On construction of two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space

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Saveliev, M.V.

1983-01-01

In the framework of the algebraic approach a construction of exactly integrable two-dimensional Riemannian manifolds embedded into enveloping Euclidean (pseudo-Euclidean) space Rsub(N) of an arbitrary dimension is presented. The construction is based on a reformulation of the Gauss, Peterson-Codazzi and Ricci equations in the form of a Lax-type representation in two-dimensional space. Here the Lax pair operators take the values in algebra SO(N)

Classification of non-Riemannian doubled-yet-gauged spacetime

Energy Technology Data Exchange (ETDEWEB)

Morand, Kevin [Universidad Andres Bello, Departamento de Ciencias Fisicas, Santiago de Chile (Chile); Universidad Tecnica Federico Santa Maria, Centro Cientifico-Tecnologico de Valparaiso, Departamento de Fisica, Valparaiso (Chile); Park, Jeong-Hyuck [Sogang University, Department of Physics, Seoul (Korea, Republic of); Institute for Basic Science (IBS), Center for Theoretical Physics of the Universe, Seoul (Korea, Republic of)

2017-10-15

Assuming O(D,D) covariant fields as the 'fundamental' variables, double field theory can accommodate novel geometries where a Riemannian metric cannot be defined, even locally. Here we present a complete classification of such non-Riemannian spacetimes in terms of two non-negative integers, (n, anti n), 0 ≤ n + anti n ≤ D. Upon these backgrounds, strings become chiral and anti-chiral over n and anti n directions, respectively, while particles and strings are frozen over the n + anti n directions. In particular, we identify (0, 0) as Riemannian manifolds, (1, 0) as non-relativistic spacetime, (1, 1) as Gomis-Ooguri non-relativistic string, (D-1, 0) as ultra-relativistic Carroll geometry, and (D, 0) as Siegel's chiral string. Combined with a covariant Kaluza-Klein ansatz which we further spell, (0, 1) leads to Newton-Cartan gravity. Alternative to the conventional string compactifications on small manifolds, non-Riemannian spacetime such as D = 10, (3, 3) may open a new scheme for the dimensional reduction from ten to four. (orig.)

Convex functions and optimization methods on Riemannian manifolds

CERN Document Server

Udrişte, Constantin

1994-01-01

This unique monograph discusses the interaction between Riemannian geometry, convex programming, numerical analysis, dynamical systems and mathematical modelling. The book is the first account of the development of this subject as it emerged at the beginning of the 'seventies. A unified theory of convexity of functions, dynamical systems and optimization methods on Riemannian manifolds is also presented. Topics covered include geodesics and completeness of Riemannian manifolds, variations of the p-energy of a curve and Jacobi fields, convex programs on Riemannian manifolds, geometrical constructions of convex functions, flows and energies, applications of convexity, descent algorithms on Riemannian manifolds, TC and TP programs for calculations and plots, all allowing the user to explore and experiment interactively with real life problems in the language of Riemannian geometry. An appendix is devoted to convexity and completeness in Finsler manifolds. For students and researchers in such diverse fields as pu...

Minimal Webs in Riemannian Manifolds

DEFF Research Database (Denmark)

Markvorsen, Steen

2008-01-01

For a given combinatorial graph $G$ a {\\it geometrization} $(G, g)$ of the graph is obtained by considering each edge of the graph as a $1-$dimensional manifold with an associated metric $g$. In this paper we are concerned with {\\it minimal isometric immersions} of geometrized graphs $(G, g......)$ into Riemannian manifolds $(N^{n}, h)$. Such immersions we call {\\em{minimal webs}}. They admit a natural 'geometric' extension of the intrinsic combinatorial discrete Laplacian. The geometric Laplacian on minimal webs enjoys standard properties such as the maximum principle and the divergence theorems, which...... are of instrumental importance for the applications. We apply these properties to show that minimal webs in ambient Riemannian spaces share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in such spaces. In particular we use appropriate versions of the divergence...

A Numerical Framework for Sobolev Metrics on the Space of Curves

DEFF Research Database (Denmark)

Bauer, Martin; Bruveris, Martins; Harms, Philipp

2017-01-01

Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable properties not present in lower order metrics...

On determining the isometry group of a Riemannian space

International Nuclear Information System (INIS)

Karlhede, A.; Maccallum, M.A.H.

1982-01-01

An extension of the recently discussed algorithm for deciding the equivalence problem for Riemannian metrics is presented. The extension determines the structure constants of the isometry group and enables us to obtain some information about its orbits, including the form of the Killing vectors in canonical coordinates. (author)

The three-body problem and equivariant Riemannian geometry

Science.gov (United States)

Alvarez-Ramírez, M.; García, A.; Meléndez, J.; Reyes-Victoria, J. G.

2017-08-01

We study the planar three-body problem with 1/r2 potential using the Jacobi-Maupertuis metric, making appropriate reductions by Riemannian submersions. We give a different proof of the Gaussian curvature's sign and the completeness of the space reported by Montgomery [Ergodic Theory Dyn. Syst. 25, 921-947 (2005)]. Moreover, we characterize the geodesics contained in great circles.

Scattering theory for Riemannian Laplacians

DEFF Research Database (Denmark)

Ito, Kenichi; Skibsted, Erik

In this paper we introduce a notion of scattering theory for the Laplace-Beltrami operator on non-compact, connected and complete Riemannian manifolds. A principal condition is given by a certain positive lower bound of the second fundamental form of angular submanifolds at infinity. Another...... condition is certain bounds of derivatives up to order one of the trace of this quantity. These conditions are shown to be optimal for existence and completeness of a wave operator. Our theory does not involve prescribed asymptotic behaviour of the metric at infinity (like asymptotic Euclidean or hyperbolic...

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.

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

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.

Single and multiple object tracking using log-euclidean Riemannian subspace and block-division appearance model.

Science.gov (United States)

Hu, Weiming; Li, Xi; Luo, Wenhan; Zhang, Xiaoqin; Maybank, Stephen; Zhang, Zhongfei

2012-12-01

Object appearance modeling is crucial for tracking objects, especially in videos captured by nonstationary cameras and for reasoning about occlusions between multiple moving objects. Based on the log-euclidean Riemannian metric on symmetric positive definite matrices, we propose an incremental log-euclidean Riemannian subspace learning algorithm in which covariance matrices of image features are mapped into a vector space with the log-euclidean Riemannian metric. Based on the subspace learning algorithm, we develop a log-euclidean block-division appearance model which captures both the global and local spatial layout information about object appearances. Single object tracking and multi-object tracking with occlusion reasoning are then achieved by particle filtering-based Bayesian state inference. During tracking, incremental updating of the log-euclidean block-division appearance model captures changes in object appearance. For multi-object tracking, the appearance models of the objects can be updated even in the presence of occlusions. Experimental results demonstrate that the proposed tracking algorithm obtains more accurate results than six state-of-the-art tracking algorithms.

L2-Harmonic Forms on Incomplete Riemannian Manifolds with Positive Ricci Curvature

Directory of Open Access Journals (Sweden)

Junya Takahashi

2018-05-01

Full Text Available We construct an incomplete Riemannian manifold with positive Ricci curvature that has non-trivial L 2 -harmonic forms and on which the L 2 -Stokes theorem does not hold. Therefore, a Bochner-type vanishing theorem does not hold for incomplete Riemannian manifolds.

Pseudo-Riemannian Novikov algebras

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Chen Zhiqi; Zhu Fuhai [School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 (China)], E-mail: chenzhiqi@nankai.edu.cn, E-mail: zhufuhai@nankai.edu.cn

2008-08-08

Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. Pseudo-Riemannian Novikov algebras denote Novikov algebras with non-degenerate invariant symmetric bilinear forms. In this paper, we find that there is a remarkable geometry on pseudo-Riemannian Novikov algebras, and give a special class of pseudo-Riemannian Novikov algebras.

Characterization of the Unit Tangent Sphere Bundle with $ g $-Natural Metric and Almost Contact B-metric Structure

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Farshad Firuzi

2017-06-01

Full Text Available We consider unit tangent sphere bundle of a Riemannian manifold $ (M,g $ as a $ (2n+1 $-dimensional manifold and we equip it with pseudo-Riemannian $ g $-natural almost contact B-metric structure. Then, by computing coefficients of the structure tensor $ F$, we completely characterize the unit tangent sphere bundle equipped to this structure, with respect to the relevant classification of almost contact B-metric structures, and determine a class such that the unit tangent sphere bundle with mentioned structure belongs to it. Also, we find some curvature conditions such that the mentioned structure satisfies each of eleven basic classes.

Multi-Frequency Polarimetric SAR Classification Based on Riemannian Manifold and Simultaneous Sparse Representation

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Fan Yang

2015-07-01

Full Text Available Normally, polarimetric SAR classification is a high-dimensional nonlinear mapping problem. In the realm of pattern recognition, sparse representation is a very efficacious and powerful approach. As classical descriptors of polarimetric SAR, covariance and coherency matrices are Hermitian semidefinite and form a Riemannian manifold. Conventional Euclidean metrics are not suitable for a Riemannian manifold, and hence, normal sparse representation classification cannot be applied to polarimetric SAR directly. This paper proposes a new land cover classification approach for polarimetric SAR. There are two principal novelties in this paper. First, a Stein kernel on a Riemannian manifold instead of Euclidean metrics, combined with sparse representation, is employed for polarimetric SAR land cover classification. This approach is named Stein-sparse representation-based classification (SRC. Second, using simultaneous sparse representation and reasonable assumptions of the correlation of representation among different frequency bands, Stein-SRC is generalized to simultaneous Stein-SRC for multi-frequency polarimetric SAR classification. These classifiers are assessed using polarimetric SAR images from the Airborne Synthetic Aperture Radar (AIRSAR sensor of the Jet Propulsion Laboratory (JPL and the Electromagnetics Institute Synthetic Aperture Radar (EMISAR sensor of the Technical University of Denmark (DTU. Experiments on single-band and multi-band data both show that these approaches acquire more accurate classification results in comparison to many conventional and advanced classifiers.

Geometric control theory and sub-Riemannian geometry

CERN Document Server

Boscain, Ugo; Gauthier, Jean-Paul; Sarychev, Andrey; Sigalotti, Mario

2014-01-01

This volume presents recent advances in the interaction between Geometric Control Theory and sub-Riemannian geometry. On the one hand, Geometric Control Theory used the differential geometric and Lie algebraic language for studying controllability, motion planning, stabilizability and optimality for control systems. The geometric approach turned out to be fruitful in applications to robotics, vision modeling, mathematical physics etc. On the other hand, Riemannian geometry and its generalizations, such as  sub-Riemannian, Finslerian  geometry etc., have been actively adopting methods developed in the scope of geometric control. Application of these methods  has led to important results regarding geometry of sub-Riemannian spaces, regularity of sub-Riemannian distances, properties of the group  of diffeomorphisms of sub-Riemannian manifolds, local geometry and equivalence of distributions and sub-Riemannian structures, regularity of the Hausdorff volume.

Dark energy and dark matter from hidden symmetry of gravity model with a non-Riemannian volume form

Energy Technology Data Exchange (ETDEWEB)

Guendelman, Eduardo [Ben-Gurion University of the Negev, Department of Physics, Beersheba (Israel); Nissimov, Emil; Pacheva, Svetlana [Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy, Sofia (Bulgaria)

2015-10-15

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold - one standard Riemannian given by √(-g) (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless ''dust'' fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe's epoch without evolution pathologies. (orig.)

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.

Metric Structures on Fibered Manifolds Through Partitions of Unity

Directory of Open Access Journals (Sweden)

Hulya Kadioglu

2016-05-01

Full Text Available The notion of partitions of unity is extremely useful as it allows one to extend local constructions on Euclidean patches to global ones. It is widely used in many fields in mathematics. Therefore, prolongation of this useful tool to another manifold may help constructing many geometric structures. In this paper, we construct a partition of unity on a fiber bundle by using a given partition of unity on the base manifold. On the other hand we show that the converse is also possible if it is a vector bundle. As an application, we define a Riemannian metric on the fiber bundle by using induced partition of unity on the fiber bundle.

Bilinear Regularized Locality Preserving Learning on Riemannian Graph for Motor Imagery BCI.

Science.gov (United States)

Xie, Xiaofeng; Yu, Zhu Liang; Gu, Zhenghui; Zhang, Jun; Cen, Ling; Li, Yuanqing

2018-03-01

In off-line training of motor imagery-based brain-computer interfaces (BCIs), to enhance the generalization performance of the learned classifier, the local information contained in test data could be used to improve the performance of motor imagery as well. Further considering that the covariance matrices of electroencephalogram (EEG) signal lie on Riemannian manifold, in this paper, we construct a Riemannian graph to incorporate the information of training and test data into processing. The adjacency and weight in Riemannian graph are determined by the geodesic distance of Riemannian manifold. Then, a new graph embedding algorithm, called bilinear regularized locality preserving (BRLP), is derived upon the Riemannian graph for addressing the problems of high dimensionality frequently arising in BCIs. With a proposed regularization term encoding prior information of EEG channels, the BRLP could obtain more robust performance. Finally, an efficient classification algorithm based on extreme learning machine is proposed to perform on the tangent space of learned embedding. Experimental evaluations on the BCI competition and in-house data sets reveal that the proposed algorithms could obtain significantly higher performance than many competition algorithms after using same filter process.

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

Exact solutions for isometric embeddings of pseudo-Riemannian manifolds

International Nuclear Information System (INIS)

Amery, G; Moodley, J

2014-01-01

Embeddings into higher dimensions are of direct importance in the study of higher dimensional theories of our Universe, in high energy physics and in classical general relativity. Theorems have been established that guarantee the existence of local and global codimension-1 embeddings between pseudo-Riemannian manifolds, particularly for Einstein embedding spaces. A technique has been provided to determine solutions to such embeddings. However, general solutions have not yet been found and most known explicit solutions are for embedded spaces with relatively simple Ricci curvature. Motivated by this, we have considered isometric embeddings of 4-dimensional pseudo-Riemannian spacetimes into 5-dimensional Einstein manifolds. We have applied the technique to treat specific 4-dimensional cases of interest in astrophysics and cosmology (including the global monopole exterior and Vaidya-de Sitter-class solutions), and provided novel physical insights into, for example, Einstein-Gauss-Bonnet gravity. Since difficulties arise in solving the 5-dimensional equations for given 4-dimensional spaces, we have also investigated embedded spaces, which admit bulks with a particular metric form. These analyses help to provide insight to the general embedding problem

Do extended bodies move alon.o the geodesics of the Riemannian space-time

International Nuclear Information System (INIS)

Denisov, V.I.; Logunov, A.A.; Mestvirishvili, M.A.

1980-01-01

Motion of a massive self-gravitating body in the gravitational field of a distant massive source has been considered in the post-Newtonian approximation of the arbitrary metric gravitational theory. The comparison of the massive body center of mass acceleration with that of a point one, moving in Riemannian space-time, whose metrics formally is equivalent to the metrics of two moving massive bodies, makes it clear that in any metric gravitation theory, possessing energy-momentum conservation lows for matter and gravitational field, taken together, massive body does not move generally speaking along the geodesics of Riemannian space-time. Application of the obtained general formulae to the system Earth-Sun and using of the experimental results from lunar-laser-ranging has shown that the Earth during its motion along the orbit, oscillates with respect to the reference geodesic of the geometry with the period of 1 hour and the amplitude not less than 10 -2 cm, which is a post-Newtonian quantity. Therefore the deviation of the Earth motion from the geodesic may be observed in a relevant experiment, which will have a post-Newtonian accuracy. The difference in accelerations of the Earth c.m. and a prob body makes up 10 -7 in the post-Newtonian approximation from the value of the Earth acceleration. The ratio of the passive gravitational mass (defined according to Will) to the inertial mass for the Earth is not equal to unity, and differs from it by the value of approximately 10 -8

Metrics for Probabilistic Geometries

DEFF Research Database (Denmark)

Tosi, Alessandra; Hauberg, Søren; Vellido, Alfredo

2014-01-01

the distribution over mappings is given by a Gaussian process. We treat the corresponding latent variable model as a Riemannian manifold and we use the expectation of the metric under the Gaussian process prior to define interpolating paths and measure distance between latent points. We show how distances...

Dynamic graphs, community detection, and Riemannian geometry

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Bakker, Craig; Halappanavar, Mahantesh; Visweswara Sathanur, Arun

2018-03-29

A community is a subset of a wider network where the members of that subset are more strongly connected to each other than they are to the rest of the network. In this paper, we consider the problem of identifying and tracking communities in graphs that change over time {dynamic community detection} and present a framework based on Riemannian geometry to aid in this task. Our framework currently supports several important operations such as interpolating between and averaging over graph snapshots. We compare these Riemannian methods with entry-wise linear interpolation and that the Riemannian methods are generally better suited to dynamic community detection. Next steps with the Riemannian framework include developing higher-order interpolation methods (e.g. the analogues of polynomial and spline interpolation) and a Riemannian least-squares regression method for working with noisy data.

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

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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.

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.)

Harmonic Riemannian Maps on Locally Conformal Kaehler Manifolds

Indian Academy of Sciences (India)

We study harmonic Riemannian maps on locally conformal Kaehler manifolds ( l c K manifolds). We show that if a Riemannian holomorphic map between l c K manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we ...

Riemannian geometry

CERN Document Server

Petersen, Peter

2016-01-01

Intended for a one year course, this text serves as a single source, introducing readers to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few Works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory. The book will appeal to a readership that have a basic knowledge of standard manifold theory, including tensors, forms, and Lie groups. Important revisions to the third edition include: a substantial addition of unique and enriching exercises scattered throughout the text; inclusion of an increased number of coordinate calculations of connection and curvature; addition of general formulas for curvature on Lie Groups and submersions; integration of variational calculus into the text allowing for an early treatment of the Sphere theorem using a proof by Berger; incorporation of several recent results about manifolds with posit...

Thermodynamic metrics and optimal paths.

Science.gov (United States)

Sivak, David A; Crooks, Gavin E

2012-05-11

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.

Needle decompositions in Riemannian geometry

CERN Document Server

Klartag, Bo'az

2017-01-01

The localization technique from convex geometry is generalized to the setting of Riemannian manifolds whose Ricci curvature is bounded from below. In a nutshell, the author's method is based on the following observation: When the Ricci curvature is non-negative, log-concave measures are obtained when conditioning the Riemannian volume measure with respect to a geodesic foliation that is orthogonal to the level sets of a Lipschitz function. The Monge mass transfer problem plays an important role in the author's analysis.

Riemannian computing in computer vision

CERN Document Server

Srivastava, Anuj

2016-01-01

This book presents a comprehensive treatise on Riemannian geometric computations and related statistical inferences in several computer vision problems. This edited volume includes chapter contributions from leading figures in the field of computer vision who are applying Riemannian geometric approaches in problems such as face recognition, activity recognition, object detection, biomedical image analysis, and structure-from-motion. Some of the mathematical entities that necessitate a geometric analysis include rotation matrices (e.g. in modeling camera motion), stick figures (e.g. for activity recognition), subspace comparisons (e.g. in face recognition), symmetric positive-definite matrices (e.g. in diffusion tensor imaging), and function-spaces (e.g. in studying shapes of closed contours).   ·         Illustrates Riemannian computing theory on applications in computer vision, machine learning, and robotics ·         Emphasis on algorithmic advances that will allow re-application in other...

The positive action conjecture and asymptotically euclidean metrics in quantum gravity

International Nuclear Information System (INIS)

Gibbons, G.W.; Pope, C.N.

1979-01-01

The positive action conjecture requires that the action of any asymptotically Euclidean 4-dimensional Riemannian metric be positive, vanishing if and only if the space is flat. Because any Ricci flat, asymptotically Euclidean metric has zero action and is local extremum of the action which is a local minimum at flat space, the conjecture requires that there are no Ricci flat asymptotically Euclidean metrics other than flat space, which would establish that flat space is the only local minimum. We prove this for metrics on R 4 and a large class of more complicated topologies and for self-dual metrics. We show that if Rsupμsubμ >= 0 there are no bound states of the Dirac equation and discuss the relevance to possible baryon non-conserving processes mediated by gravitational instantons. We conclude that these are forbidden in the lowest stationary phase approximation. We give a detailed discussion of instantons invariant under an SU(2) or SO(3) isometry group. We find all regular solutions, none of which is asymptotically Euclidean and all of which possess a further Killing vector. In an appendix we construct an approximate self-dual metric on K3 - the only simply connected compact manifold which admits a self-dual metric. (orig.) [de

The decomposition of global conformal invariants

CERN Document Server

Alexakis, Spyros

2012-01-01

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Dese

Higher-order Jordan Osserman pseudo-Riemannian manifolds

International Nuclear Information System (INIS)

Gilkey, Peter B; Ivanova, Raina; Zhang Tan

2002-01-01

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds

Higher-order Jordan Osserman pseudo-Riemannian manifolds

Energy Technology Data Exchange (ETDEWEB)

Gilkey, Peter B [Mathematics Department, University of Oregon, Eugene, OR 97403 (United States); Ivanova, Raina [Mathematics Department, University of Hawaii - Hilo, 200 W Kawili St, Hilo, HI 96720 (United States); Zhang Tan [Department of Mathematics and Statistics, Murray State University, Murray, KY 42071 (United States)

2002-09-07

We study the higher-order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and non-trivial examples of higher-order Osserman manifolds.

Comparison theorems in Riemannian geometry

CERN Document Server

Cheeger, Jeff

2008-01-01

The central theme of this book is the interaction between the curvature of a complete Riemannian manifold and its topology and global geometry. The first five chapters are preparatory in nature. They begin with a very concise introduction to Riemannian geometry, followed by an exposition of Toponogov's theorem-the first such treatment in a book in English. Next comes a detailed presentation of homogeneous spaces in which the main goal is to find formulas for their curvature. A quick chapter of Morse theory is followed by one on the injectivity radius. Chapters 6-9 deal with many of the most re

Comparison of exit time moment spectra for extrinsic metric balls

DEFF Research Database (Denmark)

Hurtado, Ana; Markvorsen, Steen; Palmer, Vicente

2012-01-01

We prove explicit upper and lower bounds for the $L^1$-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds $P^m$ in ambient Riemannian spaces $N^n$. We assume that $P$ and $N$ both have controlled radial curvatures (mean curvature and sectional curvature...... obtain new intrinsic comparison results for the exit time spectra for metric balls in the ambient manifolds $N^n$ themselves....

Natural metrics and least-committed priors for articulated tracking

DEFF Research Database (Denmark)

Hauberg, Søren; Sommer, Stefan Horst; Pedersen, Kim Steenstrup

2012-01-01

of joint positions, which is embedded in a high dimensional Euclidean space. This Riemannian manifold inherits the metric from the embedding space, such that distances are measured as the combined physical length that joints travel during movements. We then develop a least-committed Brownian motion model...

Wave fields in Weyl spaces and conditions for the existence of a preferred pseudo-Riemannian structure

International Nuclear Information System (INIS)

Audretsch, J.; Gaehler, F.; Straumann, N.

1984-01-01

Previous axiomatic approaches to general relativity which led to a Weylian structure of space-time are supplemented by a physical condition which implies the existence of a preferred pseudo-Riemannian structure. It is stipulated that the trajectories of the short wave limit of classical massive fields agree with the geodesics of the Weyl connection and it is shown that this is equivalent to the vanishing of the covariant derivative of a ''mass function'' of nontrivial Weyl type.This in turn is proven to be equivalent to the existence of a preferred metric of the conformal structure such that the Weyl connection is reducible to a connection of the bundle of orthonormal frames belonging to this distinguished metric. (orig.)

Embeddings for the Schwarzschild metric: classification and new results

International Nuclear Information System (INIS)

Paston, S A; Sheykin, A A

2012-01-01

We suggest a method to search the embeddings of Riemannian spaces with a high enough symmetry in a flat ambient space. It is based on a procedure of construction surfaces with a given symmetry. The method is used to classify the embeddings of the Schwarzschild metric which have the symmetry of this solution, and all such embeddings in a six-dimensional ambient space (i.e. a space with a minimal possible dimension) are constructed. Four of the six possible embeddings are already known, while the two others are new. One of the new embeddings is asymptotically flat, while the other embeddings in a six-dimensional ambient space do not have this property. The asymptotically flat embedding can be of use in the analysis of the many-body problem, as well as for the development of gravity description as a theory of a surface in a flat ambient space. (paper)

Riemannian multi-manifold modeling and clustering in brain networks

Science.gov (United States)

Slavakis, Konstantinos; Salsabilian, Shiva; Wack, David S.; Muldoon, Sarah F.; Baidoo-Williams, Henry E.; Vettel, Jean M.; Cieslak, Matthew; Grafton, Scott T.

2017-08-01

This paper introduces Riemannian multi-manifold modeling in the context of brain-network analytics: Brainnetwork time-series yield features which are modeled as points lying in or close to a union of a finite number of submanifolds within a known Riemannian manifold. Distinguishing disparate time series amounts thus to clustering multiple Riemannian submanifolds. To this end, two feature-generation schemes for brain-network time series are put forth. The first one is motivated by Granger-causality arguments and uses an auto-regressive moving average model to map low-rank linear vector subspaces, spanned by column vectors of appropriately defined observability matrices, to points into the Grassmann manifold. The second one utilizes (non-linear) dependencies among network nodes by introducing kernel-based partial correlations to generate points in the manifold of positivedefinite matrices. Based on recently developed research on clustering Riemannian submanifolds, an algorithm is provided for distinguishing time series based on their Riemannian-geometry properties. Numerical tests on time series, synthetically generated from real brain-network structural connectivity matrices, reveal that the proposed scheme outperforms classical and state-of-the-art techniques in clustering brain-network states/structures.

Proceedings – Mathematical Sciences | Indian Academy of Sciences

Indian Academy of Sciences (India)

The main purpose of the present paper is to construct Riemannian almost product structures on the (1, 1)-tensor bundle equipped with Cheeger–Gromoll type metric over a Riemannian manifold and present some results concerning these structures.

Piecewise linear manifolds: Einstein metrics and Ricci flows

International Nuclear Information System (INIS)

Schrader, Robert

2016-01-01

This article provides an attempt to extend concepts from the theory of Riemannian manifolds to piecewise linear (p.l.) spaces. In particular we propose an analogue of the Ricci tensor, which we give the name of an Einstein vector field . On a given set of p.l. spaces we define and discuss (normalized) Einstein flows. p.l. Einstein metrics are defined and examples are provided. Criteria for flows to approach Einstein metrics are formulated. Second variations of the total scalar curvature at a specific Einstein space are calculated. (paper)

Riemannian geometry in an orthogonal frame

CERN Document Server

Cartan, Elie Joseph

2001-01-01

Foreword by S S Chern. In 1926-27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course he solved a series of problems in Euclidean and non-Euclidean spaces, as well as a series of variational problems on geodesics. In 1960, Sergei P Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. This book has many innovations, such as the n

a Super Voxel-Based Riemannian Graph for Multi Scale Segmentation of LIDAR Point Clouds

Science.gov (United States)

Li, Minglei

2018-04-01

Automatically segmenting LiDAR points into respective independent partitions has become a topic of great importance in photogrammetry, remote sensing and computer vision. In this paper, we cast the problem of point cloud segmentation as a graph optimization problem by constructing a Riemannian graph. The scale space of the observed scene is explored by an octree-based over-segmentation with different depths. The over-segmentation produces many super voxels which restrict the structure of the scene and will be used as nodes of the graph. The Kruskal coordinates are used to compute edge weights that are proportional to the geodesic distance between nodes. Then we compute the edge-weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths between super voxel nodes on the scene surface. The final segmentation results are generated by clustering similar super voxels and cutting off the weak edges in the graph. The performance of this method was evaluated on LiDAR point clouds for both indoor and outdoor scenes. Additionally, extensive comparisons to state of the art techniques show that our algorithm outperforms on many metrics.

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...

Sub-Riemannian geometry and optimal transport

CERN Document Server

Rifford, Ludovic

2014-01-01

The book provides an introduction to sub-Riemannian geometry and optimal transport and presents some of the recent progress in these two fields. The text is completely self-contained: the linear discussion, containing all the proofs of the stated results, leads the reader step by step from the notion of distribution at the very beginning to the existence of optimal transport maps for Lipschitz sub-Riemannian structure. The combination of geometry presented from an analytic point of view and of optimal transport, makes the book interesting for a very large community. This set of notes grew from a series of lectures given by the author during a CIMPA school in Beirut, Lebanon.

Spinorial Characterizations of Surfaces into 3-dimensional Pseudo-Riemannian Space Forms

International Nuclear Information System (INIS)

Lawn, Marie-Amélie; Roth, Julien

2011-01-01

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. This generalizes a recent work of the first author for spacelike immersed Lorentzian surfaces in ℝ 2,1 to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0, 2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.

Curvature properties of four-dimensional Walker metrics

International Nuclear Information System (INIS)

Chaichi, M; Garcia-Rio, E; Matsushita, Y

2005-01-01

A Walker n-manifold is a semi-Riemannian manifold, which admits a field of parallel null r-planes, r ≤ n/2. In the present paper we study curvature properties of a Walker 4-manifold (M, g) which admits a field of parallel null 2-planes. The metric g is necessarily of neutral signature (+ + - -). Such a Walker 4-manifold is the lowest dimensional example not of Lorentz type. There are three functions of coordinates which define a Walker metric. Some recent work shows that a Walker 4-manifold of restricted type whose metric is characterized by two functions exhibits a large variety of symplectic structures, Hermitian structures, Kaehler structures, etc. For such a restricted Walker 4-manifold, we shall study mainly curvature properties, e.g., conditions for a Walker metric to be Einstein, Osserman, or locally conformally flat, etc. One of our main results is the exact solutions to the Einstein equations for a restricted Walker 4-manifold

New Riemannian Priors on the Univariate Normal Model

Directory of Open Access Journals (Sweden)

Salem Said

2014-07-01

Full Text Available The current paper introduces new prior distributions on the univariate normal model, with the aim of applying them to the classification of univariate normal populations. These new prior distributions are entirely based on the Riemannian geometry of the univariate normal model, so that they can be thought of as “Riemannian priors”. Precisely, if {pθ ; θ ∈ Θ} is any parametrization of the univariate normal model, the paper considers prior distributions G( θ - , γ with hyperparameters θ - ∈ Θ and γ > 0, whose density with respect to Riemannian volume is proportional to exp(−d2(θ, θ - /2γ2, where d2(θ, θ - is the square of Rao’s Riemannian distance. The distributions G( θ - , γ are termed Gaussian distributions on the univariate normal model. The motivation for considering a distribution G( θ - , γ is that this distribution gives a geometric representation of a class or cluster of univariate normal populations. Indeed, G( θ - , γ has a unique mode θ - (precisely, θ - is the unique Riemannian center of mass of G( θ - , γ, as shown in the paper, and its dispersion away from θ - is given by γ.  Therefore, one thinks of members of the class represented by G( θ - , γ as being centered around θ - and  lying within a typical  distance determined by γ. The paper defines rigorously the Gaussian distributions G( θ - , γ and describes an algorithm for computing maximum likelihood estimates of their hyperparameters. Based on this algorithm and on the Laplace approximation, it describes how the distributions G( θ - , γ can be used as prior distributions for Bayesian classification of large univariate normal populations. In a concrete application to texture image classification, it is shown that  this  leads  to  an  improvement  in  performance  over  the  use  of  conjugate  priors.

The Explicit Construction of Einstein Finsler Metrics with Non-Constant Flag Curvature

Directory of Open Access Journals (Sweden)

Enli Guo

2009-04-01

Full Text Available By using the Hawking Taub-NUT metric, this note gives an explicit construction of a 3-parameter family of Einstein Finsler metrics of non-constant flag curvature in terms of navigation representation.

A PEG Construction of LDPC Codes Based on the Betweenness Centrality Metric

Directory of Open Access Journals (Sweden)

BHURTAH-SEEWOOSUNGKUR, I.

2016-05-01

Full Text Available Progressive Edge Growth (PEG constructions are usually based on optimizing the distance metric by using various methods. In this work however, the distance metric is replaced by a different one, namely the betweenness centrality metric, which was shown to enhance routing performance in wireless mesh networks. A new type of PEG construction for Low-Density Parity-Check (LDPC codes is introduced based on the betweenness centrality metric borrowed from social networks terminology given that the bipartite graph describing the LDPC is analogous to a network of nodes. The algorithm is very efficient in filling edges on the bipartite graph by adding its connections in an edge-by-edge manner. The smallest graph size the new code could construct surpasses those obtained from a modified PEG algorithm - the RandPEG algorithm. To the best of the authors' knowledge, this paper produces the best regular LDPC column-weight two graphs. In addition, the technique proves to be competitive in terms of error-correcting performance. When compared to MacKay, PEG and other recent modified-PEG codes, the algorithm gives better performance over high SNR due to its particular edge and local graph properties.

On the de Rham–Wu decomposition for Riemannian and Lorentzian manifolds

International Nuclear Information System (INIS)

Galaev, Anton S

2014-01-01

It is explained how to find the de Rham decomposition of a Riemannian manifold and the Wu decomposition of a Lorentzian manifold. For that it is enough to find parallel symmetric bilinear forms on the manifold, and do some linear algebra. This result will allow to compute the connected holonomy group of an arbitrary Riemannian or Lorentzian manifold. (paper)

Greenroads : a sustainability performance metric for roadway design and construction.

Science.gov (United States)

2009-11-01

Greenroads is a performance metric for quantifying sustainable practices associated with roadway design and construction. Sustainability is defined as having seven key components: ecology, equity, economy, extent, expectations, experience and exposur...

Divergence theorem for symmetric (0,2)-tensor fields on a semi-Riemannian manifold with boundary

International Nuclear Information System (INIS)

Ezin, J.P.; Mouhamadou Hassirou; Tossa, J.

2005-08-01

We prove in this paper a divergence theorem for symmetric (0,2)-tensors on a semi-Riemannian manifold with boundary. As a consequence we establish the complete divergence theorem on a semi-Riemannian manifold with any kinds of smooth boundaries. This result contains the previous attempts to write this theorem on a semi-Riemannian manifold as Unal results. A vanishing theorem for gradient timelike Killing vector fields on Einstein semi-Riemannian manifolds is obtained. As a tool, an induced volume form is defined for a degenerate boundary by using a star like operator that we define on degenerate submanifolds. (author)

Steiner minimal trees in small neighbourhoods of points in Riemannian manifolds

Science.gov (United States)

Chikin, V. M.

2017-07-01

In contrast to the Euclidean case, almost no Steiner minimal trees with concrete boundaries on Riemannian manifolds are known. A result describing the types of Steiner minimal trees on a Riemannian manifold for arbitrary small boundaries is obtained. As a consequence, it is shown that for sufficiently small regular n-gons with n≥ 7 their boundaries without a longest side are Steiner minimal trees. Bibliography: 22 titles.

Quantum theory of spinor field in four-dimensional Riemannian space-time

International Nuclear Information System (INIS)

Shavokhina, N.S.

1996-01-01

The review deals with the spinor field in the four-dimensional Riemannian space-time. The field beys the Dirac-Fock-Ivanenko equation. Principles of quantization of the spinor field in the Riemannian space-time are formulated which in a particular case of the plane space-time are equivalent to the canonical rules of quantization. The formulated principles are exemplified by the De Sitter space-time. The study of quantum field theory in the De Sitter space-time is interesting because it itself leads to a method of an invariant well for plane space-time. However, the study of the quantum spinor field theory in an arbitrary Riemannian space-time allows one to take into account the influence of the external gravitational field on the quantized spinor field. 60 refs

STRUCTURE TENSOR IMAGE FILTERING USING RIEMANNIAN L1 AND L∞ CENTER-OF-MASS

Directory of Open Access Journals (Sweden)

Jesus Angulo

2014-06-01

Full Text Available Structure tensor images are obtained by a Gaussian smoothing of the dyadic product of gradient image. These images give at each pixel a n×n symmetric positive definite matrix SPD(n, representing the local orientation and the edge information. Processing such images requires appropriate algorithms working on the Riemannian manifold on the SPD(n matrices. This contribution deals with structure tensor image filtering based on Lp geometric averaging. In particular, L1 center-of-mass (Riemannian median or Fermat-Weber point and L∞ center-of-mass (Riemannian circumcenter can be obtained for structure tensors using recently proposed algorithms. Our contribution in this paper is to study the interest of L1 and L∞ Riemannian estimators for structure tensor image processing. In particular, we compare both for two image analysis tasks: (i structure tensor image denoising; (ii anomaly detection in structure tensor images.

Hoelder continuity of energy minimizer maps between Riemannian polyhedra

International Nuclear Information System (INIS)

Bouziane, Taoufik

2004-10-01

The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the Hoelder continuity of local energy minimizers between Riemannian polyhedra with the target spaces without focal points. With this new result, we also complete our existence theorem obtained elsewhere, and consequently we generalize completely, to the case of target polyhedra without focal points (which is a weaker geometric condition than the nonpositivity of the curvature), the Eells-Fuglede's existence and regularity theorem which is the new version of the famous Eells-Sampson's theorem. (author)

Quantum mechanics on Riemannian manifold in Schwinger's quantization approach II

International Nuclear Information System (INIS)

Chepilko, N.M.; Romanenko, A.V.

2001-01-01

The extended Schwinger quantization procedure is used for constructing quantum mechanics on a manifold with a group structure. The considered manifold M is a homogeneous Riemannian space with the given action of an isometry transformation group. Using the identification of M with the quotient space G/H, where H is the isotropy group of an arbitrary fixed point of M, we show that quantum mechanics on G/H possesses a gauge structure, described by a gauge potential that is the connection 1-form of the principal fiber bundle G(G/H, H). The coordinate representation of quantum mechanics and the procedure for selecting the physical sector of the states are developed. (orig.)

Spinorial characterizations of surfaces into 3-dimensional psuedo-Riemannian space forms

OpenAIRE

Lawn , Marie-Amélie; Roth , Julien

2011-01-01

9 pages; We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in $\\mathbb{R}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well ...

Conservation laws in quantum mechanics on a Riemannian manifold

International Nuclear Information System (INIS)

Chepilko, N.M.

1992-01-01

In Refs. 1-5 the quantum dynamics of a particle on a Riemannian manifold V n is considered. The advantage of Ref. 5, in comparison with Refs. 1-4, is the fact that in it the differential-geometric character of the theory and the covariant definition (via the known Lagrangian of the particle) of the algebra of quantum-mechanical operators on V n are mutually consistent. However, in Ref. 5 the procedure for calculating the expectation values of operators from the known wave function of the particle is not discussed. In the authors view, this question is problematical and requires special study. The essence of the problem is that integration on a Riemannian manifold V n , unlike that of a Euclidean manifold R n , is uniquely defined only for scalars. For this reason, the calculation of the expectation value of, e.g., the operator of the momentum or angular momentum of a particle on V n is not defined in the usual sense. However, this circumstance was not taken into account by the authors of Refs. 1-4, in which quantum mechanics on a Riemannian manifold V n was studied. In this paper the author considers the conservation laws and a procedure for calculating observable quantities in the classical mechanics (Sec. 2) and quantum mechanics (Sec. 3) of a particle on V n . It is found that a key role here is played by the Killing vectors of the Riemannian manifold V n . It is shown that the proposed approach to the problem satisfies the correspondence principle for both the classical and the quantum mechanics of a particle on a Euclidean manifold R n

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

Absence of embedded eigenvalues for Riemannian Laplacians

DEFF Research Database (Denmark)

Ito, Kenichi; Skibsted, Erik

Schrödinger operators on non-compact connected Riemannian manifolds. A principal example is given by a manifold with an end (possibly more than one) in which geodesic coordinates are naturally defined. In this case one of our geometric conditions is a positive lower bound of the second fundamenta...

Aspects of quasi-Riemannian Kaluza-Klein theory

International Nuclear Information System (INIS)

Viswanathan, K.S.; Wong, B.

1985-01-01

We consider the applications of quasi-Riemannian geometry in Kaluza-Klein theories. We find that such theories cannot be implemented for all choices of the tangent group G/sub T/ and internal space G/H for reasons of gauge invariance. Coupling of fermions to gravity poses further problems in these theories

Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors

Directory of Open Access Journals (Sweden)

Andrei A. Malykh

2013-11-01

Full Text Available We demonstrate how a combination of our recently developed methods of partner symmetries, symmetry reduction in group parameters and a new version of the group foliation method can produce noninvariant solutions of complex Monge-Ampère equation (CMA and provide a lift from invariant solutions of CMA satisfying Boyer-Finley equation to non-invariant ones. Applying these methods, we obtain a new noninvariant solution of CMA and the corresponding Ricci-flat anti-self-dual Einstein-Kähler metric with Euclidean signature without Killing vectors, together with Riemannian curvature two-forms. There are no singularities of the metric and curvature in a bounded domain if we avoid very special choices of arbitrary functions of a single variable in our solution. This metric does not describe gravitational instantons because the curvature is not concentrated in a bounded domain.

CMC Hypersurfaces on Riemannian and Semi-Riemannian Manifolds

International Nuclear Information System (INIS)

Perdomo, Oscar M.

2012-01-01

In this paper we generalize the explicit formulas for constant mean curvature (CMC) immersion of hypersurfaces of Euclidean spaces, spheres and hyperbolic spaces given in Perdomo (Asian J Math 14(1):73–108, 2010; Rev Colomb Mat 45(1):81–96, 2011) to provide explicit examples of several families of immersions with constant mean curvature and non constant principal curvatures, in semi-Riemannian manifolds with constant sectional curvature. In particular, we prove that every h is an element of [-1,-(2√n-1/n can be realized as the constant curvature of a complete immersion of S 1 n-1 x R in the (n + 1)-dimensional de Sitter space S 1 n+1 . We provide 3 types of immersions with CMC in the Minkowski space, 5 types of immersion with CMC in the de Sitter space and 5 types of immersion with CMC in the anti de Sitter space. At the end of the paper we analyze the families of examples that can be extended to closed hypersurfaces.

Robust Covariance Estimators Based on Information Divergences and Riemannian Manifold

Directory of Open Access Journals (Sweden)

Xiaoqiang Hua

2018-03-01

Full Text Available This paper proposes a class of covariance estimators based on information divergences in heterogeneous environments. In particular, the problem of covariance estimation is reformulated on the Riemannian manifold of Hermitian positive-definite (HPD matrices. The means associated with information divergences are derived and used as the estimators. Without resorting to the complete knowledge of the probability distribution of the sample data, the geometry of the Riemannian manifold of HPD matrices is considered in mean estimators. Moreover, the robustness of mean estimators is analyzed using the influence function. Simulation results indicate the robustness and superiority of an adaptive normalized matched filter with our proposed estimators compared with the existing alternatives.

A Riemannian scalar measure for diffusion tensor images

NARCIS (Netherlands)

Astola, L.J.; Fuster, A.; Florack, L.M.J.

2010-01-01

We study a well-known scalar quantity in Riemannian geometry, the Ricci scalar, in the context of Diffusion Tensor Imaging (DTI), which is an emerging non-invasive medical imaging modality. We derive a physical interpretation for the Ricci scalar and explore experimentally its significance in DTI.

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

Science.gov (United States)

Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir

2016-08-01

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

Conformal changes of metrics and the initial-value problem of general relativity

International Nuclear Information System (INIS)

Mielke, E.W.

1977-01-01

Conformal techniques are reviewed with respect to applications to the initial-value problem of general relativity. Invariant transverse traceless decompositions of tensors, one of its main tools, are related to representations of the group of 'conformeomorphisms' acting on the space of all Riemannian metrics on M. Conformal vector fields, a kernel in the decomposition, are analyzed on compact manifolds with constant scalar curvature. The realization of arbitrary functions as scalar curvature of conformally equivalent metrics, a generalization of Yamabe's (Osaka Math. J.; 12:12 (1960)) conjecture, is applied to the Hamiltonian constraint and to the issue of positive energy of gravitational fields. Various approaches to the solution of the initial-value equations produced by altering the scaling behaviour of the second fundamental form are compared. (author)

Pseudo harmonic morphisms on Riemannian polyhedra

International Nuclear Information System (INIS)

Aprodu, M.A.; Bouziane, T.

2004-10-01

The aim of this paper is to extend the notion of pseudo harmonic morphism (introduced by Loubeau) to the case when the source manifold is an admissible Riemannian polyhedron. We define these maps to be harmonic in the sense of Eells-Fuglede and pseudo-horizontally weakly conformal in our sense. We characterize them by means of germs of harmonic functions on the source polyhedron, in the sense of Korevaar-Schoen, and germs of holomorphic functions on the Kaehler target manifold. (author)

A special form of SPD covariance matrix for interpretation and visualization of data manipulated with Riemannian geometry

Science.gov (United States)

Congedo, Marco; Barachant, Alexandre

2015-01-01

Currently the Riemannian geometry of symmetric positive definite (SPD) matrices is gaining momentum as a powerful tool in a wide range of engineering applications such as image, radar and biomedical data signal processing. If the data is not natively represented in the form of SPD matrices, typically we may summarize them in such form by estimating covariance matrices of the data. However once we manipulate such covariance matrices on the Riemannian manifold we lose the representation in the original data space. For instance, we can evaluate the geometric mean of a set of covariance matrices, but not the geometric mean of the data generating the covariance matrices, the space of interest in which the geometric mean can be interpreted. As a consequence, Riemannian information geometry is often perceived by non-experts as a "black-box" tool and this perception prevents a wider adoption in the scientific community. Hereby we show that we can overcome this limitation by constructing a special form of SPD matrix embedding both the covariance structure of the data and the data itself. Incidentally, whenever the original data can be represented in the form of a generic data matrix (not even square), this special SPD matrix enables an exhaustive and unique description of the data up to second-order statistics. This is achieved embedding the covariance structure of both the rows and columns of the data matrix, allowing naturally a wide range of possible applications and bringing us over and above just an interpretability issue. We demonstrate the method by manipulating satellite images (pansharpening) and event-related potentials (ERPs) of an electroencephalography brain-computer interface (BCI) study. The first example illustrates the effect of moving along geodesics in the original data space and the second provides a novel estimation of ERP average (geometric mean), showing that, in contrast to the usual arithmetic mean, this estimation is robust to outliers. In

On the Chern-Gauss-Bonnet theorem for the noncommutative 4-sphere

Science.gov (United States)

Arnlind, Joakim; Wilson, Mitsuru

2017-01-01

We construct a differential calculus over the noncommutative 4-sphere in the framework of pseudo-Riemannian calculi, and show that for every metric in a conformal class of perturbations of the round metric, there exists a unique metric and torsion-free connection. Furthermore, we find a localization of the projective module corresponding to the space of vector fields, which allows us to formulate a Chern-Gauss-Bonnet type theorem for the noncommutative 4-sphere.

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.

Geometric calculus: a new computational tool for Riemannian geometry

International Nuclear Information System (INIS)

Moussiaux, A.; Tombal, P.

1988-01-01

We compare geometric calculus applied to Riemannian geometry with Cartan's exterior calculus method. The correspondence between the two methods is clearly established. The results obtained by a package written in an algebraic language and doing general manipulations on multivectors are compared. We see that the geometric calculus is as powerful as exterior calculus

On Averaging Rotations

DEFF Research Database (Denmark)

Gramkow, Claus

1999-01-01

In this article two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very offten the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belo...... approximations to the Riemannian metric, and that the subsequent corrections are inherient in the least squares estimation. Keywords: averaging rotations, Riemannian metric, matrix, quaternion......In this article two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very offten the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong...

Scale-invariant gravity: spacetime recovered

International Nuclear Information System (INIS)

Kelleher, Bryan

2004-01-01

The configuration space of general relativity is superspace-the space of all Riemannian 3-metrics modulo diffeomorphisms. However, it has been argued that the configuration space for gravity should be conformal superspace-the space of all Riemannian 3-metrics modulo diffeomorphisms and conformal transformations. Recently a manifestly three-dimensional theory was constructed with conformal superspace as the configuration space. Here a fully four-dimensional action is constructed so as to be invariant under conformal transformations of the 4-metric using general relativity as a guide. This action is then decomposed to a (3 + 1)-dimensional form and from this to its Jacobi form. The surprising thing is that the new theory turns out to be precisely the original three-dimensional theory. The physical data are identified and used to find the physical representation of the theory. In this representation the theory is extremely similar to general relativity. The clarity of the four-dimensional picture should prove very useful for comparing the theory with those aspects of general relativity which are usually treated in the four-dimensional framework

On integrability of certain rank 2 sub-Riemannian structures

Czech Academy of Sciences Publication Activity Database

Kruglikov, B.S.; Vollmer, A.; Lukes-Gerakopoulos, Georgios

2017-01-01

Roč. 22, č. 5 (2017), s. 502-519 ISSN 1560-3547 R&D Projects: GA ČR(CZ) GJ17-06962Y Institutional support: RVO:67985815 Keywords : sub-Riemannian geodesic flow * Killing tensor * integral Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics OBOR OECD: Astronomy (including astrophysics,space science) Impact factor: 1.562, year: 2016

Conformal pure radiation with parallel rays

International Nuclear Information System (INIS)

Leistner, Thomas; Paweł Nurowski

2012-01-01

We define pure radiation metrics with parallel rays to be n-dimensional pseudo-Riemannian metrics that admit a parallel null line bundle K and whose Ricci tensor vanishes on vectors that are orthogonal to K. We give necessary conditions in terms of the Weyl, Cotton and Bach tensors for a pseudo-Riemannian metric to be conformal to a pure radiation metric with parallel rays. Then, we derive conditions in terms of the tractor calculus that are equivalent to the existence of a pure radiation metric with parallel rays in a conformal class. We also give analogous results for n-dimensional pseudo-Riemannian pp-waves. (paper)

The metric and curvature properties of H-space

International Nuclear Information System (INIS)

Hansen, R.O.; Newman, E.T.; Penrose, R.; Tod, K.P.

1978-01-01

The space H of asymptotically (left-) shear-free cuts of the future null infinity (good cuts) of an asymptotically flat space-time M is defined. The connection between this space and the asymptotic projective twistor space of M is discussed, and this relation is used to prove that H is four-complex-dimensional for sufficiently 'calm' gravitational radiation in M. The metric on H-space is defined by a simple contour integral expression and is found to be complex Riemannian. The good cut equation governing H-space is solved to three orders by a Taylor series and the solution is used to demonstrate that the curvature of H-space is always a self dual (left flat) solution of the Einstein vacuum equations. (author)

Transformation optics, isotropic chiral media and non-Riemannian geometry

International Nuclear Information System (INIS)

Horsley, S A R

2011-01-01

The geometrical interpretation of electromagnetism in transparent media (transformation optics) is extended to include chiral media that are isotropic but inhomogeneous. It was found that such media may be described through introducing the non-Riemannian geometrical property of torsion into the Maxwell equations, and it is shown how such an interpretation may be applied to the design of optical devices.

On the concircular curvature tensor of Riemannian manifolds

International Nuclear Information System (INIS)

Rahman, M.S.; Lal, S.

1990-06-01

Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs

Geometric Description of Fibre Bundle Surface for Birkhoff System

International Nuclear Information System (INIS)

Li-Mei, Cao; Hua-Fei, Sun; Zhen-Ning, Zhang

2009-01-01

A fibre bundle surface for the Birkhoff system is constructed. The metric and the Riemannian connection of the surface are defined and the representation of the Gaussian curvature of this surface is presented. Finally, three examples for the Birkhoff system are given to illustrate our results. (general)

Einstein solvmanifolds and the pre-Einstein derivation

OpenAIRE

Nikolayevsky, Y.

2008-01-01

An Einstein nilradical is a nilpotent Lie algebra, which can be the nilradical of a metric Einstein solvable Lie algebra. The classification of Riemannian Einstein solvmanifolds (possibly, of all noncompact homogeneous Einstein spaces) can be reduced to determining, which nilpotent Lie algebras are Einstein nilradicals and to finding, for every Einstein nilradical, its Einstein metric solvable extension. For every nilpotent Lie algebra, we construct an (essentially unique) derivation, the pre...

Maxwell Strata and Cut Locus in the Sub-Riemannian Problem on the Engel Group

Science.gov (United States)

Ardentov, Andrei A.; Sachkov, Yuri L.

2017-12-01

We consider the nilpotent left-invariant sub-Riemannian structure on the Engel group. This structure gives a fundamental local approximation of a generic rank 2 sub-Riemannian structure on a 4-manifold near a generic point (in particular, of the kinematic models of a car with a trailer). On the other hand, this is the simplest sub-Riemannian structure of step three. We describe the global structure of the cut locus (the set of points where geodesics lose their global optimality), the Maxwell set (the set of points that admit more than one minimizer), and the intersection of the cut locus with the caustic (the set of conjugate points along all geodesics). The group of symmetries of the cut locus is described: it is generated by a one-parameter group of dilations R+ and a discrete group of reflections Z2 × Z2 × Z2. The cut locus admits a stratification with 6 three-dimensional strata, 12 two-dimensional strata, and 2 one-dimensional strata. Three-dimensional strata of the cut locus are Maxwell strata of multiplicity 2 (for each point there are 2 minimizers). Two-dimensional strata of the cut locus consist of conjugate points. Finally, one-dimensional strata are Maxwell strata of infinite multiplicity, they consist of conjugate points as well. Projections of sub-Riemannian geodesics to the 2-dimensional plane of the distribution are Euler elasticae. For each point of the cut locus, we describe the Euler elasticae corresponding to minimizers coming to this point. Finally, we describe the structure of the optimal synthesis, i. e., the set of minimizers for each terminal point in the Engel group.

Does Negative Type Characterize the Round Sphere?

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2007-01-01

We discuss the measure theoretic metric invariants extent, mean distance and symmetry ratio and their relation to the concept of negative type of a metric space. A conjecture stating that a compact Riemannian manifold with symmetry ratio 1 must be a round sphere, was put forward in a previous paper....... We resolve this conjecture in the class of Riemannian symmetric spaces by showing, that a Riemannian manifold with symmetry ratio 1 must be of negative type and that the only compact Riemannian symmetric spaces of negative type are the round spheres....

On Riemannian manifolds (Mn, g) of quasi-constant curvature

International Nuclear Information System (INIS)

Rahman, M.S.

1995-07-01

A Riemannian manifold (M n , g) of quasi-constant curvature is defined. It is shown that an (M n , g) in association with other class of manifolds gives rise, under certain conditions, to a manifold of quasi-constant curvature. Some observations on how a manifold of quasi-constant curvature accounts for a pseudo Ricci-symmetric manifold and quasi-umbilical hypersurface are made. (author). 10 refs

An existence result of energy minimizer maps between Riemannian polyhedra

International Nuclear Information System (INIS)

Bouziane, T.

2004-06-01

In this paper, we prove the existence of energy minimizers in each free homotopy class of maps between polyhedra with target space without focal points. Our proof involves a careful study of some geometric properties of Riemannian polyhedra without focal points. Among other things, we show that on the relevant polyhedra, there exists a convex supporting function. (author)

Special metrics and group actions in geometry

CERN Document Server

Fino, Anna; Musso, Emilio; Podestà, Fabio; Vezzoni, Luigi

2017-01-01

The volume is a follow-up to the INdAM meeting “Special metrics and quaternionic geometry” held in Rome in November 2015. It offers a panoramic view of a selection of cutting-edge topics in differential geometry, including 4-manifolds, quaternionic and octonionic geometry, twistor spaces, harmonic maps, spinors, complex and conformal geometry, homogeneous spaces and nilmanifolds, special geometries in dimensions 5–8, gauge theory, symplectic and toric manifolds, exceptional holonomy and integrable systems. The workshop was held in honor of Simon Salamon, a leading international scholar at the forefront of academic research who has made significant contributions to all these subjects. The articles published here represent a compelling testimony to Salamon’s profound and longstanding impact on the mathematical community. Target readership includes graduate students and researchers working in Riemannian and complex geometry, Lie theory and mathematical physics.

On some hypersurfaces with time like normal bundle in pseudo Riemannian space forms

International Nuclear Information System (INIS)

Kashani, S.M.B.

1995-12-01

In this work we classify immersed hypersurfaces with constant sectional curvature in pseudo Riemannian space forms if the normal bundle is time like and the mean curvature is constant. (author). 9 refs

Diffeomorphometry and geodesic positioning systems for human anatomy.

Science.gov (United States)

Miller, Michael I; Younes, Laurent; Trouvé, Alain

2014-03-01

The Computational Anatomy project has largely been a study of large deformations within a Riemannian framework as an efficient point of view for generating metrics between anatomical configurations. This approach turns D'Arcy Thompson's comparative morphology of human biological shape and form into a metrizable space. Since the metric is constructed based on the geodesic length of the flows of diffeomorphisms connecting the forms, we call it diffeomorphometry . Just as importantly, since the flows describe algebraic group action on anatomical submanifolds and associated functional measurements, they become the basis for positioning information, which we term geodesic positioning . As well the geodesic connections provide Riemannian coordinates for locating forms in the anatomical orbit, which we call geodesic coordinates . These three components taken together - the metric, geodesic positioning of information, and geodesic coordinates - we term the geodesic positioning system . We illustrate via several examples in human and biological coordinate systems and machine learning of the statistical representation of shape and form.

Completion of a Dislocated Metric Space

Directory of Open Access Journals (Sweden)

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.

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...

Contour Propagation With Riemannian Elasticity Regularization

DEFF Research Database (Denmark)

Bjerre, Troels; Hansen, Mads Fogtmann; Sapru, W.

2011-01-01

Purpose/Objective(s): Adaptive techniques allow for correction of spatial changes during the time course of the fractionated radiotherapy. Spatial changes include tumor shrinkage and weight loss, causing tissue deformation and residual positional errors even after translational and rotational image...... the planning CT onto the rescans and correcting to reflect actual anatomical changes. For deformable registration, a free-form, multi-level, B-spline deformation model with Riemannian elasticity, penalizing non-rigid local deformations, and volumetric changes, was used. Regularization parameters was defined...... on the original delineation and tissue deformation in the time course between scans form a better starting point than rigid propagation. There was no significant difference of locally and globally defined regularization. The method used in the present study suggests that deformed contours need to be reviewed...

On Darboux's approach to R-separability of variables. Classification of conformally flat 4-dimensional binary metrics

International Nuclear Information System (INIS)

Szereszewski, A; Sym, A

2015-01-01

The standard method of separation of variables in PDEs called the Stäckel–Robertson–Eisenhart (SRE) approach originated in the papers by Robertson (1928 Math. Ann. 98 749–52) and Eisenhart (1934 Ann. Math. 35 284–305) on separability of variables in the Schrödinger equation defined on a pseudo-Riemannian space equipped with orthogonal coordinates, which in turn were based on the purely classical mechanics results by Paul Stäckel (1891, Habilitation Thesis, Halle). These still fundamental results have been further extended in diverse directions by e.g. Havas (1975 J. Math. Phys. 16 1461–8; J. Math. Phys. 16 2476–89) or Koornwinder (1980 Lecture Notes in Mathematics 810 (Berlin: Springer) pp 240–63). The involved separability is always ordinary (factor R = 1) and regular (maximum number of independent parameters in separation equations). A different approach to separation of variables was initiated by Gaston Darboux (1878 Ann. Sci. E.N.S. 7 275–348) which has been almost completely forgotten in today’s research on the subject. Darboux’s paper was devoted to the so-called R-separability of variables in the standard Laplace equation. At the outset he did not make any specific assumption about the separation equations (this is in sharp contrast to the SRE approach). After impressive calculations Darboux obtained a complete solution of the problem. He found not only eleven cases of ordinary separability Eisenhart (1934 Ann. Math. 35 284–305) but also Darboux–Moutard–cyclidic metrics (Bôcher 1894 Ueber die Reihenentwickelungen der Potentialtheorie (Leipzig: Teubner)) and non-regularly separable Dupin-cyclidic metrics as well. In our previous paper Darboux’s approach was extended to the case of the stationary Schrödinger equation on Riemannian spaces admitting orthogonal coordinates. In particular the class of isothermic metrics was defined (isothermicity of the metric is a necessary condition for its R-separability). An important sub

Riemannian geometry and geometric analysis

CERN Document Server

Jost, Jürgen

2017-01-01

This established reference work continues to provide its readers with a gateway to some of the most interesting developments in contemporary geometry. It offers insight into a wide range of topics, including fundamental concepts of Riemannian geometry, such as geodesics, connections and curvature; the basic models and tools of geometric analysis, such as harmonic functions, forms, mappings, eigenvalues, the Dirac operator and the heat flow method; as well as the most important variational principles of theoretical physics, such as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of quantum field theory. The present volume connects all these topics in a systematic geometric framework. At the same time, it equips the reader with the working tools of the field and enables her or him to delve into geometric research.  The 7th edition has been systematically reorganized and updated. Almost no page has been left unchanged. It also includes new material, for instance on symplectic geometry, as well as the B...

Spherical-type hypersurfaces in a Riemannian manifold

International Nuclear Information System (INIS)

Ezin, J.P.; Rigoli, M.

1988-06-01

Let M be a compact hypersurface immersed in R n and let K and L be its mean curvature function and scalar curvature respectively. A classical global problem concerning these two geometrical quantities is to find out if assuming that either K or L is constant and under some additional assumptions M is a sphere. It was demonstrated that assuming the immersion to be an embedding, the consistency of K implies M to be spherical. It was also demonstrated that the sphere is the only compact hypersurface with constant scalar curvature embedded in Euclidean space. In this paper we give a generalization of these results when the ambient space is an appropriate Riemannian manifold (N, h). 17 refs

Existence of parallel spinors on non-simply-connected Riemannian manifolds

International Nuclear Information System (INIS)

McInnes, B.

1997-04-01

It is well known, and important for applications, that Ricci-flat Riemannian manifolds of non-generic holonomy always admit a parallel [covariant constant] spinor if they are simply connected. The non-simply-connected case is much more subtle, however. We show that a parallel spinor can still be found in this case provided that the [real] dimension is not a multiple of four, and provided that the spin structure is carefully chosen. (author). 10 refs

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

On generalized de Rham-Hodge complexes, the related characteristic Chern classes and some applications to integrable multi-dimensional differential systems on Riemannian manifolds

International Nuclear Information System (INIS)

Bogolubov, Nikolai N. Jr.; Prykarpatsky, Anatoliy K.

2006-12-01

The differential-geometric aspects of generalized de Rham-Hodge complexes naturally related with integrable multi-dimensional differential systems of M. Gromov type, as well as the geometric structure of Chern characteristic classes are studied. Special differential invariants of the Chern type are constructed, their importance for the integrability of multi-dimensional nonlinear differential systems on Riemannian manifolds is discussed. An example of the three-dimensional Davey-Stewartson type nonlinear strongly integrable differential system is considered, its Cartan type connection mapping and related Chern type differential invariants are analyzed. (author)

On Averaging Rotations

DEFF Research Database (Denmark)

Gramkow, Claus

2001-01-01

In this paper two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very often the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong ...... approximations to the Riemannian metric, and that the subsequent corrections are inherent in the least squares estimation.......In this paper two common approaches to averaging rotations are compared to a more advanced approach based on a Riemannian metric. Very often the barycenter of the quaternions or matrices that represent the rotations are used as an estimate of the mean. These methods neglect that rotations belong...

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...

Riemannian and Lorentzian flow-cut theorems

Science.gov (United States)

Headrick, Matthew; Hubeny, Veronika E.

2018-05-01

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut (MFMC) theorem for boundary regions, applied recently to develop a ‘bit-thread’ interpretation of holographic entanglement entropies. We also prove various properties of the max flow and min cut, including respective nesting properties. In the Lorentzian setting, we prove the analogous MFMC theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1. This theorem includes as a special case a continuum version of Dilworth’s theorem from the theory of partially ordered sets. We include a brief review of the necessary tools from the theory of convex optimization, in particular Lagrangian duality and convex relaxation.

Validation of the updated ArthroS simulator: face and construct validity of a passive haptic virtual reality simulator with novel performance metrics.

Science.gov (United States)

Garfjeld Roberts, Patrick; Guyver, Paul; Baldwin, Mathew; Akhtar, Kash; Alvand, Abtin; Price, Andrew J; Rees, Jonathan L

2017-02-01

To assess the construct and face validity of ArthroS, a passive haptic VR simulator. A secondary aim was to evaluate the novel performance metrics produced by this simulator. Two groups of 30 participants, each divided into novice, intermediate or expert based on arthroscopic experience, completed three separate tasks on either the knee or shoulder module of the simulator. Performance was recorded using 12 automatically generated performance metrics and video footage of the arthroscopic procedures. The videos were blindly assessed using a validated global rating scale (GRS). Participants completed a survey about the simulator's realism and training utility. This new simulator demonstrated construct validity of its tasks when evaluated against a GRS (p ≤ 0.003 in all cases). Regarding it's automatically generated performance metrics, established outputs such as time taken (p ≤ 0.001) and instrument path length (p ≤ 0.007) also demonstrated good construct validity. However, two-thirds of the proposed 'novel metrics' the simulator reports could not distinguish participants based on arthroscopic experience. Face validity assessment rated the simulator as a realistic and useful tool for trainees, but the passive haptic feedback (a key feature of this simulator) is rated as less realistic. The ArthroS simulator has good task construct validity based on established objective outputs, but some of the novel performance metrics could not distinguish between surgical experience. The passive haptic feedback of the simulator also needs improvement. If simulators could offer automated and validated performance feedback, this would facilitate improvements in the delivery of training by allowing trainees to practise and self-assess.

Metric space construction for the boundary of space-time

International Nuclear Information System (INIS)

Meyer, D.A.

1986-01-01

A distance function between points in space-time is defined and used to consider the manifold as a topological metric space. The properties of the distance function are investigated: conditions under which the metric and manifold topologies agree, the relationship with the causal structure of the space-time and with the maximum lifetime function of Wald and Yip, and in terms of the space of causal curves. The space-time is then completed as a topological metric space; the resultant boundary is compared with the causal boundary and is also calculated for some pertinent examples

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 ...

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)

Perturbative stability of the approximate Killing field eigenvalue problem

International Nuclear Information System (INIS)

Beetle, Christopher; Wilder, Shawn

2014-01-01

An approximate Killing field may be defined on a compact, Riemannian geometry by solving an eigenvalue problem for a certain elliptic operator. This paper studies the effect of small perturbations in the Riemannian metric on the resulting vector field. It shows that small metric perturbations, as measured using a Sobolev-type supremum norm on the space of Riemannian geometries on a fixed manifold, yield small perturbations in the approximate Killing field, as measured using a Hilbert-type square integral norm. It also discusses applications to the problem of computing the spin of a generic black hole in general relativity. (paper)

Almost Kaehler Ricci Flows and Einstein and Lagrange-Finsler Structures on Lie Algebroids

CERN Document Server

Vacaru, Sergiu I

2015-01-01

In this work we investigate Ricci flows of almost Kaehler structures on Lie algebroids when the fundamental geometric objects are completely determined by (semi) Riemannian metrics, or effective) regular generating Lagrange/ Finsler, functions. There are constructed canonical almost symplectic connections for which the geometric flows can be represented as gradient ones and characterized by nonholonomic deformations of Grigory Perelman's functionals. The first goal of this paper is to define such thermodynamical type values and derive almost K\\"ahler - Ricci geometric evolution equations. The second goal is to study how fixed Lie algebroid, i.e. Ricci soliton, configurations can be constructed for Riemannian manifolds and/or (co) tangent bundles endowed with nonholonomic distributions modelling (generalized) Einstein or Finsler - Cartan spaces. Finally, there are provided some examples of generic off-diagonal solutions for Lie algebroid type Ricci solitons and (effective) Einstein and Lagrange-Finsler algebro...

Segmentation of High Angular Resolution Diffusion MRI using Sparse Riemannian Manifold Clustering

Science.gov (United States)

Wright, Margaret J.; Thompson, Paul M.; Vidal, René

2015-01-01

We address the problem of segmenting high angular resolution diffusion imaging (HARDI) data into multiple regions (or fiber tracts) with distinct diffusion properties. We use the orientation distribution function (ODF) to represent HARDI data and cast the problem as a clustering problem in the space of ODFs. Our approach integrates tools from sparse representation theory and Riemannian geometry into a graph theoretic segmentation framework. By exploiting the Riemannian properties of the space of ODFs, we learn a sparse representation for each ODF and infer the segmentation by applying spectral clustering to a similarity matrix built from these representations. In cases where regions with similar (resp. distinct) diffusion properties belong to different (resp. same) fiber tracts, we obtain the segmentation by incorporating spatial and user-specified pairwise relationships into the formulation. Experiments on synthetic data evaluate the sensitivity of our method to image noise and the presence of complex fiber configurations, and show its superior performance compared to alternative segmentation methods. Experiments on phantom and real data demonstrate the accuracy of the proposed method in segmenting simulated fibers, as well as white matter fiber tracts of clinical importance in the human brain. PMID:24108748

Transversal Dirac families in Riemannian foliations

International Nuclear Information System (INIS)

Glazebrook, J.F.; Kamber, F.W.

1991-01-01

We describe a family of differential operators parametrized by the transversal vector potentials of a Riemannian foliation relative to the Clifford algebra of the foliation. This family is non-elliptic but in certain ways behaves like a standard Dirac family in the absolute case as a result of its elliptic-like regularity properties. The analytic and topological indices of this family are defined as elements of K-theory in the parameter space. We indicate how the cohomology of the parameter space is described via suitable maps to Fredholm operators. We outline the proof of a theorem of Vafa-Witten type on uniform bounds for the eigenvalues of this family using a spectral flow argument. A determinant operator is also defined with the appropriate zeta function regularization dependent on the codimension of the foliation. With respect to a generalized coupled Dirac-Yang-Mills system, we indicate how chiral anomalies are located relative to the foliation. (orig.)

Gravitational Metric Tensor Exterior to Rotating Homogeneous ...

African Journals Online (AJOL)

The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...

Absolute Monotonicity of Functions Related To Estimates of First Eigenvalue of Laplace Operator on Riemannian Manifolds

Directory of Open Access Journals (Sweden)

Feng Qi

2014-10-01

Full Text Available The authors find the absolute monotonicity and complete monotonicity of some functions involving trigonometric functions and related to estimates the lower bounds of the first eigenvalue of Laplace operator on Riemannian manifolds.

On defects of the volume and curvature of the Robertson-Walker metric and construction of cosmological models

International Nuclear Information System (INIS)

Gackstatter, F.

1987-01-01

For the Robertson-Walker metric (RWM) normal coordinates are constructed and the Riemann curvature tensor is determined. Then results on the defects of the volume and curvature, derived formerly, are applied to the RWM and to cosmological models. Finally cosmological models are constructed, they describe different states of the development of the cosmos: p ∼ 0, 1/3u, 2/3u, in a unified form. A Laurent expansion of the density of energy u and pressure p is used to solve the Friedmann equations. (author)

Towards a theory of macroscopic gravity

International Nuclear Information System (INIS)

Zalaletdinov, R.M.

1993-01-01

By averaging out Cartan's structure equations for a four-dimensional Riemannian space over space regions, the structure equations for the averaged space have been derived with the procedure being valid on an arbitrary Riemannian space. The averaged space is characterized by a metric, Riemannian and non-Riemannian curvature 2-forms, and correlation 2-, 3- and 4-forms, an affine deformation 1-form being due to the non-metricity of one of two connection 1-forms. Using the procedure for the space-time averaging of the Einstein equations produces the averaged ones with the terms of geometric correction by the correlation tensors. The equations of motion for averaged energy momentum, obtained by averaging out the coritracted Bianchi identifies, also include such terms. Considering the gravitational induction tensor to be the Riemannian curvature tensor (the non-Riemannian one is then the field tensor), a theorem is proved which relates the algebraic structure of the averaged microscopic metric to that of the induction tensor. It is shown that the averaged Einstein equations can be put in the form of the Einstein equations with the conserved macroscopic energy-momentum tensor of a definite structure including the correlation functions. By using the high-frequency approximation of Isaacson with second-order correction to the microscopic metric, the self-consistency and compatibility of the equations and relations obtained are shown. Macrovacuum turns out to be Ricci non-flat, the macrovacuum source being defined in terms of the correlation functions. In the high-frequency limit the equations are shown to become Isaacson's ones with the macrovacuum source becoming Isaacson's stress tensor for gravitational waves. 17 refs

MEASURING THE PERFORMANCE OF GUYANA’S CONSTRUCTION INDUSTRY USING A SET OF PROJECT PERFORMANCE BENCHMARKING METRICS

Directory of Open Access Journals (Sweden)

Christopher J. Willis

2011-10-01

Full Text Available A study measuring the performance of Guyana’s construction industry using a set of project performance benchmarking metrics was recently completed. The underlying premise of the study was that the aggregated performance of construction projects provides a realistic assessment of the performance of the construction industry, on the basis that construction projects are the mechanism through which the construction industry creates its tangible products. The fact that an influential government agency acted as owner of the study was critical to the data collection phase. The best approach for collecting project performance data in Guyana involves the utilisation of a researcher or team of researchers mining electronic and hard copy project documents. This study analysed approximately 270 construction projects to obtain an indication of the performance of guyana’s construction industry. It was found that sea defence projects performed the worst, whereas health facility projects performed the best. The main implication of this is that sea defence projects are likely to be the least efficient and, given their critical nature, there is an argument for urgent performance improvement interventions.

Control of nonholonomic systems from sub-Riemannian geometry to motion planning

CERN Document Server

Jean, Frédéric

2014-01-01

Nonholonomic systems are control systems which depend linearly on the control. Their underlying geometry is the sub-Riemannian geometry, which plays for these systems the same role as Euclidean geometry does for linear systems. In particular the usual notions of approximations at the first order, that are essential for control purposes, have to be defined in terms of this geometry. The aim of these notes is to present these notions of approximation and their application to the motion planning problem for nonholonomic systems.

A prescription for n-dimensional Vierbeins

International Nuclear Information System (INIS)

Bokhari, A.H.; Qadir, A.

1982-06-01

Recent developments in supergravity have brought the n-dimensional Vierbein formalism into prominence. Here we provide a prescription for writing down a Vierbein given an arbitrary (in general non-diagonal) metric tensor in a Riemannian or pseudo-Riemannian space. (author)

Shaping of arm configuration space by prescription of non-Euclidean metrics with applications to human motor control

Science.gov (United States)

Biess, Armin

2013-01-01

The study of the kinematic and dynamic features of human arm movements provides insights into the computational strategies underlying human motor control. In this paper a differential geometric approach to movement control is taken by endowing arm configuration space with different non-Euclidean metric structures to study the predictions of the generalized minimum-jerk (MJ) model in the resulting Riemannian manifold for different types of human arm movements. For each metric space the solution of the generalized MJ model is given by reparametrized geodesic paths. This geodesic model is applied to a variety of motor tasks ranging from three-dimensional unconstrained movements of a four degree of freedom arm between pointlike targets to constrained movements where the hand location is confined to a surface (e.g., a sphere) or a curve (e.g., an ellipse). For the latter speed-curvature relations are derived depending on the boundary conditions imposed (periodic or nonperiodic) and the compatibility with the empirical one-third power law is shown. Based on these theoretical studies and recent experimental findings, I argue that geodesics may be an emergent property of the motor system and that the sensorimotor system may shape arm configuration space by learning metric structures through sensorimotor feedback.

A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds

Directory of Open Access Journals (Sweden)

Qiang Ru

2013-01-01

Full Text Available We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function. We show a meaningful asymptotic result which is more general than those in Huisken, 1997.

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

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

Seeley-Gilkey coefficients for fourth-order operators on Riemannian manifold

International Nuclear Information System (INIS)

Gusynin, V.P.

1990-01-01

The covariant pseudodifferential-operator method of Widom is developed for computing the coefficients in the heat kernel expansion. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimensions of space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method allows one to calculate the coefficients by computer using an analytical calculation system. The method also permits a simple generalization to manifolds with torsion and supermanifolds. (orig.)

Covariant Schrödinger semigroups on Riemannian manifolds

CERN Document Server

Güneysu, Batu

2017-01-01

This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities.  The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also inc...

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.

Vacuum structure for indefinite-metric quantum field theory

International Nuclear Information System (INIS)

Rabuffo, I.; Vitiello, G.

1978-01-01

An approach to indefinite-metric QFT is presented in which the fundamental state of the theory is constructed by taking advantage of the existence of infinitely many unitarily inequivalent representations of the commutation relations. Use of the metric operator eta is avoided. Physical states are positive normed states. The probabilistic interpretation of the norms is fully recovered. An application to a simple model is given. Considerations on the statistical aspects of the construction conclude the paper

Characterizing the round sphere by mean distance

DEFF Research Database (Denmark)

Kokkendorff, Simon Lyngby

2008-01-01

We discuss the measure theoretic metric invariants extent, rendezvous number and mean distance of a general compact metric space X and relate these to classical metric invariants such as diameter and radius. In the final section we focus attention to the category of Riemannian manifolds. The main...

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...

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

Seeley-Gilkey coefficients for the fourth-order operators on a Riemannian manifold

International Nuclear Information System (INIS)

Gusynin, V.P.

1989-01-01

A new covariant method for computing the coefficients in the heat kernel expansion is suggested. It allows one to calculate Seeley-Gilkey coefficients for both minimal and nonminimal differential operators acting on a vector bundle over a Riemannian manifold. The coefficients for the fourth-order minimal operators in arbitrary dimension of the space are calculated. In contrast to the second-order operators the coefficients for the fourth-order (and higher) operators turn out to be essentially dependent on the space dimension. The algorithmic character of the method suggested allows one to calculate coefficients by computer using the analytical calculation system. 19 refs.; 1 fig

Duality on Geodesics of Cartan Distributions and Sub-Riemannian Pseudo-Product Structures

Directory of Open Access Journals (Sweden)

Ishikawa Goo

2015-06-01

Full Text Available Given a five dimensional space endowed with a Cartan distribution, the abnormal geodesics form another five dimensional space with a cone structure. Then it is shown in (15, that, if the cone structure is regarded as a control system, then the space of abnormal geodesics of the cone structure is naturally identified with the original space. In this paper, we provide an exposition on the duality by abnormal geodesics in a wider framework, namely, in terms of quotients of control systems and sub-Riemannian pseudo-product structures. Also we consider the controllability of cone structures and describe the constrained Hamiltonian equations on normal and abnormal geodesics.

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.

A note on post-Riemannian structures of spacetime

OpenAIRE

Hehl, Friedrich W.; Muench, Uwe

1997-01-01

A four-dimensional differentiable manifold is given with an arbitrary linear connection $\\Gamma_\\alpha^\\beta=\\Gamma_{i\\alpha}^\\beta dx^i$. Megged has claimed that he can define a metric $G_{\\alpha\\beta}$ by means of a certain integral equation such that the connection is compatible with the metric. We point out that Megged's implicite definition of his metric $G_{\\alpha\\beta}$ is equivalent to the assumption of a vanishing nonmetricity. Thus his result turns out to be trivial.

Geodesic B-Preinvex Functions and Multiobjective Optimization Problems on Riemannian Manifolds

Directory of Open Access Journals (Sweden)

Sheng-lan Chen

2014-01-01

Full Text Available We introduce a class of functions called geodesic B-preinvex and geodesic B-invex functions on Riemannian manifolds and generalize the notions to the so-called geodesic quasi/pseudo B-preinvex and geodesic quasi/pseudo B-invex functions. We discuss the links among these functions under appropriate conditions and obtain results concerning extremum points of a nonsmooth geodesic B-preinvex function by using the proximal subdifferential. Moreover, we study a differentiable multiobjective optimization problem involving new classes of generalized geodesic B-invex functions and derive Kuhn-Tucker-type sufficient conditions for a feasible point to be an efficient or properly efficient solution. Finally, a Mond-Weir type duality is formulated and some duality results are given for the pair of primal and dual programming.

Introduction to global analysis minimal surfaces in Riemannian manifolds

CERN Document Server

Moore, John Douglas

2017-01-01

During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold M determine the homology of the manifold. Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on M by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs. This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed param...

Dynamos driven by poloidal flows in untwisted, curved and flat Riemannian diffusive flux tubes

International Nuclear Information System (INIS)

De Andrade, L.C.G.

2010-01-01

Recently Vishik anti-fast dynamo theorem has been tested against non-stretching flux tubes (Phys. Plasmas, 15 (2008)). In this paper, another anti dynamo theorem, called Cowling's theorem, which states that axisymmetric magnetic fields cannot support dynamo action, is carefully tested against thick tubular and curved Riemannian untwisted flows, as well as thin flux tubes in diffusive and diffusion less media. In the non-diffusive media Cowling's theorem is not violated in thin Riemann-flat untwisted flux tubes, where the Frenet curvature is negative. Nevertheless the diffusion action in the thin flux tube leads to a dynamo action driven by poloidal flows as shown by Love and Gubbins (Geophysical Res., 23 (1996) 857) in the context of geo dynamos. Actually it is shown that a slow dynamo action is obtained. In this case the Frenet and Riemann curvature still vanishes. In the case of magnetic filaments in diffusive media dynamo action is obtained when the Frenet scalar curvature is negative. Since the Riemann curvature tensor can be expressed in terms of the Frenet curvature of the magnetic flux tube axis, this result can be analogous to a recent result obtained by Chicone, Latushkin and Smith, which states that geodesic curvature in compact Riemannian manifolds can drive dynamo action in the manifold. It is also shown that in the absence of diffusion, magnetic energy does not grow but magnetic toroidal magnetic field can be generated by the poloidal field, what is called a plasma dynamo.

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.

Invariant metrics for Hamiltonian systems

International Nuclear Information System (INIS)

Rangarajan, G.; Dragt, A.J.; Neri, F.

1991-05-01

In this paper, invariant metrics are constructed for Hamiltonian systems. These metrics give rise to norms on the space of homeogeneous polynomials of phase-space variables. For an accelerator lattice described by a Hamiltonian, these norms characterize the nonlinear content of the lattice. Therefore, the performance of the lattice can be improved by minimizing the norm as a function of parameters describing the beam-line elements in the lattice. A four-fold increase in the dynamic aperture of a model FODO cell is obtained using this procedure. 7 refs

Area Regge calculus and discontinuous metrics

International Nuclear Information System (INIS)

Wainwright, Chris; Williams, Ruth M

2004-01-01

Taking the triangle areas as independent variables in the theory of Regge calculus can lead to ambiguities in the edge lengths, which can be interpreted as discontinuities in the metric. We construct solutions to area Regge calculus using a triangulated lattice and find that on a spacelike or timelike hypersurface no such discontinuity can arise. On a null hypersurface however, we can have such a situation and the resulting metric can be interpreted as a so-called refractive wave

Differential calculus on the space of Steiner minimal trees in Riemannian manifolds

International Nuclear Information System (INIS)

Ivanov, A O; Tuzhilin, A A

2001-01-01

It is proved that the length of a minimal spanning tree, the length of a Steiner minimal tree, and the Steiner ratio regarded as functions of finite subsets of a connected complete Riemannian manifold have directional derivatives in all directions. The derivatives of these functions are calculated and some properties of their critical points are found. In particular, a geometric criterion for a finite set to be critical for the Steiner ratio is found. This criterion imposes essential restrictions on the geometry of the sets for which the Steiner ratio attains its minimum, that is, the sets on which the Steiner ratio of the boundary set is equal to the Steiner ratio of the ambient space

Curvature of fluctuation geometry and its implications on Riemannian fluctuation theory

International Nuclear Information System (INIS)

Velazquez, L

2013-01-01

Fluctuation geometry was recently proposed as a counterpart approach of the Riemannian geometry of inference theory (widely known as information geometry). This theory describes the geometric features of the statistical manifold M of random events that are described by a family of continuous distributions dp(x|θ). A main goal of this work is to clarify the statistical relevance of the Levi-Civita curvature tensor R ijkl (x|θ) of the statistical manifold M. For this purpose, the notion of irreducible statistical correlations is introduced. Specifically, a distribution dp(x|θ) exhibits irreducible statistical correlations if every distribution dp(x-check|θ) obtained from dp(x|θ) by considering a coordinate change x-check = φ(x) cannot be factorized into independent distributions as dp(x-check|θ) = prod i dp (i) (x-check i |θ). It is shown that the curvature tensor R ijkl (x|θ) arises as a direct indicator about the existence of irreducible statistical correlations. Moreover, the curvature scalar R(x|θ) allows us to introduce a criterium for the applicability of the Gaussian approximation of a given distribution function. This type of asymptotic result is obtained in the framework of the second-order geometric expansion of the distribution family dp(x|θ), which appears as a counterpart development of the high-order asymptotic theory of statistical estimation. In physics, fluctuation geometry represents the mathematical apparatus of a Riemannian extension for Einstein’s fluctuation theory of statistical mechanics. Some exact results of fluctuation geometry are now employed to derive the invariant fluctuation theorems. Moreover, the curvature scalar allows us to express some asymptotic formulae that account for the system fluctuating behavior beyond the Gaussian approximation, e.g.: it appears as a second-order correction of the Legendre transformation between thermodynamic potentials, P(θ)=θ i x-bar i -s( x-bar |θ)+k 2 R(x|θ)/6. (paper)

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

Chaos based on Riemannian geometric approach to Abelian-Higgs dynamical system

International Nuclear Information System (INIS)

Kawabe, Tetsuji

2003-01-01

Based on the Riemannian geometric approach, we study chaos of the Abelian-Higgs dynamical system derived from a classical field equation consisting of a spatially homogeneous Abelian gauge field and Higgs field. Using the global indicator of chaos formulated by the sectional curvature of the ambient manifold, we show that this approach brings the same qualitative and quantitative information about order and chaos as has been provided by the Lyapunov exponents in the conventional and phenomenological approach. We confirm that the mechanism of chaos is a parametric instability of the system. By analyzing a close relation between the sectional curvature and the Gaussian curvature, we point out that the Toda-Brumer criterion becomes a sufficient condition to the criterion based on this geometric approach as to the stability condition

Riemannian geometry of Hamiltonian chaos: hints for a general theory.

Science.gov (United States)

Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

2008-10-01

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

Cut Locus Construction using Deformable Simplicial Complexes

DEFF Research Database (Denmark)

Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas; Anton, François

2011-01-01

In this paper we present a method for appproximating cut loci for a given point p on Riemannian 2D manifolds, closely related to the notion of Voronoi diagrams. Our method finds the cut locus by advecting a front of points equally distant from p along the geodesics originating at p and finding...... the domain to have disk topology. We test our method for tori of revolution and compare our results to the benchmark ones from [2]. The method, however, is generic and can be easily adapted to construct cut loci for other manifolds of genera other than 1....

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.

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.

New complete noncompact Spin(7) manifolds

International Nuclear Information System (INIS)

Cvetic, M.; Gibbons, G.W.; Lue, H.; Pope, C.N.

2002-01-01

We construct new explicit metrics on complete noncompact Riemannian 8-manifolds with holonomy Spin(7). One manifold, which we denote by (A 8 , is topologically R 8 and another, which we denote by B 8 , is the bundle of chiral spinors over S 4 . Unlike the previously-known complete noncompact metric of Spin(7) holonomy, which was also defined on the bundle of chiral spinors over S 4 , our new metrics are asymptotically locally conical (ALC): near infinity they approach a circle bundle with fibres of constant length over a cone whose base is the squashed Einstein metric on CP 3 . We construct the covariantly-constant spinor and calibrating 4-form. We also obtain an L 2 -normalisable harmonic 4-form for the (A)) 8 manifold, and two such 4-forms (of opposite dualities) for the B 8 manifold. We use the metrics to construct new supersymmetric brane solutions in M-theory and string theory. In particular, we construct resolved fractional M2-branes involving the use of the L 2 harmonic 4-forms, and show that for each manifold there is a supersymmetric example. An intriguing feature of the new A 8 and B 8 Spin(7) metrics is that they are actually the same local solution, with the two different complete manifolds corresponding to taking the radial coordinate to be either positive or negative. We make a comparison with the Taub-NUT and Taub-BOLT metrics, which by contrast do not have special holonomy. In we construct the general solution of our first-order equations for Spin(7) holonomy, and obtain further regular metrics that are complete on manifolds B 8 + and B 8 - similar to B 8

The Yamabe constant

International Nuclear Information System (INIS)

O Murchadha, N.

1991-01-01

The set of riemannian three-metrics with positive Yamabe constant defines the space of independent data for the gravitational field. The boundary of this set is investigated, and it is shown that metrics close to the boundary satisfy the positive-energy theorem. (Author) 18 refs

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 ...

Curve Matching with Applications in Medical Imaging

DEFF Research Database (Denmark)

Bauer, Martin; Bruveris, Martins; Harms, Philipp

2015-01-01

In the recent years, Riemannian shape analysis of curves and surfaces has found several applications in medical image analysis. In this paper we present a numerical discretization of second order Sobolev metrics on the space of regular curves in Euclidean space. This class of metrics has several...

Steiner trees for fixed orientation metrics

DEFF Research Database (Denmark)

Brazil, Marcus; Zachariasen, Martin

2009-01-01

We consider the problem of constructing Steiner minimum trees for a metric defined by a polygonal unit circle (corresponding to s = 2 weighted legal orientations in the plane). A linear-time algorithm to enumerate all angle configurations for degree three Steiner points is given. We provide...... a simple proof that the angle configuration for a Steiner point extends to all Steiner points in a full Steiner minimum tree, such that at most six orientations suffice for edges in a full Steiner minimum tree. We show that the concept of canonical forms originally introduced for the uniform orientation...... metric generalises to the fixed orientation metric. Finally, we give an O(s n) time algorithm to compute a Steiner minimum tree for a given full Steiner topology with n terminal leaves....

Flat deformation theorem and symmetries in spacetime

International Nuclear Information System (INIS)

Llosa, Josep; Carot, Jaume

2009-01-01

The flat deformation theorem states that given a semi-Riemannian analytic metric g on a manifold, locally there always exists a two-form F, a scalar function c, and an arbitrarily prescribed scalar constraint depending on the point x of the manifold and on F and c, say Ψ(c, F, x) = 0, such that the deformed metric η = cg - εF 2 is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric g may be written in the extended Kerr-Schild form, namely η ab := ag ab - 2bk (a l b) where η is flat and k a , l a are two null covectors such that k a l a = -1; next we show how the symmetries of g are connected to those of η, more precisely; we show that if the original metric g admits a conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric η 'inherits' that symmetry.

Problems in Systematic Application of Software Metrics and Possible Solution

OpenAIRE

Rakic, Gordana; Budimac, Zoran

2013-01-01

Systematic application of software metric techniques can lead to significant improvements of the quality of a final software product. However, there is still the evident lack of wider utilization of software metrics techniques and tools due to many reasons. In this paper we investigate some limitations of contemporary software metrics tools and then propose construction of a new tool that would solve some of the problems. We describe the promising prototype, its internal structure, and then f...

Point interactions in two- and three-dimensional Riemannian manifolds

International Nuclear Information System (INIS)

Erman, Fatih; Turgut, O Teoman

2010-01-01

We present a non-perturbative renormalization of the bound state problem of n bosons interacting with finitely many Dirac-delta interactions on two- and three-dimensional Riemannian manifolds using the heat kernel. We formulate the problem in terms of a new operator called the principal or characteristic operator Φ(E). In order to investigate the problem in more detail, we then restrict the problem to one particle sector. The lower bound of the ground state energy is found for a general class of manifolds, e.g. for compact and Cartan-Hadamard manifolds. The estimate of the bound state energies in the tunneling regime is calculated by perturbation theory. Non-degeneracy and uniqueness of the ground state is proven by the Perron-Frobenius theorem. Moreover, the pointwise bounds on the wave function is given and all these results are consistent with the one given in standard quantum mechanics. Renormalization procedure does not lead to any radical change in these cases. Finally, renormalization group equations are derived and the β function is exactly calculated. This work is a natural continuation of our previous work based on a novel approach to the renormalization of point interactions, developed by Rajeev.

Effects of Metric Change on Workers’ Tools and Training.

Science.gov (United States)

1981-07-01

understanding of the metric system, and particularly a lack of fluency in converting customary measurements to metric measuremerts, may increase the...assembly, installing, and repairing occupations 84 Painting, plastering, waterproofing, cementing , and related occupations 85 Excavating, grading... cementing , and related occupations 85 Excavating, grading, paving, and related occupations 86 Construction occupations, n.e.c. 89 Structural work

Modelling anisotropic covariance using stochastic development and sub-Riemannian frame bundle geometry

DEFF Research Database (Denmark)

Sommer, Stefan Horst; Svane, Anne Marie

2017-01-01

distributions. We discuss a factorization of the frame bundle projection map through this bundle, the natural sub-Riemannian structure of the frame bundle, the effect of holonomy, and the existence of subbundles where the Hormander condition is satisfied such that the Brownian motions have smooth transition......We discuss the geometric foundation behind the use of stochastic processes in the frame bundle of a smooth manifold to build stochastic models with applications in statistical analysis of non-linear data. The transition densities for the projection to the manifold of Brownian motions developed...... in the frame bundle lead to a family of probability distributions on the manifold. We explain how data mean and covariance can be interpreted as points in the frame bundle or, more precisely, in the bundle of symmetric positive definite 2-tensors analogously to the parameters describing Euclidean normal...

Eigenvalue pinching on spinc manifolds

Science.gov (United States)

Roos, Saskia

2017-02-01

We derive various pinching results for small Dirac eigenvalues using the classification of spinc and spin manifolds admitting nontrivial Killing spinors. For this, we introduce a notion of convergence for spinc manifolds which involves a general study on convergence of Riemannian manifolds with a principal S1-bundle. We also analyze the relation between the regularity of the Riemannian metric and the regularity of the curvature of the associated principal S1-bundle on spinc manifolds with Killing spinors.

Scalar-flat Kaehler metrics with conformal Bianchi V symmetry

Energy Technology Data Exchange (ETDEWEB)

Dunajski, Maciej [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom); Plansangkate, Prim, E-mail: M.Dunajski@damtp.cam.ac.uk, E-mail: plansang@CRM.UMontreal.ca [Centre de Recherches Mathematiques (CRM), Universite de Montreal, CP 6128, Montreal (Quebec) H3C 3J7 (Canada)

2011-06-21

We provide an affirmative answer to a question posed by Tod (1995, Twistor Theory (New York: Dekker)), and construct all four-dimensional Kaehler metrics with vanishing scalar curvature which are invariant under the conformal action of the Bianchi V group. The construction is based on the combination of twistor theory and the isomonodromic problem with two double poles. The resulting metrics are non-diagonal in the left-invariant basis and are explicitly given in terms of Bessel functions and their integrals. We also make a connection with the LeBrun ansatz, and characterize the associated solutions of the SU({infinity}) Toda equation by the existence a non-abelian two-dimensional group of point symmetries.

Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua

International Nuclear Information System (INIS)

Figueras, Pau; Lucietti, James; Wiseman, Toby

2011-01-01

The elliptic Einstein-DeTurck equation may be used to numerically find Einstein metrics on Riemannian manifolds. Static Lorentzian Einstein metrics are considered by analytically continuing to Euclidean time. The Ricci-DeTurck flow is a constructive algorithm to solve this equation, and is simple to implement when the solution is a stable fixed point, the only complication being that Ricci solitons may exist which are not Einstein. Here we extend previous work to consider the Einstein-DeTurck equation for Riemannian manifolds with boundaries, and those that continue to static Lorentzian spacetimes which are asymptotically flat, Kaluza-Klein, locally AdS or have extremal horizons. Using a maximum principle, we prove that Ricci solitons do not exist in these cases and so any solution is Einstein. We also argue that the Ricci-DeTurck flow preserves these classes of manifolds. As an example, we simulate the Ricci-DeTurck flow for a manifold with asymptotics relevant for AdS 5 /CFT 4 . Our maximum principle dictates that there are no soliton solutions, and we give strong numerical evidence that there exists a stable fixed point of the flow which continues to a smooth static Lorentzian Einstein metric. Our asymptotics are such that this describes the classical gravity dual relevant for the CFT on a Schwarzschild background in either the Unruh or Boulware vacua. It determines the leading O(N 2 c ) part of the CFT stress tensor, which interestingly is regular on both the future and past Schwarzschild horizons. (paper)

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.

Contribution to the establishment and resolution of the Schroedinger equation in a Riemannian manifold with constant curvature

International Nuclear Information System (INIS)

Rasolofoson, N.G.

2014-01-01

The properties of a physical system may vary significantly due to the presence of matter or energy. This change can be defined by the deformation of the space which is described as the variation of its curvature. In order to describe this law of physics, we have used differential geometry and studied especially a Schroedinger equation which describes a system evolving with time on a Riemannian manifold of constant curvature. Therefore, we have established and solved the Schroedinger equation using appropriate mathematics tools. As perspective, the study of string theory may be considered. [fr

Instrument Motion Metrics for Laparoscopic Skills Assessment in Virtual Reality and Augmented Reality.

Science.gov (United States)

Fransson, Boel A; Chen, Chi-Ya; Noyes, Julie A; Ragle, Claude A

2016-11-01

To determine the construct and concurrent validity of instrument motion metrics for laparoscopic skills assessment in virtual reality and augmented reality simulators. Evaluation study. Veterinarian students (novice, n = 14) and veterinarians (experienced, n = 11) with no or variable laparoscopic experience. Participants' minimally invasive surgery (MIS) experience was determined by hospital records of MIS procedures performed in the Teaching Hospital. Basic laparoscopic skills were assessed by 5 tasks using a physical box trainer. Each participant completed 2 tasks for assessments in each type of simulator (virtual reality: bowel handling and cutting; augmented reality: object positioning and a pericardial window model). Motion metrics such as instrument path length, angle or drift, and economy of motion of each simulator were recorded. None of the motion metrics in a virtual reality simulator showed correlation with experience, or to the basic laparoscopic skills score. All metrics in augmented reality were significantly correlated with experience (time, instrument path, and economy of movement), except for the hand dominance metric. The basic laparoscopic skills score was correlated to all performance metrics in augmented reality. The augmented reality motion metrics differed between American College of Veterinary Surgeons diplomates and residents, whereas basic laparoscopic skills score and virtual reality metrics did not. Our results provide construct validity and concurrent validity for motion analysis metrics for an augmented reality system, whereas a virtual reality system was validated only for the time score. © Copyright 2016 by The American College of Veterinary Surgeons.

Four dimensional sigma model coupled to the metric tensor field

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1980-02-01

We discuss the four dimensional nonlinear sigma model with an internal O(n) invariance coupled to the metric tensor field satisfying Einstein equations. We derive a bound on the coupling constant between the sigma field and the metric tensor using the theory of harmonic maps. A special attention is paid to Einstein spaces and some new explicit solutions of the model are constructed. (author)

Assessing Software Quality Through Visualised Cohesion Metrics

Directory of Open Access Journals (Sweden)

Timothy Shih

2001-05-01

Full Text Available Cohesion is one of the most important factors for software quality as well as maintainability, reliability and reusability. Module cohesion is defined as a quality attribute that seeks for measuring the singleness of the purpose of a module. The module of poor quality can be a serious obstacle to the system quality. In order to design a good software quality, software managers and engineers need to introduce cohesion metrics to measure and produce desirable software. A highly cohesion software is thought to be a desirable constructing. In this paper, we propose a function-oriented cohesion metrics based on the analysis of live variables, live span and the visualization of processing element dependency graph. We give six typical cohesion examples to be measured as our experiments and justification. Therefore, a well-defined, well-normalized, well-visualized and well-experimented cohesion metrics is proposed to indicate and thus enhance software cohesion strength. Furthermore, this cohesion metrics can be easily incorporated with software CASE tool to help software engineers to improve software quality.

MESUR: USAGE-BASED METRICS OF SCHOLARLY IMPACT

Energy Technology Data Exchange (ETDEWEB)

BOLLEN, JOHAN [Los Alamos National Laboratory; RODRIGUEZ, MARKO A. [Los Alamos National Laboratory; VAN DE SOMPEL, HERBERT [Los Alamos National Laboratory

2007-01-30

The evaluation of scholarly communication items is now largely a matter of expert opinion or metrics derived from citation data. Both approaches can fail to take into account the myriad of factors that shape scholarly impact. Usage data has emerged as a promising complement to existing methods o fassessment but the formal groundwork to reliably and validly apply usage-based metrics of schlolarly impact is lacking. The Andrew W. Mellon Foundation funded MESUR project constitutes a systematic effort to define, validate and cross-validate a range of usage-based metrics of schlolarly impact by creating a semantic model of the scholarly communication process. The constructed model will serve as the basis of a creating a large-scale semantic network that seamlessly relates citation, bibliographic and usage data from a variety of sources. A subsequent program that uses the established semantic network as a reference data set will determine the characteristics and semantics of a variety of usage-based metrics of schlolarly impact. This paper outlines the architecture and methodology adopted by the MESUR project and its future direction.

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.

Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer

International Nuclear Information System (INIS)

Khaneja, Navin; Brockett, Roger; Glaser, Steffen J.

2002-01-01

Radio-frequency pulses are used in nuclear-magnetic-resonance spectroscopy to produce unitary transfer of states. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation, and to optimize the sensitivity of the experiments. Many coherence-transfer experiments in NMR, involving a network of coupled spins, use temporary spin decoupling to produce desired effective Hamiltonians. In this paper, we demonstrate that significant time can be saved in producing an effective Hamiltonian if spin decoupling is avoided. We provide time-optimal pulse sequences for producing an important class of effective Hamiltonians in three-spin networks. These effective Hamiltonians are useful for coherence-transfer experiments in three-spin systems and implementation of indirect swap and Λ 2 (U) gates in the context of NMR quantum computing. It is shown that computing these time-optimal pulses can be reduced to geometric problems that involve computing sub-Riemannian geodesics. Using these geometric ideas, explicit expressions for the minimum time required for producing these effective Hamiltonians, transfer of coherence, and implementation of indirect swap gates, in a three-spin network are derived (Theorems 1 and 2). It is demonstrated that geometric control techniques provide a systematic way of finding time-optimal pulse sequences for transferring coherence and synthesizing unitary transformations in quantum networks, with considerable time savings (e.g., 42.3% for constructing indirect swap gates)

Absolutely minimal extensions of functions on metric spaces

International Nuclear Information System (INIS)

Milman, V A

1999-01-01

Extensions of a real-valued function from the boundary ∂X 0 of an open subset X 0 of a metric space (X,d) to X 0 are discussed. For the broad class of initial data coming under discussion (linearly bounded functions) locally Lipschitz extensions to X 0 that preserve localized moduli of continuity are constructed. In the set of these extensions an absolutely minimal extension is selected, which was considered before by Aronsson for Lipschitz initial functions in the case X 0 subset of R n . An absolutely minimal extension can be regarded as an ∞-harmonic function, that is, a limit of p-harmonic functions as p→+∞. The proof of the existence of absolutely minimal extensions in a metric space with intrinsic metric is carried out by the Perron method. To this end, ∞-subharmonic, ∞-superharmonic, and ∞-harmonic functions on a metric space are defined and their properties are established

A locally adaptive normal distribution

DEFF Research Database (Denmark)

Arvanitidis, Georgios; Hansen, Lars Kai; Hauberg, Søren

2016-01-01

entropy distribution under the given metric. The underlying metric is, however, non-parametric. We develop a maximum likelihood algorithm to infer the distribution parameters that relies on a combination of gradient descent and Monte Carlo integration. We further extend the LAND to mixture models......The multivariate normal density is a monotonic function of the distance to the mean, and its ellipsoidal shape is due to the underlying Euclidean metric. We suggest to replace this metric with a locally adaptive, smoothly changing (Riemannian) metric that favors regions of high local density...

A note on Einstein-Sasaki metrics in D ≥ 7

International Nuclear Information System (INIS)

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

2005-01-01

In this paper, we obtain new non-singular Einstein-Sasaki spaces in dimensions D ≥ 7. The local construction involves taking a circle bundle over a (D - 1)-dimensional Einstein-Kaehler metric that is itself constructed as a complex line bundle over a product of Einstein-Kaehler spaces. In general, the resulting Einstein-Sasaki spaces are singular, but if parameters in the local solutions satisfy appropriate rationality conditions, the metrics extend smoothly onto complete and non-singular compact manifolds. The seven-dimensional space, whose base is a complex line bundle over S 2 x S 2 , is discussed in detail since it has relevance in terms of the AdS/CFT correspondence

On geodesics in low regularity

Science.gov (United States)

Sämann, Clemens; Steinbauer, Roland

2018-02-01

We consider geodesics in both Riemannian and Lorentzian manifolds with metrics of low regularity. We discuss existence of extremal curves for continuous metrics and present several old and new examples that highlight their subtle interrelation with solutions of the geodesic equations. Then we turn to the initial value problem for geodesics for locally Lipschitz continuous metrics and generalize recent results on existence, regularity and uniqueness of solutions in the sense of Filippov.

Einstein metrics and Brans-Dicke superfields

International Nuclear Information System (INIS)

Marques, S.

1988-01-01

It is obtained here a space conformal to the Einstein space-time, making the transition from an internal bosonic space, constructed with the Majorana constant spinors in the Majorana representation, to a bosonic ''superspace,'' through the use of Einstein vierbeins. These spaces are related to a Grassmann space constructed with the Majorana spinors referred to above, where the ''metric'' is a function of internal bosonic coordinates. The conformal function is a scale factor in the zone of gravitational radiation. A conformal function dependent on space-time coordinates can be constructed in that region when we introduce Majorana spinors which are functions of those coordinates. With this we obtain a scalar field of Brans-Dicke type. 11 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

Nonlinear mechanics of surface growth for cylindrical and spherical elastic bodies

Science.gov (United States)

Sozio, Fabio; Yavari, Arash

2017-01-01

In this paper we formulate the initial-boundary value problems of accreting cylindrical and spherical nonlinear elastic solids in a geometric framework. It is assumed that the body grows as a result of addition of new (stress-free or pre-stressed) material on part of its boundary. We construct Riemannian material manifolds for a growing body with metrics explicitly depending on the history of applied external loads and deformation during accretion and the growth velocity. We numerically solve the governing equilibrium equations in the case of neo-Hookean solids and compare the accretion and residual stresses with those calculated using the linear mechanics of surface growth.

Roughly isometric minimal immersions into Riemannian manifolds

DEFF Research Database (Denmark)

Markvorsen, Steen

of the intrinsic combinatorial discrete Laplacian, and we will show that they share several analytic and geometric properties with their smooth (minimal submanifold) counterparts in $N$. The intrinsic properties thus obtained may hence serve as roughly invariant descriptors for the original metric space $X$....

Clustering in Hilbert simplex geometry

KAUST Repository

Nielsen, Frank; Sun, Ke

2017-01-01

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

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

Energy Technology Data Exchange (ETDEWEB)

De Cesare, Marco [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Moffat, John W. [Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada); Sakellariadou, Mairi [King' s College London, Theoretical Particle Physics and Cosmology Group, Department of Physics, London (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON (Canada)

2017-09-15

We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal. (orig.)

Self-benchmarking Guide for Laboratory Buildings: Metrics, Benchmarks, Actions

Energy Technology Data Exchange (ETDEWEB)

Mathew, Paul; Greenberg, Steve; Sartor, Dale

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.

Self-organizing weights for Internet AS-graphs and surprisingly simple routing metrics

DEFF Research Database (Denmark)

Scholz, Jan Carsten; Greiner, Martin

2011-01-01

The transport capacity of Internet-like communication networks and hence their efficiency may be improved by a factor of 5–10 through the use of highly optimized routing metrics, as demonstrated previously. The numerical determination of such routing metrics can be computationally demanding...... to an extent that prohibits both investigation of and application to very large networks. In an attempt to find a numerically less expensive way of constructing a metric with a comparable performance increase, we propose a local, self-organizing iteration scheme and find two surprisingly simple and efficient...... metrics. The new metrics have negligible computational cost and result in an approximately 5-fold performance increase, providing distinguished competitiveness with the computationally costly counterparts. They are applicable to very large networks and easy to implement in today's Internet routing...

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

Science.gov (United States)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Measures of agreement between computation and experiment:validation metrics.

Energy Technology Data Exchange (ETDEWEB)

Barone, Matthew Franklin; Oberkampf, William Louis

2005-08-01

With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables and sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric and also features that should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent free-shear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.

Determination of a Screening Metric for High Diversity DNA Libraries.

Science.gov (United States)

Guido, Nicholas J; Handerson, Steven; Joseph, Elaine M; Leake, Devin; Kung, Li A

2016-01-01

The fields of antibody engineering, enzyme optimization and pathway construction rely increasingly on screening complex variant DNA libraries. These highly diverse libraries allow researchers to sample a maximized sequence space; and therefore, more rapidly identify proteins with significantly improved activity. The current state of the art in synthetic biology allows for libraries with billions of variants, pushing the limits of researchers' ability to qualify libraries for screening by measuring the traditional quality metrics of fidelity and diversity of variants. Instead, when screening variant libraries, researchers typically use a generic, and often insufficient, oversampling rate based on a common rule-of-thumb. We have developed methods to calculate a library-specific oversampling metric, based on fidelity, diversity, and representation of variants, which informs researchers, prior to screening the library, of the amount of oversampling required to ensure that the desired fraction of variant molecules will be sampled. To derive this oversampling metric, we developed a novel alignment tool to efficiently measure frequency counts of individual nucleotide variant positions using next-generation sequencing data. Next, we apply a method based on the "coupon collector" probability theory to construct a curve of upper bound estimates of the sampling size required for any desired variant coverage. The calculated oversampling metric will guide researchers to maximize their efficiency in using highly variant libraries.

Determination of a Screening Metric for High Diversity DNA Libraries.

Directory of Open Access Journals (Sweden)

Nicholas J Guido

Full Text Available The fields of antibody engineering, enzyme optimization and pathway construction rely increasingly on screening complex variant DNA libraries. These highly diverse libraries allow researchers to sample a maximized sequence space; and therefore, more rapidly identify proteins with significantly improved activity. The current state of the art in synthetic biology allows for libraries with billions of variants, pushing the limits of researchers' ability to qualify libraries for screening by measuring the traditional quality metrics of fidelity and diversity of variants. Instead, when screening variant libraries, researchers typically use a generic, and often insufficient, oversampling rate based on a common rule-of-thumb. We have developed methods to calculate a library-specific oversampling metric, based on fidelity, diversity, and representation of variants, which informs researchers, prior to screening the library, of the amount of oversampling required to ensure that the desired fraction of variant molecules will be sampled. To derive this oversampling metric, we developed a novel alignment tool to efficiently measure frequency counts of individual nucleotide variant positions using next-generation sequencing data. Next, we apply a method based on the "coupon collector" probability theory to construct a curve of upper bound estimates of the sampling size required for any desired variant coverage. The calculated oversampling metric will guide researchers to maximize their efficiency in using highly variant libraries.

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.

On the compatible weakly nonlocal Poisson brackets of hydrodynamic type

Directory of Open Access Journals (Sweden)

Andrei Ya. Maltsev

2002-01-01

of hydrodynamic type (Ferapontov brackets and the corresponding integrable hierarchies. We show that, under the requirement of the nondegeneracy of the corresponding “first” pseudo-Riemannian metric g(0 νμ and also some nondegeneracy requirement for the nonlocal part, it is possible to introduce a “canonical” set of “integrable hierarchies” based on the Casimirs, momentum functional and some “canonical Hamiltonian functions.” We prove also that all the “higher” “positive” Hamiltonian operators and the “negative” symplectic forms have the weakly nonlocal form in this case. The same result is also true for “negative” Hamiltonian operators and “positive” symplectic structures in the case when both pseudo-Riemannian metrics g(0 νμ and g(1 νμ are nondegenerate.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

Science.gov (United States)

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

On Geodesic Exponential Kernels

DEFF Research Database (Denmark)

Feragen, Aasa; Lauze, François; Hauberg, Søren

2015-01-01

This extended abstract summarizes work presented at CVPR 2015 [1]. Standard statistics and machine learning tools require input data residing in a Euclidean space. However, many types of data are more faithfully represented in general nonlinear metric spaces or Riemannian manifolds, e.g. shapes, ......, symmetric positive definite matrices, human poses or graphs. The underlying metric space captures domain specific knowledge, e.g. non-linear constraints, which is available a priori. The intrinsic geodesic metric encodes this knowledge, often leading to improved statistical models....

$\\eta$-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.

An accurate metric for the spacetime around rotating neutron stars

Science.gov (United States)

Pappas, George

2017-04-01

The problem of having an accurate description of the spacetime around rotating neutron stars is of great astrophysical interest. For astrophysical applications, one needs to have a metric that captures all the properties of the spacetime around a rotating neutron star. Furthermore, an accurate appropriately parametrized metric, I.e. a metric that is given in terms of parameters that are directly related to the physical structure of the neutron star, could be used to solve the inverse problem, which is to infer the properties of the structure of a neutron star from astrophysical observations. In this work, we present such an approximate stationary and axisymmetric metric for the exterior of rotating neutron stars, which is constructed using the Ernst formalism and is parametrized by the relativistic multipole moments of the central object. This metric is given in terms of an expansion on the Weyl-Papapetrou coordinates with the multipole moments as free parameters and is shown to be extremely accurate in capturing the physical properties of a neutron star spacetime as they are calculated numerically in general relativity. Because the metric is given in terms of an expansion, the expressions are much simpler and easier to implement, in contrast to previous approaches. For the parametrization of the metric in general relativity, the recently discovered universal 3-hair relations are used to produce a three-parameter metric. Finally, a straightforward extension of this metric is given for scalar-tensor theories with a massless scalar field, which also admit a formulation in terms of an Ernst potential.

Bianchi type A hyper-symplectic and hyper-Kaehler metrics in 4D

International Nuclear Information System (INIS)

De Andrés, L C; Fernández, M; Ivanov, S; Santisteban, J A; Ugarte, L; Vassilev, D

2012-01-01

We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-para-Kaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures of dimension 4. (paper)

Drude-Schwarzschild Metric and the Electrical Conductivity of Metals

Directory of Open Access Journals (Sweden)

Silva P. R.

2014-07-01

Full Text Available Starting from a string with a length equal to the electron mean free path and having a unit cell equal to the Compton length of the electron, we construct a Schwarzschild-like metric. We found that this metric has a surface horizon with radius equal to the electron mean free path and its Bekenstein-like entropy is proportional to the number of squared unit cells contained in this spherical surface. The Hawking temperature is inversely proportional to the perimeter of the maximum circle of this sphere. Also, interesting analogies on some features of the particle physics are examined.

Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: a prerequisite to compare metrics

International Nuclear Information System (INIS)

Pappas, G; Apostolatos, T A

2008-01-01

We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star, which has been constructed numerically in the former coordinates, with an axially symmetric stationary metric, which is given through an analytical form in the latter coordinates. (comments, replies and notes)

Faithful transformation of quasi-isotropic to Weyl-Papapetrou coordinates: a prerequisite to compare metrics

Energy Technology Data Exchange (ETDEWEB)

Pappas, G; Apostolatos, T A [Section of Astrophysics, Astronomy and Mechanics, Department of Physics, University of Athens, Panepistimiopolis Zografos GR15783, Athens (Greece)

2008-11-21

We demonstrate how one should transform correctly quasi-isotropic coordinates to Weyl-Papapetrou coordinates in order to compare the metric around a rotating star, which has been constructed numerically in the former coordinates, with an axially symmetric stationary metric, which is given through an analytical form in the latter coordinates. (comments, replies and notes)

Fourth-rank gravity and cosmology

International Nuclear Information System (INIS)

Marrakchi, A.L.; Tapia, V.

1992-07-01

We consider the consequences of describing the metric properties of space-time through a quartic line element. The associated ''metric'' is a fourth-rank tensor G μυλπ . In order to recover a Riemannian behaviour of the geometry it is necessary to have G μυλπ = g (μυ g λπ) . We construct a theory for the gravitational field based on the fourth-rank metric G μυλπ . In the absence of matter the fourth-rank metric becomes separable and the theory coincides with General Relativity. In the presence of matter we can maintain Riemmanianicity, but now gravitation couples, as compared to General Relativity, in a different way to matter. We develop a simple cosmological model based on a FRW metric with matter described by a perfect fluid. For the present time the field equations are compatible with k OBS = O and Ω OBS t CLAS approx. 10 20 t PLANCK approx. 10 -23 s. Our final and most important result is the fact that the entropy is an increasing function of time. When interpreted at the light of General Relativity the treatment is shown to be almost equivalent to that of the standard model of cosmology combined with the inflationary scenario. (author). 16 refs, 1 fig

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

Preserved Network Metrics across Translated Texts

Science.gov (United States)

Cabatbat, Josephine Jill T.; Monsanto, Jica P.; Tapang, Giovanni A.

2014-09-01

Co-occurrence language networks based on Bible translations and the Universal Declaration of Human Rights (UDHR) translations in different languages were constructed and compared with random text networks. Among the considered network metrics, the network size, N, the normalized betweenness centrality (BC), and the average k-nearest neighbors, knn, were found to be the most preserved across translations. Moreover, similar frequency distributions of co-occurring network motifs were observed for translated texts networks.

A Comment on the geometry of some scalar-tensor theories

Energy Technology Data Exchange (ETDEWEB)

Lindstrom, U

1986-08-01

We show that the scalar field in scalar-tensor theories such as the Jordan-Brans-Dicke theory has an interpretation as a potential for the torsion in a Riemannian manifold. The relation is similar to that of the metric to the connection.

Arcmancer: Geodesics and polarized radiative transfer library

Science.gov (United States)

Pihajoki, Pauli; Mannerkoski, Matias; Nättilä, Joonas; Johansson, Peter H.

2018-05-01

Arcmancer computes geodesics and performs polarized radiative transfer in user-specified spacetimes. The library supports Riemannian and semi-Riemannian spaces of any dimension and metric; it also supports multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. Arcmancer can be used to solve various problems in numerical geometry, such as solving the curve equation of motion using adaptive integration with configurable tolerances and differential equations along precomputed curves. It also provides support for curves with an arbitrary acceleration term and generic tools for generating ray initial conditions and performing parallel computation over the image, among other tools.

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...

Tensors and their applications

CERN Document Server

Islam, Nazrul

2006-01-01

About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces

(Ln-bar, g)-spaces. General relativity over V4-bar - spaces

International Nuclear Information System (INIS)

Manoff, S.; Kolarov, A.; Dimitrov, B.

1998-01-01

The results from the considerations of differentiable manifolds with contravariant and covariant affine connections and metrics are specialized for the case of (L n bar, g)-spaces with metric transport (∇ ξ g = 0 for all ξ is T (M), g ij;k = 0 and f j i = e φ · g j i (the s.c. (pseudo)Riemannian spaces with contravariant and covariant symmetric affine connections). Einstein's theory of gravitation is considered in (pseudo)Riemannian spaces with different (not only by sign) contravariant and covariant affine connections ((V n bar)-spaces, n = 4). The Euler-Lagrange equations and the corresponding energy-momentum tensors (EMT-s) are obtained and compared with the Einstein equations and the EMT-s in V 4 -spaces. The geodesic and autoparallel equations in V 4 bar -spaces are found as different equations in contrast to the case of V 4 -spaces

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.)

A Classical Based Derivation of Time Dilation Providing First Order Accuracy to Schwarzschild's Solution of Einstein's Field Equations

Science.gov (United States)

Austin, Rickey W.

In Einstein's theory of Special Relativity (SR), one method to derive relativistic kinetic energy is via applying the classical work-energy theorem to relativistic momentum. This approach starts with a classical based work-energy theorem and applies SR's momentum to the derivation. One outcome of this derivation is relativistic kinetic energy. From this derivation, it is rather straight forward to form a kinetic energy based time dilation function. In the derivation of General Relativity a common approach is to bypass classical laws as a starting point. Instead a rigorous development of differential geometry and Riemannian space is constructed, from which classical based laws are derived. This is in contrast to SR's approach of starting with classical laws and applying the consequences of the universal speed of light by all observers. A possible method to derive time dilation due to Newtonian gravitational potential energy (NGPE) is to apply SR's approach to deriving relativistic kinetic energy. It will be shown this method gives a first order accuracy compared to Schwarzschild's metric. The SR's kinetic energy and the newly derived NGPE derivation are combined to form a Riemannian metric based on these two energies. A geodesic is derived and calculations compared to Schwarzschild's geodesic for an orbiting test mass about a central, non-rotating, non-charged massive body. The new metric results in high accuracy calculations when compared to Einsteins General Relativity's prediction. The new method provides a candidate approach for starting with classical laws and deriving General Relativity effects. This approach mimics SR's method of starting with classical mechanics when deriving relativistic equations. As a compliment to introducing General Relativity, it provides a plausible scaffolding method from classical physics when teaching introductory General Relativity. A straight forward path from classical laws to General Relativity will be derived. This derivation

Bianchi type A hyper-symplectic and hyper-K\\"ahler metrics in 4D

OpenAIRE

de Andrés, Luis C.; Fernández, Marisa; Ivanov, Stefan; Santisteban, José A.; Ugarte, Luis; Vassilev, Dimiter

2011-01-01

We present a simple explicit construction of hyper-Kaehler and hyper-symplectic (also known as neutral hyper-Kaehler or hyper-parakaehler) metrics in 4D using the Bianchi type groups of class A. The construction underlies a correspondence between hyper-Kaehler and hyper-symplectic structures in dimension four.

A Metrics Approach for Collaborative Systems

Directory of Open Access Journals (Sweden)

Cristian CIUREA

2009-01-01

Full Text Available This article presents different types of collaborative systems, their structure and classification. This paper defines the concept of virtual campus as a collaborative system. It builds architecture for virtual campus oriented on collaborative training processes. It analyses the quality characteristics of collaborative systems and propose techniques for metrics construction and validation in order to evaluate them. The article analyzes different ways to increase the efficiency and the performance level in collaborative banking systems.

Geodesic deviation and Minikowski space

International Nuclear Information System (INIS)

Barraco, D.; Kozameh, C.; Newman, E.T.; Tod, P.

1990-01-01

The authors study the properties of the solution space of local surface-forming null sub-congruences in the neighborhood of a given null geodesic in a pseudo-Riemannian space-time. This solution space is a three-dimensional manifold, naturally endowed with a conformal Minkowski metric

Symmetries and conserved quantities in geodesic motion

International Nuclear Information System (INIS)

Hojman, S.; Nunez, L.; Patino, A.; Rago, H.

1986-01-01

Recently obtained results linking several constants of motion to one (non-Noetherian) symmetry to the problem of geodesic motion in Riemannian space-times are applied. The construction of conserved quantities in geodesic motion as well as the deduction of geometrical statements about Riemannian space-times are achieved

Color Texture Image Retrieval Based on Local Extrema Features and Riemannian Distance

Directory of Open Access Journals (Sweden)

Minh-Tan Pham

2017-10-01

Full Text Available A novel efficient method for content-based image retrieval (CBIR is developed in this paper using both texture and color features. Our motivation is to represent and characterize an input image by a set of local descriptors extracted from characteristic points (i.e., keypoints within the image. Then, dissimilarity measure between images is calculated based on the geometric distance between the topological feature spaces (i.e., manifolds formed by the sets of local descriptors generated from each image of the database. In this work, we propose to extract and use the local extrema pixels as our feature points. Then, the so-called local extrema-based descriptor (LED is generated for each keypoint by integrating all color, spatial as well as gradient information captured by its nearest local extrema. Hence, each image is encoded by an LED feature point cloud and Riemannian distances between these point clouds enable us to tackle CBIR. Experiments performed on several color texture databases including Vistex, STex, color Brodazt, USPtex and Outex TC-00013 using the proposed approach provide very efficient and competitive results compared to the state-of-the-art methods.

Inferring imagined speech using EEG signals: a new approach using Riemannian manifold features

Science.gov (United States)

Nguyen, Chuong H.; Karavas, George K.; Artemiadis, Panagiotis

2018-02-01

Objective. In this paper, we investigate the suitability of imagined speech for brain-computer interface (BCI) applications. Approach. A novel method based on covariance matrix descriptors, which lie in Riemannian manifold, and the relevance vector machines classifier is proposed. The method is applied on electroencephalographic (EEG) signals and tested in multiple subjects. Main results. The method is shown to outperform other approaches in the field with respect to accuracy and robustness. The algorithm is validated on various categories of speech, such as imagined pronunciation of vowels, short words and long words. The classification accuracy of our methodology is in all cases significantly above chance level, reaching a maximum of 70% for cases where we classify three words and 95% for cases of two words. Significance. The results reveal certain aspects that may affect the success of speech imagery classification from EEG signals, such as sound, meaning and word complexity. This can potentially extend the capability of utilizing speech imagery in future BCI applications. The dataset of speech imagery collected from total 15 subjects is also published.

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)

Physics in space-time with scale-dependent metrics

Science.gov (United States)

Balankin, Alexander S.

2013-10-01

We construct three-dimensional space Rγ3 with the scale-dependent metric and the corresponding Minkowski space-time Mγ,β4 with the scale-dependent fractal (DH) and spectral (DS) dimensions. The local derivatives based on scale-dependent metrics are defined and differential vector calculus in Rγ3 is developed. We state that Mγ,β4 provides a unified phenomenological framework for dimensional flow observed in quite different models of quantum gravity. Nevertheless, the main attention is focused on the special case of flat space-time M1/3,14 with the scale-dependent Cantor-dust-like distribution of admissible states, such that DH increases from DH=2 on the scale ≪ℓ0 to DH=4 in the infrared limit ≫ℓ0, where ℓ0 is the characteristic length (e.g. the Planck length, or characteristic size of multi-fractal features in heterogeneous medium), whereas DS≡4 in all scales. Possible applications of approach based on the scale-dependent metric to systems of different nature are briefly discussed.

State of the art metrics for aspect oriented programming

Science.gov (United States)

Ghareb, Mazen Ismaeel; Allen, Gary

2018-04-01

The quality evaluation of software, e.g., defect measurement, gains significance with higher use of software applications. Metric measurements are considered as the primary indicator of imperfection prediction and software maintenance in various empirical studies of software products. However, there is no agreement on which metrics are compelling quality indicators for novel development approaches such as Aspect Oriented Programming (AOP). AOP intends to enhance programming quality, by providing new and novel constructs for the development of systems, for example, point cuts, advice and inter-type relationships. Hence, it is not evident if quality pointers for AOP can be derived from direct expansions of traditional OO measurements. Then again, investigations of AOP do regularly depend on established coupling measurements. Notwithstanding the late reception of AOP in empirical studies, coupling measurements have been adopted as useful markers of flaw inclination in this context. In this paper we will investigate the state of the art metrics for measurement of Aspect Oriented systems development.

On transverse exponential stability and its use in incremental stability, observer and synchronization

NARCIS (Netherlands)

Andrieu, Vincent; Jayawardhana, Bayu; Praly, Laurent

2013-01-01

We study the relation between the exponential stability of an invariant manifold and the existence of a Riemannian metric for which the flow is “transversally” contracting. More precisely, we investigate how the following properties are related to each other: i). A manifold is “transversally”

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).

Non-self-dual nonlinear gravitons

International Nuclear Information System (INIS)

Yasskin, P.B.; Isenberg, J.A.

1982-01-01

Penrose has given a twistor description of all self-dual complex Riemannian space-times. This construction is modified to characterize all complex Riemannian space-times and all complex teleparallel space-times. This construction may be useful in finding non-self-dual solutions to the gravitational field equations (Einstein's or otherwise) without or with sources. It may also lead to a nonperturbative method for computing path integrals. Whereas Penrose shows that a self-dual space-time may be specified by a deformation of projective twistor space (the set of α planes in complex Minkowski space), it is found that a Riemannian or teleparallel space-time may be described by a deformation of projective ambitwistor space (the set of null geodesics in complex Minkowski space). (author)

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.

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.

Singularities of plane complex curves and limits of Kähler metrics with cone singularities. I: Tangent Cones

Directory of Open Access Journals (Sweden)

Borbon Martin de

2017-02-01

Full Text Available The goal of this article is to provide a construction and classification, in the case of two complex dimensions, of the possible tangent cones at points of limit spaces of non-collapsed sequences of Kähler-Einstein metrics with cone singularities. The proofs and constructions are completely elementary, nevertheless they have an intrinsic beauty. In a few words; tangent cones correspond to spherical metrics with cone singularities in the projective line by means of the Kähler quotient construction with respect to the S1-action generated by the Reeb vector field, except in the irregular case ℂβ₁×ℂβ₂ with β₂/ β₁ ∉ Q.

The metric on field space, functional renormalization, and metric–torsion quantum gravity

International Nuclear Information System (INIS)

Reuter, Martin; Schollmeyer, Gregor M.

2016-01-01

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.

Comparison of Employer Productivity Metrics to Lost Productivity Estimated by Commonly Used Questionnaires.

Science.gov (United States)

Gardner, Bethany T; Dale, Ann Marie; Buckner-Petty, Skye; Van Dillen, Linda; Amick, Benjamin C; Evanoff, Bradley

2016-02-01

The aim of the study was to assess construct and discriminant validity of four health-related work productivity loss questionnaires in relation to employer productivity metrics, and to describe variation in economic estimates of productivity loss provided by the questionnaires in healthy workers. Fifty-eight billing office workers completed surveys including health information and four productivity loss questionnaires. Employer productivity metrics and work hours were also obtained. Productivity loss questionnaires were weakly to moderately correlated with employer productivity metrics. Workers with more health complaints reported greater health-related productivity loss than healthier workers, but showed no loss on employer productivity metrics. Economic estimates of productivity loss showed wide variation among questionnaires, yet no loss of actual productivity. Additional studies are needed comparing questionnaires with objective measures in larger samples and other industries, to improve measurement methods for health-related productivity loss.

Comparison of employer productivity metrics to lost productivity estimated by commonly used questionnaires

Science.gov (United States)

Gardner, Bethany T.; Dale, Ann Marie; Buckner-Petty, Skye; Van Dillen, Linda; Amick, Benjamin C.; Evanoff, Bradley

2016-01-01

Objective To assess construct and discriminant validity of four health-related work productivity loss questionnaires in relation to employer productivity metrics, and to describe variation in economic estimates of productivity loss provided by the questionnaires in healthy workers. Methods 58 billing office workers completed surveys including health information and four productivity loss questionnaires. Employer productivity metrics and work hours were also obtained. Results Productivity loss questionnaires were weakly to moderately correlated with employer productivity metrics. Workers with more health complaints reported greater health-related productivity loss than healthier workers, but showed no loss on employer productivity metrics. Economic estimates of productivity loss showed wide variation among questionnaires, yet no loss of actual productivity. Conclusions Additional studies are needed comparing questionnaires with objective measures in larger samples and other industries, to improve measurement methods for health-related productivity loss. PMID:26849261

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.)

1/4-pinched contact sphere theorem

DEFF Research Database (Denmark)

Ge, Jian; Huang, Yang

2016-01-01

Given a closed contact 3-manifold with a compatible Riemannian metric, we show that if the sectional curvature is 1/4-pinched, then the contact structure is universally tight. This result improves the Contact Sphere Theorem in [EKM12], where a 4/9-pinching constant was imposed. Some tightness...

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 ...

Local adjacency metric dimension of sun graph and stacked book graph

Science.gov (United States)

Yulisda Badri, Alifiah; Darmaji

2018-03-01

A graph is a mathematical system consisting of a non-empty set of nodes and a set of empty sides. One of the topics to be studied in graph theory is the metric dimension. Application in the metric dimension is the navigation robot system on a path. Robot moves from one vertex to another vertex in the field by minimizing the errors that occur in translating the instructions (code) obtained from the vertices of that location. To move the robot must give different instructions (code). In order for the robot to move efficiently, the robot must be fast to translate the code of the nodes of the location it passes. so that the location vertex has a minimum distance. However, if the robot must move with the vertex location on a very large field, so the robot can not detect because the distance is too far.[6] In this case, the robot can determine its position by utilizing location vertices based on adjacency. The problem is to find the minimum cardinality of the required location vertex, and where to put, so that the robot can determine its location. The solution to this problem is the dimension of adjacency metric and adjacency metric bases. Rodrguez-Velzquez and Fernau combine the adjacency metric dimensions with local metric dimensions, thus becoming the local adjacency metric dimension. In the local adjacency metric dimension each vertex in the graph may have the same adjacency representation as the terms of the vertices. To obtain the local metric dimension of values in the graph of the Sun and the stacked book graph is used the construction method by considering the representation of each adjacent vertex of the graph.

Duality constructions from quantum state manifolds

Science.gov (United States)

Kriel, J. N.; van Zyl, H. J. R.; Scholtz, F. G.

2015-11-01

The formalism of quantum state space geometry on manifolds of generalised coherent states is proposed as a natural setting for the construction of geometric dual descriptions of non-relativistic quantum systems. These state manifolds are equipped with natural Riemannian and symplectic structures derived from the Hilbert space inner product. This approach allows for the systematic construction of geometries which reflect the dynamical symmetries of the quantum system under consideration. We analyse here in detail the two dimensional case and demonstrate how existing results in the AdS 2 /CF T 1 context can be understood within this framework. We show how the radial/bulk coordinate emerges as an energy scale associated with a regularisation procedure and find that, under quite general conditions, these state manifolds are asymptotically anti-de Sitter solutions of a class of classical dilaton gravity models. For the model of conformal quantum mechanics proposed by de Alfaro et al. [1] the corresponding state manifold is seen to be exactly AdS 2 with a scalar curvature determined by the representation of the symmetry algebra. It is also shown that the dilaton field itself is given by the quantum mechanical expectation values of the dynamical symmetry generators and as a result exhibits dynamics equivalent to that of a conformal mechanical system.

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

Metrics of quantum states

International Nuclear Information System (INIS)

Ma Zhihao; Chen Jingling

2011-01-01

In this work we study metrics of quantum states, which are natural generalizations of the usual trace metric and Bures metric. Some useful properties of the metrics are proved, such as the joint convexity and contractivity under quantum operations. Our result has a potential application in studying the geometry of quantum states as well as the entanglement detection.

Prescribed curvature tensor in locally conformally flat manifolds

Science.gov (United States)

Pina, Romildo; Pieterzack, Mauricio

2018-01-01

A global existence theorem for the prescribed curvature tensor problem in locally conformally flat manifolds is proved for a special class of tensors R. Necessary and sufficient conditions for the existence of a metric g ¯ , conformal to Euclidean g, are determined such that R ¯ = R, where R ¯ is the Riemannian curvature tensor of the metric g ¯ . The solution to this problem is given explicitly for special cases of the tensor R, including the case where the metric g ¯ is complete on Rn. Similar problems are considered for locally conformally flat manifolds.

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.

A Short Description of Electromagnetism Using the Finsler Geometry

Directory of Open Access Journals (Sweden)

Otilia Lungu

2011-12-01

Full Text Available Abstract. It is well known that a Randers metric is a deformation of a Riemannian metric alfa(x,y=sqrt(a_ij(xy^iy^j using a 1-form beta(x,y=beta_i(xy^i. In this paper we are replacing beta(x,y with beta_2(x,y=sqrt(beta_ij(xy^iy^j. We obtain a new space and we are going to study some of its properties.Key words: electromagnetism, Finsler space, Randers spaces.

Dynamical construction of Horava-Lifshitz geometry

OpenAIRE

Banerjee, Rabin; Mukherjee, Pradip

2015-01-01

We derive the projectable version of Horava - Lifshitz gravity from the localisation of the Galilean symmetry. Specifically we provide a dynamical construction of the metric, from first principles, that reproduces the transformations of the physical variables - lapse, shift and spatial component of the metric. Also, the measure defining the action is reproduced. The geometrical basis of the Horava-Lifshitz gravity is thereby revealed which also elucidates its difference from the Newton-Cartan...

A condition metric for Eucalyptus woodland derived from expert evaluations.

Science.gov (United States)

Sinclair, Steve J; Bruce, Matthew J; Griffioen, Peter; Dodd, Amanda; White, Matthew D

2018-02-01

The evaluation of ecosystem quality is important for land-management and land-use planning. Evaluation is unavoidably subjective, and robust metrics must be based on consensus and the structured use of observations. We devised a transparent and repeatable process for building and testing ecosystem metrics based on expert data. We gathered quantitative evaluation data on the quality of hypothetical grassy woodland sites from experts. We used these data to train a model (an ensemble of 30 bagged regression trees) capable of predicting the perceived quality of similar hypothetical woodlands based on a set of 13 site variables as inputs (e.g., cover of shrubs, richness of native forbs). These variables can be measured at any site and the model implemented in a spreadsheet as a metric of woodland quality. We also investigated the number of experts required to produce an opinion data set sufficient for the construction of a metric. The model produced evaluations similar to those provided by experts, as shown by assessing the model's quality scores of expert-evaluated test sites not used to train the model. We applied the metric to 13 woodland conservation reserves and asked managers of these sites to independently evaluate their quality. To assess metric performance, we compared the model's evaluation of site quality with the managers' evaluations through multidimensional scaling. The metric performed relatively well, plotting close to the center of the space defined by the evaluators. Given the method provides data-driven consensus and repeatability, which no single human evaluator can provide, we suggest it is a valuable tool for evaluating ecosystem quality in real-world contexts. We believe our approach is applicable to any ecosystem. © 2017 State of Victoria.

Riemannian geometry of thermodynamics and systems with repulsive power-law interactions.

Science.gov (United States)

Ruppeiner, George

2005-07-01

A Riemannian geometric theory of thermodynamics based on the postulate that the curvature scalar R is proportional to the inverse free energy density is used to investigate three-dimensional fluid systems of identical classical point particles interacting with each other via a power-law potential energy gamma r(-alpha) . Such systems are useful in modeling melting transitions. The limit alpha-->infinity corresponds to the hard sphere gas. A thermodynamic limit exists only for short-range (alpha>3) and repulsive (gamma>0) interactions. The geometric theory solutions for given alpha>3 , gamma>0 , and any constant temperature T have the following properties: (1) the thermodynamics follows from a single function b (rho T(-3/alpha) ) , where rho is the density; (2) all solutions are equivalent up to a single scaling constant for rho T(-3/alpha) , related to gamma via the virial theorem; (3) at low density, solutions correspond to the ideal gas; (4) at high density there are solutions with pressure and energy depending on density as expected from solid state physics, though not with a Dulong-Petit heat capacity limit; (5) for 33.7913 a phase transition is required to go between these regimes; (7) for any alpha>3 we may include a first-order phase transition, which is expected from computer simulations; and (8) if alpha-->infinity, the density approaches a finite value as the pressure increases to infinity, with the pressure diverging logarithmically in the density difference.

Superintegrability on Three-Dimensional Riemannian and Relativistic Spaces of Constant Curvature

Directory of Open Access Journals (Sweden)

Francisco José Herranz

2006-01-01

Full Text Available A family of classical superintegrable Hamiltonians, depending on an arbitrary radial function, which are defined on the 3D spherical, Euclidean and hyperbolic spaces as well as on the (2+1D anti-de Sitter, Minkowskian and de Sitter spacetimes is constructed. Such systems admit three integrals of the motion (besides the Hamiltonian which are explicitly given in terms of ambient and geodesic polar coordinates. The resulting expressions cover the six spaces in a unified way as these are parametrized by two contraction parameters that govern the curvature and the signature of the metric on each space. Next two maximally superintegrable Hamiltonians are identified within the initial superintegrable family by finding the remaining constant of the motion. The former potential is the superposition of a (curved central harmonic oscillator with other three oscillators or centrifugal barriers (depending on each specific space, so that this generalizes the Smorodinsky-Winternitz system. The latter one is a superposition of the Kepler-Coulomb potential with another two oscillators or centrifugal barriers. As a byproduct, the Laplace-Runge-Lenz vector for these spaces is deduced. Furthermore both potentials are analysed in detail for each particular space. Some comments on their generalization to arbitrary dimension are also presented.

Constructing a no-reference H.264/AVC bitstream-based video quality metric using genetic programming-based symbolic regression

OpenAIRE

Staelens, Nicolas; Deschrijver, Dirk; Vladislavleva, E; Vermeulen, Brecht; Dhaene, Tom; Demeester, Piet

2013-01-01

In order to ensure optimal quality of experience toward end users during video streaming, automatic video quality assessment becomes an important field-of-interest to video service providers. Objective video quality metrics try to estimate perceived quality with high accuracy and in an automated manner. In traditional approaches, these metrics model the complex properties of the human visual system. More recently, however, it has been shown that machine learning approaches can also yield comp...

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.

Localized Multi-Model Extremes Metrics for the Fourth National Climate Assessment

Science.gov (United States)

Thompson, T. R.; Kunkel, K.; Stevens, L. E.; Easterling, D. R.; Biard, J.; Sun, L.

2017-12-01

We have performed localized analysis of scenario-based datasets for the Fourth National Climate Assessment (NCA4). These datasets include CMIP5-based Localized Constructed Analogs (LOCA) downscaled simulations at daily temporal resolution and 1/16th-degree spatial resolution. Over 45 temperature and precipitation extremes metrics have been processed using LOCA data, including threshold, percentile, and degree-days calculations. The localized analysis calculates trends in the temperature and precipitation extremes metrics for relatively small regions such as counties, metropolitan areas, climate zones, administrative areas, or economic zones. For NCA4, we are currently addressing metropolitan areas as defined by U.S. Census Bureau Metropolitan Statistical Areas. Such localized analysis provides essential information for adaptation planning at scales relevant to local planning agencies and businesses. Nearly 30 such regions have been analyzed to date. Each locale is defined by a closed polygon that is used to extract LOCA-based extremes metrics specific to the area. For each metric, single-model data at each LOCA grid location are first averaged over several 30-year historical and future periods. Then, for each metric, the spatial average across the region is calculated using model weights based on both model independence and reproducibility of current climate conditions. The range of single-model results is also captured on the same localized basis, and then combined with the weighted ensemble average for each region and each metric. For example, Boston-area cooling degree days and maximum daily temperature is shown below for RCP8.5 (red) and RCP4.5 (blue) scenarios. We also discuss inter-regional comparison of these metrics, as well as their relevance to risk analysis for adaptation planning.

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.

Wireless sensor network performance metrics for building applications

Energy Technology Data Exchange (ETDEWEB)

Jang, W.S. (Department of Civil Engineering Yeungnam University 214-1 Dae-Dong, Gyeongsan-Si Gyeongsangbuk-Do 712-749 South Korea); Healy, W.M. [Building and Fire Research Laboratory, 100 Bureau Drive, Gaithersburg, MD 20899-8632 (United States)

2010-06-15

Metrics are investigated to help assess the performance of wireless sensors in buildings. Wireless sensor networks present tremendous opportunities for energy savings and improvement in occupant comfort in buildings by making data about conditions and equipment more readily available. A key barrier to their adoption, however, is the uncertainty among users regarding the reliability of the wireless links through building construction. Tests were carried out that examined three performance metrics as a function of transmitter-receiver separation distance, transmitter power level, and obstruction type. These tests demonstrated, via the packet delivery rate, a clear transition from reliable to unreliable communications at different separation distances. While the packet delivery rate is difficult to measure in actual applications, the received signal strength indication correlated well with the drop in packet delivery rate in the relatively noise-free environment used in these tests. The concept of an equivalent distance was introduced to translate the range of reliability in open field operation to that seen in a typical building, thereby providing wireless system designers a rough estimate of the necessary spacing between sensor nodes in building applications. It is anticipated that the availability of straightforward metrics on the range of wireless sensors in buildings will enable more widespread sensing in buildings for improved control and fault detection. (author)

Remarks on G-Metric Spaces

Directory of Open Access Journals (Sweden)

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.

Variational study of spectral shifts. II

International Nuclear Information System (INIS)

Peton, A.

1979-01-01

In a static gravitational field the paths of light are curved. This property can be a priori stated for a V 3 Riemannian manifold: through any two points of V 3 it is possible to draw two families of curves, the straight lines of Euclidean geometry and the photon trajectories z. A fibration of the Galilean space-time can be performed in an original way, by taking the z-trajectories of the photons as the base, the isochronic surfaces as fibres, and 'the equal length time on a z trajectory to reach a given point' as the equivalence relation. The straight lines of Euclidean geometry can then carry the classical mechanics time t, and the z trajectories can carry the optics time (T). These times are related by d(T)=F(x,t)dt. If the Universe is classed as a pseudo-Riemannian manifold of normal hyperbolic type Csup(infinity), the time (T) determined above can be taken as the time coordinate in V 4 . Under these conditions d(S) 2 =F 2 ds 2 , where d(S) 2 is the metric of the Riemannian manifold, conforming to the metric ds 2 and allowing (T) as the cosmic time. The results previously achieved by the author (Peton, 1979) can be used to find 1+zsub(G)=F(Asub(s), tsub(s))/F(Asub(O),tsub(O)) where zsub(G) denotes the shift of the spectral lines due to the metric. In the case of relative motion between O and S, 1+z'=(1+zsub(G))(1+βsub(r))(1-β 2 )sup(-1/2)). The Doppler-Fizeau effect therefore appears as a result of the application of the Fermat principle. (Auth.)

Diagnostic on the appropriation of metrics in software medium enterprises of Medellin city

Directory of Open Access Journals (Sweden)

Piedad Metaute P.

2016-06-01

Full Text Available This article was produced as a result of the investigation, "Ownership and use of metrics in software medium-sized city of Medellin." The objective of this research was to conduct an assessment of the ownership and use of metrics, seeking to make recommendations that contribute to the strengthening of academia and the productive sector in this topic. The methodology used was based on documentary review related to international norms, standards, methodologies, guides and tools that address software quality metrics especially applicable during Software Engineering. The main sources consulted were books, journals and articles, which could raise the foundation for such research, likewise, field research was used, it applied to medium-sized enterprises engaged in the construction of the product, where contact he had with people involved in these processes, of which data pertaining to real contexts where the events are generated are obtained. topics were addressed as project control, process control, software engineering, control of product quality software, application time metrics, applying metrics at different stages, certifications metrics, methodologies, tools used, processes where contributions in their application, types of tests which are applied, among others, which resulted, argued discussion findings generated from the respective regulations, best practices and needs of different contexts where they are used metrics apply software products in addition to the respective conclusions and practical implications that allowed for an assessment of the ownership and use of metrics in software medium-sized city of Medellin, as well as some suggestions for the academy, aimed at strengthening subjects whose responsibility generating skills in Software Engineering, especially in the metrics, and contextualized for significant contributions to the industry.

On the conformal equivalence of harmonic maps and exponentially harmonic maps

International Nuclear Information System (INIS)

Hong Minchun.

1991-06-01

Suppose that (M,g) and (N,h) are compact smooth Riemannian manifolds without boundaries. For m = dim M ≥3, and Φ: (M,g) → (N,h) is exponentially harmonic, there exists a smooth metric g-tilde conformally equivalent to g such that Φ: (M,g-tilde) → (N,h) is harmonic. (author). 7 refs

Geodesics in (Rn, d1

Directory of Open Access Journals (Sweden)

Mehmet KILIÇ

2016-09-01

Full Text Available The notion of geodesic, which may be regarded as an extension of the line segment in Euclidean geometry to the space we study in, has an important place in many branches of geometry, such as Riemannian geometry, Metric geometry, to name but a few. In this article, the concept of geodesic in a metric space will be introduced, then geodesics in the space (Rn, d1 will be characterized. Furthermore, some examples will be presented to demonstrate the effectiveness of the main result.

Monge-Ampere equations and tensorial functors

International Nuclear Information System (INIS)

Tunitsky, Dmitry V

2009-01-01

We consider differential-geometric structures associated with Monge-Ampere equations on manifolds and use them to study the contact linearization of such equations. We also consider the category of Monge-Ampere equations (the morphisms are contact diffeomorphisms) and a number of subcategories. We are chiefly interested in subcategories of Monge-Ampere equations whose objects are locally contact equivalent to equations linear in the second derivatives (semilinear equations), linear in derivatives, almost linear, linear in the second derivatives and independent of the first derivatives, linear, linear and independent of the first derivatives, equations with constant coefficients or evolution equations. We construct a number of functors from the category of Monge-Ampere equations and from some of its subcategories to the category of tensorial objects (that is, multi-valued sections of tensor bundles). In particular, we construct a pseudo-Riemannian metric for every generic Monge-Ampere equation. These functors enable us to establish effectively verifiable criteria for a Monge-Ampere equation to belong to the subcategories listed above.

New Metrics from a Fractional Gravitational Field

International Nuclear Information System (INIS)

El-Nabulsi, Rami Ahmad

2017-01-01

Agop et al. proved in Commun. Theor. Phys. (2008) that, a Reissner–Nordstrom type metric is obtained, if gauge gravitational field in a fractal spacetime is constructed by means of concepts of scale relativity. We prove in this short communication that similar result is obtained if gravity in D-spacetime dimensions is fractionalized by means of the Glaeske–Kilbas–Saigo fractional. Besides, non-singular gravitational fields are obtained without using extra-dimensions. We present few examples to show that these gravitational fields hold a number of motivating features in spacetime physics. (paper)

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....

Can Tweets Predict Citations? Metrics of Social Impact Based on Twitter and Correlation with Traditional Metrics of Scientific Impact

Science.gov (United States)

2011-01-01

Background Citations in peer-reviewed articles and the impact factor are generally accepted measures of scientific impact. Web 2.0 tools such as Twitter, blogs or social bookmarking tools provide the possibility to construct innovative article-level or journal-level metrics to gauge impact and influence. However, the relationship of the these new metrics to traditional metrics such as citations is not known. Objective (1) To explore the feasibility of measuring social impact of and public attention to scholarly articles by analyzing buzz in social media, (2) to explore the dynamics, content, and timing of tweets relative to the publication of a scholarly article, and (3) to explore whether these metrics are sensitive and specific enough to predict highly cited articles. Methods Between July 2008 and November 2011, all tweets containing links to articles in the Journal of Medical Internet Research (JMIR) were mined. For a subset of 1573 tweets about 55 articles published between issues 3/2009 and 2/2010, different metrics of social media impact were calculated and compared against subsequent citation data from Scopus and Google Scholar 17 to 29 months later. A heuristic to predict the top-cited articles in each issue through tweet metrics was validated. Results A total of 4208 tweets cited 286 distinct JMIR articles. The distribution of tweets over the first 30 days after article publication followed a power law (Zipf, Bradford, or Pareto distribution), with most tweets sent on the day when an article was published (1458/3318, 43.94% of all tweets in a 60-day period) or on the following day (528/3318, 15.9%), followed by a rapid decay. The Pearson correlations between tweetations and citations were moderate and statistically significant, with correlation coefficients ranging from .42 to .72 for the log-transformed Google Scholar citations, but were less clear for Scopus citations and rank correlations. A linear multivariate model with time and tweets as significant

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.

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.

A tensor formulation of the equation of transfer for spherically symmetric flows. [radiative transfer in seven dimensional Riemannian space

Science.gov (United States)

Haisch, B. M.

1976-01-01

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

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.

Lie symmetries for systems of evolution equations

Science.gov (United States)

Paliathanasis, Andronikos; Tsamparlis, Michael

2018-01-01

The Lie symmetries for a class of systems of evolution equations are studied. The evolution equations are defined in a bimetric space with two Riemannian metrics corresponding to the space of the independent and dependent variables of the differential equations. The exact relation of the Lie symmetries with the collineations of the bimetric space is determined.

Formal matched asymptotics for degenerate Ricci flow neckpinches

International Nuclear Information System (INIS)

Angenent, Sigurd B; Isenberg, James; Knopf, Dan

2011-01-01

Gu and Zhu (2008 Commun. Anal. Geom. 16 467–94) have shown that type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on S n+1 (n≥2). In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit

Representation of symmetric metric connection via Riemann-Christoffel curvature tensor

International Nuclear Information System (INIS)

Selikhov, A.V.

1989-01-01

Bivector σ-bar μ ν ' which is the Jacoby matrix of the transformation to the Riemanian coordinates is considered in the paper. Basing on the dual nature of σ-bar μ ν ' the representation of metric connection (Christoffel symbols) have been obtained at the Riemanian coordinates via Riemann-Christoffel curvature tensor; the covariant conserved four-momentum in the general theory of relativity have been constructed. 11 refs

SciSpark: Highly Interactive and Scalable Model Evaluation and Climate Metrics for Scientific Data and Analysis

Data.gov (United States)

National Aeronautics and Space Administration — We will construct SciSpark, a scalable system for interactive model evaluation and for the rapid development of climate metrics and analyses. SciSpark directly...

On A Nonlinear Generalization of Sparse Coding and Dictionary Learning.

Science.gov (United States)

Xie, Yuchen; Ho, Jeffrey; Vemuri, Baba

2013-01-01

Existing dictionary learning algorithms are based on the assumption that the data are vectors in an Euclidean vector space ℝ d , and the dictionary is learned from the training data using the vector space structure of ℝ d and its Euclidean L 2 -metric. However, in many applications, features and data often originated from a Riemannian manifold that does not support a global linear (vector space) structure. Furthermore, the extrinsic viewpoint of existing dictionary learning algorithms becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to the application. This paper proposes a novel framework for sparse coding and dictionary learning for data on a Riemannian manifold, and it shows that the existing sparse coding and dictionary learning methods can be considered as special (Euclidean) cases of the more general framework proposed here. We show that both the dictionary and sparse coding can be effectively computed for several important classes of Riemannian manifolds, and we validate the proposed method using two well-known classification problems in computer vision and medical imaging analysis.

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.

The Ricci flow part IV : long-time solutions and related topics

CERN Document Server

Chow, Bennett; Glickenstein, David; Isenberg, James

2015-01-01

Ricci flow is a powerful technique using a heat-type equation to deform Riemannian metrics on manifolds to better metrics in the search for geometric decompositions. With the fourth part of their volume on techniques and applications of the theory, the authors discuss long-time solutions of the Ricci flow and related topics. In dimension 3, Perelman completed Hamilton's program to prove Thurston's geometrization conjecture. In higher dimensions the Ricci flow has remarkable properties, which indicates its usefulness to understand relations between the geometry and topology of manifolds. This b

On quantum field theory in gravitational background

International Nuclear Information System (INIS)

Haag, R.; Narnhofer, H.; Stein, U.

1984-02-01

We discuss Quantum Fields on Riemannian space-time. A principle of local definitness is introduced which is needed beyond equations of motion and commutation relations to fix the theory uniquely. It also allows to formulate local stability. In application to a region with a time-like Killing vector field and horizons it yields the value of the Hawking temperature. The concept of vacuum and particles in a non stationary metric is treated in the example of the Robertson-Walker metric and some remarks on detectors in non inertial motion are added. (orig.)

The geometry of warped product singularities

Science.gov (United States)

Stoica, Ovidiu Cristinel

In this article, the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian manifolds which are semi-regular are constructed as warped products. Applications include cosmological models and black holes solutions with semi-regular singularities. Such singularities are compatible with a certain reformulation of the Einstein equation, which in addition holds at semi-regular singularities too.

Machine learning classifier using abnormal brain network topological metrics in major depressive disorder.

Science.gov (United States)

Guo, Hao; Cao, Xiaohua; Liu, Zhifen; Li, Haifang; Chen, Junjie; Zhang, Kerang

2012-12-05

Resting state functional brain networks have been widely studied in brain disease research. However, it is currently unclear whether abnormal resting state functional brain network metrics can be used with machine learning for the classification of brain diseases. Resting state functional brain networks were constructed for 28 healthy controls and 38 major depressive disorder patients by thresholding partial correlation matrices of 90 regions. Three nodal metrics were calculated using graph theory-based approaches. Nonparametric permutation tests were then used for group comparisons of topological metrics, which were used as classified features in six different algorithms. We used statistical significance as the threshold for selecting features and measured the accuracies of six classifiers with different number of features. A sensitivity analysis method was used to evaluate the importance of different features. The result indicated that some of the regions exhibited significantly abnormal nodal centralities, including the limbic system, basal ganglia, medial temporal, and prefrontal regions. Support vector machine with radial basis kernel function algorithm and neural network algorithm exhibited the highest average accuracy (79.27 and 78.22%, respectively) with 28 features (Pdisorder is associated with abnormal functional brain network topological metrics and statistically significant nodal metrics can be successfully used for feature selection in classification algorithms.

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.

Gödel metrics with chronology protection in Horndeski gravities

Science.gov (United States)

Geng, Wei-Jian; Li, Shou-Long; Lü, H.; Wei, Hao

2018-05-01

Gödel universe, one of the most interesting exact solutions predicted by General Relativity, describes a homogeneous rotating universe containing naked closed time-like curves (CTCs). It was shown that such CTCs are the consequence of the null energy condition in General Relativity. In this paper, we show that the Gödel-type metrics with chronology protection can emerge in Einstein-Horndeski gravity. We construct such exact solutions also in Einstein-Horndeski-Maxwell and Einstein-Horndeski-Proca theories.

The approximation gap for the metric facility location problem is not yet closed

NARCIS (Netherlands)

Byrka, J.; Aardal, K.I.

2007-01-01

We consider the 1.52-approximation algorithm of Mahdian et al. for the metric uncapacitated facility location problem. We show that their algorithm does not close the gap with the lower bound on approximability, 1.463, by providing a construction of instances for which its approximation ratio is not

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

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...

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,

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

Self-adjointness of the Gaffney Laplacian on Vector Bundles

International Nuclear Information System (INIS)

Bandara, Lashi; Milatovic, Ognjen

2015-01-01

We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator

Self-adjointness of the Gaffney Laplacian on Vector Bundles

Energy Technology Data Exchange (ETDEWEB)

Bandara, Lashi, E-mail: lashi.bandara@chalmers.se [Chalmers University of Technology and University of Gothenburg, Mathematical Sciences (Sweden); Milatovic, Ognjen, E-mail: omilatov@unf.edu [University of North Florida, Department of Mathematics and Statistics (United States)

2015-12-15

We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hypothesis that the Cauchy boundary is polar, we demonstrate the self-adjointness of this Laplacian. Furthermore, we show that negligible boundary is a necessary and sufficient condition for the self-adjointness of this operator.

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

A new approach toward geometrical concept of black hole thermodynamics

Energy Technology Data Exchange (ETDEWEB)

Hendi, Seyed Hossein [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of); Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of); Panahiyan, Shahram; Panah, Behzad Eslam; Momennia, Mehrab [Shiraz University, Physics Department and Biruni Observatory, College of Sciences, Shiraz (Iran, Islamic Republic of)

2015-10-15

Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity. (orig.)

A new approach toward geometrical concept of black hole thermodynamics

International Nuclear Information System (INIS)

Hendi, Seyed Hossein; Panahiyan, Shahram; Panah, Behzad Eslam; Momennia, Mehrab

2015-01-01

Motivated by the energy representation of Riemannian metric, in this paper we study different approaches toward the geometrical concept of black hole thermodynamics. We investigate thermodynamical Ricci scalar of Weinhold, Ruppeiner and Quevedo metrics and show that their number and location of divergences do not coincide with phase transition points arisen from heat capacity. Next, we introduce a new metric to solve these problems. We show that the denominator of the Ricci scalar of the new metric contains terms which coincide with different types of phase transitions. We elaborate the effectiveness of the new metric and shortcomings of the previous metrics with some examples. Furthermore, we find a characteristic behavior of the new thermodynamical Ricci scalar which enables one to distinguish two types of phase transitions. In addition, we generalize the new metric for the cases of more than two extensive parameters and show that in these cases the divergencies of thermodynamical Ricci scalar coincide with phase transition points of the heat capacity. (orig.)

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...

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.

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.

Large curvature and background scale independence in single-metric approximations to asymptotic safety

Energy Technology Data Exchange (ETDEWEB)

Morris, Tim R. [STAG Research Centre & Department of Physics and Astronomy, University of Southampton,Highfield, Southampton, SO17 1BJ (United Kingdom)

2016-11-25

In single-metric approximations to the exact renormalization group (RG) for quantum gravity, it has been not been clear how to treat the large curvature domain beyond the point where the effective cutoff scale k is less than the lowest eigenvalue of the appropriate modified Laplacian. We explain why this puzzle arises from background dependence, resulting in Wilsonian RG concepts being inapplicable. We show that when properly formulated over an ensemble of backgrounds, the Wilsonian RG can be restored. This in turn implies that solutions should be smooth and well defined no matter how large the curvature is taken. Even for the standard single-metric type approximation schemes, this construction can be rigorously derived by imposing a modified Ward identity (mWI) corresponding to rescaling the background metric by a constant factor. However compatibility in this approximation requires the space-time dimension to be six. Solving the mWI and flow equation simultaneously, new variables are then derived that are independent of overall background scale.

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)

Real analysis and applications

CERN Document Server

Botelho, Fabio Silva

2018-01-01

This textbook introduces readers to real analysis in one and n dimensions. It is divided into two parts: Part I explores real analysis in one variable, starting with key concepts such as the construction of the real number system, metric spaces, and real sequences and series. In turn, Part II addresses the multi-variable aspects of real analysis. Further, the book presents detailed, rigorous proofs of the implicit theorem for the vectorial case by applying the Banach fixed-point theorem and the differential forms concept to surfaces in Rn. It also provides a brief introduction to Riemannian geometry. With its rigorous, elegant proofs, this self-contained work is easy to read, making it suitable for undergraduate and beginning graduate students seeking a deeper understanding of real analysis and applications, and for all those looking for a well-founded, detailed approach to real analysis.

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.

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.

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.

Smooth and Energy Saving Gait Planning for Humanoid Robot Using Geodesics

Directory of Open Access Journals (Sweden)

Liandong Zhang

2012-01-01

Full Text Available A novel gait planning method using geodesics for humanoid robot is given in this paper. Both the linear inverted pendulum model and the exact Single Support Phase (SSP are studied in our energy optimal gait planning based on geodesics. The kinetic energy of a 2-dimension linear inverted pendulum is obtained at first. We regard the kinetic energy as the Riemannian metric and the geodesic on this metric is studied and this is the shortest line between two points on the Riemannian surface. This geodesic is the optimal kinetic energy gait for the COG because the kinetic energy along geodesic is invariant according to the geometric property of geodesics and the walking is smooth and energy saving. Then the walking in Single Support Phase is studied and the energy optimal gait for the swing leg is obtained using our geodesics method. Finally, experiments using state-of-the-art method and using our geodesics optimization method are carried out respectively and the corresponding currents of the joint motors are recorded. With the currents comparing results, the feasibility of this new gait planning method is verified.

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.

Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity

International Nuclear Information System (INIS)

Vacaru, Sergiu I.; Irwin, Klee

2017-01-01

Geometric methods for constructing exact solutions of equations of motion with first order α ' corrections to the heterotic supergravity action implying a nontrivial Yang-Mills sector and six-dimensional, 6-d, almost-Kaehler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections, and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher-dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections; in particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non-) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kaehler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in the 4-d case and to generalize the solutions to non-vacuum configurations in (super-) gravity/string theories. (orig.)

Off-diagonal deformations of Kerr metrics and black ellipsoids in heterotic supergravity

Energy Technology Data Exchange (ETDEWEB)

Vacaru, Sergiu I. [Quantum Gravity Research, Topanga, CA (United States); University ' ' Al. I. Cuza' ' , Project IDEI, Iasi (Romania); Irwin, Klee [Quantum Gravity Research, Topanga, CA (United States)

2017-01-15

Geometric methods for constructing exact solutions of equations of motion with first order α{sup '} corrections to the heterotic supergravity action implying a nontrivial Yang-Mills sector and six-dimensional, 6-d, almost-Kaehler internal spaces are studied. In 10-d spacetimes, general parametrizations for generic off-diagonal metrics, nonlinear and linear connections, and matter sources, when the equations of motion decouple in very general forms are considered. This allows us to construct a variety of exact solutions when the coefficients of fundamental geometric/physical objects depend on all higher-dimensional spacetime coordinates via corresponding classes of generating and integration functions, generalized effective sources and integration constants. Such generalized solutions are determined by generic off-diagonal metrics and nonlinear and/or linear connections; in particular, as configurations which are warped/compactified to lower dimensions and for Levi-Civita connections. The corresponding metrics can have (non-) Killing and/or Lie algebra symmetries and/or describe (1+2)-d and/or (1+3)-d domain wall configurations, with possible warping nearly almost-Kaehler manifolds, with gravitational and gauge instantons for nonlinear vacuum configurations and effective polarizations of cosmological and interaction constants encoding string gravity effects. A series of examples of exact solutions describing generic off-diagonal supergravity modifications to black hole/ellipsoid and solitonic configurations are provided and analyzed. We prove that it is possible to reproduce the Kerr and other type black solutions in general relativity (with certain types of string corrections) in the 4-d case and to generalize the solutions to non-vacuum configurations in (super-) gravity/string theories. (orig.)

SU-G-BRB-16: Vulnerabilities in the Gamma Metric

International Nuclear Information System (INIS)

Neal, B; Siebers, J

2016-01-01

Purpose: To explore vulnerabilities in the gamma index metric that undermine its wide use as a radiation therapy quality assurance tool. Methods: 2D test field pairs (images) are created specifically to achieve high gamma passing rates, but to also include gross errors by exploiting the distance-to-agreement and percent-passing components of the metric. The first set has no requirement of clinical practicality, but is intended to expose vulnerabilities. The second set exposes clinically realistic vulnerabilities. To circumvent limitations inherent to user-specific tuning of prediction algorithms to match measurements, digital test cases are manually constructed, thereby mimicking high-quality image prediction. Results: With a 3 mm distance-to-agreement metric, changing field size by ±6 mm results in a gamma passing rate over 99%. For a uniform field, a lattice of passing points spaced 5 mm apart results in a passing rate of 100%. Exploiting the percent-passing component, a 10×10 cm"2 field can have a 95% passing rate when an 8 cm"2=2.8×2.8 cm"2 highly out-of-tolerance (e.g. zero dose) square is missing from the comparison image. For clinically realistic vulnerabilities, an arc plan for which a 2D image is created can have a >95% passing rate solely due to agreement in the lateral spillage, with the failing 5% in the critical target region. A field with an integrated boost (e.g whole brain plus small metastases) could neglect the metastases entirely, yet still pass with a 95% threshold. All the failure modes described would be visually apparent on a gamma-map image. Conclusion: The %gamma<1 metric has significant vulnerabilities. High passing rates can obscure critical faults in hypothetical and delivered radiation doses. Great caution should be used with gamma as a QA metric; users should inspect the gamma-map. Visual analysis of gamma-maps may be impractical for cine acquisition.

SU-G-BRB-16: Vulnerabilities in the Gamma Metric

Energy Technology Data Exchange (ETDEWEB)

Neal, B; Siebers, J [University of Virginia Health System, Charlottesville, VA (United States)

2016-06-15

Purpose: To explore vulnerabilities in the gamma index metric that undermine its wide use as a radiation therapy quality assurance tool. Methods: 2D test field pairs (images) are created specifically to achieve high gamma passing rates, but to also include gross errors by exploiting the distance-to-agreement and percent-passing components of the metric. The first set has no requirement of clinical practicality, but is intended to expose vulnerabilities. The second set exposes clinically realistic vulnerabilities. To circumvent limitations inherent to user-specific tuning of prediction algorithms to match measurements, digital test cases are manually constructed, thereby mimicking high-quality image prediction. Results: With a 3 mm distance-to-agreement metric, changing field size by ±6 mm results in a gamma passing rate over 99%. For a uniform field, a lattice of passing points spaced 5 mm apart results in a passing rate of 100%. Exploiting the percent-passing component, a 10×10 cm{sup 2} field can have a 95% passing rate when an 8 cm{sup 2}=2.8×2.8 cm{sup 2} highly out-of-tolerance (e.g. zero dose) square is missing from the comparison image. For clinically realistic vulnerabilities, an arc plan for which a 2D image is created can have a >95% passing rate solely due to agreement in the lateral spillage, with the failing 5% in the critical target region. A field with an integrated boost (e.g whole brain plus small metastases) could neglect the metastases entirely, yet still pass with a 95% threshold. All the failure modes described would be visually apparent on a gamma-map image. Conclusion: The %gamma<1 metric has significant vulnerabilities. High passing rates can obscure critical faults in hypothetical and delivered radiation doses. Great caution should be used with gamma as a QA metric; users should inspect the gamma-map. Visual analysis of gamma-maps may be impractical for cine acquisition.

A new method of constructing scalar-flat Kaehler surfaces

International Nuclear Information System (INIS)

Kim, Jongsu; Pontecorvo, M.

1993-10-01

Building on the work of Donaldson-Friedman we present a geometric way of constructing anti-self-dual hermitian metrics on compact complex surfaces which is based on the relative complex deformations of singular 3-folds with divisors. Some of the consequences are that under a mild condition, fully described by LeBrun-Singer, any blow up of a scalar-flat Kaehler surface admits scalar-flat Kaehler metrics; this is used to prove that such extremal Kaehler metrics exists on an open dense subset of the moduli space of non-minimal ruled surfaces of genus g ≥ 2. Related results have been obtained by LeBrun-Singer. (author). 25 refs

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)

Topological sigma B model in 4-dimensions

International Nuclear Information System (INIS)

Jun, Hyun-Keun; Park, Jae-Suk

2008-01-01

We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensional topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.

Basic performance metrics of in-line inspection tools

Energy Technology Data Exchange (ETDEWEB)

Timashev, Sviatoslav A. [Russian Academy of Sciences (Russian Federation). Ural Branch. Science and Engineering Center

2003-07-01

The paper discusses current possibilities and drawbacks of in-line inspection (ILI) in detecting, identifying, locating and sizing of all types of defects in oil and gas pipelines. A full set of consistent and universal ILI tool performance metrics is constructed. A holistic methodology that extracts maximum value from the ILI measurements in defect detecting, locating, identifying, sizing and verifying the results of ILI is presented. The outlined approach is being implemented as a software component of a multi-purpose HR MFL ILI tool and is proposed for the new API 1163 ILI Qualification Standard. (author)

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.

Asset Decommissioning Risk Metrics for Floating Structures in the Gulf of Mexico.

Science.gov (United States)

Kaiser, Mark J

2015-08-01

Public companies in the United States are required to report standardized values of their proved reserves and asset retirement obligations on an annual basis. When compared, these two measures provide an aggregate indicator of corporate decommissioning risk but, because of their consolidated nature, cannot readily be decomposed at a more granular level. The purpose of this article is to introduce a decommissioning risk metric defined in terms of the ratio of the expected value of an asset's reserves to its expected cost of decommissioning. Asset decommissioning risk (ADR) is more difficult to compute than a consolidated corporate risk measure, but can be used to quantify the decommissioning risk of structures and to perform regional comparisons, and also provides market signals of future decommissioning activity. We formalize two risk metrics for decommissioning and apply the ADR metric to the deepwater Gulf of Mexico (GOM) floater inventory. Deepwater oil and gas structures are expensive to construct, and at the end of their useful life, will be expensive to decommission. The value of proved reserves for the 42 floating structures in the GOM circa January 2013 is estimated to range between $37 and $80 billion for future oil prices between 60 and 120 $/bbl, which is about 10 to 20 times greater than the estimated $4.3 billion to decommission the inventory. Eni's Allegheny and MC Offshore's Jolliet tension leg platforms have ADR metrics less than one and are approaching the end of their useful life. Application of the proposed metrics in the regulatory review of supplemental bonding requirements in the U.S. Outer Continental Shelf is suggested to complement the current suite of financial metrics employed. © 2015 Society for Risk Analysis.

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

Indefinite-metric quantum field theory of general relativity, 5

International Nuclear Information System (INIS)

Nakanishi, Noboru

1979-01-01

The indefinite-metric quantum field theory of general relativity is extended to the coupled system of the gravitational field and a Dirac field on the basis of the vierbein formalism. The six extra degrees of freedom involved in vierbein are made unobservable by introducing an extra subsidiary condition Q sub(s) + phys> = 0, where Q sub(s) denotes a new BRS charge corresponding to the local Lorentz invariance. It is shown that a manifestly covariant, unitary, canonical theory can be constructed consistently on the basis of the vierbein formalism. (author)

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

Lipschitz Metrics for a Class of Nonlinear Wave Equations

Science.gov (United States)

Bressan, Alberto; Chen, Geng

2017-12-01

The nonlinear wave equation {u_{tt}-c(u)(c(u)u_x)_x=0} determines a flow of conservative solutions taking values in the space {H^1(R)}. However, this flow is not continuous with respect to the natural H 1 distance. The aim of this paper is to construct a new metric which renders the flow uniformly Lipschitz continuous on bounded subsets of {H^1(R)}. For this purpose, H 1 is given the structure of a Finsler manifold, where the norm of tangent vectors is defined in terms of an optimal transportation problem. For paths of piecewise smooth solutions, one can carefully estimate how the weighted length grows in time. By the generic regularity result proved in [7], these piecewise regular paths are dense and can be used to construct a geodesic distance with the desired Lipschitz property.

The use of virtual reality for training in carotid artery stenting: a construct validation study

DEFF Research Database (Denmark)

Berry, M.; Reznick, R.; Lystig, T.

2008-01-01

difference in video-gaming habits was demonstrated. Conclusion: With the exception of the metrics of performance time and fluoroscopic use, construct validity of the Procedicus-VIST carotid metrics were not confirmed. Virtual reality simulation as a training method was valued more by novices than...

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…

A step-indexed Kripke model of hidden state via recursive properties on recursively defined metric spaces

DEFF Research Database (Denmark)

Birkedal, Lars; Schwinghammer, Jan; Støvring, Kristian

2010-01-01

for Chargu´eraud and Pottier’s type and capability system including frame and anti-frame rules, based on the operational semantics and step-indexed heap relations. The worlds are constructed as a recursively defined predicate on a recursively defined metric space, which provides a considerably simpler...

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

Stabilization of rotational motion with application to spacecraft attitude control

DEFF Research Database (Denmark)

Wisniewski, Rafal

2000-01-01

for global stabilization of a rotary motion. Along with a model of the system formulated in the Hamilton's canonical from the algorithm uses information about a required potential energy and a dissipation term. The control action is the sum of the gradient of the potential energy and the dissipation force......The objective of this paper is to develop a control scheme for stabilization of a hamiltonian system. The method generalizes the results available in the literature on motion control in the Euclidean space to an arbitrary differrential manifol equipped with a metric. This modification is essencial...... on a Riemannian manifold. The Lyapnov stability theory is adapted and reformulated to fit to the new framework of Riemannian manifolds. Toillustrate the results a spacecraft attitude control problem is considered. Firstly, a global canonical representation for the spacecraft motion is found, then three spacecraft...

Stabilization of rotational motion with application to spacecraft attitude control

DEFF Research Database (Denmark)

Wisniewski, Rafal

2001-01-01

for global stabilization of a rotary motion. Along with a model of the system formulated in the Hamilton's canonical from the algorithm uses information about a required potential energy and a dissipation term. The control action is the sum of the gradient of the potential energy and the dissipation force......The objective of this paper is to develop a control scheme for stabilization of a hamiltonian system. The method generalizes the results available in the literature on motion control in the Euclidean space to an arbitrary differrential manifol equipped with a metric. This modification is essencial...... on a Riemannian manifold. The Lyapnov stability theory is adapted and reformulated to fit to the new framework of Riemannian manifolds. Toillustrate the results a spacecraft attitude control problem is considered. Firstly, a global canonical representation for the spacecraft motion is found, then three spacecraft...

Sensitivity analysis of human brain structural network construction

Directory of Open Access Journals (Sweden)

Kuang Wei

2017-12-01

Full Text Available Network neuroscience leverages diffusion-weighted magnetic resonance imaging and tractography to quantify structural connectivity of the human brain. However, scientists and practitioners lack a clear understanding of the effects of varying tractography parameters on the constructed structural networks. With diffusion images from the Human Connectome Project (HCP, we characterize how structural networks are impacted by the spatial resolution of brain atlases, total number of tractography streamlines, and grey matter dilation with various graph metrics. We demonstrate how injudicious combinations of highly refined brain parcellations and low numbers of streamlines may inadvertently lead to disconnected network models with isolated nodes. Furthermore, we provide solutions to significantly reduce the likelihood of generating disconnected networks. In addition, for different tractography parameters, we investigate the distributions of values taken by various graph metrics across the population of HCP subjects. Analyzing the ranks of individual subjects within the graph metric distributions, we find that the ranks of individuals are affected differently by atlas scale changes. Our work serves as a guideline for researchers to optimize the selection of tractography parameters and illustrates how biological characteristics of the brain derived in network neuroscience studies can be affected by the choice of atlas parcellation schemes. Diffusion tractography has been proven to be a promising noninvasive technique to study the network properties of the human brain. However, how various tractography and network construction parameters affect network properties has not been studied using a large cohort of high-quality data. We utilize data provided by the Human Connectome Project to characterize the changes to network properties induced by varying the brain parcellation atlas scales, the number of reconstructed tractography tracks, and the degree of grey

The decomposition of deformation: New metrics to enhance shape analysis in medical imaging.

Science.gov (United States)

Varano, Valerio; Piras, Paolo; Gabriele, Stefano; Teresi, Luciano; Nardinocchi, Paola; Dryden, Ian L; Torromeo, Concetta; Puddu, Paolo E

2018-05-01

In landmarks-based Shape Analysis size is measured, in most cases, with Centroid Size. Changes in shape are decomposed in affine and non affine components. Furthermore the non affine component can be in turn decomposed in a series of local deformations (partial warps). If the extent of deformation between two shapes is small, the difference between Centroid Size and m-Volume increment is barely appreciable. In medical imaging applied to soft tissues bodies can undergo very large deformations, involving large changes in size. The cardiac example, analyzed in the present paper, shows changes in m-Volume that can reach the 60%. We show here that standard Geometric Morphometrics tools (landmarks, Thin Plate Spline, and related decomposition of the deformation) can be generalized to better describe the very large deformations of biological tissues, without losing a synthetic description. In particular, the classical decomposition of the space tangent to the shape space in affine and non affine components is enriched to include also the change in size, in order to give a complete description of the tangent space to the size-and-shape space. The proposed generalization is formulated by means of a new Riemannian metric describing the change in size as change in m-Volume rather than change in Centroid Size. This leads to a redefinition of some aspects of the Kendall's size-and-shape space without losing Kendall's original formulation. This new formulation is discussed by means of simulated examples using 2D and 3D platonic shapes as well as a real example from clinical 3D echocardiographic data. We demonstrate that our decomposition based approaches discriminate very effectively healthy subjects from patients affected by Hypertrophic Cardiomyopathy. Copyright © 2018 Elsevier B.V. All rights reserved.

Multivariate Tensor-based Brain Anatomical Surface Morphometry via Holomorphic One-Forms

OpenAIRE

Wang, Yalin; Chan, Tony F.; Toga, Arthur W.; Thompson, Paul M.

2009-01-01

Here we introduce multivariate tensor-based surface morphometry using holomorphic one-forms to study brain anatomy. We computed new statistics from the Riemannian metric tensors that retain the full information in the deformation tensor fields. We introduce two different holomorphic one-forms that induce different surface conformal parameterizations. We applied this framework to 3D MRI data to analyze hippocampal surface morphometry in Alzheimer’s Disease (AD; 26 subjects), lateral ventricula...

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

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).

General-Covariant Quantum Mechanics of Dirac Particle in Curved Space-Times

International Nuclear Information System (INIS)

Tagirov, Eh.A.

1994-01-01

A general covariant analog of the standard non-relativistic Quantum Mechanics with relativistic corrections in normal geodesic frames in the general Riemannian space-time is constructed for the Dirac particle. Not only the Pauli equation with hermitian Hamiltonian and the pre-Hilbert structure of space of its solutions but also the matrix elements of hermitian operators of momentum, (curvilinear) spatial coordinates and spin of the particle are deduced as general-covariant asymptotic approximation in c -2 , c being the velocity of light, to their naturally determined general-relativistic pre images. It is shown that the Hamiltonian in the Pauli equation originated by the Dirac equation is unitary equivalent to the operator of energy, originated by the metric energy-momentum tensor of the spinor field. Commutation and other properties of the observables connected with the considered change of geometrical background of Quantum Mechanics are briefly discussed. 7 refs

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.

Section sigma models coupled to symplectic duality bundles on Lorentzian four-manifolds

Science.gov (United States)

Lazaroiu, C. I.; Shahbazi, C. S.

2018-06-01

We give the global mathematical formulation of a class of generalized four-dimensional theories of gravity coupled to scalar matter and to Abelian gauge fields. In such theories, the scalar fields are described by a section of a surjective pseudo-Riemannian submersion π over space-time, whose total space carries a Lorentzian metric making the fibers into totally-geodesic connected Riemannian submanifolds. In particular, π is a fiber bundle endowed with a complete Ehresmann connection whose transport acts through isometries between the fibers. In turn, the Abelian gauge fields are "twisted" by a flat symplectic vector bundle defined over the total space of π. This vector bundle is endowed with a vertical taming which locally encodes the gauge couplings and theta angles of the theory and gives rise to the notion of twisted self-duality, of crucial importance to construct the theory. When the Ehresmann connection of π is integrable, we show that our theories are locally equivalent to ordinary Einstein-Scalar-Maxwell theories and hence provide a global non-trivial extension of the universal bosonic sector of four-dimensional supergravity. In this case, we show using a special trivializing atlas of π that global solutions of such models can be interpreted as classical "locally-geometric" U-folds. In the non-integrable case, our theories differ locally from ordinary Einstein-Scalar-Maxwell theories and may provide a geometric description of classical U-folds which are "locally non-geometric".

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

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.

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)

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.

Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

Directory of Open Access Journals (Sweden)

Golovaty Yuriy

2017-04-01

Full Text Available We are interested in the evolution phenomena on star-like networks composed of several branches which vary considerably in physical properties. The initial boundary value problem for singularly perturbed hyperbolic differential equation on a metric graph is studied. The hyperbolic equation becomes degenerate on a part of the graph as a small parameter goes to zero. In addition, the rates of degeneration may differ in different edges of the graph. Using the boundary layer method the complete asymptotic expansions of solutions are constructed and justified.

Information geometry of density matrices and state estimation

International Nuclear Information System (INIS)

Brody, Dorje C

2011-01-01

Given a pure state vector |x) and a density matrix ρ-hat, the function p(x|ρ-hat)= defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to define a unitary invariant Riemannian metric on the space of density matrices. An alternative derivation of the metric, based on square-root density matrices and trace norms, is provided. This is applied to the problem of quantum-state estimation. In the simplest case of unitary parameter estimation, new higher-order corrections to the uncertainty relations, applicable to general mixed states, are derived. (fast track communication)

Detecting Anisotropic Inclusions Through EIT

Science.gov (United States)

Cristina, Jan; Päivärinta, Lassi

2017-12-01

We study the evolution equation {partialtu=-Λtu} where {Λt} is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary {Σt}. We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the restriction of harmonic functions on M}=Σ_{0 to the boundaries of {partialΣt}. Consequently we are able to derive a lower bound for the difference of the Dirichlet-Neumann maps in terms of the difference of a background metrics g and an inclusion metric {g+χ_{Σ}(h-g)} on a manifold M.

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

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...

Identification of robust statistical downscaling methods based on a comprehensive suite of performance metrics for South Korea

Science.gov (United States)

Eum, H. I.; Cannon, A. J.

2015-12-01

Climate models are a key provider to investigate impacts of projected future climate conditions on regional hydrologic systems. However, there is a considerable mismatch of spatial resolution between GCMs and regional applications, in particular a region characterized by complex terrain such as Korean peninsula. Therefore, a downscaling procedure is an essential to assess regional impacts of climate change. Numerous statistical downscaling methods have been used mainly due to the computational efficiency and simplicity. In this study, four statistical downscaling methods [Bias-Correction/Spatial Disaggregation (BCSD), Bias-Correction/Constructed Analogue (BCCA), Multivariate Adaptive Constructed Analogs (MACA), and Bias-Correction/Climate Imprint (BCCI)] are applied to downscale the latest Climate Forecast System Reanalysis data to stations for precipitation, maximum temperature, and minimum temperature over South Korea. By split sampling scheme, all methods are calibrated with observational station data for 19 years from 1973 to 1991 are and tested for the recent 19 years from 1992 to 2010. To assess skill of the downscaling methods, we construct a comprehensive suite of performance metrics that measure an ability of reproducing temporal correlation, distribution, spatial correlation, and extreme events. In addition, we employ Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to identify robust statistical downscaling methods based on the performance metrics for each season. The results show that downscaling skill is considerably affected by the skill of CFSR and all methods lead to large improvements in representing all performance metrics. According to seasonal performance metrics evaluated, when TOPSIS is applied, MACA is identified as the most reliable and robust method for all variables and seasons. Note that such result is derived from CFSR output which is recognized as near perfect climate data in climate studies. Therefore, the

Using research metrics to evaluate the International Atomic Energy Agency guidelines on quality assurance for R&D

Energy Technology Data Exchange (ETDEWEB)

Bodnarczuk, M.

1994-06-01

The objective of the International Atomic Energy Agency (IAEA) Guidelines on Quality Assurance for R&D is to provide guidance for developing quality assurance (QA) programs for R&D work on items, services, and processes important to safety, and to support the siting, design, construction, commissioning, operation, and decommissioning of nuclear facilities. The standard approach to writing papers describing new quality guidelines documents is to present a descriptive overview of the contents of the document. I will depart from this approach. Instead, I will first discuss a conceptual framework of metrics for evaluating and improving basic and applied experimental science as well as the associated role that quality management should play in understanding and implementing these metrics. I will conclude by evaluating how well the IAEA document addresses the metrics from this conceptual framework and the broader principles of quality management.

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...

Application of the Levenshtein Distance Metric for the Construction of Longitudinal Data Files

Science.gov (United States)

Doran, Harold C.; van Wamelen, Paul B.

2010-01-01

The analysis of longitudinal data in education is becoming more prevalent given the nature of testing systems constructed for No Child Left Behind Act (NCLB). However, constructing the longitudinal data files remains a significant challenge. Students move into new schools, but in many cases the unique identifiers (ID) that should remain constant…

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.

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...

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.

Optical nano artifact metrics using silicon random nanostructures

Science.gov (United States)

Matsumoto, Tsutomu; Yoshida, Naoki; Nishio, Shumpei; Hoga, Morihisa; Ohyagi, Yasuyuki; Tate, Naoya; Naruse, Makoto

2016-08-01

Nano-artifact metrics exploit unique physical attributes of nanostructured matter for authentication and clone resistance, which is vitally important in the age of Internet-of-Things where securing identities is critical. However, expensive and huge experimental apparatuses, such as scanning electron microscopy, have been required in the former studies. Herein, we demonstrate an optical approach to characterise the nanoscale-precision signatures of silicon random structures towards realising low-cost and high-value information security technology. Unique and versatile silicon nanostructures are generated via resist collapse phenomena, which contains dimensions that are well below the diffraction limit of light. We exploit the nanoscale precision ability of confocal laser microscopy in the height dimension; our experimental results demonstrate that the vertical precision of measurement is essential in satisfying the performances required for artifact metrics. Furthermore, by using state-of-the-art nanostructuring technology, we experimentally fabricate clones from the genuine devices. We demonstrate that the statistical properties of the genuine and clone devices are successfully exploited, showing that the liveness-detection-type approach, which is widely deployed in biometrics, is valid in artificially-constructed solid-state nanostructures. These findings pave the way for reasonable and yet sufficiently secure novel principles for information security based on silicon random nanostructures and optical technologies.

Rigidity of generalized Bach-flat vacuum static spaces

Science.gov (United States)

Yun, Gabjin; Hwang, Seungsu

2017-11-01

In this paper, we study the structure of generalized Bach-flat vacuum static spaces. Generalized Bach-flat metrics are considered as extensions of both Einstein and Bach-flat metrics. First, we prove that a compact Riemannian n-manifold with n ≥ 4 which is a generalized Bach-flat vacuum static space is Einstein. A generalized Bach-flat vacuum static space with the potential function f having compact level sets is either Ricci-flat or a warped product with zero scalar curvature when n ≥ 5, and when n = 4, it is Einstein if f has its minimum. Secondly, we consider critical metrics for another quadratic curvature functional involving the Ricci tensor, and prove similar results. Lastly, by applying the technique developed above, we prove Besse conjecture when the manifold is generalized Bach-flat.

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.

A Step-Indexed Kripke Model of Hidden State via Recursive Properties on Recursively Defined Metric Spaces

DEFF Research Database (Denmark)

Schwinghammer, Jan; Birkedal, Lars; Støvring, Kristian

2011-01-01

´eraud and Pottier’s type and capability system including both frame and anti-frame rules. The model is a possible worlds model based on the operational semantics and step-indexed heap relations, and the worlds are constructed as a recursively defined predicate on a recursively defined metric space. We also extend...

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...

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

Estimating physical activity in children: impact of pedometer wear time and metric.

Science.gov (United States)

Laurson, Kelly R; Welk, Gregory J; Eisenmann, Joey C

2015-01-01

The purpose of this study was to provide a practical demonstration of the impact of monitoring frame and metric when assessing pedometer-determined physical activity (PA) in youth. Children (N = 1111) were asked to wear pedometers over a 7-day period during which time worn and steps were recorded each day. Varying data-exclusion criteria were used to demonstrate changes in estimates of PA. Steps were expressed using several metrics and criteria, and construct validity was demonstrated via correlations with adiposity. Meaningful fluctuations in average steps per day and percentage meeting PA recommendations were apparent when different criteria were used. Children who wore the pedometer longer appeared more active, with each minute the pedometer was worn each day accounting for an approximate increase of 11 and 8 steps for boys and girls, respectively (P < .05). Using more restrictive exclusion criteria led to stronger correlations between indices of steps per day, steps per minute, steps per leg length, steps per minute per leg length, and obesity. Wear time has a meaningful impact on estimates of PA. This should be considered when determining exclusion criteria and making comparisons between studies. Results also suggest that incorporating wear time per day and leg length into the metric may increase validity of PA estimates.

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.

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…

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.

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.

Conformal maps between pseudo-Finsler spaces

Science.gov (United States)

Voicu, Nicoleta

The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary for field-theoretical applications and by proposing a technique that reduces some problems involving pseudo-Finslerian conformal vector fields to their pseudo-Riemannian counterparts. Also, we point out, by constructing classes of examples, that conformal groups of flat (locally Minkowskian) pseudo-Finsler spaces can be much richer than both flat Finslerian and pseudo-Euclidean conformal groups.

arXiv Hybrid Fluid Models from Mutual Effective Metric Couplings

CERN Document Server

Kurkela, Aleksi; Preis, Florian; Rebhan, Anton; Soloviev, Alexander

Motivated by a semi-holographic approach to the dynamics of quark-gluon plasma which combines holographic and perturbative descriptions of a strongly coupled infrared and a more weakly coupled ultraviolet sector, we construct a hybrid two-fluid model where interactions between its two sectors are encoded by their effective metric backgrounds, which are determined mutually by their energy-momentum tensors. We derive the most general consistent ultralocal interactions such that the full system has a total conserved energy-momentum tensor in flat Minkowski space and study its consequences in and near thermal equilibrium by working out its phase structure and its hydrodynamic modes.

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.

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)

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.

Hyperspin manifolds

International Nuclear Information System (INIS)

Finkelstein, D.; Finkelstein, S.R.; Holm, C.

1986-01-01

Riemannian manifolds are but one of three ways to extrapolate from fourdimensional Minkowskian manifolds to spaces of higher dimension, and not the most plausible. If we take seriously a certain construction of time space from spinors, and replace the underlying binary spinors by N-ary hyperspinors with new ''internal'' components besides the usual two ''external'' ones, this leads to a second line, the hyperspin manifolds /sub n/ and their tangent spaces d/sub n/, different in structure and symmetry group from the Riemannian line, except that the binary spaces d 2 (Minkowski time space) and 2 (Minkowskian manifold) lie on both. d/sub n/ and /sub n/ have dimension n = N 2 . In hyperspin manifolds the energies of modes of motion multiply instead of adding their squares, and the N-ary chronometric form is not quadratic, but N-ic, with determinantal normal form. For the nine-dimensional ternary hyperspin manifold, we construct the trino, trine-Gordon, and trirac equations and their mass spectra in flat time space. It is possible that our four-dimensional time space sits in a hyperspin manifold rather than in a Kaluza-Klein Riemannian manifold. If so, then gauge quanta with spin-3 exist

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

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.

Geometric flows and (some of) their physical applications

CERN Document Server

Bakas, Ioannis

2005-01-01

The geometric evolution equations provide new ways to address a variety of non-linear problems in Riemannian geometry, and, at the same time, they enjoy numerous physical applications, most notably within the renormalization group analysis of non-linear sigma models and in general relativity. They are divided into classes of intrinsic and extrinsic curvature flows. Here, we review the main aspects of intrinsic geometric flows driven by the Ricci curvature, in various forms, and explain the intimate relation between Ricci and Calabi flows on Kahler manifolds using the notion of super-evolution. The integration of these flows on two-dimensional surfaces relies on the introduction of a novel class of infinite dimensional algebras with infinite growth. It is also explained in this context how Kac's K_2 simple Lie algebra can be used to construct metrics on S^2 with prescribed scalar curvature equal to the sum of any holomorphic function and its complex conjugate; applications of this special problem to general re...

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).

Learning a Novel Detection Metric for the Detection of O’Connell Effect Eclipsing Binaries

Science.gov (United States)

Johnston, Kyle; Haber, Rana; Knote, Matthew; Caballero-Nieves, Saida Maria; Peter, Adrian; Petit, Véronique

2018-01-01

With the advent of digital astronomy, new benefits and new challenges have been presented to the modern day astronomer. No longer can the astronomer rely on manual processing, instead the profession as a whole has begun to adopt more advanced computational means. Here we focus on the construction and application of a novel time-domain signature extraction methodology and the development of a supporting supervised pattern detection algorithm for the targeted identification of eclipsing binaries which demonstrate a feature known as the O’Connell Effect. A methodology for the reduction of stellar variable observations (time-domain data) into Distribution Fields (DF) is presented. Push-Pull metric learning, a variant of LMNN learning, is used to generate a learned distance metric for the specific detection problem proposed. The metric will be trained on a set of a labelled Kepler eclipsing binary data, in particular systems showing the O’Connell effect. Performance estimates will be presented, as well the results of the detector applied to an unlabeled Kepler EB data set; this work is a crucial step in the upcoming era of big data from the next generation of big telescopes, such as LSST.

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...

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...

From the Weyl theory to a theory of locally anisotropic space-time

International Nuclear Information System (INIS)

Bogoslovsky, G.Yu.

1991-01-01

It is shown that Weyl ideas, pertaining to local conformal invariance, find natural embodiment within the framework of a relativistic theory based on a viable Finslerian model of space-time. This is associated with the peculiar property of the conformal invariant Finslerian metric which describes a locally anisotropic space of events. The local conformal transformations of the Riemannian metric tensor leave invariant rest masses as well as all observables and thus appear as local gauge transformations. The corresponding Finslerian theory of gravitation turns out, as a result, to be an Abelian gauge theory. It satisfies the principle of correspondence with Einstein theory and predicts a number of nontrivial physical effects accessible for experimental test under laboratory conditions. 13 refs

The geometric background-field method, renormalization and the Wess-Zumino term in non-linear sigma-models

International Nuclear Information System (INIS)

Mukhi, S.

1986-01-01

A simple recursive algorithm is presented which generates the reparametrization-invariant background-field expansion for non-linear sigma-models on manifolds with an arbitrary riemannian metric. The method is also applicable to Wess-Zumino terms and to counterterms. As an example, the general-metric model is expanded to sixth order and compared with previous results. For locally symmetric spaces, we actually obtain a general formula for the nth order term. The method is shown to facilitate the study of models with Wess-Zumino terms. It is demonstrated that, for chiral models, the Wess-Zumino term is unrenormalized to all orders in perturbation theory even when the model is not conformally invariant. (orig.)

Inverse curvature flows in asymptotically Robertson Walker spaces

Science.gov (United States)

Kröner, Heiko

2018-04-01

In this paper we consider inverse curvature flows in a Lorentzian manifold N which is the topological product of the real numbers with a closed Riemannian manifold and equipped with a Lorentzian metric having a future singularity so that N is asymptotically Robertson Walker. The flow speeds are future directed and given by 1 / F where F is a homogeneous degree one curvature function of class (K*) of the principal curvatures, i.e. the n-th root of the Gauss curvature. We prove longtime existence of these flows and that the flow hypersurfaces converge to smooth functions when they are rescaled with a proper factor which results from the asymptotics of the metric.

Analytic continuation of tgensor fields along geodesics by covariant Taylor series

International Nuclear Information System (INIS)

Tsirulev, A.N.

1995-01-01

It is shown that in a certain normal neighborhood of a submanifold-the analog of a normal neighborhood of a point-the covariant derivatives of all orders of an arbitrary tensor field and of the curvature and torsion along geodesics normal to the submanifold, taken at points of the submanifold, determine under conditions of analyticity the given tensor field by Taylor series with tensor coefficients. Explicit expressions are obtained that provide a recursive procedure for calculating the coefficients of the series in any order. Special cases of the expansion of the components of a pseudo-Riemannian metric with respect to a metric connection without torsion for a point and hypersurface are considered

Extended general relativity: Large-scale antigravity and short-scale gravity with ω=-1 from five-dimensional vacuum

International Nuclear Information System (INIS)

Madriz Aguilar, Jose Edgar; Bellini, Mauricio

2009-01-01

Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we obtain in the framework of the induced matter theory an effective 4D static and spherically symmetric metric which give us ordinary gravitational solutions on small (planetary and astrophysical) scales, but repulsive (anti gravitational) forces on very large (cosmological) scales with ω=-1. Our approach is an unified manner to describe dark energy, dark matter and ordinary matter. We illustrate the theory with two examples, the solar system and the great attractor. From the geometrical point of view, these results follow from the assumption that exists a confining force that make possible that test particles move on a given 4D hypersurface.

Extended general relativity: Large-scale antigravity and short-scale gravity with ω=-1 from five-dimensional vacuum

Science.gov (United States)

Madriz Aguilar, José Edgar; Bellini, Mauricio

2009-08-01

Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we obtain in the framework of the induced matter theory an effective 4D static and spherically symmetric metric which give us ordinary gravitational solutions on small (planetary and astrophysical) scales, but repulsive (anti gravitational) forces on very large (cosmological) scales with ω=-1. Our approach is an unified manner to describe dark energy, dark matter and ordinary matter. We illustrate the theory with two examples, the solar system and the great attractor. From the geometrical point of view, these results follow from the assumption that exists a confining force that make possible that test particles move on a given 4D hypersurface.

Extended general relativity: Large-scale antigravity and short-scale gravity with {omega}=-1 from five-dimensional vacuum

Energy Technology Data Exchange (ETDEWEB)

Madriz Aguilar, Jose Edgar [Instituto de Fisica de la Universidad de Guanajuato, C.P. 37150, Leon Guanajuato (Mexico); Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina)], E-mail: madriz@mdp.edu.ar; Bellini, Mauricio [Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET) (Argentina)], E-mail: mbellini@mdp.edu.ar

2009-08-31

Considering a five-dimensional (5D) Riemannian spacetime with a particular stationary Ricci-flat metric, we obtain in the framework of the induced matter theory an effective 4D static and spherically symmetric metric which give us ordinary gravitational solutions on small (planetary and astrophysical) scales, but repulsive (anti gravitational) forces on very large (cosmological) scales with {omega}=-1. Our approach is an unified manner to describe dark energy, dark matter and ordinary matter. We illustrate the theory with two examples, the solar system and the great attractor. From the geometrical point of view, these results follow from the assumption that exists a confining force that make possible that test particles move on a given 4D hypersurface.

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.

Spectral asymmetry of the massless Dirac operator on a 3-torus

International Nuclear Information System (INIS)

Downes, Robert J.; Vassiliev, Dmitri; Levitin, Michael

2013-01-01

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant

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

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.

Hyperbolic spaces are of strictly negative type

DEFF Research Database (Denmark)

Hjorth, Poul G.; Kokkendorff, Simon L.; Markvorsen, Steen

2002-01-01

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative....... The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type....

Ghost properties of generalized theories of gravitation

International Nuclear Information System (INIS)

Mann, R.B.; Moffat, J.W.

1982-01-01

We investigate theories of gravitation, in which spacetime is non-Riemannian and the metric g/sub munu/ is nonsymmetric, for ghosts and tachyons, using a spin-projection operator formalism. Ghosts are removed not by gauge invariance but by a Lagrange multiplier W/sub μ/, which occurs due to the breaking of projective invariance in the theory. Unified theories based on a Lagrangian containing a term lambdag/sup munu/g/sub / are proved to contain ghosts or tachyons

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...

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.

Emergence of the scale-invariant proportion in a flock from the metric-topological interaction.

Science.gov (United States)

Niizato, Takayuki; Murakami, Hisashi; Gunji, Yukio-Pegio

2014-05-01

Recently, it has become possible to more precisely analyze flocking behavior. Such research has prompted a reconsideration of the notion of neighborhoods in the theoretical model. Flocking based on topological distance is one such result. In a topological flocking model, a bird does not interact with its neighbors on the basis of a fixed-size neighborhood (i.e., on the basis of metric distance), but instead interacts with its nearest seven neighbors. Cavagna et al., moreover, found a new phenomenon in flocks that can be explained by neither metric distance nor topological distance: they found that correlated domains in a flock were larger than the metric and topological distance and that these domains were proportional to the total flock size. However, the role of scale-free correlation is still unclear. In a previous study, we constructed a metric-topological interaction model on three-dimensional spaces and showed that this model exhibited scale-free correlation. In this study, we found that scale-free correlation in a two-dimensional flock was more robust than in a three-dimensional flock for the threshold parameter. Furthermore, we also found a qualitative difference in behavior from using the fluctuation coherence, which we observed on three-dimensional flocking behavior. Our study suggests that two-dimensional flocks try to maintain a balance between the flock size and flock mobility by breaking into several smaller flocks. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

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.

Metrics to assess ecological condition, change, and impacts in sandy beach ecosystems.

Science.gov (United States)

Schlacher, Thomas A; Schoeman, David S; Jones, Alan R; Dugan, Jenifer E; Hubbard, David M; Defeo, Omar; Peterson, Charles H; Weston, Michael A; Maslo, Brooke; Olds, Andrew D; Scapini, Felicita; Nel, Ronel; Harris, Linda R; Lucrezi, Serena; Lastra, Mariano; Huijbers, Chantal M; Connolly, Rod M

2014-11-01

Complexity is increasingly the hallmark in environmental management practices of sandy shorelines. This arises primarily from meeting growing public demands (e.g., real estate, recreation) whilst reconciling economic demands with expectations of coastal users who have modern conservation ethics. Ideally, shoreline management is underpinned by empirical data, but selecting ecologically-meaningful metrics to accurately measure the condition of systems, and the ecological effects of human activities, is a complex task. Here we construct a framework for metric selection, considering six categories of issues that authorities commonly address: erosion; habitat loss; recreation; fishing; pollution (litter and chemical contaminants); and wildlife conservation. Possible metrics were scored in terms of their ability to reflect environmental change, and against criteria that are widely used for judging the performance of ecological indicators (i.e., sensitivity, practicability, costs, and public appeal). From this analysis, four types of broadly applicable metrics that also performed very well against the indicator criteria emerged: 1.) traits of bird populations and assemblages (e.g., abundance, diversity, distributions, habitat use); 2.) breeding/reproductive performance sensu lato (especially relevant for birds and turtles nesting on beaches and in dunes, but equally applicable to invertebrates and plants); 3.) population parameters and distributions of vertebrates associated primarily with dunes and the supralittoral beach zone (traditionally focused on birds and turtles, but expandable to mammals); 4.) compound measurements of the abundance/cover/biomass of biota (plants, invertebrates, vertebrates) at both the population and assemblage level. Local constraints (i.e., the absence of birds in highly degraded urban settings or lack of dunes on bluff-backed beaches) and particular issues may require alternatives. Metrics - if selected and applied correctly - provide

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

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.

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

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.

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.

On iterative solution of nonlinear functional equations in a metric space

Directory of Open Access Journals (Sweden)

Rabindranath Sen

1983-01-01

Full Text Available Given that A and P as nonlinear onto and into self-mappings of a complete metric space R, we offer here a constructive proof of the existence of the unique solution of the operator equation Au=Pu, where u∈R, by considering the iterative sequence Aun+1=Pun (u0 prechosen, n=0,1,2,…. We use Kannan's criterion [1] for the existence of a unique fixed point of an operator instead of the contraction mapping principle as employed in [2]. Operator equations of the form Anu=Pmu, where u∈R, n and m positive integers, are also treated.

The information metric on the moduli space of instantons with global symmetries

Directory of Open Access Journals (Sweden)

Emanuel Malek

2016-02-01

Full Text Available In this note we revisit Hitchin's prescription [1] of the Fisher metric as a natural measure on the moduli space of instantons that encodes the space–time symmetries of a classical field theory. Motivated by the idea of the moduli space of supersymmetric instantons as an emergent space in the sense of the gauge/gravity duality, we extend the prescription to encode also global symmetries of the underlying theory. We exemplify our construction with the instanton solution of the CPN sigma model on R2.

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.

Measuring scientific impact beyond academia: An assessment of existing impact metrics and proposed improvements.

Science.gov (United States)

Ravenscroft, James; Liakata, Maria; Clare, Amanda; Duma, Daniel

2017-01-01

How does scientific research affect the world around us? Being able to answer this question is of great importance in order to appropriately channel efforts and resources in science. The impact by scientists in academia is currently measured by citation based metrics such as h-index, i-index and citation counts. These academic metrics aim to represent the dissemination of knowledge among scientists rather than the impact of the research on the wider world. In this work we are interested in measuring scientific impact beyond academia, on the economy, society, health and legislation (comprehensive impact). Indeed scientists are asked to demonstrate evidence of such comprehensive impact by authoring case studies in the context of the Research Excellence Framework (REF). We first investigate the extent to which existing citation based metrics can be indicative of comprehensive impact. We have collected all recent REF impact case studies from 2014 and we have linked these to papers in citation networks that we constructed and derived from CiteSeerX, arXiv and PubMed Central using a number of text processing and information retrieval techniques. We have demonstrated that existing citation-based metrics for impact measurement do not correlate well with REF impact results. We also consider metrics of online attention surrounding scientific works, such as those provided by the Altmetric API. We argue that in order to be able to evaluate wider non-academic impact we need to mine information from a much wider set of resources, including social media posts, press releases, news articles and political debates stemming from academic work. We also provide our data as a free and reusable collection for further analysis, including the PubMed citation network and the correspondence between REF case studies, grant applications and the academic literature.

Measuring scientific impact beyond academia: An assessment of existing impact metrics and proposed improvements.

Directory of Open Access Journals (Sweden)

James Ravenscroft

Full Text Available How does scientific research affect the world around us? Being able to answer this question is of great importance in order to appropriately channel efforts and resources in science. The impact by scientists in academia is currently measured by citation based metrics such as h-index, i-index and citation counts. These academic metrics aim to represent the dissemination of knowledge among scientists rather than the impact of the research on the wider world. In this work we are interested in measuring scientific impact beyond academia, on the economy, society, health and legislation (comprehensive impact. Indeed scientists are asked to demonstrate evidence of such comprehensive impact by authoring case studies in the context of the Research Excellence Framework (REF. We first investigate the extent to which existing citation based metrics can be indicative of comprehensive impact. We have collected all recent REF impact case studies from 2014 and we have linked these to papers in citation networks that we constructed and derived from CiteSeerX, arXiv and PubMed Central using a number of text processing and information retrieval techniques. We have demonstrated that existing citation-based metrics for impact measurement do not correlate well with REF impact results. We also consider metrics of online attention surrounding scientific works, such as those provided by the Altmetric API. We argue that in order to be able to evaluate wider non-academic impact we need to mine information from a much wider set of resources, including social media posts, press releases, news articles and political debates stemming from academic work. We also provide our data as a free and reusable collection for further analysis, including the PubMed citation network and the correspondence between REF case studies, grant applications and the academic literature.

Essential equivalence of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) and steepest-entropy-ascent models of dissipation for nonequilibrium thermodynamics.

Science.gov (United States)

Montefusco, Alberto; Consonni, Francesco; Beretta, Gian Paolo

2015-04-01

By reformulating the steepest-entropy-ascent (SEA) dynamical model for nonequilibrium thermodynamics in the mathematical language of differential geometry, we compare it with the primitive formulation of the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) model and discuss the main technical differences of the two approaches. In both dynamical models the description of dissipation is of the "entropy-gradient" type. SEA focuses only on the dissipative, i.e., entropy generating, component of the time evolution, chooses a sub-Riemannian metric tensor as dissipative structure, and uses the local entropy density field as potential. GENERIC emphasizes the coupling between the dissipative and nondissipative components of the time evolution, chooses two compatible degenerate structures (Poisson and degenerate co-Riemannian), and uses the global energy and entropy functionals as potentials. As an illustration, we rewrite the known GENERIC formulation of the Boltzmann equation in terms of the square root of the distribution function adopted by the SEA formulation. We then provide a formal proof that in more general frameworks, whenever all degeneracies in the GENERIC framework are related to conservation laws, the SEA and GENERIC models of the dissipative component of the dynamics are essentially interchangeable, provided of course they assume the same kinematics. As part of the discussion, we note that equipping the dissipative structure of GENERIC with the Leibniz identity makes it automatically SEA on metric leaves.

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.

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.

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.)

Asset Attribution Stability and Portfolio Construction: An Educational Example

Science.gov (United States)

Chong, James T.; Jennings, William P.; Phillips, G. Michael

2014-01-01

This paper illustrates how a third statistic from asset pricing models, the R-squared statistic, may have information that can help in portfolio construction. Using a traditional CAPM model in comparison to an 18-factor Arbitrage Pricing Style Model, a portfolio separation test is conducted. Portfolio returns and risk metrics are compared using…

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

Two-Dimensional One-Component Plasma on Flamm's Paraboloid

Science.gov (United States)

Fantoni, Riccardo; Téllez, Gabriel

2008-11-01

We study the classical non-relativistic two-dimensional one-component plasma at Coulomb coupling Γ=2 on the Riemannian surface known as Flamm's paraboloid which is obtained from the spatial part of the Schwarzschild metric. At this special value of the coupling constant, the statistical mechanics of the system are exactly solvable analytically. The Helmholtz free energy asymptotic expansion for the large system has been found. The density of the plasma, in the thermodynamic limit, has been carefully studied in various situations.

A New Look to Massive Neutron Cores

OpenAIRE

Bel, Ll.

2002-01-01

We reconsider the problem of modelling static spherically symmetric perfect fluid configurations with an equation of state from a point of view of that requires the use of the concept of principal transform of a 3-dimensional Riemannian metric. We discuss from this new point of view the meaning of those familiar quantities that we call density, pressure and geometry in a relativistic context. This is not simple semantics. To prove it we apply the new ideas to recalculate the maximum mass that...

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

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.

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.

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.

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

Table for constructing the spin coefficients in general relativity

International Nuclear Information System (INIS)

Cocke, W.J.

1989-01-01

The spin coefficients in spinor calculus in Riemannian space-time are linear functions of the curls of the connecting quantities (the Infeld--Van der Waerden symbols). We show that in the Newman-Penrose formalism the expressions for the spin coefficients are quite manageable, if they are written in terms of the Newman-Penrose tetrad vectors. We present a table of the components of the spin coefficients explicitly in terms of the curls of the individual tetrad vectors

Informatics in radiology: Efficiency metrics for imaging device productivity.

Science.gov (United States)

Hu, Mengqi; Pavlicek, William; Liu, Patrick T; Zhang, Muhong; Langer, Steve G; Wang, Shanshan; Place, Vicki; Miranda, Rafael; Wu, Teresa Tong

2011-01-01

Acute awareness of the costs associated with medical imaging equipment is an ever-present aspect of the current healthcare debate. However, the monitoring of productivity associated with expensive imaging devices is likely to be labor intensive, relies on summary statistics, and lacks accepted and standardized benchmarks of efficiency. In the context of the general Six Sigma DMAIC (design, measure, analyze, improve, and control) process, a World Wide Web-based productivity tool called the Imaging Exam Time Monitor was developed to accurately and remotely monitor imaging efficiency with use of Digital Imaging and Communications in Medicine (DICOM) combined with a picture archiving and communication system. Five device efficiency metrics-examination duration, table utilization, interpatient time, appointment interval time, and interseries time-were derived from DICOM values. These metrics allow the standardized measurement of productivity, to facilitate the comparative evaluation of imaging equipment use and ongoing efforts to improve efficiency. A relational database was constructed to store patient imaging data, along with device- and examination-related data. The database provides full access to ad hoc queries and can automatically generate detailed reports for administrative and business use, thereby allowing staff to monitor data for trends and to better identify possible changes that could lead to improved productivity and reduced costs in association with imaging services. © RSNA, 2011.

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.

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.

Euler numbers of four-dimensional rotating black holes with the Euclidean signature

International Nuclear Information System (INIS)

Ma Zhengze

2003-01-01

For a black hole's spacetime manifold in the Euclidean signature, its metric is positive definite and therefore a Riemannian manifold. It can be regarded as a gravitational instanton and a topological characteristic which is the Euler number to which it is associated. In this paper we derive a formula for the Euler numbers of four-dimensional rotating black holes by the integral of the Euler density on the spacetime manifolds of black holes. Using this formula, we obtain that the Euler numbers of Kerr and Kerr-Newman black holes are 2. We also obtain that the Euler number of the Kerr-Sen metric in the heterotic string theory with one boost angle nonzero is 2, which is in accordance with its topology

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.

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)

The algebra of space-time as basis of a quantum field theory of all fermions and interactions

International Nuclear Information System (INIS)

Wolf, A.K.

2005-01-01

In this thesis a construction of a grand unified theory on the base of algebras of vector fields on a Riemannian space-time is described. Hereby from the vector and covector fields a Clifford-geometrical algebra is generated. (HSI)

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.

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.

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...

MESUR metrics from scholarly usage of resources

CERN Document Server

CERN. Geneva; Van de Sompel, Herbert

2007-01-01

Usage data is increasingly regarded as a valuable resource in the assessment of scholarly communication items. However, the development of quantitative, usage-based indicators of scholarly impact is still in its infancy. The Digital Library Research & Prototyping Team at the Los Alamos National Laboratory's Research library has therefore started a program to expand the set of usage-based tools for the assessment of scholarly communication items. The two-year MESUR project, funded by the Andrew W. Mellon Foundation, aims to define and validate a range of usage-based impact metrics, and issue guidelines with regards to their characteristics and proper application. The MESUR project is constructing a large-scale semantic model of the scholarly community that seamlessly integrates a wide range of bibliographic, citation and usage data. Functioning as a reference data set, this model is analyzed to characterize the intricate networks of typed relationships that exist in the scholarly community. The resulting c...

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 ...

Hearing loss among older construction workers: Updated analyses.

Science.gov (United States)

Dement, John; Welch, Laura S; Ringen, Knut; Cranford, Kim; Quinn, Patricia

2018-04-01

A prior study of this construction worker population found significant noise-associated hearing loss. This follow-up study included a much larger study population and consideration of additional risk factors. Data included audiometry, clinical chemistry, personal history, and work history. Qualitative exposure metrics for noise and solvents were developed. Analyses compared construction workers to an internal reference group with lower exposures and an external worker population with low noise exposure. Among participants (n = 19 127) an overall prevalence of hearing loss of 58% was observed, with significantly increased prevalence across all construction trades. Construction workers had significantly increased risk of hearing loss compared to reference populations, with increasing risk by work duration. Noise exposure, solvent exposure, hypertension, and smoking were significant risk factors in multivariate models. Results support a causal relationship between construction trades work and hearing loss. Prevention should focus on reducing exposure to noise, solvents, and cigarette smoke. © 2018 Wiley Periodicals, Inc.

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)

Metric-based approach and tool for modeling the I and C system using Markov chains

International Nuclear Information System (INIS)

Butenko, Valentyna; Kharchenko, Vyacheslav; Odarushchenko, Elena; Butenko, Dmitriy

2015-01-01

Markov's chains (MC) are well-know and widely applied in dependability and performability analysis of safety-critical systems, because of the flexible representation of system components dependencies and synchronization. There are few radblocks for greater application of the MC: accounting the additional system components increases the model state-space and complicates analysis; the non-numerically sophisticated user may find it difficult to decide between the variety of numerical methods to determine the most suitable and accurate for their application. Thus obtaining the high accurate and trusted modeling results becomes a nontrivial task. In this paper, we present the metric-based approach for selection of the applicable solution approach, based on the analysis of MCs stiffness, decomposability, sparsity and fragmentedness. Using this selection procedure the modeler can provide the verification of earlier obtained results. The presented approach was implemented in utility MSMC, which supports the MC construction, metric-based analysis, recommendations shaping and model solution. The model can be exported to the wall-known off-the-shelf mathematical packages for verification. The paper presents the case study of the industrial NPP I and C system, manufactured by RPC Radiy. The paper shows an application of metric-based approach and MSMC fool for dependability and safety analysis of RTS, and procedure of results verification. (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.

Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations

International Nuclear Information System (INIS)

Mestdag, T; Crampin, M

2008-01-01

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated with Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper, we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory

Metric Learning for Hyperspectral Image Segmentation

Science.gov (United States)

Bue, Brian D.; Thompson, David R.; Gilmore, Martha S.; Castano, Rebecca

2011-01-01

We present a metric learning approach to improve the performance of unsupervised hyperspectral image segmentation. Unsupervised spatial segmentation can assist both user visualization and automatic recognition of surface features. Analysts can use spatially-continuous segments to decrease noise levels and/or localize feature boundaries. However, existing segmentation methods use tasks-agnostic measures of similarity. Here we learn task-specific similarity measures from training data, improving segment fidelity to classes of interest. Multiclass Linear Discriminate Analysis produces a linear transform that optimally separates a labeled set of training classes. The defines a distance metric that generalized to a new scenes, enabling graph-based segmentation that emphasizes key spectral features. We describe tests based on data from the Compact Reconnaissance Imaging Spectrometer (CRISM) in which learned metrics improve segment homogeneity with respect to mineralogical classes.

Validation of Metrics as Error Predictors

Science.gov (United States)

Mendling, Jan

In this chapter, we test the validity of metrics that were defined in the previous chapter for predicting errors in EPC business process models. In Section 5.1, we provide an overview of how the analysis data is generated. Section 5.2 describes the sample of EPCs from practice that we use for the analysis. Here we discuss a disaggregation by the EPC model group and by error as well as a correlation analysis between metrics and error. Based on this sample, we calculate a logistic regression model for predicting error probability with the metrics as input variables in Section 5.3. In Section 5.4, we then test the regression function for an independent sample of EPC models from textbooks as a cross-validation. Section 5.5 summarizes the findings.

Predicting class testability using object-oriented metrics

NARCIS (Netherlands)

M. Bruntink (Magiel); A. van 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

Software Power Metric Model: An Implementation | Akwukwuma ...

African Journals Online (AJOL)

... and the execution time (TIME) in each case was recorded. We then obtain the application functions point count. Our result shows that the proposed metric is computable, consistent in its use of unit, and is programming language independent. Keywords: Software attributes, Software power, measurement, Software metric, ...

Meter Detection in Symbolic Music Using Inner Metric Analysis

NARCIS (Netherlands)

de Haas, W.B.; Volk, A.

2016-01-01

In this paper we present PRIMA: a new model tailored to symbolic music that detects the meter and the first downbeat position of a piece. Given onset data, the metrical structure of a piece is interpreted using the Inner Metric Analysis (IMA) model. IMA identifies the strong and weak metrical

Heun Polynomials and Exact Solutions for the Massless Dirac Particle in the C-Metric

Science.gov (United States)

Kar, Priyasri; Singh, Ritesh K.; Dasgupta, Ananda; Panigrahi, Prasanta K.

2018-03-01

The equation of motion of a massless Dirac particle in the C-metric leads to the general Heun equation (GHE) for the radial and the polar variables. The GHE, under certain parametric conditions, is cast in terms of a new set of su(1, 1) generators involving differential operators of degrees ±1/2 and 0. Additional Heun polynomials are obtained using this new algebraic structure and are used to construct some exact solutions for the radial and the polar parts of the Dirac equation.

Performance metrics for the evaluation of hyperspectral chemical identification systems

Science.gov (United States)

Truslow, Eric; Golowich, Steven; Manolakis, Dimitris; Ingle, Vinay

2016-02-01

Remote sensing of chemical vapor plumes is a difficult but important task for many military and civilian applications. Hyperspectral sensors operating in the long-wave infrared regime have well-demonstrated detection capabilities. However, the identification of a plume's chemical constituents, based on a chemical library, is a multiple hypothesis testing problem which standard detection metrics do not fully describe. We propose using an additional performance metric for identification based on the so-called Dice index. Our approach partitions and weights a confusion matrix to develop both the standard detection metrics and identification metric. Using the proposed metrics, we demonstrate that the intuitive system design of a detector bank followed by an identifier is indeed justified when incorporating performance information beyond the standard detection metrics.

Verification of Equivalence of the Axial Gauge to the Coulomb Gauge in QED by Embedding in the Indefinite Metric Hilbert Space : Particles and Fields

OpenAIRE

Yuji, NAKAWAKI; Azuma, TANAKA; Kazuhiko, OZAKI; Division of Physics and Mathematics, Faculty of Engineering Setsunan University; Junior College of Osaka Institute of Technology; Faculty of General Education, Osaka Institute of Technology

1994-01-01

Gauge Equivalence of the A_3=0 (axial) gauge to the Coulomb gauge is directly verified in QED. For that purpose a pair of conjugate zero-norm fields are introduced. This enables us to construct a canonical formulation in the axial gauge embedded in the indefinite metric Hilbert space in such a way that the Feynman rules are not altered. In the indefinite metric Hilbert space we can implement a gauge transformation, which otherwise has to be carried out only by hand, as main parts of a canonic...

Decision Analysis for Metric Selection on a Clinical Quality Scorecard.

Science.gov (United States)

Guth, Rebecca M; Storey, Patricia E; Vitale, Michael; Markan-Aurora, Sumita; Gordon, Randolph; Prevost, Traci Q; Dunagan, Wm Claiborne; Woeltje, Keith F

2016-09-01

Clinical quality scorecards are used by health care institutions to monitor clinical performance and drive quality improvement. Because of the rapid proliferation of quality metrics in health care, BJC HealthCare found it increasingly difficult to select the most impactful scorecard metrics while still monitoring metrics for regulatory purposes. A 7-step measure selection process was implemented incorporating Kepner-Tregoe Decision Analysis, which is a systematic process that considers key criteria that must be satisfied in order to make the best decision. The decision analysis process evaluates what metrics will most appropriately fulfill these criteria, as well as identifies potential risks associated with a particular metric in order to identify threats to its implementation. Using this process, a list of 750 potential metrics was narrowed to 25 that were selected for scorecard inclusion. This decision analysis process created a more transparent, reproducible approach for selecting quality metrics for clinical quality scorecards. © The Author(s) 2015.

Common fixed point theorems in intuitionistic fuzzy metric spaces and L-fuzzy metric spaces with nonlinear contractive condition

International Nuclear Information System (INIS)

Jesic, Sinisa N.; Babacev, Natasa A.

2008-01-01

The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2004;22:1039-46] and L-fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L-fuzzy metric spaces. Chaos, Solitons and Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458-64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436-40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261-3]. Some examples and comments according to the preceding results are given

43 CFR 12.915 - Metric system of measurement.

Science.gov (United States)

2010-10-01

... procurements, grants, and other business-related activities. Metric implementation may take longer where the... recipient, such as when foreign competitors are producing competing products in non-metric units. (End of...

Cophenetic metrics for phylogenetic trees, after Sokal and Rohlf.

Science.gov (United States)

Cardona, Gabriel; Mir, Arnau; Rosselló, Francesc; Rotger, Lucía; Sánchez, David

2013-01-16

Phylogenetic tree comparison metrics are an important tool in the study of evolution, and hence the definition of such metrics is an interesting problem in phylogenetics. In a paper in Taxon fifty years ago, Sokal and Rohlf proposed to measure quantitatively the difference between a pair of phylogenetic trees by first encoding them by means of their half-matrices of cophenetic values, and then comparing these matrices. This idea has been used several times since then to define dissimilarity measures between phylogenetic trees but, to our knowledge, no proper metric on weighted phylogenetic trees with nested taxa based on this idea has been formally defined and studied yet. Actually, the cophenetic values of pairs of different taxa alone are not enough to single out phylogenetic trees with weighted arcs or nested taxa. For every (rooted) phylogenetic tree T, let its cophenetic vectorφ(T) consist of all pairs of cophenetic values between pairs of taxa in T and all depths of taxa in T. It turns out that these cophenetic vectors single out weighted phylogenetic trees with nested taxa. We then define a family of cophenetic metrics dφ,p by comparing these cophenetic vectors by means of Lp norms, and we study, either analytically or numerically, some of their basic properties: neighbors, diameter, distribution, and their rank correlation with each other and with other metrics. The cophenetic metrics can be safely used on weighted phylogenetic trees with nested taxa and no restriction on degrees, and they can be computed in O(n2) time, where n stands for the number of taxa. The metrics dφ,1 and dφ,2 have positive skewed distributions, and they show a low rank correlation with the Robinson-Foulds metric and the nodal metrics, and a very high correlation with each other and with the splitted nodal metrics. The diameter of dφ,p, for p⩾1 , is in O(n(p+2)/p), and thus for low p they are more discriminative, having a wider range of values.

Finite Metric Spaces of Strictly negative Type

DEFF Research Database (Denmark)

Hjorth, Poul G.

If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...