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

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo

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

Ionising radiation exposure from medical imaging – A review of Patient's (un) awareness

Introduction: Medical imaging is the main source of artificial radiation exposure. Evidence, however, suggests that patients are poorly informed about radiation exposure when attending diagnostic scans. This review provides an overview of published literature with a focus on nuclear medicine patients on the level of awareness of radiation exposure from diagnostic imaging. Methods: A review of available literature on awareness, knowledge and perception of ionising radiation in medical imaging was conducted. Articles that met the inclusion criteria were subjected to critical appraisal using the Mixed Methods Appraisal Tool. Results: 140 articles identified and screened for eligibility, 24 critically assessed and 4 studies included in synthesis. All studies demonstrated that patients were generally lacking awareness about radiation exposure and highlighted a lack of communication between healthcare professionals and patients with respect to radiation exposure. Conclusion: Studies demonstrate a need to better inform patients about their radiation exposure, and further studies focusing on nuclear medicine patients are particularly warranted. Implications for practice: Adequate and accurate information is crucial to ensure the principle of informed consent is present

Ultrastructure of Spermatozoa From Domesticated Birds: Comparative Study of Turkey, Chicken and Guinea Fowl

Typical for non-passerine birds, the spermatozoa of the turkey, chicken and guinea fowl were vermiform with a maximum width of 0.5-0. 7μm and lengths of 90μm for chicken sperm, and 75-80μm for those of the turkey and guinea. An acrosome, nucleus, midpiece and flagellum could be distinguished by SEM. The acrosomal cap projected over a perforatorium surrounded by granular material. At its base, the cap encircled apical projections of the nucleus. The nucleus consisted of dense chromatin, and formed a concave implantation fossa where it joined the midpiece of the tail. For turkey and chicken spermatozoa, the neck region of the midpiece consisted of a proximal centriole and its pericentriolar processes oriented perpendicularly to an elongated distal centriole, but guinea sperm contained only a single elongated centriole and associated pericentriolar projections. The centrioles plus their projections to the implantation fossa constituted the non-striated connecting piece. The distal centriole served as the precursor of the flagellum and was longest for turkey sperm. Enveloping the distal centriole and extending to the annulus were 25-30 helically arranged mitochondria. Flagellum ultrastructure consisted of the typical 9 + 2 microtubular axonemal complex but outer dense fibers were absent. A hypertonic diluent immobilized the sperm, condensing the flagellar matrix and obliterating the radial links. Variations in ultrastructure of the above structures between sperm of the three species is discussed and compared with sperm ultrastructure from other non-passerine birds

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

Expansive homeomorphisms of the plane

This article tackles the problem of the classification of expansive homeomorphisms of the plane. Necessary and sufficient conditions for a homeomorphism to be conjugate to a linear hyperbolic automorphism will be presented. The techniques involve topological and metric aspects of the plane. The use of a Lyapunov metric function which defines the same topology as the one induced by the usual metric but that, in general, is not equivalent to it is an example of such techniques. The discovery of a hypothesis about the behavior of Lyapunov functions at infinity allows us to generalize some results that are valid in the compact context. Additional local properties allow us to obtain another classification theorem.Comment: 29 pages, 22 figure

Learning SO(3) Equivariant Representations with Spherical CNNs

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.Comment: Camera-ready. Accepted to ECCV'18 as oral presentatio

Comments on Closed Bianchi Models

We show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (A) no anisotropic expansion is allowed for Bianchi type V and VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to show them, we put into geometric terms what is meant by spatial homogeneity and employ a mathematical result on 3-manifolds. We make clear the relation between the Bianchi type symmetry of space-time and spatial compactness, some part of which seem to be unnoticed in the literature. Especially, it is shown under what conditions class B Bianchi models do not possess compact spatial sections. Finally we briefly describe how this study is useful in investigating global dynamics in (3+1)-dimensional gravity.Comment: 14 pages with one table, KUCP-5

Right-veering diffeomorphisms of compact surfaces with boundary II

We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and the monoid of products of positive Dehn twists, with the help of the Rademacher function. We then generalize to the braid group B_n on n strands by relating the signature and the Maslov index. Finally, we discuss the symplectic fillability in the pseudo-Anosov case by comparing with the work of Roberts [Ro1,Ro2].Comment: 25 pages, 5 figure