-related cancers (except kidney) showed overall favourable trends, except in Poland and Russia. Age-standardized mortality from stomach cancer has been declining in all countries for both sexes. Colorectal mortalityhas been declining, except in Poland and Russia. Liver cancer mortality increased in all countries, except in Japan, France and Italy, which had the highest rates in the past. Breast cancer mortality decreased for most countries, except for Japan, Poland and Russia. Trends for age-standardized uterine cancer rates in the USA, Canada and the UK were increasing over the last decade. Ovarian cancer rates showed declines in most countries. With the exception of Russia, prostate cancer rates showed overall declines. Lymphoid neoplasm rates have been declining in both sexes, except in Poland and Russia. CONCLUSION: Over the last decades, age-standardized cancer mortality in the elderly has been decreasing in major countries worldwideand for major cancer sites, with the major exception of lung and uterine cancer in women and liver, pancreas and kidney cancers in both sexes. Cancer mortality for the elderly in Central and Eastern Europe remains comparatively high

Global trends in nasopharyngeal cancer mortality since 1970 and predictions for 2020 : Focus on low-risk areas

Nasopharyngeal cancer (NPC) mortality shows great disparity between endemic high risk areas, where non-keratinizing carcinoma (NKC) histology is prevalent, and non-endemic low risk regions, where the keratinizing squamous cell carcinoma (KSCC) type is more frequent. We used the World Health Organization database to calculate NPC mortality trends from 1970 to 2014 in several countries worldwide. For the European Union (EU), the United States (US) and Japan, we also predicted trends to 2020. In 2012, the highest age-standardized (world standard) rates were in Hong Kong (4.51/100,000 men and 1.15/100,000 women), followed by selected Eastern European countries. The lowest rates were in Northern Europe and Latin America. EU rates were 0.27/100,000 men and 0.09/100,000 women, US rates were 0.20/100,000 men and 0.08/100,000 women and Japanese rates were 0.16/100,000 men and 0.04/100,000 women. NPC mortality trends were favourable for several countries. The decline was 1215% in men and 125% in women between 2002 and 2012 in the EU, 1212% in men and 129% in women in the US and about 1230% in both sexes in Hong Kong and Japan. The favourable patterns in Europe and the United States are predicted to continue. Changes in salted fish and preserved food consumption account for the fall in NKC. Smoking and alcohol prevalence disparities between sexes and geographic areas may explain the different rates and trends observed for KSCC and partially for NKC. Dietary patterns, as well as improvement in management of the disease, may partly account for the observed trends, too

Global estimates of pregnancies at risk of Plasmodium falciparum and Plasmodium vivax infection in 2020 and changes in risk patterns since 2000.

BACKGROUND: Women are at risk of severe adverse pregnancy outcomes attributable to Plasmodium spp. infection in malaria-endemic areas. Malaria control efforts since 2000 have aimed to reduce this burden of disease. METHODS: We used data from the Malaria Atlas Project and WorldPop to calculate global pregnancies at-risk of Plasmodium spp. infection. We categorised pregnancies as occurring in areas of stable and unstable P. falciparum and P. vivax transmission. We further stratified stable endemicity as hypo-endemic, meso-endemic, hyper-endemic, or holo-endemic, and estimated pregnancies at risk in 2000, 2005, 2010, 2015, 2017, and 2020. FINDINGS: In 2020, globally 120.4M pregnancies were at risk of P. falciparum, two-thirds (81.0M, 67.3%) were in areas of stable transmission; 85 2M pregnancies were at risk of P. vivax, 93.9% (80.0M) were in areas of stable transmission. An estimated 64.6M pregnancies were in areas with both P. falciparum and P. vivax transmission. The number of pregnancies at risk of each of P. falciparum and P. vivax worldwide decreased between 2000 and 2020, with the exception of sub-Saharan Africa, where the total number of pregnancies at risk of P. falciparum increased from 37 3M in 2000 to 52 4M in 2020. INTERPRETATION: Historic investments in malaria control have reduced the number of women at risk of malaria in pregnancy in all endemic regions except sub-Saharan Africa. Population growth in Africa has outpaced reductions in malaria prevalence. Interventions that reduce the risk of malaria in pregnancy are needed as much today as ever