The instrumental genesis process in future primary teachers using Dynamic Geometry Software

Science.gov (United States)

Ruiz-López, Natalia

2018-05-01

This paper, which describes a study undertaken with pairs of future primary teachers using GeoGebra software to solve geometry problems, includes a brief literature review, the theoretical framework and methodology used. An analysis of the instrumental genesis process for a pair participating in the case study is also provided. This analysis addresses the techniques and types of dragging used, the obstacles to learning encountered, a description of the interaction between the pair and their interaction with the teacher, and the type of language used. Based on this analysis, possibilities and limitations of the instrumental genesis process are identified for the development of geometric competencies such as conjecture creation, property checking and problem researching. It is also suggested that the methodology used in the analysis of the problem solving process may be useful for those teachers and researchers who want to integrate Dynamic Geometry Software (DGS) in their classrooms.

Geometry and Combinatorics

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2002-01-01

The subject of this Ph.D.-thesis is somewhere in between continuous and discrete geometry. Chapter 2 treats the geometry of finite point sets in semi-Riemannian hyperquadrics,using a matrix whose entries are a trigonometric function of relative distances in a given point set. The distance...... to the geometry of a simplex in a semi-Riemannian hyperquadric. In chapter 3 we study which finite metric spaces that are realizable in a hyperbolic space in the limit where curvature goes to -∞. We show that such spaces are the so called leaf spaces, the set of degree 1 vertices of weighted trees. We also...... establish results on the limiting geometry of such an isometrically realized leaf space simplex in hyperbolic space, when curvature goes to -∞. Chapter 4 discusses negative type of metric spaces. We give a measure theoretic treatment of this concept and related invariants. The theory developed...

Methods of information geometry

CERN Document Server

Amari, Shun-Ichi

2000-01-01

Information geometry provides the mathematical sciences with a new framework of analysis. It has emerged from the investigation of the natural differential geometric structure on manifolds of probability distributions, which consists of a Riemannian metric defined by the Fisher information and a one-parameter family of affine connections called the \\alpha-connections. The duality between the \\alpha-connection and the (-\\alpha)-connection together with the metric play an essential role in this geometry. This kind of duality, having emerged from manifolds of probability distributions, is ubiquitous, appearing in a variety of problems which might have no explicit relation to probability theory. Through the duality, it is possible to analyze various fundamental problems in a unified perspective. The first half of this book is devoted to a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability d...

The Instrumental Genesis Process in Future Primary Teachers Using Dynamic Geometry Software

Science.gov (United States)

Ruiz-López, Natalia

2018-01-01

This paper, which describes a study undertaken with pairs of future primary teachers using GeoGebra software to solve geometry problems, includes a brief literature review, the theoretical framework and methodology used. An analysis of the instrumental genesis process for a pair participating in the case study is also provided. This analysis…

A Metric for Heterotic Moduli

Science.gov (United States)

Candelas, Philip; de la Ossa, Xenia; McOrist, Jock

2017-12-01

Heterotic vacua of string theory are realised, at large radius, by a compact threefold with vanishing first Chern class together with a choice of stable holomorphic vector bundle. These form a wide class of potentially realistic four-dimensional vacua of string theory. Despite all their phenomenological promise, there is little understanding of the metric on the moduli space of these. What is sought is the analogue of special geometry for these vacua. The metric on the moduli space is important in phenomenology as it normalises D-terms and Yukawa couplings. It is also of interest in mathematics, since it generalises the metric, first found by Kobayashi, on the space of gauge field connections, to a more general context. Here we construct this metric, correct to first order in {α^{\\backprime}}, in two ways: first by postulating a metric that is invariant under background gauge transformations of the gauge field, and also by dimensionally reducing heterotic supergravity. These methods agree and the resulting metric is Kähler, as is required by supersymmetry. Checking the metric is Kähler is intricate and the anomaly cancellation equation for the H field plays an essential role. The Kähler potential nevertheless takes a remarkably simple form: it is the Kähler potential of special geometry with the Kähler form replaced by the {α^{\\backprime}}-corrected hermitian form.

A practical exposure-equivalent metric for instrumentation noise in x-ray imaging systems

International Nuclear Information System (INIS)

Yadava, G K; Kuhls-Gilcrist, A T; Rudin, S; Patel, V K; Hoffmann, K R; Bednarek, D R

2008-01-01

The performance of high-sensitivity x-ray imagers may be limited by additive instrumentation noise rather than by quantum noise when operated at the low exposure rates used in fluoroscopic procedures. The equipment-invasive instrumentation noise measures (in terms of electrons) are generally difficult to make and are potentially not as helpful in clinical practice as would be a direct radiological representation of such noise that may be determined in the field. In this work, we define a clinically relevant representation for instrumentation noise in terms of noise-equivalent detector entrance exposure, termed the instrumentation noise-equivalent exposure (INEE), which can be determined through experimental measurements of noise-variance or signal-to-noise ratio (SNR). The INEE was measured for various detectors, thus demonstrating its usefulness in terms of providing information about the effective operating range of the various detectors. A simulation study is presented to demonstrate the robustness of this metric against post-processing, and its dependence on inherent detector blur. These studies suggest that the INEE may be a practical gauge to determine and compare the range of quantum-limited performance for clinical x-ray detectors of different design, with the implication that detector performance at exposures below the INEE will be instrumentation-noise limited rather than quantum-noise limited

Projective geometry and projective metrics

CERN Document Server

Busemann, Herbert

2005-01-01

The basic results and methods of projective and non-Euclidean geometry are indispensable for the geometer, and this book--different in content, methods, and point of view from traditional texts--attempts to emphasize that fact. Results of special theorems are discussed in detail only when they are needed to develop a feeling for the subject or when they illustrate a general method. On the other hand, an unusual amount of space is devoted to the discussion of the fundamental concepts of distance, motion, area, and perpendicularity.Topics include the projective plane, polarities and conic sectio

Optical geometry

International Nuclear Information System (INIS)

Robinson, I.; Trautman, A.

1988-01-01

The geometry of classical physics is Lorentzian; but weaker geometries are often more appropriate: null geodesics and electromagnetic fields, for example, are well known to be objects of conformal geometry. To deal with a single null congruence, or with the radiative electromagnetic fields associated with it, even less is needed: flag geometry for the first, optical geometry, with which this paper is chiefly concerned, for the second. The authors establish a natural one-to-one correspondence between optical geometries, considered locally, and three-dimensional Cauchy-Riemann structures. A number of Lorentzian geometries are shown to be equivalent from the optical point of view. For example the Goedel universe, the Taub-NUT metric and Hauser's twisting null solution have an optical geometry isomorphic to the one underlying the Robinson congruence in Minkowski space. The authors present general results on the problem of lifting a CR structure to a Lorentz manifold and, in particular, to Minkowski space; and exhibit the relevance of the deviation form to this problem

Metric diffusion along foliations

CERN Document Server

Walczak, Szymon M

2017-01-01

Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.

SIMPATIQCO: a server-based software suite which facilitates monitoring the time course of LC-MS performance metrics on Orbitrap instruments.

Science.gov (United States)

Pichler, Peter; Mazanek, Michael; Dusberger, Frederico; Weilnböck, Lisa; Huber, Christian G; Stingl, Christoph; Luider, Theo M; Straube, Werner L; Köcher, Thomas; Mechtler, Karl

2012-11-02

While the performance of liquid chromatography (LC) and mass spectrometry (MS) instrumentation continues to increase, applications such as analyses of complete or near-complete proteomes and quantitative studies require constant and optimal system performance. For this reason, research laboratories and core facilities alike are recommended to implement quality control (QC) measures as part of their routine workflows. Many laboratories perform sporadic quality control checks. However, successive and systematic longitudinal monitoring of system performance would be facilitated by dedicated automatic or semiautomatic software solutions that aid an effortless analysis and display of QC metrics over time. We present the software package SIMPATIQCO (SIMPle AuTomatIc Quality COntrol) designed for evaluation of data from LTQ Orbitrap, Q-Exactive, LTQ FT, and LTQ instruments. A centralized SIMPATIQCO server can process QC data from multiple instruments. The software calculates QC metrics supervising every step of data acquisition from LC and electrospray to MS. For each QC metric the software learns the range indicating adequate system performance from the uploaded data using robust statistics. Results are stored in a database and can be displayed in a comfortable manner from any computer in the laboratory via a web browser. QC data can be monitored for individual LC runs as well as plotted over time. SIMPATIQCO thus assists the longitudinal monitoring of important QC metrics such as peptide elution times, peak widths, intensities, total ion current (TIC) as well as sensitivity, and overall LC-MS system performance; in this way the software also helps identify potential problems. The SIMPATIQCO software package is available free of charge.

Metrical and dynamical aspects in complex analysis

CERN Document Server

2017-01-01

The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.

Goedel-type metrics in various dimensions

International Nuclear Information System (INIS)

Guerses, Metin; Karasu, Atalay; Sarioglu, Oezguer

2005-01-01

Goedel-type metrics are introduced and used in producing charged dust solutions in various dimensions. The key ingredient is a (D - 1)-dimensional Riemannian geometry which is then employed in constructing solutions to the Einstein-Maxwell field equations with a dust distribution in D dimensions. The only essential field equation in the procedure turns out to be the source-free Maxwell's equation in the relevant background. Similarly the geodesics of this type of metric are described by the Lorentz force equation for a charged particle in the lower dimensional geometry. It is explicitly shown with several examples that Goedel-type metrics can be used in obtaining exact solutions to various supergravity theories and in constructing spacetimes that contain both closed timelike and closed null curves and that contain neither of these. Among the solutions that can be established using non-flat backgrounds, such as the Tangherlini metrics in (D - 1)-dimensions, there exists a class which can be interpreted as describing black-hole-type objects in a Goedel-like universe

Jacobi-Maupertuis metric and Kepler equation

Science.gov (United States)

Chanda, Sumanto; Gibbons, Gary William; Guha, Partha

This paper studies the application of the Jacobi-Eisenhart lift, Jacobi metric and Maupertuis transformation to the Kepler system. We start by reviewing fundamentals and the Jacobi metric. Then we study various ways to apply the lift to Kepler-related systems: first as conformal description and Bohlin transformation of Hooke’s oscillator, second in contact geometry and third in Houri’s transformation [T. Houri, Liouville integrability of Hamiltonian systems and spacetime symmetry (2016), www.geocities.jp/football_physician/publication.html], coupled with Milnor’s construction [J. Milnor, On the geometry of the Kepler problem, Am. Math. Mon. 90 (1983) 353-365] with eccentric anomaly.

Flow equation, conformal symmetry, and anti-de Sitter geometry

Science.gov (United States)

Aoki, Sinya; Yokoyama, Shuichi

2018-03-01

We argue that the anti-de Sitter (AdS) geometry in d+1 dimensions naturally emerges from an arbitrary conformal field theory in d dimensions using the free flow equation. We first show that an induced metric defined from the flowed field generally corresponds to the quantum information metric, called the Bures or Helstrom metric, if the flowed field is normalized appropriately. We next verify that the induced metric computed explicitly with the free flow equation always becomes the AdS metric when the theory is conformal. We finally prove that the conformal symmetry in d dimensions converts to the AdS isometry in d+1 dimensions after d-dimensional quantum averaging. This guarantees the emergence of AdS geometry without explicit calculation.

Physical meaning of the optical reference geometry

International Nuclear Information System (INIS)

Abramowicz, M.A.

1990-09-01

I show that contrary to a popular misconception the optical reference geometry, introduced a few years ago as a formally possible metric of a 3-space corresponding to a static spacetime, is quite satisfactory also from the physical point of view. The optical reference geometry has a clear physical meaning, as it may be constructed experimentally by measuring light round travel time between static observers. Distances and directions in the optical reference geometry are more strongly connected to experiment than distances and directions in the widely used directly projected metric (discussed e.g. in Landau and Lifshitz textbook. In addition, the optical reference geometry is more natural and convenient than the directly projected one in application to dynamics. In the optical geometry dynamical behaviour of matter is described by concepts and formulae identical to those well known in Newtonian dynamics on a given two dimensional (curved) surface. (author). 22 refs

Towards Video Quality Metrics Based on Colour Fractal Geometry

Directory of Open Access Journals (Sweden)

Richard Noël

2010-01-01

Full Text Available Vision is a complex process that integrates multiple aspects of an image: spatial frequencies, topology and colour. Unfortunately, so far, all these elements were independently took into consideration for the development of image and video quality metrics, therefore we propose an approach that blends together all of them. Our approach allows for the analysis of the complexity of colour images in the RGB colour space, based on the probabilistic algorithm for calculating the fractal dimension and lacunarity. Given that all the existing fractal approaches are defined only for gray-scale images, we extend them to the colour domain. We show how these two colour fractal features capture the multiple aspects that characterize the degradation of the video signal, based on the hypothesis that the quality degradation perceived by the user is directly proportional to the modification of the fractal complexity. We claim that the two colour fractal measures can objectively assess the quality of the video signal and they can be used as metrics for the user-perceived video quality degradation and we validated them through experimental results obtained for an MPEG-4 video streaming application; finally, the results are compared against the ones given by unanimously-accepted metrics and subjective tests.

Invariance group of the Finster metric function

International Nuclear Information System (INIS)

Asanov, G.S.

1985-01-01

An invariance group of the Finsler metric function is introduced and studied that directly generalized the respective concept (a group of Euclidean rolations) of the Rieman geometry. A sequential description of the isotopic invariance of physical fields on the base of the Finsler geometry is possible in terms of this group

Momentum-space cigar geometry in topological phases

Science.gov (United States)

Palumbo, Giandomenico

2018-01-01

In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.

Information geometry

CERN Document Server

Ay, Nihat; Lê, Hông Vân; Schwachhöfer, Lorenz

2017-01-01

The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, inf...

Torsional heterotic geometries

International Nuclear Information System (INIS)

Becker, Katrin; Sethi, Savdeep

2009-01-01

We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. We propose the existence of a much larger landscape of compact torsional geometries using string duality. Finally, we present some quantum exact metrics that correspond to NS5-branes placed on an elliptic space. These metrics describe how torus isometries are broken by NS flux.

Geometry on the space of geometries

International Nuclear Information System (INIS)

Christodoulakis, T.; Zanelli, J.

1988-06-01

We discuss the geometric structure of the configuration space of pure gravity. This is an infinite dimensional manifold, M, where each point represents one spatial geometry g ij (x). The metric on M is dictated by geometrodynamics, and from it, the Christoffel symbols and Riemann tensor can be found. A ''free geometry'' tracing a geodesic on the manifold describes the time evolution of space in the strong gravity limit. In a regularization previously introduced by the authors, it is found that M does not have the same dimensionality, D, everywhere, and that D is not a scalar, although it is covariantly constant. In this regularization, it is seen that the path integral measure can be absorbed in a renormalization of the cosmological constant. (author). 19 refs

Applications of Affine and Weyl geometry

CERN Document Server

García-Río, Eduardo; Nikcevic, Stana

2013-01-01

Pseudo-Riemannian geometry is, to a large extent, the study of the Levi-Civita connection, which is the unique torsion-free connection compatible with the metric structure. There are, however, other affine connections which arise in different contexts, such as conformal geometry, contact structures, Weyl structures, and almost Hermitian geometry. In this book, we reverse this point of view and instead associate an auxiliary pseudo-Riemannian structure of neutral signature to certain affine connections and use this correspondence to study both geometries. We examine Walker structures, Riemannia

A Lorentzian quantum geometry

Energy Technology Data Exchange (ETDEWEB)

Grotz, Andreas

2011-10-07

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

A Lorentzian quantum geometry

International Nuclear Information System (INIS)

Grotz, Andreas

2011-01-01

In this thesis, a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems is proposed. After giving the general definition of causal fermion systems, we deduce space-time as a topological space with an underlying causal structure. Restricting attention to systems of spin dimension two, we derive the objects of our quantum geometry: the spin space, the tangent space endowed with a Lorentzian metric, connection and curvature. In order to get the correspondence to classical differential geometry, we construct examples of causal fermion systems by regularizing Dirac sea configurations in Minkowski space and on a globally hyperbolic Lorentzian manifold. When removing the regularization, the objects of our quantum geometry reduce to the common objects of spin geometry on Lorentzian manifolds, up to higher order curvature corrections.

Classroom reconstruction of the Schwarzschild metric

OpenAIRE

Kassner, Klaus

2015-01-01

A promising way to introduce general relativity in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on differential geometry in its full glory and permits to emphasize physical aspects before attacking the field equations. Even so, in terms of motivation, lacking justification of the metric employed may pose an obstacle. The paper discusses how to establish the we...

Noncommutative geometry inspired black holes in Rastall gravity

Energy Technology Data Exchange (ETDEWEB)

Ma, Meng-Sen [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China); Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China)

2017-09-15

Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR. (orig.)

Topics in Riemannian geometry

International Nuclear Information System (INIS)

Ezin, J.P.

1988-08-01

The lectures given at the ''5th Symposium of Mathematics in Abidjan: Differential Geometry and Mechanics'' are presented. They are divided into four chapters: Riemannian metric on a differential manifold, curvature tensor fields on a Riemannian manifold, some classical functionals on Riemannian manifolds and questions. 11 refs

Geometry of Theory Space and RG Flows

Science.gov (United States)

Kar, Sayan

The space of couplings of a given theory is the arena of interest in this article. Equipped with a metric ansatz akin to the Fisher information matrix in the space of parameters in statistics (similar metrics in physics are the Zamolodchikov metric or the O'Connor-Stephens metric) we investigate the geometry of theory space through a study of specific examples. We then look into renormalisation group flows in theory space and make an attempt to characterise such flows via its isotropic expansion, rotation and shear. Consequences arising from the evolution equation for the isotropic expansion are discussed. We conclude by pointing out generalisations and pose some open questions.

Relativistic sonic geometry for isothermal accretion in the Kerr metric

Science.gov (United States)

Arif Shaikh, Md

2018-03-01

We linearly perturb advective isothermal transonic accretion onto rotating astrophysical black holes to study the emergence of the relativistic acoustic spacetime and to investigate how the salient features of this spacetime is influenced by the spin angular momentum of the black hole. We have perturbed three different quantities—the velocity potential, the mass accretion rate and the relativistic Bernoulli’s constant to show that the acoustic metric obtained for these three cases are the same up to a conformal factor. By constructing the required causal structures, it has been demonstrated that the acoustic black holes are formed at the transonic points of the flow and the acoustic white holes are formed at the shock location. The corresponding acoustic surface gravity has been computed in terms of the relevant accretion variables and the background metric elements. We have performed a linear stability analysis of the background stationary flow.

Metric reconstruction from Weyl scalars

Energy Technology Data Exchange (ETDEWEB)

Whiting, Bernard F; Price, Larry R [Department of Physics, PO Box 118440, University of Florida, Gainesville, FL 32611 (United States)

2005-08-07

The Kerr geometry has remained an elusive world in which to explore physics and delve into the more esoteric implications of general relativity. Following the discovery, by Kerr in 1963, of the metric for a rotating black hole, the most major advance has been an understanding of its Weyl curvature perturbations based on Teukolsky's discovery of separable wave equations some ten years later. In the current research climate, where experiments across the globe are preparing for the first detection of gravitational waves, a more complete understanding than concerns just the Weyl curvature is now called for. To understand precisely how comparatively small masses move in response to the gravitational waves they emit, a formalism has been developed based on a description of the whole spacetime metric perturbation in the neighbourhood of the emission region. Presently, such a description is not available for the Kerr geometry. While there does exist a prescription for obtaining metric perturbations once curvature perturbations are known, it has become apparent that there are gaps in that formalism which are still waiting to be filled. The most serious gaps include gauge inflexibility, the inability to include sources-which are essential when the emitting masses are considered-and the failure to describe the l = 0 and 1 perturbation properties. Among these latter properties of the perturbed spacetime, arising from a point mass in orbit, are the perturbed mass and axial component of angular momentum, as well as the very elusive Carter constant for non-axial angular momentum. A status report is given on recent work which begins to repair these deficiencies in our current incomplete description of Kerr metric perturbations.

Metric reconstruction from Weyl scalars

International Nuclear Information System (INIS)

Whiting, Bernard F; Price, Larry R

2005-01-01

The Kerr geometry has remained an elusive world in which to explore physics and delve into the more esoteric implications of general relativity. Following the discovery, by Kerr in 1963, of the metric for a rotating black hole, the most major advance has been an understanding of its Weyl curvature perturbations based on Teukolsky's discovery of separable wave equations some ten years later. In the current research climate, where experiments across the globe are preparing for the first detection of gravitational waves, a more complete understanding than concerns just the Weyl curvature is now called for. To understand precisely how comparatively small masses move in response to the gravitational waves they emit, a formalism has been developed based on a description of the whole spacetime metric perturbation in the neighbourhood of the emission region. Presently, such a description is not available for the Kerr geometry. While there does exist a prescription for obtaining metric perturbations once curvature perturbations are known, it has become apparent that there are gaps in that formalism which are still waiting to be filled. The most serious gaps include gauge inflexibility, the inability to include sources-which are essential when the emitting masses are considered-and the failure to describe the l = 0 and 1 perturbation properties. Among these latter properties of the perturbed spacetime, arising from a point mass in orbit, are the perturbed mass and axial component of angular momentum, as well as the very elusive Carter constant for non-axial angular momentum. A status report is given on recent work which begins to repair these deficiencies in our current incomplete description of Kerr metric perturbations

A family of metrics on the moduli space of CP2 instantons

International Nuclear Information System (INIS)

Habermann, L.

1992-01-01

A family of Riemannian metrics on the moduli space of irreducible self-dual connections of instanton number k=1 over CP 2 is considered. We find explicit formulas for these metrics and deduce conclusions concerning the geometry of the instant space. (orig.)

Fluctuating twistor-beam solutions and Pre-Quantum Kerr-Schild geometry

Energy Technology Data Exchange (ETDEWEB)

Burinskii, Alexander, E-mail: bur@ibrae.ac.r [Laboratory of Theoretical Physics, NSI Russian Academy of Sciences, B.Tulskaya 52, Moscow, 115191 (Russian Federation)

2010-04-01

Kerr-Schild (KS) geometry is based on a congruence of twistors which is determined by the Kerr theorem. We describe time-dependent KS solutions for electromagnetic excitations of black-holes taking into account the consistent back-reaction to metric. The exact solutions have the form of singular beam-like pulses supported on twistor null lines of the Kerr congruence. The twistor-beams have very strong back reaction to metric and BH horizon and produce a fluctuating KS geometry which takes an intermediate position between the Classical and Quantum gravity.

Fluctuating twistor-beam solutions and Pre-Quantum Kerr-Schild geometry

International Nuclear Information System (INIS)

Burinskii, Alexander

2010-01-01

Kerr-Schild (KS) geometry is based on a congruence of twistors which is determined by the Kerr theorem. We describe time-dependent KS solutions for electromagnetic excitations of black-holes taking into account the consistent back-reaction to metric. The exact solutions have the form of singular beam-like pulses supported on twistor null lines of the Kerr congruence. The twistor-beams have very strong back reaction to metric and BH horizon and produce a fluctuating KS geometry which takes an intermediate position between the Classical and Quantum gravity.

Non-commutative geometry inspired charged black holes

International Nuclear Information System (INIS)

Ansoldi, Stefano; Nicolini, Piero; Smailagic, Anais; Spallucci, Euro

2007-01-01

We find a new, non-commutative geometry inspired, solution of the coupled Einstein-Maxwell field equations describing a variety of charged, self-gravitating objects, including extremal and non-extremal black holes. The metric smoothly interpolates between de Sitter geometry, at short distance, and Reissner-Nordstrom geometry far away from the origin. Contrary to the ordinary Reissner-Nordstrom spacetime there is no curvature singularity in the origin neither 'naked' nor shielded by horizons. We investigate both Hawking process and pair creation in this new scenario

Code subspaces for LLM geometries

Science.gov (United States)

Berenstein, David; Miller, Alexandra

2018-03-01

We consider effective field theory around classical background geometries with a gauge theory dual, specifically those in the class of LLM geometries. These are dual to half-BPS states of N= 4 SYM. We find that the language of code subspaces is natural for discussing the set of nearby states, which are built by acting with effective fields on these backgrounds. This work extends our previous work by going beyond the strict infinite N limit. We further discuss how one can extract the topology of the state beyond N→∞ and find that, as before, uncertainty and entanglement entropy calculations provide a useful tool to do so. Finally, we discuss obstructions to writing down a globally defined metric operator. We find that the answer depends on the choice of reference state that one starts with. Therefore, within this setup, there is ambiguity in trying to write an operator that describes the metric globally.

Foundations of arithmetic differential geometry

CERN Document Server

Buium, Alexandru

2017-01-01

The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is "intrinsically curved"; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

The Riemannian geometry is not sufficient for the geometrization of the Maxwell's equations

Science.gov (United States)

Kulyabov, Dmitry S.; Korolkova, Anna V.; Velieva, Tatyana R.

2018-04-01

The transformation optics uses geometrized Maxwell's constitutive equations to solve the inverse problem of optics, namely to solve the problem of finding the parameters of the medium along the paths of propagation of the electromagnetic field. For the geometrization of Maxwell's constitutive equations, the quadratic Riemannian geometry is usually used. This is due to the use of the approaches of the general relativity. However, there arises the question of the insufficiency of the Riemannian structure for describing the constitutive tensor of the Maxwell's equations. The authors analyze the structure of the constitutive tensor and correlate it with the structure of the metric tensor of Riemannian geometry. It is concluded that the use of the quadratic metric for the geometrization of Maxwell's equations is insufficient, since the number of components of the metric tensor is less than the number of components of the constitutive tensor. A possible solution to this problem may be a transition to Finslerian geometry, in particular, the use of the Berwald-Moor metric to establish the structural correspondence between the field tensors of the electromagnetic field.

Influence of the geometry of curved artificial canals on the fracture of rotary nickel-titanium instruments subjected to cyclic fatigue tests.

Science.gov (United States)

Lopes, Hélio P; Vieira, Márcia V B; Elias, Carlos N; Gonçalves, Lucio S; Siqueira, José F; Moreira, Edson J L; Vieira, Victor T L; Souza, Letícia C

2013-05-01

This study evaluated the influence of different features of canal curvature geometry on the number of cycles to fracture of a rotary nickel-titanium endodontic instrument subjected to a cyclic fatigue test. BioRaCe BR4C instruments (FKG Dentaire, La Chaux-de Fonds, Switzerland) were tested in 4 grooves simulating curved metallic artificial canals, each one measuring 1.5 mm in width, 20 mm in total length, and 3.5 mm in depth with a U-shaped bottom. The parameters of curvature including the radius and arc lengths and the position of the arc differed in the 4 canal designs. Fractured surfaces and helical shafts of the separated instruments were analyzed by scanning electron microscopy. The Student's t test showed that a significantly lower number of cycles to fracture values were observed for instruments tested in canals with the smallest radius, the longest arc, and the arc located in the middle portion of the canal. Scanning electron microscopic analysis of the fracture surfaces revealed morphologic characteristics of ductile fracture. Plastic deformation was not observed in the helical shaft of the fractured instruments. Curvature geometry including the radius and arc lengths and the position of the arc along the root canal influence the number of cycles to fracture of rotary nickel-titanium instruments subjected to flexural load. Copyright © 2013 American Association of Endodontists. Published by Elsevier Inc. All rights reserved.

Rainbows without unicorns: metric structures in theories with modified dispersion relations

International Nuclear Information System (INIS)

Lobo, Iarley P.; Loret, Niccolo; Nettel, Francisco

2017-01-01

Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations. (orig.)

Rainbows without unicorns: metric structures in theories with modified dispersion relations

Science.gov (United States)

Lobo, Iarley P.; Loret, Niccoló; Nettel, Francisco

2017-07-01

Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations.

Rainbows without unicorns: metric structures in theories with modified dispersion relations

Energy Technology Data Exchange (ETDEWEB)

Lobo, Iarley P. [Universita ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); ICRANet, Pescara (Italy); CAPES Foundation, Ministry of Education of Brazil, Brasilia (Brazil); Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); INFN Sezione Roma 1 (Italy); Loret, Niccolo [Ruder Boskovic Institute, Division of Theoretical Physics, Zagreb (Croatia); Nettel, Francisco [Universita ' ' La Sapienza' ' , Dipartimento di Fisica, Rome (Italy); Universidad Nacional Autonoma de Mexico, Instituto de Ciencias Nucleares, Mexico (Mexico); INFN Sezione Roma 1 (Italy)

2017-07-15

Rainbow metrics are a widely used approach to the metric formalism for theories with modified dispersion relations. They have had a huge success in the quantum gravity phenomenology literature, since they allow one to introduce momentum-dependent space-time metrics into the description of systems with a modified dispersion relation. In this paper, we introduce the reader to some realizations of this general idea: the original rainbow metrics proposal, the momentum-space-inspired metric and a Finsler geometry approach. As the main result of this work we also present an alternative definition of a four-velocity dependent metric which allows one to handle the massless limit. This paper aims to highlight some of their properties and how to properly describe their relativistic realizations. (orig.)

On the Application of Replica Molding Technology for the Indirect Measurement of Surface and Geometry of Micromilled Components

DEFF Research Database (Denmark)

Baruffi, Federico; Parenti, Paolo; Cacciatore, Francesco

2017-01-01

the replica molding technology. The method consists of obtaining a replica of the feature that is inaccessible for standard measurement devices and performing its indirect measurement. This paper examines the performance of a commercial replication media applied to the indirect measurement of micromilled...... components. Two specifically designed micromilled benchmark samples were used to assess the accuracy in replicating both surface texture and geometry. A 3D confocal microscope and a focus variation instrument were employed and the associated uncertainties were evaluated. The replication method proved...... to be suitable for characterizing micromilled surface texture even though an average overestimation in the nano-metric level of the Sa parameter was observed. On the other hand, the replicated geometry generally underestimated that of the master, often leading to a different measurement output considering...

Critique of information geometry

International Nuclear Information System (INIS)

Skilling, John

2014-01-01

As applied to probability, information geometry fails because probability distributions do not form a metric space. Probability theory rests on a compelling foundation of elementary symmetries, which also support information (aka minus entropy, Kullback-Leibler) H(p;q) as the unique measure of divergence from source probability distribution q to destination p. Because the only compatible connective H is from≠to asymmetric, H(p;q)≠H(q;p), there can be no compatible geometrical distance (which would necessarily be from=to symmetric). Hence there is no distance relationship compatible with the structure of probability theory. Metrics g and densities sqrt(det(g)) interpreted as prior probabilities follow from the definition of distance, and must fail likewise. Various metrics and corresponding priors have been proposed, Fisher's being the most popular, but all must behave unacceptably. This is illustrated with simple counter-examples

Guide to Computational Geometry Processing

DEFF Research Database (Denmark)

Bærentzen, Jakob Andreas; Gravesen, Jens; Anton, François

be processed before it is useful. This Guide to Computational Geometry Processing reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. This is balanced with an introduction...... to the theoretical and mathematical underpinnings of each technique, enabling the reader to not only implement a given method, but also to understand the ideas behind it, its limitations and its advantages. Topics and features: Presents an overview of the underlying mathematical theory, covering vector spaces......, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations Reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces Examines techniques for computing curvature from polygonal meshes Describes...

Lectures on discrete geometry

CERN Document Server

2002-01-01

Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...

Bosonization in a two-dimensional Riemann Cartan geometry

International Nuclear Information System (INIS)

Denardo, G.; Spallucci, E.

1987-01-01

We study the vacuum functional for a Dirac field in a two dimensional Riemann-Cartan geometry. Torsion is treated as a quantum variable while the metric is considered as a classical background field. Decoupling spinors from the non-Riemannian part of the geometry introduces a chiral Jacobian into the vacuum generating functional. We compute this functional Jacobian determinant by means of the Alvarez method. Finally, we show that the effective action for the background geometry is of the Liouville type and does not preserve any memory of the initial torsion field. (author)

Donaldson invariants in algebraic geometry

International Nuclear Information System (INIS)

Goettsche, L.

2000-01-01

In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

Weyl-Invariant Extension of the Metric-Affine Gravity

International Nuclear Information System (INIS)

Vazirian, R.; Tanhayi, M. R.; Motahar, Z. A.

2015-01-01

Metric-affine geometry provides a nontrivial extension of the general relativity where the metric and connection are treated as the two independent fundamental quantities in constructing the spacetime (with nonvanishing torsion and nonmetricity). In this paper, we study the generic form of action in this formalism and then construct the Weyl-invariant version of this theory. It is shown that, in Weitzenböck space, the obtained Weyl-invariant action can cover the conformally invariant teleparallel action. Finally, the related field equations are obtained in the general case.

The odd side of torsion geometry

DEFF Research Database (Denmark)

Conti, Diego; Madsen, Thomas Bruun

2014-01-01

We introduce and study a notion of `Sasaki with torsion structure' (ST) as an odd-dimensional analogue of Kähler with torsion geometry (KT). These are normal almost contact metric manifolds that admit a unique compatible connection with 3-form torsion. Any odd-dimensional compact Lie group is sho...

Differential geometry

CERN Document Server

Ciarlet, Philippe G

2007-01-01

This book gives the basic notions of differential geometry, such as the metric tensor, the Riemann curvature tensor, the fundamental forms of a surface, covariant derivatives, and the fundamental theorem of surface theory in a selfcontained and accessible manner. Although the field is often considered a classical one, it has recently been rejuvenated, thanks to the manifold applications where it plays an essential role. The book presents some important applications to shells, such as the theory of linearly and nonlinearly elastic shells, the implementation of numerical methods for shells, and

Classification of digital affine noncommutative geometries

Science.gov (United States)

Majid, Shahn; Pachoł, Anna

2018-03-01

It is known that connected translation invariant n-dimensional noncommutative differentials dxi on the algebra k[x1, …, xn] of polynomials in n-variables over a field k are classified by commutative algebras V on the vector space spanned by the coordinates. These data also apply to construct differentials on the Heisenberg algebra "spacetime" with relations [xμ, xν] = λΘμν, where Θ is an antisymmetric matrix, as well as to Lie algebras with pre-Lie algebra structures. We specialise the general theory to the field k =F2 of two elements, in which case translation invariant metrics (i.e., with constant coefficients) are equivalent to making V a Frobenius algebra. We classify all of these and their quantum Levi-Civita bimodule connections for n = 2, 3, with partial results for n = 4. For n = 2, we find 3 inequivalent differential structures admitting 1, 2, and 3 invariant metrics, respectively. For n = 3, we find 6 differential structures admitting 0, 1, 2, 3, 4, 7 invariant metrics, respectively. We give some examples for n = 4 and general n. Surprisingly, not all our geometries for n ≥ 2 have zero quantum Riemann curvature. Quantum gravity is normally seen as a weighted "sum" over all possible metrics but our results are a step towards a deeper approach in which we must also "sum" over differential structures. Over F2 we construct some of our algebras and associated structures by digital gates, opening up the possibility of "digital geometry."

Some Progress in Conformal Geometry

Directory of Open Access Journals (Sweden)

Sun-Yung A. Chang

2007-12-01

Full Text Available This is a survey paper of our current research on the theory of partial differential equations in conformal geometry. Our intention is to describe some of our current works in a rather brief and expository fashion. We are not giving a comprehensive survey on the subject and references cited here are not intended to be complete. We introduce a bubble tree structure to study the degeneration of a class of Yamabe metrics on Bach flat manifolds satisfying some global conformal bounds on compact manifolds of dimension 4. As applications, we establish a gap theorem, a finiteness theorem for diffeomorphism type for this class, and diameter bound of the $sigma_2$-metrics in a class of conformal 4-manifolds. For conformally compact Einstein metrics we introduce an eigenfunction compactification. As a consequence we obtain some topological constraints in terms of renormalized volumes.

A Novel Riemannian Metric Based on Riemannian Structure and Scaling Information for Fixed Low-Rank Matrix Completion.

Science.gov (United States)

Mao, Shasha; Xiong, Lin; Jiao, Licheng; Feng, Tian; Yeung, Sai-Kit

2017-05-01

Riemannian optimization has been widely used to deal with the fixed low-rank matrix completion problem, and Riemannian metric is a crucial factor of obtaining the search direction in Riemannian optimization. This paper proposes a new Riemannian metric via simultaneously considering the Riemannian geometry structure and the scaling information, which is smoothly varying and invariant along the equivalence class. The proposed metric can make a tradeoff between the Riemannian geometry structure and the scaling information effectively. Essentially, it can be viewed as a generalization of some existing metrics. Based on the proposed Riemanian metric, we also design a Riemannian nonlinear conjugate gradient algorithm, which can efficiently solve the fixed low-rank matrix completion problem. By experimenting on the fixed low-rank matrix completion, collaborative filtering, and image and video recovery, it illustrates that the proposed method is superior to the state-of-the-art methods on the convergence efficiency and the numerical performance.

More on microstate geometries of 4d black holes

International Nuclear Information System (INIS)

Bianchi, M.; Morales, J.F.; Pieri, L.; Zinnato, N.

2017-01-01

We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ 3 . Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.

More on microstate geometries of 4d black holes

Energy Technology Data Exchange (ETDEWEB)

Bianchi, M. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Morales, J.F. [I.N.F.N. - Sezione di Roma 2 and Università di Roma Tor Vergata, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Roma (Italy); Pieri, L. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy); Center for Research in String Theory, School of Physics and Astronomy,Queen Mary University of London, Mile End Road, London, E1 4NS (United Kingdom); Zinnato, N. [Università di Roma Tor Vergata and I.N.F.N, Dipartimento di Fisica,Via della Ricerca Scientifica, I-00133 Rome (Italy)

2017-05-29

We construct explicit examples of microstate geometries of four-dimensional black holes that lift to smooth horizon-free geometries in five dimensions. Solutions consist of half-BPS D-brane atoms distributed in ℝ{sup 3}. Charges and positions of the D-brane centers are constrained by the bubble equations and boundary conditions ensuring the regularity of the metric and the match with the black hole geometry. In the case of three centers, we find that the moduli spaces of solutions includes disjoint one-dimensional components of (generically) finite volume.

Real symplectic formulation of local special geometry

CERN Document Server

Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar

2006-01-01

We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\\mathbf{Sp}(2n,\\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\\frac{\\partial S}{\\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.

Riemannian geometry during the second half of the twentieth century

CERN Document Server

Berger, Marcel

1999-01-01

In the last fifty years of the twentieth century Riemannian geometry has exploded with activity. Berger marks the start of this period with Rauch's pioneering paper of 1951, which contains the first real pinching theorem and an amazing leap in the depth of the connection between geometry and topology. Since then, the field has become so rich that it is almost impossible for the uninitiated to find their way through it. Textbooks on the subject invariably must choose a particular approach, thus narrowing the path. In this book, Berger provides a truly remarkable survey of the main developments in Riemannian geometry in the last fifty years, focusing his main attention on the following five areas: Curvature and topology; the construction of and the classification of space forms; distinguished metrics, especially Einstein metrics; eigenvalues and eigenfunctions of the Laplacian; the study of periodic geodesics and the geodesic flow. Other topics are treated in less detail in a separate section. Berger's survey p...

Geometry in a dynamical system without space: Hyperbolic Geometry in Kuramoto Oscillator Systems

Science.gov (United States)

Engelbrecht, Jan; Chen, Bolun; Mirollo, Renato

Kuramoto oscillator networks have the special property that their time evolution is constrained to lie on 3D orbits of the Möbius group acting on the N-fold torus TN which explains the N - 3 constants of motion discovered by Watanabe and Strogatz. The dynamics for phase models can be further reduced to 2D invariant sets in T N - 1 which have a natural geometry equivalent to the unit disk Δ with hyperbolic metric. We show that the classic Kuramoto model with order parameter Z1 (the first moment of the oscillator configuration) is a gradient flow in this metric with a unique fixed point on each generic 2D invariant set, corresponding to the hyperbolic barycenter of an oscillator configuration. This gradient property makes the dynamics especially easy to analyze. We exhibit several new families of Kuramoto oscillator models which reduce to gradient flows in this metric; some of these have a richer fixed point structure including non-hyperbolic fixed points associated with fixed point bifurcations. Work Supported by NSF DMS 1413020.

Functional integration over geometries

International Nuclear Information System (INIS)

Mottola, E.

1995-01-01

The geometric construction of the functional integral over coset spaces M/G is reviewed. The inner product on the cotangent space of infinitesimal deformations of M defines an invariant distance and volume form, or functional integration measure on the full configuration space. Then, by a simple change of coordinates parameterizing the gauge fiber G, the functional measure on the coset space M/G is deduced. This change of integration variables leads to a Jacobian which is entirely equivalent to the Faddeev--Popov determinant of the more traditional gauge fixed approach in non-abelian gauge theory. If the general construction is applied to the case where G is the group of coordinate reparameterizations of spacetime, the continuum functional integral over geometries, i.e. metrics modulo coordinate reparameterizations may be defined. The invariant functional integration measure is used to derive the trace anomaly and effective action for the conformal part of the metric in two and four dimensional spacetime. In two dimensions this approach generates the Polyakov--Liouville action of closed bosonic non-critical string theory. In four dimensions the corresponding effective action leads to novel conclusions on the importance of quantum effects in gravity in the far infrared, and in particular, a dramatic modification of the classical Einstein theory at cosmological distance scales, signaled first by the quantum instability of classical de Sitter spacetime. Finite volume scaling relations for the functional integral of quantum gravity in two and four dimensions are derived, and comparison with the discretized dynamical triangulation approach to the integration over geometries are discussed. Outstanding unsolved problems in both the continuum definition and the simplicial approach to the functional integral over geometries are highlighted

Electrodynamics and Spacetime Geometry: Foundations

Science.gov (United States)

Cabral, Francisco; Lobo, Francisco S. N.

2017-02-01

We explore the intimate connection between spacetime geometry and electrodynamics. This link is already implicit in the constitutive relations between the field strengths and excitations, which are an essential part of the axiomatic structure of electromagnetism, clearly formulated via integration theory and differential forms. We review the foundations of classical electromagnetism based on charge and magnetic flux conservation, the Lorentz force and the constitutive relations. These relations introduce the conformal part of the metric and allow the study of electrodynamics for specific spacetime geometries. At the foundational level, we discuss the possibility of generalizing the vacuum constitutive relations, by relaxing the fixed conditions of homogeneity and isotropy, and by assuming that the symmetry properties of the electro-vacuum follow the spacetime isometries. The implications of this extension are briefly discussed in the context of the intimate connection between electromagnetism and the geometry (and causal structure) of spacetime.

Geometry of the TJ-II in Astra 6.0

International Nuclear Information System (INIS)

Lopez-Bruna, D.; Romero, J.A.; Castejon, F.

2006-01-01

One of the most exploited features of the TJ-II Heliac, a facility in the Laboratorio Nacional de Fusion (CIEMAT, Madrid), is its ability to explore plasmas in different magnetic configurations. For this reason, there are available libraries that provide the metrics and associated magnitudes for many among all possible configurations. On the other hand, the transport codes that can normally be used to perform transport calculations cannot dea properly with these geometries, which is especially delicate when there are induced plasma currents. In the present work we adopt ASTRA, a transport analysis shell, to study the approximations performed when calculations that impose axi-symmetry (as ASTRA does) are performed on magnetic configurations that are not really axi-symmetric. After describing how we obtain those TJ-II metric averages that must be set in ASTRA, we perform two comparisons: (i) we obtain the vacuum rotational transform as deduced from the metric coefficients but imposing axisymmetry, and compare the results with the rotational transform yielded by the existing libraries; and (ii) we build a ID transport code with TJ-II metrics so its results can be compared with those of ASTRA. In both cases, the differences found indicate that evaluating the evolution of the rotational transform under ohmic induction and transport evolution is acceptable assuming that the geometry itself does not evolve. (Author) 11 refs

Geometry of conics

CERN Document Server

Akopyan, A V

2007-01-01

The book is devoted to the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, the authors move to less trivial results, both classical and contemporary. In particular, the chapter on projective properties of conics contains a detailed analysis of the polar correspondence, pencils of conics, and the Poncelet theorem. In the chapter on metric properties of conics the authors discuss, in particular, inscribed conics, normals to conics, and the Poncelet theorem for confoca

General relativity: An erfc metric

Science.gov (United States)

Plamondon, Réjean

2018-06-01

This paper proposes an erfc potential to incorporate in a symmetric metric. One key feature of this model is that it relies on the existence of an intrinsic physical constant σ, a star-specific proper length that scales all its surroundings. Based thereon, the new metric is used to study the space-time geometry of a static symmetric massive object, as seen from its interior. The analytical solutions to the Einstein equation are presented, highlighting the absence of singularities and discontinuities in such a model. The geodesics are derived in their second- and first-order differential formats. Recalling the slight impact of the new model on the classical general relativity tests in the solar system, a number of facts and open problems are briefly revisited on the basis of a heuristic definition of σ. A special attention is given to gravitational collapses and non-singular black holes.

Applanation optical coherence elastography: noncontact measurement of intraocular pressure, corneal biomechanical properties, and corneal geometry with a single instrument

Science.gov (United States)

Singh, Manmohan; Han, Zhaolong; Nair, Achuth; Schill, Alexander; Twa, Michael D.; Larin, Kirill V.

2017-02-01

Current clinical tools provide critical information about ocular health such as intraocular pressure (IOP). However, they lack the ability to quantify tissue material properties, which are potent markers for ocular tissue health and integrity. We describe a single instrument to measure the eye-globe IOP, quantify corneal biomechanical properties, and measure corneal geometry with a technique termed applanation optical coherence elastography (Appl-OCE). An ultrafast OCT system enabled visualization of corneal dynamics during noncontact applanation tonometry and direct measurement of micro air-pulse induced elastic wave propagation. Our preliminary results show that the proposed Appl-OCE system can be used to quantify IOP, corneal biomechanical properties, and corneal geometry, which builds a solid foundation for a unique device that can provide a more complete picture of ocular health.

Theory of liquid crystal elastomers and polymer networks : Connection between neoclassical theory and differential geometry.

Science.gov (United States)

Nguyen, Thanh-Son; Selinger, Jonathan V

2017-09-01

In liquid crystal elastomers and polymer networks, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymers. Previous theoretical research has described these materials through two different approaches: a neoclassical theory based on the liquid crystal director and the deformation gradient tensor, and a geometric elasticity theory based on the difference between the actual metric tensor and a reference metric. Here, we connect those two approaches using a formalism based on differential geometry. Through this connection, we determine how both the director and the geometry respond to a change of temperature.

A Practitioners’ Perspective on Developmental Models, Metrics and Community

Directory of Open Access Journals (Sweden)

Chad Stewart

2009-12-01

Full Text Available This article builds on a paper by Stein and Heikkinen (2009, and suggestsways to expand and improve our measurement of the quality of the developmentalmodels, metrics and instruments and the results we get in collaborating with clients. Wesuggest that this dialogue needs to be about more than stage development measured by(even calibrated stage development-focused, linguistic-based, developmental psychologymetrics that produce lead indicators and are shown to be reliable and valid bypsychometric qualities alone. The article first provides a brief overview of ourbackground and biases, and an applied version of Ken Wilber’s Integral OperatingSystem that has provided increased development, client satisfaction, and contribution toour communities measured by verifiable, tangible results (as well as intangible resultssuch as increased ability to cope with complex surroundings, reduced stress and growthin developmental stages to better fit to the environment in which our clients wereengaged at that time. It then addresses four key points raised by Stein and Heikkinen(need for quality control, defining and deciding on appropriate metrics, building a systemto evaluate models and metrics, and clarifying and increasing the reliability and validityof the models and metrics we use by providing initial concrete steps to:• Adopt a systemic value-chain approach• Measure results in addition to language• Build on the evaluation system for instruments, models and metrics suggested byStein & Heikkinen• Clarify and improve the reliability and validity of the instruments, models andmetrics we useWe complete the article with an echoing call for the community of AppliedDevelopmental Theory suggested by Ross (2008 and Stein and Heikkinen, a briefdescription of that community (from our perspective, and a table that builds on Table 2proposed by Stein and Heikkinen.

Euclidean geometry and its subgeometries

CERN Document Server

Specht, Edward John; Calkins, Keith G; Rhoads, Donald H

2015-01-01

In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of the...

Thin shells joining local cosmic string geometries

Energy Technology Data Exchange (ETDEWEB)

Eiroa, Ernesto F. [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Rubin de Celis, Emilio; Simeone, Claudio [Universidad de Buenos Aires, Ciudad Universitaria Pabellon I, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina); Ciudad Universitaria Pabellon I, IFIBA-CONICET, Buenos Aires (Argentina)

2016-10-15

In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)

Thin shells joining local cosmic string geometries

International Nuclear Information System (INIS)

Eiroa, Ernesto F.; Rubin de Celis, Emilio; Simeone, Claudio

2016-01-01

In this article we present a theoretical construction of spacetimes with a thin shell that joins two different local cosmic string geometries. We study two types of global manifolds, one representing spacetimes with a thin shell surrounding a cosmic string or an empty region with Minkowski metric, and the other corresponding to wormholes which are not symmetric across the throat located at the shell. We analyze the stability of the static configurations under perturbations preserving the cylindrical symmetry. For both types of geometries we find that the static configurations can be stable for suitable values of the parameters. (orig.)

A new perspective on relativity an odyssey in non-Euclidean geometries

CERN Document Server

Lavenda, Bernard H

2012-01-01

Starting off from noneuclidean geometries, apart from the method of Einstein's equations, this book derives and describes the phenomena of gravitation and diffraction. A historical account is presented, exposing the missing link in Einstein's construction of the theory of general relativity: the uniformly rotating disc, together with his failure to realize, that the Beltrami metric of hyperbolic geometry with constant curvature describes exactly the uniform acceleration observed.

Effect of canal preparation with TRUShape and Vortex rotary instruments on three-dimensional geometry of oval root canals.

Science.gov (United States)

Arias, Ana; Paqué, Frank; Shyn, Stephanie; Murphy, Sarah; Peters, Ove A

2018-04-01

The purpose of this study was to assess the geometry of non-round root canals after preparation with TRUShape (a novel instrument with s-shaped longitudinal design) in comparison to conventional rotary instrumentation using micro-computed tomography. Twenty distal root canals of mandibular molars were randomly distributed in two groups to be shaped with either TRUShape or Vortex rotaries. Percentages of unprepared surface and volume of dentin removal for the entire canal and for the apical 4 mm were calculated. Canal transportation and the structure model index (SMI) were assessed. Data were compared with Student t-tests. Shaping with both techniques resulted in similar prepared surface and volume of dentin removed, as well as the extent of canal transportation. The SMI shape factor was significantly lower for TRUShape preparations (P = 0.04) suggesting less rounding during rotary preparation. Although both instruments were suitable for the preparation of oval canals, TRUShape appeared to better conform to the original ribbon-shaped anatomy. © 2017 Australian Society of Endodontology Inc.

Metric freeness and projectivity for classical and quantum normed modules

Energy Technology Data Exchange (ETDEWEB)

Helemskii, A Ya [M. V. Lomonosov Moscow State University, Moscow (Russian Federation)

2013-07-31

In functional analysis, there are several diverse approaches to the notion of projective module. We show that a certain general categorical scheme contains all basic versions as special cases. In this scheme, the notion of free object comes to the foreground, and, in the best categories, projective objects are precisely retracts of free ones. We are especially interested in the so-called metric version of projectivity and characterize the metrically free classical and quantum (= operator) normed modules. Informally speaking, so-called extremal projectivity, which was known earlier, is interpreted as a kind of 'asymptotical metric projectivity'. In addition, we answer the following specific question in the geometry of normed spaces: what is the structure of metrically projective modules in the simplest case of normed spaces? We prove that metrically projective normed spaces are precisely the subspaces of l{sub 1}(M) (where M is a set) that are denoted by l{sub 1}{sup 0}(M) and consist of finitely supported functions. Thus, in this case, projectivity coincides with freeness. Bibliography: 28 titles.

Cosmological implications of modified gravity induced by quantum metric fluctuations

Energy Technology Data Exchange (ETDEWEB)

Liu, Xing [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, Yat Sen School, Guangzhou (China); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Liang, Shi-Dong [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics, Guangzhou (China)

2016-08-15

We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors. (orig.)

Predicting a contact's sensitivity to initial conditions using metrics of frictional coupling

International Nuclear Information System (INIS)

Flicek, Robert C.; Hills, David A.; Brake, Matthew Robert W.

2016-01-01

This paper presents a method for predicting how sensitive a frictional contact’s steady-state behavior is to its initial conditions. Previous research has proven that if a contact is uncoupled, i.e. if slip displacements do not influence the contact pressure distribution, then its steady-state response is independent of initial conditions, but if the contact is coupled, the steady-state response depends on initial conditions. In this paper, two metrics for quantifying coupling in discrete frictional systems are examined. These metrics suggest that coupling is dominated by material dissimilarity due to Dundurs’ composite material parameter β when β ≥ 0.2, but geometric mismatch becomes the dominant source of coupling for smaller values of β. Based on a large set of numerical simulations with different contact geometries, material combinations, and friction coefficients, a contact’s sensitivity to initial conditions is found to be correlated with the product of the coupling metric and the friction coefficient. For cyclic shear loading, this correlation is maintained for simulations with different contact geometries, material combinations, and friction coefficients. Furthermore, for cyclic bulk loading, the correlation is only maintained when the contact edge angle is held constant.

Singular value decomposition metrics show limitations of detector design in diffuse fluorescence tomography.

Science.gov (United States)

Leblond, Frederic; Tichauer, Kenneth M; Pogue, Brian W

2010-11-29

The spatial resolution and recovered contrast of images reconstructed from diffuse fluorescence tomography data are limited by the high scattering properties of light propagation in biological tissue. As a result, the image reconstruction process can be exceedingly vulnerable to inaccurate prior knowledge of tissue optical properties and stochastic noise. In light of these limitations, the optimal source-detector geometry for a fluorescence tomography system is non-trivial, requiring analytical methods to guide design. Analysis of the singular value decomposition of the matrix to be inverted for image reconstruction is one potential approach, providing key quantitative metrics, such as singular image mode spatial resolution and singular data mode frequency as a function of singular mode. In the present study, these metrics are used to analyze the effects of different sources of noise and model errors as related to image quality in the form of spatial resolution and contrast recovery. The image quality is demonstrated to be inherently noise-limited even when detection geometries were increased in complexity to allow maximal tissue sampling, suggesting that detection noise characteristics outweigh detection geometry for achieving optimal reconstructions.

Aspects of differential geometry II

CERN Document Server

Gilkey, Peter

2015-01-01

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment. Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given. In Chapter 6, Lie groups and Lie algebras are dealt with. The exponential map, the classical groups, and geodesics in the context of a bi-invariant metric are discussed. The de Rham cohomology of compact Lie groups an...

Software metrics: The key to quality software on the NCC project

Science.gov (United States)

Burns, Patricia J.

1993-01-01

Network Control Center (NCC) Project metrics are captured during the implementation and testing phases of the NCCDS software development lifecycle. The metrics data collection and reporting function has interfaces with all elements of the NCC project. Close collaboration with all project elements has resulted in the development of a defined and repeatable set of metrics processes. The resulting data are used to plan and monitor release activities on a weekly basis. The use of graphical outputs facilitates the interpretation of progress and status. The successful application of metrics throughout the NCC project has been instrumental in the delivery of quality software. The use of metrics on the NCC Project supports the needs of the technical and managerial staff. This paper describes the project, the functions supported by metrics, the data that are collected and reported, how the data are used, and the improvements in the quality of deliverable software since the metrics processes and products have been in use.

Probability of stochastic processes and spacetime geometry

International Nuclear Information System (INIS)

Canessa, E.

2007-01-01

We made a first attempt to associate a probabilistic description of stochastic processes like birth-death processes with spacetime geometry in the Schwarzschild metrics on distance scales from the macro- to the micro-domains. We idealize an ergodic system in which system states communicate through a curved path composed of transition arrows where each arrow corresponds to a positive, analogous birth or death rate. (author)

Current capabilities of transient two-phase flow instruments

International Nuclear Information System (INIS)

Solbrig, C.W.; Kondic, N.N.

1979-01-01

The measurement of two phase flow phenomena in transient conditions representative of a Loss-of-Coolant Accident requires the use of sophisticated instruments and the further development of other instruments. Measurements made in large size pipes are often flow regime dependent. The flow regimes encountered depend upon the system geometry, transient effects, heat transfer, etc. The geometries in which these measurements must be made, the instruments which are currently used, new instruments being developed, the facilities used to calibrate these instruments, and the improvements which must be made to measurement capabilities are described

77 FR 66848 - Minimum Clinically Important Difference: An Outcome Metric in Orthopaedic Device Science and...

Science.gov (United States)

2012-11-07

...] Minimum Clinically Important Difference: An Outcome Metric in Orthopaedic Device Science and Regulation... Clinically Important Difference: An Outcome Metric in Orthopaedic Device Science and Regulation.'' FDA is co... (MCID) for patient-reported outcome (PRO) instruments used in orthopaedic extremity device-related...

A new approach for gravity localization in six-dimensional geometries

International Nuclear Information System (INIS)

Santos, Victor Pereira do Nascimento; Almeida, Carlos Alberto Santos de

2011-01-01

Full text: The idea that spacetime may have more than four dimensions is old, originally presented as an attempt to unify Maxwell's theory of Electromagnetism with the brand-new gravitation theory of Einstein. Such extra dimensions are in principle unobservable to the energy scales currently available. However, its effects can be seen in short distance gravity experiments and in observations in cosmology. Also, it is used as a mechanism to explain the difference between the energy scales of the weak force and gravity, which is called the hierarchy problem. The current framework for the extra dimension scenario is consider the four-dimensional known universe as embedded in a higher dimensional space called bulk. The form of this bulk determines how we perceive gravity in our universe; then, the behaviour of gravitational field depends on the geometry of the bulk. Metric solutions were already presented for string-like defect, with and without matter sources, where was shown that the gravity Newtonian potential grows with the inverse cube of distance. Such correction arises from a very particular mass spectrum for the gravitational field, which already contains the orbital angular momentum contributions. In this work we study the behaviour of gravitational field in a extra-dimensional braneworld scenario, using non-factorizable geometries (which preserves Poincare symmetry) and setting suitable matter distributions in order to verify its localization, for several geometries. For such geometries it is possible to find explicit solutions for the tensor fluctuations of the metric. (author)

Conformal, Riemannian and Lagrangian geometry the 2000 Barrett lectures

CERN Document Server

Chang, Sun-Yung A; Grove, Karsten; Yang, Paul C; Freire, Alexandre

2002-01-01

Recent developments in topology and analysis have led to the creation of new lines of investigation in differential geometry. The 2000 Barrett Lectures present the background, context and main techniques of three such lines by means of surveys by leading researchers. The first chapter (by Alice Chang and Paul Yang) introduces new classes of conformal geometric invariants, and then applies powerful techniques in nonlinear differential equations to derive results on compactifications of manifolds and on Yamabe-type variational problems for these invariants. This is followed by Karsten Grove's lectures, which focus on the use of isometric group actions and metric geometry techniques to understand new examples and classification results in Riemannian geometry, especially in connection with positive curvature. The chapter written by Jon Wolfson introduces the emerging field of Lagrangian variational problems, which blends in novel ways the structures of symplectic geometry and the techniques of the modern calculus...

Observations on the Darboux coordinates for rigid special geometry

CERN Document Server

Ferrara, Sergio; Ferrara, Sergio; Macia, Oscar

2006-01-01

We exploit some relations which exist when (rigid) special geometry is formulated in real symplectic special coordinates $P^I=(p^\\Lambda,q_\\Lambda), I=1,...,2n$. The central role of the real $2n\\times 2n$ matrix $M(\\Re \\mathcal{F},\\Im \\mathcal{F})$, where $\\mathcal{F} = \\partial_\\Lambda\\partial_\\Sigma F$ and $F$ is the holomorphic prepotential, is elucidated in the real formalism. The property $M\\Omega M=\\Omega$ with $\\Omega$ being the invariant symplectic form is used to prove several identities in the Darboux formulation. In this setting the matrix $M$ coincides with the (negative of the) Hessian matrix $H(S)=\\frac{\\partial^2 S}{\\partial P^I\\partial P^J}$ of a certain hamiltonian real function $S(P)$, which also provides the metric of the special K\\"ahler manifold. When $S(P)=S(U+\\bar U)$ is regarded as a "K\\"ahler potential'' of a complex manifold with coordinates $U^I=\\frac12(P^I+iZ^I)$, then it provides a K\\"ahler metric of an hyperk\\"ahler manifold which describes the hypermultiplet geometry obtained by...

Open Problem: Kernel methods on manifolds and metric spaces

DEFF Research Database (Denmark)

Feragen, Aasa; Hauberg, Søren

2016-01-01

Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong...... linear properties. This negative result hints that radial kernel are perhaps not suitable over geodesic metric spaces after all. Here, however, we present evidence that large intervals of bandwidths exist where geodesic exponential kernels have high probability of being positive definite over finite...... datasets, while still having significant predictive power. From this we formulate conjectures on the probability of a positive definite kernel matrix for a finite random sample, depending on the geometry of the data space and the spread of the sample....

Weyl metrics and wormholes

Energy Technology Data Exchange (ETDEWEB)

Gibbons, Gary W. [DAMTP, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA U.K. (United Kingdom); Volkov, Mikhail S., E-mail: gwg1@cam.ac.uk, E-mail: volkov@lmpt.univ-tours.fr [Laboratoire de Mathématiques et Physique Théorique, LMPT CNRS—UMR 7350, Université de Tours, Parc de Grandmont, Tours, 37200 France (France)

2017-05-01

We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.

Finsler geometry, relativity and gauge theories

International Nuclear Information System (INIS)

Asanov, G.S.

1985-01-01

This book provides a self-contained account of the Finslerian techniques which aim to synthesize the ideas of Finslerian metrical generalization of Riemannian geometry to merge with the primary physical concepts of general relativity and gauge field theories. The geometrization of internal symmetries in terms of Finslerian geometry, as well as the formulation of Finslerian generalization of gravitational field equations and equations of motion of matter, are two key points used to expound the techniques. The Clebsch representation of the canonical momentum field is used to formulate the Hamilton-Jacobi theory for homogeneous Lagrangians of classical mechanics. As an auxillary mathematical apparatus, the author uses invariance identities which systematically reflect the covariant properties of geometrical objects. The results of recent studies of special Finsler spaces are also applied. The book adds substantially to the mathematical monographs by Rund (1959) and Rund and Bear (1972), all basic results of the latter being reflected. It is the author's hope that thorough exploration of the materrial presented will tempt the reader to revise the habitual physical concepts supported conventionally by Riemannian geometry. (Auth.)

Unified tractable model for downlink MIMO cellular networks using stochastic geometry

KAUST Repository

Afify, Laila H.

2016-07-26

Several research efforts are invested to develop stochastic geometry models for cellular networks with multiple antenna transmission and reception (MIMO). On one hand, there are models that target abstract outage probability and ergodic rate for simplicity. On the other hand, there are models that sacrifice simplicity to target more tangible performance metrics such as the error probability. Both types of models are completely disjoint in terms of the analytic steps to obtain the performance measures, which makes it challenging to conduct studies that account for different performance metrics. This paper unifies both techniques and proposes a unified stochastic-geometry based mathematical paradigm to account for error probability, outage probability, and ergodic rates in MIMO cellular networks. The proposed model is also unified in terms of the antenna configurations and leads to simpler error probability analysis compared to existing state-of-the-art models. The core part of the analysis is based on abstracting unnecessary information conveyed within the interfering signals by assuming Gaussian signaling. To this end, the accuracy of the proposed framework is verified against state-of-the-art models as well as system level simulations. We provide via this unified study insights on network design by reflecting system parameters effect on different performance metrics. © 2016 IEEE.

Geometry and analysis on manifolds in memory of professor Shoshichi Kobayashi

CERN Document Server

Mabuchi, Toshiki; Maeda, Yoshiaki; Noguchi, Junjiro; Weinstein, Alan

2015-01-01

This volume is dedicated to the memory of Shoshichi Kobayashi, and gathers contributions from distinguished researchers working on topics close to his research areas. The book is organized into three parts, with the first part presenting an overview of Professor Shoshichi Kobayashi’s career. This is followed by two expository course lectures (the second part) on recent topics in extremal Kähler metrics and value distribution theory, which will be helpful for graduate students in mathematics interested in new topics in complex geometry and complex analysis. Lastly, the third part of the volume collects authoritative research papers on differential geometry and complex analysis. Professor Shoshichi Kobayashi was a recognized international leader in the areas of differential and complex geometry. He contributed crucial ideas that are still considered fundamental in these fields. The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables ...

Compactifications of deformed conifolds, branes and the geometry of qubits

Energy Technology Data Exchange (ETDEWEB)

Cvetič, M. [Department of Physics and Astronomy,University of Pennsylvania, Philadelphia, PA 19104 (United States); Center for Applied Mathematics and Theoretical Physics,University of Maribor, SI2000 Maribor (Slovenia); Gibbons, G.W. [Department of Physics and Astronomy,University of Pennsylvania, Philadelphia, PA 19104 (United States); DAMTP, Centre for Mathematical Sciences,Cambridge University, Wilberforce Road, Cambridge CB3 OWA (United Kingdom); Laboratoire de Mathématiques et Physique Théorique CNRS-UMR 7350,Fédération Denis Poisson, Université François-Rabelais Tours,Parc de Grandmont, 37200 Tours (France); LE STUDIUM, Loire Valley Institute for Advanced Studies,Tours and Orleans (France); Pope, C.N. [DAMTP, Centre for Mathematical Sciences,Cambridge University, Wilberforce Road, Cambridge CB3 OWA (United Kingdom); George P. & Cynthia W. Mitchell Institute for Fundamental Physics and Astronomy,Texas A& M University, College Station, TX 77843-4242 (United States)

2016-01-22

We present three families of exact, cohomogeneity-one Einstein metrics in (2n+2) dimensions, which are generalizations of the Stenzel construction of Ricci-flat metrics to those with a positive cosmological constant. The first family of solutions are Fubini-Study metrics on the complex projective spaces ℂℙ{sup n+1}, written in a Stenzel form, whose principal orbits are the Stiefel manifolds V{sub 2}(ℝ{sup n+2})=SO(n+2)/SO(n) divided by ℤ{sub 2}. The second family are also Einstein-Kähler metrics, now on the Grassmannian manifolds G{sub 2}(ℝ{sup n+3})=SO(n+3)/((SO(n+1)×SO(2)), whose principal orbits are the Stiefel manifolds V{sub 2}(ℝ{sup n+2}) (with no ℤ{sub 2} factoring in this case). The third family are Einstein metrics on the product manifolds S{sup n+1}×S{sup n+1}, and are Kähler only for n=1. Some of these metrics are believed to play a role in studies of consistent string theory compactifications and in the context of the AdS/CFT correspondence. We also elaborate on the geometric approach to quantum mechanics based on the Kähler geometry of Fubini-Study metrics on ℂℙ{sup n+1}, and we apply the formalism to study the quantum entanglement of qubits.

Complex Monge–Ampère equations and geodesics in the space of Kähler metrics

CERN Document Server

2012-01-01

The purpose of these lecture notes is to provide an introduction to the theory of complex Monge–Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (Kähler–Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford–Taylor), Monge–Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi–Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli–Kohn–Nirenberg–Spruc...

Axisymmetric plasma equilibria in a Kerr metric

Science.gov (United States)

Elsässer, Klaus

2001-10-01

Plasma equilibria near a rotating black hole are considered within the multifluid description. An isothermal two-component plasma with electrons and positrons or ions is determined by four structure functions and the boundary conditions. These structure functions are the Bernoulli function and the toroidal canonical momentum per mass for each species. The quasi-neutrality assumption (no charge density, no toroidal current) allows to solve Maxwell's equations analytically for any axisymmetric stationary metric, and to reduce the fluid equations to one single scalar equation for the stream function \\chi of the positrons or ions, respectively. The basic smallness parameter is the ratio of the skin depth of electrons to the scale length of the metric and fluid quantities, and, in the case of an electron-ion plasma, the mass ratio m_e/m_i. The \\chi-equation can be solved by standard methods, and simple solutions for a Kerr geometry are available; they show characteristic flow patterns, depending on the structure functions and the boundary conditions.

FINAL REPORT: GEOMETRY AND ELEMENTARY PARTICLE PHYSICS

Energy Technology Data Exchange (ETDEWEB)

Singer, Isadore M.

2008-03-04

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists’ quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Final Report: Geometry And Elementary Particle Physics

International Nuclear Information System (INIS)

Singer, Isadore M.

2008-01-01

The effect on mathematics of collaborations between high-energy theoretical physics and modern mathematics has been remarkable. Mirror symmetry has revolutionized enumerative geometry, and Seiberg-Witten invariants have greatly simplified the study of four manifolds. And because of their application to string theory, physicists now need to know cohomology theory, characteristic classes, index theory, K-theory, algebraic geometry, differential geometry, and non-commutative geometry. Much more is coming. We are experiencing a deeper contact between the two sciences, which will stimulate new mathematics essential to the physicists quest for the unification of quantum mechanics and relativity. Our grant, supported by the Department of Energy for twelve years, has been instrumental in promoting an effective interaction between geometry and string theory, by supporting the Mathematical Physics seminar, postdoc research, collaborations, graduate students and several research papers.

Extended DBI massive gravity with generalized fiducial metric

Science.gov (United States)

Chullaphan, Tossaporn; Tannukij, Lunchakorn; Wongjun, Pitayuth

2015-06-01

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.

Extended DBI massive gravity with generalized fiducial metric

International Nuclear Information System (INIS)

Chullaphan, Tossaporn; Tannukij, Lunchakorn; Wongjun, Pitayuth

2015-01-01

We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.

The appropriateness of using various Minkowskian metrics for representing cognitive configurations

OpenAIRE

G D Richardson

1981-01-01

Cognitive mapping has been a rapidly growing area of research concerned with how cognitive information about environments is represented, interpreted, and used. One area of research has been concerned with what geometry best represents cognitive spatial information. This paper further pursues this topic by examining which of three Minkowskian metrics (city-block, Euclidean, dominance) is most appropriate for representing cognitive configurations.

Relevance of motion-related assessment metrics in laparoscopic surgery.

Science.gov (United States)

Oropesa, Ignacio; Chmarra, Magdalena K; Sánchez-González, Patricia; Lamata, Pablo; Rodrigues, Sharon P; Enciso, Silvia; Sánchez-Margallo, Francisco M; Jansen, Frank-Willem; Dankelman, Jenny; Gómez, Enrique J

2013-06-01

Motion metrics have become an important source of information when addressing the assessment of surgical expertise. However, their direct relationship with the different surgical skills has not been fully explored. The purpose of this study is to investigate the relevance of motion-related metrics in the evaluation processes of basic psychomotor laparoscopic skills and their correlation with the different abilities sought to measure. A framework for task definition and metric analysis is proposed. An explorative survey was first conducted with a board of experts to identify metrics to assess basic psychomotor skills. Based on the output of that survey, 3 novel tasks for surgical assessment were designed. Face and construct validation was performed, with focus on motion-related metrics. Tasks were performed by 42 participants (16 novices, 22 residents, and 4 experts). Movements of the laparoscopic instruments were registered with the TrEndo tracking system and analyzed. Time, path length, and depth showed construct validity for all 3 tasks. Motion smoothness and idle time also showed validity for tasks involving bimanual coordination and tasks requiring a more tactical approach, respectively. Additionally, motion smoothness and average speed showed a high internal consistency, proving them to be the most task-independent of all the metrics analyzed. Motion metrics are complementary and valid for assessing basic psychomotor skills, and their relevance depends on the skill being evaluated. A larger clinical implementation, combined with quality performance information, will give more insight on the relevance of the results shown in this study.

Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families

Directory of Open Access Journals (Sweden)

Frédéric Barbaresco

2016-11-01

Full Text Available We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical observables like energy, heat, and moment as pure geometrical objects. Using geometric Planck temperature of Souriau model and symplectic cocycle notion, the Fisher metric is identified as a Souriau geometric heat capacity. The Souriau model is based on affine representation of Lie group and Lie algebra that we compare with Koszul works on G/K homogeneous space and bijective correspondence between the set of G-invariant flat connections on G/K and the set of affine representations of the Lie algebra of G. In the framework of Lie group thermodynamics, an Euler-Poincaré equation is elaborated with respect to thermodynamic variables, and a new variational principal for thermodynamics is built through an invariant Poincaré-Cartan-Souriau integral. The Souriau-Fisher metric is linked to KKS (Kostant–Kirillov–Souriau 2-form that associates a canonical homogeneous symplectic manifold to the co-adjoint orbits. We apply this model in the framework of information geometry for the action of an affine group for exponential families, and provide some illustrations of use cases for multivariate gaussian densities. Information geometry is presented in the context of the seminal work of Fréchet and his Clairaut-Legendre equation. The Souriau model of statistical physics is validated as compatible with the Balian gauge model of thermodynamics. We recall the precursor work of Casalis on affine group invariance for natural exponential families.

Engineering graphics theoretical foundations of engineering geometry for design

CERN Document Server

Brailov, Aleksandr Yurievich

2016-01-01

This professional treatise on engineering graphics emphasizes engineering geometry as the theoretical foundation for communication of design ideas with real world structures and products. It considers each theoretical notion of engineering geometry as a complex solution of direct- and inverse-problems of descriptive geometry and each solution of basic engineering problems presented is accompanied by construction of biunique two- and three-dimension models of geometrical images. The book explains the universal structure of formal algorithms of the solutions of positional, metric, and axonometric problems, as well as the solutions of problems of construction in developing a curvilinear surface. The book further characterizes and explains the added laws of projective connections to facilitate construction of geometrical images in any of eight octants. Laws of projective connections allow constructing the complex drawing of a geometrical image in the American system of measurement and the European system of measu...

Analog geometry in an expanding fluid from AdS/CFT perspective

Science.gov (United States)

Bilić, Neven; Domazet, Silvije; Tolić, Dijana

2015-04-01

The dynamics of an expanding hadron fluid at temperatures below the chiral transition is studied in the framework of AdS/CFT correspondence. We establish a correspondence between the asymptotic AdS geometry in the 4 + 1 dimensional bulk with the analog spacetime geometry on its 3 + 1 dimensional boundary with the background fluid undergoing a spherical Bjorken type expansion. The analog metric tensor on the boundary depends locally on the soft pion dispersion relation and the four-velocity of the fluid. The AdS/CFT correspondence provides a relation between the pion velocity and the critical temperature of the chiral phase transition.

Geometry and dynamics of a tidally deformed black hole

International Nuclear Information System (INIS)

Poisson, Eric; Vlasov, Igor

2010-01-01

The metric of a nonrotating black hole deformed by a tidal interaction is calculated and expressed as an expansion in the strength of the tidal coupling. The expansion parameter is the inverse length scale R -1 , where R is the radius of curvature of the external spacetime in which the black hole moves. The expansion begins at order R -2 , and it is carried out through order R -4 . The metric is parametrized by a number of tidal multipole moments, which specify the black hole's tidal environment. The tidal moments are freely-specifiable functions of time that are related to the Weyl tensor of the external spacetime. At order R -2 the metric involves the tidal quadrupole moments E ab and B ab . At order R -3 it involves the time derivative of the quadrupole moments and the tidal octupole moments E abc and B abc . At order R -4 the metric involves the second time derivative of the quadrupole moments, the first time derivative of the octupole moments, the tidal hexadecapole moments E abcd and B abcd , and bilinear combinations of the quadrupole moments. The metric is presented in a light-cone coordinate system that possesses a clear geometrical meaning: The advanced-time coordinate v is constant on past light cones that converge toward the black hole; the angles θ and φ are constant on the null generators of each light cone; and the radial coordinate r is an affine parameter on each generator, which decreases as the light cones converge toward the black hole. The coordinates are well-behaved on the black-hole horizon, and they are adjusted so that the coordinate description of the horizon is the same as in the Schwarzschild geometry: r=2M+O(R -5 ). At the order of accuracy maintained in this work, the horizon is a stationary null hypersurface foliated by apparent horizons; it is an isolated horizon in the sense of Ashtekar and Krishnan. As an application of our results we examine the induced geometry and dynamics of the horizon, and calculate the rate at which the

Covariant electrodynamics in linear media: Optical metric

Science.gov (United States)

Thompson, Robert T.

2018-03-01

While the postulate of covariance of Maxwell's equations for all inertial observers led Einstein to special relativity, it was the further demand of general covariance—form invariance under general coordinate transformations, including between accelerating frames—that led to general relativity. Several lines of inquiry over the past two decades, notably the development of metamaterial-based transformation optics, has spurred a greater interest in the role of geometry and space-time covariance for electrodynamics in ponderable media. I develop a generally covariant, coordinate-free framework for electrodynamics in general dielectric media residing in curved background space-times. In particular, I derive a relation for the spatial medium parameters measured by an arbitrary timelike observer. In terms of those medium parameters I derive an explicit expression for the pseudo-Finslerian optical metric of birefringent media and show how it reduces to a pseudo-Riemannian optical metric for nonbirefringent media. This formulation provides a basis for a unified approach to ray and congruence tracing through media in curved space-times that may smoothly vary among positively refracting, negatively refracting, and vacuum.

Quantum κ-deformed differential geometry and field theory

Science.gov (United States)

Mercati, Flavio

2016-03-01

I introduce in κ-Minkowski noncommutative spacetime the basic tools of quantum differential geometry, namely bicovariant differential calculus, Lie and inner derivatives, the integral, the Hodge-∗ and the metric. I show the relevance of these tools for field theory with an application to complex scalar field, for which I am able to identify a vector-valued four-form which generalizes the energy-momentum tensor. Its closedness is proved, expressing in a covariant form the conservation of energy-momentum.

Clustering in Hilbert simplex geometry

KAUST Repository

Nielsen, Frank

2017-04-03

Clustering categorical distributions in the probability simplex is a fundamental primitive often met in applications dealing with histograms or mixtures of multinomials. Traditionally, the differential-geometric structure of the probability simplex has been used either by (i) setting the Riemannian metric tensor to the Fisher information matrix of the categorical distributions, or (ii) defining the information-geometric structure induced by a smooth dissimilarity measure, called a divergence. In this paper, we introduce a novel computationally-friendly non-Riemannian framework for modeling the probability simplex: Hilbert simplex geometry. We discuss the pros and cons of those three statistical modelings, and compare them experimentally for clustering tasks.

Real tunneling geometries and the large-scale topology of the universe

International Nuclear Information System (INIS)

Gibbons, G.W.; Hartle, J.B.

1990-01-01

If the topology and geometry of spacetime are quantum-mechanically variable, then the particular classical large-scale topology and geometry observed in our universe must be statistical predictions of its initial condition. This paper examines the predictions of the ''no boundary'' initial condition for the present large-scale topology and geometry. Finite-action real tunneling solutions of Einstein's equation are important for such predictions. These consist of compact Riemannian (Euclidean) geometries joined to a Lorentzian cosmological geometry across a spacelike surface of vanishing extrinsic curvature. The classification of such solutions is discussed and general constraints on their topology derived. For example, it is shown that, if the Euclidean Ricci tensor is positive, then a real tunneling solution can nucleate only a single connected Lorentzian spacetime (the unique conception theorem). Explicit examples of real tunneling solutions driven by a cosmological constant are exhibited and their implications for cosmic baldness described. It is argued that the most probable large-scale spacetime predicted by the real tunneling solutions of the ''no-boundary'' initial condition has the topology RxS 3 with the de Sitter metric

Global Differential Geometry and Global Analysis

CERN Document Server

Pinkall, Ulrich; Simon, Udo; Wegner, Berd

1991-01-01

All papers appearing in this volume are original research articles and have not been published elsewhere. They meet the requirements that are necessary for publication in a good quality primary journal. E.Belchev, S.Hineva: On the minimal hypersurfaces of a locally symmetric manifold. -N.Blasic, N.Bokan, P.Gilkey: The spectral geometry of the Laplacian and the conformal Laplacian for manifolds with boundary. -J.Bolton, W.M.Oxbury, L.Vrancken, L.M. Woodward: Minimal immersions of RP2 into CPn. -W.Cieslak, A. Miernowski, W.Mozgawa: Isoptics of a strictly convex curve. -F.Dillen, L.Vrancken: Generalized Cayley surfaces. -A.Ferrandez, O.J.Garay, P.Lucas: On a certain class of conformally flat Euclidean hypersurfaces. -P.Gauduchon: Self-dual manifolds with non-negative Ricci operator. -B.Hajduk: On the obstruction group toexistence of Riemannian metrics of positive scalar curvature. -U.Hammenstaedt: Compact manifolds with 1/4-pinched negative curvature. -J.Jost, Xiaowei Peng: The geometry of moduli spaces of stabl...

Spatial reorientation by geometry in bumblebees.

Directory of Open Access Journals (Sweden)

Valeria Anna Sovrano

Full Text Available Human and non-human animals are capable of using basic geometric information to reorient in an environment. Geometric information includes metric properties associated with spatial surfaces (e.g., short vs. long wall and left-right directionality or 'sense' (e.g. a long wall to the left of a short wall. However, it remains unclear whether geometric information is encoded by explicitly computing the layout of surface geometry or by matching images of the environment. View-based spatial encoding is generally thought to hold for insect navigation and, very recently, evidence for navigation by geometry has been reported in ants but only in a condition which does not allow the animals to use features located far from the goal. In this study we tested the spatial reorientation abilities of bumblebees (Bombus terrestris. After spatial disorientation, by passive rotation both clockwise and anticlockwise, bumblebees had to find one of the four exit holes located in the corners of a rectangular enclosure. Bumblebees systematically confused geometrically equivalent exit corners (i.e. corners with the same geometric arrangement of metric properties and sense, for example a short wall to the left of a long wall. However, when one wall of the enclosure was a different colour, bumblebees appeared to combine this featural information (either near or far from the goal with geometric information to find the correct exit corner. Our results show that bumblebees are able to use both geometric and featural information to reorient themselves, even when features are located far from the goal.

Sharp metric obstructions for quasi-Einstein metrics

Science.gov (United States)

Case, Jeffrey S.

2013-02-01

Using the tractor calculus to study smooth metric measure spaces, we adapt results of Gover and Nurowski to give sharp metric obstructions to the existence of quasi-Einstein metrics on suitably generic manifolds. We do this by introducing an analogue of the Weyl tractor W to the setting of smooth metric measure spaces. The obstructions we obtain can be realized as tensorial invariants which are polynomial in the Riemann curvature tensor and its divergence. By taking suitable limits of their tensorial forms, we then find obstructions to the existence of static potentials, generalizing to higher dimensions a result of Bartnik and Tod, and to the existence of potentials for gradient Ricci solitons.

Geometric Transformations in Engineering Geometry

Directory of Open Access Journals (Sweden)

I. F. Borovikov

2015-01-01

Full Text Available Recently, for business purposes, in view of current trends and world experience in training engineers, research and faculty staff there has been a need to transform traditional courses of descriptive geometry into the course of engineering geometry in which the geometrical transformations have to become its main section. On the basis of critical analysis the paper gives suggestions to improve a presentation technique of this section both in the classroom and in academic literature, extend an application scope of geometrical transformations to solve the position and metric tasks and simulation of surfaces, as well as to design complex engineering configurations, which meet a number of pre-specified conditions.The article offers to make a number of considerable amendments to the terms and definitions used in the existing courses of descriptive geometry. It draws some conclusions and makes the appropriate proposals on feasibility of coordination in teaching the movement transformation in the courses of analytical and descriptive geometry. This will provide interdisciplinary team teaching and allow students to be convinced that a combination of analytical and graphic ways to solve geometric tasks is useful and reasonable.The traditional sections of learning courses need to be added with a theory of projective and bi-rational transformations. In terms of application simplicity and convenience it is enough to consider the central transformations when solving the applied tasks. These transformations contain a beam of sub-invariant (low-invariant straight lines on which the invariant curve induces non-involution and involution projectivities. The expediency of nonlinear transformations application is shown in the article by a specific example of geometric modeling of the interfacing surface "spar-blade".Implementation of these suggestions will contribute to a real transformation of a traditional course of descriptive geometry to the engineering geometry

Prototypic Development and Evaluation of a Medium Format Metric Camera

Science.gov (United States)

Hastedt, H.; Rofallski, R.; Luhmann, T.; Rosenbauer, R.; Ochsner, D.; Rieke-Zapp, D.

2018-05-01

Engineering applications require high-precision 3D measurement techniques for object sizes that vary between small volumes (2-3 m in each direction) and large volumes (around 20 x 20 x 1-10 m). The requested precision in object space (1σ RMS) is defined to be within 0.1-0.2 mm for large volumes and less than 0.01 mm for small volumes. In particular, focussing large volume applications the availability of a metric camera would have different advantages for several reasons: 1) high-quality optical components and stabilisations allow for a stable interior geometry of the camera itself, 2) a stable geometry leads to a stable interior orientation that enables for an a priori camera calibration, 3) a higher resulting precision can be expected. With this article the development and accuracy evaluation of a new metric camera, the ALPA 12 FPS add|metric will be presented. Its general accuracy potential is tested against calibrated lengths in a small volume test environment based on the German Guideline VDI/VDE 2634.1 (2002). Maximum length measurement errors of less than 0.025 mm are achieved with different scenarios having been tested. The accuracy potential for large volumes is estimated within a feasibility study on the application of photogrammetric measurements for the deformation estimation on a large wooden shipwreck in the German Maritime Museum. An accuracy of 0.2 mm-0.4 mm is reached for a length of 28 m (given by a distance from a lasertracker network measurement). All analyses have proven high stabilities of the interior orientation of the camera and indicate the applicability for a priori camera calibration for subsequent 3D measurements.

PROTOTYPIC DEVELOPMENT AND EVALUATION OF A MEDIUM FORMAT METRIC CAMERA

Directory of Open Access Journals (Sweden)

H. Hastedt

2018-05-01

Full Text Available Engineering applications require high-precision 3D measurement techniques for object sizes that vary between small volumes (2–3 m in each direction and large volumes (around 20 x 20 x 1–10 m. The requested precision in object space (1σ RMS is defined to be within 0.1–0.2 mm for large volumes and less than 0.01 mm for small volumes. In particular, focussing large volume applications the availability of a metric camera would have different advantages for several reasons: 1 high-quality optical components and stabilisations allow for a stable interior geometry of the camera itself, 2 a stable geometry leads to a stable interior orientation that enables for an a priori camera calibration, 3 a higher resulting precision can be expected. With this article the development and accuracy evaluation of a new metric camera, the ALPA 12 FPS add|metric will be presented. Its general accuracy potential is tested against calibrated lengths in a small volume test environment based on the German Guideline VDI/VDE 2634.1 (2002. Maximum length measurement errors of less than 0.025 mm are achieved with different scenarios having been tested. The accuracy potential for large volumes is estimated within a feasibility study on the application of photogrammetric measurements for the deformation estimation on a large wooden shipwreck in the German Maritime Museum. An accuracy of 0.2 mm–0.4 mm is reached for a length of 28 m (given by a distance from a lasertracker network measurement. All analyses have proven high stabilities of the interior orientation of the camera and indicate the applicability for a priori camera calibration for subsequent 3D measurements.

Metric dimensional reduction at singularities with implications to Quantum Gravity

International Nuclear Information System (INIS)

Stoica, Ovidiu Cristinel

2014-01-01

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being just non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained

Designing new guides and instruments using McStas

CERN Document Server

Farhi, E; Wildes, A R; Ghosh, R; Lefmann, K

2002-01-01

With the increasing complexity of modern neutron-scattering instruments, the need for powerful tools to optimize their geometry and physical performances (flux, resolution, divergence, etc.) has become essential. As the usual analytical methods reach their limit of validity in the description of fine effects, the use of Monte Carlo simulations, which can handle these latter, has become widespread. The McStas program was developed at Riso National Laboratory in order to provide neutron scattering instrument scientists with an efficient and flexible tool for building Monte Carlo simulations of guides, neutron optics and instruments. To date, the McStas package has been extensively used at the Institut Laue-Langevin, Grenoble, France, for various studies including cold and thermal guides with ballistic geometry, diffractometers, triple-axis, backscattering and time-of-flight spectrometers. In this paper, we present some simulation results concerning different guide geometries that may be used in the future at th...

Poincare ball embeddings of the optical geometry

International Nuclear Information System (INIS)

Abramowicz, M A; Bengtsson, I; Karas, V; Rosquist, K

2002-01-01

It is shown that the optical geometry of the Reissner-Nordstroem exterior metric can be embedded in a hyperbolic space all the way down to its outer horizon. The adopted embedding procedure removes a breakdown of flat-space embeddings which occurs outside the horizon, at and below the Buchdahl-Bondi limit (R/M=9/4 in the Schwarzschild case). In particular, the horizon can be captured in the optical geometry embedding diagram. Moreover, by using the compact Poincare ball representation of the hyperbolic space, the embedding diagram can cover the whole extent of radius from spatial infinity down to the horizon. Attention is drawn to the advantages of such embeddings in an appropriately curved space: this approach gives compact embeddings and it clearly distinguishes the case of an extremal black hole from a non-extremal one in terms of the topology of the embedded horizon

Metrical connection in space-time, Newton's and Hubble's laws

International Nuclear Information System (INIS)

Maeder, A.

1978-01-01

The theory of gravitation in general relativity is not scale invariant. Here, we follow Dirac's proposition of a scale invariant theory of gravitation (i.e. a theory in which the equations keep their form when a transformation of scale is made). We examine some concepts of Weyl's geometry, like the metrical connection, the scale transformations and invariance, and we discuss their consequences for the equation of the geodetic motion and for its Newtonian limit. Under general conditions, we show that the only non-vanishing component of the coefficient of metrical connection may be identified with Hubble's constant. In this framework, the equivalent to the Newtonian approximation for the equation of motion contains an additional acceleration term Hdr vector /dt, which produces an expansion of gravitational systems. The velocity of this expansion is shown to increase linearly with the distance between interacting objects. The relative importance of this new expansion term to the Newtonian one varies like (2rhosub(c)/rho)sup(1/2), where rhosub(c) is the critical density of the Einsteinde Sitter model and rho is the mean density of the considered gravitational configuration. Thus, this 'generalized expansion' is important essentially for systems of mean density not too much above the critical density. Finally, our main conclusion is that in the integrable Weyl geometry, Hubble's law - like Newton's law - would appear as an intrinsic property of gravitation, being only the most visible manifestation of a general effect characterizing the gravitational interaction. (orig.) [de

METRIC EVALUATION PIPELINE FOR 3D MODELING OF URBAN SCENES

Directory of Open Access Journals (Sweden)

M. Bosch

2017-05-01

Full Text Available Publicly available benchmark data and metric evaluation approaches have been instrumental in enabling research to advance state of the art methods for remote sensing applications in urban 3D modeling. Most publicly available benchmark datasets have consisted of high resolution airborne imagery and lidar suitable for 3D modeling on a relatively modest scale. To enable research in larger scale 3D mapping, we have recently released a public benchmark dataset with multi-view commercial satellite imagery and metrics to compare 3D point clouds with lidar ground truth. We now define a more complete metric evaluation pipeline developed as publicly available open source software to assess semantically labeled 3D models of complex urban scenes derived from multi-view commercial satellite imagery. Evaluation metrics in our pipeline include horizontal and vertical accuracy and completeness, volumetric completeness and correctness, perceptual quality, and model simplicity. Sources of ground truth include airborne lidar and overhead imagery, and we demonstrate a semi-automated process for producing accurate ground truth shape files to characterize building footprints. We validate our current metric evaluation pipeline using 3D models produced using open source multi-view stereo methods. Data and software is made publicly available to enable further research and planned benchmarking activities.

Metric Evaluation Pipeline for 3d Modeling of Urban Scenes

Science.gov (United States)

Bosch, M.; Leichtman, A.; Chilcott, D.; Goldberg, H.; Brown, M.

2017-05-01

Publicly available benchmark data and metric evaluation approaches have been instrumental in enabling research to advance state of the art methods for remote sensing applications in urban 3D modeling. Most publicly available benchmark datasets have consisted of high resolution airborne imagery and lidar suitable for 3D modeling on a relatively modest scale. To enable research in larger scale 3D mapping, we have recently released a public benchmark dataset with multi-view commercial satellite imagery and metrics to compare 3D point clouds with lidar ground truth. We now define a more complete metric evaluation pipeline developed as publicly available open source software to assess semantically labeled 3D models of complex urban scenes derived from multi-view commercial satellite imagery. Evaluation metrics in our pipeline include horizontal and vertical accuracy and completeness, volumetric completeness and correctness, perceptual quality, and model simplicity. Sources of ground truth include airborne lidar and overhead imagery, and we demonstrate a semi-automated process for producing accurate ground truth shape files to characterize building footprints. We validate our current metric evaluation pipeline using 3D models produced using open source multi-view stereo methods. Data and software is made publicly available to enable further research and planned benchmarking activities.

$\\eta$-metric structures

OpenAIRE

Gaba, Yaé Ulrich

2017-01-01

In this paper, we discuss recent results about generalized metric spaces and fixed point theory. We introduce the notion of $\\eta$-cone metric spaces, give some topological properties and prove some fixed point theorems for contractive type maps on these spaces. In particular we show that theses $\\eta$-cone metric spaces are natural generalizations of both cone metric spaces and metric type spaces.

KEMAJUAN BELAJAR SISWA PADA GEOMETRI TRANSFORMASI MENGGUNAKAN AKTIVITAS REFLEKSI GEOMETRI

Directory of Open Access Journals (Sweden)

Irkham Ulil Albab

2014-10-01

Full Text Available Abstrak: Penelitian ini bertujuan untuk mendeskripsikan kemajuan belajar siswa pada materi geometri transformasi yang didukung dengan serangkaian aktivitas belajar berdasarkan Pendidikan Matematika Realistik Indonesia. Penelitian didesain melalui tiga tahap, yaitu tahapan perancangan desain awal, pengujian desain melalui pembelajaran awal dan pembelajaran eksperimental, dan tahap analisis retrospektif. Dalam penelitian ini, Hypothetical Learning Trajectory, HLT (HLT berperan penting sebagai desain pembelajaran sekaligus instrumen penelitian. HLT diujikan terhadap 26 siswa kelas VII. Data dikumpulkan dengan teknik wawancara, pengamatan, dan catatan lapangan. Hasil penelitian menunjukkan bahwa desain pembelajaran ini mampu menstimulasi siswa untuk memberikan karakteristik refleksi dan transformasi geometri lainnya secara informal, mengklasifikasikannya dalam transformasi isometri pada level kedua, dan menemukan garis bantuan refleksi pada level yang lebih formal. Selain itu, garis bantuan refleksi digunakan oleh siswa untuk menggambar bayangan refleksi dan pola pencerminan serta memahami bentuk rotasi dan translasi sebagai kombinasi refleksi adalah level tertinggi. Keyword: transformasi geometri, kombinasi refleksi, rotasi, translasi, design research, HLT STUDENTS’ LEARNING PROGRESS ON TRANSFORMATION GEOMETRY USING THE GEOMETRY REFLECTION ACTIVITIES Abstract: This study was aimed at describing the students’ learning progress on transformation geometry supported by a set of learning activities based on Indonesian Realistic Mathematics Education. The study was designed into three stages, that is, the preliminary design stage, the design testing through initial instruction and experiment, and the restrospective analysis stage. In this study, Hypothetical Learning Trajectory (HLT played an important role as an instructional design and a research instrument. HLT was tested to 26 seventh grade students. The data were collected through interviews

Reconstructing 1/2 BPS space-time metrics from matrix models and spin chains

International Nuclear Information System (INIS)

Vazquez, Samuel E.

2007-01-01

Using the anti-de Sitter/conformal field theories (AdS/CFT) correspondence, we address the question of how to measure complicated space-time metrics using gauge theory probes. In particular, we consider the case of the 1/2 Bogomol'nyi-Prasad-Sommerfield geometries of type IIB supergravity. These geometries are classified by certain droplets in a two-dimensional spacelike hypersurface. We show how to reconstruct the full metric inside these droplets using the one-loop N=4 super Yang-Mills theory dilatation operator. This is done by considering long operators in the SU(2) sector, which are dual to fast rotating strings on the droplets. We develop new powerful techniques for large N complex matrix models that allow us to construct the Hamiltonian for these strings. We find that the Hamiltonian can be mapped to a dynamical spin chain. That is, the length of the chain is not fixed. Moreover, all of these spin chains can be explicitly constructed using an interesting algebra which is derived from the matrix model. Our techniques work for general droplet configurations. As an example, we study a single elliptical droplet and the hypotrochoid

On the near horizon rotating black hole geometries with NUT charges

Energy Technology Data Exchange (ETDEWEB)

Galajinsky, Anton; Orekhov, Kirill [Tomsk Polytechnic University, Laboratory of Mathematical Physics, Tomsk (Russian Federation)

2016-09-15

The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2, 1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d = 4 and d = 5 where the vacuum Einstein equations reduce to a coupled set of ordinary differential equations. In four dimensions the analysis can be carried out in full generality and the resulting metric describes the d = 4 near horizon Kerr-NUT black hole. In five dimensions we choose a specific ansatz whose structure is similar to the d = 5 near horizon Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters is constructed. A particular member of this family, which is characterized by three parameters, seems to be a natural candidate to describe the d = 5 near horizon Myers- Perry black hole with a NUT charge. (orig.)

On the near horizon rotating black hole geometries with NUT charges

International Nuclear Information System (INIS)

Galajinsky, Anton; Orekhov, Kirill

2016-01-01

The near horizon geometries are usually constructed by implementing a specific limit to a given extreme black hole configuration. Their salient feature is that the isometry group includes the conformal subgroup SO(2, 1). In this work, we turn the logic around and use the conformal invariants for constructing Ricci-flat metrics in d = 4 and d = 5 where the vacuum Einstein equations reduce to a coupled set of ordinary differential equations. In four dimensions the analysis can be carried out in full generality and the resulting metric describes the d = 4 near horizon Kerr-NUT black hole. In five dimensions we choose a specific ansatz whose structure is similar to the d = 5 near horizon Myers-Perry black hole. A Ricci-flat metric involving five arbitrary parameters is constructed. A particular member of this family, which is characterized by three parameters, seems to be a natural candidate to describe the d = 5 near horizon Myers- Perry black hole with a NUT charge. (orig.)

Selecting landscape metrics as indicators of spatial heterogeneity-A comparison among Greek landscapes

Science.gov (United States)

Plexida, Sofia G.; Sfougaris, Athanassios I.; Ispikoudis, Ioannis P.; Papanastasis, Vasilios P.

2014-02-01

This paper investigates the spatial heterogeneity of three landscapes along an altitudinal gradient and different human land use. The main aim was the identification of appropriate landscape indicators using different extents. ASTER image was used to create a land cover map consisting of three landscapes which differed in altitude and land use. A number of landscape metrics quantifying patch complexity, configuration, diversity and connectivity were derived from the thematic map at the landscape level. There were significant differences among the three landscapes regarding these four aspects of landscape heterogeneity. The analysis revealed a specific pattern of land use where lowlands are being increasingly utilized by humans (percentage of agricultural land = 65.84%) characterized by physical connectedness (high values of Patch Cohesion Index) and relatively simple geometries (low values of fractal dimension index). The landscape pattern of uplands was found to be highly diverse based upon the Shannon Diversity index. After selecting the scale (600 ha) where metrics values stabilized, it was shown that metrics were more correlated at the small scale of 60 ha. From the original 24 metrics, 14 individual metrics with high Spearman correlation coefficient and Variance Inflation Factor criterion were eliminated, leaving 10 representative metrics for subsequent analysis. Data reduction analysis showed that Patch Density, Area-Weighted Mean Fractal Dimension Index and Patch Cohesion Index are suitable to describe landscape patterns irrespective of the scale. A systematic screening of these metrics could enhance a deeper understanding of the results obtained by them and contribute to a sustainable landscape management of Mediterranean landscapes.

Metrics in Keplerian orbits quotient spaces

Science.gov (United States)

Milanov, Danila V.

2018-03-01

Quotient spaces of Keplerian orbits are important instruments for the modelling of orbit samples of celestial bodies on a large time span. We suppose that variations of the orbital eccentricities, inclinations and semi-major axes remain sufficiently small, while arbitrary perturbations are allowed for the arguments of pericentres or longitudes of the nodes, or both. The distance between orbits or their images in quotient spaces serves as a numerical criterion for such problems of Celestial Mechanics as search for common origin of meteoroid streams, comets, and asteroids, asteroid families identification, and others. In this paper, we consider quotient sets of the non-rectilinear Keplerian orbits space H. Their elements are identified irrespective of the values of pericentre arguments or node longitudes. We prove that distance functions on the quotient sets, introduced in Kholshevnikov et al. (Mon Not R Astron Soc 462:2275-2283, 2016), satisfy metric space axioms and discuss theoretical and practical importance of this result. Isometric embeddings of the quotient spaces into R^n, and a space of compact subsets of H with Hausdorff metric are constructed. The Euclidean representations of the orbits spaces find its applications in a problem of orbit averaging and computational algorithms specific to Euclidean space. We also explore completions of H and its quotient spaces with respect to corresponding metrics and establish a relation between elements of the extended spaces and rectilinear trajectories. Distance between an orbit and subsets of elliptic and hyperbolic orbits is calculated. This quantity provides an upper bound for the metric value in a problem of close orbits identification. Finally the invariance of the equivalence relations in H under coordinates change is discussed.

The Extended HANDS Characterization and Analysis of Metric Biases

Science.gov (United States)

Kelecy, T.; Knox, R.; Cognion, R.

The Extended High Accuracy Network Determination System (Extended HANDS) consists of a network of low cost, high accuracy optical telescopes designed to support space surveillance and development of space object characterization technologies. Comprising off-the-shelf components, the telescopes are designed to provide sub arc-second astrometric accuracy. The design and analysis team are in the process of characterizing the system through development of an error allocation tree whose assessment is supported by simulation, data analysis, and calibration tests. The metric calibration process has revealed 1-2 arc-second biases in the right ascension and declination measurements of reference satellite position, and these have been observed to have fairly distinct characteristics that appear to have some dependence on orbit geometry and tracking rates. The work presented here outlines error models developed to aid in development of the system error budget, and examines characteristic errors (biases, time dependence, etc.) that might be present in each of the relevant system elements used in the data collection and processing, including the metric calibration processing. The relevant reference frames are identified, and include the sensor (CCD camera) reference frame, Earth-fixed topocentric frame, topocentric inertial reference frame, and the geocentric inertial reference frame. The errors modeled in each of these reference frames, when mapped into the topocentric inertial measurement frame, reveal how errors might manifest themselves through the calibration process. The error analysis results that are presented use satellite-sensor geometries taken from periods where actual measurements were collected, and reveal how modeled errors manifest themselves over those specific time periods. These results are compared to the real calibration metric data (right ascension and declination residuals), and sources of the bias are hypothesized. In turn, the actual right ascension and

PREDICTION METRICS FOR CHEMICAL DETECTION IN LONG-WAVE INFRARED HYPERSPECTRAL IMAGERY

Energy Technology Data Exchange (ETDEWEB)

Chilton, M.; Walsh, S.J.; Daly, D.S.

2009-01-01

Natural and man-made chemical processes generate gaseous plumes that may be detected by hyperspectral imaging, which produces a matrix of spectra affected by the chemical constituents of the plume, the atmosphere, the bounding background surface and instrument noise. A physics-based model of observed radiance shows that high chemical absorbance and low background emissivity result in a larger chemical signature. Using simulated hyperspectral imagery, this study investigated two metrics which exploited this relationship. The objective was to explore how well the chosen metrics predicted when a chemical would be more easily detected when comparing one background type to another. The two predictor metrics correctly rank ordered the backgrounds for about 94% of the chemicals tested as compared to the background rank orders from Whitened Matched Filtering (a detection algorithm) of the simulated spectra. These results suggest that the metrics provide a reasonable summary of how the background emissivity and chemical absorbance interact to produce the at-sensor chemical signal. This study suggests that similarly effective predictors that account for more general physical conditions may be derived.

Geometry of the TJ-II in Astra 6.0; Geometria del TJ-II en Astra 6.0

Energy Technology Data Exchange (ETDEWEB)

Lopez-Bruna, D.; Romero, J.A.; Castejon, F.

2006-07-01

One of the most exploited features of the TJ-II Heliac, a facility in the Laboratorio Nacional de Fusion (CIEMAT, Madrid), is its ability to explore plasmas in different magnetic configurations. For this reason, there are available libraries that provide the metrics and associated magnitudes for many among all possible configurations. On the other hand, the transport codes that can normally be used to perform transport calculations cannot dea properly with these geometries, which is especially delicate when there are induced plasma currents. In the present work we adopt ASTRA, a transport analysis shell, to study the approximations performed when calculations that impose axi-symmetry (as ASTRA does) are performed on magnetic configurations that are not really axi-symmetric. After describing how we obtain those TJ-II metric averages that must be set in ASTRA, we perform two comparisons: (i) we obtain the vacuum rotational transform as deduced from the metric coefficients but imposing axisymmetry, and compare the results with the rotational transform yielded by the existing libraries; and (ii) we build a ID transport code with TJ-II metrics so its results can be compared with those of ASTRA. In both cases, the differences found indicate that evaluating the evolution of the rotational transform under ohmic induction and transport evolution is acceptable assuming that the geometry itself does not evolve. (Author) 11 refs.

On the geometry of fracture and frustration

NARCIS (Netherlands)

Koning, Vinzenz

2014-01-01

Geometric frustration occurs when local order cannot propagate through space. A common example is the surface of a soccer ball, which cannot be tiled with hexaganons only. Geometric frustration can also be present in materials. In fact, geometry can act as an instrument to design the mechanical,

Technical Note: Error metrics for estimating the accuracy of needle/instrument placement during transperineal magnetic resonance/ultrasound-guided prostate interventions.

Science.gov (United States)

Bonmati, Ester; Hu, Yipeng; Villarini, Barbara; Rodell, Rachael; Martin, Paul; Han, Lianghao; Donaldson, Ian; Ahmed, Hashim U; Moore, Caroline M; Emberton, Mark; Barratt, Dean C

2018-04-01

Image-guided systems that fuse magnetic resonance imaging (MRI) with three-dimensional (3D) ultrasound (US) images for performing targeted prostate needle biopsy and minimally invasive treatments for prostate cancer are of increasing clinical interest. To date, a wide range of different accuracy estimation procedures and error metrics have been reported, which makes comparing the performance of different systems difficult. A set of nine measures are presented to assess the accuracy of MRI-US image registration, needle positioning, needle guidance, and overall system error, with the aim of providing a methodology for estimating the accuracy of instrument placement using a MR/US-guided transperineal approach. Using the SmartTarget fusion system, an MRI-US image alignment error was determined to be 2.0 ± 1.0 mm (mean ± SD), and an overall system instrument targeting error of 3.0 ± 1.2 mm. Three needle deployments for each target phantom lesion was found to result in a 100% lesion hit rate and a median predicted cancer core length of 5.2 mm. The application of a comprehensive, unbiased validation assessment for MR/US guided systems can provide useful information on system performance for quality assurance and system comparison. Furthermore, such an analysis can be helpful in identifying relationships between these errors, providing insight into the technical behavior of these systems. © 2018 American Association of Physicists in Medicine.

The neutron instrument simulation package, NISP

International Nuclear Information System (INIS)

Seeger, P.A.; Daemen, L.L.

2004-01-01

The Neutron Instrument Simulation Package (NISP) performs complete source-to-detector simulations of neutron instruments, including neutrons that do not follow the expected path. The original user interface (MC( ) Web) is a web-based application, http://strider.lansce.lanl.gov/NISP/Welcome.html. This report describes in detail the newer standalone Windows version, NISP( ) Win. Instruments are assembled from menu-selected elements, including neutron sources, collimation and transport elements, samples, analyzers, and detectors. Magnetic field regions may also be specified for the propagation of polarized neutrons including spin precession. Either interface writes a geometry file that is used as input to the Monte Carlo engine (MC( ) Run) in the user's computer. Both the interface and the engine rely on a subroutine library, MCLIB. The package is completely open source. New features include capillary optics, temperature dependence of Al and Be, revised source files for ISIS, and visualization of neutron trajectories at run time. Also, a single-crystal sample type has been successfully imported from McStas (with more generalized geometry), demonstrating the capability of including algorithms from other sources, and NISP( ) Win may render the instrument in a virtual reality file. Results are shown for two instruments under development.

Average methods and their applications in Differential Geometry I

OpenAIRE

Vincze, Csaba

2013-01-01

In Minkowski geometry the metric features are based on a compact convex body containing the origin in its interior. This body works as a unit ball with its boundary formed by the unit vectors. Using one-homogeneous extension we have a so-called Minkowski functional to measure the lenght of vectors. The half of its square is called the energy function. Under some regularity conditions we can introduce an average Euclidean inner product by integrating the Hessian matrix of the energy function o...

Intrinsic Losses Based on Information Geometry and Their Applications

Directory of Open Access Journals (Sweden)

Yao Rong

2017-08-01

Full Text Available One main interest of information geometry is to study the properties of statistical models that do not depend on the coordinate systems or model parametrization; thus, it may serve as an analytic tool for intrinsic inference in statistics. In this paper, under the framework of Riemannian geometry and dual geometry, we revisit two commonly-used intrinsic losses which are respectively given by the squared Rao distance and the symmetrized Kullback–Leibler divergence (or Jeffreys divergence. For an exponential family endowed with the Fisher metric and α -connections, the two loss functions are uniformly described as the energy difference along an α -geodesic path, for some α ∈ { − 1 , 0 , 1 } . Subsequently, the two intrinsic losses are utilized to develop Bayesian analyses of covariance matrix estimation and range-spread target detection. We provide an intrinsically unbiased covariance estimator, which is verified to be asymptotically efficient in terms of the intrinsic mean square error. The decision rules deduced by the intrinsic Bayesian criterion provide a geometrical justification for the constant false alarm rate detector based on generalized likelihood ratio principle.

On ruled surface in 3-dimensional almost contact metric manifold

Science.gov (United States)

Karacan, Murat Kemal; Yuksel, Nural; Ikiz, Hasibe

In this paper, we study ruled surface in 3-dimensional almost contact metric manifolds by using surface theory defined by Gök [Surfaces theory in contact geometry, PhD thesis (2010)]. We also studied the theory of curves using cross product defined by Camcı. In this study, we obtain the distribution parameters of the ruled surface and then some results and theorems are presented with special cases. Moreover, some relationships among asymptotic curve and striction line of the base curve of the ruled surface have been found.

Harmonic mapping character of Rosen's bimetric theory of gravity and the geometry of its harmonic mapping space

International Nuclear Information System (INIS)

Stoeger, W.R.; Whitman, A.P.; Knill, R.J.

1985-01-01

After showing that Rosen's bimetric theory of gravity is a harmonic map, the geometry of the ten-dimensional harmonic mapping space (HMS), and of its nine-dimensional symmetric submanifolds, which are the leaves of the codimension one foliation of the HMS, is detailed. Both structures are global affinely symmetric spaces. For each, the metric, connections, and Riemann, Ricci, and scalar curvatures are given. The Killing vectors in each case are also worked out and related to the ''conserved quantities'' naturally associated with the harmonic mapping character of the theory. The structure of the Rosen HMS is very much like that determined by the DeWitt metric on the six-dimensional Wheeler superspace of all positive definite three-dimensional metrics. It is clear that a slight modification of the Rosen HMS metric will yield the corresponding metric on the space of all four-dimensional metrics of Lorentz signature. Finally, interesting avenues of further research are indicated, particularly with respect to the structure and comparison of Lagrangian-based gravitational theories which are similar to Einstein's general relativity

Geometry of the 2+1 black hole

International Nuclear Information System (INIS)

Banados, M.; Henneaux, M.; Teitelboim, C.; Zanelli, J.

1993-01-01

The geometry of the spinning black holes of standard Einstein theory in 2+1 dimensions, with a negative cosmological constant, and without couplings to matter, is analyzed in detail. It is shown that the black hole arises from identifications of points of anti--de Sitter space by a discrete subgroup of SO(2,2). The generic black hole is a smooth manifold in the metric sense. The surface r=0 is not a curvature singularity but, rather, a singularity in the causal structure. Continuing past it would introduce closed timelike lines. However, simple examples show the regularity of the metric at r=0 to be unstable: couplings to matter bring in a curvature singularity there. Kruskal coordinates and Penrose diagrams are exhibited. Special attention is given to the limiting cases of (i) the spinless hole of zero mass, which differs from anti--de Sitter space and plays the role of the vacuum, and (ii) the spinning hole of maximal angular momentum. A thorough classification of the elements of the Lie algebra of SO(2,2) is given in an appendix

Hypermultiplets and hypercomplex geometry from six to three dimensions

International Nuclear Information System (INIS)

Rosseel, Jan; Proeyen, Antoine van

2004-01-01

The formulation of hypermultiplets that has been developed for five-dimensional matter multiplets is by dimensional reductions translated into the appropriate spinor language for six and four dimensions. We also treat the theories without actions that have the geometrical structure of hypercomplex geometry. The latter is the generalization of hyper-Kaehler geometry that does not require a Hermitian metric and hence corresponds to field equations without action. The translation tables of this paper allow the direct application of superconformal tensor calculus for the hypermultiplets using the available Weyl multiplets in six and four dimensions. Furthermore, the hypermultiplets in three dimensions that result from reduction of vector multiplets in four dimensions are considered, leading to a superconformal formulation of the c-map and an expression for the main geometric quantities of the hyper-Kaehler manifolds in the image of this map

General Geometry and Geometry of Electromagnetism

OpenAIRE

Shahverdiyev, Shervgi S.

2002-01-01

It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is geometry underlying Electromagnetism. Action for electromagnetic field and Maxwell equations are derived from curvature function of geometry underlying Electromagnetism. And it is shown that equation of motion for a particle interacting with electromagnetic...

Semantic metrics

OpenAIRE

Hu, Bo; Kalfoglou, Yannis; Dupplaw, David; Alani, Harith; Lewis, Paul; Shadbolt, Nigel

2006-01-01

In the context of the Semantic Web, many ontology-related operations, e.g. ontology ranking, segmentation, alignment, articulation, reuse, evaluation, can be boiled down to one fundamental operation: computing the similarity and/or dissimilarity among ontological entities, and in some cases among ontologies themselves. In this paper, we review standard metrics for computing distance measures and we propose a series of semantic metrics. We give a formal account of semantic metrics drawn from a...

Metric modular spaces

CERN Document Server

Chistyakov, Vyacheslav

2015-01-01

Aimed toward researchers and graduate students familiar with elements of functional analysis, linear algebra, and general topology; this book contains a general study of modulars, modular spaces, and metric modular spaces. Modulars may be thought of as generalized velocity fields and serve two important purposes: generate metric spaces in a unified manner and provide a weaker convergence, the modular convergence, whose topology is non-metrizable in general. Metric modular spaces are extensions of metric spaces, metric linear spaces, and classical modular linear spaces. The topics covered include the classification of modulars, metrizability of modular spaces, modular transforms and duality between modular spaces, metric  and modular topologies. Applications illustrated in this book include: the description of superposition operators acting in modular spaces, the existence of regular selections of set-valued mappings, new interpretations of spaces of Lipschitzian and absolutely continuous mappings, the existe...

Next-Generation Metrics: Responsible Metrics & Evaluation for Open Science

Energy Technology Data Exchange (ETDEWEB)

Wilsdon, J.; Bar-Ilan, J.; Peters, I.; Wouters, P.

2016-07-01

Metrics evoke a mixed reaction from the research community. A commitment to using data to inform decisions makes some enthusiastic about the prospect of granular, real-time analysis o of research and its wider impacts. Yet we only have to look at the blunt use of metrics such as journal impact factors, h-indices and grant income targets, to be reminded of the pitfalls. Some of the most precious qualities of academic culture resist simple quantification, and individual indicators often struggle to do justice to the richness and plurality of research. Too often, poorly designed evaluation criteria are “dominating minds, distorting behaviour and determining careers (Lawrence, 2007).” Metrics hold real power: they are constitutive of values, identities and livelihoods. How to exercise that power to more positive ends has been the focus of several recent and complementary initiatives, including the San Francisco Declaration on Research Assessment (DORA1), the Leiden Manifesto2 and The Metric Tide3 (a UK government review of the role of metrics in research management and assessment). Building on these initiatives, the European Commission, under its new Open Science Policy Platform4, is now looking to develop a framework for responsible metrics for research management and evaluation, which can be incorporated into the successor framework to Horizon 2020. (Author)

An Innovative Metric to Evaluate Satellite Precipitation's Spatial Distribution

Science.gov (United States)

Liu, H.; Chu, W.; Gao, X.; Sorooshian, S.

2011-12-01

Thanks to its capability to cover the mountains, where ground measurement instruments cannot reach, satellites provide a good means of estimating precipitation over mountainous regions. In regions with complex terrains, accurate information on high-resolution spatial distribution of precipitation is critical for many important issues, such as flood/landslide warning, reservoir operation, water system planning, etc. Therefore, in order to be useful in many practical applications, satellite precipitation products should possess high quality in characterizing spatial distribution. However, most existing validation metrics, which are based on point/grid comparison using simple statistics, cannot effectively measure satellite's skill of capturing the spatial patterns of precipitation fields. This deficiency results from the fact that point/grid-wised comparison does not take into account of the spatial coherence of precipitation fields. Furth more, another weakness of many metrics is that they can barely provide information on why satellite products perform well or poor. Motivated by our recent findings of the consistent spatial patterns of the precipitation field over the western U.S., we developed a new metric utilizing EOF analysis and Shannon entropy. The metric can be derived through two steps: 1) capture the dominant spatial patterns of precipitation fields from both satellite products and reference data through EOF analysis, and 2) compute the similarities between the corresponding dominant patterns using mutual information measurement defined with Shannon entropy. Instead of individual point/grid, the new metric treat the entire precipitation field simultaneously, naturally taking advantage of spatial dependence. Since the dominant spatial patterns are shaped by physical processes, the new metric can shed light on why satellite product can or cannot capture the spatial patterns. For demonstration, a experiment was carried out to evaluate a satellite

The use of direct geometry spectrometers in molecular spectroscopy

International Nuclear Information System (INIS)

Parker, Stewart F; Ramirez-Cuesta, Anibal J; Albers, Peter W; Lennon, David

2014-01-01

The advantages and disadvantages of the use of direct geometry spectrometers for molecular spectroscopy and catalysis studies are described. We show that both direct and indirect geometry INS spectrometers are important tools for the study of industrially relevant areas such as catalysis, proton conductors and gas separation. We propose a novel hybrid instrument, Cerberus, that would offer high sensitivity and high-to-reasonable resolution across the entire 'mid-infrared' spectral range that would effectively advance research in these areas

Synoptic evaluation of scale-dependent metrics for hydrographic line feature geometry

Science.gov (United States)

Stanislawski, Larry V.; Buttenfield, Barbara P.; Raposo, Paulo; Cameron, Madeline; Falgout, Jeff T.

2015-01-01

conterminous United States and compared to topographic metrics. A concurrent processing workflow is implemented using a Linux high-performance computing cluster to simultaneously process multiple subbasins, and thereby complete the work in a fraction of the time required for a single-process environment. In addition, similar metrics are generated for several levels of simplification of the hydrographic features to quantify the effects of simplification over the various landscape conditions. Objectives of this exploratory investigation are to quantify geometric characteristics of linear hydrographic features over the various terrain conditions within the conterminous United States and thereby illuminate relations between stream geomorphological conditions and cartographic representation. The synoptic view of these characteristics over regional watersheds that is afforded through concurrent processing, in conjunction with terrain conditions, may reveal patterns for classifying cartographic stream features into stream geomorphological classes. Furthermore, the synoptic measurement of the amount of change in geometric characteristics caused by the several levels of simplification can enable estimation of tolerance values that appropriately control simplification-induced geometric change of the cartographic features within the various geomorphological classes in the country. Hence, these empirically derived rules or relations could help generate multiscale-representations of features through automated generalization that adequately maintain surface drainage variations and patterns reflective of the natural stream geomorphological conditions across the country.

Extended differential geometry as a basis for physical field theory

International Nuclear Information System (INIS)

Bruce, M.H.

1984-01-01

An extension of Riemann differential geometry is considered as a broadened uniform basis for physical field theory. The requirements for such a theory are set and interpreted as a generalized Ricci calculus capable of supporting certain physical affine motions and metric constraints. Both tensor and spinor languages are considered and a variational calculus is formulated within the geometry. The dominant emergent feature is the replacement of ordinary derivatives by generalized differential operators involving the usual Christoffel symbols as well as more general connection parameters. Then the Euler-Lagrange equations with constraints may be regarded as a general differential geometry and an action principle is formulated to give equations of motion in terms of generalized momentum operations. A cononical momentum tensor is employed which yields, by a generalized boundary variations of the action a set of conservation laws. The formulation is then applied to such diverse topics as the generalizing of the Dirac equation, the Lorentz and radiation terms for a charged particle, the relativistic rotator, and considerations on a geometric origin for the the Einstein energy density tensor

Arbitrariness of geometry and the aether

International Nuclear Information System (INIS)

Browne, P.F.

1976-01-01

As emphasized by Milne, an observer ultimately depends on the transmission and reception of light signals for the measurement of natural lengths and periods remote from his world point. The laws of geometry which are obeyed when these lengths and periods are plotted on a space--time depend, inevitably, on assumptions concerning the dependence of light velocity on the spatial and temporal coordinates. A convention regarding light velocity fixes the geometry, and conversely. However, the convention of flat space--time implies nonintegrable ''radar distances'' unless the concept of coordinate-dependent units of measure is employed. Einstein's space--time has the advantage of admitting a special reference system R with respect to which the aether fluid is at rest and the total gravitational field vanishes. A holonomic transformation from R to another reference system R belonging to the same space--time introduces a nonpermanent gravitational field and holonomic aether motion. A nonholonomic transformation from R to a reference system R* which belongs to a different space--time introduces a permanent gravitational field and nonholonomic aether motion. The arbitrariness of geometry is expressed by extending covariance to include the latter transformation. By means of a nonholonomic (or units) transformation it is possible, with the aid of the principle of equivalence, to obtain the Schwarzschild and de Sitter metrics from the Newtonian fields that would arise in a flat space--time description. Some light is thrown on the interpretation of cosmological models

Baby universe metric equivalent to an interior black-hole metric

International Nuclear Information System (INIS)

Gonzalez-Diaz, P.F.

1991-01-01

It is shown that the maximally extended metric corresponding to a large wormhole is the unique possible wormhole metric whose baby universe sector is conformally equivalent ot the maximal inextendible Kruskal metric corresponding to the interior region of a Schwarzschild black hole whose gravitational radius is half the wormhole neck radius. The physical implications of this result in the black hole evaporation process are discussed. (orig.)

HIFI - a dedicated HIgh-FIeld diffraction and spectroscopy instrument

International Nuclear Information System (INIS)

Steffens, P.; Enderle, M.; Boehm, M.; Roux, S.

2011-01-01

The outstanding scientific impact of single-crystal neutron diffraction and spectroscopy in steady state vertical magnetic fields up to 15 T (17 T without dilution fringe) is reflected in numerous high-profile publications. Magnetic fields 30 T - 35 T in vertical geometry allow to address enigmatic questions without equivalence at lower fields. The constraints implied by such magnetic fields demand a specially designed dedicated instrument. Since the vertical field geometry is crucial for single-crystal diffraction as well as spectroscopy, the solid angle of scattered neutrons is restricted, and a high-flux reactor is best suited to host a corresponding instrument. We propose a world-wide unique versatile instrument for diffraction and spectroscopy in vertical steady fields of 30 T. (authors)

Neurosurgical virtual reality simulation metrics to assess psychomotor skills during brain tumor resection.

Science.gov (United States)

Azarnoush, Hamed; Alzhrani, Gmaan; Winkler-Schwartz, Alexander; Alotaibi, Fahad; Gelinas-Phaneuf, Nicholas; Pazos, Valérie; Choudhury, Nusrat; Fares, Jawad; DiRaddo, Robert; Del Maestro, Rolando F

2015-05-01

Virtual reality simulator technology together with novel metrics could advance our understanding of expert neurosurgical performance and modify and improve resident training and assessment. This pilot study introduces innovative metrics that can be measured by the state-of-the-art simulator to assess performance. Such metrics cannot be measured in an operating room and have not been used previously to assess performance. Three sets of performance metrics were assessed utilizing the NeuroTouch platform in six scenarios with simulated brain tumors having different visual and tactile characteristics. Tier 1 metrics included percentage of brain tumor resected and volume of simulated "normal" brain tissue removed. Tier 2 metrics included instrument tip path length, time taken to resect the brain tumor, pedal activation frequency, and sum of applied forces. Tier 3 metrics included sum of forces applied to different tumor regions and the force bandwidth derived from the force histogram. The results outlined are from a novice resident in the second year of training and an expert neurosurgeon. The three tiers of metrics obtained from the NeuroTouch simulator do encompass the wide variability of technical performance observed during novice/expert resections of simulated brain tumors and can be employed to quantify the safety, quality, and efficiency of technical performance during simulated brain tumor resection. Tier 3 metrics derived from force pyramids and force histograms may be particularly useful in assessing simulated brain tumor resections. Our pilot study demonstrates that the safety, quality, and efficiency of novice and expert operators can be measured using metrics derived from the NeuroTouch platform, helping to understand how specific operator performance is dependent on both psychomotor ability and cognitive input during multiple virtual reality brain tumor resections.

Einstein-Gauss-Bonnet metrics: black holes, black strings and a staticity theorem

International Nuclear Information System (INIS)

Bogdanos, C.; Charmousis, C.; Gouteraux, B.; Zegers, R.

2009-01-01

We find the general solution of the 6-dimensional Einstein-Gauss-Bonnet equations in a large class of space and time-dependent warped geometries. Several distinct families of solutions are found, some of which include black string metrics, space and time-dependent solutions and black holes with exotic horizons. Among these, some are shown to verify a Birkhoff type staticity theorem, although here, the usual assumption of maximal symmetry on the horizon is relaxed, allowing exotic horizon geometries. We provide explicit examples of such static exotic black holes, including ones whose horizon geometry is that of a Bergman space. We find that the situation is very different from higher-dimensional general relativity, where Einstein spaces are admissible black hole horizons and the associated black hole potential is not even affected. In Einstein-Gauss-Bonnet theory, on the contrary, the non-trivial Weyl tensor of such exotic horizons is exposed to the bulk dynamics through the higher order Gauss-Bonnet term, severely constraining the allowed horizon geometries and adding a novel charge-like parameter to the black hole potential. The latter is related to the Euler characteristic of the four-dimensional horizon and provides, in some cases, additional black hole horizons.

WIMT in Gullstraend-Painleve and Reissner-Nordstroem metrics: induced stable gravito-magnetic monopoles

Energy Technology Data Exchange (ETDEWEB)

Romero, Jesus Martin [Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Mar del Plata (Argentina); Bellini, Mauricio [Universidad Nacional de Mar del Plata, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Mar del Plata (Argentina)

2015-05-15

The aim of this work is to apply Weitzeboeck Induced Matter Theory (WIMT) to Gullstraend-Painleve and Reissner-Nordstroem metrics in the framework of WIMT. This is a newly developed method that extends Induced Matter Theory from a curved 5D manifold using the Weitzeboeck's geometry, using the fact that the Riemann-Weitzenboeck curvature tensor is always null. We obtain the presence of currents whose interpretation can lead to the presence of stable gravito-magnetic monopoles. (orig.)

WIMT in Gullstraend-Painleve and Reissner-Nordstroem metrics: induced stable gravito-magnetic monopoles

International Nuclear Information System (INIS)

Romero, Jesus Martin; Bellini, Mauricio

2015-01-01

The aim of this work is to apply Weitzeboeck Induced Matter Theory (WIMT) to Gullstraend-Painleve and Reissner-Nordstroem metrics in the framework of WIMT. This is a newly developed method that extends Induced Matter Theory from a curved 5D manifold using the Weitzeboeck's geometry, using the fact that the Riemann-Weitzenboeck curvature tensor is always null. We obtain the presence of currents whose interpretation can lead to the presence of stable gravito-magnetic monopoles. (orig.)

Stochastic Geometry and Quantum Gravity: Some Rigorous Results

Science.gov (United States)

Zessin, H.

The aim of these lectures is a short introduction into some recent developments in stochastic geometry which have one of its origins in simplicial gravity theory (see Regge Nuovo Cimento 19: 558-571, 1961). The aim is to define and construct rigorously point processes on spaces of Euclidean simplices in such a way that the configurations of these simplices are simplicial complexes. The main interest then is concentrated on their curvature properties. We illustrate certain basic ideas from a mathematical point of view. An excellent representation of this area can be found in Schneider and Weil (Stochastic and Integral Geometry, Springer, Berlin, 2008. German edition: Stochastische Geometrie, Teubner, 2000). In Ambjørn et al. (Quantum Geometry Cambridge University Press, Cambridge, 1997) you find a beautiful account from the physical point of view. More recent developments in this direction can be found in Ambjørn et al. ("Quantum gravity as sum over spacetimes", Lect. Notes Phys. 807. Springer, Heidelberg, 2010). After an informal axiomatic introduction into the conceptual foundations of Regge's approach the first lecture recalls the concepts and notations used. It presents the fundamental zero-infinity law of stochastic geometry and the construction of cluster processes based on it. The second lecture presents the main mathematical object, i.e. Poisson-Delaunay surfaces possessing an intrinsic random metric structure. The third and fourth lectures discuss their ergodic behaviour and present the two-dimensional Regge model of pure simplicial quantum gravity. We terminate with the formulation of basic open problems. Proofs are given in detail only in a few cases. In general the main ideas are developed. Sufficiently complete references are given.

Properties of C-metric spaces

Science.gov (United States)

Croitoru, Anca; Apreutesei, Gabriela; Mastorakis, Nikos E.

2017-09-01

The subject of this paper belongs to the theory of approximate metrics [23]. An approximate metric on X is a real application defined on X × X that satisfies only a part of the metric axioms. In a recent paper [23], we introduced a new type of approximate metric, named C-metric, that is an application which satisfies only two metric axioms: symmetry and triangular inequality. The remarkable fact in a C-metric space is that a topological structure induced by the C-metric can be defined. The innovative idea of this paper is that we obtain some convergence properties of a C-metric space in the absence of a metric. In this paper we investigate C-metric spaces. The paper is divided into four sections. Section 1 is for Introduction. In Section 2 we recall some concepts and preliminary results. In Section 3 we present some properties of C-metric spaces, such as convergence properties, a canonical decomposition and a C-fixed point theorem. Finally, in Section 4 some conclusions are highlighted.

Learning Low-Dimensional Metrics

OpenAIRE

Jain, Lalit; Mason, Blake; Nowak, Robert

2017-01-01

This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric;4) we also bound the accuracy ...

Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS_5×S"5 spacetime

International Nuclear Information System (INIS)

Zhang, Jia-Lin; Cai, Rong-Gen; Yu, Hongwei

2015-01-01

We study the thermodynamics and thermodynamic geometry of a five-dimensional Schwarzschild AdS black hole in AdS_5×S"5 spacetime by treating the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the chemical potential is always negative in the stable branch of black hole thermodynamics and it has a chance to be positive, but appears in the unstable branch. We calculate the scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric and Quevedo metric, respectively and we find that the scalar curvature in the Weinhold metric is always vanishing, while in the Ruppeiner metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed chemical potential, and in the Quevedo metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed number of colors and to the vanishing of the heat capacity with fixed chemical potential.

Nuclear instrumentation for uranium exploration

International Nuclear Information System (INIS)

Sarma, Ch. V.N.; Sarma, C.V.R.; Sreehari, R.

1999-01-01

Instrumentation required for uranium exploration may be broadly classified based on surface and sub-surface measurement of gamma-ray intensity. Surface measurement of gross and spectral gamma intensity are carried out by employing portable Geiger Mueller/scintillation counters and four-channel spectrometers. Measurement of thoron ( 220 Rn) and radon ( 222 Rn) in the soil gas is being carried out by closed circuit technique using radon measuring system. Radiometric mapping of trenches, pits and mine-faces are carried out using shielded probe with 2π source geometry, whereas logging sonde with instruments through the steel armoured cable are employed for point to 4π geometry. Spectral borehole logging system with built-in multi-channel analyser (MCA) has been developed for the uranium exploration programme for AMD. Note-book PC based high sensitivity air-borne gamma-ray spectrometric survey system has been designed, developed and test flown. (author)

Scalar-metric and scalar-metric-torsion gravitational theories

International Nuclear Information System (INIS)

Aldersley, S.J.

1977-01-01

The techniques of dimensional analysis and of the theory of tensorial concomitants are employed to study field equations in gravitational theories which incorporate scalar fields of the Brans-Dicke type. Within the context of scalar-metric gravitational theories, a uniqueness theorem for the geometric (or gravitational) part of the field equations is proven and a Lagrangian is determined which is uniquely specified by dimensional analysis. Within the context of scalar-metric-torsion gravitational theories a uniqueness theorem for field Lagrangians is presented and the corresponding Euler-Lagrange equations are given. Finally, an example of a scalar-metric-torsion theory is presented which is similar in many respects to the Brans-Dicke theory and the Einstein-Cartan theory

Role of marketing metrics in strategic brand management

Directory of Open Access Journals (Sweden)

Mamula Tatjana

2012-01-01

Full Text Available This paper shows the role and importance of a brand as a strategic instrument of a company, that ensures sustainability of company's performance in the market on a longer-term basis. To achieve brand competitiveness, it is necessary to manage its equity, which is presented in this paper as an imperative of everyday business operations. Brand evaluation in strategic management is conducted by measuring brand performance in the market, finding measures and ways to manage the brand successfully in order to increase its equity using the set of marketing metric indicators.

METRIC context unit architecture

Energy Technology Data Exchange (ETDEWEB)

Simpson, R.O.

1988-01-01

METRIC is an architecture for a simple but powerful Reduced Instruction Set Computer (RISC). Its speed comes from the simultaneous processing of several instruction streams, with instructions from the various streams being dispatched into METRIC's execution pipeline as they become available for execution. The pipeline is thus kept full, with a mix of instructions for several contexts in execution at the same time. True parallel programming is supported within a single execution unit, the METRIC Context Unit. METRIC's architecture provides for expansion through the addition of multiple Context Units and of specialized Functional Units. The architecture thus spans a range of size and performance from a single-chip microcomputer up through large and powerful multiprocessors. This research concentrates on the specification of the METRIC Context Unit at the architectural level. Performance tradeoffs made during METRIC's design are discussed, and projections of METRIC's performance are made based on simulation studies.

Fractal geometry and computer graphics

CERN Document Server

Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele

1992-01-01

Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...

Development of quality control and instrumentation performance metrics for diffuse optical spectroscopic imaging instruments in the multi-center clinical environment

Science.gov (United States)

Keene, Samuel T.; Cerussi, Albert E.; Warren, Robert V.; Hill, Brian; Roblyer, Darren; Leproux, AnaÑ--s.; Durkin, Amanda F.; O'Sullivan, Thomas D.; Haghany, Hosain; Mantulin, William W.; Tromberg, Bruce J.

2013-03-01

Instrument equivalence and quality control are critical elements of multi-center clinical trials. We currently have five identical Diffuse Optical Spectroscopic Imaging (DOSI) instruments enrolled in the American College of Radiology Imaging Network (ACRIN, #6691) trial located at five academic clinical research sites in the US. The goal of the study is to predict the response of breast tumors to neoadjuvant chemotherapy in 60 patients. In order to reliably compare DOSI measurements across different instruments, operators and sites, we must be confident that the data quality is comparable. We require objective and reliable methods for identifying, correcting, and rejecting low quality data. To achieve this goal, we developed and tested an automated quality control algorithm that rejects data points below the instrument noise floor, improves tissue optical property recovery, and outputs a detailed data quality report. Using a new protocol for obtaining dark-noise data, we applied the algorithm to ACRIN patient data and successfully improved the quality of recovered physiological data in some cases.

Geometries

CERN Document Server

Sossinsky, A B

2012-01-01

The book is an innovative modern exposition of geometry, or rather, of geometries; it is the first textbook in which Felix Klein's Erlangen Program (the action of transformation groups) is systematically used as the basis for defining various geometries. The course of study presented is dedicated to the proposition that all geometries are created equal--although some, of course, remain more equal than others. The author concentrates on several of the more distinguished and beautiful ones, which include what he terms "toy geometries", the geometries of Platonic bodies, discrete geometries, and classical continuous geometries. The text is based on first-year semester course lectures delivered at the Independent University of Moscow in 2003 and 2006. It is by no means a formal algebraic or analytic treatment of geometric topics, but rather, a highly visual exposition containing upwards of 200 illustrations. The reader is expected to possess a familiarity with elementary Euclidean geometry, albeit those lacking t...

Observable traces of non-metricity: New constraints on metric-affine gravity

Science.gov (United States)

Delhom-Latorre, Adrià; Olmo, Gonzalo J.; Ronco, Michele

2018-05-01

Relaxing the Riemannian condition to incorporate geometric quantities such as torsion and non-metricity may allow to explore new physics associated with defects in a hypothetical space-time microstructure. Here we show that non-metricity produces observable effects in quantum fields in the form of 4-fermion contact interactions, thereby allowing us to constrain the scale of non-metricity to be greater than 1 TeV by using results on Bahbah scattering. Our analysis is carried out in the framework of a wide class of theories of gravity in the metric-affine approach. The bound obtained represents an improvement of several orders of magnitude to previous experimental constraints.

Algebraic structure of Robinson–Trautman and Kundt geometries in arbitrary dimension

International Nuclear Information System (INIS)

Podolský, J; Švarc, R

2015-01-01

We investigate the Weyl tensor algebraic structure of a fully general family of D-dimensional geometries that admit a non-twisting and shear-free null vector field k. From the coordinate components of the curvature tensor we explicitly derive all Weyl scalars of various boost weights. This enables us to give a complete algebraic classification of the metrics in the case when the optically privileged null direction k is a (multiple) Weyl aligned null direction (WAND). No field equations are applied, so the results are valid not only in Einstein's gravity, including its extension to higher dimensions, but also in any metric gravitation theory that admits non-twisting and shear-free spacetimes. We prove that all such geometries are of type I(b), or more special, and we derive surprisingly simple necessary and sufficient conditions under which k is a double, triple or quadruple WAND. All possible algebraically special types, including the refinement to subtypes, are thus identified, namely II(a), II(b), II(c), II(d), III(a), III(b), N, O, II i , III i , D, D(a), D(b), D(c), D(d), and their combinations. Some conditions are identically satisfied in four dimensions. We discuss both important subclasses, namely the Kundt family of geometries with the vanishing expansion (Θ=0) and the Robinson–Trautman family (Θ ≠ 0, and in particular Θ=1/r). Finally, we apply Einstein's field equations and obtain a classification of all Robinson–Trautman vacuum spacetimes. This reveals fundamental algebraic differences in the D>4 and D=4 cases, namely that in higher dimensions there only exist such spacetimes of types D(a) ≡ D(abd), D(c) ≡ D(bcd) and O. (paper)

The Inelastic Instrument suite at the SNS

International Nuclear Information System (INIS)

Granroth, Garrett E; Abernathy, Douglas L; Ehlers, Georg; Hagen, Mark E; Herwig, Kenneth W; Mamontov, Eugene; Ohl, Michael E; Wildgruber, Christoph U

2008-01-01

The instruments in the extensive suite of spectrometers at the SNS are in various stages of installation and commissioning. The Back Scattering Spectrometer (BASIS) is installed and is in commissioning. It's near backscattering analyzer crystals provide the 3 eV resolution as expected. BASIS will enter the user program in the fall of 2007. The ARCS wide angular-range thermal to epithermal neutron spectrometer will come on line in the fall of 2007 followed shortly by the Cold Neutron Chopper Spectrometer. These two direct geometry instruments provide moderate resolution and the ability to trade resolution for flux. In addition both instruments have detector coverage out to 140o to provide a large Q range. The SEQUOIA spectrometer, complete in 2008, is the direct geometry instrument that will provide fine resolution in the thermal to epithermal range. The Spin-Echo spectrometer, to be completed on a similar time scale, will provide the finest energy resolution worldwide. The HYSPEC spectrometer, available no later than 2011, will provide polarized capabilities and optimized flux in the thermal energy range. Finally, the Vision chemical spectrometer will use crystal analyzers to study energy transfers into the epithermal range

EVA: laparoscopic instrument tracking based on Endoscopic Video Analysis for psychomotor skills assessment.

Science.gov (United States)

Oropesa, Ignacio; Sánchez-González, Patricia; Chmarra, Magdalena K; Lamata, Pablo; Fernández, Alvaro; Sánchez-Margallo, Juan A; Jansen, Frank Willem; Dankelman, Jenny; Sánchez-Margallo, Francisco M; Gómez, Enrique J

2013-03-01

The EVA (Endoscopic Video Analysis) tracking system is a new system for extracting motions of laparoscopic instruments based on nonobtrusive video tracking. The feasibility of using EVA in laparoscopic settings has been tested in a box trainer setup. EVA makes use of an algorithm that employs information of the laparoscopic instrument's shaft edges in the image, the instrument's insertion point, and the camera's optical center to track the three-dimensional position of the instrument tip. A validation study of EVA comprised a comparison of the measurements achieved with EVA and the TrEndo tracking system. To this end, 42 participants (16 novices, 22 residents, and 4 experts) were asked to perform a peg transfer task in a box trainer. Ten motion-based metrics were used to assess their performance. Construct validation of the EVA has been obtained for seven motion-based metrics. Concurrent validation revealed that there is a strong correlation between the results obtained by EVA and the TrEndo for metrics, such as path length (ρ = 0.97), average speed (ρ = 0.94), or economy of volume (ρ = 0.85), proving the viability of EVA. EVA has been successfully validated in a box trainer setup, showing the potential of endoscopic video analysis to assess laparoscopic psychomotor skills. The results encourage further implementation of video tracking in training setups and image-guided surgery.

Koszul information geometry and Souriau Lie group thermodynamics

Energy Technology Data Exchange (ETDEWEB)

Barbaresco, Frédéric, E-mail: frederic.barbaresco@thalesgroup.com

2015-01-13

The François Massieu 1869 idea to derive some mechanical and thermal properties of physical systems from 'Characteristic Functions', was developed by Gibbs and Duhem in thermodynamics with the concept of potentials, and introduced by Poincaré in probability. This paper deals with generalization of this Characteristic Function concept by Jean-Louis Koszul in Mathematics and by Jean-Marie Souriau in Statistical Physics. The Koszul-Vinberg Characteristic Function (KVCF) on convex cones will be presented as cornerstone of 'Information Geometry' theory, defining Koszul Entropy as Legendre transform of minus the logarithm of KVCF, and Fisher Information Metrics as hessian of these dual functions, invariant by their automorphisms. In parallel, Souriau has extended the Characteristic Function in Statistical Physics looking for other kinds of invariances through co-adjoint action of a group on its momentum space, defining physical observables like energy, heat and momentum as pure geometrical objects. In covariant Souriau model, Gibbs equilibriums states are indexed by a geometric parameter, the Geometric (Planck) Temperature, with values in the Lie algebra of the dynamical Galileo/Poincaré groups, interpreted as a space-time vector, giving to the metric tensor a null Lie derivative. Fisher Information metric appears as the opposite of the derivative of Mean 'Moment map' by geometric temperature, equivalent to a Geometric Capacity or Specific Heat. These elements has been developed by author in [10][11].

Geometry and project: the example of Piazza della Vittoria in Genoa

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Luisa Cogorno

2012-06-01

Full Text Available The study on the Genoese architectures in the thirties of Piazza della Vittoria  highlights the paramount  role of geometry for the project. The square, created by architect Marcello Piacentini between 1927 and 1930, stands opposite the railway station Genoa Brignole, pursuing a very logical representation: a new, very wide square surrounded by arcades ... the new civic-wordly heart of the  city (M. Piacentini. The methodological tool applied for the critical reading  was the  integrated relief: perceptual and historical analysis, relief and graphic representation of the whole and of the details, reconstruction of the compositional logic, study of materials used; the different phases showed the trasversality of the role of geometry –verified by the metric survey and by the compositive reading of the proportions- and the presence of dimensional canons unusual for the city.

Metrics to describe the effects of landscape pattern on hydrology in a lotic peatland

Science.gov (United States)

Yuan, J.; Cohen, M. J.; Kaplan, D. A.; Acharya, S.; Larsen, L.; Nungesser, M.

2013-12-01

Strong reciprocal interactions exist between landscape patterns and ecological processes. Hydrology is the dominant abiotic driver of ecological processes in wetlands, particularly flowing wetlands, but is both the control on and controlled by the geometry of vegetation patterning. Landscape metrics are widely used to quantitatively link pattern and process. Our goal here was to use several candidate spatial pattern metrics to predict the effects of wetland vegetation pattern on hydrologic regime, specifically hydroperiod, in the ridge-slough patterned landscape of the Everglades. The metrics focus on the capacity for longitudinally connected flow, and thus the ability of this low-gradient patterned landscape to route water from upstream. We first explored flow friction cost (FFC), a weighted spatial distance procedure wherein ridges have a high flow cost than sloughs by virtue of their elevation and vegetation structure, to evaluate water movement through different landscape configurations. We also investigated existing published flow metrics, specifically the Directional Connectivity Index (DCI) and Landscape Discharge Competence (LDC), that seek to quantify connectivity, one of the sentinel targets of ecological restoration. Hydroperiod was estimated using a numerical hydrologic model (SWIFT 2D) in real and synthetic landscapes with varying vegetation properties ( patch anisotropy, ridge density). Synthetic landscapes were constrained by the geostatistical properties of the best conserved patterned, and contained five anisotropy levels and seven ridge density levels. These were used to construct the relationship between landscape metrics and hydroperiod. Then, using historical images from 1940 to 2004, we applied the metrics toback-cast hydroperiod. Current vegetation maps were used to test scale dependency for each metric. Our results suggest that both FFC and DCI are good predictors of hydroperiod under free flowing conditions, and that they can be used

Effectiveness of Discovery Learning-Based Transformation Geometry Module

Science.gov (United States)

Febriana, R.; Haryono, Y.; Yusri, R.

2017-09-01

Development of transformation geometry module is conducted because the students got difficulties to understand the existing book. The purpose of the research was to find out the effectiveness of discovery learning-based transformation geometry module toward student’s activity. Model of the development was Plomp model consisting preliminary research, prototyping phase and assessment phase. The research was focused on assessment phase where it was to observe the designed product effectiveness. The instrument was observation sheet. The observed activities were visual activities, oral activities, listening activities, mental activities, emotional activities and motor activities. Based on the result of the research, it is found that visual activities, learning activities, writing activities, the student’s activity is in the criteria very effective. It can be concluded that the use of discovery learning-based transformation geometry module use can increase the positive student’s activity and decrease the negative activity.

Nonparametric Information Geometry: From Divergence Function to Referential-Representational Biduality on Statistical Manifolds

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Jun Zhang

2013-12-01

Full Text Available Divergence functions are the non-symmetric “distance” on the manifold, Μθ, of parametric probability density functions over a measure space, (Χ,μ. Classical information geometry prescribes, on Μθ: (i a Riemannian metric given by the Fisher information; (ii a pair of dual connections (giving rise to the family of α-connections that preserve the metric under parallel transport by their joint actions; and (iii a family of divergence functions ( α-divergence defined on Μθ x Μθ, which induce the metric and the dual connections. Here, we construct an extension of this differential geometric structure from Μθ (that of parametric probability density functions to the manifold, Μ, of non-parametric functions on X, removing the positivity and normalization constraints. The generalized Fisher information and α-connections on M are induced by an α-parameterized family of divergence functions, reflecting the fundamental convex inequality associated with any smooth and strictly convex function. The infinite-dimensional manifold, M, has zero curvature for all these α-connections; hence, the generally non-zero curvature of M can be interpreted as arising from an embedding of Μθ into Μ. Furthermore, when a parametric model (after a monotonic scaling forms an affine submanifold, its natural and expectation parameters form biorthogonal coordinates, and such a submanifold is dually flat for α = ± 1, generalizing the results of Amari’s α-embedding. The present analysis illuminates two different types of duality in information geometry, one concerning the referential status of a point (measurable function expressed in the divergence function (“referential duality” and the other concerning its representation under an arbitrary monotone scaling (“representational duality”.

Fault Management Metrics

Science.gov (United States)

Johnson, Stephen B.; Ghoshal, Sudipto; Haste, Deepak; Moore, Craig

2017-01-01

This paper describes the theory and considerations in the application of metrics to measure the effectiveness of fault management. Fault management refers here to the operational aspect of system health management, and as such is considered as a meta-control loop that operates to preserve or maximize the system's ability to achieve its goals in the face of current or prospective failure. As a suite of control loops, the metrics to estimate and measure the effectiveness of fault management are similar to those of classical control loops in being divided into two major classes: state estimation, and state control. State estimation metrics can be classified into lower-level subdivisions for detection coverage, detection effectiveness, fault isolation and fault identification (diagnostics), and failure prognosis. State control metrics can be classified into response determination effectiveness and response effectiveness. These metrics are applied to each and every fault management control loop in the system, for each failure to which they apply, and probabilistically summed to determine the effectiveness of these fault management control loops to preserve the relevant system goals that they are intended to protect.

Completion of a Dislocated Metric Space

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P. Sumati Kumari

2015-01-01

Full Text Available We provide a construction for the completion of a dislocated metric space (abbreviated d-metric space; we also prove that the completion of the metric associated with a d-metric coincides with the metric associated with the completion of the d-metric.

Metrics with vanishing quantum corrections

International Nuclear Information System (INIS)

Coley, A A; Hervik, S; Gibbons, G W; Pope, C N

2008-01-01

We investigate solutions of the classical Einstein or supergravity equations that solve any set of quantum corrected Einstein equations in which the Einstein tensor plus a multiple of the metric is equated to a symmetric conserved tensor T μν (g αβ , ∂ τ g αβ , ∂ τ ∂ σ g αβ , ...,) constructed from sums of terms, the involving contractions of the metric and powers of arbitrary covariant derivatives of the curvature tensor. A classical solution, such as an Einstein metric, is called universal if, when evaluated on that Einstein metric, T μν is a multiple of the metric. A Ricci flat classical solution is called strongly universal if, when evaluated on that Ricci flat metric, T μν vanishes. It is well known that pp-waves in four spacetime dimensions are strongly universal. We focus attention on a natural generalization; Einstein metrics with holonomy Sim(n - 2) in which all scalar invariants are zero or constant. In four dimensions we demonstrate that the generalized Ghanam-Thompson metric is weakly universal and that the Goldberg-Kerr metric is strongly universal; indeed, we show that universality extends to all four-dimensional Sim(2) Einstein metrics. We also discuss generalizations to higher dimensions

Geometry

CERN Document Server

Prasolov, V V

2015-01-01

This book provides a systematic introduction to various geometries, including Euclidean, affine, projective, spherical, and hyperbolic geometries. Also included is a chapter on infinite-dimensional generalizations of Euclidean and affine geometries. A uniform approach to different geometries, based on Klein's Erlangen Program is suggested, and similarities of various phenomena in all geometries are traced. An important notion of duality of geometric objects is highlighted throughout the book. The authors also include a detailed presentation of the theory of conics and quadrics, including the theory of conics for non-Euclidean geometries. The book contains many beautiful geometric facts and has plenty of problems, most of them with solutions, which nicely supplement the main text. With more than 150 figures illustrating the arguments, the book can be recommended as a textbook for undergraduate and graduate-level courses in geometry.

Remarks on G-Metric Spaces

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Bessem Samet

2013-01-01

Full Text Available In 2005, Mustafa and Sims (2006 introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.

A View on Optimal Transport from Noncommutative Geometry

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Francesco D'Andrea

2010-07-01

Full Text Available We discuss the relation between the Wasserstein distance of order 1 between probability distributions on a metric space, arising in the study of Monge-Kantorovich transport problem, and the spectral distance of noncommutative geometry. Starting from a remark of Rieffel on compact manifolds, we first show that on any - i.e. non-necessary compact - complete Riemannian spin manifolds, the two distances coincide. Then, on convex manifolds in the sense of Nash embedding, we provide some natural upper and lower bounds to the distance between any two probability distributions. Specializing to the Euclidean space R^n, we explicitly compute the distance for a particular class of distributions generalizing Gaussian wave packet. Finally we explore the analogy between the spectral and the Wasserstein distances in the noncommutative case, focusing on the standard model and the Moyal plane. In particular we point out that in the two-sheet space of the standard model, an optimal-transport interpretation of the metric requires a cost function that does not vanish on the diagonal. The latest is similar to the cost function occurring in the relativistic heat equation.

Quantum Riemannian geometry of phase space and nonassociativity

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Beggs Edwin J.

2017-04-01

Full Text Available Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics but also differential forms, bundles and Riemannian structures at this level. The data for the algebra quantisation is a classical Poisson bracket while the data for quantum differential forms is a Poisson-compatible connection. We give an introduction to our recent result whereby further classical data such as classical bundles, metrics etc. all become quantised in a canonical ‘functorial’ way at least to 1st order in deformation theory. The theory imposes compatibility conditions between the classical Riemannian and Poisson structures as well as new physics such as typical nonassociativity of the differential structure at 2nd order. We develop in detail the case of ℂℙn where the commutation relations have the canonical form [wi, w̄j] = iλδij similar to the proposal of Penrose for quantum twistor space. Our work provides a canonical but ultimately nonassociative differential calculus on this algebra and quantises the metric and Levi-Civita connection at lowest order in λ.

Critical geometry of a thermal big bang

Science.gov (United States)

Afshordi, Niayesh; Magueijo, João

2016-11-01

We explore the space of scalar-tensor theories containing two nonconformal metrics, and find a discontinuity pointing to a "critical" cosmological solution. Due to the different maximal speeds of propagation for matter and gravity, the cosmological fluctuations start off inside the horizon even without inflation, and will more naturally have a thermal origin (since there is never vacuum domination). The critical model makes an unambiguous, nontuned prediction for the spectral index of the scalar fluctuations: nS=0.96478 (64 ) . Considering also that no gravitational waves are produced, we have unveiled the most predictive model on offer. The model has a simple geometrical interpretation as a probe 3-brane embedded in an E AdS2×E3 geometry.

Common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition

International Nuclear Information System (INIS)

Abu-Donia, H.M.

2007-01-01

Some common fixed point theorems for multi-valued mappings under φ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for φ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding ε ∞ -space [El-Naschie MS. On the unification of the fundamental forces and complex time in the ε ∞ -space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45

Common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition

Energy Technology Data Exchange (ETDEWEB)

Abu-Donia, H.M. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)

2007-10-15

Some common fixed point theorems for multi-valued mappings under {phi}-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for {phi}-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding {epsilon} {sup {infinity}}-space [El-Naschie MS. On the unification of the fundamental forces and complex time in the {epsilon} {sup {infinity}}-space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45].

Evaluation Metrics for Simulations of Tropical South America

Science.gov (United States)

Gallup, S.; Baker, I. T.; Denning, A. S.; Cheeseman, M.; Haynes, K. D.; Phillips, M.

2017-12-01

The evergreen broadleaf forest of the Amazon Basin is the largest rainforest on earth, and has teleconnections to global climate and carbon cycle characteristics. This region defies simple characterization, spanning large gradients in total rainfall and seasonal variability. Broadly, the region can be thought of as trending from light-limited in its wettest areas to water-limited near the ecotone, with individual landscapes possibly exhibiting the characteristics of either (or both) limitations during an annual cycle. A basin-scale classification of mean behavior has been elusive, and ecosystem response to seasonal cycles and anomalous drought events has resulted in some disagreement in the literature, to say the least. However, new observational platforms and instruments make characterization of the heterogeneity and variability more feasible.To evaluate simulations of ecophysiological function, we develop metrics that correlate various observational products with meteorological variables such as precipitation and radiation. Observations include eddy covariance fluxes, Solar Induced Fluorescence (SIF, from GOME2 and OCO2), biomass and vegetation indices. We find that the modest correlation between SIF and precipitation decreases with increasing annual precipitation, although the relationship is not consistent between products. Biomass increases with increasing precipitation. Although vegetation indices are generally correlated with biomass and precipitation, they can saturate or experience retrieval issues during cloudy periods.Using these observational products and relationships, we develop a set of model evaluation metrics. These metrics are designed to call attention to models that get "the right answer only if it's for the right reason," and provide an opportunity for more critical evaluation of model physics. These metrics represent a testbed that can be applied to multiple models as a means to evaluate their performance in tropical South America.

Metric-adjusted skew information

DEFF Research Database (Denmark)

Liang, Cai; Hansen, Frank

2010-01-01

on a bipartite system and proved superadditivity of the Wigner-Yanase-Dyson skew informations for such states. We extend this result to the general metric-adjusted skew information. We finally show that a recently introduced extension to parameter values 1 ...We give a truly elementary proof of the convexity of metric-adjusted skew information following an idea of Effros. We extend earlier results of weak forms of superadditivity to general metric-adjusted skew information. Recently, Luo and Zhang introduced the notion of semi-quantum states...... of (unbounded) metric-adjusted skew information....

Large geometry secondary ion mass spectrometry (LG-SIMS) for the enhancement of nuclear safeguards applications

International Nuclear Information System (INIS)

Helberg, P.M.L.; Wallenius, M.; Vincent, C.; Albert, N.; Peres, P.; Truyens, J.

2013-01-01

A new LG-SIMS (Large Geometry Secondary Ion Mass Spectrometry) laboratory is currently being established at the Joint Research Centre, the Institute of Transuranium Elements for the purpose of improving the analytical capabilities within the European Commission. The laboratory will mainly be used for analysing uranium bearing aerosol particles collected on cotton swipes from nuclear Safeguards inspections but it will also be used for Nuclear Forensics and other Safeguards related applications. Until recently, this type of analysis has predominantly been performed using the small geometry CAMECA IMS 3F-7F instrument series. These instruments provide both particle screening and isotope ratio capabilities. The performance of these instruments was however limited by the occurrence of isobaric interferences, in particular for the minor isotopes ( 234 U, 236 U), that could not be resolved without compromising the transmission of the instrument. A recent breakthrough to solve this problem has been the implementation of Large Geometry SIMS, the CAMECA 1270 / 1280 / 1280-HR models, for this type of analysis. This instrument has originally been developed for geosciences applications requiring both high transmission and high mass resolution capabilities. This came out to be a key instrumental advantage also for uranium particle analyses, as it allows efficient removal of common molecular interferences with minimum loss in transmission. Furthermore an electrostatic ion optical device has been added for increasing the mass dispersion which allows the simultaneous detection of all uranium isotopes. The Automated Particle Measurement (APM) software has been developed to perform screening measurement in an automated mode. Combined with the APM screening software, LG-SIMS instruments greatly improve the overall performance and throughput of isotopic analyses of U particles for nuclear Safeguards purposes. The paper is followed by the slides of the presentation. (A.C.)

Software metrics: Software quality metrics for distributed systems. [reliability engineering

Science.gov (United States)

Post, J. V.

1981-01-01

Software quality metrics was extended to cover distributed computer systems. Emphasis is placed on studying embedded computer systems and on viewing them within a system life cycle. The hierarchy of quality factors, criteria, and metrics was maintained. New software quality factors were added, including survivability, expandability, and evolvability.

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

Science.gov (United States)

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

Surface geometry of a rotating black hole in a magnetic field

International Nuclear Information System (INIS)

Kulkarni, R.; Dadhich, N.

1986-01-01

We study the intrinsic geometry of the surface of a rotating black hole in a uniform magnetic field, using a metric discovered by Ernst and Wild. Rotating black holes are analogous to material rotating bodies according to Smarr since black holes also tend to become more oblate on being spun up. Our study shows that the presence of a strong magnetic field ensures that a black hole actually becomes increasingly prolate on being spun up. Studying the intrinsic geometry of the black-hole surface also gives rise to an interesting embedding problem. Smarr shows that a Kerr black hole cannot be globally isometrically embedded in R 3 if its specific angular momentum a exceeds (√3 /2)mapprox.0.866. . .m. We show that in the presence of a magnetic field of strength B, satisfying 2- √3 2 m 2 3 for all values of the angular momentum

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

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Dan Wen

2018-05-01

Full Text Available We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer k. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index k of the background black hole metric, which shows that a larger k makes it harder for the condensation to form. We also observe that the index k affects the conductivity and the gap frequency of the holographic superconductors.

A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

Science.gov (United States)

Wen, Dan; Yu, Hongwei; Pan, Qiyuan; Lin, Kai; Qian, Wei-Liang

2018-05-01

We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer k. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index k of the background black hole metric, which shows that a larger k makes it harder for the condensation to form. We also observe that the index k affects the conductivity and the gap frequency of the holographic superconductors.

Transverse force on a moving vortex with the acoustic geometry

International Nuclear Information System (INIS)

Zhang Pengming; Cao Liming; Duan Yishi; Zhong Chengkui

2004-01-01

We consider the transverse force on a moving vortex with the acoustic metric using the phi-mapping topological current theory. In the frame of effective space-time geometry the vortex appear naturally by virtue of the vortex tensor in the Lorentz space-time and we show that it is just the vortex derived with the order parameter in the condensed matter. With the usual Lagrangian we obtain the equation of motion for the vortex. At last, we show that the transverse force on the moving vortex in our equation is just the usual Magnus force in a simple model

The metric system: An introduction

Science.gov (United States)

Lumley, Susan M.

On 13 Jul. 1992, Deputy Director Duane Sewell restated the Laboratory's policy on conversion to the metric system which was established in 1974. Sewell's memo announced the Laboratory's intention to continue metric conversion on a reasonable and cost effective basis. Copies of the 1974 and 1992 Administrative Memos are contained in the Appendix. There are three primary reasons behind the Laboratory's conversion to the metric system. First, Public Law 100-418, passed in 1988, states that by the end of fiscal year 1992 the Federal Government must begin using metric units in grants, procurements, and other business transactions. Second, on 25 Jul. 1991, President George Bush signed Executive Order 12770 which urged Federal agencies to expedite conversion to metric units. Third, the contract between the University of California and the Department of Energy calls for the Laboratory to convert to the metric system. Thus, conversion to the metric system is a legal requirement and a contractual mandate with the University of California. Public Law 100-418 and Executive Order 12770 are discussed in more detail later in this section, but first they examine the reasons behind the nation's conversion to the metric system. The second part of this report is on applying the metric system.

The metric system: An introduction

Energy Technology Data Exchange (ETDEWEB)

Lumley, S.M.

1995-05-01

On July 13, 1992, Deputy Director Duane Sewell restated the Laboratory`s policy on conversion to the metric system which was established in 1974. Sewell`s memo announced the Laboratory`s intention to continue metric conversion on a reasonable and cost effective basis. Copies of the 1974 and 1992 Administrative Memos are contained in the Appendix. There are three primary reasons behind the Laboratory`s conversion to the metric system. First, Public Law 100-418, passed in 1988, states that by the end of fiscal year 1992 the Federal Government must begin using metric units in grants, procurements, and other business transactions. Second, on July 25, 1991, President George Bush signed Executive Order 12770 which urged Federal agencies to expedite conversion to metric units. Third, the contract between the University of California and the Department of Energy calls for the Laboratory to convert to the metric system. Thus, conversion to the metric system is a legal requirement and a contractual mandate with the University of California. Public Law 100-418 and Executive Order 12770 are discussed in more detail later in this section, but first they examine the reasons behind the nation`s conversion to the metric system. The second part of this report is on applying the metric system.

Evaluation of dose-volume metrics for microbeam radiation therapy dose distributions in head phantoms of various sizes using Monte Carlo simulations

Science.gov (United States)

Anderson, Danielle; Siegbahn, E. Albert; Fallone, B. Gino; Serduc, Raphael; Warkentin, Brad

2012-05-01

This work evaluates four dose-volume metrics applied to microbeam radiation therapy (MRT) using simulated dosimetric data as input. We seek to improve upon the most frequently used MRT metric, the peak-to-valley dose ratio (PVDR), by analyzing MRT dose distributions from a more volumetric perspective. Monte Carlo simulations were used to calculate dose distributions in three cubic head phantoms: a 2 cm mouse head, an 8 cm cat head and a 16 cm dog head. The dose distribution was calculated for a 4 × 4 mm2 microbeam array in each phantom, as well as a 16 × 16 mm2 array in the 8 cm cat head, and a 32 × 32 mm2 array in the 16 cm dog head. Microbeam widths of 25, 50 and 75 µm and center-to-center spacings of 100, 200 and 400 µm were considered. The metrics calculated for each simulation were the conventional PVDR, the peak-to-mean valley dose ratio (PMVDR), the mean dose and the percentage volume below a threshold dose. The PVDR ranged between 3 and 230 for the 2 cm mouse phantom, and between 2 and 186 for the 16 cm dog phantom depending on geometry. The corresponding ranges for the PMVDR were much smaller, being 2-49 (mouse) and 2-46 (dog), and showed a slightly weaker dependence on phantom size and array size. The ratio of the PMVDR to the PVDR varied from 0.21 to 0.79 for the different collimation configurations, indicating a difference between the geometric dependence on outcome that would be predicted by these two metrics. For unidirectional irradiation, the mean lesion dose was 102%, 79% and 42% of the mean skin dose for the 2 cm mouse, 8 cm cat and 16 cm dog head phantoms, respectively. However, the mean lesion dose recovered to 83% of the mean skin dose in the 16 cm dog phantom in intersecting cross-firing regions. The percentage volume below a 10% dose threshold was highly dependent on geometry, with ranges for the different collimation configurations of 2-87% and 33-96% for the 2 cm mouse and 16 cm dog heads, respectively. The results of this study

Evaluation of dose-volume metrics for microbeam radiation therapy dose distributions in head phantoms of various sizes using Monte Carlo simulations

International Nuclear Information System (INIS)

Anderson, Danielle; Fallone, B Gino; Warkentin, Brad; Siegbahn, E Albert; Serduc, Raphael

2012-01-01

This work evaluates four dose-volume metrics applied to microbeam radiation therapy (MRT) using simulated dosimetric data as input. We seek to improve upon the most frequently used MRT metric, the peak-to-valley dose ratio (PVDR), by analyzing MRT dose distributions from a more volumetric perspective. Monte Carlo simulations were used to calculate dose distributions in three cubic head phantoms: a 2 cm mouse head, an 8 cm cat head and a 16 cm dog head. The dose distribution was calculated for a 4 × 4 mm 2 microbeam array in each phantom, as well as a 16 × 16 mm 2 array in the 8 cm cat head, and a 32 × 32 mm 2 array in the 16 cm dog head. Microbeam widths of 25, 50 and 75 µm and center-to-center spacings of 100, 200 and 400 µm were considered. The metrics calculated for each simulation were the conventional PVDR, the peak-to-mean valley dose ratio (PMVDR), the mean dose and the percentage volume below a threshold dose. The PVDR ranged between 3 and 230 for the 2 cm mouse phantom, and between 2 and 186 for the 16 cm dog phantom depending on geometry. The corresponding ranges for the PMVDR were much smaller, being 2–49 (mouse) and 2–46 (dog), and showed a slightly weaker dependence on phantom size and array size. The ratio of the PMVDR to the PVDR varied from 0.21 to 0.79 for the different collimation configurations, indicating a difference between the geometric dependence on outcome that would be predicted by these two metrics. For unidirectional irradiation, the mean lesion dose was 102%, 79% and 42% of the mean skin dose for the 2 cm mouse, 8 cm cat and 16 cm dog head phantoms, respectively. However, the mean lesion dose recovered to 83% of the mean skin dose in the 16 cm dog phantom in intersecting cross-firing regions. The percentage volume below a 10% dose threshold was highly dependent on geometry, with ranges for the different collimation configurations of 2–87% and 33–96% for the 2 cm mouse and 16 cm dog heads, respectively. The results of this

Attack-Resistant Trust Metrics

Science.gov (United States)

Levien, Raph

The Internet is an amazingly powerful tool for connecting people together, unmatched in human history. Yet, with that power comes great potential for spam and abuse. Trust metrics are an attempt to compute the set of which people are trustworthy and which are likely attackers. This chapter presents two specific trust metrics developed and deployed on the Advogato Website, which is a community blog for free software developers. This real-world experience demonstrates that the trust metrics fulfilled their goals, but that for good results, it is important to match the assumptions of the abstract trust metric computation to the real-world implementation.

Symmetries of the dual metrics

International Nuclear Information System (INIS)

Baleanu, D.

1998-01-01

The geometric duality between the metric g μν and a Killing tensor K μν is studied. The conditions were found when the symmetries of the metric g μν and the dual metric K μν are the same. Dual spinning space was constructed without introduction of torsion. The general results are applied to the case of Kerr-Newmann metric

Mechanical response of nickel-titanium instruments with different cross-sectional designs during shaping of simulated curved canals.

Science.gov (United States)

Kim, H C; Kim, H J; Lee, C J; Kim, B M; Park, J K; Versluis, A

2009-07-01

To evaluate how different cross-sectional designs affect stress distribution in nickel-titanium (NiTi) instruments during bending, torsion and simulated shaping of a curved canal. Four NiTi rotary instruments with different cross-sectional geometries were selected: ProFile and HeroShaper systems with a common triangle-based cross section, Mtwo with an S-shaped rectangle-based design and NRT with a modified rectangle-based design. The geometries of the selected files were scanned in a micro-CT and three-dimensional finite-element models were created for each system. Stiffness characteristics for each file system were determined in a series of bending and torsional conditions. Canal shaping was simulated by inserting models of the rotating file into a 45 degrees curved canal model. Stress distribution in the instruments was recorded during simulated shaping. After the instruments were retracted from the canal, residual stresses and permanent bending of their tips due to plastic deformation were determined. The greatest bending and torsional stiffness occurred in the NRT file. During simulated shaping, the instruments with triangle-based cross-sectional geometry had more even stress distributions along their length and had lower stress concentrations than the instruments with rectangle-based cross sections. Higher residual stresses and plastic deformations were found in the Mtwo and NRT with rectangle-based cross-sectional geometries. Nickel-titanium instruments with rectangle-based cross-sectional designs created higher stress differentials during simulated canal shaping and may encounter higher residual stress and plastic deformation than instruments with triangle-based cross sections.

Metrically adjusted questionnaires can provide more information for scientists- an example from the tourism.

Science.gov (United States)

Sindik, Joško; Miljanović, Maja

2017-03-01

The article deals with the issue of research methodology, illustrating the use of known research methods for new purposes. Questionnaires that originally do not have metric characteristics can be called »handy questionnaires«. In this article, the author is trying to consider the possibilities of their improved scientific usability, which can be primarily ensured by improving their metric characteristics, consequently using multivariate instead of univariate statistical methods. In order to establish the base for the application of multivariate statistical procedures, the main idea is to develop strategies to design measurement instruments from parts of the handy questionnaires. This can be accomplished in two ways: before deciding upon the methods for data collection (redesigning the handy questionnaires) and before the collection of the data (a priori) or after the data has been collected, without modifying the questionnaire (a posteriori). The basic principles of applying these two strategies of the metrical adaptation of handy questionnaires are described.

Overview of journal metrics

Directory of Open Access Journals (Sweden)

Kihong Kim

2018-02-01

Full Text Available Various kinds of metrics used for the quantitative evaluation of scholarly journals are reviewed. The impact factor and related metrics including the immediacy index and the aggregate impact factor, which are provided by the Journal Citation Reports, are explained in detail. The Eigenfactor score and the article influence score are also reviewed. In addition, journal metrics such as CiteScore, Source Normalized Impact per Paper, SCImago Journal Rank, h-index, and g-index are discussed. Limitations and problems that these metrics have are pointed out. We should be cautious to rely on those quantitative measures too much when we evaluate journals or researchers.

Evaluation Strategies in Financial Education: Evaluation with Imperfect Instruments

Science.gov (United States)

Robinson, Lauren; Dudensing, Rebekka; Granovsky, Nancy L.

2016-01-01

Program evaluation often suffers due to time constraints, imperfect instruments, incomplete data, and the need to report standardized metrics. This article about the evaluation process for the Wi$eUp financial education program showcases the difficulties inherent in evaluation and suggests best practices for assessing program effectiveness. We…

Geometry of illumination, luminance contrast, and gloss perception.

Science.gov (United States)

Leloup, Frédéric B; Pointer, Michael R; Dutré, Philip; Hanselaer, Peter

2010-09-01

The influence of both the geometry of illumination and luminance contrast on gloss perception has been examined using the method of paired comparison. Six achromatic glass samples having different lightness were illuminated by two light sources. Only one of these light sources was visible in reflection by the observer. By separate adjustment of the intensity of both light sources, the luminance of both the reflected image and the adjacent off-specular surroundings could be individually varied. It was found that visual gloss appraisal did not correlate with instrumentally measured specular gloss; however, psychometric contrast seemed to be a much better correlate. It has become clear that not only the sample surface characteristics determine gloss perception: the illumination geometry could be an even more important factor.

The Graph, Geometry and Symmetries of the Genetic Code with Hamming Metric

Directory of Open Access Journals (Sweden)

Reijer Lenstra

2015-07-01

Full Text Available The similarity patterns of the genetic code result from similar codons encoding similar messages. We develop a new mathematical model to analyze these patterns. The physicochemical characteristics of amino acids objectively quantify their differences and similarities; the Hamming metric does the same for the 64 codons of the codon set. (Hamming distances equal the number of different codon positions: AAA and AAC are at 1-distance; codons are maximally at 3-distance. The CodonPolytope, a 9-dimensional geometric object, is spanned by 64 vertices that represent the codons and the Euclidian distances between these vertices correspond one-to-one with intercodon Hamming distances. The CodonGraph represents the vertices and edges of the polytope; each edge equals a Hamming 1-distance. The mirror reflection symmetry group of the polytope is isomorphic to the largest permutation symmetry group of the codon set that preserves Hamming distances. These groups contain 82,944 symmetries. Many polytope symmetries coincide with the degeneracy and similarity patterns of the genetic code. These code symmetries are strongly related with the face structure of the polytope with smaller faces displaying stronger code symmetries. Splitting the polytope stepwise into smaller faces models an early evolution of the code that generates this hierarchy of code symmetries. The canonical code represents a class of 41,472 codes with equivalent symmetries; a single class among an astronomical number of symmetry classes comprising all possible codes.

Holographic Spherically Symmetric Metrics

Science.gov (United States)

Petri, Michael

The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.

Latent geometry of bipartite networks

Science.gov (United States)

Kitsak, Maksim; Papadopoulos, Fragkiskos; Krioukov, Dmitri

2017-03-01

Despite the abundance of bipartite networked systems, their organizing principles are less studied compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

Intelligent Patching of Conceptual Geometry for CFD Analysis

Science.gov (United States)

Li, Wu

2010-01-01

The iPatch computer code for intelligently patching surface grids was developed to convert conceptual geometry to computational fluid dynamics (CFD) geometry (see figure). It automatically uses bicubic B-splines to extrapolate (if necessary) each surface in a conceptual geometry so that all the independently defined geometric components (such as wing and fuselage) can be intersected to form a watertight CFD geometry. The software also computes the intersection curves of surface patches at any resolution (up to 10.4 accuracy) specified by the user, and it writes the B-spline surface patches, and the corresponding boundary points, for the watertight CFD geometry in the format that can be directly used by the grid generation tool VGRID. iPatch requires that input geometry be in PLOT3D format where each component surface is defined by a rectangular grid {(x(i,j), y(i,j), z(i,j)):1less than or equal to i less than or equal to m, 1 less than or equal to j less than or equal to n} that represents a smooth B-spline surface. All surfaces in the PLOT3D file conceptually represent a watertight geometry of components of an aircraft on the half-space y greater than or equal to 0. Overlapping surfaces are not allowed, but could be fixed by a utility code "fixp3d". The fixp3d utility code first finds the two grid lines on the two surface grids that are closest to each other in Hausdorff distance (a metric to measure the discrepancies of two sets); then uses one of the grid lines as the transition line, extending grid lines on one grid to the other grid to form a merged grid. Any two connecting surfaces shall have a "visually" common boundary curve, or can be described by an intersection relationship defined in a geometry specification file. The intersection of two surfaces can be at a conceptual level. However, the intersection is directional (along either i or j index direction), and each intersecting grid line (or its spine extrapolation) on the first surface should intersect

Quantum cosmology of a Bianchi III LRS geometry coupled to a source free electromagnetic field

Science.gov (United States)

Karagiorgos, A.; Pailas, T.; Dimakis, N.; Terzis, Petros A.; Christodoulakis, T.

2018-03-01

We consider a Bianchi type III axisymmetric geometry in the presence of an electromagnetic field. A first result at the classical level is that the symmetry of the geometry need not be applied on the electromagnetic tensor Fμν the algebraic restrictions, implied by the Einstein field equations to the stress energy tensor Tμν, suffice to reduce the general Fμν to the appropriate form. The classical solution thus found contains a time dependent electric and a constant magnetic charge. The solution is also reachable from the corresponding mini-superspace action, which is strikingly similar to the Reissner-Nordstr{öm one. This points to a connection between the black hole geometry and the cosmological solution here found, which is the analog of the known correlation between the Schwarzschild and the Kantowski-Sachs metrics. The configuration space is drastically modified by the presence of the magnetic charge from a 3D flat to a 3D pp wave geometry. We map the emerging linear and quadratic classical integrals of motion, to quantum observables. Along with the Wheeler-DeWitt equation these observables provide unique, up to constants, wave functions. The employment of a Bohmian interpretation of these quantum states results in deterministic (semi-classical) geometries most of which are singularity free.

Small-scale instrumentation for nuclear magnetic resonance of porous media

International Nuclear Information System (INIS)

Bluemich, Bernhard; Casanova, Federico; Dabrowski, Martin; Danieli, Ernesto; Haber, Agnes; Van Landeghem, Maxime; Haber-Pohlmeier, Sabina; Olaru, Alexandra; Perlo, Juan; Sucre, Oscar; Evertz, Loribeth

2011-01-01

The investigation of fluids confined to porous media is the oldest topic of investigation with small-scale nuclear magnetic resonance (NMR) instruments, as such instruments are mobile and can be moved to the site of the object, such as the borehole of an oil well. While the analysis was originally restricted by the inferior homogeneity of the employed magnets to relaxation measurements, today, portable magnets are available for all types of NMR measurements concerning relaxometry, imaging and spectroscopy in two types of geometries. These geometries refer to closed magnets that surround the sample and open magnets, which are brought close to the object for measurement. The current state of the art of portable, small-scale NMR instruments is reviewed and recent applications of such instruments are featured. These include the porosity analysis and description of diesel particulate filters, the determination of the moisture content in walls from gray concrete, new approaches to analyze the pore space and moisture migration in soil, and the constitutional analysis of the mortar base of ancient wall paintings.

Model-Based Referenceless Quality Metric of 3D Synthesized Images Using Local Image Description.

Science.gov (United States)

Gu, Ke; Jakhetiya, Vinit; Qiao, Jun-Fei; Li, Xiaoli; Lin, Weisi; Thalmann, Daniel

2017-07-28

New challenges have been brought out along with the emerging of 3D-related technologies such as virtual reality (VR), augmented reality (AR), and mixed reality (MR). Free viewpoint video (FVV), due to its applications in remote surveillance, remote education, etc, based on the flexible selection of direction and viewpoint, has been perceived as the development direction of next-generation video technologies and has drawn a wide range of researchers' attention. Since FVV images are synthesized via a depth image-based rendering (DIBR) procedure in the "blind" environment (without reference images), a reliable real-time blind quality evaluation and monitoring system is urgently required. But existing assessment metrics do not render human judgments faithfully mainly because geometric distortions are generated by DIBR. To this end, this paper proposes a novel referenceless quality metric of DIBR-synthesized images using the autoregression (AR)-based local image description. It was found that, after the AR prediction, the reconstructed error between a DIBR-synthesized image and its AR-predicted image can accurately capture the geometry distortion. The visual saliency is then leveraged to modify the proposed blind quality metric to a sizable margin. Experiments validate the superiority of our no-reference quality method as compared with prevailing full-, reduced- and no-reference models.

Hadamard States for the Klein-Gordon Equation on Lorentzian Manifolds of Bounded Geometry

Science.gov (United States)

Gérard, Christian; Oulghazi, Omar; Wrochna, Michał

2017-06-01

We consider the Klein-Gordon equation on a class of Lorentzian manifolds with Cauchy surface of bounded geometry, which is shown to include examples such as exterior Kerr, Kerr-de Sitter spacetime and the maximal globally hyperbolic extension of the Kerr outer region. In this setup, we give an approximate diagonalization and a microlocal decomposition of the Cauchy evolution using a time-dependent version of the pseudodifferential calculus on Riemannian manifolds of bounded geometry. We apply this result to construct all pure regular Hadamard states (and associated Feynman inverses), where regular refers to the state's two-point function having Cauchy data given by pseudodifferential operators. This allows us to conclude that there is a one-parameter family of elliptic pseudodifferential operators that encodes both the choice of (pure, regular) Hadamard state and the underlying spacetime metric.

Metric regularity and subdifferential calculus

International Nuclear Information System (INIS)

Ioffe, A D

2000-01-01

The theory of metric regularity is an extension of two classical results: the Lyusternik tangent space theorem and the Graves surjection theorem. Developments in non-smooth analysis in the 1980s and 1990s paved the way for a number of far-reaching extensions of these results. It was also well understood that the phenomena behind the results are of metric origin, not connected with any linear structure. At the same time it became clear that some basic hypotheses of the subdifferential calculus are closely connected with the metric regularity of certain set-valued maps. The survey is devoted to the metric theory of metric regularity and its connection with subdifferential calculus in Banach spaces

Context-dependent ATC complexity metric

NARCIS (Netherlands)

Mercado Velasco, G.A.; Borst, C.

2015-01-01

Several studies have investigated Air Traffic Control (ATC) complexity metrics in a search for a metric that could best capture workload. These studies have shown how daunting the search for a universal workload metric (one that could be applied in different contexts: sectors, traffic patterns,

Instanton strings and hyper-Kaehler geometry

International Nuclear Information System (INIS)

Dijkgraaf, Robbert

1999-01-01

We discuss two-dimensional sigma models on moduli spaces of instantons on K3 surfaces. These N = (4, 4) superconformal field theories describe the near-horizon dynamics of the D1-D5-brane system and are dual to string theory on AdS 3 . We derive a precise map relating the moduli of the K3 type 1113 string compactification to the moduli of these conformal field theories and the corresponding classical hyper-Kahler geometry. We conclude that in the absence of background gauge fields, the metric on the instanton moduli spaces degenerates exactly to the orbifold symmetric product of K3. Turning on a self-dual NS B-field deforms this symmetric product to a manifold that is diffeomorphic to the Hilbert scheme. We also comment on the mathematical applications of string duality to the global issues of deformations of hyper-Kaehler manifolds

Surface geometry of 5D black holes and black rings

International Nuclear Information System (INIS)

Frolov, Valeri P.; Goswami, Rituparno

2007-01-01

We discuss geometrical properties of the horizon surface of five-dimensional rotating black holes and black rings. Geometrical invariants characterizing these 3D geometries are calculated. We obtain a global embedding of the 5D rotating black horizon surface into a flat space. We also describe the Kaluza-Klein reduction of the black ring solution (along the direction of its rotation) which, though it is nakedly singular, relates this solution to the 4D metric of a static black hole distorted by the presence of external scalar (dilaton) and vector ('electromagnetic') fields. The properties of the reduced black hole horizon and its embedding in E 3 are briefly discussed

DLA Energy Biofuel Feedstock Metrics Study

Science.gov (United States)

2012-12-11

moderately/highly in- vasive  Metric 2: Genetically modified organism ( GMO ) hazard, Yes/No and Hazard Category  Metric 3: Species hybridization...4– biofuel distribution Stage # 5– biofuel use Metric 1: State inva- siveness ranking Yes Minimal Minimal No No Metric 2: GMO hazard Yes...may utilize GMO microbial or microalgae species across the applicable biofuel life cycles (stages 1–3). The following consequence Metrics 4–6 then

Multi-Institutional Development of a Mastoidectomy Performance Evaluation Instrument.

Science.gov (United States)

Kerwin, Thomas; Hittle, Brad; Stredney, Don; De Boeck, Paul; Wiet, Gregory

A method for rating surgical performance of a mastoidectomy procedure that is shown to apply universally across teaching institutions has not yet been devised. This work describes the development of a rating instrument created from a multi-institutional consortium. Using a participatory design and a modified Delphi approach, a multi-institutional group of expert otologists constructed a 15-element task-based checklist for evaluating mastoidectomy performance. This instrument was further refined into a 14-element checklist focusing on the concept of safety after using it to rate a large and varied population of performances. Twelve otolaryngological surgical training programs in the United States. A total of 14 surgeons from 12 different institutions took part in the construction of the instrument. By using 14 experts from 12 different institutions and a literature review, individual metrics were identified, rated as to the level of importance and operationally defined to create a rating scale for mastoidectomy performance. Initial use of the rating scale showed modest rater agreement. The operational definitions of individual metrics were modified to emphasize "safe" as opposed to "proper" technique. A second rating instrument was developed based on this feedback. Using a consensus-building approach with multiple rounds of communication between experts is a feasible way to construct a rating instrument for mastoidectomy. Expert opinion alone using a Delphi method provides face and content validity evidence, however, this is not sufficient to develop a universally acceptable rating instrument. A continued process of development and experimentation to demonstrate evidence for reliability and validity making use of a large population of raters and performances is necessary to achieve universal acceptance. Copyright © 2017 Association of Program Directors in Surgery. Published by Elsevier Inc. All rights reserved.

Discrete causal theory emergent spacetime and the causal metric hypothesis

CERN Document Server

Dribus, Benjamin F

2017-01-01

This book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. Spacetime structure is of central importance to physics beyond general relativity and the standard model. The causal metric hypothesis treats causal relations as the basis of this structure. The book develops the consequences of this hypothesis under the assumption of a fundamental scale, with smooth spacetime geometry viewed as emergent. This approach resembles causal set theory, but differs in important ways; for example, the relative viewpoint, emphasizing relations between pairs of events, and relationships between pairs of histories, is central. The book culminates in a dynamical law for quantum spacetime, derived via generalized path summation.

Relative-locality distant observers and the phenomenology of momentum-space geometry

International Nuclear Information System (INIS)

Amelino-Camelia, Giovanni; Rosati, Giacomo; Trevisan, Gabriele; Arzano, Michele; Kowalski-Glikman, Jerzy

2012-01-01

We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincare-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincare connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source. (paper)

Relative-locality distant observers and the phenomenology of momentum-space geometry

Science.gov (United States)

Amelino-Camelia, Giovanni; Arzano, Michele; Kowalski-Glikman, Jerzy; Rosati, Giacomo; Trevisan, Gabriele

2012-04-01

We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a κ-Poincaré-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory, simultaneously emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of Freidel and Smolin (2011 arXiv:1103.5626) on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the κ-Poincaré connection introduces a small (but observably large) dependence of the time of detection, for simultaneously emitted particles, on some properties of the interactions producing the particles at the source.

Symmetries of Taub-NUT dual metrics

International Nuclear Information System (INIS)

Baleanu, D.; Codoban, S.

1998-01-01

Recently geometric duality was analyzed for a metric which admits Killing tensors. An interesting example arises when the manifold has Killing-Yano tensors. The symmetries of the dual metrics in the case of Taub-NUT metric are investigated. Generic and non-generic symmetries of dual Taub-NUT metric are analyzed

Rigid supersymmetry on 5-dimensional Riemannian manifolds and contact geometry

International Nuclear Information System (INIS)

Pan, Yiwen

2014-01-01

In this note we generalize the methods of http://dx.doi.org/10.1007/JHEP08(2012)141, http://dx.doi.org/10.1007/JHEP01(2013)072 and http://dx.doi.org/10.1007/JHEP05(2013)017 to 5-dimensional Riemannian manifolds M. We study the relations between the geometry of M and the number of solutions to a generalized Killing spinor equation obtained from a 5-dimensional supergravity. The existence of 1 pair of solutions is related to almost contact metric structures. We also discuss special cases related to M=S 1 ×M 4 , which leads to M being foliated by submanifolds with special properties, such as Quaternion-Kähler. When there are 2 pairs of solutions, the closure of the isometry sub-algebra generated by the solutions requires M to be S 3 or T 3 -fibration over a Riemann surface. 4 pairs of solutions pin down the geometry of M to very few possibilities. Finally, we propose a new supersymmetric theory for N=1 vector multiplet on K-contact manifold admitting solutions to the Killing spinor equation

Metric learning

CERN Document Server

Bellet, Aurelien; Sebban, Marc

2015-01-01

Similarity between objects plays an important role in both human cognitive processes and artificial systems for recognition and categorization. How to appropriately measure such similarities for a given task is crucial to the performance of many machine learning, pattern recognition and data mining methods. This book is devoted to metric learning, a set of techniques to automatically learn similarity and distance functions from data that has attracted a lot of interest in machine learning and related fields in the past ten years. In this book, we provide a thorough review of the metric learnin

Technical Privacy Metrics: a Systematic Survey

OpenAIRE

Wagner, Isabel; Eckhoff, David

2018-01-01

The file attached to this record is the author's final peer reviewed version The goal of privacy metrics is to measure the degree of privacy enjoyed by users in a system and the amount of protection offered by privacy-enhancing technologies. In this way, privacy metrics contribute to improving user privacy in the digital world. The diversity and complexity of privacy metrics in the literature makes an informed choice of metrics challenging. As a result, instead of using existing metrics, n...

On Information Metrics for Spatial Coding.

Science.gov (United States)

Souza, Bryan C; Pavão, Rodrigo; Belchior, Hindiael; Tort, Adriano B L

2018-04-01

The hippocampal formation is involved in navigation, and its neuronal activity exhibits a variety of spatial correlates (e.g., place cells, grid cells). The quantification of the information encoded by spikes has been standard procedure to identify which cells have spatial correlates. For place cells, most of the established metrics derive from Shannon's mutual information (Shannon, 1948), and convey information rate in bits/s or bits/spike (Skaggs et al., 1993, 1996). Despite their widespread use, the performance of these metrics in relation to the original mutual information metric has never been investigated. In this work, using simulated and real data, we find that the current information metrics correlate less with the accuracy of spatial decoding than the original mutual information metric. We also find that the top informative cells may differ among metrics, and show a surrogate-based normalization that yields comparable spatial information estimates. Since different information metrics may identify different neuronal populations, we discuss current and alternative definitions of spatially informative cells, which affect the metric choice. Copyright © 2018 IBRO. Published by Elsevier Ltd. All rights reserved.

Generalized Painleve-Gullstrand metrics

Energy Technology Data Exchange (ETDEWEB)

Lin Chunyu [Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan (China)], E-mail: l2891112@mail.ncku.edu.tw; Soo Chopin [Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan (China)], E-mail: cpsoo@mail.ncku.edu.tw

2009-02-02

An obstruction to the implementation of spatially flat Painleve-Gullstrand (PG) slicings is demonstrated, and explicitly discussed for Reissner-Nordstroem and Schwarzschild-anti-deSitter spacetimes. Generalizations of PG slicings which are not spatially flat but which remain regular at the horizons are introduced. These metrics can be obtained from standard spherically symmetric metrics by physical Lorentz boosts. With these generalized PG metrics, problematic contributions to the imaginary part of the action in the Parikh-Wilczek derivation of Hawking radiation due to the obstruction can be avoided.

Geometry and Mechanics of Chiral Pod Opening

Science.gov (United States)

Sharon, Eran; Armon, Shahaf; Efrati, Efi; Kupferman, Raz

2012-02-01

We study the geometry and mechanics that drive the opening of Bauhinia seeds pods. The pod valve wall consists of two fibrous layers oriented at ± 45^o with respect to the pod axis. Upon drying, each of the layers shrinks uniaxially, perpendicularly to the fibers orientation. This active deformation turn the valve into an incompatible sheet with reference saddle-like curvature tensor and a flat (Euclidean) reference metric. These two intrinsic properties are incompatible. The shape is, therefore, selected by a stretching-bending competition. Strips cut from the valve tissue and from synthetic model material adopt various helical configurations. We provide analytical expressions for these configurations in the bending and stretching dominated regimes. Surface measurements show the transition from minimal surfaces (narrow limit) to cylindrical ones (wide limit). Finally, we show how plants use these mechanical principles using different tissue architectures.

Pengembangan Perangkat Pembelajaran Geometri Ruang dengan Model Proving Theorem

Directory of Open Access Journals (Sweden)

Bambang Eko Susilo

2016-03-01

Full Text Available Kemampuan berpikir kritis dan kreatif mahasiswa masih lemah. Hal ini ditemukan pada mahasiswa yang mengambil mata kuliah Geometri Ruang yaitu dalam membuktikan soal-soal pembuktian (problem to proof. Mahasiswa masih menyelesaikan secara algoritmik atau prosedural sehingga diperlukan pengembangan perangkat pembelajaran Geometri Ruang berbasis kompetensi dan konservasi dengan model Proving Theorem. Dalam penelitian ini perangkat perkuliahan yang dikembangkan yaitu Silabus, Satuan Acara Perkuliahan (SAP, Kontrak Perkuliahan, Media Pembelajaran, Bahan Ajar, Tes UTS dan UAS serta Angket Karakter Konservasi telah dilaksanakan dengan baik dengan kriteria (1 validasi perangkat pembelajaran mata kuliah Geometri ruang berbasis kompetensi dan konservasi dengan model proving theorem berkategori baik dan layak digunakan dan (2 keterlaksanaan RPP pada pembelajaran yang dikembangkan secara keseluruhan berkategori baik.Critical and creative thinking abilities of students still weak. It is found in students who take Space Geometry subjects that is in solving problems to to prove. Students still finish in algorithmic or procedural so that the required the development of Space Geometry learning tools based on competency and conservation with Proving Theorem models. This is a research development which refers to the 4-D models that have been modified for the Space Geometry learning tools, second semester academic year 2014/2015. Instruments used include validation sheet, learning tools and character assessment questionnaire. In this research, the learning tools are developed, namely Syllabus, Lesson Plan, Lecture Contract, Learning Media, Teaching Material, Tests, and Character Conservation Questionnaire had been properly implemented with the criteria (1 validation of Space Geometry learning tools based on competency and conservation with Proving Theorem models categorized good and feasible to use, and (2 the implementation of Lesson Plan on learning categorized

Kerr metric in the deSitter background

International Nuclear Information System (INIS)

Vaidya, P.C.

1984-01-01

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein's equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild's exterior metric with cosmological constant. (author)

Introducing geometry concept based on history of Islamic geometry

Science.gov (United States)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Kerr metric in cosmological background

Energy Technology Data Exchange (ETDEWEB)

Vaidya, P C [Gujarat Univ., Ahmedabad (India). Dept. of Mathematics

1977-06-01

A metric satisfying Einstein's equation is given which in the vicinity of the source reduces to the well-known Kerr metric and which at large distances reduces to the Robertson-Walker metric of a nomogeneous cosmological model. The radius of the event horizon of the Kerr black hole in the cosmological background is found out.

Finite Element Study on Continuous Rotating versus Reciprocating Nickel-Titanium Instruments.

Science.gov (United States)

El-Anwar, Mohamed I; Yousief, Salah A; Kataia, Engy M; El-Wahab, Tarek M Abd

2016-01-01

In the present study, GTX and ProTaper as continuous rotating endodontic files were numerically compared with WaveOne reciprocating file using finite element analysis, aiming at having a low cost, accurate/trustworthy comparison as well as finding out the effect of instrument design and manufacturing material on its lifespan. Two 3D finite element models were especially prepared for this comparison. Commercial engineering CAD/CAM package was used to model full detailed flute geometries of the instruments. Multi-linear materials were defined in analysis by using real strain-stress data of NiTi and M-Wire. Non-linear static analysis was performed to simulate the instrument inside root canal at a 45° angle in the apical portion and subjected to 0.3 N.cm torsion. The three simulations in this study showed that M-Wire is slightly more resistant to failure than conventional NiTi. On the other hand, both materials are fairly similar in case of severe locking conditions. For the same instrument geometry, M-Wire instruments may have longer lifespan than the conventional NiTi ones. In case of severe locking conditions both materials will fail similarly. Larger cross sectional area (function of instrument taper) resisted better to failure than the smaller ones, while the cross sectional shape and its cutting angles could affect instrument cutting efficiency.

Towards linearization of atmospheric radiative transfer in spherical geometry

International Nuclear Information System (INIS)

Walter, Holger H.; Landgraf, Jochen

2005-01-01

We present a general approach for the linearization of radiative transfer in a spherical planetary atmosphere. The approach is based on the forward-adjoint perturbation theory. In the first part we develop the theoretical background for a linearization of radiative transfer in spherical geometry. Using an operator formulation of radiative transfer allows one to derive the linearization principles in a universally valid notation. The application of the derived principles is demonstrated for a radiative transfer problem in simplified spherical geometry in the second part of this paper. Here, we calculate the derivatives of the radiance at the top of the atmosphere with respect to the absorption properties of a trace gas species in the case of a nadir-viewing satellite instrument

Nonperturbative quantum geometries

International Nuclear Information System (INIS)

Jacobson, T.; California Univ., Santa Barbara; Smolin, L.; California Univ., Santa Barbara

1988-01-01

Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states. Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field - and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described. The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric. (orig.)

Two classes of metric spaces

Directory of Open Access Journals (Sweden)

Isabel Garrido

2016-04-01

Full Text Available The class of metric spaces (X,d known as small-determined spaces, introduced by Garrido and Jaramillo, are properly defined by means of some type of real-valued Lipschitz functions on X. On the other hand, B-simple metric spaces introduced by Hejcman are defined in terms of some kind of bornologies of bounded subsets of X. In this note we present a common framework where both classes of metric spaces can be studied which allows us to see not only the relationships between them but also to obtain new internal characterizations of these metric properties.

Diagram of the Saturn V Launch Vehicle in Metric

Science.gov (United States)

1971-01-01

This is a good cutaway diagram of the Saturn V launch vehicle showing the three stages, the instrument unit, and the Apollo spacecraft. The chart on the right presents the basic technical data in clear metric detail. The Saturn V is the largest and most powerful launch vehicle in the United States. The towering, 111 meter, Saturn V was a multistage, multiengine launch vehicle standing taller than the Statue of Liberty. Altogether, the Saturn V engines produced as much power as 85 Hoover Dams. Development of the Saturn V was the responsibility of the Marshall Space Flight Center at Huntsville, Alabama, directed by Dr. Wernher von Braun.

Toward automated assessment of health Web page quality using the DISCERN instrument.

Science.gov (United States)

Allam, Ahmed; Schulz, Peter J; Krauthammer, Michael

2017-05-01

As the Internet becomes the number one destination for obtaining health-related information, there is an increasing need to identify health Web pages that convey an accurate and current view of medical knowledge. In response, the research community has created multicriteria instruments for reliably assessing online medical information quality. One such instrument is DISCERN, which measures health Web page quality by assessing an array of features. In order to scale up use of the instrument, there is interest in automating the quality evaluation process by building machine learning (ML)-based DISCERN Web page classifiers. The paper addresses 2 key issues that are essential before constructing automated DISCERN classifiers: (1) generation of a robust DISCERN training corpus useful for training classification algorithms, and (2) assessment of the usefulness of the current DISCERN scoring schema as a metric for evaluating the performance of these algorithms. Using DISCERN, 272 Web pages discussing treatment options in breast cancer, arthritis, and depression were evaluated and rated by trained coders. First, different consensus models were compared to obtain a robust aggregated rating among the coders, suitable for a DISCERN ML training corpus. Second, a new DISCERN scoring criterion was proposed (features-based score) as an ML performance metric that is more reflective of the score distribution across different DISCERN quality criteria. First, we found that a probabilistic consensus model applied to the DISCERN instrument was robust against noise (random ratings) and superior to other approaches for building a training corpus. Second, we found that the established DISCERN scoring schema (overall score) is ill-suited to measure ML performance for automated classifiers. Use of a probabilistic consensus model is advantageous for building a training corpus for the DISCERN instrument, and use of a features-based score is an appropriate ML metric for automated DISCERN

Geometry through history Euclidean, hyperbolic, and projective geometries

CERN Document Server

Dillon, Meighan I

2018-01-01

Presented as an engaging discourse, this textbook invites readers to delve into the historical origins and uses of geometry. The narrative traces the influence of Euclid’s system of geometry, as developed in his classic text The Elements, through the Arabic period, the modern era in the West, and up to twentieth century mathematics. Axioms and proof methods used by mathematicians from those periods are explored alongside the problems in Euclidean geometry that lead to their work. Students cultivate skills applicable to much of modern mathematics through sections that integrate concepts like projective and hyperbolic geometry with representative proof-based exercises. For its sophisticated account of ancient to modern geometries, this text assumes only a year of college mathematics as it builds towards its conclusion with algebraic curves and quaternions. Euclid’s work has affected geometry for thousands of years, so this text has something to offer to anyone who wants to broaden their appreciation for the...

On characterizations of quasi-metric completeness

Energy Technology Data Exchange (ETDEWEB)

Dag, H.; Romaguera, S.; Tirado, P.

2017-07-01

Hu proved in [4] that a metric space (X, d) is complete if and only if for any closed subspace C of (X, d), every Banach contraction on C has fixed point. Since then several authors have investigated the problem of characterizing the metric completeness by means of fixed point theorems. Recently this problem has been studied in the more general context of quasi-metric spaces for different notions of completeness. Here we present a characterization of a kind of completeness for quasi-metric spaces by means of a quasi-metric versions of Hu’s theorem. (Author)

Auto-associative Kernel Regression Model with Weighted Distance Metric for Instrument Drift Monitoring

International Nuclear Information System (INIS)

Shin, Ho Cheol; Park, Moon Ghu; You, Skin

2006-01-01

Recently, many on-line approaches to instrument channel surveillance (drift monitoring and fault detection) have been reported worldwide. On-line monitoring (OLM) method evaluates instrument channel performance by assessing its consistency with other plant indications through parametric or non-parametric models. The heart of an OLM system is the model giving an estimate of the true process parameter value against individual measurements. This model gives process parameter estimate calculated as a function of other plant measurements which can be used to identify small sensor drifts that would require the sensor to be manually calibrated or replaced. This paper describes an improvement of auto associative kernel regression (AAKR) by introducing a correlation coefficient weighting on kernel distances. The prediction performance of the developed method is compared with conventional auto-associative kernel regression

Metric Ambiguity and Flow in Rap Music: A Corpus-Assisted Study of Outkast's "Mainstream" (1996

Directory of Open Access Journals (Sweden)

Mitchell Ohriner

2017-01-01

Full Text Available Recent years have seen the rise of musical corpus studies, primarily detailing harmonic tendencies of tonal music. This article extends this scholarship by addressing a new genre (rap music and a new parameter of focus (rhythm. More specifically, I use corpus methods to investigate the relation between metric ambivalence in the instrumental parts of a rap track (i.e., the beat and an emcee's rap delivery (i.e., the flow. Unlike virtually every other rap track, the instrumental tracks of Outkast's "Mainstream" (1996 simultaneously afford hearing both a four-beat and a three-beat metric cycle. Because three-beat durations between rhymes, phrase endings, and reiterated rhythmic patterns are rare in rap music, an abundance of them within a verse of "Mainstream" suggests that an emcee highlights the three-beat cycle, especially if that emcee is not prone to such durations more generally. Through the construction of three corpora, one representative of the genre as a whole, and two that are artist specific, I show how the emcee T-Mo Goodie's expressive practice highlights the rare three-beat affordances of the track.

Noncommutative geometry and its application to the standard model

Energy Technology Data Exchange (ETDEWEB)

Martinetti, Pierre [Georg-August Universitaet, Goettingen (Germany)

2009-07-01

We give an overview of the description of the standard model of particle physics minimally coupled to gravity within the framework of noncommutative geometry. Especially we study in detail the metric structure of spacetime that emerges from the spectral triple recently proposed by Chamseddine, Connes and Marcolli. Within this framework points of spacetime acquire an internal structure inherited from the gauge group of the standard model. A distance is defined on this generalized spacetime which is fully encoded by the Yang-Mills gauge fields together with the Higgs field. We focus on some explicit examples, underlying the link between this distance and other distances well known by physicists and mathematicians, such has the Carnot-Caratheodory horizontal distance or the Monge-Kantorovitch transport distance.

Designing new guides and instruments using McStas

DEFF Research Database (Denmark)

Farhi, E.; Hansen, T.; Wildes, A.

2002-01-01

of guides, neutron optics and instruments [1]. To date, the McStas package has been extensively used at the Institut Laue-Langevin, Grenoble, France, for various studies including cold and thermal guides with ballistic geometry, diffractometers, triple-axis, backscattering and time-of-flight spectrometers...

Status of the JWST Integrated Science Instrument Module

Science.gov (United States)

Greenhouse, Matthew A.; Dunn, Jamie; Kimble, Randy A.; Lambros, Scott; Lundquist, Ray; Rauscher, Bernard J.; Van Campen, Julie

2015-01-01

The James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) is the science instrument payload of the JWST. It is one of three system elements that comprise the JWST space vehicle. It consists of four science sensors, a fine guidance sensor, and nine other subsystems that support them. At 1.4 metric tons, it comprises approximately 20% of the JWST mass. The ISIM is currently at 100% integration and has completed 2 of 3 planned element-level space simulation tests. The ISIM is on schedule to be delivered for integration with the Optical Telescope Element during 2015. In this poster, we present an overview of the ISIM and its status.

Engineering performance metrics

Science.gov (United States)

Delozier, R.; Snyder, N.

1993-03-01

Implementation of a Total Quality Management (TQM) approach to engineering work required the development of a system of metrics which would serve as a meaningful management tool for evaluating effectiveness in accomplishing project objectives and in achieving improved customer satisfaction. A team effort was chartered with the goal of developing a system of engineering performance metrics which would measure customer satisfaction, quality, cost effectiveness, and timeliness. The approach to developing this system involved normal systems design phases including, conceptual design, detailed design, implementation, and integration. The lessons teamed from this effort will be explored in this paper. These lessons learned may provide a starting point for other large engineering organizations seeking to institute a performance measurement system accomplishing project objectives and in achieving improved customer satisfaction. To facilitate this effort, a team was chartered to assist in the development of the metrics system. This team, consisting of customers and Engineering staff members, was utilized to ensure that the needs and views of the customers were considered in the development of performance measurements. The development of a system of metrics is no different than the development of any type of system. It includes the steps of defining performance measurement requirements, measurement process conceptual design, performance measurement and reporting system detailed design, and system implementation and integration.

External and internal geometry of European adults.

Science.gov (United States)

Bertrand, Samuel; Skalli, Wafa; Delacherie, Laurent; Bonneau, Dominique; Kalifa, Gabriel; Mitton, David

2006-12-15

The primary objective of the study was to bring a deeper knowledge of the human anthropometry, investigating the external and internal body geometry of small women, mid-sized men and tall men. Sixty-four healthy European adults were recruited. External measurements were performed using classical anthropometric instruments. Internal measurements of the trunk bones were performed using a stereo-radiographic 3D reconstruction technique. Besides the original procedure presented in this paper for performing in vivo geometrical data acquisition on numerous volunteers, this study provides an extensive description of both external and internal (trunk skeleton) human body geometry for three morphotypes. Moreover, this study proposes a global external and internal geometrical description of 5th female 50th male and 95th male percentile subjects. This study resulted in a unique geometrical database enabling improvement for numerical models of the human body for crash test simulation and offering numerous possibilities in the anthropometry field.

Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology

Energy Technology Data Exchange (ETDEWEB)

Ukwatta, Eranga, E-mail: eukwatt1@jhu.edu; Arevalo, Hermenegild; Pashakhanloo, Farhad; Prakosa, Adityo; Vadakkumpadan, Fijoy [Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland 21205 and Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Rajchl, Martin [Department of Computing, Imperial College London, London SW7 2AZ (United Kingdom); White, James [Stephenson Cardiovascular MR Centre, University of Calgary, Calgary, Alberta T2N 2T9 (Canada); Herzka, Daniel A.; McVeigh, Elliot [Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Lardo, Albert C. [Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 and Division of Cardiology, Johns Hopkins Institute of Medicine, Baltimore, Maryland 21224 (United States); Trayanova, Natalia A. [Institute for Computational Medicine, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21205 (United States); Department of Biomedical Engineering, Johns Hopkins Institute of Medicine, Baltimore, Maryland 21205 (United States)

2015-08-15

Purpose: Accurate three-dimensional (3D) reconstruction of myocardial infarct geometry is crucial to patient-specific modeling of the heart aimed at providing therapeutic guidance in ischemic cardiomyopathy. However, myocardial infarct imaging is clinically performed using two-dimensional (2D) late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) techniques, and a method to build accurate 3D infarct reconstructions from the 2D LGE-CMR images has been lacking. The purpose of this study was to address this need. Methods: The authors developed a novel methodology to reconstruct 3D infarct geometry from segmented low-resolution (Lo-res) clinical LGE-CMR images. Their methodology employed the so-called logarithm of odds (LogOdds) function to implicitly represent the shape of the infarct in segmented image slices as LogOdds maps. These 2D maps were then interpolated into a 3D image, and the result transformed via the inverse of LogOdds to a binary image representing the 3D infarct geometry. To assess the efficacy of this method, the authors utilized 39 high-resolution (Hi-res) LGE-CMR images, including 36 in vivo acquisitions of human subjects with prior myocardial infarction and 3 ex vivo scans of canine hearts following coronary ligation to induce infarction. The infarct was manually segmented by trained experts in each slice of the Hi-res images, and the segmented data were downsampled to typical clinical resolution. The proposed method was then used to reconstruct 3D infarct geometry from the downsampled images, and the resulting reconstructions were compared with the manually segmented data. The method was extensively evaluated using metrics based on geometry as well as results of electrophysiological simulations of cardiac sinus rhythm and ventricular tachycardia in individual hearts. Several alternative reconstruction techniques were also implemented and compared with the proposed method. Results: The accuracy of the LogOdds method in reconstructing 3D

Analytical study on optically measured surface profiles of referential geometry using a finite-difference time-domain method

International Nuclear Information System (INIS)

Fujii, A; Hayashi, S; Fujii, S; Yanagi, K

2014-01-01

This paper deals with the functional performance of optical surface texture measuring instruments on the market. It is well known that their height response curves against certain referential geometry are not always identical to each other. So, a more precise study on the optical instrument's characteristics is greatly needed. Firstly, we developed a new simulation tool using a finite-difference time-domain technique, which enables the prediction of the height response curve against the fundamental surface geometry in the case of the confocal laser scanning microscope. Secondly, by utilizing this new simulation tool, measurement results, including outliers, were compared with the analytical simulation results. The comparison showed the consistency, which indicates that necessary conditions of surface measurement standards for verifying the instrument performance can be established. Consequently, we suggest that the maximum measurable slope angle must be added to evaluation subjects as significant metrological characteristics of measuring instruments, along with the lateral period limit. Finally, we propose a procedure to determine the lateral period limit in an ISO standard. (paper)

Brand metrics that matter

NARCIS (Netherlands)

Muntinga, D.; Bernritter, S.

2017-01-01

Het merk staat steeds meer centraal in de organisatie. Het is daarom essentieel om de gezondheid, prestaties en ontwikkelingen van het merk te meten. Het is echter een uitdaging om de juiste brand metrics te selecteren. Een enorme hoeveelheid metrics vraagt de aandacht van merkbeheerders. Maar welke

Privacy Metrics and Boundaries

NARCIS (Netherlands)

L-F. Pau (Louis-François)

2005-01-01

textabstractThis paper aims at defining a set of privacy metrics (quantitative and qualitative) in the case of the relation between a privacy protector ,and an information gatherer .The aims with such metrics are: -to allow to assess and compare different user scenarios and their differences; for

Architectural geometry

KAUST Repository

Pottmann, Helmut

2014-11-26

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Architectural geometry

KAUST Repository

Pottmann, Helmut; Eigensatz, Michael; Vaxman, Amir; Wallner, Johannes

2014-01-01

Around 2005 it became apparent in the geometry processing community that freeform architecture contains many problems of a geometric nature to be solved, and many opportunities for optimization which however require geometric understanding. This area of research, which has been called architectural geometry, meanwhile contains a great wealth of individual contributions which are relevant in various fields. For mathematicians, the relation to discrete differential geometry is significant, in particular the integrable system viewpoint. Besides, new application contexts have become available for quite some old-established concepts. Regarding graphics and geometry processing, architectural geometry yields interesting new questions but also new objects, e.g. replacing meshes by other combinatorial arrangements. Numerical optimization plays a major role but in itself would be powerless without geometric understanding. Summing up, architectural geometry has become a rewarding field of study. We here survey the main directions which have been pursued, we show real projects where geometric considerations have played a role, and we outline open problems which we think are significant for the future development of both theory and practice of architectural geometry.

Two lectures on D-geometry and noncommutative geometry

International Nuclear Information System (INIS)

Douglas, M.R.

1999-01-01

This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has appeared in D-brane and Matrix theory physics. (author)

Optimization of measurement geometries used by the C.I.R. 'Gamma Spectrometry' working group

International Nuclear Information System (INIS)

Escarieux, M.

1979-01-01

The choice of measurement geometry is closely tied to the objective sought in gamma quantitative analysis which consists in identifying the radionuclides present in a sample and in determining the voluminal quantities. The too low efficiency of the detector and the levels of activity sought make it necessary to place the sample in contact with the casing of the detector and select a sample geometry suited to the measurement. In point of fact this choice is often determined by other criteria, availability of the container for example, and this leads the laboratories taking part in the 'Gamma Spectrometry' Working Group of the Comite d'Instrumentation de Radioprotection to adopt joint gamma measurement geometries [fr

Riemann-Cartan geometry of nonlinear disclination mechanics

KAUST Repository

Yavari, A.

2012-03-23

In the continuous theory of defects in nonlinear elastic solids, it is known that a distribution of disclinations leads, in general, to a non-trivial residual stress field. To study this problem, we consider the particular case of determining the residual stress field of a cylindrically symmetric distribution of parallel wedge disclinations. We first use the tools of differential geometry to construct a Riemannian material manifold in which the body is stress-free. This manifold is metric compatible, has zero torsion, but has non-vanishing curvature. The problem then reduces to embedding this manifold in Euclidean 3-space following the procedure of a classical nonlinear elastic problem. We show that this embedding can be elegantly accomplished by using Cartan\\'s method of moving frames and compute explicitly the residual stress field for various distributions in the case of a neo-Hookean material. © 2012 The Author(s).

New Sensors for Cultural Heritage Metric Survey: The ToF Cameras

Directory of Open Access Journals (Sweden)

Filiberto Chiabrando

2011-12-01

Full Text Available ToF cameras are new instruments based on CCD/CMOS sensors which measure distances instead of radiometry. The resulting point clouds show the same properties (both in terms of accuracy and resolution of the point clouds acquired by means of traditional LiDAR devices. ToF cameras are cheap instruments (less than 10.000 € based on video real time distance measurements and can represent an interesting alternative to the more expensive LiDAR instruments. In addition, the limited weight and dimensions of ToF cameras allow a reduction of some practical problems such as transportation and on-site management. Most of the commercial ToF cameras use the phase-shift method to measure distances. Due to the use of only one wavelength, most of them have limited range of application (usually about 5 or 10 m. After a brief description of the main characteristics of these instruments, this paper explains and comments the results of the first experimental applications of ToF cameras in Cultural Heritage 3D metric survey.  The possibility to acquire more than 30 frames/s and future developments of these devices in terms of use of more than one wavelength to overcome the ambiguity problem allow to foresee new interesting applications.

Twistor geometry

NARCIS (Netherlands)

van den Broek, P.M.

1984-01-01

The aim of this paper is to give a detailed exposition of the relation between the geometry of twistor space and the geometry of Minkowski space. The paper has a didactical purpose; no use has been made of differential geometry and cohomology.

Moving from gamma passing rates to patient DVH-based QA metrics in pretreatment dose QA

Energy Technology Data Exchange (ETDEWEB)

Zhen, Heming; Nelms, Benjamin E.; Tome, Wolfgang A. [Department of Medical Physics, University of Wisconsin, Madison, Wisconsin 53705 (United States); Department of Human Oncology, University of Wisconsin, Madison, Wisconsin 53792 and Canis Lupus LLC, Merrimac, Wisconsin 53561 (United States); Department of Medical Physics, University of Wisconsin, Madison, Wisconsin 53705 and Department of Human Oncology, University of Wisconsin, Madison, Wisconsin 53792 (United States)

2011-10-15

Purpose: The purpose of this work is to explore the usefulness of the gamma passing rate metric for per-patient, pretreatment dose QA and to validate a novel patient-dose/DVH-based method and its accuracy and correlation. Specifically, correlations between: (1) gamma passing rates for three 3D dosimeter detector geometries vs clinically relevant patient DVH-based metrics; (2) Gamma passing rates of whole patient dose grids vs DVH-based metrics, (3) gamma passing rates filtered by region of interest (ROI) vs DVH-based metrics, and (4) the capability of a novel software algorithm that estimates corrected patient Dose-DVH based on conventional phan-tom QA data are analyzed. Methods: Ninety six unique ''imperfect'' step-and-shoot IMRT plans were generated by applying four different types of errors on 24 clinical Head/Neck patients. The 3D patient doses as well as the dose to a cylindrical QA phantom were then recalculated using an error-free beam model to serve as a simulated measurement for comparison. Resulting deviations to the planned vs simulated measured DVH-based metrics were generated, as were gamma passing rates for a variety of difference/distance criteria covering: dose-in-phantom comparisons and dose-in-patient comparisons, with the in-patient results calculated both over the whole grid and per-ROI volume. Finally, patient dose and DVH were predicted using the conventional per-beam planar data as input into a commercial ''planned dose perturbation'' (PDP) algorithm, and the results of these predicted DVH-based metrics were compared to the known values. Results: A range of weak to moderate correlations were found between clinically relevant patient DVH metrics (CTV-D95, parotid D{sub mean}, spinal cord D1cc, and larynx D{sub mean}) and both 3D detector and 3D patient gamma passing rate (3%/3 mm, 2%/2 mm) for dose-in-phantom along with dose-in-patient for both whole patient volume and filtered per-ROI. There was

Geometry

Indian Academy of Sciences (India)

. In the previous article we looked at the origins of synthetic and analytic geometry. More practical minded people, the builders and navigators, were studying two other aspects of geometry- trigonometry and integral calculus. These are actually ...

Cyber threat metrics.

Energy Technology Data Exchange (ETDEWEB)

Frye, Jason Neal; Veitch, Cynthia K.; Mateski, Mark Elliot; Michalski, John T.; Harris, James Mark; Trevino, Cassandra M.; Maruoka, Scott

2012-03-01

Threats are generally much easier to list than to describe, and much easier to describe than to measure. As a result, many organizations list threats. Fewer describe them in useful terms, and still fewer measure them in meaningful ways. This is particularly true in the dynamic and nebulous domain of cyber threats - a domain that tends to resist easy measurement and, in some cases, appears to defy any measurement. We believe the problem is tractable. In this report we describe threat metrics and models for characterizing threats consistently and unambiguously. The purpose of this report is to support the Operational Threat Assessment (OTA) phase of risk and vulnerability assessment. To this end, we focus on the task of characterizing cyber threats using consistent threat metrics and models. In particular, we address threat metrics and models for describing malicious cyber threats to US FCEB agencies and systems.

Fixed point theory in metric type spaces

CERN Document Server

Agarwal, Ravi P; O’Regan, Donal; Roldán-López-de-Hierro, Antonio Francisco

2015-01-01

Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise natur...

Deep Transfer Metric Learning.

Science.gov (United States)

Junlin Hu; Jiwen Lu; Yap-Peng Tan; Jie Zhou

2016-12-01

Conventional metric learning methods usually assume that the training and test samples are captured in similar scenarios so that their distributions are assumed to be the same. This assumption does not hold in many real visual recognition applications, especially when samples are captured across different data sets. In this paper, we propose a new deep transfer metric learning (DTML) method to learn a set of hierarchical nonlinear transformations for cross-domain visual recognition by transferring discriminative knowledge from the labeled source domain to the unlabeled target domain. Specifically, our DTML learns a deep metric network by maximizing the inter-class variations and minimizing the intra-class variations, and minimizing the distribution divergence between the source domain and the target domain at the top layer of the network. To better exploit the discriminative information from the source domain, we further develop a deeply supervised transfer metric learning (DSTML) method by including an additional objective on DTML, where the output of both the hidden layers and the top layer are optimized jointly. To preserve the local manifold of input data points in the metric space, we present two new methods, DTML with autoencoder regularization and DSTML with autoencoder regularization. Experimental results on face verification, person re-identification, and handwritten digit recognition validate the effectiveness of the proposed methods.

Energy functionals for Calabi-Yau metrics

International Nuclear Information System (INIS)

Headrick, M; Nassar, A

2013-01-01

We identify a set of ''energy'' functionals on the space of metrics in a given Kähler class on a Calabi-Yau manifold, which are bounded below and minimized uniquely on the Ricci-flat metric in that class. Using these functionals, we recast the problem of numerically solving the Einstein equation as an optimization problem. We apply this strategy, using the ''algebraic'' metrics (metrics for which the Kähler potential is given in terms of a polynomial in the projective coordinates), to the Fermat quartic and to a one-parameter family of quintics that includes the Fermat and conifold quintics. We show that this method yields approximations to the Ricci-flat metric that are exponentially accurate in the degree of the polynomial (except at the conifold point, where the convergence is polynomial), and therefore orders of magnitude more accurate than the balanced metrics, previously studied as approximations to the Ricci-flat metric. The method is relatively fast and easy to implement. On the theoretical side, we also show that the functionals can be used to give a heuristic proof of Yau's theorem

Environmental forcing metrics to quantify short-term foredune morphodynamics

Science.gov (United States)

Spore, N.; Conery, I.; Brodie, K. L.; Palmsten, M.

2016-12-01

Coastal foredunes evolve continuously due to competing aeolian and hydrodynamic processes. Onshore to shore-parallel winds transport sand to the dune while storm-driven surge and wave runup remove sand from the dune. Dune-growth requires periods of time when the wind exceeds a threshold velocity to initiate transport and the relative geometry of the dry beach to the wind direction to create large fetches. This study aims to derive an aeolian transport potential (ATP) metric from the precipitation, available fetch (a function of wind angle and dry-beach width), and a threshold wind speed to initiate transport. ATP is then combined with a hydrodynamic transport potential (HTP) metric, defined as the number of hours of wave impact to the foredune or upper beach, to assess the time-dependent magnitude of the forcing factors affecting morphological evolution of the foredune between monthly terrestrial lidar surveys.This study focuses on two distinctly different dune fields and their frontal or incipient dune ridges in Duck, NC at the USACE Field Research Facility (FRF): (1) an undisturbed, tall and narrow recently impacted dune with a near vertical face; and (2) an undisturbed, shorter and wider dune with gentler and more hummocky slopes. The two sites are separated by dune toe position were extracted from the DEMs and compared to the ATP and HTP values between the surveys to evaluate the dominant factors affecting sediment flux to the system.

Advanced Instrumentation for Positron Emission Tomography [PET

Science.gov (United States)

Derenzo, S. E.; Budinger, T. F.

1985-04-01

This paper summarizes the physical processes and medical science goals that underlay modern instrumentation design for Positron Emission Tomography. The paper discusses design factors such as detector material, crystalphototube coupling, shielding geometry, sampling motion, electronics design, time-of-flight, and the interrelationships with quantitative accuracy, spatial resolution, temporal resolution, maximum data rates, and cost.

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

International Nuclear Information System (INIS)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh

2013-01-01

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes

Magnetic geometry and physics of advanced divertors: The X-divertor and the snowflake

Energy Technology Data Exchange (ETDEWEB)

Kotschenreuther, Mike; Valanju, Prashant; Covele, Brent; Mahajan, Swadesh [Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)

2013-10-15

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust—the scrape-off layer. A primary result of our analysis is the emergence of a physical “metric,” the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics—the Standard Divertor (DI = 1), and two advanced geometries—the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes.

Spectrum-efficient multi-channel design for coexisting IEEE 802.15.4 networks: A stochastic geometry approach

KAUST Repository

Elsawy, Hesham

2014-07-01

For networks with random topologies (e.g., wireless ad-hoc and sensor networks) and dynamically varying channel gains, choosing the long term operating parameters that optimize the network performance metrics is very challenging. In this paper, we use stochastic geometry analysis to develop a novel framework to design spectrum-efficient multi-channel random wireless networks based on the IEEE 802.15.4 standard. The proposed framework maximizes both spatial and time domain frequency utilization under channel gain uncertainties to minimize the number of frequency channels required to accommodate a certain population of coexisting IEEE 802.15.4 networks. The performance metrics are the outage probability and the self admission failure probability. We relax the single channel assumption that has been used traditionally in the stochastic geometry analysis. We show that the intensity of the admitted networks does not increase linearly with the number of channels and the rate of increase of the intensity of the admitted networks decreases with the number of channels. By using graph theory, we obtain the minimum required number of channels to accommodate a certain intensity of coexisting networks under a self admission failure probability constraint. To this end, we design a superframe structure for the coexisting IEEE 802.15.4 networks and a method for time-domain interference alignment. © 2002-2012 IEEE.

Phase space descriptions for simplicial 4D geometries

International Nuclear Information System (INIS)

Dittrich, Bianca; Ryan, James P

2011-01-01

Starting from the canonical phase space for discretized (4D) BF theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated with loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area-angle Regge calculus, as defined in [1] (prior to the imposition of gluing constraints, which ensure the metricity of the triangulation). Finally, we show that for a subclass of triangulations one can construct first-class Hamiltonian and diffeomorphism constraints leading to flat 4D spacetimes.

Regge calculus from discontinuous metrics

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2003-01-01

Regge calculus is considered as a particular case of the more general system where the linklengths of any two neighbouring 4-tetrahedra do not necessarily coincide on their common face. This system is treated as that one described by metric discontinuous on the faces. In the superspace of all discontinuous metrics the Regge calculus metrics form some hypersurface defined by continuity conditions. Quantum theory of the discontinuous metric system is assumed to be fixed somehow in the form of quantum measure on (the space of functionals on) the superspace. The problem of reducing this measure to the Regge hypersurface is addressed. The quantum Regge calculus measure is defined from a discontinuous metric measure by inserting the δ-function-like phase factor. The requirement that continuity conditions be imposed in a 'face-independent' way fixes this factor uniquely. The term 'face-independent' means that this factor depends only on the (hyper)plane spanned by the face, not on it's form and size. This requirement seems to be natural from the viewpoint of existence of the well-defined continuum limit maximally free of lattice artefacts

Numerical Calabi-Yau metrics

International Nuclear Information System (INIS)

Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene

2008-01-01

We develop numerical methods for approximating Ricci flat metrics on Calabi-Yau hypersurfaces in projective spaces. Our approach is based on finding balanced metrics and builds on recent theoretical work by Donaldson. We illustrate our methods in detail for a one parameter family of quintics. We also suggest several ways to extend our results

Metrics for Evaluation of Student Models

Science.gov (United States)

Pelanek, Radek

2015-01-01

Researchers use many different metrics for evaluation of performance of student models. The aim of this paper is to provide an overview of commonly used metrics, to discuss properties, advantages, and disadvantages of different metrics, to summarize current practice in educational data mining, and to provide guidance for evaluation of student…

Molecular geometry

CERN Document Server

Rodger, Alison

1995-01-01

Molecular Geometry discusses topics relevant to the arrangement of atoms. The book is comprised of seven chapters that tackle several areas of molecular geometry. Chapter 1 reviews the definition and determination of molecular geometry, while Chapter 2 discusses the unified view of stereochemistry and stereochemical changes. Chapter 3 covers the geometry of molecules of second row atoms, and Chapter 4 deals with the main group elements beyond the second row. The book also talks about the complexes of transition metals and f-block elements, and then covers the organometallic compounds and trans

Real time noninvasive assessment of external trunk geometry during surgical correction of adolescent idiopathic scoliosis

Directory of Open Access Journals (Sweden)

Mac-Thiong Jean-Marc

2009-02-01

Full Text Available Abstract Background The correction of trunk deformity is crucial in scoliosis surgery, especially for the patient's self-image. However, direct visualization of external scoliotic trunk deformity during surgical correction is difficult due to the covering draping sheets. Methods An optoelectronic camera system with 10 passive markers is used to track the trunk geometry of 5 scoliotic patients during corrective surgery. The position of 10 anatomical landmarks and 5 trunk indices computed from the position of the passive markers are compared during and after instrumentation of the spine. Results Internal validation of the accuracy of tracking was evaluated at 0.41 +/- 0.05 mm RMS. Intra operative tracking during surgical maneuvers shows improvement of the shoulder balance during and after correction of the spine. Improvement of the overall patient balance is observed. At last, a minor increase of the spinal length can be noticed. Conclusion Tracking of the external geometry of the trunk during surgical correction is useful to monitor changes occurring under the sterile draping sheets. Moreover, this technique can used be used to reach the optimal configuration on the operating frame before proceeding to surgery. The current tracking technique was able to detect significant changes in trunk geometry caused by posterior instrumentation of the spine despite significant correction of the spinal curvature. It could therefore become relevant for computer-assisted guidance of surgical maneuvers when performing posterior instrumentation of the scoliotic spine, provide important insights during positioning of patients.

Space–time and spatial geodesic orbits in Schwarzschild geometry

Science.gov (United States)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

GALAXI: Gallium anode low-angle x-ray instrument

Directory of Open Access Journals (Sweden)

Emmanuel Kentzinger

2016-03-01

Full Text Available The high brilliance laboratory small angle X-ray scattering instrument GALAXI, which is operated by JCNS, Forschungszentrum Jülich, permits the investigation of chemical correlations in bulk materials or of structures deposited on a surface at nanometre and mesoscopic length scales. The instrument is capable to perform GISAXS experiments in reflection at grazing incidence as well as SAXS experiments in transmission geometry. The X-ray flux on sample is comparable or higher than the one obtained at a comparable beamline at a second generation synchrotron radiation source.

Development of Geometry Normalized Electromagnetic System (GNES) instrument for metal defect detection

Science.gov (United States)

Zakaria, Zakaria; Surbakti, Muhammad Syukri; Syahreza, Saumi; Mat Jafri, Mohd. Zubir; Tan, Kok Chooi

2017-10-01

It has been already made, calibrated and tested a geometry normalized electromagnetic system (GNES) for metal defect examination. The GNES has an automatic data acquisition system which supporting the efficiency and accuracy of the measurement. The data will be displayed on the computer monitor as a graphic display then saved automatically in the Microsoft Excel format. The transmitter will transmit the frequency pair (FP) signals i.e. 112.5 Hz and 337.5 Hz; 112.5 Hz and 1012.5 Hz; 112.5 Hz and 3037.5 Hz; 337.5 Hz and 1012.5 Hz; 337.5 Hz and 3037.5 Hz. Simultaneous transmissions of two electromagnetic waves without distortions by the transmitter will induce an eddy current in the metal. This current, in turn, will produce secondary electromagnetic fields which are measured by the receiver together with the primary fields. Measurement of percent change of a vertical component of the fields will give the percent response caused by the metal or the defect. The response examinations were performed by the models with various type of defect for the master curves. The materials of samples as a plate were using Aluminum, Brass, and Copper. The more of the defects is the more reduction of the eddy current response. The defect contrasts were tended to decrease when the more depth of the defect position. The magnitude and phase of the eddy currents will affect the loading on the coil thus its impedance. The defect must interrupt the surface eddy current flow to be detected. Defect lying parallel to the current path will not cause any significant interruption and may not be detected. The main factors which affect the eddy current response are metal conductivity, permeability, frequency, and geometry.

Establishing a common metric for depressive symptoms: linking the BDI-II, CES-D, and PHQ-9 to PROMIS depression.

Science.gov (United States)

Choi, Seung W; Schalet, Benjamin; Cook, Karon F; Cella, David

2014-06-01

Interest in measuring patient-reported outcomes has increased dramatically in recent decades. This has simultaneously produced numerous assessment options and confusion. In the case of depressive symptoms, there are many commonly used options for measuring the same or a very similar concept. Public and professional reporting of scores can be confused by multiple scale ranges, normative levels, and clinical thresholds. A common reporting metric would have great value and can be achieved when similar instruments are administered to a single sample and then linked to each other to produce cross-walk score tables (e.g., Dorans, 2007; Kolen & Brennan, 2004). Using multiple procedures based on item response theory and equipercentile methods, we produced cross-walk tables linking 3 popular "legacy" depression instruments-the Center for Epidemiologic Studies Depression Scale (Radloff, 1977; N = 747), the Beck Depression Inventory-II (Beck, Steer, & Brown, 1996; N = 748), and the 9-item Patient Health Questionnaire (Kroenke, Spitzer, & Williams, 2001; N = 1,120)-to the depression metric of the National Institutes of Health (NIH) Patient-Reported Outcomes Measurement Information System (PROMIS; Cella et al., 2010). The PROMIS Depression metric is centered on the U.S. general population, matching the marginal distributions of gender, age, race, and education in the 2000 U.S. census (Liu et al., 2010). The linking relationships were evaluated by resampling small subsets and estimating confidence intervals for the differences between the observed and linked PROMIS scores; in addition, PROMIS cutoff scores for depression severity were estimated to correspond with those commonly used with the legacy measures. Our results allow clinicians and researchers to retrofit existing data of 3 popular depression measures to the PROMIS Depression metric and vice versa.

Issues in Benchmark Metric Selection

Science.gov (United States)

Crolotte, Alain

It is true that a metric can influence a benchmark but will esoteric metrics create more problems than they will solve? We answer this question affirmatively by examining the case of the TPC-D metric which used the much debated geometric mean for the single-stream test. We will show how a simple choice influenced the benchmark and its conduct and, to some extent, DBMS development. After examining other alternatives our conclusion is that the “real” measure for a decision-support benchmark is the arithmetic mean.

A contest of sensors in close range 3D imaging: performance evaluation with a new metric test object

Directory of Open Access Journals (Sweden)

M. Hess

2014-06-01

Full Text Available An independent means of 3D image quality assessment is introduced, addressing non-professional users of sensors and freeware, which is largely characterized as closed-sourced and by the absence of quality metrics for processing steps, such as alignment. A performance evaluation of commercially available, state-of-the-art close range 3D imaging technologies is demonstrated with the help of a newly developed Portable Metric Test Artefact. The use of this test object provides quality control by a quantitative assessment of 3D imaging sensors. It will enable users to give precise specifications which spatial resolution and geometry recording they expect as outcome from their 3D digitizing process. This will lead to the creation of high-quality 3D digital surrogates and 3D digital assets. The paper is presented in the form of a competition of teams, and a possible winner will emerge.

Robustness of climate metrics under climate policy ambiguity

International Nuclear Information System (INIS)

Ekholm, Tommi; Lindroos, Tomi J.; Savolainen, Ilkka

2013-01-01

Highlights: • We assess the economic impacts of using different climate metrics. • The setting is cost-efficient scenarios for three interpretations of the 2C target. • With each target setting, the optimal metric is different. • Therefore policy ambiguity prevents the selection of an optimal metric. • Robust metric values that perform well with multiple policy targets however exist. -- Abstract: A wide array of alternatives has been proposed as the common metrics with which to compare the climate impacts of different emission types. Different physical and economic metrics and their parameterizations give diverse weights between e.g. CH 4 and CO 2 , and fixing the metric from one perspective makes it sub-optimal from another. As the aims of global climate policy involve some degree of ambiguity, it is not possible to determine a metric that would be optimal and consistent with all policy aims. This paper evaluates the cost implications of using predetermined metrics in cost-efficient mitigation scenarios. Three formulations of the 2 °C target, including both deterministic and stochastic approaches, shared a wide range of metric values for CH 4 with which the mitigation costs are only slightly above the cost-optimal levels. Therefore, although ambiguity in current policy might prevent us from selecting an optimal metric, it can be possible to select robust metric values that perform well with multiple policy targets

Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology & Symplectic Geometry, Noncommutative Geometry and Physics

CERN Document Server

Eliashberg, Yakov; Maeda, Yoshiaki; Symplectic, Poisson, and Noncommutative geometry

2014-01-01

Symplectic geometry originated in physics, but it has flourished as an independent subject in mathematics, together with its offspring, symplectic topology. Symplectic methods have even been applied back to mathematical physics. Noncommutative geometry has developed an alternative mathematical quantization scheme based on a geometric approach to operator algebras. Deformation quantization, a blend of symplectic methods and noncommutative geometry, approaches quantum mechanics from a more algebraic viewpoint, as it addresses quantization as a deformation of Poisson structures. This volume contains seven chapters based on lectures given by invited speakers at two May 2010 workshops held at the Mathematical Sciences Research Institute: Symplectic and Poisson Geometry in Interaction with Analysis, Algebra and Topology (honoring Alan Weinstein, one of the key figures in the field) and Symplectic Geometry, Noncommutative Geometry and Physics. The chapters include presentations of previously unpublished results and ...

Web metrics for library and information professionals

CERN Document Server

Stuart, David

2014-01-01

This is a practical guide to using web metrics to measure impact and demonstrate value. The web provides an opportunity to collect a host of different metrics, from those associated with social media accounts and websites to more traditional research outputs. This book is a clear guide for library and information professionals as to what web metrics are available and how to assess and use them to make informed decisions and demonstrate value. As individuals and organizations increasingly use the web in addition to traditional publishing avenues and formats, this book provides the tools to unlock web metrics and evaluate the impact of this content. The key topics covered include: bibliometrics, webometrics and web metrics; data collection tools; evaluating impact on the web; evaluating social media impact; investigating relationships between actors; exploring traditional publications in a new environment; web metrics and the web of data; the future of web metrics and the library and information professional.Th...

Partial rectangular metric spaces and fixed point theorems.

Science.gov (United States)

Shukla, Satish

2014-01-01

The purpose of this paper is to introduce the concept of partial rectangular metric spaces as a generalization of rectangular metric and partial metric spaces. Some properties of partial rectangular metric spaces and some fixed point results for quasitype contraction in partial rectangular metric spaces are proved. Some examples are given to illustrate the observed results.

Metric elasticity in a collapsing star: Gravitational radiation coupled to torsional motion

International Nuclear Information System (INIS)

Gerlach, U.H.; Scott, J.F.

1986-01-01

Torsional oscillatory matter motion as well as differential rotation couple via the linearized Einstein field equations to the gravitational degrees of freedom. For an arbitrary spherically symmetric background, such as that of a wildly pulsating or a catastrophically collapsing star, we exhibit (a) the strain tensor and (b) the corresponding stress-energy tensor. It is found that in the star there are two elasticity tensors. One expresses the familiar elasticity of matter, the other expresses the elasticity of the geometry. This metric elasticity is responsible for coupling the gravitational and matter degrees of freedom. The two coupled scalar wave equations for these degrees of freedom are exhibited. Also exhibited are their characteristics as well as the junction conditions for their solutions across any spherical surface of discontinuity

A Kerr-NUT metric

International Nuclear Information System (INIS)

Vaidya, P.C.; Patel, L.K.; Bhatt, P.V.

1976-01-01

Using Galilean time and retarded distance as coordinates the usual Kerr metric is expressed in form similar to the Newman-Unti-Tamburino (NUT) metric. The combined Kerr-NUT metric is then investigated. In addition to the Kerr and NUT solutions of Einstein's equations, three other types of solutions are derived. These are (i) the radiating Kerr solution, (ii) the radiating NUT solution satisfying Rsub(ik) = sigmaxisub(i)xisub(k), xisub(i)xisup(i) = 0, and (iii) the associated Kerr solution satisfying Rsub(ik) = 0. Solution (i) is distinct from and simpler than the one reported earlier by Vaidya and Patel (Phys. Rev.; D7:3590 (1973)). Solutions (ii) and (iii) gave line elements which have the axis of symmetry as a singular line. (author)

Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

Science.gov (United States)

Savickas, David

2015-04-01

General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

Stationary and protable instruments for assay of HEU [highly enriched uranium] solids holdup

International Nuclear Information System (INIS)

Russo, P.A.; Sprinkle, J.K. Jr.; Stephens, M.M.; Brumfield, T.L.; Gunn, C.S.; Watson, D.R.

1987-01-01

Two NaI(Tl)-based instruments, one stationary and one portable, designed for automated assay of highly enriched uranium (HEU) solids holdup, are being evaluated at the scrap recovery facility of the Oak Ridge Y-12 Plant. The stationary instrument, a continuous monitor of HEU within the filters of the chip burner exhaust system, measures the HEU deposits that accumulate erratically and rapidly during chip burner operation. The portable system was built to assay HEU in over 100 m of elevated piping used to transfer UO 3 , UO 2 , and UF 4 powder to, from, and between the fluid bed conversion furnances and the powder storage hoods. Both instruments use two detector heads. Both provide immediate automatic readout of accumulated HEU mass. The 186-keV 235 U gamma ray is the assay signature, and the 60-keV gamma ray from an 241 Am source attached to each detector is used to normalize the 186-keV rate. The measurement geometries were selected for compatibility with simple calibration models. The assay calibrations were calculated from these models and were verified and normalized with measurements of HEU standards built to match geometries of uniform accumulations on the surfaces of the process equipment. This instrumentation effort demonstrates that simple calibration models can often be applied to unique measurement geometries, minimizing the otherwise unreasonable requirements for calibration standards and allowing extension of the measurements to other process locations

Background metric in supergravity theories

International Nuclear Information System (INIS)

Yoneya, T.

1978-01-01

In supergravity theories, we investigate the conformal anomaly of the path-integral determinant and the problem of fermion zero modes in the presence of a nontrivial background metric. Except in SO(3) -invariant supergravity, there are nonvanishing conformal anomalies. As a consequence, amplitudes around the nontrivial background metric contain unpredictable arbitrariness. The fermion zero modes which are explicitly constructed for the Euclidean Schwarzschild metric are interpreted as an indication of the supersymmetric multiplet structure of a black hole. The degree of degeneracy of a black hole is 2/sup 4n/ in SO(n) supergravity

Daylight metrics and energy savings

Energy Technology Data Exchange (ETDEWEB)

Mardaljevic, John; Heschong, Lisa; Lee, Eleanor

2009-12-31

The drive towards sustainable, low-energy buildings has increased the need for simple, yet accurate methods to evaluate whether a daylit building meets minimum standards for energy and human comfort performance. Current metrics do not account for the temporal and spatial aspects of daylight, nor of occupants comfort or interventions. This paper reviews the historical basis of current compliance methods for achieving daylit buildings, proposes a technical basis for development of better metrics, and provides two case study examples to stimulate dialogue on how metrics can be applied in a practical, real-world context.

Information Geometry of Non-Equilibrium Processes in a Bistable System with a Cubic Damping

Directory of Open Access Journals (Sweden)

Rainer Hollerbach

2017-06-01

Full Text Available A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs, it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference between the two PDFs. This metric structure then provides a key link between stochastic systems and information geometry. For a non-equilibrium process, we define an infinitesimal distance at any time by comparing two PDFs at times infinitesimally apart and sum these distances in time. The total distance along the trajectory of the system quantifies the total number of different states that the system undergoes in time and is called the information length. By using this concept, we investigate the information geometry of non-equilibrium processes involved in disorder-order transitions between the critical and subcritical states in a bistable system. Specifically, we compute time-dependent PDFs, information length, the rate of change in information length, entropy change and Fisher information in disorder-to-order and order-to-disorder transitions and discuss similarities and disparities between the two transitions. In particular, we show that the total information length in order-to-disorder transition is much larger than that in disorder-to-order transition and elucidate the link to the drastically different evolution of entropy in both transitions. We also provide the comparison of the results with those in the case of the transition between the subcritical and supercritical states and discuss implications for fitness.

Metrics for energy resilience

International Nuclear Information System (INIS)

Roege, Paul E.; Collier, Zachary A.; Mancillas, James; McDonagh, John A.; Linkov, Igor

2014-01-01

Energy lies at the backbone of any advanced society and constitutes an essential prerequisite for economic growth, social order and national defense. However there is an Achilles heel to today's energy and technology relationship; namely a precarious intimacy between energy and the fiscal, social, and technical systems it supports. Recently, widespread and persistent disruptions in energy systems have highlighted the extent of this dependence and the vulnerability of increasingly optimized systems to changing conditions. Resilience is an emerging concept that offers to reconcile considerations of performance under dynamic environments and across multiple time frames by supplementing traditionally static system performance measures to consider behaviors under changing conditions and complex interactions among physical, information and human domains. This paper identifies metrics useful to implement guidance for energy-related planning, design, investment, and operation. Recommendations are presented using a matrix format to provide a structured and comprehensive framework of metrics relevant to a system's energy resilience. The study synthesizes previously proposed metrics and emergent resilience literature to provide a multi-dimensional model intended for use by leaders and practitioners as they transform our energy posture from one of stasis and reaction to one that is proactive and which fosters sustainable growth. - Highlights: • Resilience is the ability of a system to recover from adversity. • There is a need for methods to quantify and measure system resilience. • We developed a matrix-based approach to generate energy resilience metrics. • These metrics can be used in energy planning, system design, and operations

Development of material measures for performance verifying surface topography measuring instruments

International Nuclear Information System (INIS)

Leach, Richard; Giusca, Claudiu; Rickens, Kai; Riemer, Oltmann; Rubert, Paul

2014-01-01

The development of two irregular-geometry material measures for performance verifying surface topography measuring instruments is described. The material measures are designed to be used to performance verify tactile and optical areal surface topography measuring instruments. The manufacture of the material measures using diamond turning followed by nickel electroforming is described in detail. Measurement results are then obtained using a traceable stylus instrument and a commercial coherence scanning interferometer, and the results are shown to agree to within the measurement uncertainties. The material measures are now commercially available as part of a suite of material measures aimed at the calibration and performance verification of areal surface topography measuring instruments

Balanced metrics for vector bundles and polarised manifolds

DEFF Research Database (Denmark)

Garcia Fernandez, Mario; Ross, Julius

2012-01-01

leads to a Hermitian-Einstein metric on E and a constant scalar curvature Kähler metric in c_1(L). For special values of α, limits of balanced metrics are solutions of a system of coupled equations relating a Hermitian-Einstein metric on E and a Kähler metric in c1(L). For this, we compute the top two......We consider a notion of balanced metrics for triples (X, L, E) which depend on a parameter α, where X is smooth complex manifold with an ample line bundle L and E is a holomorphic vector bundle over X. For generic choice of α, we prove that the limit of a convergent sequence of balanced metrics...

Integrability and black-hole microstate geometries

Science.gov (United States)

Bena, Iosif; Turton, David; Walker, Robert; Warner, Nicholas P.

2017-11-01

We examine some recently-constructed families of asymptotically-AdS3 × S^3 supergravity solutions that have the same charges and mass as supersymmetric D1-D5- P black holes, but that cap off smoothly with no horizon. These solutions, known as superstrata, are quite complicated, however we show that, for an infinite family of solutions, the null geodesic problem is completely integrable, due to the existence of a non-trivial conformal Killing tensor that provides a quadratic conservation law for null geodesics. This implies that the massless scalar wave equation is separable. For another infinite family of solutions, we find that there is a non-trivial conformal Killing tensor only when the left-moving angular momentum of the massless scalar is zero. We also show that, for both these families, the metric degrees of freedom have the form they would take if they arose from a consistent truncation on S^3 down to a (2 + 1)-dimensional space-time. We discuss some of the broader consequences of these special properties for the physics of these black-hole microstate geometries.

Investigation of Stability of Precise Geodetic Instruments Used in Deformation Monitoring

Science.gov (United States)

Woźniak, Marek; Odziemczyk, Waldemar

2017-12-01

Monitoring systems using automated electronic total stations are an important element of safety control of many engineering objects. In order to ensure the appropriate credibility of acquired data, it is necessary that instruments (total stations in most of the cases) used for measurements meet requirements of measurement accuracy, as well as the stability of instrument axis system geometry. With regards to the above, it is expedient to conduct quality control of data acquired using electronic total stations in the context of performed measurement procedures. This paper presents results of research conducted at the Faculty of Geodesy and Cartography at Warsaw University of Technology investigating the stability of "basic" error values (collimation, zero location for V circle, inclination), for two types of automatic total stations: TDA 5005 and TCRP 1201+. Research provided also information concerning the influence of temperature changes upon the stability of investigated instrument's optical parameters. Results are presented in graphical analytic technique. Final conclusions propose methods, which allow avoiding negative results of measuring tool-set geometry changes during conducting precise deformation monitoring measurements.

The blepharospasm disability scale: an instrument for the assessment of functional health in blepharospasm

NARCIS (Netherlands)

Lindeboom, R.; de Haan, R.; Aramideh, M.; Speelman, J. D.

1995-01-01

Assessment of the functional status in patients with blepharospasm is of major importance for clinical practice and outcome studies. The Blepharospasm Disability Scale (BDS) is specifically directed to measure the disability in these patients. The metric properties of this instrument were evaluated.

The metrics of science and technology

CERN Document Server

Geisler, Eliezer

2000-01-01

Dr. Geisler's far-reaching, unique book provides an encyclopedic compilation of the key metrics to measure and evaluate the impact of science and technology on academia, industry, and government. Focusing on such items as economic measures, patents, peer review, and other criteria, and supported by an extensive review of the literature, Dr. Geisler gives a thorough analysis of the strengths and weaknesses inherent in metric design, and in the use of the specific metrics he cites. His book has already received prepublication attention, and will prove especially valuable for academics in technology management, engineering, and science policy; industrial R&D executives and policymakers; government science and technology policymakers; and scientists and managers in government research and technology institutions. Geisler maintains that the application of metrics to evaluate science and technology at all levels illustrates the variety of tools we currently possess. Each metric has its own unique strengths and...

Extending cosmology: the metric approach

OpenAIRE

Mendoza, S.

2012-01-01

Comment: 2012, Extending Cosmology: The Metric Approach, Open Questions in Cosmology; Review article for an Intech "Open questions in cosmology" book chapter (19 pages, 3 figures). Available from: http://www.intechopen.com/books/open-questions-in-cosmology/extending-cosmology-the-metric-approach

Metrics, Media and Advertisers: Discussing Relationship

Directory of Open Access Journals (Sweden)

Marco Aurelio de Souza Rodrigues

2014-11-01

Full Text Available This study investigates how Brazilian advertisers are adapting to new media and its attention metrics. In-depth interviews were conducted with advertisers in 2009 and 2011. In 2009, new media and its metrics were celebrated as innovations that would increase advertising campaigns overall efficiency. In 2011, this perception has changed: New media’s profusion of metrics, once seen as an advantage, started to compromise its ease of use and adoption. Among its findings, this study argues that there is an opportunity for media groups willing to shift from a product-focused strategy towards a customer-centric one, through the creation of new, simple and integrative metrics. 

Measuring Information Security: Guidelines to Build Metrics

Science.gov (United States)

von Faber, Eberhard

Measuring information security is a genuine interest of security managers. With metrics they can develop their security organization's visibility and standing within the enterprise or public authority as a whole. Organizations using information technology need to use security metrics. Despite the clear demands and advantages, security metrics are often poorly developed or ineffective parameters are collected and analysed. This paper describes best practices for the development of security metrics. First attention is drawn to motivation showing both requirements and benefits. The main body of this paper lists things which need to be observed (characteristic of metrics), things which can be measured (how measurements can be conducted) and steps for the development and implementation of metrics (procedures and planning). Analysis and communication is also key when using security metrics. Examples are also given in order to develop a better understanding. The author wants to resume, continue and develop the discussion about a topic which is or increasingly will be a critical factor of success for any security managers in larger organizations.

In-pile Instrumentation Development

International Nuclear Information System (INIS)

Vermeeren, L.

2005-01-01

Advanced irradiations in research reactors require the on-line monitoring of crucial parameters like neutron fluxes, gamma dose rates, central fuel rod temperatures, fission gas release pressures and small geometry changes. Our activities in this field aim at a detailed understanding of the sensor behaviour in the irradiation conditions in order to extract reliable real-time information. The objectives of work performed by SCK-CEN are to study of the on-line in-pile measurement of gamma and neutron fluxes in real time and to investigate parasitic radiation-induced signals in instrumentation cables

Active Metric Learning for Supervised Classification

OpenAIRE

Kumaran, Krishnan; Papageorgiou, Dimitri; Chang, Yutong; Li, Minhan; Takáč, Martin

2018-01-01

Clustering and classification critically rely on distance metrics that provide meaningful comparisons between data points. We present mixed-integer optimization approaches to find optimal distance metrics that generalize the Mahalanobis metric extensively studied in the literature. Additionally, we generalize and improve upon leading methods by removing reliance on pre-designated "target neighbors," "triplets," and "similarity pairs." Another salient feature of our method is its ability to en...

Test and Delivery of the Chemin Mineralogical Instrument for Mars Science Laboratory

Science.gov (United States)

Blake, D. F.; Vaniman, D.; Anderson, R.; Bish, D.; Chipera, S.; Chemtob, S.; Crisp, J.; DesMarais, D. J.; Downs, R.; Feldman, S.;

Arithmetic noncommutative geometry

CERN Document Server

Marcolli, Matilde

2005-01-01

Arithmetic noncommutative geometry denotes the use of ideas and tools from the field of noncommutative geometry, to address questions and reinterpret in a new perspective results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at archimedean places of arithmetic surfaces and varieties. The main reason why noncommutative geometry can be expected to say something about topics of arithmetic interest lies in the fact that it provides the right framework in which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry, such as moduli spaces (of which modular curves are the simplest case) or arithmetic varieties (completed by suitable "fibers at infinity"), by adding boundaries...

Multimetric indices: How many metrics?

Science.gov (United States)

Multimetric indices (MMI’s) often include 5 to 15 metrics, each representing a different attribute of assemblage condition, such as species diversity, tolerant taxa, and nonnative taxa. Is there an optimal number of metrics for MMIs? To explore this question, I created 1000 9-met...

Metrics for Polyphonic Sound Event Detection

Directory of Open Access Journals (Sweden)

Annamaria Mesaros

2016-05-01

Full Text Available This paper presents and discusses various metrics proposed for evaluation of polyphonic sound event detection systems used in realistic situations where there are typically multiple sound sources active simultaneously. The system output in this case contains overlapping events, marked as multiple sounds detected as being active at the same time. The polyphonic system output requires a suitable procedure for evaluation against a reference. Metrics from neighboring fields such as speech recognition and speaker diarization can be used, but they need to be partially redefined to deal with the overlapping events. We present a review of the most common metrics in the field and the way they are adapted and interpreted in the polyphonic case. We discuss segment-based and event-based definitions of each metric and explain the consequences of instance-based and class-based averaging using a case study. In parallel, we provide a toolbox containing implementations of presented metrics.

Robustness Metrics: Consolidating the multiple approaches to quantify Robustness

DEFF Research Database (Denmark)

Göhler, Simon Moritz; Eifler, Tobias; Howard, Thomas J.

2016-01-01

robustness metrics; 3) Functional expectancy and dispersion robustness metrics; and 4) Probability of conformance robustness metrics. The goal was to give a comprehensive overview of robustness metrics and guidance to scholars and practitioners to understand the different types of robustness metrics...

Common Metrics for Human-Robot Interaction

Science.gov (United States)

Steinfeld, Aaron; Lewis, Michael; Fong, Terrence; Scholtz, Jean; Schultz, Alan; Kaber, David; Goodrich, Michael

2006-01-01

This paper describes an effort to identify common metrics for task-oriented human-robot interaction (HRI). We begin by discussing the need for a toolkit of HRI metrics. We then describe the framework of our work and identify important biasing factors that must be taken into consideration. Finally, we present suggested common metrics for standardization and a case study. Preparation of a larger, more detailed toolkit is in progress.

WIMT in Gullstränd–Painlevé and Reissner–Nordström metrics: induced stable gravito-magnetic monopoles

Energy Technology Data Exchange (ETDEWEB)

Romero, Jesús Martín, E-mail: jesusromero@conicet.gov.ar [Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina); Bellini, Mauricio, E-mail: mbellini@mdp.edu.ar [Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Mar del Plata (Argentina)

2015-05-08

The aim of this work is to apply Weitzeböck Induced Matter Theory (WIMT) to Gullstränd–Painlevé and Reissner–Nordström metrics in the framework of WIMT. This is a newly developed method that extends Induced Matter Theory from a curved 5D manifold using the Weitzeböck’s geometry, using the fact that the Riemann–Weitzenböck curvature tensor is always null. We obtain the presence of currents whose interpretation can lead to the presence of stable gravito-magnetic monopoles.

Narrowing the Gap Between QoS Metrics and Web QoE Using Above-the-fold Metrics

OpenAIRE

da Hora, Diego Neves; Asrese, Alemnew; Christophides, Vassilis; Teixeira, Renata; Rossi, Dario

2018-01-01

International audience; Page load time (PLT) is still the most common application Quality of Service (QoS) metric to estimate the Quality of Experience (QoE) of Web users. Yet, recent literature abounds with proposals for alternative metrics (e.g., Above The Fold, SpeedIndex and variants) that aim at better estimating user QoE. The main purpose of this work is thus to thoroughly investigate a mapping between established and recently proposed objective metrics and user QoE. We obtain ground tr...

Higher geometry an introduction to advanced methods in analytic geometry

CERN Document Server

Woods, Frederick S

2005-01-01

For students of mathematics with a sound background in analytic geometry and some knowledge of determinants, this volume has long been among the best available expositions of advanced work on projective and algebraic geometry. Developed from Professor Woods' lectures at the Massachusetts Institute of Technology, it bridges the gap between intermediate studies in the field and highly specialized works.With exceptional thoroughness, it presents the most important general concepts and methods of advanced algebraic geometry (as distinguished from differential geometry). It offers a thorough study

Non-Riemannian geometry

CERN Document Server

Eisenhart, Luther Pfahler

2005-01-01

This concise text by a prominent mathematician deals chiefly with manifolds dominated by the geometry of paths. Topics include asymmetric and symmetric connections, the projective geometry of paths, and the geometry of sub-spaces. 1927 edition.

Explanation of Rotation Curves in Galaxies and Clusters of them, by Generalization of Schwarzschild Metric and Combination with MOND, eliminating Dark Matter

Science.gov (United States)

Vossos, Spyridon; Vossos, Elias

2017-12-01

by the light of Euclidean Closed Linear Transformations of Complex Spacetime endowed with the Corresponding Metric. Of course, may also be applied by scientists who prefer the hyperbolic geometry of Classic Relativity (CR).

Factor structure of the Tomimatsu-Sato metrics

International Nuclear Information System (INIS)

Perjes, Z.

1989-02-01

Based on an earlier result stating that δ = 3 Tomimatsu-Sato (TS) metrics can be factored over the field of integers, an analogous representation for higher TS metrics was sought. It is shown that the factoring property of TS metrics follows from the structure of special Hankel determinants. A set of linear algebraic equations determining the factors was defined, and the factors of the first five TS metrics were tabulated, together with their primitive factors. (R.P.) 4 refs.; 2 tabs

Geometry of Quantum States

International Nuclear Information System (INIS)

Hook, D W

2008-01-01

applications of the geometric approach. The first four chapters contain the standard mathematics required to understand the rest of the material presented: specific areas in colour theory, set theory, probability theory, differential geometry and projective geometry are all covered with an eye to the material that follows. Chapter 5 starts the first real discussion of quantum theory in GQS and serves as an elegant, succinct introduction to the geometry which underlies quantum theory. This may be the most worthwhile chapter for the casual reader who wants to understand the key ideas in this field. Chapter 6 builds on the discussion in Chapter 5, introducing a group theoretic approach to understand coherent states and Chapter 7 describes a geometric tool in the form of an approach to complex projective geometry called 'the stellar representation'. Chapter 8 returns to a more purely quantum mechanical discussion as the authors turn to study the space of density matrices. This chapter completes the discussion which started in Chapter 5. Chapter 9 begins the part of the book concerned with applications of the geometric approach. From this point on the book aims, specifically, to prepare the reader for the material in Chapter 15 beginning with a discussion on the purification of mixed quantum states. In the succeeding chapters a definite choice has been made to present a geometric approach to certain quantum information problems. For example, Chapter 10 contains an extremely well formulated discussion of measurement and positive operator-valued measures with several well illustrated examples and Chapter 11 reopens the discussion of density matrices. Entropy and majorization are again revisited in Chapter 12 in much greater detail than in previous chapters. Chapters 13 and 14 concern themselves with a discussion of various metrics and their relation to the problem of distinguishing between probability distributions and their suitability as probability measures. (book review)

ST-intuitionistic fuzzy metric space with properties

Science.gov (United States)

Arora, Sahil; Kumar, Tanuj

2017-07-01

In this paper, we define ST-intuitionistic fuzzy metric space and the notion of convergence and completeness properties of cauchy sequences is studied. Further, we prove some properties of ST-intuitionistic fuzzy metric space. Finally, we introduce the concept of symmetric ST Intuitionistic Fuzzy metric space.

Differential geometry and topology with a view to dynamical systems

CERN Document Server

Burns, Keith

2005-01-01

MANIFOLDSIntroductionReview of topological conceptsSmooth manifoldsSmooth mapsTangent vectors and the tangent bundleTangent vectors as derivationsThe derivative of a smooth mapOrientationImmersions, embeddings and submersionsRegular and critical points and valuesManifolds with boundarySard's theoremTransversalityStabilityExercisesVECTOR FIELDS AND DYNAMICAL SYSTEMSIntroductionVector fieldsSmooth dynamical systemsLie derivative, Lie bracketDiscrete dynamical systemsHyperbolic fixed points and periodic orbitsExercisesRIEMANNIAN METRICSIntroductionRiemannian metricsStandard geometries on surfacesExercisesRIEMANNIAN CONNECTIONS AND GEODESICSIntroductionAffine connectionsRiemannian connectionsGeodesicsThe exponential mapMinimizing properties of geodesicsThe Riemannian distanceExercisesCURVATUREIntroductionThe curvature tensorThe second fundamental formSectional and Ricci curvaturesJacobi fieldsManifolds of constant curvatureConjugate pointsHorizontal and vertical sub-bundlesThe geodesic flowExercisesTENSORS AND DI...

The Geometry Conference

CERN Document Server

Bárány, Imre; Vilcu, Costin

2016-01-01

This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.

Hyperbolic geometry

CERN Document Server

Iversen, Birger

1992-01-01

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics

General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry

Science.gov (United States)

Savickas, David

2014-03-01

The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.

Comparing the Psychometric Properties of Two Physical Activity Self-Efficacy Instruments in Urban, Adolescent Girls: Validity, Measurement Invariance, and Reliability

Science.gov (United States)

Voskuil, Vicki R.; Pierce, Steven J.; Robbins, Lorraine B.

2017-01-01

Aims: This study compared the psychometric properties of two self-efficacy instruments related to physical activity. Factorial validity, cross-group and longitudinal invariance, and composite reliability were examined. Methods: Secondary analysis was conducted on data from a group randomized controlled trial investigating the effect of a 17-week intervention on increasing moderate to vigorous physical activity among 5th–8th grade girls (N = 1,012). Participants completed a 6-item Physical Activity Self-Efficacy Scale (PASE) and a 7-item Self-Efficacy for Exercise Behaviors Scale (SEEB) at baseline and post-intervention. Confirmatory factor analyses for intervention and control groups were conducted with Mplus Version 7.4 using robust weighted least squares estimation. Model fit was evaluated with the chi-square index, comparative fit index, and root mean square error of approximation. Composite reliability for latent factors with ordinal indicators was computed from Mplus output using SAS 9.3. Results: Mean age of the girls was 12.2 years (SD = 0.96). One-third of the girls were obese. Girls represented a diverse sample with over 50% indicating black race and an additional 19% identifying as mixed or other race. Both instruments demonstrated configural invariance for simultaneous analysis of cross-group and longitudinal invariance based on alternative fit indices. However, simultaneous metric invariance was not met for the PASE or the SEEB instruments. Partial metric invariance for the simultaneous analysis was achieved for the PASE with one factor loading identified as non-invariant. Partial metric invariance was not met for the SEEB. Longitudinal scalar invariance was achieved for both instruments in the control group but not the intervention group. Composite reliability for the PASE ranged from 0.772 to 0.842. Reliability for the SEEB ranged from 0.719 to 0.800 indicating higher reliability for the PASE. Reliability was more stable over time in the control

Geometry of the Universe

International Nuclear Information System (INIS)

Gurevich, L.Eh.; Gliner, Eh.B.

1978-01-01

Problems of investigating the Universe space-time geometry are described on a popular level. Immediate space-time geometries, corresponding to three cosmologic models are considered. Space-time geometry of a closed model is the spherical Riemann geonetry, of an open model - is the Lobachevskij geometry; and of a plane model - is the Euclidean geometry. The Universe real geometry in the contemporary epoch of development is based on the data testifying to the fact that the Universe is infinitely expanding

Pragmatic security metrics applying metametrics to information security

CERN Document Server

Brotby, W Krag

2013-01-01

Other books on information security metrics discuss number theory and statistics in academic terms. Light on mathematics and heavy on utility, PRAGMATIC Security Metrics: Applying Metametrics to Information Security breaks the mold. This is the ultimate how-to-do-it guide for security metrics.Packed with time-saving tips, the book offers easy-to-follow guidance for those struggling with security metrics. Step by step, it clearly explains how to specify, develop, use, and maintain an information security measurement system (a comprehensive suite of metrics) to

Defining a Progress Metric for CERT RMM Improvement

Science.gov (United States)

2017-09-14

REV-03.18.2016.0 Defining a Progress Metric for CERT-RMM Improvement Gregory Crabb Nader Mehravari David Tobar September 2017 TECHNICAL ...fendable resource allocation decisions. Technical metrics measure aspects of controls implemented through technology (systems, soft- ware, hardware...implementation metric would be the percentage of users who have received anti-phishing training . • Effectiveness/efficiency metrics measure whether

IT Project Management Metrics

Directory of Open Access Journals (Sweden)

2007-01-01

Full Text Available Many software and IT projects fail in completing theirs objectives because different causes of which the management of the projects has a high weight. In order to have successfully projects, lessons learned have to be used, historical data to be collected and metrics and indicators have to be computed and used to compare them with past projects and avoid failure to happen. This paper presents some metrics that can be used for the IT project management.

Mass Customization Measurements Metrics

DEFF Research Database (Denmark)

Nielsen, Kjeld; Brunø, Thomas Ditlev; Jørgensen, Kaj Asbjørn

2014-01-01

A recent survey has indicated that 17 % of companies have ceased mass customizing less than 1 year after initiating the effort. This paper presents measurement for a company’s mass customization performance, utilizing metrics within the three fundamental capabilities: robust process design, choice...... navigation, and solution space development. A mass customizer when assessing performance with these metrics can identify within which areas improvement would increase competitiveness the most and enable more efficient transition to mass customization....

Metrical Phonology: German Sound System.

Science.gov (United States)

Tice, Bradley S.

Metrical phonology, a linguistic process of phonological stress assessment and diagrammatic simplification of sentence and word stress, is discussed as it is found in the English and German languages. The objective is to promote use of metrical phonology as a tool for enhancing instruction in stress patterns in words and sentences, particularly in…

Construction of Einstein-Sasaki metrics in D≥7

International Nuclear Information System (INIS)

Lue, H.; Pope, C. N.; Vazquez-Poritz, J. F.

2007-01-01

We construct explicit Einstein-Kaehler metrics in all even dimensions D=2n+4≥6, in terms of a 2n-dimensional Einstein-Kaehler base metric. These are cohomogeneity 2 metrics which have the new feature of including a NUT-type parameter, or gravomagnetic charge, in addition to..' in addition to mass and rotation parameters. Using a canonical construction, these metrics all yield Einstein-Sasaki metrics in dimensions D=2n+5≥7. As is commonly the case in this type of construction, for suitable choices of the free parameters the Einstein-Sasaki metrics can extend smoothly onto complete and nonsingular manifolds, even though the underlying Einstein-Kaehler metric has conical singularities. We discuss some explicit examples in the case of seven-dimensional Einstein-Sasaki spaces. These new spaces can provide supersymmetric backgrounds in M theory, which play a role in the AdS 4 /CFT 3 correspondence

National Metrical Types in Nineteenth Century Art Song

Directory of Open Access Journals (Sweden)

Leigh VanHandel

2010-01-01

Full Text Available William Rothstein’s article “National metrical types in music of the eighteenth and early nineteenth centuries” (2008 proposes a distinction between the metrical habits of 18th and early 19th century German music and those of Italian and French music of that period. Based on theoretical treatises and compositional practice, he outlines these national metrical types and discusses the characteristics of each type. This paper presents the results of a study designed to determine whether, and to what degree, Rothstein’s characterizations of national metrical types are present in 19th century French and German art song. Studying metrical habits in this genre may provide a lens into changing metrical conceptions of 19th century theorists and composers, as well as to the metrical habits and compositional style of individual 19th century French and German art song composers.

A Metric on Phylogenetic Tree Shapes.

Science.gov (United States)

Colijn, C; Plazzotta, G

2018-01-01

The shapes of evolutionary trees are influenced by the nature of the evolutionary process but comparisons of trees from different processes are hindered by the challenge of completely describing tree shape. We present a full characterization of the shapes of rooted branching trees in a form that lends itself to natural tree comparisons. We use this characterization to define a metric, in the sense of a true distance function, on tree shapes. The metric distinguishes trees from random models known to produce different tree shapes. It separates trees derived from tropical versus USA influenza A sequences, which reflect the differing epidemiology of tropical and seasonal flu. We describe several metrics based on the same core characterization, and illustrate how to extend the metric to incorporate trees' branch lengths or other features such as overall imbalance. Our approach allows us to construct addition and multiplication on trees, and to create a convex metric on tree shapes which formally allows computation of average tree shapes. © The Author(s) 2017. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

Software Quality Assurance Metrics

Science.gov (United States)

McRae, Kalindra A.

2004-01-01

Software Quality Assurance (SQA) is a planned and systematic set of activities that ensures conformance of software life cycle processes and products conform to requirements, standards and procedures. In software development, software quality means meeting requirements and a degree of excellence and refinement of a project or product. Software Quality is a set of attributes of a software product by which its quality is described and evaluated. The set of attributes includes functionality, reliability, usability, efficiency, maintainability, and portability. Software Metrics help us understand the technical process that is used to develop a product. The process is measured to improve it and the product is measured to increase quality throughout the life cycle of software. Software Metrics are measurements of the quality of software. Software is measured to indicate the quality of the product, to assess the productivity of the people who produce the product, to assess the benefits derived from new software engineering methods and tools, to form a baseline for estimation, and to help justify requests for new tools or additional training. Any part of the software development can be measured. If Software Metrics are implemented in software development, it can save time, money, and allow the organization to identify the caused of defects which have the greatest effect on software development. The summer of 2004, I worked with Cynthia Calhoun and Frank Robinson in the Software Assurance/Risk Management department. My task was to research and collect, compile, and analyze SQA Metrics that have been used in other projects that are not currently being used by the SA team and report them to the Software Assurance team to see if any metrics can be implemented in their software assurance life cycle process.

Metric Power and the Academic Self: Neoliberalism, Knowledge and Resistance in the British University

Directory of Open Access Journals (Sweden)

Zeena Feldman

2018-01-01

Full Text Available This article discusses the experience of being an academic in the UK in the contemporary climate of neoliberal capitalism and ‘metric power’ (Beers 2016. Drawing on existing literature and our own practice, the first portion of the paper explores the relationship between neoliberalism, metrics and knowledge. We then examine how neoliberal mantras and instruments impact the university’s structures and processes, and reflect on consequences for the academic self. We take as a starting point the context of increasing workloads and the pressure on academics to excel in multiple roles, from ‘world-leading’ researchers to ‘excellent’ teachers and ‘service providers’ to professional administrators performing recruitment and (selfmarketing tasks. Neoliberal academia, we suggest, promotes a meritocratic ideology of individual achievement that frames success and failure as purely personal ‘achievements’, which encourages a competitive ethos and chronic self-criticism. This article insists that these problems need to be understood in the context of neoliberal policy-making and the corporatisation of knowledge, including funding cuts and grant imperatives, the low status of teaching, the cynical instrumentation of university league tables, and increased institutional reliance on precarious academic labour. The article goes on to focus on responses that resist, challenge or, in some cases, compound, the problems identified in part one. Responses by dissatisfied academics range in style and approach – some decide against an academic career; others adopt a strategy of individual withdrawal within the system by trying to create and protect spaces of independence – for example, by refusing to engage beyond officially required minimums. This article argues that opportunities for positive systemic change can be found in collective efforts to oppose the status quo and to create alternatives for how academic labour is organised. Therein

On organizing principles of discrete differential geometry. Geometry of spheres

International Nuclear Information System (INIS)

Bobenko, Alexander I; Suris, Yury B

2007-01-01

Discrete differential geometry aims to develop discrete equivalents of the geometric notions and methods of classical differential geometry. This survey contains a discussion of the following two fundamental discretization principles: the transformation group principle (smooth geometric objects and their discretizations are invariant with respect to the same transformation group) and the consistency principle (discretizations of smooth parametrized geometries can be extended to multidimensional consistent nets). The main concrete geometric problem treated here is discretization of curvature-line parametrized surfaces in Lie geometry. Systematic use of the discretization principles leads to a discretization of curvature-line parametrization which unifies circular and conical nets.

Degraded visual environment image/video quality metrics

Science.gov (United States)

Baumgartner, Dustin D.; Brown, Jeremy B.; Jacobs, Eddie L.; Schachter, Bruce J.

2014-06-01

A number of image quality metrics (IQMs) and video quality metrics (VQMs) have been proposed in the literature for evaluating techniques and systems for mitigating degraded visual environments. Some require both pristine and corrupted imagery. Others require patterned target boards in the scene. None of these metrics relates well to the task of landing a helicopter in conditions such as a brownout dust cloud. We have developed and used a variety of IQMs and VQMs related to the pilot's ability to detect hazards in the scene and to maintain situational awareness. Some of these metrics can be made agnostic to sensor type. Not only are the metrics suitable for evaluating algorithm and sensor variation, they are also suitable for choosing the most cost effective solution to improve operating conditions in degraded visual environments.

Software for simulation and design of neutron scattering instrumentation

DEFF Research Database (Denmark)

Bertelsen, Mads

designed using the software. The Union components uses a new approach to simulation of samples in McStas. The properties of a sample are split into geometrical and material, simplifying user input, and allowing the construction of complicated geometries such as sample environments. Multiple scattering...... from conventional choices. Simulation of neutron scattering instrumentation is used when designing instrumentation, but also to understand instrumental effects on the measured scattering data. The Monte Carlo ray-tracing package McStas is among the most popular, capable of simulating the path of each...... neutron through the instrument using an easy to learn language. The subject of the defended thesis is contributions to the McStas language in the form of the software package guide_bot and the Union components.The guide_bot package simplifies the process of optimizing neutron guides by writing the Mc...

Geometry and its applications

CERN Document Server

Meyer, Walter J

2006-01-01

Meyer''s Geometry and Its Applications, Second Edition, combines traditional geometry with current ideas to present a modern approach that is grounded in real-world applications. It balances the deductive approach with discovery learning, and introduces axiomatic, Euclidean geometry, non-Euclidean geometry, and transformational geometry. The text integrates applications and examples throughout and includes historical notes in many chapters. The Second Edition of Geometry and Its Applications is a significant text for any college or university that focuses on geometry''s usefulness in other disciplines. It is especially appropriate for engineering and science majors, as well as future mathematics teachers.* Realistic applications integrated throughout the text, including (but not limited to): - Symmetries of artistic patterns- Physics- Robotics- Computer vision- Computer graphics- Stability of architectural structures- Molecular biology- Medicine- Pattern recognition* Historical notes included in many chapters...

The Jacobi metric for timelike geodesics in static spacetimes

Science.gov (United States)

Gibbons, G. W.

2016-01-01

It is shown that the free motion of massive particles moving in static spacetimes is given by the geodesics of an energy-dependent Riemannian metric on the spatial sections analogous to Jacobi's metric in classical dynamics. In the massless limit Jacobi's metric coincides with the energy independent Fermat or optical metric. For stationary metrics, it is known that the motion of massless particles is given by the geodesics of an energy independent Finslerian metric of Randers type. The motion of massive particles is governed by neither a Riemannian nor a Finslerian metric. The properies of the Jacobi metric for massive particles moving outside the horizon of a Schwarschild black hole are described. By constrast with the massless case, the Gaussian curvature of the equatorial sections is not always negative.

Geometry of Hamiltonian chaos

DEFF Research Database (Denmark)

Horwitz, Lawrence; Zion, Yossi Ben; Lewkowicz, Meir

2007-01-01

The characterization of chaotic Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor in the structure of the Hamiltonian is extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce ...

Relaxed metrics and indistinguishability operators: the relationship

Energy Technology Data Exchange (ETDEWEB)

Martin, J.

2017-07-01

In 1982, the notion of indistinguishability operator was introduced by E. Trillas in order to fuzzify the crisp notion of equivalence relation (/cite{Trillas}). In the study of such a class of operators, an outstanding property must be pointed out. Concretely, there exists a duality relationship between indistinguishability operators and metrics. The aforesaid relationship was deeply studied by several authors that introduced a few techniques to generate metrics from indistinguishability operators and vice-versa (see, for instance, /cite{BaetsMesiar,BaetsMesiar2}). In the last years a new generalization of the metric notion has been introduced in the literature with the purpose of developing mathematical tools for quantitative models in Computer Science and Artificial Intelligence (/cite{BKMatthews,Ma}). The aforementioned generalized metrics are known as relaxed metrics. The main target of this talk is to present a study of the duality relationship between indistinguishability operators and relaxed metrics in such a way that the aforementioned classical techniques to generate both concepts, one from the other, can be extended to the new framework. (Author)

Information geometry of Gaussian channels

International Nuclear Information System (INIS)

Monras, Alex; Illuminati, Fabrizio

2010-01-01

We define a local Riemannian metric tensor in the manifold of Gaussian channels and the distance that it induces. We adopt an information-geometric approach and define a metric derived from the Bures-Fisher metric for quantum states. The resulting metric inherits several desirable properties from the Bures-Fisher metric and is operationally motivated by distinguishability considerations: It serves as an upper bound to the attainable quantum Fisher information for the channel parameters using Gaussian states, under generic constraints on the physically available resources. Our approach naturally includes the use of entangled Gaussian probe states. We prove that the metric enjoys some desirable properties like stability and covariance. As a by-product, we also obtain some general results in Gaussian channel estimation that are the continuous-variable analogs of previously known results in finite dimensions. We prove that optimal probe states are always pure and bounded in the number of ancillary modes, even in the presence of constraints on the reduced state input in the channel. This has experimental and computational implications. It limits the complexity of optimal experimental setups for channel estimation and reduces the computational requirements for the evaluation of the metric: Indeed, we construct a converging algorithm for its computation. We provide explicit formulas for computing the multiparametric quantum Fisher information for dissipative channels probed with arbitrary Gaussian states and provide the optimal observables for the estimation of the channel parameters (e.g., bath couplings, squeezing, and temperature).

Design integration of favorable geometry, structural support and containment

International Nuclear Information System (INIS)

Purcell, J.A.; McGehee, G.A.

1991-07-01

In designs for fissile processes at Savannah River site, different approaches have been used to provide engineered margins of safety for criticality with containment and seismic resistance as additional requirements. These requirements are frequently at odds in engineered systems. This paper proposes a plan to take advantage of vessels with favorable geometry to provide seismic resistance and to support a glovebox for containment. Thin slab tanks, small diameter pencil tanks, annular tanks, and other novel designs have been used for criticality safety. The requirement for DBE seismic resistance and rigid control of dimensions leads the designer to consider annular tanks for meeting these requirements. The high strength of annular tanks may logically be used to support secondary containment. Hands-on access to all instruments, piping etc. within containment can be provided through gloveports, thus a specialized glovebox. This paper examines the advantages of using an annular tank design to provide favorable geometry, structural support and containment

Classification in medical images using adaptive metric k-NN

Science.gov (United States)

Chen, C.; Chernoff, K.; Karemore, G.; Lo, P.; Nielsen, M.; Lauze, F.

2010-03-01

The performance of the k-nearest neighborhoods (k-NN) classifier is highly dependent on the distance metric used to identify the k nearest neighbors of the query points. The standard Euclidean distance is commonly used in practice. This paper investigates the performance of k-NN classifier with respect to different adaptive metrics in the context of medical imaging. We propose using adaptive metrics such that the structure of the data is better described, introducing some unsupervised learning knowledge in k-NN. We investigated four different metrics are estimated: a theoretical metric based on the assumption that images are drawn from Brownian Image Model (BIM), the normalized metric based on variance of the data, the empirical metric is based on the empirical covariance matrix of the unlabeled data, and an optimized metric obtained by minimizing the classification error. The spectral structure of the empirical covariance also leads to Principal Component Analysis (PCA) performed on it which results the subspace metrics. The metrics are evaluated on two data sets: lateral X-rays of the lumbar aortic/spine region, where we use k-NN for performing abdominal aorta calcification detection; and mammograms, where we use k-NN for breast cancer risk assessment. The results show that appropriate choice of metric can improve classification.

Geometry Skill Analysis In Problem Solving Reviewed From The Difference Of Cognitive Style Students Junior High School

Directory of Open Access Journals (Sweden)

Andi Saparuddin Nur

2017-12-01

Full Text Available This study aimed to analyze the geometry skills in solving problems in terms of cognitive styles differences in the students of SMP Negeri Urumb. The type of this research is descriptive research that is qualitative with case study approach. The subject of this research is all students of SMP Negeri Urumb. Subject selection is done by using snowball sampling technique. The main instrument in this study is the researchers themselves and accompanied by supporting instruments such as diagnostic tests, geometry solving test, and interview guides. Validity and reliability of data is done through credibility test, transferability test, dependability test, and confirmability test. Data analysis consists of data collection, data reduction, data presentation, and conclusions. The results of this study were (1 reflective FI subjects showing visual, verbal, drawing, and logic skills with level of geometry thinking at level 2 (informal deduction; (2 impulsive FI subjects exhibiting visual, verbal, and drawing skills with geometric thinking level at level 1 (analysis, (3 reflective FD subjects exhibit visual skills, and draw with level of geometric thinking at level 0 (visualization, and (4 impulsive FD subjects exhibit visual, verbal skills with geometric level thinking at level 0 (visualization.

Measurable Control System Security through Ideal Driven Technical Metrics

Energy Technology Data Exchange (ETDEWEB)

Miles McQueen; Wayne Boyer; Sean McBride; Marie Farrar; Zachary Tudor

2008-01-01

The Department of Homeland Security National Cyber Security Division supported development of a small set of security ideals as a framework to establish measurable control systems security. Based on these ideals, a draft set of proposed technical metrics was developed to allow control systems owner-operators to track improvements or degradations in their individual control systems security posture. The technical metrics development effort included review and evaluation of over thirty metrics-related documents. On the bases of complexity, ambiguity, or misleading and distorting effects the metrics identified during the reviews were determined to be weaker than necessary to aid defense against the myriad threats posed by cyber-terrorism to human safety, as well as to economic prosperity. Using the results of our metrics review and the set of security ideals as a starting point for metrics development, we identified thirteen potential technical metrics - with at least one metric supporting each ideal. Two case study applications of the ideals and thirteen metrics to control systems were then performed to establish potential difficulties in applying both the ideals and the metrics. The case studies resulted in no changes to the ideals, and only a few deletions and refinements to the thirteen potential metrics. This led to a final proposed set of ten core technical metrics. To further validate the security ideals, the modifications made to the original thirteen potential metrics, and the final proposed set of ten core metrics, seven separate control systems security assessments performed over the past three years were reviewed for findings and recommended mitigations. These findings and mitigations were then mapped to the security ideals and metrics to assess gaps in their coverage. The mappings indicated that there are no gaps in the security ideals and that the ten core technical metrics provide significant coverage of standard security issues with 87% coverage. Based

Rapporteur Report: Sources and Exposure Metrics for ELF Epidemiology (Part 1) (invited paper)

International Nuclear Information System (INIS)

Matthes, R.

1999-01-01

High quality epidemiological studies on the possible link between exposure to non-ionizing radiation and human health effects are of great importance for radiation protection in this area. The main sources of ELF fields are domestic appliances, different electrical energy distribution systems and all kinds of electrical machinery and devices at the workplace. In general, ELF fields present in the environment, show complex temporal patterns and spatial distributions, depending on the generating source. The complete characterisation of the different field sources often requires highly sophisticated instrumentation, and this is therefore not feasible within the scope of epidemiological studies. On average, individual exposure from ELF fields is low in both the working environment and in residential areas. Only at certain workplaces are people subject to significant ELF exposure with regard to biological effects. Different methods have been developed to determine levels of exposure received by study subjects, with the aim to rank exposed and non-exposed groups in epidemiological studies. These include spot measurements, calculations or modelling. The different methods used to estimate total exposure in epidemiological studies may result to a differing extent in a misclassification of the study subjects. Equally important for future studies is the selection of the appropriate exposure metric. The most widely used metric so far is the time-weighted average and thus represents a quasi standard metric for use in epidemiological studies. Beside, wire codes have been used for a long time in residential studies and job titles are often used in occupational studies. On the basis of the experience gained in previous studies, it would be desirable to develop standardised, state-of-the-art protocols to improve exposure assessment. New surrogates and metrics were proposed as the basis for further studies. But only few of these have recently undergone preliminary testing. A

Experiential space is hardly metric

Czech Academy of Sciences Publication Activity Database

Šikl, Radovan; Šimeček, Michal; Lukavský, Jiří

2008-01-01

Roč. 2008, č. 37 (2008), s. 58-58 ISSN 0301-0066. [European Conference on Visual Perception. 24.08-28.08.2008, Utrecht] R&D Projects: GA ČR GA406/07/1676 Institutional research plan: CEZ:AV0Z70250504 Keywords : visual space perception * metric and non-metric perceptual judgments * ecological validity Subject RIV: AN - Psychology

High resolution metric imaging payload

Science.gov (United States)

Delclaud, Y.

2017-11-01

Alcatel Space Industries has become Europe's leader in the field of high and very high resolution optical payloads, in the frame work of earth observation system able to provide military government with metric images from space. This leadership allowed ALCATEL to propose for the export market, within a French collaboration frame, a complete space based system for metric observation.

Instrumentation optimization for positron emission mammography

International Nuclear Information System (INIS)

Moses, William W.; Qi, Jinyi

2003-01-01

The past several years have seen designs for PET cameras optimized to image the breast, commonly known as Positron Emission Mammography or PEM cameras. The guiding principal behind PEM instrumentation is that a camera whose field of view is restricted to a single breast has higher performance and lower cost than a conventional PET camera. The most common geometry is a pair of parallel planes of detector modules, although geometries that encircle the breast have also been proposed. The ability of the detector modules to measure the depth of interaction (DOI) is also a relevant feature. This paper finds that while both the additional solid angle coverage afforded by encircling the breast and the decreased blurring afforded by the DOI measurement improve performance, the ability to measure DOI is more important than the ability to encircle the breast

A comparison of two reciprocating instruments using bending stress and cyclic fatigue tests

Directory of Open Access Journals (Sweden)

Pantaleo SCELZA

2015-01-01

Full Text Available The aim of this study was to comparatively evaluate the bending resistance at 45º, the static and dynamic cyclic fatigue life, and the fracture type of the WaveOne (Dentsply Maillefer, Ballaigues, Switzerland 25-08 and Reciproc (VDW, Munich, Germany 25-08 instruments. A total of 60 nickel-titanium (NiTi instruments (30 Reciproc and 30 WaveOne from three different lots, each of which was 25 mm in length, were tested. The bending resistance was evaluated through the results of a cantilever-bending test conducted using a universal testing machine. Static and dynamic cyclic fatigue testing was conducted using a custom-made device. For the static and dynamic tests, a cast Ni-Cr-Mo-Ti alloy metal block with an artificial canal measuring 1.77 mm in diameter and 20.00 mm in total length was used. A scanning electron microscope was used to determine the type of fracture. Statistical analyses were performed on the results. The WaveOne instrument was less flexible than the Reciproc (p < 0.05. The Reciproc instrument showed better resistance in the static and dynamic cyclic fatigue tests (p < 0.05. The transverse cross-section and geometry of the instruments were important factors in their resistance to bending and cyclic fracture. Both of the instruments showed ductile-type fracture characteristics. It can be concluded that the Reciproc 25-08 instrument was more resistant to static and dynamic cyclic fatigue than the WaveOne 25-08 instrument, while the WaveOne 25-08 instrument was less flexible. Bending and resistance to cyclic fracture were influenced by the instruments’ geometries and transverse cross-sections. Both of the instruments showed ductile-type fracture characteristics.

Beautiful geometry

CERN Document Server

Maor, Eli

2014-01-01

If you've ever thought that mathematics and art don't mix, this stunning visual history of geometry will change your mind. As much a work of art as a book about mathematics, Beautiful Geometry presents more than sixty exquisite color plates illustrating a wide range of geometric patterns and theorems, accompanied by brief accounts of the fascinating history and people behind each. With artwork by Swiss artist Eugen Jost and text by acclaimed math historian Eli Maor, this unique celebration of geometry covers numerous subjects, from straightedge-and-compass constructions to intriguing configur

Smart Grid Status and Metrics Report Appendices

Energy Technology Data Exchange (ETDEWEB)

Balducci, Patrick J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Antonopoulos, Chrissi A. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Clements, Samuel L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Gorrissen, Willy J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Kirkham, Harold [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Ruiz, Kathleen A. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Smith, David L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Weimar, Mark R. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Gardner, Chris [APQC, Houston, TX (United States); Varney, Jeff [APQC, Houston, TX (United States)

2014-07-01

A smart grid uses digital power control and communication technology to improve the reliability, security, flexibility, and efficiency of the electric system, from large generation through the delivery systems to electricity consumers and a growing number of distributed generation and storage resources. To convey progress made in achieving the vision of a smart grid, this report uses a set of six characteristics derived from the National Energy Technology Laboratory Modern Grid Strategy. The Smart Grid Status and Metrics Report defines and examines 21 metrics that collectively provide insight into the grid’s capacity to embody these characteristics. This appendix presents papers covering each of the 21 metrics identified in Section 2.1 of the Smart Grid Status and Metrics Report. These metric papers were prepared in advance of the main body of the report and collectively form its informational backbone.

Implications of Metric Choice for Common Applications of Readmission Metrics

OpenAIRE

Davies, Sheryl; Saynina, Olga; Schultz, Ellen; McDonald, Kathryn M; Baker, Laurence C

2013-01-01

Objective. To quantify the differential impact on hospital performance of three readmission metrics: all-cause readmission (ACR), 3M Potential Preventable Readmission (PPR), and Centers for Medicare and Medicaid 30-day readmission (CMS).

Revolutions of Geometry

CERN Document Server

O'Leary, Michael

2010-01-01

Guides readers through the development of geometry and basic proof writing using a historical approach to the topic. In an effort to fully appreciate the logic and structure of geometric proofs, Revolutions of Geometry places proofs into the context of geometry's history, helping readers to understand that proof writing is crucial to the job of a mathematician. Written for students and educators of mathematics alike, the book guides readers through the rich history and influential works, from ancient times to the present, behind the development of geometry. As a result, readers are successfull

LRS Bianchi Type II Massive String Cosmological Models with Magnetic Field in Lyra's Geometry

Directory of Open Access Journals (Sweden)

Raj Bali

2013-01-01

Full Text Available Bianchi type II massive string cosmological models with magnetic field and time dependent gauge function ( in the frame work of Lyra's geometry are investigated. The magnetic field is in -plane. To get the deterministic solution, we have assumed that the shear ( is proportional to the expansion (. This leads to , where and are metric potentials and is a constant. We find that the models start with a big bang at initial singularity and expansion decreases due to lapse of time. The anisotropy is maintained throughout but the model isotropizes when . The physical and geometrical aspects of the model in the presence and absence of magnetic field are also discussed.

Prognostic Performance Metrics

Data.gov (United States)

National Aeronautics and Space Administration — This chapter presents several performance metrics for offline evaluation of prognostics algorithms. A brief overview of different methods employed for performance...

Differential die-away instrument: Report on comparison of fuel assembly experiments and simulations

Energy Technology Data Exchange (ETDEWEB)

Goodsell, Alison Victoria [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Henzl, Vladimir [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Swinhoe, Martyn Thomas [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Rael, Carlos D. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Desimone, David J. [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2015-01-14

Experimental results of the assay of mock-up (fresh) fuel with the differential die-away (DDA) instrument were compared to the Monte Carlo N-Particle eXtended (MCNPX) simulation results. Most principal experimental observables, the die-away time and the in tegral of the DDA signal in several time domains, have been found in good agreement with the MCNPX simulation results. The remaining discrepancies between the simulation and experimental results are likely due to small differences between the actual experimental setup and the simulated geometry, including uncertainty in the DT neutron generator yield. Within this report we also present a sensitivity study of the DDA instrument which is a complex and sensitive system and demonstrate to what degree it can be impacted by geometry, material composition, and electronics performance.

Analogy and Dynamic Geometry System Used to Introduce Three-Dimensional Geometry

Science.gov (United States)

Mammana, M. F.; Micale, B.; Pennisi, M.

2012-01-01

We present a sequence of classroom activities on Euclidean geometry, both plane and space geometry, used to make three dimensional geometry more catchy and simple. The activity consists of a guided research activity that leads the students to discover unexpected properties of two apparently distant geometrical entities, quadrilaterals and…

Adaptive metric kernel regression

DEFF Research Database (Denmark)

Goutte, Cyril; Larsen, Jan

2000-01-01

Kernel smoothing is a widely used non-parametric pattern recognition technique. By nature, it suffers from the curse of dimensionality and is usually difficult to apply to high input dimensions. In this contribution, we propose an algorithm that adapts the input metric used in multivariate...... regression by minimising a cross-validation estimate of the generalisation error. This allows to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms...

qcML: an exchange format for quality control metrics from mass spectrometry experiments.

Science.gov (United States)

Walzer, Mathias; Pernas, Lucia Espona; Nasso, Sara; Bittremieux, Wout; Nahnsen, Sven; Kelchtermans, Pieter; Pichler, Peter; van den Toorn, Henk W P; Staes, An; Vandenbussche, Jonathan; Mazanek, Michael; Taus, Thomas; Scheltema, Richard A; Kelstrup, Christian D; Gatto, Laurent; van Breukelen, Bas; Aiche, Stephan; Valkenborg, Dirk; Laukens, Kris; Lilley, Kathryn S; Olsen, Jesper V; Heck, Albert J R; Mechtler, Karl; Aebersold, Ruedi; Gevaert, Kris; Vizcaíno, Juan Antonio; Hermjakob, Henning; Kohlbacher, Oliver; Martens, Lennart

2014-08-01

Quality control is increasingly recognized as a crucial aspect of mass spectrometry based proteomics. Several recent papers discuss relevant parameters for quality control and present applications to extract these from the instrumental raw data. What has been missing, however, is a standard data exchange format for reporting these performance metrics. We therefore developed the qcML format, an XML-based standard that follows the design principles of the related mzML, mzIdentML, mzQuantML, and TraML standards from the HUPO-PSI (Proteomics Standards Initiative). In addition to the XML format, we also provide tools for the calculation of a wide range of quality metrics as well as a database format and interconversion tools, so that existing LIMS systems can easily add relational storage of the quality control data to their existing schema. We here describe the qcML specification, along with possible use cases and an illustrative example of the subsequent analysis possibilities. All information about qcML is available at http://code.google.com/p/qcml. © 2014 by The American Society for Biochemistry and Molecular Biology, Inc.

qcML: An Exchange Format for Quality Control Metrics from Mass Spectrometry Experiments*

Science.gov (United States)

Walzer, Mathias; Pernas, Lucia Espona; Nasso, Sara; Bittremieux, Wout; Nahnsen, Sven; Kelchtermans, Pieter; Pichler, Peter; van den Toorn, Henk W. P.; Staes, An; Vandenbussche, Jonathan; Mazanek, Michael; Taus, Thomas; Scheltema, Richard A.; Kelstrup, Christian D.; Gatto, Laurent; van Breukelen, Bas; Aiche, Stephan; Valkenborg, Dirk; Laukens, Kris; Lilley, Kathryn S.; Olsen, Jesper V.; Heck, Albert J. R.; Mechtler, Karl; Aebersold, Ruedi; Gevaert, Kris; Vizcaíno, Juan Antonio; Hermjakob, Henning; Kohlbacher, Oliver; Martens, Lennart

2014-01-01

Quality control is increasingly recognized as a crucial aspect of mass spectrometry based proteomics. Several recent papers discuss relevant parameters for quality control and present applications to extract these from the instrumental raw data. What has been missing, however, is a standard data exchange format for reporting these performance metrics. We therefore developed the qcML format, an XML-based standard that follows the design principles of the related mzML, mzIdentML, mzQuantML, and TraML standards from the HUPO-PSI (Proteomics Standards Initiative). In addition to the XML format, we also provide tools for the calculation of a wide range of quality metrics as well as a database format and interconversion tools, so that existing LIMS systems can easily add relational storage of the quality control data to their existing schema. We here describe the qcML specification, along with possible use cases and an illustrative example of the subsequent analysis possibilities. All information about qcML is available at http://code.google.com/p/qcml. PMID:24760958

New generation in process-control colorimetric instrumentation

Science.gov (United States)

Ladson, Jack A.

1992-08-01

Colorimetric performance parameters (repeatability and reproducibility) of a new spectrophotometer/colorimeter manufactured by BYK-Gardner, Inc. are reported. The color- viewTM spectrophotometer (CVS) uses forty-five degree illumination and zero degree viewing geometry relative to the plane of the test specimen. The CVS is designed for the measurement of diffuse reflectance factor. It is designed to conform to national and international recommendations for Spectrophotometry and Colorimetry. Colorimetric performance was evaluated by measuring colored tiles manufactured by the British Ceramic Research Association (BCRA). Instrument repeatability was recorded after an hour, eight hours, and thirty days. Routine performance of the CVS shows that color difference repeatability over short and medium time periods is within 0.15 CIELAB color difference unit. The long term repeatability is within 0.4 unit. Reproducibility was evaluated by making color measurements on BCRA tiles with 54 instruments. Measurements made on CVS instruments indicate that its reproducibility is better than the reproducibility of product standards. Reproducibility is well within the requirement for industrial applications. Actually, the repeatability and reproducibility is comparable to that of reference instruments in national standardizing laboratories.

Application of three-dimensional simulation at lecturing on descriptive geometry

Directory of Open Access Journals (Sweden)

Tel'noy Viktor Ivanovich

2014-05-01

Full Text Available Teaching descriptive geometry has its own characteristics. Need not only to inform students of a certain amount of knowledge on the subject, but also to develop their spatial imagination as well as the right to develop the skills of logical thinking. Practice of teaching the discipline showed that students face serious difficulties in the process of its study. This is due to the relatively low level of their schooling in geometry and technical drawing, and lacking in high spatial imagination. They find it difficult to imagine the geometrical image of the object of study and mentally convert it on the plane. Because of this, there is a need to find ways to effectively teach the discipline «Descriptive Geometry» at university. In the context of global informatization and computerization of the educational process, implementation of graphically programs for the development of design documentation and 3D modeling is one of the most promising applications of information technology in the process of solving these problems. With the help of three-dimensional models the best visibility in the classroom is achieved. When conducting lectures on descriptive geometry it is requested to use three-dimensional modeling not only as didactic means (demonstrativeness means, but also as a method of teaching (learning tool to deal with various graphics tasks. Bearing this in mind, the essence of the implementation of 3D modeling is revealed with the aim of better understanding of the algorithms for solving both positional and metric tasks using spatial representation of graphic constructions. It is shown that the possibility to consider the built model from different angles is of particular importance, as well as the use of transparency properties for illustrating the results of solving geometric problems. Using 3D models together with their display on the plane, as well as text information promotes better assimilation and more lasting memorization of the

Geometry of lattice field theory

International Nuclear Information System (INIS)

Honan, T.J.

1986-01-01

Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus

Energy-Based Metrics for Arthroscopic Skills Assessment.

Science.gov (United States)

Poursartip, Behnaz; LeBel, Marie-Eve; McCracken, Laura C; Escoto, Abelardo; Patel, Rajni V; Naish, Michael D; Trejos, Ana Luisa

2017-08-05

Minimally invasive skills assessment methods are essential in developing efficient surgical simulators and implementing consistent skills evaluation. Although numerous methods have been investigated in the literature, there is still a need to further improve the accuracy of surgical skills assessment. Energy expenditure can be an indication of motor skills proficiency. The goals of this study are to develop objective metrics based on energy expenditure, normalize these metrics, and investigate classifying trainees using these metrics. To this end, different forms of energy consisting of mechanical energy and work were considered and their values were divided by the related value of an ideal performance to develop normalized metrics. These metrics were used as inputs for various machine learning algorithms including support vector machines (SVM) and neural networks (NNs) for classification. The accuracy of the combination of the normalized energy-based metrics with these classifiers was evaluated through a leave-one-subject-out cross-validation. The proposed method was validated using 26 subjects at two experience levels (novices and experts) in three arthroscopic tasks. The results showed that there are statistically significant differences between novices and experts for almost all of the normalized energy-based metrics. The accuracy of classification using SVM and NN methods was between 70% and 95% for the various tasks. The results show that the normalized energy-based metrics and their combination with SVM and NN classifiers are capable of providing accurate classification of trainees. The assessment method proposed in this study can enhance surgical training by providing appropriate feedback to trainees about their level of expertise and can be used in the evaluation of proficiency.

Principle of space existence and De Sitter metric

International Nuclear Information System (INIS)

Mal'tsev, V.K.

1990-01-01

The selection principle for the solutions of the Einstein equations suggested in a series of papers implies the existence of space (g ik ≠ 0) only in the presence of matter (T ik ≠0). This selection principle (principle of space existence, in the Markov terminology) implies, in the general case, the absence of the cosmological solution with the De Sitter metric. On the other hand, the De Sitter metric is necessary for describing both inflation and deflation periods of the Universe. It is shown that the De Sitter metric is also allowed by the selection principle under discussion if the metric experiences the evolution into the Friedmann metric

Design of virtual three-dimensional instruments for sound control

Science.gov (United States)

Mulder, Axel Gezienus Elith

An environment for designing virtual instruments with 3D geometry has been prototyped and applied to real-time sound control and design. It enables a sound artist, musical performer or composer to design an instrument according to preferred or required gestural and musical constraints instead of constraints based only on physical laws as they apply to an instrument with a particular geometry. Sounds can be created, edited or performed in real-time by changing parameters like position, orientation and shape of a virtual 3D input device. The virtual instrument can only be perceived through a visualization and acoustic representation, or sonification, of the control surface. No haptic representation is available. This environment was implemented using CyberGloves, Polhemus sensors, an SGI Onyx and by extending a real- time, visual programming language called Max/FTS, which was originally designed for sound synthesis. The extension involves software objects that interface the sensors and software objects that compute human movement and virtual object features. Two pilot studies have been performed, involving virtual input devices with the behaviours of a rubber balloon and a rubber sheet for the control of sound spatialization and timbre parameters. Both manipulation and sonification methods affect the naturalness of the interaction. Informal evaluation showed that a sonification inspired by the physical world appears natural and effective. More research is required for a natural sonification of virtual input device features such as shape, taking into account possible co- articulation of these features. While both hands can be used for manipulation, left-hand-only interaction with a virtual instrument may be a useful replacement for and extension of the standard keyboard modulation wheel. More research is needed to identify and apply manipulation pragmatics and movement features, and to investigate how they are co-articulated, in the mapping of virtual object

What can article-level metrics do for you?

Science.gov (United States)

Fenner, Martin

2013-10-01

Article-level metrics (ALMs) provide a wide range of metrics about the uptake of an individual journal article by the scientific community after publication. They include citations, usage statistics, discussions in online comments and social media, social bookmarking, and recommendations. In this essay, we describe why article-level metrics are an important extension of traditional citation-based journal metrics and provide a number of example from ALM data collected for PLOS Biology.

About the possibility of a generalized metric

International Nuclear Information System (INIS)

Lukacs, B.; Ladik, J.

1991-10-01

The metric (the structure of the space-time) may be dependent on the properties of the object measuring it. The case of size dependence of the metric was examined. For this dependence the simplest possible form of the metric tensor has been constructed which fulfils the following requirements: there be two extremal characteristic scales; the metric be unique and the usual between them; the change be sudden in the neighbourhood of these scales; the size of the human body appear as a parameter (postulated on the basis of some philosophical arguments). Estimates have been made for the two extremal length scales according to existing observations. (author) 19 refs

Beyond metrics? Utilizing 'soft intelligence' for healthcare quality and safety.

Science.gov (United States)

Martin, Graham P; McKee, Lorna; Dixon-Woods, Mary

2015-10-01

Formal metrics for monitoring the quality and safety of healthcare have a valuable role, but may not, by themselves, yield full insight into the range of fallibilities in organizations. 'Soft intelligence' is usefully understood as the processes and behaviours associated with seeking and interpreting soft data-of the kind that evade easy capture, straightforward classification and simple quantification-to produce forms of knowledge that can provide the basis for intervention. With the aim of examining current and potential practice in relation to soft intelligence, we conducted and analysed 107 in-depth qualitative interviews with senior leaders, including managers and clinicians, involved in healthcare quality and safety in the English National Health Service. We found that participants were in little doubt about the value of softer forms of data, especially for their role in revealing troubling issues that might be obscured by conventional metrics. Their struggles lay in how to access softer data and turn them into a useful form of knowing. Some of the dominant approaches they used risked replicating the limitations of hard, quantitative data. They relied on processes of aggregation and triangulation that prioritised reliability, or on instrumental use of soft data to animate the metrics. The unpredictable, untameable, spontaneous quality of soft data could be lost in efforts to systematize their collection and interpretation to render them more tractable. A more challenging but potentially rewarding approach involved processes and behaviours aimed at disrupting taken-for-granted assumptions about quality, safety, and organizational performance. This approach, which explicitly values the seeking out and the hearing of multiple voices, is consistent with conceptual frameworks of organizational sensemaking and dialogical understandings of knowledge. Using soft intelligence this way can be challenging and discomfiting, but may offer a critical defence against the

Adaptive Metric Kernel Regression

DEFF Research Database (Denmark)

Goutte, Cyril; Larsen, Jan

1998-01-01

Kernel smoothing is a widely used nonparametric pattern recognition technique. By nature, it suffers from the curse of dimensionality and is usually difficult to apply to high input dimensions. In this paper, we propose an algorithm that adapts the input metric used in multivariate regression...... by minimising a cross-validation estimate of the generalisation error. This allows one to automatically adjust the importance of different dimensions. The improvement in terms of modelling performance is illustrated on a variable selection task where the adaptive metric kernel clearly outperforms the standard...

Low geometry counter for the absolute measurement of the activity of alpha-emitting sources

International Nuclear Information System (INIS)

Garcia-Torano, E.; Acena, M.L.

1989-01-01

A low-geometry counter is described which allows the absolute determination of the activity for alpha-emitting sources. A Si implanted detector is used to obtain the spectrum of the sample. Two samples are measured with this counter and a 2 π gridded ion chamber. The results an their uncertainties for both instruments are discussed. (Author)

Ideal Based Cyber Security Technical Metrics for Control Systems

Energy Technology Data Exchange (ETDEWEB)

W. F. Boyer; M. A. McQueen

2007-10-01

Much of the world's critical infrastructure is at risk from attack through electronic networks connected to control systems. Security metrics are important because they provide the basis for management decisions that affect the protection of the infrastructure. A cyber security technical metric is the security relevant output from an explicit mathematical model that makes use of objective measurements of a technical object. A specific set of technical security metrics are proposed for use by the operators of control systems. Our proposed metrics are based on seven security ideals associated with seven corresponding abstract dimensions of security. We have defined at least one metric for each of the seven ideals. Each metric is a measure of how nearly the associated ideal has been achieved. These seven ideals provide a useful structure for further metrics development. A case study shows how the proposed metrics can be applied to an operational control system.

Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics

International Nuclear Information System (INIS)

Rivera Hernandez, Sergio

2012-01-01

massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples.

Tensorial spacetime geometries carrying predictive, interpretable and quantizable matter dynamics

Energy Technology Data Exchange (ETDEWEB)

Rivera Hernandez, Sergio

2012-02-15

massless particles in any hyperbolic, time-orientable and energy-distinguishing geometry. In the third part of the thesis, we explore how tensorial spacetime geometries fare when one wants to quantize particles and fields on them. This study is motivated, in part, in order to provide the tools to calculate the rate at which superluminal particles radiate off energy to become infraluminal, as explained above. Remarkably, it is again the three geometric conditions of hyperbolicity, time-orientability and energy-distinguishability that allow the quantization of general linear electrodynamics on an area metric spacetime and the quantization of massive point particles obeying any admissible dispersion relation. We explore the issue of field equations of all possible derivative order in rather systematic fashion, and prove a practically most useful theorem that determines Dirac algebras allowing the reduction of derivative orders. The final part of the thesis presents the sketch of a truly remarkable result that was obtained building on the work of the present thesis. Particularly based on the subtle duality maps between momenta and velocities in general tensorial spacetimes, it could be shown that gravitational dynamics for hyperbolic, time-orientable and energy distinguishable geometries need not be postulated, but the formidable physical problem of their construction can be reduced to a mere mathematical task: the solution of a system of homogeneous linear partial differential equations. This far-reaching physical result on modified gravity theories is a direct, but difficult to derive, outcome of the findings in the present thesis. Throughout the thesis, the abstract theory is illustrated through instructive examples.

THE ROLE OF ARTICLE LEVEL METRICS IN SCIENTIFIC PUBLISHING

Directory of Open Access Journals (Sweden)

Vladimir TRAJKOVSKI

2016-04-01

Full Text Available Emerging metrics based on article-level does not exclude traditional metrics based on citations to the journal, but complements them. Article-level metrics (ALMs provide a wide range of metrics about the uptake of an individual journal article by the scientific community after publication. They include citations, statistics of usage, discussions in online comments and social media, social bookmarking, and recommendations. In this editorial, the role of article level metrics in publishing scientific papers has been described. Article-Level Metrics (ALMs are rapidly emerging as important tools to quantify how individual articles are being discussed, shared, and used. Data sources depend on the tool, but they include classic metrics indicators depending on citations, academic social networks (Mendeley, CiteULike, Delicious and social media (Facebook, Twitter, blogs, and Youtube. The most popular tools used to apply this new metrics are: Public Library of Science - Article-Level Metrics, Altmetric, Impactstory and Plum Analytics. Journal Impact Factor (JIF does not consider impact or influence beyond citations count as this count reflected only through Thomson Reuters’ Web of Science® database. JIF provides indicator related to the journal, but not related to a published paper. Thus, altmetrics now becomes an alternative metrics for performance assessment of individual scientists and their contributed scholarly publications. Macedonian scholarly publishers have to work on implementing of article level metrics in their e-journals. It is the way to increase their visibility and impact in the world of science.

The Advanced Limiter Test-I (ALT-I) variable-geometry pump limiter module

International Nuclear Information System (INIS)

Pontau, A.E.; Malinowski, M.E.; Ver Berkmoes, A.A.; Guthrie, S.E.; Watson, R.D.; Goebel, D.M.; Campbell, G.A.

1984-01-01

The ALT-I variable geometry module has been designed to address many of the issues not previously settled by earlier experiments. The goal is to study the basic processes involved in pump limiter operation as well as demonstrate its utility and effect on the plasma. The flexibility and extensive instrumentation of ALT-I will offer a unique opportunity to parameterize operation and facilitate the engineering design of future pump limiters. (orig.)

Characterising risk - aggregated metrics: radiation and noise

International Nuclear Information System (INIS)

Passchier, W.

1998-01-01

The characterisation of risk is an important phase in the risk assessment - risk management process. From the multitude of risk attributes a few have to be selected to obtain a risk characteristic or profile that is useful for risk management decisions and implementation of protective measures. One way to reduce the number of attributes is aggregation. In the field of radiation protection such an aggregated metric is firmly established: effective dose. For protection against environmental noise the Health Council of the Netherlands recently proposed a set of aggregated metrics for noise annoyance and sleep disturbance. The presentation will discuss similarities and differences between these two metrics and practical limitations. The effective dose has proven its usefulness in designing radiation protection measures, which are related to the level of risk associated with the radiation practice in question, given that implicit judgements on radiation induced health effects are accepted. However, as the metric does not take into account the nature of radiation practice, it is less useful in policy discussions on the benefits and harm of radiation practices. With respect to the noise exposure metric, only one effect is targeted (annoyance), and the differences between sources are explicitly taken into account. This should make the metric useful in policy discussions with respect to physical planning and siting problems. The metric proposed has only significance on a population level, and can not be used as a predictor for individual risk. (author)

Supplier selection using different metric functions

Directory of Open Access Journals (Sweden)

Omosigho S.E.

2015-01-01

Full Text Available Supplier selection is an important component of supply chain management in today’s global competitive environment. Hence, the evaluation and selection of suppliers have received considerable attention in the literature. Many attributes of suppliers, other than cost, are considered in the evaluation and selection process. Therefore, the process of evaluation and selection of suppliers is a multi-criteria decision making process. The methodology adopted to solve the supplier selection problem is intuitionistic fuzzy TOPSIS (Technique for Order Preference by Similarity to the Ideal Solution. Generally, TOPSIS is based on the concept of minimum distance from the positive ideal solution and maximum distance from the negative ideal solution. We examine the deficiencies of using only one metric function in TOPSIS and propose the use of spherical metric function in addition to the commonly used metric functions. For empirical supplier selection problems, more than one metric function should be used.

77 FR 12832 - Non-RTO/ISO Performance Metrics; Commission Staff Request Comments on Performance Metrics for...

Science.gov (United States)

2012-03-02

... Performance Metrics; Commission Staff Request Comments on Performance Metrics for Regions Outside of RTOs and... performance communicate about the benefits of RTOs and, where appropriate, (2) changes that need to be made to... common set of performance measures for markets both within and outside of ISOs/RTOs. As recommended by...

Regional Sustainability: The San Luis Basin Metrics Project

Science.gov (United States)

There are a number of established, scientifically supported metrics of sustainability. Many of the metrics are data intensive and require extensive effort to collect data and compute. Moreover, individual metrics may not capture all aspects of a system that are relevant to sust...

Probabilistic metric spaces

CERN Document Server

Schweizer, B

2005-01-01

Topics include special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. 1983 edition, updated with 3 new appendixes. Includes 17 illustrations.

Metric solution of a spinning mass

International Nuclear Information System (INIS)

Sato, H.

1982-01-01

Studies on a particular class of asymptotically flat and stationary metric solutions called the Kerr-Tomimatsu-Sato class are reviewed about its derivation and properties. For a further study, an almost complete list of the papers worked on the Tomimatsu-Sato metrics is given. (Auth.)

Software architecture analysis tool : software architecture metrics collection

NARCIS (Netherlands)

Muskens, J.; Chaudron, M.R.V.; Westgeest, R.

2002-01-01

The Software Engineering discipline lacks the ability to evaluate software architectures. Here we describe a tool for software architecture analysis that is based on metrics. Metrics can be used to detect possible problems and bottlenecks in software architectures. Even though metrics do not give a

Generalized tolerance sensitivity and DEA metric sensitivity

OpenAIRE

Neralić, Luka; E. Wendell, Richard

2015-01-01

This paper considers the relationship between Tolerance sensitivity analysis in optimization and metric sensitivity analysis in Data Envelopment Analysis (DEA). Herein, we extend the results on the generalized Tolerance framework proposed by Wendell and Chen and show how this framework includes DEA metric sensitivity as a special case. Further, we note how recent results in Tolerance sensitivity suggest some possible extensions of the results in DEA metric sensitivity.

On Nakhleh's metric for reduced phylogenetic networks

OpenAIRE

Cardona, Gabriel; Llabrés, Mercè; Rosselló, Francesc; Valiente Feruglio, Gabriel Alejandro

2009-01-01

We prove that Nakhleh’s metric for reduced phylogenetic networks is also a metric on the classes of tree-child phylogenetic networks, semibinary tree-sibling time consistent phylogenetic networks, and multilabeled phylogenetic trees. We also prove that it separates distinguishable phylogenetic networks. In this way, it becomes the strongest dissimilarity measure for phylogenetic networks available so far. Furthermore, we propose a generalization of that metric that separates arbitrary phyl...

Generalized tolerance sensitivity and DEA metric sensitivity

Directory of Open Access Journals (Sweden)

Luka Neralić

2015-03-01

Full Text Available This paper considers the relationship between Tolerance sensitivity analysis in optimization and metric sensitivity analysis in Data Envelopment Analysis (DEA. Herein, we extend the results on the generalized Tolerance framework proposed by Wendell and Chen and show how this framework includes DEA metric sensitivity as a special case. Further, we note how recent results in Tolerance sensitivity suggest some possible extensions of the results in DEA metric sensitivity.

Social Media Metrics Importance and Usage Frequency in Latvia

Directory of Open Access Journals (Sweden)

Ronalds Skulme

2017-12-01

Full Text Available Purpose of the article: The purpose of this paper was to explore which social media marketing metrics are most often used and are most important for marketing experts in Latvia and can be used to evaluate marketing campaign effectiveness. Methodology/methods: In order to achieve the aim of this paper several theoretical and practical research methods were used, such as theoretical literature analysis, surveying and grouping. First of all, theoretical research about social media metrics was conducted. Authors collected information about social media metric grouping methods and the most frequently mentioned social media metrics in the literature. The collected information was used as the foundation for the expert surveys. The expert surveys were used to collect information from Latvian marketing professionals to determine which social media metrics are used most often and which social media metrics are most important in Latvia. Scientific aim: The scientific aim of this paper was to identify if social media metrics importance varies depending on the consumer purchase decision stage. Findings: Information about the most important and most often used social media marketing metrics in Latvia was collected. A new social media grouping framework is proposed. Conclusions: The main conclusion is that the importance and the usage frequency of the social media metrics is changing depending of consumer purchase decisions stage the metric is used to evaluate.

A comparison theorem of the Kobayashi metric and the Bergman metric on a class of Reinhardt domains

International Nuclear Information System (INIS)

Weiping Yin.

1990-03-01

A comparison theorem for the Kobayashi and Bergman metric is given on a class of Reinhardt domains in C n . In the meantime, we obtain a class of complete invariant Kaehler metrics for these domains of the special cases. (author). 5 refs

Geometry essentials for dummies

CERN Document Server

Ryan, Mark

2011-01-01

Just the critical concepts you need to score high in geometry This practical, friendly guide focuses on critical concepts taught in a typical geometry course, from the properties of triangles, parallelograms, circles, and cylinders, to the skills and strategies you need to write geometry proofs. Geometry Essentials For Dummies is perfect for cramming or doing homework, or as a reference for parents helping kids study for exams. Get down to the basics - get a handle on the basics of geometry, from lines, segments, and angles, to vertices, altitudes, and diagonals Conque

Using Activity Metrics for DEVS Simulation Profiling

Directory of Open Access Journals (Sweden)

Muzy A.

2014-01-01

Full Text Available Activity metrics can be used to profile DEVS models before and during the simulation. It is critical to get good activity metrics of models before and during their simulation. Having a means to compute a-priori activity of components (analytic activity may be worth when simulating a model (or parts of it for the first time. After, during the simulation, analytic activity can be corrected using dynamic one. In this paper, we introduce McCabe cyclomatic complexity metric (MCA to compute analytic activity. Both static and simulation activity metrics have been implemented through a plug-in of the DEVSimPy (DEVS Simulator in Python language environment and applied to DEVS models.

Tracker Performance Metric

National Research Council Canada - National Science Library

Olson, Teresa; Lee, Harry; Sanders, Johnnie

2002-01-01

.... We have developed the Tracker Performance Metric (TPM) specifically for this purpose. It was designed to measure the output performance, on a frame-by-frame basis, using its output position and quality...

Metrication: An economic wake-up call for US industry

Science.gov (United States)

Carver, G. P.

1993-03-01

As the international standard of measurement, the metric system is one key to success in the global marketplace. International standards have become an important factor in international economic competition. Non-metric products are becoming increasingly unacceptable in world markets that favor metric products. Procurement is the primary federal tool for encouraging and helping U.S. industry to convert voluntarily to the metric system. Besides the perceived unwillingness of the customer, certain regulatory language, and certain legal definitions in some states, there are no major impediments to conversion of the remaining non-metric industries to metric usage. Instead, there are good reasons for changing, including an opportunity to rethink many industry standards and to take advantage of size standardization. Also, when the remaining industries adopt the metric system, they will come into conformance with federal agencies engaged in similar activities.

Conformal and related changes of metric on the product of two almost contact metric manifolds.

OpenAIRE

Blair, D. E.

1990-01-01

This paper studies conformal and related changes of the product metric on the product of two almost contact metric manifolds. It is shown that if one factor is Sasakian, the other is not, but that locally the second factor is of the type studied by Kenmotsu. The results are more general and given in terms of trans-Sasakian, α-Sasakian and β-Kenmotsu structures.

Wild hummingbirds can use the geometry of a flower array.

Science.gov (United States)

Hornsby, Mark A W; Healy, Susan D; Hurly, T Andrew

2017-06-01

Animals use cues from their environment to orient in space and to navigate their surroundings. Geometry is a cue whose informational content may originate from the metric properties of a given environment, and its use has been demonstrated in the laboratory in nearly every species of animal tested. However, it is not clear whether geometric information, used by animals typically tested in small, rectangular boxes, is directly relevant to animals in their natural environment. Here we present the first data that confirm the use of geometric cues by a free-living animal in the wild. We trained rufous hummingbirds to visit a rectangular array of four artificial flowers, one of which was rewarded. In some trials a conspicuous landmark cued the reward. Following array translocation and rotation, we presented hummingbirds with three tests. When trained and tested with the landmark, or when trained and tested without it, hummingbirds failed to show geometric learning. However, when trained with a landmark but tested without it, hummingbirds produced the classic geometric response, showing that they had learned the geometric relationships (distance and direction) of several non-reward visual elements of the environment. While it remains that the use of geometry to relocate a reward may be an experimental artefact, its use is not confined to the laboratory. Copyright © 2017 Elsevier B.V. All rights reserved.

Extremal limits of the C metric: Nariai, Bertotti-Robinson, and anti-Nariai C metrics

International Nuclear Information System (INIS)

Dias, Oscar J.C.; Lemos, Jose P.S.

2003-01-01

In two previous papers we have analyzed the C metric in a background with a cosmological constant Λ, namely, the de-Sitter (dS) C metric (Λ>0), and the anti-de Sitter (AdS) C metric (Λ 0, Λ=0, and Λ 2 xS-tilde 2 ) to each point in the deformed two-sphere S-tilde 2 corresponds a dS 2 spacetime, except for one point which corresponds to a dS 2 spacetime with an infinite straight strut or string. There are other important new features that appear. One expects that the solutions found in this paper are unstable and decay into a slightly nonextreme black hole pair accelerated by a strut or by strings. Moreover, the Euclidean version of these solutions mediate the quantum process of black hole pair creation that accompanies the decay of the dS and AdS spaces

Graev metrics on free products and HNN extensions

DEFF Research Database (Denmark)

Slutsky, Konstantin

2014-01-01

We give a construction of two-sided invariant metrics on free products (possibly with amalgamation) of groups with two-sided invariant metrics and, under certain conditions, on HNN extensions of such groups. Our approach is similar to the Graev's construction of metrics on free groups over pointed...

Validation of Metrics for Collaborative Systems

OpenAIRE

Ion IVAN; Cristian CIUREA

2008-01-01

This paper describe the new concepts of collaborative systems metrics validation. The paper define the quality characteristics of collaborative systems. There are proposed a metric to estimate the quality level of collaborative systems. There are performed measurements of collaborative systems quality using a specially designed software.

g-Weak Contraction in Ordered Cone Rectangular Metric Spaces

Directory of Open Access Journals (Sweden)

S. K. Malhotra

2013-01-01

Full Text Available We prove some common fixed-point theorems for the ordered g-weak contractions in cone rectangular metric spaces without assuming the normality of cone. Our results generalize some recent results from cone metric and cone rectangular metric spaces into ordered cone rectangular metric spaces. Examples are provided which illustrate the results.

Minimizing pulling geometry errors in atomic force microscope single molecule force spectroscopy.

Science.gov (United States)

Rivera, Monica; Lee, Whasil; Ke, Changhong; Marszalek, Piotr E; Cole, Daniel G; Clark, Robert L

2008-10-01

In atomic force microscopy-based single molecule force spectroscopy (AFM-SMFS), it is assumed that the pulling angle is negligible and that the force applied to the molecule is equivalent to the force measured by the instrument. Recent studies, however, have indicated that the pulling geometry errors can drastically alter the measured force-extension relationship of molecules. Here we describe a software-based alignment method that repositions the cantilever such that it is located directly above the molecule's substrate attachment site. By aligning the applied force with the measurement axis, the molecule is no longer undergoing combined loading, and the full force can be measured by the cantilever. Simulations and experimental results verify the ability of the alignment program to minimize pulling geometry errors in AFM-SMFS studies.

The dynamics of metric-affine gravity

International Nuclear Information System (INIS)

Vitagliano, Vincenzo; Sotiriou, Thomas P.; Liberati, Stefano

2011-01-01

Highlights: → The role and the dynamics of the connection in metric-affine theories is explored. → The most general second order action does not lead to a dynamical connection. → Including higher order invariants excites new degrees of freedom in the connection. → f(R) actions are also discussed and shown to be a non- representative class. - Abstract: Metric-affine theories of gravity provide an interesting alternative to general relativity: in such an approach, the metric and the affine (not necessarily symmetric) connection are independent quantities. Furthermore, the action should include covariant derivatives of the matter fields, with the covariant derivative naturally defined using the independent connection. As a result, in metric-affine theories a direct coupling involving matter and connection is also present. The role and the dynamics of the connection in such theories is explored. We employ power counting in order to construct the action and search for the minimal requirements it should satisfy for the connection to be dynamical. We find that for the most general action containing lower order invariants of the curvature and the torsion the independent connection does not carry any dynamics. It actually reduces to the role of an auxiliary field and can be completely eliminated algebraically in favour of the metric and the matter field, introducing extra interactions with respect to general relativity. However, we also show that including higher order terms in the action radically changes this picture and excites new degrees of freedom in the connection, making it (or parts of it) dynamical. Constructing actions that constitute exceptions to this rule requires significant fine tuned and/or extra a priori constraints on the connection. We also consider f(R) actions as a particular example in order to show that they constitute a distinct class of metric-affine theories with special properties, and as such they cannot be used as representative toy

The definitive guide to IT service metrics

CERN Document Server

McWhirter, Kurt

2012-01-01

Used just as they are, the metrics in this book will bring many benefits to both the IT department and the business as a whole. Details of the attributes of each metric are given, enabling you to make the right choices for your business. You may prefer and are encouraged to design and create your own metrics to bring even more value to your business - this book will show you how to do this, too.

Planning geometry lessons with learning platforms

DEFF Research Database (Denmark)

Tamborg, Andreas Lindenskov

mathematics teachers’ joint planning of a lesson in geometry with a learning platform called Meebook is analyzed using the instrumental approach. It is concluded that the interface in Meebook orients the teachers work toward what the students should do rather than what they should learn, although the latter......This paper investigates how mathematics teachers plan lessons with a recently implemented Danish learning platform designed to support teachers in planning lessons in line with a recent objective-oriented curriculum. Drawing on data from observations of and interviews with teachers, three...... is a key intention behind the implementation of the platform. It is also concluded that when the teachers succeed in using learning objectives actively in their planning, the objectives support the teachers in designing lessons that correspond with their intentions. The paper concludes with a discussion...

NASA education briefs for the classroom. Metrics in space

Science.gov (United States)

The use of metric measurement in space is summarized for classroom use. Advantages of the metric system over the English measurement system are described. Some common metric units are defined, as are special units for astronomical study. International system unit prefixes and a conversion table of metric/English units are presented. Questions and activities for the classroom are recommended.

Enhancing Authentication Models Characteristic Metrics via ...

African Journals Online (AJOL)

In this work, we derive the universal characteristic metrics set for authentication models based on security, usability and design issues. We then compute the probability of the occurrence of each characteristic metrics in some single factor and multifactor authentication models in order to determine the effectiveness of these ...

Validation of Metrics for Collaborative Systems

Directory of Open Access Journals (Sweden)

Ion IVAN

2008-01-01

Full Text Available This paper describe the new concepts of collaborative systems metrics validation. The paper define the quality characteristics of collaborative systems. There are proposed a metric to estimate the quality level of collaborative systems. There are performed measurements of collaborative systems quality using a specially designed software.

Complex analysis and geometry

CERN Document Server

Silva, Alessandro

1993-01-01

The papers in this wide-ranging collection report on the results of investigations from a number of linked disciplines, including complex algebraic geometry, complex analytic geometry of manifolds and spaces, and complex differential geometry.

Understanding Acceptance of Software Metrics--A Developer Perspective

Science.gov (United States)

Umarji, Medha

2009-01-01

Software metrics are measures of software products and processes. Metrics are widely used by software organizations to help manage projects, improve product quality and increase efficiency of the software development process. However, metrics programs tend to have a high failure rate in organizations, and developer pushback is one of the sources…

Measuring reliability under epistemic uncertainty: Review on non-probabilistic reliability metrics

Directory of Open Access Journals (Sweden)

Kang Rui

2016-06-01

Full Text Available In this paper, a systematic review of non-probabilistic reliability metrics is conducted to assist the selection of appropriate reliability metrics to model the influence of epistemic uncertainty. Five frequently used non-probabilistic reliability metrics are critically reviewed, i.e., evidence-theory-based reliability metrics, interval-analysis-based reliability metrics, fuzzy-interval-analysis-based reliability metrics, possibility-theory-based reliability metrics (posbist reliability and uncertainty-theory-based reliability metrics (belief reliability. It is pointed out that a qualified reliability metric that is able to consider the effect of epistemic uncertainty needs to (1 compensate the conservatism in the estimations of the component-level reliability metrics caused by epistemic uncertainty, and (2 satisfy the duality axiom, otherwise it might lead to paradoxical and confusing results in engineering applications. The five commonly used non-probabilistic reliability metrics are compared in terms of these two properties, and the comparison can serve as a basis for the selection of the appropriate reliability metrics.

A rotating hairy AdS3 black hole with the metric having only one Killing vector field

International Nuclear Information System (INIS)

Iizuka, Norihiro; Ishibashi, Akihiro; Maeda, Kengo

2015-01-01

We perturbatively construct a three-dimensional rotating AdS black hole with a real scalar hair. We choose the mass of a scalar field slightly above the Breitenlohner-Freedman bound and impose a general boundary condition for the bulk scalar field at AdS infinity. We first show that rotating BTZ black holes are unstable against scalar field perturbations under our more general boundary condition. Next we construct a rotating hairy black hole perturbatively with respect to a small amplitude ϵ of the scalar field, up to O(ϵ 4 ). Our hairy black hole is stationary and exhibits no dissipation, but the lumps of the non-linearly perturbed geometry break axial symmetry, thus providing the first example of a rotating black hole whose metric admits only one Killing vector field. Furthermore, we numerically show that the entropy of our hairy black hole is larger than that of the BTZ black hole with the same energy and the angular momentum. We briefly discuss if our rotating hairy black hole in lumpy geometry could be the endpoint of the instability.

Construction of self-dual codes in the Rosenbloom-Tsfasman metric

Science.gov (United States)

Krisnawati, Vira Hari; Nisa, Anzi Lina Ukhtin

2017-12-01

Linear code is a very basic code and very useful in coding theory. Generally, linear code is a code over finite field in Hamming metric. Among the most interesting families of codes, the family of self-dual code is a very important one, because it is the best known error-correcting code. The concept of Hamming metric is develop into Rosenbloom-Tsfasman metric (RT-metric). The inner product in RT-metric is different from Euclid inner product that is used to define duality in Hamming metric. Most of the codes which are self-dual in Hamming metric are not so in RT-metric. And, generator matrix is very important to construct a code because it contains basis of the code. Therefore in this paper, we give some theorems and methods to construct self-dual codes in RT-metric by considering properties of the inner product and generator matrix. Also, we illustrate some examples for every kind of the construction.

Chaotic inflation with metric and matter perturbations

International Nuclear Information System (INIS)

Feldman, H.A.; Brandenberger, R.H.

1989-01-01

A perturbative scheme to analyze the evolution of both metric and scalar field perturbations in an expanding universe is developed. The scheme is applied to study chaotic inflation with initial metric and scalar field perturbations present. It is shown that initial gravitational perturbations with wavelength smaller than the Hubble radius rapidly decay. The metric simultaneously picks up small perturbations determined by the matter inhomogeneities. Both are frozen in once the wavelength exceeds the Hubble radius. (orig.)

Phantom metrics with Killing spinors

Directory of Open Access Journals (Sweden)

W.A. Sabra

2015-11-01

Full Text Available We study metric solutions of Einstein–anti-Maxwell theory admitting Killing spinors. The analogue of the IWP metric which admits a space-like Killing vector is found and is expressed in terms of a complex function satisfying the wave equation in flat (2+1-dimensional space–time. As examples, electric and magnetic Kasner spaces are constructed by allowing the solution to depend only on the time coordinate. Euclidean solutions are also presented.

Space-time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry, conventionality, and underdetermination

Science.gov (United States)

Pitts, J. Brian

2016-02-01

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz

Characterizing the Peano fluidic muscle and the effects of its geometry properties on its behavior

Science.gov (United States)

Veale, Allan Joshua; Xie, Sheng Quan; Anderson, Iain Alexander

2016-06-01

In this work, we explore the basic static and dynamic behavior of a hydraulically actuated Peano muscle and how its geometry affects key static and dynamic performance metrics. The Peano muscle, or pouch motor is a fluid powered artificial muscle. Similar to McKibben pneumatic artificial muscles (PAMs), it has the ability to generate the high forces of biological muscles with the low threshold pressure of pleated PAMs, but in a slim, easily distributed form. We found that Peano muscles have similar characteristics to other PAMs, but produce lower free-strains. A test rig capable of measuring high-speed flow rates with a Venturi tube revealed that their efficiency peaks at about 40% during highly dynamic movements. Peano muscles with more tubes and of a greater size do not move faster. Also, their muscle tubes should have an aspect ratio of at least 1:3 and channel width greater than 20% to maximize performance. These findings suggest that finite element modeling be used to optimize more complex Peano muscle geometries.

Smarandache Spaces as a New Extension of the Basic Space-Time of General Relativity

Directory of Open Access Journals (Sweden)

Rabounski D.

2010-04-01

Full Text Available This short letter manifests how Smarandache geometries can be employed in order to extend the “classical” basis of the General Theory of Relativity (Riemannian geometry through joining the properties of two or more (different geometries in the same single space. Perspectives in this way seem much profitable: the basic space-time of General Relativity can be extended to not only metric geometries, but even to non-metric ones (where no distances can be measured, or to spaces of the mixed kind which possess the properties of both metric and non-metric spaces (the latter should be referred to as “semi-metric spaces”. If both metric and non-metric properties possessed at the same (at least one point of a space, it is one of Smarandache geometries, and should be re- ferred to as “Smarandache semi-metric space”. Such spaces can be introduced accord- ing to the mathematical apparatus of physically observable quantities (chronometric invariants, if we consider a breaking of the observable space metric in the continuous background of the fundamental metric tensor.

Invariant metric for nonlinear symplectic maps

Indian Academy of Sciences (India)

In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥ 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we ...

Two-dimensional manifolds with metrics of revolution

International Nuclear Information System (INIS)

Sabitov, I Kh

2000-01-01

This is a study of the topological and metric structure of two-dimensional manifolds with a metric that is locally a metric of revolution. In the case of compact manifolds this problem can be thoroughly investigated, and in particular it is explained why there are no closed analytic surfaces of revolution in R 3 other than a sphere and a torus (moreover, in the smoothness class C ∞ such surfaces, understood in a certain generalized sense, exist in any topological class)

Gravitational lensing in metric theories of gravity

International Nuclear Information System (INIS)

Sereno, Mauro

2003-01-01

Gravitational lensing in metric theories of gravity is discussed. I introduce a generalized approximate metric element, inclusive of both post-post-Newtonian contributions and a gravitomagnetic field. Following Fermat's principle and standard hypotheses, I derive the time delay function and deflection angle caused by an isolated mass distribution. Several astrophysical systems are considered. In most of the cases, the gravitomagnetic correction offers the best perspectives for an observational detection. Actual measurements distinguish only marginally different metric theories from each other

The uniqueness of the Fisher metric as information metric

Czech Academy of Sciences Publication Activity Database

Le, Hong-Van

2017-01-01

Roč. 69, č. 4 (2017), s. 879-896 ISSN 0020-3157 Institutional support: RVO:67985840 Keywords : Chentsov’s theorem * mixed topology * monotonicity of the Fisher metric Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 1.049, year: 2016 https://link.springer.com/article/10.1007%2Fs10463-016-0562-0

Onboard calibration and monitoring for the SWIFT instrument

International Nuclear Information System (INIS)

Rahnama, P; McDade, I; Shepherd, G; Gault, W

2012-01-01

The SWIFT (Stratospheric Wind Interferometer for Transport studies) instrument is a proposed space-based field-widened Doppler Michelson interferometer designed to measure stratospheric winds and ozone densities using a passive optical technique called Doppler Michelson imaging interferometry. The onboard calibration and monitoring procedures for the SWIFT instrument are described in this paper. Sample results of the simulations of onboard calibration measurements are presented and discussed. This paper also discusses the results of the derivation of the calibrations and monitoring requirements for the SWIFT instrument. SWIFT's measurement technique and viewing geometry are briefly described. The reference phase calibration and filter monitoring for the SWIFT instrument are two of the main critical design issues. In this paper it is shown that in order to meet SWIFT's science requirements, Michelson interferometer optical path difference monitoring corresponding to a phase calibration accuracy of ∼10 −3 radians, filter passband monitoring corresponding to phase accuracy of ∼5 × 10 −3 radians and a thermal stability of 10 −3 K s −1 are required. (paper)

Hybrid metric-Palatini stars

Science.gov (United States)

Danilǎ, Bogdan; Harko, Tiberiu; Lobo, Francisco S. N.; Mak, M. K.

2017-02-01

We consider the internal structure and the physical properties of specific classes of neutron, quark and Bose-Einstein condensate stars in the recently proposed hybrid metric-Palatini gravity theory, which is a combination of the metric and Palatini f (R ) formalisms. It turns out that the theory is very successful in accounting for the observed phenomenology, since it unifies local constraints at the Solar System level and the late-time cosmic acceleration, even if the scalar field is very light. In this paper, we derive the equilibrium equations for a spherically symmetric configuration (mass continuity and Tolman-Oppenheimer-Volkoff) in the framework of the scalar-tensor representation of the hybrid metric-Palatini theory, and we investigate their solutions numerically for different equations of state of neutron and quark matter, by adopting for the scalar field potential a Higgs-type form. It turns out that the scalar-tensor definition of the potential can be represented as an Clairaut differential equation, and provides an explicit form for f (R ) given by f (R )˜R +Λeff, where Λeff is an effective cosmological constant. Furthermore, stellar models, described by the stiff fluid, radiation-like, bag model and the Bose-Einstein condensate equations of state are explicitly constructed in both general relativity and hybrid metric-Palatini gravity, thus allowing an in-depth comparison between the predictions of these two gravitational theories. As a general result it turns out that for all the considered equations of state, hybrid gravity stars are more massive than their general relativistic counterparts. Furthermore, two classes of stellar models corresponding to two particular choices of the functional form of the scalar field (constant value, and logarithmic form, respectively) are also investigated. Interestingly enough, in the case of a constant scalar field the equation of state of the matter takes the form of the bag model equation of state describing

The universal connection and metrics on moduli spaces

International Nuclear Information System (INIS)

Massamba, Fortune; Thompson, George

2003-11-01

We introduce a class of metrics on gauge theoretic moduli spaces. These metrics are made out of the universal matrix that appears in the universal connection construction of M. S. Narasimhan and S. Ramanan. As an example we construct metrics on the c 2 = 1 SU(2) moduli space of instantons on R 4 for various universal matrices. (author)

Reproducibility of graph metrics in fMRI networks

Directory of Open Access Journals (Sweden)

Qawi K Telesford

2010-12-01

Full Text Available The reliability of graph metrics calculated in network analysis is essential to the interpretation of complex network organization. These graph metrics are used to deduce the small-world properties in networks. In this study, we investigated the test-retest reliability of graph metrics from functional magnetic resonance imaging (fMRI data collected for two runs in 45 healthy older adults. Graph metrics were calculated on data for both runs and compared using intraclass correlation coefficient (ICC statistics and Bland-Altman (BA plots. ICC scores describe the level of absolute agreement between two measurements and provide a measure of reproducibility. For mean graph metrics, ICC scores were high for clustering coefficient (ICC=0.86, global efficiency (ICC=0.83, path length (ICC=0.79, and local efficiency (ICC=0.75; the ICC score for degree was found to be low (ICC=0.29. ICC scores were also used to generate reproducibility maps in brain space to test voxel-wise reproducibility for unsmoothed and smoothed data. Reproducibility was uniform across the brain for global efficiency and path length, but was only high in network hubs for clustering coefficient, local efficiency and degree. BA plots were used to test the measurement repeatability of all graph metrics. All graph metrics fell within the limits for repeatability. Together, these results suggest that with exception of degree, mean graph metrics are reproducible and suitable for clinical studies. Further exploration is warranted to better understand reproducibility across the brain on a voxel-wise basis.

Instrument design and optimization using genetic algorithms

International Nuclear Information System (INIS)

Hoelzel, Robert; Bentley, Phillip M.; Fouquet, Peter

2006-01-01

This article describes the design of highly complex physical instruments by using a canonical genetic algorithm (GA). The procedure can be applied to all instrument designs where performance goals can be quantified. It is particularly suited to the optimization of instrument design where local optima in the performance figure of merit are prevalent. Here, a GA is used to evolve the design of the neutron spin-echo spectrometer WASP which is presently being constructed at the Institut Laue-Langevin, Grenoble, France. A comparison is made between this artificial intelligence approach and the traditional manual design methods. We demonstrate that the search of parameter space is more efficient when applying the genetic algorithm, and the GA produces a significantly better instrument design. Furthermore, it is found that the GA increases flexibility, by facilitating the reoptimization of the design after changes in boundary conditions during the design phase. The GA also allows the exploration of 'nonstandard' magnet coil geometries. We conclude that this technique constitutes a powerful complementary tool for the design and optimization of complex scientific apparatus, without replacing the careful thought processes employed in traditional design methods

Instrument design and optimization using genetic algorithms

Science.gov (United States)

Hölzel, Robert; Bentley, Phillip M.; Fouquet, Peter

2006-10-01

This article describes the design of highly complex physical instruments by using a canonical genetic algorithm (GA). The procedure can be applied to all instrument designs where performance goals can be quantified. It is particularly suited to the optimization of instrument design where local optima in the performance figure of merit are prevalent. Here, a GA is used to evolve the design of the neutron spin-echo spectrometer WASP which is presently being constructed at the Institut Laue-Langevin, Grenoble, France. A comparison is made between this artificial intelligence approach and the traditional manual design methods. We demonstrate that the search of parameter space is more efficient when applying the genetic algorithm, and the GA produces a significantly better instrument design. Furthermore, it is found that the GA increases flexibility, by facilitating the reoptimization of the design after changes in boundary conditions during the design phase. The GA also allows the exploration of "nonstandard" magnet coil geometries. We conclude that this technique constitutes a powerful complementary tool for the design and optimization of complex scientific apparatus, without replacing the careful thought processes employed in traditional design methods.

Complexity Metrics for Workflow Nets

DEFF Research Database (Denmark)

Lassen, Kristian Bisgaard; van der Aalst, Wil M.P.

2009-01-01

analysts have difficulties grasping the dynamics implied by a process model. Recent empirical studies show that people make numerous errors when modeling complex business processes, e.g., about 20 percent of the EPCs in the SAP reference model have design flaws resulting in potential deadlocks, livelocks......, etc. It seems obvious that the complexity of the model contributes to design errors and a lack of understanding. It is not easy to measure complexity, however. This paper presents three complexity metrics that have been implemented in the process analysis tool ProM. The metrics are defined...... for a subclass of Petri nets named Workflow nets, but the results can easily be applied to other languages. To demonstrate the applicability of these metrics, we have applied our approach and tool to 262 relatively complex Protos models made in the context of various student projects. This allows us to validate...

Sustainability Metrics: The San Luis Basin Project

Science.gov (United States)

Sustainability is about promoting humanly desirable dynamic regimes of the environment. Metrics: ecological footprint, net regional product, exergy, emergy, and Fisher Information. Adaptive management: (1) metrics assess problem, (2) specific problem identified, and (3) managemen...

Standardised metrics for global surgical surveillance.

Science.gov (United States)

Weiser, Thomas G; Makary, Martin A; Haynes, Alex B; Dziekan, Gerald; Berry, William R; Gawande, Atul A

2009-09-26

Public health surveillance relies on standardised metrics to evaluate disease burden and health system performance. Such metrics have not been developed for surgical services despite increasing volume, substantial cost, and high rates of death and disability associated with surgery. The Safe Surgery Saves Lives initiative of WHO's Patient Safety Programme has developed standardised public health metrics for surgical care that are applicable worldwide. We assembled an international panel of experts to develop and define metrics for measuring the magnitude and effect of surgical care in a population, while taking into account economic feasibility and practicability. This panel recommended six measures for assessing surgical services at a national level: number of operating rooms, number of operations, number of accredited surgeons, number of accredited anaesthesia professionals, day-of-surgery death ratio, and postoperative in-hospital death ratio. We assessed the feasibility of gathering such statistics at eight diverse hospitals in eight countries and incorporated them into the WHO Guidelines for Safe Surgery, in which methods for data collection, analysis, and reporting are outlined.

THE EFFECT OF NON-ROUTINE GEOMETRY PROBLEM ON ELEMENTARY STUDENTS BELIEF IN MATHEMATICS: A CASE STUDY

Directory of Open Access Journals (Sweden)

Khoerul Umam

2018-03-01

Full Text Available Many learners hold traditional beliefs about perimeter and area that a shape with a larger area must have a larger perimeter while shape with the same perimeter must have the same area. To address this issue, non-routine geometry problem is given. This qualitative descriptive research used to reach the goal and to explore the effect of non-routine geometry problem on elementary student belief in mathematics. The instrument has been developed to accommodate intuitive student belief and student’s belief about the concept of perimeter. The results provide evidence that students’ intuitive belief about perimeter can be change through non-routine geometry problem which is required understanding and some mathematical analysis. Fortunately, the problem has helped the elementary students revise and correct their beliefs, thoughts, and understandings relating to the circumference of shape.

Developing a Security Metrics Scorecard for Healthcare Organizations.

Science.gov (United States)

Elrefaey, Heba; Borycki, Elizabeth; Kushniruk, Andrea

2015-01-01

In healthcare, information security is a key aspect of protecting a patient's privacy and ensuring systems availability to support patient care. Security managers need to measure the performance of security systems and this can be achieved by using evidence-based metrics. In this paper, we describe the development of an evidence-based security metrics scorecard specific to healthcare organizations. Study participants were asked to comment on the usability and usefulness of a prototype of a security metrics scorecard that was developed based on current research in the area of general security metrics. Study findings revealed that scorecards need to be customized for the healthcare setting in order for the security information to be useful and usable in healthcare organizations. The study findings resulted in the development of a security metrics scorecard that matches the healthcare security experts' information requirements.

Landscape pattern metrics and regional assessment

Science.gov (United States)

O'Neill, R. V.; Riitters, K.H.; Wickham, J.D.; Jones, K.B.

1999-01-01

The combination of remote imagery data, geographic information systems software, and landscape ecology theory provides a unique basis for monitoring and assessing large-scale ecological systems. The unique feature of the work has been the need to develop and interpret quantitative measures of spatial pattern-the landscape indices. This article reviews what is known about the statistical properties of these pattern metrics and suggests some additional metrics based on island biogeography, percolation theory, hierarchy theory, and economic geography. Assessment applications of this approach have required interpreting the pattern metrics in terms of specific environmental endpoints, such as wildlife and water quality, and research into how to represent synergystic effects of many overlapping sources of stress.

Geometry

CERN Document Server

Pedoe, Dan

1988-01-01

""A lucid and masterly survey."" - Mathematics Gazette Professor Pedoe is widely known as a fine teacher and a fine geometer. His abilities in both areas are clearly evident in this self-contained, well-written, and lucid introduction to the scope and methods of elementary geometry. It covers the geometry usually included in undergraduate courses in mathematics, except for the theory of convex sets. Based on a course given by the author for several years at the University of Minnesota, the main purpose of the book is to increase geometrical, and therefore mathematical, understanding and to he

Self-benchmarking Guide for Cleanrooms: Metrics, Benchmarks, Actions

Energy Technology Data Exchange (ETDEWEB)

Mathew, Paul; Sartor, Dale; Tschudi, William

2009-07-13

This guide describes energy efficiency metrics and benchmarks that can be used to track the performance of and identify potential opportunities to reduce energy use in laboratory buildings. This guide is primarily intended for personnel who have responsibility for managing energy use in existing laboratory facilities - including facilities managers, energy managers, and their engineering consultants. Additionally, laboratory planners and designers may also use the metrics and benchmarks described in this guide for goal-setting in new construction or major renovation. This guide provides the following information: (1) A step-by-step outline of the benchmarking process. (2) A set of performance metrics for the whole building as well as individual systems. For each metric, the guide provides a definition, performance benchmarks, and potential actions that can be inferred from evaluating this metric. (3) A list and descriptions of the data required for computing the metrics. This guide is complemented by spreadsheet templates for data collection and for computing the benchmarking metrics. This guide builds on prior research supported by the national Laboratories for the 21st Century (Labs21) program, supported by the U.S. Department of Energy and the U.S. Environmental Protection Agency. Much of the benchmarking data are drawn from the Labs21 benchmarking database and technical guides. Additional benchmark data were obtained from engineering experts including laboratory designers and energy managers.

Metrics Are Needed for Collaborative Software Development

Directory of Open Access Journals (Sweden)

Mojgan Mohtashami

2011-10-01

Full Text Available There is a need for metrics for inter-organizational collaborative software development projects, encompassing management and technical concerns. In particular, metrics are needed that are aimed at the collaborative aspect itself, such as readiness for collaboration, the quality and/or the costs and benefits of collaboration in a specific ongoing project. We suggest questions and directions for such metrics, spanning the full lifespan of a collaborative project, from considering the suitability of collaboration through evaluating ongoing projects to final evaluation of the collaboration.

Predicting class testability using object-oriented metrics

OpenAIRE

Bruntink, Magiel; Deursen, Arie

2004-01-01

textabstractIn this paper we investigate factors of the testability of object-oriented software systems. The starting point is given by a study of the literature to obtain both an initial model of testability and existing OO metrics related to testability. Subsequently, these metrics are evaluated by means of two case studies of large Java systems for which JUnit test cases exist. The goal of this paper is to define and evaluate a set of metrics that can be used to assess the testability of t...

Software metrics a rigorous and practical approach

CERN Document Server

Fenton, Norman

2014-01-01

A Framework for Managing, Measuring, and Predicting Attributes of Software Development Products and ProcessesReflecting the immense progress in the development and use of software metrics in the past decades, Software Metrics: A Rigorous and Practical Approach, Third Edition provides an up-to-date, accessible, and comprehensive introduction to software metrics. Like its popular predecessors, this third edition discusses important issues, explains essential concepts, and offers new approaches for tackling long-standing problems.New to the Third EditionThis edition contains new material relevant

Hermitian-Einstein metrics on parabolic stable bundles

International Nuclear Information System (INIS)

Li Jiayu; Narasimhan, M.S.

1995-12-01

Let M-bar be a compact complex manifold of complex dimension two with a smooth Kaehler metric and D a smooth divisor on M-bar. If E is a rank 2 holomorphic vector bundle on M-bar with a stable parabolic structure along D, we prove the existence of a metric on E' = E module MbarD (compatible with the parabolic structure) which is Hermitian-Einstein with respect to the restriction of Kaehler metric of M-barD. A converse is also proved. (author). 24 refs

A Geometrical Method for Sound-Hole Size and Location Enhancement in Lute Family Musical Instruments: The Golden Method

Directory of Open Access Journals (Sweden)

Soheil Jafari

2017-11-01

Full Text Available This paper presents a new analytical approach, the Golden Method, to enhance sound-hole size and location in musical instruments of the lute family in order to obtain better sound damping characteristics based on the concept of the golden ratio and the instrument geometry. The main objective of the paper is to increase the capability of lute family musical instruments in keeping a note for a certain time at a certain level to enhance the instruments’ orchestral characteristics. For this purpose, a geometry-based analytical method, the Golden Method is first described in detail in an itemized feature. A new musical instrument is then developed and tested to confirm the ability of the Golden Method in optimizing the acoustical characteristics of musical instruments from a damping point of view by designing the modified sound-hole. Finally, the new-developed instrument is tested, and the obtained results are compared with those of two well-known instruments to confirm the effectiveness of the proposed method. The experimental results show that the suggested method is able to increase the sound damping time by at least 2.4% without affecting the frequency response function and other acoustic characteristics of the instrument. This methodology could be used as the first step in future studies on design, optimization and evaluation of musical instruments of the lute family (e.g., lute, oud, barbat, mandolin, setar, and etc..

Complex algebraic geometry

CERN Document Server

Kollár, János

1997-01-01

This volume contains the lectures presented at the third Regional Geometry Institute at Park City in 1993. The lectures provide an introduction to the subject, complex algebraic geometry, making the book suitable as a text for second- and third-year graduate students. The book deals with topics in algebraic geometry where one can reach the level of current research while starting with the basics. Topics covered include the theory of surfaces from the viewpoint of recent higher-dimensional developments, providing an excellent introduction to more advanced topics such as the minimal model program. Also included is an introduction to Hodge theory and intersection homology based on the simple topological ideas of Lefschetz and an overview of the recent interactions between algebraic geometry and theoretical physics, which involve mirror symmetry and string theory.

CMS geometry through 2020

International Nuclear Information System (INIS)

Osborne, I; Brownson, E; Eulisse, G; Jones, C D; Sexton-Kennedy, E; Lange, D J

2014-01-01

CMS faces real challenges with upgrade of the CMS detector through 2020 and beyond. One of the challenges, from the software point of view, is managing upgrade simulations with the same software release as the 2013 scenario. We present the CMS geometry description software model, its integration with the CMS event setup and core software. The CMS geometry configuration and selection is implemented in Python. The tools collect the Python configuration fragments into a script used in CMS workflow. This flexible and automated geometry configuration allows choosing either transient or persistent version of the same scenario and specific version of the same scenario. We describe how the geometries are integrated and validated, and how we define and handle different geometry scenarios in simulation and reconstruction. We discuss how to transparently manage multiple incompatible geometries in the same software release. Several examples are shown based on current implementation assuring consistent choice of scenario conditions. The consequences and implications for multiple/different code algorithms are discussed.

Coverage Metrics for Model Checking

Science.gov (United States)

Penix, John; Visser, Willem; Norvig, Peter (Technical Monitor)

2001-01-01

When using model checking to verify programs in practice, it is not usually possible to achieve complete coverage of the system. In this position paper we describe ongoing research within the Automated Software Engineering group at NASA Ames on the use of test coverage metrics to measure partial coverage and provide heuristic guidance for program model checking. We are specifically interested in applying and developing coverage metrics for concurrent programs that might be used to support certification of next generation avionics software.

Future of the PCI Readmission Metric.

Science.gov (United States)

Wasfy, Jason H; Yeh, Robert W

2016-03-01

Between 2013 and 2014, the Centers for Medicare and Medicaid Services and the National Cardiovascular Data Registry publically reported risk-adjusted 30-day readmission rates after percutaneous coronary intervention (PCI) as a pilot project. A key strength of this public reporting effort included risk adjustment with clinical rather than administrative data. Furthermore, because readmission after PCI is common, expensive, and preventable, this metric has substantial potential to improve quality and value in American cardiology care. Despite this, concerns about the metric exist. For example, few PCI readmissions are caused by procedural complications, limiting the extent to which improved procedural technique can reduce readmissions. Also, similar to other readmission measures, PCI readmission is associated with socioeconomic status and race. Accordingly, the metric may unfairly penalize hospitals that care for underserved patients. Perhaps in the context of these limitations, Centers for Medicare and Medicaid Services has not yet included PCI readmission among metrics that determine Medicare financial penalties. Nevertheless, provider organizations may still wish to focus on this metric to improve value for cardiology patients. PCI readmission is associated with low-risk chest discomfort and patient anxiety. Therefore, patient education, improved triage mechanisms, and improved care coordination offer opportunities to minimize PCI readmissions. Because PCI readmission is common and costly, reducing PCI readmission offers provider organizations a compelling target to improve the quality of care, and also performance in contracts involve shared financial risk. © 2016 American Heart Association, Inc.

Instrumented impact testing machine with reduced specimen oscillation effects

International Nuclear Information System (INIS)

Rintamaa, R.; Rahka, K.; Wallin, K.

1984-07-01

Owing to small and inexpensive specimens the Charpy impact test is widely used in quality control and alloy development. Limitations in power reactor survellance capsules it is also widely used for safety analysis purposes. Instrumenting the tup and computerizing data acquisition, makes dynamic fracture mechanics data measurement possible and convenient. However, the dynamic effects (inertia forces, specimen oscillations) in the impact test cause inaccuracies in the recorded load-time diagram and hence diminish the reliability of the calculated dynamic fracture mechanics parameters. To decrease inaccuracies a new pendulum type of instrumented impact test apparatus has been developed and constructed in the Metals Laboratory of the Technical Research Centre of Finland. This tester is based on a new principle involving inverted test geometry. The purpose of the geometry inversion is to reduce inertia load and specimen oscillation effects. Further, the new impact tester has some other novel features: e.g. the available initia impact energy is about double compared to the conventional standard (300 J) impact tester allowing the use of larger (10 x 20 x 110 mm) bend specimens than normal Charpy specimens. Also, the rotation asix in the three point bending is nearly stationary making COD-measurements possible. An experimental test series is described in which the inertia effects and specimen oscillations are compared in the conventional and new impact tester utilizing Charpy V-notch specimens. Comparison of the two test geometries is also made with the aid of an analytical model using finite element method (FEM) analysis. (author)

Model assessment using a multi-metric ranking technique

Science.gov (United States)

Fitzpatrick, P. J.; Lau, Y.; Alaka, G.; Marks, F.

2017-12-01

Validation comparisons of multiple models presents challenges when skill levels are similar, especially in regimes dominated by the climatological mean. Assessing skill separation will require advanced validation metrics and identifying adeptness in extreme events, but maintain simplicity for management decisions. Flexibility for operations is also an asset. This work postulates a weighted tally and consolidation technique which ranks results by multiple types of metrics. Variables include absolute error, bias, acceptable absolute error percentages, outlier metrics, model efficiency, Pearson correlation, Kendall's Tau, reliability Index, multiplicative gross error, and root mean squared differences. Other metrics, such as root mean square difference and rank correlation were also explored, but removed when the information was discovered to be generally duplicative to other metrics. While equal weights are applied, weights could be altered depending for preferred metrics. Two examples are shown comparing ocean models' currents and tropical cyclone products, including experimental products. The importance of using magnitude and direction for tropical cyclone track forecasts instead of distance, along-track, and cross-track are discussed. Tropical cyclone intensity and structure prediction are also assessed. Vector correlations are not included in the ranking process, but found useful in an independent context, and will be briefly reported.

Metric learning for DNA microarray data analysis

International Nuclear Information System (INIS)

Takeuchi, Ichiro; Nakagawa, Masao; Seto, Masao

2009-01-01

In many microarray studies, gene set selection is an important preliminary step for subsequent main task such as tumor classification, cancer subtype identification, etc. In this paper, we investigate the possibility of using metric learning as an alternative to gene set selection. We develop a simple metric learning algorithm aiming to use it for microarray data analysis. Exploiting a property of the algorithm, we introduce a novel approach for extending the metric learning to be adaptive. We apply the algorithm to previously studied microarray data on malignant lymphoma subtype identification.

Differential geometry in string models

International Nuclear Information System (INIS)

Alvarez, O.

1986-01-01

In this article the author reviews the differential geometric approach to the quantization of strings. A seminal paper demonstrates the connection between the trace anomaly and the critical dimension. The role played by the Faddeev-Popov ghosts has been instrumental in much of the subsequent work on the quantization of strings. This paper discusses the differential geometry of two dimensional surfaces and its importance in the quantization of strings. The path integral quantization approach to strings will be carefully analyzed to determine the correct effective measure for string theories. The choice of measure for the path integral is determined by differential geometric considerations. Once the measure is determined, the manifest diffeomorphism invariance of the theory will have to be broken by using the Faddeev-Popov ansatz. The gauge fixed theory is studied in detail with emphasis on the role of conformal and gravitational anomalies. In the analysis, the path integral formulation of the gauge fixed theory requires summing over all the distinct complex structures on the manifold

Analisis Keterampilan Geometri Siswa Dalam Memecahkan Masalah Geometri Berdasarkan Tingkat Berpikir Van Hiele

OpenAIRE

Muhassanah, Nuraini; Sujadi, Imam; Riyadi, Riyadi

2014-01-01

The objective of this research was to describe the VIII grade students geometry skills atSMP N 16 Surakarta in the level 0 (visualization), level 1 (analysis), and level 2 (informaldeduction) van Hiele level of thinking in solving the geometry problem. This research was aqualitative research in the form of case study analyzing deeply the students geometry skill insolving the geometry problem based on van Hiele level of thingking. The subject of this researchwas nine students of VIII grade at ...

Comparison of luminance based metrics in different lighting conditions

DEFF Research Database (Denmark)

Wienold, J.; Kuhn, T.E.; Christoffersen, J.

In this study, we evaluate established and newly developed metrics for predicting glare using data from three different research studies. The evaluation covers two different targets: 1. How well the user’s perception of glare magnitude correlates to the prediction of the glare metrics? 2. How well...... do the glare metrics describe the subjects’ disturbance by glare? We applied Spearman correlations, logistic regressions and an accuracy evaluation, based on an ROC-analysis. The results show that five of the twelve investigated metrics are failing at least one of the statistical tests. The other...... seven metrics CGI, modified DGI, DGP, Ev, average Luminance of the image Lavg, UGP and UGR are passing all statistical tests. DGP, CGI, DGI_mod and UGP have largest AUC and might be slightly more robust. The accuracy of the predictions of afore mentioned seven metrics for the disturbance by glare lies...

A bi-metric theory of gravitation

International Nuclear Information System (INIS)

Rosen, N.

1975-01-01

The bi-metric theory of gravitation proposed previously is simplified in that the auxiliary conditions are discarded, the two metric tensors being tied together only by means of the boundary conditions. Some of the properties of the field of a particle are investigated; there is no black hole, and it appears that no gravitational collapse can take place. Although the proposed theory and general relativity are at present observationally indistinguishable, some differences are pointed out which may some day be susceptible of observation. An alternative bi-metric theory is considered which gives for the precession of the perihelion 5/6 of the value given by general relativity; it seems less satisfactory than the present theory from the aesthetic point of view. (author)

Algorithms in Algebraic Geometry

CERN Document Server

Dickenstein, Alicia; Sommese, Andrew J

2008-01-01

In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

Prioritizing Urban Habitats for Connectivity Conservation: Integrating Centrality and Ecological Metrics.

Science.gov (United States)

Poodat, Fatemeh; Arrowsmith, Colin; Fraser, David; Gordon, Ascelin

2015-09-01

Connectivity among fragmented areas of habitat has long been acknowledged as important for the viability of biological conservation, especially within highly modified landscapes. Identifying important habitat patches in ecological connectivity is a priority for many conservation strategies, and the application of 'graph theory' has been shown to provide useful information on connectivity. Despite the large number of metrics for connectivity derived from graph theory, only a small number have been compared in terms of the importance they assign to nodes in a network. This paper presents a study that aims to define a new set of metrics and compares these with traditional graph-based metrics, used in the prioritization of habitat patches for ecological connectivity. The metrics measured consist of "topological" metrics, "ecological metrics," and "integrated metrics," Integrated metrics are a combination of topological and ecological metrics. Eight metrics were applied to the habitat network for the fat-tailed dunnart within Greater Melbourne, Australia. A non-directional network was developed in which nodes were linked to adjacent nodes. These links were then weighted by the effective distance between patches. By applying each of the eight metrics for the study network, nodes were ranked according to their contribution to the overall network connectivity. The structured comparison revealed the similarity and differences in the way the habitat for the fat-tailed dunnart was ranked based on different classes of metrics. Due to the differences in the way the metrics operate, a suitable metric should be chosen that best meets the objectives established by the decision maker.

Non-Euclidean geometry

CERN Document Server

Kulczycki, Stefan

2008-01-01

This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of suff

Comparative Study of Trace Metrics between Bibliometrics and Patentometrics

Directory of Open Access Journals (Sweden)

Fred Y. Ye

2016-06-01

Full Text Available Purpose: To comprehensively evaluate the overall performance of a group or an individual in both bibliometrics and patentometrics. Design/methodology/approach: Trace metrics were applied to the top 30 universities in the 2014 Academic Ranking of World Universities (ARWU — computer sciences, the top 30 ESI highly cited papers in the computer sciences field in 2014, as well as the top 30 assignees and the top 30 most cited patents in the National Bureau of Economic Research (NBER computer hardware and software category. Findings: We found that, by applying trace metrics, the research or marketing impact efficiency, at both group and individual levels, was clearly observed. Furthermore, trace metrics were more sensitive to the different publication-citation distributions than the average citation and h-index were. Research limitations: Trace metrics considered publications with zero citations as negative contributions. One should clarify how he/she evaluates a zero-citation paper or patent before applying trace metrics. Practical implications: Decision makers could regularly examinine the performance of their university/company by applying trace metrics and adjust their policies accordingly. Originality/value: Trace metrics could be applied both in bibliometrics and patentometrics and provide a comprehensive view. Moreover, the high sensitivity and unique impact efficiency view provided by trace metrics can facilitate decision makers in examining and adjusting their policies.

SPICE: A Geometry Information System Supporting Planetary Mapping, Remote Sensing and Data Mining

Science.gov (United States)

Acton, C.; Bachman, N.; Semenov, B.; Wright, E.

2013-01-01

SPICE is an information system providing space scientists ready access to a wide assortment of space geometry useful in planning science observations and analyzing the instrument data returned therefrom. The system includes software used to compute many derived parameters such as altitude, LAT/LON and lighting angles, and software able to find when user-specified geometric conditions are obtained. While not a formal standard, it has achieved widespread use in the worldwide planetary science community

Evaluating and Estimating the WCET Criticality Metric

DEFF Research Database (Denmark)

Jordan, Alexander

2014-01-01

a programmer (or compiler) from targeting optimizations the right way. A possible resort is to use a metric that targets WCET and which can be efficiently computed for all code parts of a program. Similar to dynamic profiling techniques, which execute code with input that is typically expected...... for the application, based on WCET analysis we can indicate how critical a code fragment is, in relation to the worst-case bound. Computing such a metric on top of static analysis, incurs a certain overhead though, which increases with the complexity of the underlying WCET analysis. We present our approach...... to estimate the Criticality metric, by relaxing the precision of WCET analysis. Through this, we can reduce analysis time by orders of magnitude, while only introducing minor error. To evaluate our estimation approach and share our garnered experience using the metric, we evaluate real-time programs, which...

A convergence theory for probabilistic metric spaces | Jäger ...

African Journals Online (AJOL)

We develop a theory of probabilistic convergence spaces based on Tardiff's neighbourhood systems for probabilistic metric spaces. We show that the resulting category is a topological universe and we characterize a subcategory that is isomorphic to the category of probabilistic metric spaces. Keywords: Probabilistic metric ...

Indefinite metric fields and the renormalization group

International Nuclear Information System (INIS)

Sherry, T.N.

1976-11-01

The renormalization group equations are derived for the Green functions of an indefinite metric field theory. In these equations one retains the mass dependence of the coefficient functions, since in the indefinite metric theories the masses cannot be neglected. The behavior of the effective coupling constant in the asymptotic and infrared limits is analyzed. The analysis is illustrated by means of a simple model incorporating indefinite metric fields. The model scales at first order, and at this order also the effective coupling constant has both ultra-violet and infra-red fixed points, the former being the bare coupling constant

Kerr-Newman metric in deSitter background

International Nuclear Information System (INIS)

Patel, L.K.; Koppar, S.S.; Bhatt, P.V.

1987-01-01

In addition to the Kerr-Newman metric with cosmological constant several other metrics are presented giving Kerr-Newman type solutions of Einstein-Maxwell field equations in the background of deSitter universe. The electromagnetic field in all the solutions is assumed to be source-free. A new metric of what may be termed as an electrovac rotating deSitter space-time- a space-time devoid of matter but containing source-free electromagnetic field and a null fluid with twisting rays-has been presented. In the absence of the electromagnetic field, these solutions reduce to those discussed by Vaidya (1984). 8 refs. (author)

The independence of software metrics taken at different life-cycle stages

Science.gov (United States)

Kafura, D.; Canning, J.; Reddy, G.

1984-01-01

Over the past few years a large number of software metrics have been proposed and, in varying degrees, a number of these metrics have been subjected to empirical validation which demonstrated the utility of the metrics in the software development process. Attempts to classify these metrics and to determine if the metrics in these different classes appear to be measuring distinct attributes of the software product are studied. Statistical analysis is used to determine the degree of relationship among the metrics.

Geometry and billiards

CERN Document Server

Tabachnikov, Serge

2005-01-01

Mathematical billiards describe the motion of a mass point in a domain with elastic reflections off the boundary or, equivalently, the behavior of rays of light in a domain with ideally reflecting boundary. From the point of view of differential geometry, the billiard flow is the geodesic flow on a manifold with boundary. This book is devoted to billiards in their relation with differential geometry, classical mechanics, and geometrical optics. The topics covered include variational principles of billiard motion, symplectic geometry of rays of light and integral geometry, existence and nonexistence of caustics, optical properties of conics and quadrics and completely integrable billiards, periodic billiard trajectories, polygonal billiards, mechanisms of chaos in billiard dynamics, and the lesser-known subject of dual (or outer) billiards. The book is based on an advanced undergraduate topics course (but contains more material than can be realistically taught in one semester). Although the minimum prerequisit...