A realization of the Hecke algebra on the space of period functions for Gamma_0(n)

The standard realization of the Hecke algebra on classical holomorphic cusp forms and the corresponding period polynomials is well known. In this article we consider a nonstandard realization of the Hecke algebra on Maass cusp forms for the Hecke congruence subgroups Gamma_0(n). We show that the vector valued period functions derived recently by Hilgert, Mayer and Movasati as special eigenfunctions of the transfer operator for Gamma_0(n) are indeed related to the Maass cusp forms for these groups. This leads also to a simple interpretation of the ``Hecke like'' operators of these authors in terms of the aforementioned non standard realization of the Hecke algebra on the space of vector valued period functions.Comment: 30 pages; corrected typos and fixed incomplete proofs in section

Cache-Oblivious Persistence

Partial persistence is a general transformation that takes a data structure and allows queries to be executed on any past state of the structure. The cache-oblivious model is the leading model of a modern multi-level memory hierarchy.We present the first general transformation for making cache-oblivious model data structures partially persistent

Hierarchy of the Selberg zeta functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Comment: 14 page

Mirror, Mirror 2017: International Comparison Reflects Flaws and Opportunities for Better U.S. Health Care

ABSTRACTIssue: The United States health care system spends far more than other high-income countries, yet has previously documented gaps in the quality of care.Goal: This report compares health care system performance in Australia, Canada, France, Germany, the Netherlands, New Zealand, Norway, Sweden, Switzerland, the United Kingdom, and the United States.Methods: Seventy-two indicators were selected in five domains: Care Process, Access, Administrative Efficiency, Equity, and Health Care Outcomes. Data sources included Commonwealth Fund international surveys of patients and physicians and selected measures from OECD, WHO, and the European Observatory on Health Systems and Policies. We calculated performance scores for each domain, as well as an overall score for each country.Key findings: The U.S. ranked last on performance overall, and ranked last or near last on the Access, Administrative Efficiency, Equity, and Health Care Outcomes domains. The top-ranked countries overall were the U.K., Australia, and the Netherlands. Based on a broad range of indicators, the U.S. health system is an outlier, spending far more but falling short of the performance achieved by other high-income countries. The results suggest the U.S. health care system should look at other countries' approaches if it wants to achieve an affordable high-performing health care system that serves all Americans

Older Americans Were Sicker and Faced More Financial Barriers to Health Care Than Counterparts in Other Countries

An international survey of older adults finds that seniors in the United States are sicker than their counterparts in 10 other high-income countries and face greater financial barriers to health care, despite the universal coverage that Medicare provides. Across all the countries, few elderly adults discuss mental health concerns with their primary care providers. Moreover, nearly a quarter are considered "high need" — meaning they have three or more chronic conditions or require help with basic tasks of daily living

Monodromy of Cyclic Coverings of the Projective Line

We show that the image of the pure braid group under the monodromy action on the homology of a cyclic covering of degree d of the projective line is an arithmetic group provided the number of branch points is sufficiently large compared to the degree.Comment: 47 pages (to appear in Inventiones Mathematicae

Spectral simplicity and asymptotic separation of variables

We describe a method for comparing the real analytic eigenbranches of two families of quadratic forms that degenerate as t tends to zero. One of the families is assumed to be amenable to `separation of variables' and the other one not. With certain additional assumptions, we show that if the families are asymptotic at first order as t tends to 0, then the generic spectral simplicity of the separable family implies that the eigenbranches of the second family are also generically one-dimensional. As an application, we prove that for the generic triangle (simplex) in Euclidean space (constant curvature space form) each eigenspace of the Laplacian is one-dimensional. We also show that for all but countably many t, the geodesic triangle in the hyperbolic plane with interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure

Association of urinary uromodulin with kidney function decline and mortality: the health ABC study .

BackgroundUrine uromodulin (uUMOD) is a protein secreted by the kidney tubule. Recent studies have suggested that higher uUMOD may be associated with improved kidney and mortality outcomes.MethodsUsing a case-cohort design, we evaluated the association between baseline uUMOD levels and ≥ 30% estimated glomerular filtration rate (eGFR) decline, incident chronic kidney disease (CKD), rapid kidney function decline, and mortality using standard and modified Cox proportional hazards regression.ResultsThe median value of uUMOD was 25.8 µg/mL, mean age of participants was 74 years, 48% were women, and 39% were black. Persons with higher uUMOD had lower prevalence of diabetes and coronary artery disease (CAD), and had lower systolic blood pressure. Persons with higher uUMOD also had higher eGFR, lower urinary albumin to creatinine ratio (ACR), and lower C-reactive protein (CRP). There was no association of uUMOD with > 30% eGFR decline. In comparison to those in the lowest quartile of uUMOD, those in the highest quartile had a significantly (53%) lower risk of incident CKD (CI 73%, 18%) and a 51% lower risk of rapid kidney function decline (CI 76%, 1%) after multivariable adjustment. Higher uUMOD was associated with lower risk of mortality in demographic adjusted models, but not after multivariable adjustment.ConclusionHigher levels of uUMOD are associated with lower risk of incident CKD and rapid kidney function decline. Additional studies are needed in the general population and in persons with advanced CKD to confirm these findings.