93,274 research outputs found
Eta invariants with spectral boundary conditions
We study the asymptotics of the heat trace \Tr\{fPe^{-tP^2}\} where is
an operator of Dirac type, where is an auxiliary smooth smearing function
which is used to localize the problem, and where we impose spectral boundary
conditions. Using functorial techniques and special case calculations, the
boundary part of the leading coefficients in the asymptotic expansion is found.Comment: 19 pages, LaTeX, extended Introductio
Universal curvature identities
We study scalar and symmetric 2-form valued universal curvature identities.
We use this to establish the Gauss-Bonnet theorem using heat equation methods,
to give a new proof of a result of Kuz'mina and Labbi concerning the
Euler-Lagrange equations of the Gauss-Bonnet integral, and to give a new
derivation of the Euh-Park-Sekigawa identity.Comment: 11 page
Tensor Minkowski Functionals for random fields on the sphere
We generalize the translation invariant tensor-valued Minkowski Functionals
which are defined on two-dimensional flat space to the unit sphere. We apply
them to level sets of random fields. The contours enclosing boundaries of level
sets of random fields give a spatial distribution of random smooth closed
curves. We obtain analytic expressions for the ensemble expectation values for
the matrix elements of the tensor-valued Minkowski Functionals for isotropic
Gaussian and Rayleigh fields. We elucidate the way in which the elements of the
tensor Minkowski Functionals encode information about the nature and
statistical isotropy (or departure from isotropy) of the field. We then
implement our method to compute the tensor-valued Minkowski Functionals
numerically and demonstrate how they encode statistical anisotropy and
departure from Gaussianity by applying the method to maps of the Galactic
foreground emissions from the PLANCK data.Comment: 1+23 pages, 5 figures, Significantly expanded from version 1. To
appear in JCA
The Solar pp and hep Processes in Effective Field Theory
The strategy of modern effective field theory is exploited to pin down
accurately the flux factors for the and processes in the Sun.
The technique used is to combine the high accuracy established in few-nucleon
systems of the "standard nuclear physics approach" (SNPA) and the systematic
power counting of chiral perturbation theory (ChPT) into a consistent effective
field theory framework. Using highly accurate wave functions obtained in the
SNPA and working to \nlo3 in the chiral counting for the current, we make
totally parameter-free and error-controlled predictions for the and
processes in the Sun.Comment: 5 pages, aipproc macros are included. Talk given at International
Nuclear Physics Conference 2001, Berkeley, California, July 30 - August 3,
200
Paired and altruistic kidney donation in the UK: algorithms and experimentation
We study the computational problem of identifying optimal
sets of kidney exchanges in the UK. We show how to expand an integer
programming-based formulation [1, 19] in order to model the criteria that
constitute the UK definition of optimality. The software arising from this
work has been used by the National Health Service Blood and Transplant
to find optimal sets of kidney exchanges for their National Living Donor
Kidney Sharing Schemes since July 2008.We report on the characteristics
of the solutions that have been obtained in matching runs of the scheme
since this time. We then present empirical results arising from the real
datasets that stem from these matching runs, with the aim of establishing
the extent to which the particular optimality criteria that are present
in the UK influence the structure of the solutions that are ultimately
computed. A key observation is that allowing 4-way exchanges would be
likely to lead to a significant number of additional transplants
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Generalised additive dependency inflated models including aggregated covariates
Let us assume that X, Y and U are observed and that the conditional mean of U given X and Y can be expressed via an additive dependency of X, λ(X)Y and X + Y for some unspecified function . This structured regression model can be transferred to a hazard model or a density model when applied on some appropriate grid, and has important forecasting applications via structured marker dependent hazards models or structured density models including age-period-cohort relationships. The structured regression model is also important when the severity of the dependent variable has a complicated dependency on waiting times X, Y and the total waiting time X+Y . In case the conditional mean of U approximates a density, the regression model can be used to analyse the age-period-cohort model, also when exposure data are not available. In case the conditional mean of U approximates a marker dependent hazard, the regression model introduces new relevant age-period-cohort time scale interdependencies in understanding longevity. A direct use of the regression relationship introduced in this paper is the estimation of the severity of outstanding liabilities in non-life insurance companies. The technical approach taken is to use B-splines to capture the underlying one-dimensional unspecified functions. It is shown via finite sample simulation studies and an application for forecasting future asbestos related deaths in the UK that the B-spline approach works well in practice. Special consideration has been given to ensure identifiability of all models considered
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