830 research outputs found
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
Spectral statistics for quantized skew translations on the torus
We study the spectral statistics for quantized skew translations on the
torus, which are ergodic but not mixing for irrational parameters. It is shown
explicitly that in this case the level--spacing distribution and other common
spectral statistics, like the number variance, do not exist in the
semiclassical limit.Comment: 7 pages. One figure, include
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
Statistical properties of spectral fluctuations for a quantum system with infinitely many components
Extending the idea formulated in Makino {\it{et al}}[Phys.Rev.E
{\bf{67}},066205], that is based on the Berry--Robnik approach [M.V. Berry and
M. Robnik, J. Phys. A {\bf{17}}, 2413], we investigate the statistical
properties of a two-point spectral correlation for a classically integrable
quantum system. The eigenenergy sequence of this system is regarded as a
superposition of infinitely many independent components in the semiclassical
limit. We derive the level number variance (LNV) in the limit of infinitely
many components and discuss its deviations from Poisson statistics. The slope
of the limiting LNV is found to be larger than that of Poisson statistics when
the individual components have a certain accumulation. This property agrees
with the result from the semiclassical periodic-orbit theory that is applied to
a system with degenerate torus actions[D. Biswas, M.Azam,and S.V.Lawande, Phys.
Rev. A {\bf 43}, 5694].Comment: 6 figures, 10 page
Graph Partitioning Induced Phase Transitions
We study the percolation properties of graph partitioning on random regular
graphs with N vertices of degree . Optimal graph partitioning is directly
related to optimal attack and immunization of complex networks. We find that
for any partitioning process (even if non-optimal) that partitions the graph
into equal sized connected components (clusters), the system undergoes a
percolation phase transition at where is the fraction of
edges removed to partition the graph. For optimal partitioning, at the
percolation threshold, we find where is the size of the
clusters and where is their diameter. Additionally,
we find that undergoes multiple non-percolation transitions for
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
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