2,425 research outputs found
Solution of the symmetric eigenproblem AX=lambda BX by delayed division
Delayed division is an iterative method for solving the linear eigenvalue problem AX = lambda BX for a limited number of small eigenvalues and their corresponding eigenvectors. The distinctive feature of the method is the reduction of the problem to an approximate triangular form by systematically dropping quadratic terms in the eigenvalue lambda. The report describes the pivoting strategy in the reduction and the method for preserving symmetry in submatrices at each reduction step. Along with the approximate triangular reduction, the report extends some techniques used in the method of inverse subspace iteration. Examples are included for problems of varying complexity
The Generalized Ricci Flow for 3D Manifolds with One Killing Vector
We consider 3D flow equations inspired by the renormalization group (RG)
equations of string theory with a three dimensional target space. By modifying
the flow equations to include a U(1) gauge field, and adding carefully chosen
De Turck terms, we are able to extend recent 2D results of Bakas to the case of
a 3D Riemannian metric with one Killing vector. In particular, we show that the
RG flow with De Turck terms can be reduced to two equations: the continual Toda
flow solved by Bakas, plus its linearizaton. We find exact solutions which flow
to homogeneous but not always isotropic geometries
Circles in the Sky: Finding Topology with the Microwave Background Radiation
If the universe is finite and smaller than the distance to the surface of
last scatter, then the signature of the topology of the universe is writ large
on the microwave background sky. We show that the microwave background will be
identified at the intersections of the surface of last scattering as seen by
different ``copies'' of the observer. Since the surface of last scattering is a
two-sphere, these intersections will be circles, regardless of the background
geometry or topology. We therefore propose a statistic that is sensitive to all
small, locally homogeneous topologies. Here, small means that the distance to
the surface of last scatter is smaller than the ``topology scale'' of the
universe.Comment: 14 pages, 10 figures, IOP format. This paper is a direct descendant
of gr-qc/9602039. To appear in a special proceedings issue of Class. Quant.
Grav. covering the Cleveland Topology & Cosmology Worksho
New insight into cataract formation -- enhanced stability through mutual attraction
Small-angle neutron scattering experiments and molecular dynamics simulations
combined with an application of concepts from soft matter physics to complex
protein mixtures provide new insight into the stability of eye lens protein
mixtures. Exploring this colloid-protein analogy we demonstrate that weak
attractions between unlike proteins help to maintain lens transparency in an
extremely sensitive and non-monotonic manner. These results not only represent
an important step towards a better understanding of protein condensation
diseases such as cataract formation, but provide general guidelines for tuning
the stability of colloid mixtures, a topic relevant for soft matter physics and
industrial applications.Comment: 4 pages, 4 figures. Accepted for publication on Phys. Rev. Let
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Radiation exposure awareness from patients undergoing nuclear medicine diagnostic 99mTc-MDP bone scans and 2-deoxy-2-(18F) fluoro-D-glucose PET/computed tomography scans
INTRODUCTION: Medical imaging is on average the largest source of artificial radiation exposure worldwide. This study seeks to understand patient's awareness of radiation exposure derived from nuclear medicine diagnostic scans and assess if current information provided by leaflets is adequate.
METHODS: Single-centre cross-sectional questionnaire study applied to bone scan and FDG PET/computed tomography patients, at a nuclear medicine and PET/computed tomography department over a 15-week period in 2018. Questionnaires on dose comparators were designed in collaboration with patients, public, and experts in radiation exposure. Qualitative data were analysed using thematic analysis and quantitative data using SPSS (V. 24).
RESULTS: A total of 102 questionnaires were completed (bone scan = 50; FDG PET/computed tomography = 52). Across both groups, 33/102 (32.4%) patients reported having a reasonable understanding of nuclear medicine and 21/102 (20.6%) reported a reasonable knowledge of ionising radiations. When asked to compare the exposure dose of respective scans with common comparators 8/50 (16%) of bone scan patients and 11/52 (21.2%) FDG PET/computed tomography answered correctly. On leaflet information, 15/85 (17.6%) patients reported the leaflets do not provide enough information on radiation exposure and of these 10/15 (66.7%) commented the leaflets should incorporate more information on radiation exposure dose.
CONCLUSION: More observational and qualitative studies in collaboration with patients are warranted to evaluate patients' understanding and preferences in communication of radiation exposure from nuclear medicine imaging. This will ensure communication tools and guidelines developed to comply with ionising radiation (medical exposure) regulation 2017 are according to patients needs and preferences
Reconstructing the global topology of the universe from the cosmic microwave background
If the universe is multiply-connected and sufficiently small, then the last
scattering surface wraps around the universe and intersects itself. Each circle
of intersection appears as two distinct circles on the microwave sky. The
present article shows how to use the matched circles to explicitly reconstruct
the global topology of space.Comment: 6 pages, 2 figures, IOP format. To be published in the proceedings of
the Cleveland Cosmology and Topology Workshop 17-19 Oct 1997. Submitted to
Class. Quant. Gra
Holography for the Lorentz Group Racah Coefficients
A known realization of the Lorentz group Racah coefficients is given by an
integral of a product of 6 ``propagators'' over 4 copies of the hyperbolic
space. These are ``bulk-to-bulk'' propagators in that they are functions of two
points in the hyperbolic space. It is known that the bulk-to-bulk propagator
can be constructed out of two bulk-to-boundary ones. We point out that there is
another way to obtain the same object. Namely, one can use two bulk-to-boundary
and one boundary-to-boundary propagator. Starting from this construction and
carrying out the bulk integrals we obtain a realization of the Racah
coefficients that is ``holographic'' in the sense that it only involves
boundary objects. This holographic realization admits a geometric
interpretation in terms of an ``extended'' tetrahedron.Comment: 12 pages, 2 figures; v2: minor changes; v3: "extended" tetrahedron
interpretation adde
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