Depperschmidt, Andrej; Pfaffelhuber, Peter
2011-01-01
A marked metric measure space (mmm-space) is a triple (X,r,mu), where (X,r) is a complete and separable metric space and mu is a probability measure on XxI for some Polish space I of possible marks. We study the space of all (equivalence classes of) marked metric measure spaces for some fixed I. It arises as state space in the construction of Markov processes which take values in random graphs, e.g. tree-valued dynamics describing randomly evolving genealogical structures in population models. We derive here the topological properties of the space of mmm-spaces needed to study convergence in distribution of random mmm-spaces. Extending the notion of the Gromov-weak topology introduced in (Greven, Pfaffelhuber and Winter, 2009), we define the marked Gromov-weak topology, which turns the set of mmm-spaces into a Polish space. We give a characterization of tightness for families of distributions of random mmm- spaces and identify a convergence determining algebra of functions, called polynomials.
Angles between Curves in Metric Measure Spaces
Han Bang-Xian
2017-08-01
Full Text Available The goal of the paper is to study the angle between two curves in the framework of metric (and metric measure spaces. More precisely, we give a new notion of angle between two curves in a metric space. Such a notion has a natural interplay with optimal transportation and is particularly well suited for metric measure spaces satisfying the curvature-dimension condition. Indeed one of the main results is the validity of the cosine formula on RCD*(K, N metric measure spaces. As a consequence, the new introduced notions are compatible with the corresponding classical ones for Riemannian manifolds, Ricci limit spaces and Alexandrov spaces.
Lipschitz correspondence between metric measure spaces and random distance matrices
Gadgil, Siddhartha
2011-01-01
Given a metric space with a Borel probability measure, for each integer $N$ we obtain a probability distribution on $N\\times N$ distance matrices by considering the distances between pairs of points in a sample consisting of $N$ points chosen indepenedently from the metric space with respect to the given measure. We show that this gives an asymptotically bi-Lipschitz relation between metric measure spaces and the corresponding distance matrices. This is an effective version of a result of Vershik that metric measure spaces are determined by associated distributions on infinite random matrices.
Metric measure space as a framework for gravitation
Rahmanpour, Nafiseh; Shojaie, Hossein
2016-10-01
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar f, dubbed as density function, which here appears as a conformal degree of freedom. In this framework, we present conformally invariant field equations, the relevant identities and geodesic equations. In metric measure space, the volume element and accordingly the operators with integral based definitions are modified. For instance, the divergence operator in this space differs from the Riemannian one. As a result, a gravitational theory formulated in this space has a generalized second Bianchi identity and a generalized conservation of energy-momentum tensor. It is shown how, by using the generalized identity for conservation of energy-momentum tensor, one can obtain a conformally invariant geodesic equation. By comparison of the geodesic equations in metric measure space with the Bohmian trajectories, in both relativistic and non-relativistic regimes, a relation between density function f and the quantum potential is proposed. This suggests metric measure space to be considered as a suitable framework for geometric description of Bohm's quantum mechanics. On the other hand, as it is known, Weyl geometry is one of the main approaches to construct conformally invariant gravitational models. Regarding the fact that the connection in the integrable Weyl space is modified and in metric measure space remains the same as it is in the Riemann space, the mathematical analogy between these two spaces is also discussed.
Metric Measure Space as a Framework for Gravitation
Rahmanpour, Nafiseh
2016-01-01
In this manuscript, we show how conformal invariance can be incorporated in a classical theory of gravitation, in the context of metric measure space. Metric measure space involves a geometrical scalar $f$, dubbed as density function, which here appears as a conformal degree of freedom. In this framework, we present conformally invariant field equations, the relevant identities and geodesic equations. In metric measure space, the volume element and accordingly the operators with integral based definitions are modified. For instance, the divergence operator in this space differs from the Riemannian one. As a result, a gravitational theory formulated in this space has a generalized second Bianchi identity and a generalized conservation of energy-momentum tensor. It is shown how, by using the generalized identity for conservation of energy-momentum tensor, one can obtain a conformally invariant geodesic equation. By comparison of the geodesic equations in metric measure space with the Bohmian trajectories, in bo...
Thin and fat sets for doubling measures in metric spaces
Ojala, Tuomo; Suomala, Ville
2011-01-01
We consider sets in uniformly perfect metric spaces which are null for every doubling measure of the space or which have positive measure for all doubling measures. These sets are called thin and fat, respectively. In our main results, we give sufficient conditions for certain cut-out sets being thin or fat.
Equivalence of Gromov-Prohorov- and Gromov's Box-Metric on the Space of Metric Measure Spaces
Löhr, Wolfgang
2011-01-01
Stochastic processes with values in the space of metric measure spaces (complete separable metric spaces equipped with a probability measure) are becoming more and more important in probability theory, especially for the modelling of evolutionary systems, where at each time the whole phylogenetic tree is considered. Greven, Pfaffelhuber and Winter introduced the Gromov-Prohorov metric d_{GPW} on the space of metric measure spaces and showed that it induces the Gromov-weak topology. They also conjectured that this topology coincides with the topology induced by Gromov's Box_1 metric. In this note, we show that this is indeed true, and the metrics are even bi-Lipschitz equivalent. More precisely, d_{GPW}= 1/2 Box_{1/2} and hence d_{GPW} <= Box_1 <= 2d_{GPW}.
On the differential structure of metric measure spaces and applications
Gigli, Nicola
2015-01-01
The main goals of this paper are: (i) To develop an abstract differential calculus on metric measure spaces by investigating the duality relations between differentials and gradients of Sobolev functions. This will be achieved without calling into play any sort of analysis in charts, our assumptions being: the metric space is complete and separable and the measure is Radon and non-negative. (ii) To employ these notions of calculus to provide, via integration by parts, a general definition of distributional Laplacian, thus giving a meaning to an expression like \\Delta g=\\mu, where g is a functi
THE SEMIGROUP OF METRIC MEASURE SPACES AND ITS INFINITELY DIVISIBLE PROBABILITY MEASURES.
Evans, Steven N; Molchanov, Ilya
2017-01-01
A metric measure space is a complete, separable metric space equipped with a probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second. The resulting set of equivalence classes can be metrized with the Gromov-Prohorov metric of Greven, Pfaffelhuber and Winter. We consider the natural binary operation ⊞ on this space that takes two metric measure spaces and forms their Cartesian product equipped with the sum of the two metrics and the product of the two probability measures. We show that the metric measure spaces equipped with this operation form a cancellative, commutative, Polish semigroup with a translation invariant metric. There is an explicit family of continuous semicharacters that is extremely useful for, inter alia, establishing that there are no infinitely divisible elements and that each element has a unique factorization into prime elements. We investigate the interaction between the semigroup structure and the natural action of the positive real numbers on this space that arises from scaling the metric. For example, we show that for any given positive real numbers a, b, c the trivial space is the only space that satisfies a ⊞ b = c . We establish that there is no analogue of the law of large numbers: if X1, X2, … is an identically distributed independent sequence of random spaces, then no subsequence of [Formula: see text] converges in distribution unless each Xk is almost surely equal to the trivial space. We characterize the infinitely divisible probability measures and the Lévy processes on this semigroup, characterize the stable probability measures and establish a counterpart of the LePage representation for the latter class.
RELATIONS BETWEEN PACKING PREMEASURE AND MEASURE ON METRIC SPACE
无
2007-01-01
Let X be a metric space andμ a finite Borel measure on X. Let (P)q,tμ and Pq,tμ be the packing premeasure and the packing measure on X, respectively, defined by the gauge (μB(x, r))q (2r)t, where q, t ∈ R. For any compact set E of finite packing premeasure the authors prove: (1) if q ≤ 0 then (P)q,tμ(E) =Pq,tμ(E); (2) if q ＞ 0 andμ is doubling on E then (P)q,tμ(E) and Pq,tμ(E) are both zero or neither.
Metric measure spaces with Riemannian Ricci curvature bounded from below
Ambrosio, Luigi; Savaré, Giuseppe
2011-01-01
In this paper we introduce a synthetic notion of Riemannian Ricci bounds from below for metric measure spaces (X,d,m) which is stable under measured Gromov-Hausdorff convergence and rules out Finsler geometries. It can be given in terms of an enforcement of the Lott, Sturm and Villani geodesic convexity condition for the entropy coupled with the linearity of the heat flow. Besides stability, it enjoys the same tensorization, global-to-local and local-to-global properties. In these spaces, that we call RCD(K,\\infty) spaces, we prove that the heat flow (which can be equivalently characterized either as the flow associated to the Dirichlet form, or as the Wasserstein gradient flow of the entropy) satisfies Wasserstein contraction estimates and several regularity properties, in particular Bakry-Emery estimates and the L^\\infty-Lip Feller regularization. We also prove that the distance induced by the Dirichlet form coincides with d, that the local energy measure has density given by the square of Cheeger's relaxed...
Ambrosio, Luigi; Savaré, Giuseppe
2012-01-01
We provide a quick overview of various calculus tools and of the main results concerning the heat flow on compact metric measure spaces, with applications to spaces with lower Ricci curvature bounds. Topics include the Hopf-Lax semigroup and the Hamilton-Jacobi equation in metric spaces, a new approach to differentiation and to the theory of Sobolev spaces over metric measure spaces, the equivalence of the L^2-gradient flow of a suitably defined "Dirichlet energy" and the Wasserstein gradient flow of the relative entropy functional, a metric version of Brenier's Theorem, and a new (stronger) definition of Ricci curvature bound from below for metric measure spaces. This new notion is stable w.r.t. measured Gromov-Hausdorff convergence and it is strictly connected with the linearity of the heat flow.
NORMALLY DISTRIBUTED PROBABILITY MEASURE ON THE METRIC SPACE OF NORMS
Á.G. HORVÁTH
2013-01-01
In this paper we propose a method to construct probability measures on the space of convex bodies. For this purpose, first, we introduce the notion of thinness of a body. Then we show the existence of a measure with the property that its pushforward by the thinness function is a probability measure of truncated normal distribution. Finally, we improve this method to find a measure satisfying some important properties in geometric measure theory.
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...
Nakasho Kazuhisa
2016-09-01
Full Text Available In this article, we mainly formalize in Mizar [2] the equivalence among a few compactness definitions of metric spaces, norm spaces, and the real line. In the first section, we formalized general topological properties of metric spaces. We discussed openness and closedness of subsets in metric spaces in terms of convergence of element sequences. In the second section, we firstly formalize the definition of sequentially compact, and then discuss the equivalence of compactness, countable compactness, sequential compactness, and totally boundedness with completeness in metric spaces.
-Metric Space: A Generalization
Farshid Khojasteh
2013-01-01
Full Text Available We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.
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.
Mass Customization Measurements Metrics
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....
Uniformly Convex Metric Spaces
Kell Martin
2014-01-01
In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented and a weak topology of such spaces is analyzed. This topology called co-convex topology agrees with the usualy weak topology in Banach spaces. An example of a $CAT(0)$-spaces with weak topology which is not Hausdorff is given. This answers questions raised b...
Isospectral Metrics on Projective Spaces
Rueckriemen, Ralf
2011-01-01
We construct isospectral non isometric metrics on real and complex projective space. We recall the construction using isometric torus actions by Carolyn Gordon in chapter 2. In chapter 3 we will recall some facts about complex projective space. In chapter 4 we build the isospectral metrics. Chapter 5 is devoted to the non isometry proof of the metrics built in chapter 4. In chapter 6 isospectral metrics on real projective space are derived from metrics on the sphere.
Ramified optimal transportation in geodesic metric spaces
Xia, Qinglan
2009-01-01
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels, draining and irrigation systems. Here, we extend the study of ramified optimal transportation between probability measures from Euclidean spaces to a geodesic metric space. We investigate the existence as well as the behavior of optimal transport paths under various properties of the metric such as completeness, doubling, or curvature upper boundedness. We also introduce the transport dimension of a probability measure on a complete geodesic metric space, and show that the transport dimension of a probability measure is bounded above by the Minkowski dimension and below by the Hausdorff dimension of the measure. Moreover, we introduce a metric, called "the dimensional distance", on the space of probability measures. This metric gives a geometric meaning to the transport dimen...
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.
Generalized metric spaces and mappings
Lin, Shou
2016-01-01
The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.
Ambrosio, Luigi; Savaré, Giuseppe
2011-01-01
This and a companion forthcoming paper are devoted to a deeper understanding of the heat flow in metric measure spaces (X,d,m). Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani and Sturm. Indeed, the development of a "calculus" in this class of spaces is one of our motivations. In this paper the main goals are: (i) The proof of equivalence of the heat flow in L2 generated by a suitable Dirichlet energy and the Wasserstein gradient flow in the space of probability measuress of the relative entropy functional w.r.t. m. (ii) The equivalence of two weak notions of modulus of the gradient: the first one (inspired by Cheeger), that we call relaxed gradient, is defined by L2(X,m)-relaxation of the pointwise Lipschitz constant in the class of Lipschitz functions; the second one (inspired by Shanmugalingam), that we call weak upper gradient, is based on the validity of the fundamental theorem of calculus along almost all curves. These two notions of gradien...
Moduli spaces of riemannian metrics
Tuschmann, Wilderich
2015-01-01
This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.
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.
Lagrange Spaces with (γ,β-Metric
Suresh K. Shukla
2013-01-01
Full Text Available We study Lagrange spaces with (γ,β-metric, where γ is a cubic metric and β is a 1-form. We obtain fundamental metric tensor, its inverse, Euler-Lagrange equations, semispray coefficients, and canonical nonlinear connection for a Lagrange space endowed with a (γ,β-metric. Several other properties of such space are also discussed.
A Metric Conceptual Space Algebra
Adams, Benjamin; Raubal, Martin
The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.
Infinitesimally Lipschitz functions on metric spaces
Durand, E
2009-01-01
For a metric space $X$, we study the space $D^{\\infty}(X)$ of bounded functions on $X$ whose infinitesimal Lipschitz constant is uniformly bounded. $D^{\\infty}(X)$ is compared with the space $\\LIP^{\\infty}(X)$ of bounded Lipschitz functions on $X$, in terms of different properties regarding the geometry of $X$. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare $D^{\\infty}(X)$ with the Newtonian-Sobolev space $N^{1, \\infty}(X)$. In particular, if $X$ supports a doubling measure and satisfies a local Poincar{\\'e} inequality, we obtain that $D^{\\infty}(X)=N^{1, \\infty}(X)$.
A Unification of G-Metric, Partial Metric, and b-Metric Spaces
Nawab Hussain
2014-01-01
Full Text Available Using the concepts of G-metric, partial metric, and b-metric spaces, we define a new concept of generalized partial b-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.
Finite Metric Spaces of Strictly Negative Type
Hjorth, Poul; Lisonek, P.; Markvorsen, Steen
1998-01-01
We prove that, if a finite metric space is of strictly negative type, then its transfinite diameter is uniquely realized by the infinite extender (load vector). Finite metric spaces that have this property include all spaces on two, three, or four points, all trees, and all finite subspaces of Eu...
On Decomposable Measures Induced by Metrics
Dong Qiu
2012-01-01
Full Text Available We prove that for a given normalized compact metric space it can induce a σ-max-superdecomposable measure, by constructing a Hausdorff pseudometric on its power set. We also prove that the restriction of this set function to the algebra of all measurable sets is a σ-max-decomposable measure. Finally we conclude this paper with two open problems.
Fixed point theory in metric type spaces
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...
Discrete homology theory for metric spaces
H. Barcelo (Hélène); V. Capraro (Valerio); J. A. White; H. Barcelo (Hélène)
2014-01-01
htmlabstractWe define and study a notion of discrete homology theory for metric spaces. Instead of working with simplicial homology, our chain complexes are given by Lipschitz maps from an n n -dimensional cube to a fixed metric space. We prove that the resulting homology theory satisfies a
Statistical Structures on Metric Path Spaces
Mircea CRASMAREANU; Cristina-Elena HRETCANU
2012-01-01
The authors extend the notion of statistical structure from Riemannian geometry to the general framework of path spaces endowed with a nonlinear connection and a generalized metric.Two particular cases of statistical data are defined.The existence and uniqueness of a nonlinear connection corresponding to these classes is proved.Two Koszul tensors are introduced in accordance with the Riemannian approach.As applications,the authors treat the Finslerian (α,β)-metrics and the Beil metrics used in relativity and field theories while the support Riemannian metric is the Fisher-Rao metric of a statistical model.
Finite Metric Spaces of Strictly negative Type
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 distan...... matrix of a finite metric space is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points....
Entropy of continuous maps on quasi-metric spaces
Sayyari, Y.; Molaei, M.; Moghayer, S.M.
2015-01-01
The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are associated to a given quasi-metric space are introduced and the
Topology on locally finite metric spaces
Capraro, Valerio
2011-01-01
The necessity of a theory of General Topology and, most of all, of Algebraic Topology on locally finite metric spaces comes from many areas of research in both Applied and Pure Mathematics: Molecular Biology, Mathematical Chemistry, Computer Science, Topological Graph Theory and Metric Geometry. In this paper we propose the basic notions of such a theory and some applications: we replace the classical notions of continuous function, homeomorphism and homotopic equivalence with the notions of NPP-function, NPP-local-isomorphism and NPP-homotopy (NPP stands for Nearest Point Preserving); we also introduce the notion of NPP-isomorphism. We construct three invariants under NPP-isomorphisms and, in particular, we define the fundamental group of a locally finite metric space. As first applications, we propose the following: motivated by the longstanding question whether there is a purely metric condition which extends the notion of amenability of a group to any metric space, we propose the property SN (Small Neighb...
Gravesen, Jens
2015-01-01
The space of colours is a fascinating space. It is a real vector space, but no matter what inner product you put on the space the resulting Euclidean distance does not correspond to human perception of difference between colours. In 1942 MacAdam performed the first experiments on colour matching ...
Isometry groups of proper metric spaces
Niemiec, Piotr
2012-01-01
Given a locally compact Polish space X, a necessary and sufficient condition for a group G of homeomorphisms of X to be the full isometry group of (X,d) for some proper metric d on X is given. It is shown that every locally compact Polish group G acts freely on GxY as the full isometry group of GxY with respect to a certain proper metric on GxY, where Y is an arbitrary locally compact Polish space with (card(G),card(Y)) different from (1,2). Locally compact Polish groups which act effectively and almost transitively on complete metric spaces as full isometry groups are characterized. Locally compact Polish non-Abelian groups on which every left invariant metric is automatically right invariant are characterized and fully classified. It is demonstrated that for every locally compact Polish space X having more than two points the set of proper metrics d such that Iso(X,d) = {id} is dense in the space of all proper metrics on X.
Dynamical Systems on Spectral Metric Spaces
Bellissard, Jean V; Reihani, Kamran
2010-01-01
Let (A,H,D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A having a bounded commutator with D is dense. A spectral metric space, the noncommutative analog of a complete metric space, is a spectral triple (A,H,D) with additional properties which guaranty that the Connes metric induces the weak*-topology on the state space of A. A *-automorphism respecting the metric defined a dynamical system. This article gives various answers to the question: is there a canonical spectral triple based upon the crossed product algebra AxZ, characterizing the metric properties of the dynamical system ? If $\\alpha$ is the noncommutative analog of an isometry the answer is yes. Otherwise, the metric bundle construction of Connes and Moscovici is used to replace (A,$\\alpha$) by an equivalent dynamical system acting isometrically. The difficulties relating to the non compactness of this new system are di...
Boolean metric spaces and Boolean algebraic varieties
Avilés, Antonio
2009-01-01
The concepts of Boolean metric space and convex combination are used to characterize polynomial maps in a class of commutative Von Neumann regular rings including Boolean rings and p-rings, that we have called CFG-rings. In those rings, the study of the category of algebraic varieties (i.e. sets of solutions to a finite number of polynomial equations with polynomial maps as morphisms) is equivalent to the study of a class of Boolean metric spaces, that we call here CFG-spaces.
Strong Ideal Convergence in Probabilistic Metric Spaces
Celaleddin Şençimen; Serpil Pehlivan
2009-06-01
In the present paper we introduce the concepts of strongly ideal convergent sequence and strong ideal Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong ideal limit points and the strong ideal cluster points of a sequence in this space and investigate some properties of these concepts.
Metric scales for emotion measurement
Martin Junge
2016-09-01
Full Text Available The scale quality of indirect and direct scalings of the intensity of emotional experiences was investigated from the perspective of representational measurement theory. Study 1 focused on sensory pleasantness and disgust, Study 2 on surprise and amusement, and Study 3 on relief and disappointment. In each study, the emotion intensities elicited by a set of stimuli were estimated using Ordinal Difference Scaling, an indirect probabilistic scaling method based on graded pair comparisons. The obtained scale values were used to select test cases for the quadruple axiom, a central axiom of difference measurement. A parametric bootstrap test was used to decide whether the participants’ difference judgments systematically violated the axiom. Most participants passed this test. The indirect scalings of these participants were then linearly correlated with their direct emotion intensity ratings to determine whether they agreed with them up to measurement error, and hence might be metric as well. The majority of the participants did not pass this test. The findings suggest that Ordinal Difference Scaling allows to measure emotion intensity on a metric scale level for most participants. As a consequence, quantitative emotion theories become amenable to empirical test on the individual level using indirect measurements of emotional experience.
Nonhomogeneous Variational Problems and Quasi-Minimizers on Metric Spaces
Gong, Jasun; Parviainen, Mikko
2010-01-01
We show that quasi-minimizers of non-homogeneous energy functionals on metric measure spaces are locally H\\"older continuous and satisfy the Harnack inequality. We assume that the spaces are doubling and support a Poincar\\'e inequality. The proof is based on the De Giorgi method, combined with the "expansion of positivity" technique.
Codes in W*-Metric Spaces: Theory and Examples
Bumgardner, Christopher J.
2011-01-01
We introduce a "W*"-metric space, which is a particular approach to non-commutative metric spaces where a "quantum metric" is defined on a von Neumann algebra. We generalize the notion of a quantum code and quantum error correction to the setting of finite dimensional "W*"-metric spaces, which includes codes and error correction for classical…
g-Weak Contraction in Ordered Cone Rectangular Metric Spaces
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.
Bilipschitz embeddings of metric spaces into Euclidean spaces
Semmes, S.
1999-01-01
When does a metric space admit a bilipschitz embedding into some finite-dimensional Euclidean space? There does not seem to be a simple answer to this question. Results of Assouad [A1], [A2], [A3] do provide a simple answer if one permits some small («snowflake») deformations of the metric, but unfortunately these deformations immediately disrupt some basic aspects of geometry and analysis, like rectifiability, differentiability, and curves of finite length. Here we discuss a (somewhat techni...
Menger curvature and rectifiability in metric spaces
2012-01-01
We show that for any metric space $X$ the condition \\[ \\int_X\\int_X\\int_X c(z_1,z_2,z_3)^2\\, d\\Hm z_1\\, d\\Hm z_2\\, d\\Hm z_3 < \\infty, \\] where $c(z_1,z_2,z_3)$ is the Menger curvature of the triple $(z_1,z_2,z_3)$, guarantees that $X$ is rectifiable.
Multi-Armed Bandits in Metric Spaces
Kleinberg, Robert; Upfal, Eli
2008-01-01
In a multi-armed bandit problem, an online algorithm chooses from a set of strategies in a sequence of trials so as to maximize the total payoff of the chosen strategies. While the performance of bandit algorithms with a small finite strategy set is quite well understood, bandit problems with large strategy sets are still a topic of very active investigation, motivated by practical applications such as online auctions and web advertisement. The goal of such research is to identify broad and natural classes of strategy sets and payoff functions which enable the design of efficient solutions. In this work we study a very general setting for the multi-armed bandit problem in which the strategies form a metric space, and the payoff function satisfies a Lipschitz condition with respect to the metric. We refer to this problem as the "Lipschitz MAB problem". We present a complete solution for the multi-armed problem in this setting. That is, for every metric space (L,X) we define an isometry invariant which bounds f...
FIXED POINT RESULTS ON METRIC-TYPE SPACES
Monica COSENTINO; Peyman SALIMI; Pasquale VETRO
2014-01-01
In this paper we obtain fixed point and common fixed point theorems for self-mappings defined on a metric-type space, an ordered metric-type space or a normal cone metric space. Moreover, some examples and an application to integral equations are given to illustrate the usability of the obtained results.
Geodesics in the space of K\\"ahler cone metrics
Calama, Simone
2012-01-01
In this paper, we prove the existence and uniqueness of the weak cone geodesics in the space of K\\"ahler cone metrics by solving the singular, homogeneous complex Monge-Amp\\`{e}re equation. As an application, we prove the metric space structure of the appropriate subspace of the space of K\\"ahler cone metrics.
Stability results for generalized contractions in partial metric spaces
Fatma Al- Sirehy
2012-07-01
Full Text Available In 1994, Mathews [7] introduced the notion of partial metric spaces as a part of his study of denotational semantics of data.ow networks and obtained a generalization of the Banach contraction principle in partial metric spaces. In this paper, we prove stability results in partial metric spaces.
Black Holes, Holography and Moduli Space Metric
Sen-Gupta, K; Gupta, Kumar S.; Sen, Siddhartha
2007-01-01
String theory can accommodate black holes with the black hole parameters related to string moduli. It is a well known but remarkable feature that the near horizon geometry of a large class of black holes arising from string theory contains a BTZ part. A mathematical theorem (Sullivan's Theorem) relates the three dimensional geometry of the BTZ metric to the conformal structures of a two dimensional space, thus providing a precise kinematic statement of holography. Using this theorem it is possible to argue that the string moduli space in this region has to have negative curvature from the BTZ part of the associated spacetime. This is consistent with a recent conjecture of Ooguri and Vafa on string moduli space.
Probabilistic G-Metric space and some fixed point results
A. R. Janfada
2013-01-01
Full Text Available In this note we introduce the notions of generalized probabilistic metric spaces and generalized Menger probabilistic metric spaces. After making our elementary observations and proving some basic properties of these spaces, we are going to prove some fixed point result in these spaces.
Network Community Detection on Metric Space
Suman Saha
2015-08-01
Full Text Available Community detection in a complex network is an important problem of much interest in recent years. In general, a community detection algorithm chooses an objective function and captures the communities of the network by optimizing the objective function, and then, one uses various heuristics to solve the optimization problem to extract the interesting communities for the user. In this article, we demonstrate the procedure to transform a graph into points of a metric space and develop the methods of community detection with the help of a metric defined for a pair of points. We have also studied and analyzed the community structure of the network therein. The results obtained with our approach are very competitive with most of the well-known algorithms in the literature, and this is justified over the large collection of datasets. On the other hand, it can be observed that time taken by our algorithm is quite less compared to other methods and justifies the theoretical findings.
The entire sequence over Musielak p-metric space
C. Murugesan
2016-04-01
Full Text Available In this paper, we introduce fibonacci numbers of Γ2(F sequence space over p-metric spaces defined by Musielak function and examine some topological properties of the resulting these spaces.
Presic-Boyd-Wong Type Results in Ordered Metric Spaces
Satish Shukla
2014-04-01
Full Text Available The purpose of this paper is to prove some Presic-Boyd-Wong type fixed point theorems in ordered metric spaces. The results of this paper generalize the famous results of Presic and Boyd-Wong in ordered metric spaces. We also initiate the homotopy result in product spaces. Some examples are provided which illustrate the results proved herein.
FIXED POINTS THEOREMS IN MULTI-METRIC SPACES
Laurentiu I. Calmutchi
2011-07-01
Full Text Available The aim of the present article is to give some general methods inthe fixed point theory for mappings of general topological spaces. Using the notions of the multi-metric space and of the E-metric space, we proved the analogous of several classical theorems: Banach fixed point principle, Theorems of Edelstein, Meyers, Janos etc.
Extension of contractive maps in the Menger probabilistic metric space
Razani, Abdolrahman [Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288 Qazvin (Iran, Islamic Republic of)]. E-mail: razani@ipm.ir; Fouladgar, Kaveh [Stanford University, Mathematics Building 380, 450 Serra Mall, Stanford, CA 94305-2125 (United States)]. E-mail: kfouladgar@yahoo.com
2007-12-15
In this article, the topological properties of the Menger probabilistic metric spaces and the mappings between these spaces are studied. In addition, contractive and k-contractive mappings are introduced. As an application, a new fixed point theorem in a chainable Menger probabilistic metric space is proved.
Self-similarity of complex networks and hidden metric spaces
Serrano, M Angeles; Boguna, Marian
2007-01-01
We demonstrate that the self-similarity of some scale-free networks with respect to a simple degree-thresholding renormalization scheme finds a natural interpretation in the assumption that network nodes exist in hidden metric spaces. Clustering, i.e., cycles of length three, plays a crucial role in this framework as a topological reflection of the triangle inequality in the hidden geometry. We prove that a class of hidden variable models with underlying metric spaces are able to accurately reproduce the self-similarity properties that we measured in the real networks. Our findings indicate that hidden geometries underlying these real networks are a plausible explanation for their observed topologies and, in particular, for their self-similarity with respect to the degree-based renormalization.
Efficient Regression in Metric Spaces via Approximate Lipschitz Extension
Gottlieb, Lee-Ad; Krauthgamer, Robert
2011-01-01
We present a framework for performing efficient regression in general metric spaces. Roughly speaking, our regressor predicts the value at a new point by computing a Lipschitz extension -- the smoothest function consistent with the observed data -- while performing an optimized structural risk minimization to avoid overfitting. The offline (learning) and online (inference) stages can be solved by convex programming, but this naive approach has runtime complexity O(n^3), which is prohibitive for large datasets. We design instead an algorithm that is fast when the the doubling dimension, which measures the "intrinsic" dimensionality of the metric space, is low. We use the doubling dimension multiple times; first, on the statistical front, to bound fat-shattering dimension of the class of Lipschitz functions (and obtain risk bounds); and second, on the computational front, to quickly compute a hypothesis function and a prediction based on Lipschitz extension. Our resulting regressor is both asymptotically strong...
Hardy spaces on Ahlfors-regular quasi metric spaces a sharp theory
Alvarado, Ryan
2015-01-01
Systematically building an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Ahlfors-regular quasi-metric spaces. The text is broadly divided into two main parts. The first part gives atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established ...
Topological Anosov Maps of Non-compact Metric Spaces
YANG Run-sheng
2001-01-01
Let X be a metric space. We say that a continuous surjection f: X→X is a topological Anosov map ( abbrev. TA-map) if f is expansive and has pseudo-orbit tracing property with respect to some compatible metric for X. This paper studies the properties of TA-maps of non-compact metric spaces and gives some conditions for the map to be topologically mixing.
Caristi Fixed Point Theorem in Metric Spaces with a Graph
M. R. Alfuraidan
2014-01-01
Full Text Available We discuss Caristi’s fixed point theorem for mappings defined on a metric space endowed with a graph. This work should be seen as a generalization of the classical Caristi’s fixed point theorem. It extends some recent works on the extension of Banach contraction principle to metric spaces with graph.
coincidentally commuting mappings in D-metric spaces
B. C. Dhage
2003-01-01
pairs of a single-valued and a multivalued coincidentally commuting mappings in D-metric spaces satisfying a certain generalized contraction condition. Our result generalizes more than a dozen known fixed-point theorems in D-metric spaces including those of Dhage (2000 and Rhoades (1996.
李良树; 周振荣
2012-01-01
The classical integral characterization of Holder continuous functions plays an important role in regularities of elliptic PDE's. In this paper, by taking use of Morrey and Companato space theory on metric measure spaces, we prove an integral characterization of Holder continuous functions on CC metric measure spaces.%经典的Holder连续函数的积分特征在椭圆型偏微分方程的正则性理论中发挥着重要的作用.本文的主要目的是运用度量测度空间上的Morrey空间和Companato空间理论,证明CC度量测度空间上Holder连续函数的积分特征.
Convexity and the "Pythagorean" metric of space(-time)
Kalogeropoulos, Nikos
2016-01-01
We address the question about the reasons why the "Wick-rotated", positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces providing the kinematic framework for the statistical or quantum treatments of gravity. We rely on particular moduli of convexity and smoothness which are extremized by Hilbert spaces. In the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a functional integral approach. The "Pythagorean" metric of space(-time) is then induced by such Hilbert spaces.
34 CFR 74.15 - Metric system of measurement.
2010-07-01
... 34 Education 1 2010-07-01 2010-07-01 false Metric system of measurement. 74.15 Section 74.15... Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for...
Hausdorff dimension of metric spaces and Lipschitz maps onto cubes
Keleti, Tamás; Zindulka, Ondřej
2012-01-01
We prove that a compact metric space (or more generally an analytic subset of a complete separable metric space) of Hausdorff dimension bigger than $k$ can be always mapped onto a $k$-dimensional cube by a Lipschitz map. We also show that this does not hold for arbitrary separable metric spaces. As an application we essentially answer a question of Urba\\'nski by showing that the transfinite Hausdorff dimension (introduced by him) of an analytic subset $A$ of a complete separable metric space is the integer part of $\\dim_H A$ if $\\dim_H A$ is finite but not an integer, $\\dim_H A$ or $\\dim_H A-1$ if $\\dim_H A$ is an integer and at least $\\omega_0$ if $\\dim_H A=\\infty$.
On a Theorem of Khan in a Generalized Metric Space
Jamshaid Ahmad
2013-01-01
Full Text Available Existence and uniqueness of fixed points are established for a mapping satisfying a contractive condition involving a rational expression on a generalized metric space. Several particular cases and applications as well as some illustrative examples are given.
Tripled Fixed Point in Ordered Multiplicative Metric Spaces
Laishram Shanjit
2017-06-01
Full Text Available In this paper, we present some triple fixed point theorems in partially ordered multiplicative metric spaces depended on another function. Our results generalise the results of [6] and [5].
Common Fixed Point Theorems in Intuitionistic Fuzzy Metric Spaces
H.M.Abu-Donia; A.A.Nasef
2008-01-01
The purpose of this paper is to introduce some types of compatibility of maps, and we prove some common fixed point theorems for mappings satisfying some conditions on intuitionistic fuzzy metric spaces which defined by J.H.Park.
Twistted ξ-(α,β expansive mappings in metric spaces
Poonam Nagpal
2016-04-01
Full Text Available In this paper, we introduce a pair of twisted ζ-(α,β expansive mappings in metric spaces and prove fixed point theorems for these mappings. Some examples are also provided to support our main results.
New fixed and periodic point results on cone metric spaces
Ghasem Soleimani Rad
2014-05-01
Full Text Available In this paper, several xed point theorems for T-contraction of two maps on cone metric spaces under normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.
Metric for Early Measurement of Software Complexity
Ghazal Keshavarz,
2011-06-01
Full Text Available Software quality depends on several factors such as on time delivery; within budget and fulfilling user's needs. Complexity is one of the most important factors that may affect the quality. Therefore, measuring and controlling the complexity result in improving the quality. So far, most of the researches have tried to identify and measure the complexity in design and code phase. However, whenwe have the code or design for software, it is too late to control complexity. In this article, with emphasis on Requirement Engineering process, we analyze the causes of software complexity, particularly in the first phase of software development, and propose a requirement based metric. This metric enables a software engineer to measure the complexity before actual design and implementation and choosestrategies that are appropriate to the software complexity degree, thus saving on cost and human resource wastage and, more importantly, leading to lower maintenance costs.
Metric embeddings bilipschitz and coarse embeddings into Banach spaces
Ostrovskii, Mikhail I
2013-01-01
Embeddings of discrete metric spaces into Banach spaces recently became an important tool in computer science and topology. The book will help readers to enter and to work in this very rapidly developing area having many important connections with different parts of mathematics and computer science. The purpose of the book is to present some of the most important techniques and results, mostly on bilipschitz and coarse embeddings. The topics include embeddability of locally finite metric spaces into Banach spaces is finitely determined, constructions of embeddings, distortion in terms of Poinc
Almost-isometry between Teichm\\"{u}ller metric and length-spectra metric on moduli space
Liu, Lixin
2010-01-01
We prove an analogue of Farb-Masur's theorem that the length-spectra metric on moduli space is "almost isometric" to a simple model $\\mathcal {V}(S)$ which is induced by the cone metric over the complex of curves. As an application, we know that the Teichm\\"{u}ller metric and the length-spectra metric are "almost isometric" on moduli space, while they are not even quasi-isometric on Teichm\\"{u}ller space.
CHARACTERIZATION OF BEST APPROXIMATIONS IN METRIC LINEAR SPACES
Sizwe Mabizela
2003-01-01
Let (X,d) be a real metric linear space, with translation-invariant metric d and G a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X. We also give simultaneous characterization of elements of best approximation and also consider elements of e-approximation.
Open Problem: Kernel methods on manifolds and metric spaces
Feragen, Aasa; Hauberg, Søren
2016-01-01
Radial kernels are well-suited for machine learning over general geodesic metric spaces, where pairwise distances are often the only computable quantity available. We have recently shown that geodesic exponential kernels are only positive definite for all bandwidths when the input space has strong...
Sharp Dichotomies for Regret Minimization in Metric Spaces
Kleinberg, Robert
2009-01-01
The Lipschitz multi-armed bandit (MAB) problem generalizes the classical multi-armed bandit problem by assuming one is given side information consisting of a priori upper bounds on the difference in expected payoff between certain pairs of strategies. Classical results of (Lai and Robbins 1985) and (Auer et al. 2002) imply a logarithmic regret bound for the Lipschitz MAB problem on finite metric spaces. Recent results on continuum-armed bandit problems and their generalizations imply lower bounds of $\\sqrt{t}$, or stronger, for many infinite metric spaces such as the unit interval. Is this dichotomy universal? We prove that the answer is yes: for every metric space, the optimal regret of a Lipschitz MAB algorithm is either bounded above by any $f\\in \\omega(\\log t)$, or bounded below by any $g\\in o(\\sqrt{t})$. Perhaps surprisingly, this dichotomy does not coincide with the distinction between finite and infinite metric spaces; instead it depends on whether the completion of the metric space is compact and coun...
The X2 sequence space over p-metric spaces defined by Musielak modulus
Nagarajan Subramanian
2014-10-01
Full Text Available In this paper, we introduce bonacci numbers of 2 (F sequence space over pmetric spaces defined by Musielak function and examine some topological properties of the resulting these spaces.
22 CFR 226.15 - Metric system of measurement.
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Metric system of measurement. 226.15 Section....S. NON-GOVERNMENTAL ORGANIZATIONS Pre-award Requirements § 226.15 Metric system of measurement. (a...) declares that the metric system is the preferred measurement system for U.S. trade and commerce....
45 CFR 74.15 - Metric system of measurement.
2010-10-01
... 45 Public Welfare 1 2010-10-01 2010-10-01 false Metric system of measurement. 74.15 Section 74.15... ORGANIZATIONS, AND COMMERCIAL ORGANIZATIONS Pre-Award Requirements § 74.15 Metric system of measurement. The... that the metric system is the preferred measurement system for U.S. trade and commerce. The...
22 CFR 145.15 - Metric system of measurement.
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Metric system of measurement. 145.15 Section... system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for U.S. trade...
32 CFR 22.530 - Metric system of measurement.
2010-07-01
... CFR, 1991 Comp., p. 343), states that: (1) The metric system is the preferred measurement system for U... 32 National Defense 1 2010-07-01 2010-07-01 false Metric system of measurement. 22.530 Section 22... of measurement. (a) Statutory requirement. The Metric Conversion Act of 1975, as amended by...
40 CFR 30.15 - Metric system of measurement.
2010-07-01
... 40 Protection of Environment 1 2010-07-01 2010-07-01 false Metric system of measurement. 30.15... measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205), declares that the metric system is the preferred measurement system for U.S. trade and commerce. The...
15 CFR 14.15 - Metric system of measurement.
2010-01-01
... 15 Commerce and Foreign Trade 1 2010-01-01 2010-01-01 false Metric system of measurement. 14.15... COMMERCIAL ORGANIZATIONS Pre-Award Requirements § 14.15 Metric system of measurement. The Metric Conversion... system is the preferred measurement system for U.S. trade and commerce. The Act requires each...
36 CFR 1210.15 - Metric system of measurement.
2010-07-01
... 36 Parks, Forests, and Public Property 3 2010-07-01 2010-07-01 false Metric system of measurement... system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for U.S. trade...
Some common fixed point theorems in fuzzy metric spaces
Deepak Singh
2012-04-01
Full Text Available The aim of this paper is to prove some common fixed point theorems in (GV-fuzzy metric spaces.While proving our results, we employed the idea of compatibility due to Jungck [14] together with subsequentially continuity due to Bouhadjera and Godet-Thobie [4] respectively (also alternately reciprocal continuity due to Pant [28] together with subcompatibility due to Bouhadjera and Godet-Thobie [4] as in Imdad et al. [12] wherein conditions on completeness of the underlying space (or subspaces together with conditions on continuity in respect of any one of the involved maps are relaxed. Our results substantially generalize and improve a multitude of relevant common fixed point theorems of the existing literature in metric as well as fuzzy metric spaces which include some relevant results due to Imdad et al.[10], Mihet [18], Mishra [19], Singh [28] and several others.
Convexity and the Euclidean Metric of Space-Time
Nikolaos Kalogeropoulos
2017-02-01
Full Text Available We address the reasons why the “Wick-rotated”, positive-definite, space-time metric obeys the Pythagorean theorem. An answer is proposed based on the convexity and smoothness properties of the functional spaces purporting to provide the kinematic framework of approaches to quantum gravity. We employ moduli of convexity and smoothness which are eventually extremized by Hilbert spaces. We point out the potential physical significance that functional analytical dualities play in this framework. Following the spirit of the variational principles employed in classical and quantum Physics, such Hilbert spaces dominate in a generalized functional integral approach. The metric of space-time is induced by the inner product of such Hilbert spaces.
Finite Metric Spaces of Strictly Negative Type
Hjorth, Poul; Lisonek, P.; Markvorsen, Steen
1998-01-01
of Euclidean spaces. We prove that, if the distance matrix is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points. In connection with an open problem raised...
New characterizations of Hajlasz-Sobolev spaces on metric spaces
YANG; Dachun(杨大春)
2003-01-01
This paper introduces the fractional Sobolev spaces on spaces of homogeneous type, includingmetric spaces and fractals. These Sobolev spaces include the well-known Hajfasz-Sobolev spaces as specialmodels. The author establishes various characterizations of (sharp) maximal functions for these spaces. Asapplications, the author identifies the fractional Sobolev spaces with some Lipscitz-type spaces. Moreover,some embedding theorems are also given.
Metrics on Noncompact Fuzzy Number Space (E^)n
冯玉瑚
2004-01-01
The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.
Classification of locally 2-connected compact metric spaces
Thomassen, Carsten
2005-01-01
The aim of this paper is to prove that, for compact metric spaces which do not contain infinite complete graphs, the (strong) property of being "locally 2-dimensional" is guaranteed just by a (weak) local connectivity condition. Specifically, we prove that a locally 2-connected, compact metric sp...... space M either contains an infinite complete graph or is surface like in the following sense: There exists a unique surface S such that S and M. contain the same finite graphs. Moreover, M is embeddable in S, that is, M is homeomorphic to a subset of S....
Multi-field inflation and the field-space metric
Erlich, Joshua; Wang, Zhen
2015-01-01
Multi-field inflation models include a variety of scenarios for how inflation proceeds and ends. Models with the same potential but different kinetic terms are common in the literature. We compare spiral inflation and Dante's inferno-type models, which differ only in their field-space metric. We justify a single-field effective description in these models and relate the single-field description to a mass-matrix formalism. We note the effects of the nontrivial field-space metric on inflationary observables, and consequently on the viability of these models. We also note a duality between spiral inflation and Dante's inferno models with different potentials.
Unveiling the metric structure of internal representations of space
Federico eStella
2013-04-01
Full Text Available How are neuronal representations of space organized in the hippocampus? The self-organization of such representations, thought to be driven in the CA3 network by the strong randomizing input from the Dentate Gyrus, appears to run against preserving the topology and even less the exact metricity of physical space. We present a to assess this issue quantitatively, and find that in a simple neural network model of CA3, the average topology is largely preserved, but the local metricity only to a very limited extent.
Some Fixed Point Theorem for Mapping on Complete G-Metric Spaces
2008-01-01
We prove some fixed point results for mapping satisfying sufficient conditions on complete G-metric space, also we showed that if the G-metric space (X,G) is symmetric, then the existence and uniqueness of these fixed point results follow from well-known theorems in usual metric space (X,dG), where (X,dG) is the usual metric space which defined from the G-metric space (X,G).
Integrable system on phase space with nonplanar metrics
Bogdanov, E I
2001-01-01
The problem on the integrability of the evolution system on the phase spaces with the nonplanar metrics is studied. It is shown that in the case, when the phase space is a sphere, the system Hamiltonians are generated under the action of the Poisson operators on the variations of the phase space geodesic lines and the problem on the evolution system integrability is reduced to the task on the integrability of the repers motion equations on the phase space. The bihamiltonian representation of the evaluation systems is connected with the differential-geometric properties of the phase space
Constructing Calabi-Yau metrics from hyperkaehler spaces
Lue, H [China Economics and Management Academy, Central University of Finance and Economics, Beijing, 100081 (China); Pang Yi [Key Laboratory of Frontiers in Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190 (China); Wang Zhaolong, E-mail: mrhonglu@gmail.co, E-mail: yipang@itp.ac.c, E-mail: zlwang4@email.ustc.edu.c [Interdisciplinary Center for Theoretical Study, University of Science and Technology of China, Hefei, Anhui 230026 (China)
2010-08-07
Recently, a metric construction for Calabi-Yau threefolds from a four-dimensional hyperkaehler space by adding a complex line bundle was proposed. We extend the construction by adding a U(1) factor to the holomorphic (3, 0)-form and obtain the explicit formalism for a generic hyperkaehler base. We find that a discrete choice arises: the U(1) factor can either depend solely on the fiber coordinates or vanish. In each case, the metric is determined by a differential equation for the modified Kaehler potential. As explicit examples, we obtain the generalized resolutions (up to orbifold singularity) of the cone of the Einstein-Sasaki spaces Y{sup p,q}. We also obtain a large class of new singular CY3 metrics with SU(2) x U(1) or SU(2) x U(1){sup 2} isometries.
Second order elastic metrics on the shape space of curves
Bauer, Martin; Bruveris, Martins; Harms, Philipp
2015-01-01
problems for geodesics. The combination of these algorithms allows to compute Karcher means in a Riemannian gradient-based optimization scheme. Our framework has the advantage that the constants determining the weights of the zero, first, and second order terms of the metric can be chosen freely. Moreover......Second order Sobolev metrics on the space of regular unparametrized planar curves have several desirable completeness properties not present in lower order metrics, but numerics are still largely missing. In this paper, we present algorithms to numerically solve the initial and boundary value......, due to its generality, it could be applied to more general spaces of mapping. We demonstrate the effectiveness of our approach by analyzing a collection of shapes representing physical objects....
Curved noncommutative tori as Leibniz quantum compact metric spaces
Latrémolière, Frédéric, E-mail: frederic@math.du.edu [Department of Mathematics, University of Denver, Denver, Colorado 80208 (United States)
2015-12-15
We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.
Curved noncommutative tori as Leibniz quantum compact metric spaces
Latrémolière, Frédéric
2015-12-01
We prove that curved noncommutative tori are Leibniz quantum compact metric spaces and that they form a continuous family over the group of invertible matrices with entries in the image of the quantum tori for the conjugation by modular conjugation operator in the regular representation, when this group is endowed with a natural length function.
Common Fixed Points for Multimaps in Metric Spaces
Rafa Espínola
2010-01-01
Full Text Available We discuss the existence of common fixed points in uniformly convex metric spaces for single-valued pointwise asymptotically nonexpansive or nonexpansive mappings and multivalued nonexpansive, ∗-nonexpansive, or ε-semicontinuous maps under different conditions of commutativity.
Advanced Space Propulsion Based on Vacuum (Spacetime Metric) Engineering
Puthoff, Harold E
2012-01-01
A theme that has come to the fore in advanced planning for long-range space exploration is the concept that empty space itself (the quantum vacuum, or spacetime metric) might be engineered so as to provide energy/thrust for future space vehicles. Although far-reaching, such a proposal is solidly grounded in modern physical theory, and therefore the possibility that matter/vacuum interactions might be engineered for space-flight applications is not a priori ruled out. As examples, the current development of theoretical physics addresses such topics as warp drives, traversable wormholes and time machines that provide for such vacuum engineering possibilities. We provide here from a broad perspective the physics and correlates/consequences of the engineering of the spacetime metric.
Real variables with basic metric space topology
Ash, Robert B
2009-01-01
Designed for a first course in real variables, this text presents the fundamentals for more advanced mathematical work, particularly in the areas of complex variables, measure theory, differential equations, functional analysis, and probability. Geared toward advanced undergraduate and graduate students of mathematics, it is also appropriate for students of engineering, physics, and economics who seek an understanding of real analysis.The author encourages an intuitive approach to problem solving and offers concrete examples, diagrams, and geometric or physical interpretations of results. Deta
Coupled Best Proximity Point Theorem in Metric Spaces
Animesh Gupta
2013-11-01
Full Text Available The purpose of this article is to generalized the result of W. Sintunavarat and P. Kumam [29]. We also give an example in support of our theorem for which result of W. Sintunavarat and P. Kumam [29] is not true. Moreover we establish the existence and convergence theorems of coupled best proximity points in metric spaces, we apply this results in a uniformly convex Banach space.
Ferrari, Frank, E-mail: frank.ferrari@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); Klevtsov, Semyon, E-mail: semyon.klevtsov@ulb.ac.be [Service de Physique Theorique et Mathematique, Universite Libre de Bruxelles and International Solvay Institutes, Campus de la Plaine, CP 231, 1050 Bruxelles (Belgium); ITEP, B. Cheremushkinskaya 25, Moscow 117218 (Russian Federation); Zelditch, Steve, E-mail: zelditch@math.northwestern.edu [Department of Mathematics, Northwestern University, Evanston, IL 60208 (United States)
2013-04-01
The purpose of this article is to propose a new method to define and calculate path integrals over metrics on a Kaehler manifold. The main idea is to use finite dimensional spaces of Bergman metrics, as an approximation to the full space of Kaehler metrics. We use the theory of large deviations to decide when a sequence of probability measures on the spaces of Bergman metrics tends to a limit measure on the space of all Kaehler metrics. Several examples are considered.
32 CFR 32.15 - Metric system of measurement.
2010-07-01
... comply with requirements concerning the use of the metric system at 32 CFR 22.530. ... 32 National Defense 1 2010-07-01 2010-07-01 false Metric system of measurement. 32.15 Section 32..., HOSPITALS, AND OTHER NON-PROFIT ORGANIZATIONS Pre-Award Requirements § 32.15 Metric system of...
Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems
Radenović Stojan
2010-01-01
Full Text Available We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued cone metric spaces. Examples are given to distinguish our results from the known ones.
Economic Metrics for Commercial Reusable Space Transportation Systems
Shaw, Eric J.; Hamaker, Joseph (Technical Monitor)
2000-01-01
The success of any effort depends upon the effective initial definition of its purpose, in terms of the needs to be satisfied and the goals to be fulfilled. If the desired product is "A System" that is well-characterized, these high-level need and goal statements can be transformed into system requirements by traditional systems engineering techniques. The satisfaction of well-designed requirements can be tracked by fairly straightforward cost, schedule, and technical performance metrics. Unfortunately, some types of efforts, including those that NASA terms "Programs," tend to resist application of traditional systems engineering practices. In the NASA hierarchy of efforts, a "Program" is often an ongoing effort with broad, high-level goals and objectives. A NASA "project" is a finite effort, in terms of budget and schedule, that usually produces or involves one System. Programs usually contain more than one project and thus more than one System. Special care must be taken in the formulation of NASA Programs and their projects, to ensure that lower-level project requirements are traceable to top-level Program goals, feasible with the given cost and schedule constraints, and measurable against top-level goals. NASA Programs and projects are tasked to identify the advancement of technology as an explicit goal, which introduces more complicating factors. The justification for funding of technology development may be based on the technology's applicability to more than one System, Systems outside that Program or even external to NASA. Application of systems engineering to broad-based technology development, leading to effective measurement of the benefits, can be valid, but it requires that potential beneficiary Systems be organized into a hierarchical structure, creating a "system of Systems." In addition, these Systems evolve with the successful application of the technology, which creates the necessity for evolution of the benefit metrics to reflect the changing
Systems of dyadic cubes in a doubling metric space
Hytönen, Tuomas
2010-01-01
A number of recent results in Euclidean Harmonic Analysis have exploited several adjacent systems of dyadic cubes, instead of just one fixed system. In this paper, we extend such constructions to general spaces of homogeneous type, making these tools available for Analysis on metric spaces. The results include a new (non-random) construction of boundedly many adjacent dyadic systems with useful covering properties, and a streamlined version of the random construction recently devised by H. Martikainen and the first author. We illustrate the usefulness of these constructions with applications to weighted inequalities and the BMO space; further applications will appear in forthcoming work.
Restrictive metric regularity and generalized differential calculus in Banach spaces
Bingwu Wang
2004-10-01
Full Text Available We consider nonlinear mappings f:XÃ¢Â†Â’Y between Banach spaces and study the notion of restrictive metric regularity of f around some point xÃ‚Â¯, that is, metric regularity of f from X into the metric space E=f(X. Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at xÃ‚Â¯ but its strict derivative Ã¢ÂˆÂ‡f(xÃ‚Â¯ is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.
Computing the Gromov hyperbolicity constant of a discrete metric space
Ismail, Anas
2012-07-01
Although it was invented by Mikhail Gromov, in 1987, to describe some family of groups[1], the notion of Gromov hyperbolicity has many applications and interpretations in different fields. It has applications in Biology, Networking, Graph Theory, and many other areas of research. The Gromov hyperbolicity constant of several families of graphs and geometric spaces has been determined. However, so far, the only known algorithm for calculating the Gromov hyperbolicity constant of a discrete metric space is the brute force algorithm with running time O (n4) using the four- point condition. In this thesis, we first introduce an approximation algorithm which calculates a O (log n)-approximation of the hyperbolicity constant , based on a layering approach, in time O (n2), where n is the number of points in the metric space. We also calculate the fixed base point hyperbolicity constant r for a fixed point r using a (max; min)matrix multiplication algorithm by Duan in time O (n2:688) [2]. We use this result to present a 2-approximation algorithm for calculating the hyperbolicity constant in time O (n2:688). We also provide an exact algorithm to compute the hyperbolicity constant in time O (n3:688) for a discrete metric space. We then present some partial results we obtained for designing some approximation algorithms to compute the hyperbolicity constant.
Multidimensional metrics of niche space for use with diverse analytical techniques
Bowes, Rachel E.; Thorp, James H.; Reuman, Daniel C.
2017-01-01
Multidimensional data are integral to many community-ecological studies and come in various forms, such as stable isotopes, compound specific analyses (e.g., amino acids and fatty acids), and both biodiversity and life history traits. Scientists employing such data often lack standardized metrics to evaluate communities in niche space where more than 2 dimensions are involved. To alleviate this problem, we developed a graphing and analytical approach for use with more than two variables, based on previously established stable isotope bi-plot metrics. We introduce here our community metrics as R scripts. By extending the original metrics to multiple dimensions, we created n-dimensional plots and metrics to characterize any set of quantitative measurements of a community. We demonstrate the utility of these metrics using stable isotope data; however, the approaches are applicable to many types of data. The resulting metrics provide more and better information compared to traditional analytic frameworks. The approach can be applied in many branches of community ecology, and it offers accessible metrics to quantitatively analyze the structure of communities across ecosystems and through time. PMID:28145524
Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces
Raja P
2008-01-01
Full Text Available Abstract In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.
The Lie group of automorphisms of a Courant algebroid and the moduli space of generalized metrics
Rubio, Roberto; Tipler, Carl
2016-01-01
We endow the group of automorphisms of an exact Courant algebroid over a compact manifold with an infinite dimensional Lie group structure modelled on the inverse limit of Hilbert spaces (ILH). We prove a slice theorem for the action of this Lie group on the space of generalized metrics. As an application, we show that the moduli space of generalized metrics is stratified by ILH submanifolds. Finally, we relate the moduli space of generalized metrics to the moduli space of usual metrics.
Common fixed point theorems for semigroups on metric spaces
Young-Ye Huang
1999-01-01
if S is a left reversible semigroup of selfmaps on a complete metric space (M,d such that there is a gauge function φ for which d(f(x,f(y≤φ(δ(Of (x,y for f∈S and x,y in M, where δ(Of (x,y denotes the diameter of the orbit of x,y under f, then S has a unique common fixed point ξ in M and, moreover, for any f in S and x in M, the sequence of iterates {fn(x} converges to ξ. The second result is a common fixed point theorem for a left reversible uniformly Lipschitzian semigroup of selfmaps on a bounded hyperconvex metric space (M,d.
Alabiso, Carlo
2015-01-01
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...
38 CFR 49.15 - Metric system of measurement.
2010-07-01
... measurement. 49.15 Section 49.15 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS... measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for U.S. trade and commerce. The...
Fixed Points of Multivalued Contractive Mappings in Partial Metric Spaces
Abdul Rahim Khan
2014-01-01
Full Text Available The aim of this paper is to present fixed point results of multivalued mappings in the framework of partial metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. As an application of our main result, the existence and uniqueness of bounded solution of functional equations arising in dynamic programming are established.
Spectral Metric Spaces on Extensions of C*-Algebras
Hawkins, Andrew; Zacharias, Joachim
2017-03-01
We construct spectral triples on C*-algebraic extensions of unital C*-algebras by stable ideals satisfying a certain Toeplitz type property using given spectral triples on the quotient and ideal. Our construction behaves well with respect to summability and produces new spectral quantum metric spaces out of given ones. Using our construction we find new spectral triples on the quantum 2- and 3-spheres giving a new perspective on these algebras in noncommutative geometry.
GENERALIZED H-KKM TYPE THEOREMS IN H-METRIC SPACES WITH APPLICATIONS
丁协平; 夏福全
2001-01-01
The new notions of H-metric spaces and generalized H-KKM mappings were introduced. Some generalized H-KKM type theorems for generalized H-KKM mappings with finitely metrically compactly closed values and finitely metrically compactly open values were established in H-metric spaces. These theorems generalize recent results of Khamsi and Yuan. As applications, some Ky Fan type matching theorems for finitely metrically compactly open covers and finitely metrically compactly closed covers, fixed point theorems and minimax inequality are obtained in H-metric spaces. These results generalize a number of known results in recent literature.
Fixed point theorems and stability of iterations in cone metric spaces
Yuan Qing
2012-04-01
Full Text Available In this paper, fixed point problems of weak contractions are investigated in cone metric spaces. Theorems of convergence and theorems of stability for fixed points of some weak contraction are established in cone metric spaces.
Unified Metrical Common Fixed Point Theorems in 2-Metric Spaces via an Implicit Relation
Sunny Chauhan
2013-01-01
Full Text Available We prove some common fixed point theorems for two pairs of weakly compatible mappings in 2-metric spaces via an implicit relation. As an application to our main result, we derive Bryant's type generalized fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any finite number of mappings. Our results improve and extend a host of previously known results. Moreover, we study the existence of solutions of a nonlinear integral equation.
2 CFR 215.15 - Metric system of measurement.
2010-01-01
... Programs” (56 FR 35801, 3 CFR, 1991 Comp., p. 343). ... 2 Grants and Agreements 1 2010-01-01 2010-01-01 false Metric system of measurement. 215.15 Section... measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C....
Algorithms for Planar Graphs and Graphs in Metric Spaces
Wulff-Nilsen, Christian
Algorithms for network problems play an increasingly important role in modern society. The graph structure of a network is an abstract and very useful representation that allows classical graph algorithms, such as Dijkstra and Bellman-Ford, to be applied. Real-life networks often have additional...... preprocessing time, an O(n log n) time algorithm for the replacement paths problem, and a min st-cut oracle with nearlinear preprocessing time. We also give improved time bounds for computing various graph invariants such as diameter and girth. In the second part, we consider stretch factor problems...... for geometric graphs and graphs embedded in metric spaces. Roughly speaking, the stretch factor is a real value expressing how well a (geo-)metric graph approximates the underlying complete graph w.r.t. distances. We give improved algorithms for computing the stretch factor of a given graph and for augmenting...
24 CFR 84.15 - Metric system of measurement.
2010-04-01
... business-related activities. Metric implementation may take longer where the use of the system is initially... 24 Housing and Urban Development 1 2010-04-01 2010-04-01 false Metric system of measurement. 84.15 Section 84.15 Housing and Urban Development Office of the Secretary, Department of Housing and Urban...
10 CFR 600.115 - Metric system of measurement.
2010-01-01
... 10 Energy 4 2010-01-01 2010-01-01 false Metric system of measurement. 600.115 Section 600.115 Energy DEPARTMENT OF ENERGY (CONTINUED) ASSISTANCE REGULATIONS FINANCIAL ASSISTANCE RULES Uniform..., Hospitals, and Other Nonprofit Organizations Pre-Award Requirements § 600.115 Metric system of...
Some Nonunique Fixed Point Theorems of Ćirić Type on Cone Metric Spaces
Erdal Karapınar
2010-01-01
Full Text Available Some results of (Ćirić, 1974 on a nonunique fixed point theorem on the class of metric spaces are extended to the class of cone metric spaces. Namely, nonunique fixed point theorem is proved in orbitally complete cone metric spaces under the assumption that the cone is strongly minihedral. Regarding the scalar weight of cone metric, we are able to remove the assumption of strongly minihedral.
The Metric on the Space of Yang-Mills Configurations
Orland, P
1996-01-01
A distance function on the set of physical equivalence classes of Yang-Mills configurations considered by Feynman and by Atiyah, Hitchin and Singer is studied for both the $2+1$ and $3+1$-dimensional Hamiltonians. This set equipped with this distance function is a metric space, and in fact a Riemannian manifold as Singer observed. Furthermore, this manifold is complete. Gauge configurations can be used to parametrize the manifold. The metric tensor without gauge fixing has zero eigenvalues, but is free of ambiguities on the entire manifold. In $2+1$ dimensions the problem of finding the distance from any configuration to a pure gauge configuration is an integrable system of two-dimensional differential equations. A calculus of manifolds with singular metric tensors is developed and the Riemann curvature is calculated using this calculus. The Laplacian on Yang-Mills wave functionals has a slightly different form from that claimed earlier. In $3+1$-dimensions there are field configurations an arbitrarily large ...
Measurable Control System Security through Ideal Driven Technical Metrics
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
On the metric structure of space-time
Rau, Jochen
2010-01-01
I present an analysis of the physical assumptions needed to obtain the metric structure of space-time. For this purpose I combine the axiomatic approach pioneered by Robb with ideas drawn from works on Weyl's "Raumproblem". The concept of a Lorentzian manifold is replaced by the weaker concept of an "event manifold", defined in terms of volume element, causal structure and affine connection(s). Exploiting properties of its structure group, I show that distinguishing Lorentzian manifolds from other classes of event manifolds requires the key idea of general relativity: namely that the manifold's physical structure, rather than being fixed, is itself a variable.
Fixed point theorems in complex valued metric spaces
Naval Singh
2016-07-01
Full Text Available The aim of this paper is to establish and prove several results on common fixed point for a pair of mappings satisfying more general contraction conditions portrayed by rational expressions having point-dependent control functions as coefficients in complex valued metric spaces. Our results generalize and extend the results of Azam et al. (2011 [1], Sintunavarat and Kumam (2012 [2], Rouzkard and Imdad (2012 [3], Sitthikul and Saejung (2012 [4] and Dass and Gupta (1975 [5]. To substantiate the authenticity of our results and to distinguish them from existing ones, some illustrative examples are also furnished.
Rafa Espínola
2010-01-01
Full Text Available We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for set-valued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings.
A RESULT OF SUZUKI TYPE IN PARTIAL G-METRIC SPACES
Peyman SALIMI; Pasquale VETRO
2014-01-01
Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and char-acterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920] proved an analogous fixed point result for a self-mapping on a partial metric space that characterizes the partial metric 0-completeness. In this article, we introduce the notion of partial G-metric spaces and prove a result of Suzuki type in the setting of partial G-metric spaces. We deduce also a result of common fixed point.
Fixed Points of α-Admissible Mappings in Cone Metric Spaces with Banach Algebra
S.K. Malhotra
2015-11-01
Full Text Available In this paper, we introduce the $\\alpha$-admissible mappings in the setting of cone metric spaces equipped with Banach algebra and solid cones. Our results generalize and extend several known results of metric and cone metric spaces. An example is presented which illustrates and shows the significance of results proved herein.
McFarland, Shane M.; Norcross, Jason
2016-01-01
Existing methods for evaluating EVA suit performance and mobility have historically concentrated on isolated joint range of motion and torque. However, these techniques do little to evaluate how well a suited crewmember can actually perform during an EVA. An alternative method of characterizing suited mobility through measurement of metabolic cost to the wearer has been evaluated at Johnson Space Center over the past several years. The most recent study involved six test subjects completing multiple trials of various functional tasks in each of three different space suits; the results indicated it was often possible to discern between different suit designs on the basis of metabolic cost alone. However, other variables may have an effect on real-world suited performance; namely, completion time of the task, the gravity field in which the task is completed, etc. While previous results have analyzed completion time, metabolic cost, and metabolic cost normalized to system mass individually, it is desirable to develop a single metric comprising these (and potentially other) performance metrics. This paper outlines the background upon which this single-score metric is determined to be feasible, and initial efforts to develop such a metric. Forward work includes variable coefficient determination and verification of the metric through repeated testing.
Fixed point theorems for generalized contractions in ordered metric spaces
O'Regan, Donal; Petrusel, Adrian
2008-05-01
The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, MEC. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petrusel, I.A. Rus [A. Petrusel, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.
Computing the Gromov hyperbolicity of a discrete metric space
Fournier, Hervé
2015-02-12
We give exact and approximation algorithms for computing the Gromov hyperbolicity of an n-point discrete metric space. We observe that computing the Gromov hyperbolicity from a fixed base-point reduces to a (max,min) matrix product. Hence, using the (max,min) matrix product algorithm by Duan and Pettie, the fixed base-point hyperbolicity can be determined in O(n2.69) time. It follows that the Gromov hyperbolicity can be computed in O(n3.69) time, and a 2-approximation can be found in O(n2.69) time. We also give a (2log2n)-approximation algorithm that runs in O(n2) time, based on a tree-metric embedding by Gromov. We also show that hyperbolicity at a fixed base-point cannot be computed in O(n2.05) time, unless there exists a faster algorithm for (max,min) matrix multiplication than currently known.
Idempotent probability measures on ultrametric spaces
Hubal, Oleksandra; Zarichnyi, Mykhailo
2008-07-01
Following the construction due to Hartog and Vink we introduce a metric on the set of idempotent probability measures (Maslov measures) defined on an ultrametric space. This construction determines a functor on the category of ultrametric spaces and nonexpanding maps. We prove that this functor is the functorial part of a monad on this category. This monad turns out to contain the hyperspace monad.
The information metric on the moduli space of instantons with global symmetries
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.
Measures of agreement between computation and experiment:validation metrics.
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.
On metric space valued functions of bounded essential variation
Balcerzak М.
2005-01-01
Full Text Available Let ∅≠T ⊂ R and let X be a metric space. For an ideal J ⊂ P(T and a function f:T-> X, we define the essential variation V Jess(f, T as the in mum of all variations V (g; T where g:T-> X, g = f on TE, and E in J. We show that if X is complete then the essential variation of f is equal to inf{V (f; TE : E ∈ J}. This extends former theorems of that type. We list some consequences that are analogues to the recent results by Chistyakov. Some examples of di erent kinds of essential variation are also investigated.
A metrics suite for coupling measurement of software architecture
KONG Qing-yan; LUN Li-jun; ZHAO Jia-hua; WANG Yi-he
2009-01-01
To better evaluate the quality of software architecture,a metrics suite is proposed to measure the coupling of software architecture models,in which CBC is used to measure the coupling between components,CBCC is used to measure the coupling of transferring message between components,CBCCT is used to measure the coupling of software architecture, WCBCC is used to measure the coupling of transferring message with weight between components,and WCBCCT is used to measure the coupling of message transmission with weight in the whole software architecture.The proposed algorithm for the coupling metrics is applied to the design of serve software architecture.Analysis of an example validates the feasibility of this metrics suite.
The extension of quadrupled xed point results in K-metric spaces
Ghasem Soleimani Rad
2014-05-01
Full Text Available Recently, Rahimi et al. [Comp. Appl. Math. 2013, In press] dened the conceptof quadrupled xed point in K-metric spaces and proved several quadrupled xed point theorems for solid cones on K-metric spaces. In this paper some quadrupled xed point results for T-contraction on K-metric spaces without normality condition are proved. Obtained results extend and generalize well-known comparable results in the literature.
Some Results of Fixed Points in Generalized Metric Space by Methods of Suzuki and Samet
Hojjat Afshari
2015-08-01
Full Text Available In 1992 Dhage introduced the notion of generalized metric or D-metric spaces and claimed that D-metric convergence define a Hausdorff topology and that $D$-metric is sequentially continuous in all the three variables. Many authors have taken these claims for granted and used them in proving fixed point theorems in $D$-metric spaces. In 1996 Rhoades generalized Dhages contractive condition by increasing the number of factors and proved the existence of unique fixed point of a self map in $D$-metric space. Recently motivated by the concept of compatibility for metric space. In 2002 Sing and Sharma introduced the concept of $D$-compatibility of maps in $D$-metric space and proved some fixed point theorems using a contractive condition. In this paper ,we prove some fixed point theorems and common fixed point theorems in $D^*$-complete metric spaces under particular conditions among weak compatibility. Also by Using method of Suzuki and Samet we prove some theorems in generalised metric spaces.
Asymptotic Excisions of Metric Spaces and Ideals of Asymptotic Coarse Roe Algebras
LI Jin-xiu; WANG Qin
2006-01-01
We introduce in this note the notions of asymptotic excision of proper metric spaces and asymptotic equivalence relation for subspaces of metric spaces, which are relevant in characterizing spatial ideals of the asymptotic coarse Roe algebras. We show that the lattice of the asymptotic equivalence classes of the subspaces of a proper metric space is isomorphic to the lattice of the spatial ideals of the asymptotic Roe algebra. For asymptotic excisions of the metric space, we also establish a Mayer-Vietoris sequence in K-theory of the asymptotic coarse Roe algebras.
Metric Divergence Measures and Information Value in Credit Scoring
Guoping Zeng
2013-01-01
Full Text Available Recently, a series of divergence measures have emerged from information theory and statistics and numerous inequalities have been established among them. However, none of them are a metric in topology. In this paper, we propose a class of metric divergence measures, namely, , and study their mathematical properties. We then study an important divergence measure widely used in credit scoring, called information value. In particular, we explore the mathematical reasoning of weight of evidence and suggest a better alternative to weight of evidence. Finally, we propose using as alternatives to information value to overcome its disadvantages.
Fixed Points of α-Admissible Mappings on Partial Metric Spaces
İncı M. Erhan
2014-01-01
Full Text Available In this paper, a general class of α-admissible contractions on partial metric spaces is introduced. Fixed point theorems for these contractions on partial metric spaces and their consequences are stated and proved. Illustrative example is presented.
Fixed Point Theory for Cyclic Weak $phi-$contraction in Fuzzy Metric Spaces
M. Hasan
2012-02-01
Full Text Available In this paper, we introduce cyclic weak $phi-$contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.
Best Proximity Point Theorems in Partially Ordered b-Quasi Metric Spaces
Ali Abkar
2016-11-01
Full Text Available In this paper, we introduce the notion of an ordered rational proximal contraction in partially ordered b-quasi metric spaces. We shall then prove some best proximity point theorems in partially ordered b-quasi metric spaces.
Contrasting Various Metrics for Measuring Tropical Cyclone Activity
Jia-Yuh Yu and Ping-Gin Chiu
2012-01-01
Full Text Available Popular metrics used for measuring the tropical cyclone (TC activity, including NTC (number of tropical cyclones, TCD (tropical cyclone days, ACE (accumulated cyclone energy, PDI (power dissipation index, along with two newly proposed indices: RACE (revised accumulated cyclone energy and RPDI (revised power dissipation index, are compared using the JTWC (Joint Typhoon Warning Center best-track data of TC over the western North Pacific basin. Our study shows that, while the above metrics have demonstrated various degrees of discrepancies, but in practical terms, they are all able to produce meaningful temporal and spatial changes in response to climate variability. Compared with the conventional ACE and PDI, RACE and RPDI seem to provide a more precise estimate of the total TC activity, especially in projecting the upswing trend of TC activity over the past few decades, simply because of a better approach in estimating TC wind energy. However, we would argue that there is still no need to find a _ or _ metric for TC activity because different metrics are designed to stratify different aspects of TC activity, and whether the selected metric is appropriate or not should be determined solely by the purpose of study. Except for magnitude difference, the analysis results seem insensitive to the choice of the best-track datasets.
Contrasting Various Metrics for Measuring Tropical Cyclone Activity
Jia-Yuh Yu Ping-Gin Chiu
2012-01-01
Full Text Available Popular metrics used for measuring the tropical cyclone (TC activity, including NTC (number of tropical cyclones, TCD (tropical cyclone days, ACE (accumulated cyclone energy, PDI (power dissipation index, along with two newly proposed indices: RACE (revised accumulated cyclone energy and RPDI (revised power dissipation index, are compared using the JTWC (Joint Typhoon Warning Center best-track data of TC over the western North Pacific basin. Our study shows that, while the above metrics have demonstrated various degrees of discrepancies, but in practical terms, they are all able to produce meaningful temporal and spatial changes in response to climate variability. Compared with the conventional ACE and PDI, RACE and RPDI seem to provide a more precise estimate of the total TC activity, especially in projecting the upswing trend of TC activity over the past few decades, simply because of a better approach in estimating TC wind energy. However, we would argue that there is still no need to find a ¡§universal¡¨ or ¡§best¡¨ metric for TC activity because different metrics are designed to stratify different aspects of TC activity, and whether the selected metric is appropriate or not should be determined solely by the purpose of study. Except for magnitude difference, the analysis results seem insensitive to the choice of the best-track datasets.
45 CFR 2543.15 - Metric system of measurement.
2010-10-01
... 45 Public Welfare 4 2010-10-01 2010-10-01 false Metric system of measurement. 2543.15 Section 2543.15 Public Welfare Regulations Relating to Public Welfare (Continued) CORPORATION FOR NATIONAL AND COMMUNITY SERVICE GRANTS AND AGREEMENTS WITH INSTITUTIONS OF HIGHER EDUCATION, HOSPITALS, AND OTHER NON...
10 CFR 600.306 - Metric system of measurement.
2010-01-01
... 10 Energy 4 2010-01-01 2010-01-01 false Metric system of measurement. 600.306 Section 600.306 Energy DEPARTMENT OF ENERGY (CONTINUED) ASSISTANCE REGULATIONS FINANCIAL ASSISTANCE RULES Administrative Requirements for Grants and Cooperative Agreements With For-Profit Organizations General § 600.306...
7 CFR 3019.15 - Metric system of measurement.
2010-01-01
... 7 Agriculture 15 2010-01-01 2010-01-01 false Metric system of measurement. 3019.15 Section 3019.15 Agriculture Regulations of the Department of Agriculture (Continued) OFFICE OF THE CHIEF FINANCIAL OFFICER... HIGHER EDUCATION, HOSPITALS, AND OTHER NON-PROFIT ORGANIZATIONS Pre-Award Requirements § 3019.15...
43 CFR 12.915 - Metric system of measurement.
2010-10-01
... 43 Public Lands: Interior 1 2010-10-01 2010-10-01 false Metric system of measurement. 12.915 Section 12.915 Public Lands: Interior Office of the Secretary of the Interior ADMINISTRATIVE AND AUDIT REQUIREMENTS AND COST PRINCIPLES FOR ASSISTANCE PROGRAMS Uniform Administrative Requirements for Grants...
Glockner, Helge
2006-01-01
We prove an implicit function theorem for Keller C^k_c-maps from arbitrary real or complex topological vector spaces to Frechet spaces, imposing only a certain metric estimate on the partial differentials. As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of contractions of a Frechet space. The investigations were stimulated by a recent metric approach to differentiability in Frechet spaces by Olaf Mueller. Our results also subsume generalizations of Mu...
Kaluza-Klein-Carmeli Metric from Quaternion-Clifford Space, Lorentz' Force, and Some Observables
Christianto V.
2008-04-01
Full Text Available It was known for quite long time that a quaternion space can be generalized to a Clifford space, and vice versa; but how to find its neat link with more convenient metric form in the General Relativity theory, has not been explored extensively. We begin with a representation of group with non-zero quaternions to derive closed FLRW metric [1], and from there obtains Carmeli metric, which can be extended further to become 5D and 6D metric (which we propose to call Kaluza-Klein-Carmeli metric. Thereafter we discuss some plausible implications of this metric, beyond describing a galaxy’s spiraling motion and redshift data as these have been done by Carmeli and Hartnett [4, 5, 6]. In subsequent section we explain Podkletnov’s rotating disc experiment. We also note possible implications to quantum gravity. Further observations are of course recommended in order to refute or verify this proposition.
A new approach for the sequence spaces of fuzzy level sets with the partial metric
Uğur Kadak
2014-03-01
Full Text Available In this paper, we investigate the classical sets of sequences of fuzzy numbers by using partial metric which is based on a partial ordering. Some elementary notions and concepts for partial metric and fuzzy level sets are given. In addition, several necessary and sufficient conditions for partial completeness are established by means of fuzzy level sets. Finally, we give some illustrative examples and present some results between fuzzy and partial metric spaces.
Metric-space approach to potentials and its relevance to density-functional theory
Sharp, P. M.; D'Amico, I.
2016-12-01
External potentials play a crucial role in modeling quantum systems, since, for a given interparticle interaction, they define the system Hamiltonian. We use the metric-space approach to quantum mechanics to derive, from the energy conservation law, two natural metrics for potentials. We show that these metrics are well defined for physical potentials, regardless of whether the system is in an eigenstate or if the potential is bounded. In addition, we discuss the gauge freedom of potentials and how to ensure that the metrics preserve physical relevance. Our metrics for potentials, together with the metrics for wave functions and densities from I. D'Amico et al. [Phys. Rev. Lett. 106, 050401 (2011), 10.1103/PhysRevLett.106.050401] paves the way for a comprehensive study of the two fundamental theorems of density-functional theory. We explore these by analyzing two many-body systems for which the related exact Kohn-Sham systems can be derived. First we consider the information provided by each of the metrics, and we find that the density metric performs best in distinguishing two many-body systems. Next we study for the systems at hand the one-to-one relationships among potentials, ground-state wave functions, and ground-state densities defined by the Hohenberg-Kohn theorem as relationships in metric spaces. We find that, in metric space, these relationships are monotonic and incorporate regions of linearity, at least for the systems considered. Finally, we use the metrics for wave functions and potentials in order to assess quantitatively how close the many-body and Kohn-Sham systems are: We show that, at least for the systems analyzed, both metrics provide a consistent picture, and for large regions of the parameter space the error in approximating the many-body wave function with the Kohn-Sham wave function lies under a threshold of 10%.
Jonathan D. Krieger
2014-08-01
Full Text Available Premise of the study: I present a protocol for creating geometric leaf shape metrics to facilitate widespread application of geometric morphometric methods to leaf shape measurement. Methods and Results: To quantify circularity, I created a novel shape metric in the form of the vector between a circle and a line, termed geometric circularity. Using leaves from 17 fern taxa, I performed a coordinate-point eigenshape analysis to empirically identify patterns of shape covariation. I then compared the geometric circularity metric to the empirically derived shape space and the standard metric, circularity shape factor. Conclusions: The geometric circularity metric was consistent with empirical patterns of shape covariation and appeared more biologically meaningful than the standard approach, the circularity shape factor. The protocol described here has the potential to make geometric morphometrics more accessible to plant biologists by generalizing the approach to developing synthetic shape metrics based on classic, qualitative shape descriptors.
Krieger, Jonathan D
2014-08-01
I present a protocol for creating geometric leaf shape metrics to facilitate widespread application of geometric morphometric methods to leaf shape measurement. • To quantify circularity, I created a novel shape metric in the form of the vector between a circle and a line, termed geometric circularity. Using leaves from 17 fern taxa, I performed a coordinate-point eigenshape analysis to empirically identify patterns of shape covariation. I then compared the geometric circularity metric to the empirically derived shape space and the standard metric, circularity shape factor. • The geometric circularity metric was consistent with empirical patterns of shape covariation and appeared more biologically meaningful than the standard approach, the circularity shape factor. The protocol described here has the potential to make geometric morphometrics more accessible to plant biologists by generalizing the approach to developing synthetic shape metrics based on classic, qualitative shape descriptors.
Metric of the SU(N) caloron moduli space and its relation to instantons
Diakonov, D; Diakonov, Dmitri; Gromov, Nikolay
2005-01-01
Calorons of the SU(N) gauge group with non-trivial holonomy, i.e. periodic instantons with arbitrary eigenvalues of the Polyakov line at spatial infinity, can be viewed as composed of N Bogomolnyi--Prasad--Sommerfeld (BPS) monopoles or dyons. We find the metric of the moduli space of the SU(N) calorons in terms of the constituent monopole positions and their U(1) phases. In the small temperature limit calorons reduce locally to the standard instantons with trivial holonomy, whose moduli space is usually written in terms of the instanton center, size and orientation in the color space. We show that these collective coordinates can be explicitly written through dyons positions and phases. We also check that the standard instanton measure coincides exactly with that of N dyons.
On Fixed Points of Generalized α-φ Contractive Type Mappings in Partial Metric Spaces
Priya Shahi
2016-08-01
Full Text Available Recently, Samet et al. (B. Samet, C. Vetro and P. Vetro, Fixed point theorem for $\\alpha$-$\\psi$ contractive type mappings, Nonlinear Anal. 75 (2012, 2154--2165 introduced a very interesting new category of contractive type mappings known as $\\alpha$-$\\psi$ contractive type mappings. The results obtained by Samet et al. generalize the existing fixed point results in the literature, in particular the Banach contraction principle. Further, Karapinar and Samet (E. Karapinar and B. Samet, Generalized $\\alpha$-$\\psi$-contractive type mappings and related fixed point theorems with applications, Abstract and Applied Analysis 2012 Article ID 793486, 17 pages doi:10.1155/2012/793486 generalized the $\\alpha$-$\\psi$ contractive type mappings and established some fixed point theorems for this generalized class of contractive mappings. In (G. S. Matthews, Partial metric topology, Ann. New York Acad. Sci. 728 (1994, 183--197, the author introduced and studied the concept of partial metric spaces, and obtained a Banach type fixed point theorem on complete partial metric spaces. In this paper, we establish the fixed point theorems for generalized $\\alpha$-$\\psi$ contractive mappings in the context of partial metric spaces. As consequences of our main results, we obtain fixed point theorems on partial metric spaces endowed with a partial order and that for cyclic contractive mappings. Our results extend and strengthen various known results. Some examples are also given to show that our generalization from metric spaces to partial metric spaces is real.
Hypercomplex Numbers, Associated Metric Spaces, and Extension of Relativistic Hyperboloid
Pavlov, D G
2002-01-01
We undertake to develop a successful framework for commutative-associative hypercomplex numbers with the view to explicate and study associated geometric and generalized-relativistic concepts, basing on an interesting possibility to introduce appropriate multilinear metric forms in the treatment. The scalar polyproduct, which extends the ordinary scalar product used in bilinear (Euclidean and pseudo-Euclidean) theories, has been proposed and applied to be a generalized metric base for the approach. A fundamental concept of multilinear isometry is proposed. This renders possible to muse upon various relativistic physical applications based on anisotropic {\\it versus} ordinary spatially-rotational case.
Computing Best and Worst Shortcuts of Graphs Embedded in Metric Spaces
Wulff-Nilsen, Christian; Luo, Jun
2008-01-01
Given a graph embedded in a metric space, its dilation is the maximum over all distinct pairs of vertices of the ratio between their distance in the graph and the metric distance between them. Given such a graph G with n vertices and m edges and consisting of at most two connected components, we...
Isometric Coactions of Compact Quantum Groups on Compact Quantum Metric Spaces
Johan Quaegebeur; Marie Sabbe
2012-08-01
We propose a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel, where the metric structure is given by a Lipnorm. Within this setting we study the problem of the existence of a quantum isometry group.
Fixed Point Theorems for Set-Valued Contraction Type Maps in Metric Spaces
O'Regan D
2010-01-01
Full Text Available We first give some fixed point results for set-valued self-map contractions in complete metric spaces. Then we derive a fixed point theorem for nonself set-valued contractions which are metrically inward. Our results generalize many well-known results in the literature.
Fixed Point Theorems on Generalized Metric Spaces for Mappings in a Class Of Almost φ-Contractions
Kikina Luljeta
2015-09-01
Full Text Available In this paper, we obtain some new fixed point theorems in generalized metric spaces for maps satisfying an implicit relation. The obtained results unify, generalize, enrich, complement and extend a multitude of related fixed point theorems from metric spaces to generalized metric spaces.
Yost, M
1999-07-01
Epidemiological studies on extremely low frequency (ELF) magnetic fields have widely used personal or area sampling to evaluate exposures based on the time-weighted averaged flux density magnitude (TWA field). Relatively few studies have evaluated 'alternative' exposure metrics related to field characteristics such as temporal variability, frequency harmonics, vector polarisation, spatial orientation, static fields, high frequency transients, or induced electric fields. These field attributes fall into three major categories: (1) temporal characteristics of exposure intensity and timing, (2) frequency-domain characteristics, (3) spatial characteristics. The first category describes the magnitude and time history of exposure, including the TWA field metric, which most often is the focus of MF exposure assessment. The second category depicts the waveform characteristic (harmonic content), which has been relatively poorly described in most studies. The third category describes the field vector's time-space orientation and relation to static fields. Some examples of 'alternative metrics' that have been proposed based on biological mechanisms and potential measurement techniques are examined. The limited correlation of some alternative metrics with the TWA field metric in available data suggests that substantial exposure misclassification could occur if measurement protocols only focus on average field levels. (author)
Common fixed points for generalized contractive mappings in cone metric spaces
Hassen Aydi
2012-06-01
Full Text Available The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions in cone metric spaces. Also, an example is given to illustrate our results.
Common Fixed Point Theorem in Cone Metric Space for Rational Contractions
R. Uthayakumar
2013-09-01
Full Text Available In this paper we prove the common fixed point theorem in cone metric space for rational expression in normal cone setting. Our results generalize the main result of Jaggi [10] and Dass, Gupta [11].
Banakh, Taras
2008-01-01
We introduce and study (metrically) quarter-stratifiable spaces and then apply them to generalize Rudin and Kuratowski-Montgomery theorems about the Baire and Borel complexity of separately continuous functions.
Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces
Gong, FuZhou; Liu, Yuan
2015-06-01
We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.
The best approximation of $P-$ metric space of $\\chi^{2}-$ defined by Musielak
NAGARAJAN SUBRAMANIAN
2014-06-01
Full Text Available In this paper, we introduce the idea of constructing sequence space $\\chi^{2}$ of best approximation in $p-$ metric defined by Musielak and also construct some general topological properties of approximation of $\\chi^{2}$
Tripled common fixed point theorems for w-compatible mappings in ordered cone metric spaces
P. P. Murthy
2012-07-01
Full Text Available The purpose of this note is to establish a triplet coincidence point theorem in ordered cone metric spaces over solid cone. Our result extends coupled common fixed point theorems due to Nashine, Kadelburg and Radenovic [1].
Generalized contraction resulting tripled fixed point theorems in complex valued metric spaces
Madhu Singh
2016-10-01
Full Text Available Owning the concept of complex valued metric spaces introduced by Azam et al.[1] many authors prove several fixed point results for mappings satisfying certain contraction conditions. Coupled and tripled fixed point problems have attracted much attention in recent times. In this note, common tripled fixed point theorems for a pairs of mappings satisfying certain rational contraction in complex valued metric spaces are proved. Some illustrative examples are also given which demonstrate the validity of the hypotheses of our results.
Development of Technology Readiness Level (TRL) Metrics and Risk Measures
Engel, David W.; Dalton, Angela C.; Anderson, K. K.; Sivaramakrishnan, Chandrika; Lansing, Carina
2012-10-01
This is an internal project milestone report to document the CCSI Element 7 team's progress on developing Technology Readiness Level (TRL) metrics and risk measures. In this report, we provide a brief overview of the current technology readiness assessment research, document the development of technology readiness levels (TRLs) specific to carbon capture technologies, describe the risk measures and uncertainty quantification approaches used in our research, and conclude by discussing the next steps that the CCSI Task 7 team aims to accomplish.
Towards Performance Measurement And Metrics Based Analysis of PLA Applications
Ahmed, Zeeshan
2010-01-01
This article is about a measurement analysis based approach to help software practitioners in managing the additional level complexities and variabilities in software product line applications. The architecture of the proposed approach i.e. ZAC is designed and implemented to perform preprocessesed source code analysis, calculate traditional and product line metrics and visualize results in two and three dimensional diagrams. Experiments using real time data sets are performed which concluded with the results that the ZAC can be very helpful for the software practitioners in understanding the overall structure and complexity of product line applications. Moreover the obtained results prove strong positive correlation between calculated traditional and product line measures.
Measuring the user experience collecting, analyzing, and presenting usability metrics
Tullis, Thomas
2013-01-01
Measuring the User Experience was the first book that focused on how to quantify the user experience. Now in the second edition, the authors include new material on how recent technologies have made it easier and more effective to collect a broader range of data about the user experience. As more UX and web professionals need to justify their design decisions with solid, reliable data, Measuring the User Experience provides the quantitative analysis training that these professionals need. The second edition presents new metrics such as emotional engagement, personas, k
The effect of measurement error on surveillance metrics
Weaver, Brian Phillip [Los Alamos National Laboratory; Hamada, Michael S. [Los Alamos National Laboratory
2012-04-24
The purpose of this manuscript is to describe different simulation studies that CCS-6 has performed for the purpose of understanding the effects of measurement error on the surveillance metrics. We assume that the measured items come from a larger population of items. We denote the random variable associate with an item's value of an attribute of interest as X and that X {approx} N({mu}, {sigma}{sup 2}). This distribution represents the variability in the population of interest and we wish to make inference on the parameters {mu} and {sigma} or on some function of these parameters. When an item X is selected from the larger population, a measurement is made on some attribute of it. This measurement is made with error and the true value of X is not observed. The rest of this section presents simulation results for different measurement cases encountered.
Lee, Jenny Hyunjung; McDonnell, Kevin T; Zelenyuk, Alla; Imre, Dan; Mueller, Klaus
2014-03-01
Although the euclidean distance does well in measuring data distances within high-dimensional clusters, it does poorly when it comes to gauging intercluster distances. This significantly impacts the quality of global, low-dimensional space embedding procedures such as the popular multidimensional scaling (MDS) where one can often observe nonintuitive layouts. We were inspired by the perceptual processes evoked in the method of parallel coordinates which enables users to visually aggregate the data by the patterns the polylines exhibit across the dimension axes. We call the path of such a polyline its structure and suggest a metric that captures this structure directly in high-dimensional space. This allows us to better gauge the distances of spatially distant data constellations and so achieve data aggregations in MDS plots that are more cognizant of existing high-dimensional structure similarities. Our biscale framework distinguishes far-distances from near-distances. The coarser scale uses the structural similarity metric to separate data aggregates obtained by prior classification or clustering, while the finer scale employs the appropriate euclidean distance.
Some Results on Best Proximity Points of Cyclic Contractions in Probabilistic Metric Spaces
Manuel De la Sen
2015-01-01
Full Text Available This paper investigates properties of convergence of distances of p-cyclic contractions on the union of the p subsets of an abstract set X defining probabilistic metric spaces and Menger probabilistic metric spaces as well as the characterization of Cauchy sequences which converge to the best proximity points. The existence and uniqueness of fixed points and best proximity points of p-cyclic contractions defined in induced complete Menger spaces are also discussed in the case when the associate complete metric space is a uniformly convex Banach space. On the other hand, the existence and the uniqueness of fixed points of the p-composite mappings restricted to each of the p subsets in the cyclic disposal are also investigated and some illustrative examples are given.
Kobayashi's and Teichmüller's Metrics on the Teichmüller Space of Symmetric Circle Homeomorphisms
Jun HU; Yun Ping JIANG; Zhe WANG
2011-01-01
We give a direct proof of a result of Earle, Gardiner and Lakic, that is, Kobayashi's metric and Teichmüller's metric coincide with each other on the Teichmüller space of symmetric circle homeomorphisms.
Arithmetic geometry of toric varieties. Metrics, measures and heights
Gil, José Ignacio Burgos; Sombra, Martín
2011-01-01
We show that the height of a toric variety with respect to a toric metrized line bundle can be expressed as the integral over a polytope of a certain adelic family of concave functions. To state and prove this result, we study the Arakelov geometry of toric varieties. In particular, we consider models over a discrete valuation ring, metrized line bundles, and their associated measures and heights. We show that these notions can be translated in terms of convex analysis, and are closely related to objects like polyhedral complexes, concave functions, real Monge-Amp\\`ere measures, and Legendre-Fenchel duality. We also present a closed formula for the integral over a polytope of a function of one variable composed with a linear form. This allows us to compute the height of toric varieties with respect to some interesting metrics arising from polytopes. We also compute the height of toric projective curves with respect to the Fubini-Study metric, and of some toric bundles.
Geometric approach to evolution problems in metric spaces
Stojković, Igor
2011-01-01
This PhD thesis contains four chapters where research material is presented. In the second chapter the extension of the product formulas for semigroups induced by convex functionals, from the classical Hilbert space setting to the setting of general CAT(0) spaces. In the third chapter, the non-sym
A fingerprint based metric for measuring similarities of crystalline structures.
Zhu, Li; Amsler, Maximilian; Fuhrer, Tobias; Schaefer, Bastian; Faraji, Somayeh; Rostami, Samare; Ghasemi, S Alireza; Sadeghi, Ali; Grauzinyte, Migle; Wolverton, Chris; Goedecker, Stefan
2016-01-21
Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.
A fingerprint based metric for measuring similarities of crystalline structures
Zhu, Li; Fuhrer, Tobias; Schaefer, Bastian; Grauzinyte, Migle; Goedecker, Stefan, E-mail: stefan.goedecker@unibas.ch [Department of Physics, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland); Amsler, Maximilian [Department of Physics, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland); Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208 (United States); Faraji, Somayeh; Rostami, Samare; Ghasemi, S. Alireza [Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of); Sadeghi, Ali [Physics Department, Shahid Beheshti University, G. C., Evin, 19839 Tehran (Iran, Islamic Republic of); Wolverton, Chris [Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208 (United States)
2016-01-21
Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.
A fingerprint based metric for measuring similarities of crystalline structures
Zhu, Li; Fuhrer, Tobias; Schaefer, Bastian; Faraji, Somayeh; Rostami, Samara; Ghasemi, S Alireza; Sadeghi, Ali; Grauzinyte, Migle; Wolverton, Christopher; Goedecker, Stefan
2015-01-01
Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell we introduce crystal fingerprints that can be calculated easily and allow to define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method is an useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms and high-throughput screenings.
Measurement of joint space width and erosion size
Sharp, JI; van der Heijde, D; Angwin, J; Duryea, J; Moens, HJB; Jacobs, JWG; Maillefert, JF; Strand, CV
2005-01-01
Measurement of radiographic abnormalities in metric units has been reported by several investigators during the last 15 years. Measurement of joint space in large joints has been employed in a few trials to evaluate therapy in osteoarthritis. Measurement of joint space width in small joints has been
Measurement of joint space width and erosion size
Sharp, JI; van der Heijde, D; Angwin, J; Duryea, J; Moens, HJB; Jacobs, JWG; Maillefert, JF; Strand, CV
2005-01-01
Measurement of radiographic abnormalities in metric units has been reported by several investigators during the last 15 years. Measurement of joint space in large joints has been employed in a few trials to evaluate therapy in osteoarthritis. Measurement of joint space width in small joints has been
Kroon, Cindy D.
2007-01-01
Created for a Metric Day activity, Metric Madness is a board game for two to four players. Students review and practice metric vocabulary, measurement, and calculations by playing the game. Playing time is approximately twenty to thirty minutes.
Stringy space-time foam, Finsler-like metrics and dark matter relics
Mavromatos, Nick E., E-mail: Nikolaos.Mavromatos@cern.c [CERN, Theory Division, CH-1211 Geneva 23 (Switzerland); King' s College London, Department of Physics, Strand WC2R 2LS, London (United Kingdom); Sarkar, Sarben; Vergou, Ariadne [King' s College London, Department of Physics, Strand WC2R 2LS, London (United Kingdom)
2011-01-31
We discuss modifications of the thermal dark matter (DM) relic abundances in stringy cosmologies with D-particle space-time foamy backgrounds. As a result of back-reaction of massive DM on the background space-time, owing to its interaction with D-particle defects in the foam, quantum fluctuations are induced in the space-time metric. We demonstrate that these lead to the presence of extra source terms in the Boltzmann equation used to determine the thermal dark matter relic abundances. The source terms are determined by the specific form of the induced metric deformations; the latter depend on the momentum transfer of the DM particle during its interactions with the D-particle defects and so are akin to Finsler metrics. In the case of low string scales, arising from large extra dimensions, our results may have phenomenological implications for the search of viable supersymmetric models.
The locally connected compact metric spaces embeddable in the plane
Thomassen, Carsten
2004-01-01
We prove that a 2-connected, locally connected, compact topological space M is homeomorphic to a subset of the 2-sphere if and only if M is metrizable and contains none of the Kuratowski graphs K-5 and K-3,K-3.......We prove that a 2-connected, locally connected, compact topological space M is homeomorphic to a subset of the 2-sphere if and only if M is metrizable and contains none of the Kuratowski graphs K-5 and K-3,K-3....
A new metric for measuring condition in large predatory sharks.
Irschick, D J; Hammerschlag, N
2014-09-01
A simple metric (span condition analysis; SCA) is presented for quantifying the condition of sharks based on four measurements of body girth relative to body length. Data on 104 live sharks from four species that vary in body form, behaviour and habitat use (Carcharhinus leucas, Carcharhinus limbatus, Ginglymostoma cirratum and Galeocerdo cuvier) are given. Condition shows similar levels of variability among individuals within each species. Carcharhinus leucas showed a positive relationship between condition and body size, whereas the other three species showed no relationship. There was little evidence for strong differences in condition between males and females, although more male sharks are needed for some species (e.g. G. cuvier) to verify this finding. SCA is potentially viable for other large marine or terrestrial animals that are captured live and then released.
Some Common Fixed Point Theorems in Generalized Vector Metric Spaces
Rajesh Shrivastava
2013-11-01
Full Text Available In this paper we give some theorems on point of coincidence and common fixed point for two self mappings satisfying some general contractive conditions in generalized vector spaces. Our results generalize some well-known recent results in this direction.
The Connection Between the Metric and Generalized Projection Operators in Banach Spaces
Yakov ALBER; Jin Lu LI
2007-01-01
In this paper we study the connection between the metric projection operator PK:B→K,where B is a reflexive Banach space with dual space B* and K is a non-empty closed convex subset of B, and the generalized projection oprators Πk:B→k and πk:B*→k.We also present some results in non-reflexive Banach spaces.
Principles in selecting human capital measurements and metrics
Pharny D. Chrysler-Fox
2014-02-01
Full Text Available Orientation: Physical and natural resources have been surpassed by human capital as aresource of wealth creation. As a result, senior management relies increasingly on appropriatepeople information to drive strategic change. Yet, measurement within the human resourcefunction predominantly informs decisions in support of efficiency and effectiveness. Consequently, dissimilar understanding of measurement expectations between these partieslargely continues.Research purpose: The study explored principles in selecting human capital measurements,drawing on the views and recommendations of human resource management professionals,all experts in human capital measurement.Motivation for the study: The motivation was to advance the understanding of selectingappropriate and strategic valid measurements, in order for human resource practitioners tocontribute to creating value and driving strategic change.Research design, approach and method: A qualitative approach, with purposively selectedcases from a selected panel of human capital measurement experts, generated a datasetthrough unstructured interviews, which were analysed thematically.Main findings: Nineteen themes were found. They represent a process that considers thecentrality of the business strategy and a systemic integration across multiple value chains inthe organisation through business partnering, in order to select measurements and generatemanagement level-appropriate information.Practical/managerial implications: Measurement practitioners, in partnership withmanagement from other functions, should integrate the business strategy across multiplevalue chains in order to select measurements. Analytics becomes critical in discoveringrelationships and formulating hypotheses to understand value creation. Higher educationinstitutions should produce graduates able to deal with systems thinking and to operatewithin complexity.Contribution: This study identified principles to select measurements and
The field-space metric in spiral inflation and related models
Erlich, Joshua; Olsen, Jackson; Wang, Zhen
2016-09-01
Multi-field inflation models include a variety of scenarios for how inflation proceeds and ends. Models with the same potential but different kinetic terms are common in the literature. We compare spiral inflation and Dante's inferno-type models, which differ only in their field-space metric. We justify a single-field effective description in these models and relate the single-field description to a mass-matrix formalism. We note the effects of the nontrivial field-space metric on inflationary observables, and consequently on the viability of these models. We also note a duality between spiral inflation and Dante's inferno models with different potentials.
Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction
Poom Kumam
2013-01-01
Full Text Available Ran and Reurings (2004 established an interesting analogue of Banach Contraction Principle in a complete metric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasing mappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation.
Quasi-uniformity of Minimal Weighted Energy Points on Compact Metric Spaces
Hardin, D P; Whitehouse, J T
2011-01-01
For a closed subset $K$ of a compact metric space $A$ possessing an $\\alpha$-regular measure $\\mu$ with $\\mu(K)>0$, we prove that whenever $s>\\alpha$, any sequence of weighted minimal Riesz $s$-energy configurations $\\omega_N=\\{x_{i,N}^{(s)}\\}_{i=1}^N$ on $K$ (for `nice' weights) is quasi-uniform in the sense that the ratios of its mesh norm to separation distance remain bounded as $N$ grows large. Furthermore, if $K$ is an $\\alpha$-rectifiable compact subset of Euclidean space with positive and finite $\\alpha$-dimensional Hausdorff measure, it is possible to generate such a quasi-uniform sequence of configurations that also has (as $N\\to \\infty$) a prescribed positive continuous limit distribution with respect to $\\alpha$-dimensional Hausdorff measure. As a consequence of our energy related results for the unweighted case, we deduce that if $A$ is a compact $C^1$ manifold, then there exists a sequence of $N$-point best-packing configurations on $A$ whose mesh-separation ratios have limit superior (as $N\\to \\...
Metric-space analysis of spike trains theory, algorithms, and application
Victor, J D; Victor, Jonathan D.; Purpura, Keith P.
1998-01-01
We present the mathematical basis of a new approach to the analysis of temporal coding. The foundation of the approach is the construction of several families of novel distances (metrics) between neuronal impulse trains. In contrast to most previous approaches to the analysis of temporal coding, the present approach does not attempt to embed impulse trains in a vector space, and does not assume a Euclidean notion of distance. Rather, the proposed metrics formalize physiologically-based hypotheses for what aspects of the firing pattern might be stimulus-dependent, and make essential use of the point process nature of neural discharges. We show that these families of metrics endow the space of impulse trains with related but inequivalent topological structures. We show how these metrics can be used to determine whether a set of observed responses have stimulus-dependent temporal structure without a vector-space embedding. We show how multidimensional scaling can be used to assess the similarity of these metrics...
Approximative compactness and continuity of metric projector in Banach spaces and applications
CHEN ShuTao; HUDZIK Henryk; KOWALEWSKI Wojciech; WANG YuWen; WlSLA Marek
2008-01-01
First we prove that the approximative compactness of a nonempty set C in a normed linear space can be reformulated equivalently in another way. It is known that if C is a semi-Chebyshev closed and approximately compact set in a Banach space X, then the metric projector πC from X onto C is continuous. Under the assumption that X is midpoint locally uniformly rotund, we prove that the approximative compactness of C is also necessary for the continuity of the projector πC by the method of geometry of Banach spaces. Using this general result we find some necessary and sufficient conditions for T to have a continuous Moore-Penrose metric generalized inverse T+, where T is a bounded linear operator from an approximative compact and a rotund Banach space X into a midpoint locally uniformly rotund Banach space Y.
A metric space for type Ia supernova spectra
Sasdelli, Michele; Aldering, G; Antilogus, P; Aragon, C; Bailey, S; Baltay, C; Benitez-Herrera, S; Bongard, S; Buton, C; Canto, A; Cellier-Holzem, F; Chen, J; Childress, M; Chotard, N; Copin, Y; Fakhouri, H K; Feindt, U; Fink, M; Fleury, M; Fouchez, D; Gangler, E; Guy, J; Ishida, E E O; Kim, A G; Kowalski, M; Kromer, M; Lombardo, S; Mazzali, P A; Nordin, J; Pain, R; Pécontal, E; Pereira, R; Perlmutter, S; Rabinowitz, D; Rigault, M; Runge, K; Saunders, C; Scalzo, R; Smadja, G; Suzuki, N; Tao, C; Taubenberger, S; Thomas, R C; Tilquin, A; Weaver, B A
2014-01-01
We develop a new framework for use in exploring Type Ia Supernova (SN Ia) spectra. Combining Principal Component Analysis (PCA) and Partial Least Square analysis (PLS) we are able to establish correlations between the Principal Components (PCs) and spectroscopic/photometric SNe Ia features. The technique was applied to ~120 supernova and ~800 spectra from the Nearby Supernova Factory. The ability of PCA to group together SNe Ia with similar spectral features, already explored in previous studies, is greatly enhanced by two important modifications: (1) the initial data matrix is built using derivatives of spectra over the wavelength, which increases the weight of weak lines and discards extinction, and (2) we extract time evolution information through the use of entire spectral sequences concatenated in each line of the input data matrix. These allow us to define a stable PC parameter space which can be used to characterize synthetic SN Ia spectra by means of real SN features. Using PLS, we demonstrate that th...
KONG Fan-hua; Nobukazu NAKAGOSHI; YIN Hai-wei; Akira KIKUCHI
2005-01-01
Urban green spaces have been arisen growing concern responded to the social and environmental costs of urban sprawl. A wide range of planning and policies has been and/or will be designed to protect urban green spaces and optimize their spatial pattern. A better design or planning of urban green space can make a major contribution to quality of environment and urban life, and furthermore can decide whether we can have a sustainable development in the urban area. Information about the status quo of urban green spaces can help planners design more effectively.However, how to quantify and capture such information will be the essential question we face. In this paper, to quantify the urban green space, a new method comprising gradient analysis, landscape metrics and GIS was developed through a case of Jinan City. The results demonstrate: 1) the gradient analysis is a valid and reliable instrument to quantify the urban green space spatial pattern precisely; 2) using moving window, explicit landscape metrics were spatially realized. Compared with quantifying metrics in the entire landscape, it would be better to link pattern with process and establish an important basis for analyzing the ecological and socioeconomic functions of green spaces.
Xiangbing Zhou
2012-01-01
Full Text Available We generalize a fixed point theorem in partially ordered complete metric spaces in the study of A. Amini-Harandi and H. Emami (2010. We also give an application on the existence and uniqueness of the positive solution of a multipoint boundary value problem with fractional derivatives.
Bhavana Deshpande
2014-01-01
Full Text Available We establish a common coupled fixed point theorem for weakly compatible mappings on modified intuitionistic fuzzy metric spaces. As an application of our result, we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. We also give an example to demonstrate our result.
Some Almost Generalized (ψ,ϕ-Contractions in G-Metric Spaces
Hassen Aydi
2013-01-01
Full Text Available In this paper, we introduce some almost generalized (ψ,ϕ-contractions in the setting of G-metric spaces. We prove some fixed points results for such contractions. The presented theorems improve and extend some known results in the literature. An example is also presented.
Parameter-space metric of semicoherent searches for continuous gravitational waves
Pletsch, Holger J.
2010-08-01
Continuous gravitational-wave (CW) signals such as emitted by spinning neutron stars are an important target class for current detectors. However, the enormous computational demand prohibits fully coherent broadband all-sky searches for prior unknown CW sources over wide ranges of parameter space and for yearlong observation times. More efficient hierarchical “semicoherent” search strategies divide the data into segments much shorter than one year, which are analyzed coherently; then detection statistics from different segments are combined incoherently. To optimally perform the incoherent combination, understanding of the underlying parameter-space structure is requisite. This problem is addressed here by using new coordinates on the parameter space, which yield the first analytical parameter-space metric for the incoherent combination step. This semicoherent metric applies to broadband all-sky surveys (also embedding directed searches at fixed sky position) for isolated CW sources. Furthermore, the additional metric resolution attained through the combination of segments is studied. From the search parameters (sky position, frequency, and frequency derivatives), solely the metric resolution in the frequency derivatives is found to significantly increase with the number of segments.
Dehghan, Hossein
2011-01-01
In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [ Appl. Math. Comput. 196 (2008) 422-425] which was established for nonexpansive mappings.
An Order on Subsets of Cone Metric Spaces and Fixed Points of Set-Valued Contractions
Vaezpour SM
2009-01-01
Full Text Available In this paper at first we introduce a new order on the subsets of cone metric spaces then, using this definition, we simplify the proof of fixed point theorems for contractive set-valued maps, omit the assumption of normality, and obtain some generalization of results.
A new type of contraction in a complete $G$-metric space
Nidhi Malhotra
2015-09-01
Full Text Available In this paper we extend and generalize the concept of $F$-contraction to $F$-weak contraction and prove a fixed point theorem for $F$-weak contraction in a complete $G$-metric space. The article includes a nontrivial example which verify the effectiveness and applicability of our main result.
On Fuzzy Ã‰Â›-Contractive Mappings in Fuzzy Metric Spaces
Dorel Miheţ
2007-04-01
Full Text Available We answer into affirmative an open question raised by A. Razani in 2005. An essential role in our proofs is played by the separation axiom in the definition of a fuzzy metric space in the sense of George and Veeramani.
Common Fixed Point Theorems for G–Contraction in C∗–Algebra–Valued Metric Spaces
Akbar Zada
2016-04-01
Full Text Available In this paper we prove the common fixed point theorems for two mappings in complete C∗–valued metric space endowed with the graph G = (V,E, which satisfies G-contractive condition. Also, we provide an example in support of our main result.
Fixed Point Theorems for Hybrid Rational Geraghty Contractive Mappings in Ordered b-Metric Spaces
Farzaneh Zabihi
2014-01-01
Full Text Available We introduce the new notion of a hybrid rational Geraghty contractive mapping and investigate the existence of fixed point and coincidence point for such mappings in ordered b-metric spaces. We also provide an example to illustrate the results presented herein. Finally, we establish an existence theorem for a solution of an integral equation.
On asymptotically nonexpansive mappings in q-hyperconvex T0-quasi-metric spaces
S. N. Mishra
2013-03-01
Full Text Available In this note a well known result of Khamsi [Proc. Amer. Math. Soc. 132 (2004, 365-373] onapproximate fixed points for asymptotically nonexpansive mappings on bounded hyperconvexspaces is generalized to the setting of q-hyperconvex T0-quasi-metric spaces.
Fixed point results for generalized alpha-psi-contractions in metric-like spaces and applications
Hassen Aydi
2015-05-01
Full Text Available In this article, we introduce the concept of generalized $\\alpha\\text{-}\\psi$-contraction in the context of metric-like spaces and establish some related fixed point theorems. As consequences, we obtain some known fixed point results in the literature. Some examples and an application on two-point boundary value problems for second order differential equation are also considered.
Parameter-space metric of semicoherent searches for continuous gravitational waves
Pletsch, Holger J
2010-01-01
Continuous gravitational-wave (CW) signals such as emitted by spinning neutron stars are an important target class for current detectors. However, the enormous computational demand prohibits fully-coherent broadband all-sky searches for prior unknown CW sources over wide ranges of parameter space and for year-long observation times. More efficient hierarchical "semicoherent" search strategies divide the data into segments much shorter than one year, which are analyzed coherently; then detection statistics from different segments are combined incoherently. To optimally perform the incoherent combination, understanding of the underlying parameter-space structure is requisite. This problem is addressed here by using new coordinates on the parameter space, which yield the first analytical parameter-space metric for the incoherent combination step. This semicoherent metric applies to broadband all-sky surveys (also embedding directed searches at fixed sky position) for isolated CW sources. Furthermore, the additio...
Ideals in the Roe Algebras of Discrete Metric Spaces with Coefficients in B(H)
Yingjie HU; Qin WANG
2009-01-01
The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced.It is shown that,if X has Yu's property A,the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X,where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.
An Observability Metric for Underwater Vehicle Localization Using Range Measurements
Arrichiello, Filippo; Antonelli, Gianluca; Aguiar, Antonio Pedro; Pascoal, Antonio
2013-01-01
The paper addresses observability issues related to the general problem of single and multiple Autonomous Underwater Vehicle (AUV) localization using only range measurements. While an AUV is submerged, localization devices, such as Global Navigation Satellite Systems, are ineffective, due to the attenuation of electromagnetic waves. AUV localization based on dead reckoning techniques and the use of affordable motion sensor units is also not practical, due to divergence caused by sensor bias and drift. For these reasons, localization systems often build on trilateration algorithms that rely on the measurements of the ranges between an AUV and a set of fixed transponders using acoustic devices. Still, such solutions are often expensive, require cumbersome calibration procedures and only allow for AUV localization in an area that is defined by the geometrical arrangement of the transponders. A viable alternative for AUV localization that has recently come to the fore exploits the use of complementary information on the distance from the AUV to a single transponder, together with information provided by on-board resident motion sensors, such as, for example, depth, velocity and acceleration measurements. This concept can be extended to address the problem of relative localization between two AUVs equipped with acoustic sensors for inter-vehicle range measurements. Motivated by these developments, in this paper, we show that both the problems of absolute localization of a single vehicle and the relative localization of multiple vehicles can be treated using the same mathematical framework, and tailoring concepts of observability derived for nonlinear systems, we analyze how the performance in localization depends on the types of motion imparted to the AUVs. For this effect, we propose a well-defined observability metric and validate its usefulness, both in simulation and by carrying out experimental tests with a real marine vehicle during which the performance of an
An Observability Metric for Underwater Vehicle Localization Using Range Measurements
Filippo Arrichiello
2013-11-01
Full Text Available The paper addresses observability issues related to the general problem of single and multiple Autonomous Underwater Vehicle (AUV localization using only range measurements. While an AUV is submerged, localization devices, such as Global Navigation Satellite Systems, are ineffective, due to the attenuation of electromagnetic waves. AUV localization based on dead reckoning techniques and the use of affordable motion sensor units is also not practical, due to divergence caused by sensor bias and drift. For these reasons, localization systems often build on trilateration algorithms that rely on the measurements of the ranges between an AUV and a set of fixed transponders using acoustic devices. Still, such solutions are often expensive, require cumbersome calibration procedures and only allow for AUV localization in an area that is defined by the geometrical arrangement of the transponders. A viable alternative for AUV localization that has recently come to the fore exploits the use of complementary information on the distance from the AUV to a single transponder, together with information provided by on-board resident motion sensors, such as, for example, depth, velocity and acceleration measurements. This concept can be extended to address the problem of relative localization between two AUVs equipped with acoustic sensors for inter-vehicle range measurements. Motivated by these developments, in this paper, we show that both the problems of absolute localization of a single vehicle and the relative localization of multiple vehicles can be treated using the same mathematical framework, and tailoring concepts of observability derived for nonlinear systems, we analyze how the performance in localization depends on the types of motion imparted to the AUVs. For this effect, we propose a well-defined observability metric and validate its usefulness, both in simulation and by carrying out experimental tests with a real marine vehicle during which the
On local comparison between various metrics on Teichm\\"uller spaces
Alessandrini, Daniele; Papadopoulos, Athanase; Su, Weixu
2010-01-01
There are several Teichm\\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal Teichm\\"uller space, the length spectrum Teichm\\"uller space, the Fenchel-Nielsen Teichm\\"uller space, and there are others. In general, these spaces are set-theoretically different. An important question is therefore to understand relations between these spaces. Each of these spaces is equipped with its own metric, and under some hypotheses, there are inclusions between these spaces. In this paper, we obtain local metric comparison results on these inclusions, namely, we show that the inclusions are locally bi-Lipschitz under certain hypotheses. To obtain these results, we use some hyperbolic geometry estimates that give new results also for surfaces of finite type. We recall that in the case of a surface of finite type, all these Teichm\\"uller spaces coincide setwise. In the case o...
X-ray spectropolarimetric measurements of the Kerr metric
Liu, Dan; Cheng, Yifan; Bambi, Cosimo
2015-01-01
It is thought that the spacetime geometry around black hole candidates is described by the Kerr solution, but an observational confirmation is still missing. Today, the continuum-fitting method and the analysis of the iron K$\\alpha$ line cannot unambiguously test the Kerr paradigm because of the degeneracy among the parameters of the system, in the sense that it is impossible with current X-ray data to distinguish a Kerr black hole from a non-Kerr object with different spin and observed from a different viewing angle. In this paper, we study the possibility of testing the Kerr nature of black hole candidates with X-ray spectropolarimetric measurements. As a preliminary study, we employ a model with some simplifications, but our conclusions can unlikely change with a more sophisticated description. We find that -- even in the case of high quality data -- it is impossible to test the Kerr metric and the problem is still the strong correlation between the spin and possible deviations from the Kerr geometry. The ...
Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces
Thabet Abdeljawad
2012-01-01
Full Text Available In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F:X×X→X and g:X→X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012 have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012.
Topics in Metric Approximation
Leeb, William Edward
This thesis develops effective approximations of certain metrics that occur frequently in pure and applied mathematics. We show that distances that often arise in applications, such as the Earth Mover's Distance between two probability measures, can be approximated by easily computed formulas for a wide variety of ground distances. We develop simple and easily computed characterizations both of norms measuring a function's regularity -- such as the Lipschitz norm -- and of their duals. We are particularly concerned with the tensor product of metric spaces, where the natural notion of regularity is not the Lipschitz condition but the mixed Lipschitz condition. A theme that runs throughout this thesis is that snowflake metrics (metrics raised to a power less than 1) are often better-behaved than ordinary metrics. For example, we show that snowflake metrics on finite spaces can be approximated by the average of tree metrics with a distortion bounded by intrinsic geometric characteristics of the space and not the number of points. Many of the metrics for which we characterize the Lipschitz space and its dual are snowflake metrics. We also present applications of the characterization of certain regularity norms to the problem of recovering a matrix that has been corrupted by noise. We are able to achieve an optimal rate of recovery for certain families of matrices by exploiting the relationship between mixed-variable regularity conditions and the decay of a function's coefficients in a certain orthonormal basis.
New Fixed Point Results of Single-Valued Mapping for c-Distance in Cone Metric Spaces
Zaid Mohammed Fadail
2012-01-01
Full Text Available A new concept of the c-distance in cone metric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some fixed point results in literature for c-distance in cone metric spaces by replacing the constants in contractive conditions with functions. Some supporting examples are given.
Yongjie Piao
2008-01-01
In this paper, we prove that a family of self-maps {TI,j}I,j ∈N in 2-metric space has a unique common fixed point if (I) {TI,j}I,j∈N satisfies the same type contractive con-main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.
Construction and coupling of frames in Hilbert spaces with W-metrics
German Escobar
2016-05-01
Full Text Available A definition of frames unitarily equivalent in Hilbert spaces with W-metric is stated, and a characterization is given in terms of their respective analysis operators. From a Hilbert space with a frame we construct a Hilbert space with W-metric and a frame unitarily equivalent to the given one. Finally, we prove that the coupling of two frames is a frame. Resumen. Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.
Lifshitz field theories, Snyder noncomutative space-time and momentum dependent metric
Romero, Juan M
2015-01-01
In this work, we propose three different modified relativistic particles. In the first case, we propose a particle with metrics depending on the momenta and we show that the quantum version of these systems includes different field theories, as anisotropic field theories. As a second case we propose a particle that implies a modified symplectic structure and we show that the quantum version of this system gives different noncommutative space-times, for example the Snyder space-time. In the third case, we combine both structures before mentioned, namely noncommutative space-times and momentum dependent metrics. In this last case, we show that anisotropic field theories can be seen as a limit of no commutative field theory.
On σ-images of Metric Spaces%关于度量空间的σ-映象
梁洪亮; 杨巍纳
2005-01-01
In this paper the relation between the σ-images of metrical spaces and spaces with σ-locally finite cs-network, or spaces with σ-locally finite cs*-network, or spaces with σ-locally finite sequence neighborhood network, or spaces with σ-locally finite sequence open network are established by use of σ-mapping.
Design based Object-Oriented Metrics to Measure Coupling and Cohesion
PREETI GULIA
2011-11-01
Full Text Available The object oriented design and object oriented development environment are currently popular in software organizations due to the object oriented programming languages. As the object oriented technology enters into software organizations, it has created new challenges for the companies which used only product metrics as atool for monitoring, controlling and maintaining the software product. This paper presents the new object oriented metrics namely for coupling of class by counting the number of associated classes within a class & total associated class and cohesion at the method and function level for cohesion to estimates object oriented software. In order to this, we discuss in this paper object oriented issues and measures with analysis of object oriented metrics through coupling and cohesion to check the complexity with weight count method. We also discuses the estimation process after analysis of proposed object oriented metrics to measures and check the better performance of object oriented metrics in comparison to other object oriented metrics.
On the local integrability of almost-product structures defined by space-time metrics
Delphenich, D H
2016-01-01
The splitting of the tangent bundle of space-time into temporal and spatial sub-bundles defines an almost-product structure. In particular, any space-time metric can be locally expressed in time-orthogonal form, in such a way that whether or not that almost-product structure is locally generated by a coordinate chart is a matter of the integrability of the Pfaff equation that the temporal 1-form of that expression for the metric defines. When one applies that analysis to the known exact solutions to the Einstein field equations, one finds that many of the common ones are completely-integrable, although some of the physically-interesting ones are not.
The field-space metric in spiral inflation and related models
Erlich, Joshua [High Energy Theory Group, Department of Physics, College of William and Mary,Williamsburg, VA 23187 (United States); Olsen, Jackson [School of Physics and Astronomy, University of Minnesota,Minneapolis, MN 55455 (United States); Wang, Zhen [High Energy Theory Group, Department of Physics, College of William and Mary,Williamsburg, VA 23187 (United States)
2016-09-22
Multi-field inflation models include a variety of scenarios for how inflation proceeds and ends. Models with the same potential but different kinetic terms are common in the literature. We compare spiral inflation and Dante’s inferno-type models, which differ only in their field-space metric. We justify a single-field effective description in these models and relate the single-field description to a mass-matrix formalism. We note the effects of the nontrivial field-space metric on inflationary observables, and consequently on the viability of these models. We also note a duality between spiral inflation and Dante’s inferno models with different potentials.
A fixed point of generalized T F -contraction mappings in cone metric spaces
Moradi Sirous
2011-01-01
Full Text Available Abstract In this paper, the existence of a fixed point for TF -contractive mappings on complete metric spaces and cone metric spaces is proved, where T : X → X is a one to one and closed graph function and F : P → P is non-decreasing and right continuous, with F -1(0 = -0} and F(tn → 0 implies tn → 0. Our results, extend previous results given by Meir and Keeler (J. Math. Anal. Appl. 28, 326-329, 1969, Branciari (Int. J. Math. sci. 29, 531-536, 2002, Suzuki (J. Math. Math. Sci. 2007, Rezapour et al. (J. Math. Anal. Appl. 345, 719-724, 2010, Moradi et al. (Iran. J. Math. Sci. Inf. 5, 25-32, 2010 and Khojasteh et al. (Fixed Point Theory Appl. 2010. MSC(2000: 47H10; 54H25; 28B05.
Ezer, Neta; Zumbado, Jennifer Rochlis; Sandor, Aniko; Boyer, Jennifer
2011-01-01
Human-robot systems are expected to have a central role in future space exploration missions that extend beyond low-earth orbit [1]. As part of a directed research project funded by NASA s Human Research Program (HRP), researchers at the Johnson Space Center have started to use a variety of techniques, including literature reviews, case studies, knowledge capture, field studies, and experiments to understand critical human-robot interaction (HRI) variables for current and future systems. Activities accomplished to date include observations of the International Space Station s Special Purpose Dexterous Manipulator (SPDM), Robonaut, and Space Exploration Vehicle (SEV), as well as interviews with robotics trainers, robot operators, and developers of gesture interfaces. A survey of methods and metrics used in HRI was completed to identify those most applicable to space robotics. These methods and metrics included techniques and tools associated with task performance, the quantification of human-robot interactions and communication, usability, human workload, and situation awareness. The need for more research in areas such as natural interfaces, compensations for loss of signal and poor video quality, psycho-physiological feedback, and common HRI testbeds were identified. The initial findings from these activities and planned future research are discussed. Human-robot systems are expected to have a central role in future space exploration missions that extend beyond low-earth orbit [1]. As part of a directed research project funded by NASA s Human Research Program (HRP), researchers at the Johnson Space Center have started to use a variety of techniques, including literature reviews, case studies, knowledge capture, field studies, and experiments to understand critical human-robot interaction (HRI) variables for current and future systems. Activities accomplished to date include observations of the International Space Station s Special Purpose Dexterous Manipulator
Krieger, Jonathan D.
2014-01-01
• Premise of the study: I present a protocol for creating geometric leaf shape metrics to facilitate widespread application of geometric morphometric methods to leaf shape measurement. • Methods and Results: To quantify circularity, I created a novel shape metric in the form of the vector between a circle and a line, termed geometric circularity. Using leaves from 17 fern taxa, I performed a coordinate-point eigenshape analysis to empirically identify patterns of shape covariation. I then compared the geometric circularity metric to the empirically derived shape space and the standard metric, circularity shape factor. • Conclusions: The geometric circularity metric was consistent with empirical patterns of shape covariation and appeared more biologically meaningful than the standard approach, the circularity shape factor. The protocol described here has the potential to make geometric morphometrics more accessible to plant biologists by generalizing the approach to developing synthetic shape metrics based on classic, qualitative shape descriptors. PMID:25202647
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
Kalabušić S
2009-01-01
Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation , where satisfies mixed-monotone conditions with respect to the given ordering.
Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces
Dž. Burgić
2009-01-01
Full Text Available We prove fixed point theorems for mixed-monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition than the classical Banach contraction condition for all points that are related by given ordering. We also give a global attractivity result for all solutions of the difference equation zn+1=F(zn,zn−1, n=2,3,…, where F satisfies mixed-monotone conditions with respect to the given ordering.
Common fixed point theorems for sub-sequential continuous mapping in fuzzy metric space
Arihant Jain
2013-03-01
Full Text Available The present paper deals with common fixed point theorems in fuzzy metric spaces employing the notion of sub-sequentially continuity. Moreover we have to show that in the context of sequentially continuity, the notion of compatibility and semi-compatibility of maps becomes equivalent. Our result improves recent results of Singh & Jain [13] in the sense that all maps involved in the theorems are discontinuous even at common fixed point.
Some New Weakly Contractive Type Multimaps and Fixed Point Results in Metric Spaces
Abdou AfrahAN
2009-01-01
Full Text Available Some new weakly contractive type multimaps in the setting of metric spaces are introduced, and we prove some results on the existence of fixed points for such maps under certain conditions. Our results extend and improve several known results including the corresponding recent fixed point results of Pathak and Shahzad (2009, Latif and Abdou (2009, Latif and Albar (2008, Cirić (2008, Feng and Liu (2006, and Klim and Wardowski (2007.
Bulk metric of brane world models and submanifolds in 6D pseudo-Euclidian space-time
Smolyakov, Mikhail N
2010-01-01
In this short note, five-dimensional brane world models with dS_{4} metric on the branes are discussed. The explicit coordinate transformations, which show the equivalence between the bulk metric of these brane world models and the metric induced on an appropriate submanifolds in the flat six-dimensional pseudo-Euclidean space-time, are presented. The cases of the zero and non-zero cosmological constant in the bulk are discussed in detail.
MEASURING OBJECT-ORIENTED SYSTEMS BASED ON THE EXPERIMENTAL ANALYSIS OF THE COMPLEXITY METRICS
J.S.V.R.S.SASTRY,
2011-05-01
Full Text Available Metrics are used to help a software engineer in quantitative analysis to assess the quality of the design before a system is built. The focus of Object-Oriented metrics is on the class which is the fundamental building block of the Object-Oriented architecture. These metrics are focused on internal object structure and external object structure. Internal object structure reflects the complexity of each individual entity such as methods and classes. External complexity measures the interaction among entities such as Coupling and Inheritance. This paper mainly focuses on a set of object oriented metrics that can be used to measure the quality of an object oriented design. Two types of complexity metrics in Object-Oriented paradigm namely Mood metrics and Lorenz & Kidd metrics. Mood metrics consist of Method inheritance factor(MIF, Coupling factor(CF, Attribute inheritance factor(AIF, Method hiding factor(MHF, Attribute hiding factor(AHF, and polymorphism factor(PF. Lorenz & Kidd metrics consist of Number of operations overridden (NOO, Number operations added (NOA, Specialization index(SI. Mood metrics and Lorenz & Kidd metrics measurements are used mainly by designers and testers. Designers uses these metrics to access the software early in process,making changes that will reduce complexity and improve the continuing capability of the design. Testers use to test the software for finding the complexity, performance of the system, quality of the software. This paper reviews Mood metrics and Lorenz & Kidd metrics are validates theoretically and empirically methods. In thispaper, work has been done to explore the quality of design of software components using object oriented paradigm. A number of object oriented metrics have been proposed in the literature for measuring the design attributes such as inheritance, coupling, polymorphism etc. This paper, metrics have been used to analyzevarious features of software component. Complexity of methods
Flat currents modulo p in metric spaces and filling radius inequalities
Ambrosio, Luigi
2010-01-01
We adapt the theory of currents in metric spaces, as developed by the first-mentioned author in collaboration with B. Kirchheim, to currents with coefficients in Z_p. We obtain isoperimetric inequalities mod(p) in Banach spaces and we apply these inequalities to provide a proof of Gromov's filling radius inequality which applies also to nonorientable manifolds. With this goal in mind, we use the Ekeland principle to provide quasi-minimizers of the mass mod(p) in the homology class, and use the isoperimetric inequality to give lower bounds on the growth of their mass in balls.
Kalaghatgi, Chinmay; Arun, K G
2015-01-01
Searches for gravitational waves (GWs) from binary black holes using interferometric GW detectors require the construction of template banks for performing matched filtering while analyzing the data. Placement of templates over the parameter space of binaries, as well as coincidence tests of GW triggers from multiple detectors make use of the definition of a metric over the space of gravitational waveforms. Although recent searches have employed waveform templates coherently describing the inspiral, merger and ringdown (IMR) of the coalescence, the metric used in the template banks and coincidence tests was derived from post-Newtonian inspiral waveforms. In this paper, we compute the template-space metric of the IMR waveform family IMRPhenomB over the parameter space of masses and the effective spin parameter. We also propose a coordinate system, which is a modified version of post-Newtonian chirp time coordinates, in which the metric is slowly varying over the parameter space. The match function analytically...
Computing the dilation of edge-augmented graphs in metric spaces
Wulff-Nilsen, Christian
2009-01-01
Let G=(V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n4) running time and uses O(n2) space. We show how to impr...... to improve the running time to O(n3logn) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G {(u,v)} for every pair of distinct vertices u and v.......Let G=(V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n4) running time and uses O(n2) space. We show how...
Computing the Dilation of Edge-Augmented Graphs Embedded in Metric Spaces
Wulff-Nilsen, Christian
2008-01-01
Let G = (V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n^4) running time and uses O(n^2) space. We show how to ...... to improve running time to O(n^3*log n) while maintaining quadratic space requirement. In fact, our algorithm not only determines the best shortcut but computes the dilation of G U {(u,v)} for every pair of distinct vertices u and v.......Let G = (V,E) be an undirected graph with n vertices embedded in a metric space. We consider the problem of adding a shortcut edge in G that minimizes the dilation of the resulting graph. The fastest algorithm to date for this problem has O(n^4) running time and uses O(n^2) space. We show how...
Derivation of Field Equations in Space with the Geometric Structure Generated by Metric and Torsion
Nikolay Yaremenko
2014-01-01
Full Text Available This paper is devoted to the derivation of field equations in space with the geometric structure generated by metric and torsion tensors. We also study the geometry of the space generated jointly and agreed on by the metric tensor and the torsion tensor. We showed that in such space the structure of the curvature tensor has special features and for this tensor we obtained analog Ricci-Jacobi identity and evaluated the gap that occurs at the transition from the original to the image and vice versa, in the case of infinitely small contours. We have researched the geodesic lines equation. We introduce the tensor παβ which is similar to the second fundamental tensor of hypersurfaces Yn-1, but the structure of this tensor is substantially different from the case of Riemannian spaces with zero torsion. Then we obtained formulas which characterize the change of vectors in accompanying basis relative to this basis itself. Taking into considerations our results about the structure of such space we derived from the variation principle the general field equations (electromagnetic and gravitational.
Metrically measuring liver biopsy:A chronic hepatitis B and C computer-aided morphologic description
Nicola Dioguardi; Fabio Grizzi; Barbara Fiamengo; Carlo Russo
2008-01-01
AIM:To describe a quantitative analysis method for liver biopsy sections with a machine that we have named "Dioguardi Histological Metriser" which automatically measures the residual hepatocyte mass (including hepatocytes vacuolization),inflammation,fibrosis and the loss of liver tissue tectonics.METHODS:We analysed digitised images of liver biopsy sections taken from 398 patients.The analysis with Dioguardi Histological Metriser was validated by comparison with semi-quantitative scoring system.RESULTS:The method provides:(1) the metrical extension in two-dimensions (the plane) of the residual hepatocellular set,including the area of vacuoles pertinent to abnormal lipid accumulation;(2) the geometric measure of the inflammation basin,which distinguishes intra-basin space and extra-basin dispersed parenchymal leukocytes;(3) the magnitude of collagen islets,(which were considered truncated fractals and classified into three degrees of magnitude);and (4)the tectonic index that quantifies alterations (disorders)in the organization of liver tissue.Dioguardi Histological Metriser machine allows to work at a speed of 0.1 mm2/s,scanning a whole section in 6-8 min.CONCLUSION:The results are the first standardized metrical evaluation of the geometric properties of the parenchyma,inflammation,fibrosis,and alterations in liver tissue tectonics of the biopsy sections.The present study confirms that biopsies are still valuable,not only for diagnosing chronic hepatitis,but also for quantifying changes in the organization and order of liver tissue structure.
Solution of the Dirac equation in a curved space with static metric
Alhaidari, A D
2015-01-01
Compatibility of symmetric quantization of the Dirac equation in a curved space with general covariance gives a special representation of the spin connections in which their dot product with the Dirac gamma matrices becomes equal to the "covariant divergence" of the latter. Requiring that the square of the equation gives the conventional Klein-Gordon equation in a curved space results in an operator algebra for the Dirac gamma matrices that involves the "covariant derivative" connections and the Riemann-Christoffel connections. In 1+1 space-time with static metric, we obtain exact solutions of this Dirac equation model for some examples. We also formulate the interacting theory of the model with various coupling modes and solve it in the same space for a given potential configuration.
Tichy, Wolfgang; McDonald, Jonathan R.; Miller, Warner A.
2015-01-01
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three-dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six conditions that fix translations and rotations of the embedded surface. This set of equations is discretized by means of a pseudospectral collocation point method. The resulting nonlinear system of equations are then solved by a Newton-Raphson scheme. We explain our numerical algorithm in detail. By studying several examples we show that our method converges provided we start the Newton-Raphson scheme from a suitable initial guess. Our novel method is very efficient for smooth 2-metrics.
Tichy, Wolfgang; Miller, Warner A
2014-01-01
We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six conditions that fix translations and rotations of the embedded surface. This set of equations is discretized by means of a pseudospectral collocation point method. The resulting nonlinear system of equations are then solved by a Newton-Raphson scheme. We explain our numerical algorithm in detail. By studying several examples we show that our method converges provided we start the Newton-Raphson scheme from a suitable initial guess. Our novel method is very efficient for smooth 2-metrics.
M. Eshaghi Gordji
2012-01-01
Full Text Available We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.
M. Eshaghi Gordji; H. Baghani; G. H. Kim
2012-01-01
We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.
Hallowed Olaoluwa
2015-01-01
Full Text Available In this research work, some results on the existence and approximation of common coupled fixed points of contractive maps in cone metric spaces are unified and generalized based on a new method.
田有先; 张石生
2002-01-01
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B . Ciric , Q. H. Liu , H. E.Rhoades and H. K . Xu , et al., but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces.
Frosini, Patrizio
2010-01-01
The Hausdorff distance, the Gromov-Hausdorff, the Fr\\'echet and the natural pseudo-distances are instances of dissimilarity measures widely used in shape comparison. We show that they share the property of being defined as $\\inf_\\rho F(\\rho)$ where $F$ is a suitable functional and $\\rho$ varies in a set of correspondences containing the set of homeomorphisms. Our main result states that the set of homeomorphisms cannot be enlarged to a metric space $\\mathcal{K}$, in such a way that the composition in $\\mathcal{K}$ (extending the composition of homeomorphisms) passes to the limit and, at the same time, $\\mathcal{K}$ is compact.
Discussion Part 2: Metrics and Validation Needs for Space Weather Models and Services
Glover, Alexi; Onsager, Terrance; Kuznetsova, Maria; Bingham, Suzy
2016-07-01
We invite the space weather community to contribute to a discussion on the main themes of this PSW1 event, with the aim of identifying and prioritising key issues and formulating recommendations and guidelines for policy makers, stakeholders, and data and service providers. This event particularly encourages dialogue between modellers, application developers, service providers and users of space weather products and services in order to review the state of model and service validation activities, to build upon successes, to identify challenges, and to develop a strategy for continuous assessment of space weather predictive capabilities and tracing the improvement over time, as recommended in the COSPAR Space Weather Roadmap. We discuss space weather verification & validation needs for the current generation of activities under development and in planning globally, together with perspectives for modellers and scientific community to further participate in the space weather endeavour. All Assembly participants are welcome to participate in this PSW discussion session and all are invited to submit input for the discussion to the authors ahead of the Assembly. The discussion will take place in two parts at the start and end of the PSW1 event. It is intended that the outcome of these discussion sessions will be formulated as a panel position paper on metrics and validation needs for space weather models and services.
Glover, Alexi; Onsager, Terrance; Kuznetsova, Maria; Bingham, Suzy
2016-07-01
We invite the space weather community to contribute to a discussion on the main themes of this PSW1 event, with the aim of identifying and prioritising key issues and formulating recommendations and guidelines for policy makers, stakeholders, and data and service providers. This event particularly encourages dialogue between modellers, application developers, service providers and users of space weather products and services in order to review the state of model and service validation activities, to build upon successes, to identify challenges, and to develop a strategy for continuous assessment of space weather predictive capabilities and tracing the improvement over time, as recommended in the COSPAR Space Weather Roadmap. We discuss space weather verification & validation needs for the current generation of activities under development and in planning globally, together with perspectives for modellers and scientific community to further participate in the space weather endeavour. All Assembly participants are welcome to participate in this PSW discussion session and all are invited to submit input for the discussion to the authors ahead of the Assembly. The discussion will take place in two parts at the start and end of the PSW1 event. It is intended that the outcome of these discussion sessions will be formulated as a panel position paper on metrics and validation needs for space weather models and services.
Results on n-tupled fixed points in complete asymptotically regular metric spaces
Anupam Sharma
2014-10-01
Full Text Available The notion of n-tupled fixed point is introduced by Imdad, Soliman, Choudhury and Das, Jour. of Operators, Vol. 2013, Article ID 532867. In this manuscript, we prove some n-tupled fixed point theorems (for even n for mappings having mixed monotone property in partially ordered complete asymptotically regular metric spaces. Our main theorem improves the corresponding results of Imdad, Sharma and Rao (M. Imdad, A. Sharma, K.P.R. Rao, Generalized n-tupled fixed point theorems for nonlinear contractions, preprint.
Global embedding of the Reissner-Nordstrom metric in the flat ambient space
Paston, S A
2014-01-01
We study isometric embeddings of non-extremal Reissner-Nordstrom metric describing a charged black hole. We obtain three new embeddings in the flat ambient space with minimal possible dimension. These embeddings are global, i.e. corresponding surfaces are smooth at all values of radius, including horizons. Each of the given embeddings covers one instance of the regions outside the horizon, one instance between the horizons and one instance inside the internal horizon. The lines of time for these embeddings turn out to be more complicated than circles or hyperbolas.
Geometry and dynamics in Gromov hyperbolic metric spaces with an emphasis on non-proper settings
Das, Tushar; Urbański, Mariusz
2016-01-01
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Klauder, J R
1998-01-01
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates. All quantization schemes that lead to Hilbert space vectors and Weyl operators---even those that eschew Cartesian coordinates---implicitly contain a metric on a flat phase space. This feature is demonstrated by studying the classical and quantum ``aggregations'', namely, the set of all facts and properties resident in all classical and quantum theories, respectively. Metrical quantization is an approach that elevates the flat phase space metric inherent in any canonical quantization to the level of a postulate. Far from being an unwanted structure, the flat phase space metric carries essential physical information. It is shown how the metric, when employed within a continuous-time regularization scheme, gives rise to an unambiguous quantization procedure that automatically ...
Length spectra and degeneration of flat metrics
Duchin, Moon; Rafi, Kasra
2009-01-01
In this paper we consider flat metrics (semi-translation structures) on surfaces of finite type. There are two main results. The first is a complete description of when a set of simple closed curves is spectrally rigid, that is, when the length vector determines a metric among the class of flat metrics. Secondly, we give an embedding into the space of geodesic currents and use this to get a boundary for the space of flat metrics. The geometric interpretation is that flat metrics degenerate to "mixed structures" on the surface: part flat metric and part measured foliation.
Lee, Jenny Hyunjung; McDonnell, Kevin T; Zelenyuk, Alla; Imre, Dan; Mueller, Klaus
2013-07-11
Although the Euclidean distance does well in measuring data distances within high-dimensional clusters, it does poorly when it comes to gauging inter-cluster distances. This significantly impacts the quality of global, low-dimensional space embedding procedures such as the popular multi-dimensional scaling (MDS) where one can often observe non-intuitive layouts. We were inspired by the perceptual processes evoked in the method of parallel coordinates which enables users to visually aggregate the data by the patterns the polylines exhibit across the dimension axes. We call the path of such a polyline its structure and suggest a metric that captures this structure directly in high-dimensional space. This allows us to better gauge the distances of spatially distant data constellations and so achieve data aggregations in MDS plots that are more cognizant of existing high-dimensional structure similarities. Our bi-scale framework distinguishes far-distances from near-distances. The coarser scale uses the structural similarity metric to separate data aggregates obtained by prior classification or clustering, while the finer scale employs the appropriate Euclidean distance.
SiMPSON: Efficient Similarity Search in Metric Spaces over P2P Structured Overlay Networks
Vu, Quang Hieu; Lupu, Mihai; Wu, Sai
Similarity search in metric spaces over centralized systems has been significantly studied in the database research community. However, not so much work has been done in the context of P2P networks. This paper introduces SiMPSON: a P2P system supporting similarity search in metric spaces. The aim is to answer queries faster and using less resources than existing systems. For this, each peer first clusters its own data using any off-the-shelf clustering algorithms. Then, the resulting clusters are mapped to one-dimensional values. Finally, these one-dimensional values are indexed into a structured P2P overlay. Our method slightly increases the indexing overhead, but allows us to greatly reduce the number of peers and messages involved in query processing: we trade a small amount of overhead in the data publishing process for a substantial reduction of costs in the querying phase. Based on this architecture, we propose algorithms for processing range and kNN queries. Extensive experimental results validate the claims of efficiency and effectiveness of SiMPSON.
Laowang Worawut
2011-01-01
Full Text Available Abstract Abkar and Eslamian (Nonlinear Anal. TMA, 74, 1835-1840, 2011 prove that if K is a nonempty bounded closed convex subset of a complete CAT(0 space X, t : K → K is a single-valued quasi-nonexpansive mapping and T : K → KC(K is a multivalued mapping satisfying conditions (E and (Cλ for some λ ∈ (0, 1 such that t and T commute weakly, then there exists a point z ∈ K such that z = t(z ∈ T(z. In this paper, we extend this result to the general setting of uniformly convex metric spaces. Nevertheless, condition (E of T can be weakened to the strongly demiclosedness of I - T.
A maximin characterization of the escape rate of nonexpansive mappings in metrically convex spaces
Gaubert, Stephane
2010-01-01
We establish a maximin characterization of the linear escape rate of the orbits of a nonexpansive mapping on a complete (hemi-)metric space, under a mild form of Busemann's nonpositive curvature condition (we require a distinguished family of geodesics with a common origin to satisfy a convexity inequality). This characterization, which involves horofunctions, generalizes the Collatz-Wielandt characterization of the spectral radius of a nonnegative matrix. It yields as corollaries a theorem of Kohlberg and Neyman (1981), concerning nonexpansive maps in Banach spaces, a variant of a Denjoy-Wolff type theorem of Karlsson (2001), together with a refinement of a theorem of Gunawardena and Walsh (2003), concerning order-preserving positively homogeneous self-maps of symmetric cones.
Measurement Space Drill Support
2015-08-30
address the conditions: Go to coffee shop , buy a car hot water/ coffee maker, coffee cup, thermos. Conditions that discriminate among those...Insulated coffee mug. – Thermos. – Coffee shop . Attributes Operational Impact Measures Conditions Environment Mission Threat Friendly Echelon Time...a boat. All possible solutions: coffee mug, thermos, buy coffee , not go to work, buy a portable coffee pot, get a closer job, drink water, duct
XU Dian-Yah
2000-01-01
Absorbing charged rotating (ACR) metric in de Sitter space and related energy-momentum tensor are derived.The ACR metric is very simple in advanced time coordinates. The ACR metric involves 8 independent parameters which are divided into two classes: (1) the mass M, charge Q, angular momentum per unit mass a, and cosmological constant A; (2) M/ v, 2M/ v2, Q/ v, and 2Q/ v2. The non-stationary part of the energy-momentum tensor is positive definite everywhere.
Semigroups on spaces of measures
Worm, Daniel Theodorus Hendrikus
2010-01-01
This thesis deals with Markov operators and semigroups. A Markov operator is a positive linear operator on the space of finite measures on some state space that preserves mass. A Markov semigroup is a family of Markov operators parametrised by the positive real numbers, satisfying the semigroup
Principles in selecting human capital measurements and metrics
2014-01-01
Orientation: Physical and natural resources have been surpassed by human capital as aresource of wealth creation. As a result, senior management relies increasingly on appropriatepeople information to drive strategic change. Yet, measurement within the human resourcefunction predominantly informs decisions in support of efficiency and effectiveness. Consequently, dissimilar understanding of measurement expectations between these partieslargely continues.Research purpose: The study explored pr...
Xue, Zhenyu; Vlachos, Pavlos P
2014-01-01
In particle image velocimetry (PIV) the measurement signal is contained in the recorded intensity of the particle image pattern superimposed on a variety of noise sources. The signal-to-noise-ratio (SNR) strength governs the resulting PIV cross correlation and ultimately the accuracy and uncertainty of the resulting PIV measurement. Hence we posit that correlation SNR metrics calculated from the correlation plane can be used to quantify the quality of the correlation and the resulting uncertainty of an individual measurement. In this paper we present a framework for evaluating the correlation SNR using a set of different metrics, which in turn are used to develop models for uncertainty estimation. The SNR metrics and corresponding models presented herein are expanded to be applicable to both standard and filtered correlations. In addition, the notion of a valid measurement is redefined with respect to the correlation peak width in order to be consistent with uncertainty quantification principles and distinct ...
Knowing the SCOR: using business metrics to gain measurable improvements.
Malin, Jane H
2006-07-01
By using the Supply Chain Operations Reference model, one New York hospital was able to define and measure its supply chains, determine the weak links in its processes, and identify necessary improvements.
Measuring Metrics for Social Media Marketing : Case: Marsaana Communications
Yli-Pietilä, Heidi
2016-01-01
This thesis looks into social media marketing, what relationship public relations has with social media marketing and brand equity. The challenge with utilizing social media marketing is identifying the right tools to use in measuring the success or effectiveness of it. In this thesis I investigate a set of tools a Finnish PR agency could utilize in measuring the effects of their social media marketing efforts on their client’s brand equity. This thesis topics include new media in specifi...
Measuring Metrics for Social Media Marketing : Case: Marsaana Communications
Yli-Pietilä, Heidi
2016-01-01
This thesis looks into social media marketing, what relationship public relations has with social media marketing and brand equity. The challenge with utilizing social media marketing is identifying the right tools to use in measuring the success or effectiveness of it. In this thesis I investigate a set of tools a Finnish PR agency could utilize in measuring the effects of their social media marketing efforts on their client’s brand equity. This thesis topics include new media in specifi...
Characterization of Multiplicative Metric Completeness
Badshshah e Romer
2016-03-01
Full Text Available We established fixed point theorems in multiplicative metric spaces. The obtained results generalize Banach contraction principle in multiplicative metric spaces and also characterize completeness of the underlying multiplicative metric space.
Weakly Compatible Mappings along with $CLR_{S}$ property in Fuzzy Metric Spaces
Saurabh Manro
2013-11-01
Full Text Available The aim of this work is to use newly introduced property, which is so called common limit in the range $(CLR_{S}$ for four self-mappings, and prove some theorems which satisfy this property. Moreover, we establish some new existence of a common fixed point theorem for generalized contractive mappings in fuzzy metric spaces by using this new property and give some examples to support our results. Ours results does not require condition of closeness of range and so our theorems generalize, unify, and extend many results in literature. Our results improve and extend the results of Cho et al. [4], Pathak et al. [20] and Imdad et. al. [10] besides several known results.
M. De La Sen
2014-01-01
Full Text Available This paper presents some results concerning the properties of distances and existence and uniqueness of best proximity points of p-cyclic proximal, weak proximal contractions, and some of their generalizations for the non-self-mapping T:⋃i∈p-Ai→⋃i∈p-Bi (p≥2, where Ai and Bi, ∀i∈p-={1,2,…,p}, are nonempty subsets of X which satisfy TAi⊆Bi,∀i∈p-, such that (X,d is a metric space. The boundedness and the convergence of the sequences of distances in the domains and in their respective image sets of the cyclic proximal and weak cyclic proximal non-self-mapping, and of some of their generalizations are investigated. The existence and uniqueness of the best proximity points and the properties of convergence of the iterates to such points are also addressed.
Introducing the Balanced Scorecard: Creating Metrics to Measure Performance
Gumbus, Andra
2005-01-01
This experiential exercise presents the concept of the Balanced Scorecard (BSC) and applies it in a university setting. The Balanced Scorecard was developed 12 years ago and has grown in popularity and is used by more than 50% of the Fortune 500 companies as a performance measurement and strategic management tool. The BSC expands the traditional…
Rathee, Savita; Dhingra, Kusum; Kumar, Anil
2016-01-01
Here, we extend the notion of (E.A.) property in a convex metric space defined by Kumar and Rathee (Fixed Point Theory Appl 1-14, 2014) by introducing a new class of self-maps which satisfies the common property (E.A.) in the context of convex metric space and ensure the existence of common fixed point for this newly introduced class of self-maps. Also, we guarantee the existence of common best proximity points for this class of maps satisfying generalized non-expansive type condition. We furnish an example in support of the proved results.
Trivoli, George W.
1996-01-01
Congress and the Executive Branch have mandated that all branches of the Federal Government exert a concentrated effort to transfer appropriate government and government contractor-developed technology to the industrial use in the U.S. economy. For many years, NASA has had a formal technology transfer program to transmit information about new technologies developed for space applications into the industrial or commercial sector. Marshall Space Flight Center (MSFC) has been in the forefront of the development of U.S. industrial assistance programs using technologies developed at the Center. During 1992-93, MSFC initiated a technology transfer metrics study. The MSFC study was the first of its kind among the various NASA centers. The metrics study is a continuing process, with periodic updates that reflect on-going technology transfer activities.
Solving the Accuracy Metrics and Diversity Measures For Personalised Recommendation
I. Jenitta Magdalene,
2014-01-01
Full Text Available In the vast amount of information in the internet, to give individual attention for each users, the personalised recommendation system is used, which uses the collaborative filtering method. By the result of the survey did with some papers, the main problems like the cold start and the sparsity which were found previously have been overcome. Filtering the users when the number is large is done by the nearest neighbour approach or by the filtration approach. Due to some popular objects the accuracy of the data's are lost. To remove this influence, the method which is proposed here is a network based collaborative filtering which will create a user similarity network, where the users having similar interests of item or movies will be grouped together forming a network. Then we calculate discriminant scores for candidate objects. Validate the proposed approach by performing random sub-sampling experiments for about 20 times to get the accurate results and evaluate the method using two accuracy criteria and two diversity measures. Results show that the approach outperforms the ordinary user-based collaborative filtering method by not only enhancing the accuracy but also improving the diversity.
Nearest Neighbor Search in the Metric Space of a Complex Network for Community Detection
Suman Saha
2016-03-01
Full Text Available The objective of this article is to bridge the gap between two important research directions: (1 nearest neighbor search, which is a fundamental computational tool for large data analysis; and (2 complex network analysis, which deals with large real graphs but is generally studied via graph theoretic analysis or spectral analysis. In this article, we have studied the nearest neighbor search problem in a complex network by the development of a suitable notion of nearness. The computation of efficient nearest neighbor search among the nodes of a complex network using the metric tree and locality sensitive hashing (LSH are also studied and experimented. For evaluation of the proposed nearest neighbor search in a complex network, we applied it to a network community detection problem. Experiments are performed to verify the usefulness of nearness measures for the complex networks, the role of metric tree and LSH to compute fast and approximate node nearness and the the efficiency of community detection using nearest neighbor search. We observed that nearest neighbor between network nodes is a very efficient tool to explore better the community structure of the real networks. Several efficient approximation schemes are very useful for large networks, which hardly made any degradation of results, whereas they save lot of computational times, and nearest neighbor based community detection approach is very competitive in terms of efficiency and time.
Measuring floodplain spatial patterns using continuous surface metrics at multiple scales
Murray Scown,; Martin Thoms,; DeJager, Nathan R.
2015-01-01
Interactions between fluvial processes and floodplain ecosystems occur upon a floodplain surface that is often physically complex. Spatial patterns in floodplain topography have only recently been quantified over multiple scales, and discrepancies exist in how floodplain surfaces are perceived to be spatially organised. We measured spatial patterns in floodplain topography for pool 9 of the Upper Mississippi River, USA, using moving window analyses of eight surface metrics applied to a 1 × 1 m2 DEM over multiple scales. The metrics used were Range, SD, Skewness, Kurtosis, CV, SDCURV,Rugosity, and Vol:Area, and window sizes ranged from 10 to 1000 m in radius. Surface metric values were highly variable across the floodplain and revealed a high degree of spatial organisation in floodplain topography. Moran's I correlograms fit to the landscape of each metric at each window size revealed that patchiness existed at nearly all window sizes, but the strength and scale of patchiness changed within window size, suggesting that multiple scales of patchiness and patch structure exist in the topography of this floodplain. Scale thresholds in the spatial patterns were observed, particularly between the 50 and 100 m window sizes for all surface metrics and between the 500 and 750 m window sizes for most metrics. These threshold scales are ~ 15–20% and 150% of the main channel width (1–2% and 10–15% of the floodplain width), respectively. These thresholds may be related to structuring processes operating across distinct scale ranges. By coupling surface metrics, multi-scale analyses, and correlograms, quantifying floodplain topographic complexity is possible in ways that should assist in clarifying how floodplain ecosystems are structured.
Aksoy, Asuman Guven
2010-01-01
Using isometric embedding of metric trees into Banach spaces, this paper will investigate barycenters, type and cotype, and various measures of compactness of metric trees. A metric tree ($T$, $d$) is a metric space such that between any two of its points there is an unique arc that is isometric to an interval in $\\mathbb{R}$. We begin our investigation by examining isometric embeddings of metric trees into Banach spaces. We then investigate the possible images $x_0=\\pi ((x_1+\\ldots+x_n)/n)$, where $\\pi$ is a contractive retraction from the ambient Banach space $X$ onto $T$ (such a $\\pi$ always exists) in order to understand the "metric" barycenter of a family of points $ x_1, \\ldots,x_n$ in a tree $T$. Further, we consider the metric properties of trees such as their type and cotype. We identify various measures of compactness of metric trees (their covering numbers, $\\epsilon$-entropy and Kolmogorov widths) and the connections between them. Additionally, we prove that the limit of the sequence of Kolmogorov...
On the relative energy associated with space-times of diagonal metrics
Murat Korunur; Mustafa Salti; Ali havare
2007-05-01
In order to evaluate the energy distribution (due to matter and ﬁelds including gravitation) associated with a space-time model of generalized diagonal metric, we consider the Einstein, Bergmann–Thomson and Landau–Lifshitz energy and/or momentum deﬁnitions both in Einstein's theory of general relativity and the teleparallel gravity (the tetrad theory of gravitation). We ﬁnd same energy distribution using Einstein and Bergmann–Thomson formulations, but we also ﬁnd that the energy–momentum prescription of Landau–Lifshitz disagree in general with these deﬁnitions. We also give eight different well-known space-time models as examples, and considering these models and using our results, we calculate the energy distributions associated with them. Furthermore, we show that for the Bianchi Type-I models all the formulations give the same result. This result agrees with the previous works of Cooperstock–Israelit, Rosen, Johri et al, Banerjee–Sen, Xulu, Vargas and Saltı et al and supports the viewpoints of Albrow and Tryon.
Contractive type non-self mappings on metric spaces of hyperbolic type
Ciric, Ljubomir B.
2006-05-01
Let (X,d) be a metric space of hyperbolic type and K a nonempty closed subset of X. In this paper we study a class of mappings from K into X (not necessarily self-mappings on K), which are defined by the contractive condition (2.1) below, and a class of pairs of mappings from K into X which satisfy the condition (2.28) below. We present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of Ciric [L.B. Ciric, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts 23 (1998) 25-31; L.B. Ciric, J.S. Ume, M.S. Khan, H.K.T. Pathak, On some non-self mappings, Math. Nachr. 251 (2003) 28-33], Rhoades [B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon. 23 (1978) 457-459] and many other authors. Some examples are presented to show that our results are genuine generalizations of known results from this area.
Using measures of information content and complexity of time series as hydrologic metrics
The information theory has been previously used to develop metrics that allowed to characterize temporal patterns in soil moisture dynamics, and to evaluate and to compare performance of soil water flow models. The objective of this study was to apply information and complexity measures to characte...
Lean manufacturing measurement: the relationship between lean activities and lean metrics
Manotas Duque Diego Fernando
2007-10-01
Full Text Available Lean Manufacturing was developed by Toyota Motor company to address their specific needs in a restricted market in times of economic trouble. These concepts have been studied and proven to be transferrable and applicable to a wide variety of industries. This paper aims to integrate a set of metrics that have been proposed by different authors in such a way that they are consistent with the different stages and elements of Lean Manufacturing implementations. To achieve this, two frameworks for Lean implementations are presented and then the main factors for success are used as the basis to propose metrics that measure the advance in these factors. A tabular display of the impact of “Lean activities” on the metrics is presented, proposing that many a priori assumptions about the benefits on many different levels of improvement should be accurate. Finally, some ideas for future research and extension of the applications proposed on this paper are presented as closing points.
Gurucharan Singh Saluja
2010-01-01
Full Text Available In this paper, we give some necessary and sufficient conditions for an implicit iteration process with errors for a finite family of asymptotically quasi-nonexpansive mappings converging to a common fixed of the mappings in convex metric spaces. Our results extend and improve some recent results of Sun, Wittmann, Xu and Ori, and Zhou and Chang.
Plern Saipara
2017-03-01
Full Text Available In this paper, we suggest the modified random S-iterative process and prove the common random fixed point theorems of a finite family of random uniformly quasi-Lipschitzian operators in a generalized convex metric space. Our results improves and extends various results in the literature.
K. P. R. Sastry
2014-11-01
Full Text Available In this paper, we prove the existence and uniqueness of fixed points of generalized Geraghty contractions in partially ordered complete metric spaces under the influence of altering distances. Our results extend and generalize some of the known results.
Some Common Fixed Point Theorems for F-Contraction Type Mappings in 0-Complete Partial Metric Spaces
Satish Shukla
2013-01-01
Full Text Available We prove some common fixed point theorems for F-contractions in 0-complete partial metric spaces. Our results extend, generalize, and unify several known results in the literature. Some examples are included which show that the generalization is proper.
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...
Coordinated Observations of Space Debris as Optimisation Problem of Inter-Dependent Metrics
Sciotti, M.; Charlish, A.
2013-08-01
Optimal allocation of sensor resources is addressed in this paper in the frame of space surveillance application. Inspiration is taken from the optimal management of multi-functional sensors and netted surveillance sensors, for which the Sensor Management problem is often addressed as a Markov Decision Process. This approach allows determining the optimal decision at each discrete time instant by quantifying the expected payoff coming from the selected action. An action might be the assignment of the i -th surveillance task to the m -th sensor in the network ('tasking'), the selection of the i -th task at the k -th time slot ('scheduling'), or the activation of a specific sensor configuration for the completion of the i -th task ('resource allocation'). The common objective is the maximization of the global reward coming from the selected sequence of actions over a finite or infinite time horizon. This leads to a sequence of coordinated observations carried out by the sensor(s), which are determined statically or dynamically by the Sensor Manager. In this paper, the allocation of space surveillance resources is analysed as a management problem for sensor(s) with finite resources. The proposed allocation is driven by the operational requirements for space objects cataloguing, such as the object population coverage and the track accuracy. A sequential resource allocation strategy is formulated in order to cope with such inter-dependent, concurring performance metrics. The approach can be also extended to multiple sensors with different performance or nature. Promising results are demonstrated over a phased array radar case study.
Measuring space radiation shielding effectiveness
Bahadori, Amir; Semones, Edward; Ewert, Michael; Broyan, James; Walker, Steven
2017-09-01
Passive radiation shielding is one strategy to mitigate the problem of space radiation exposure. While space vehicles are constructed largely of aluminum, polyethylene has been demonstrated to have superior shielding characteristics for both galactic cosmic rays and solar particle events due to the high hydrogen content. A method to calculate the shielding effectiveness of a material relative to reference material from Bragg peak measurements performed using energetic heavy charged particles is described. Using accelerated alpha particles at the National Aeronautics and Space Administration Space Radiation Laboratory at Brookhaven National Laboratory, the method is applied to sample tiles from the Heat Melt Compactor, which were created by melting material from a simulated astronaut waste stream, consisting of materials such as trash and unconsumed food. The shielding effectiveness calculated from measurements of the Heat Melt Compactor sample tiles is about 10% less than the shielding effectiveness of polyethylene. Shielding material produced from the astronaut waste stream in the form of Heat Melt Compactor tiles is therefore found to be an attractive solution for protection against space radiation.
Measuring economic complexity of countries and products: which metric to use?
Mariani, Manuel Sebastian; Vidmer, Alexandre; Medo, Matsúš; Zhang, Yi-Cheng
2015-11-01
Evaluating the economies of countries and their relations with products in the global market is a central problem in economics, with far-reaching implications to our theoretical understanding of the international trade as well as to practical applications, such as policy making and financial investment planning. The recent Economic Complexity approach aims to quantify the competitiveness of countries and the quality of the exported products based on the empirical observation that the most competitive countries have diversified exports, whereas developing countries only export few low quality products - typically those exported by many other countries. Two different metrics, Fitness-Complexity and the Method of Reflections, have been proposed to measure country and product score in the Economic Complexity framework. We use international trade data and a recent ranking evaluation measure to quantitatively compare the ability of the two metrics to rank countries and products according to their importance in the network. The results show that the Fitness-Complexity metric outperforms the Method of Reflections in both the ranking of products and the ranking of countries. We also investigate a generalization of the Fitness-Complexity metric and show that it can produce improved rankings provided that the input data are reliable.
Information Entropy-Based Metrics for Measuring Emergences in Artificial Societies
Mingsheng Tang
2014-08-01
Full Text Available Emergence is a common phenomenon, and it is also a general and important concept in complex dynamic systems like artificial societies. Usually, artificial societies are used for assisting in resolving several complex social issues (e.g., emergency management, intelligent transportation system with the aid of computer science. The levels of an emergence may have an effect on decisions making, and the occurrence and degree of an emergence are generally perceived by human observers. However, due to the ambiguity and inaccuracy of human observers, to propose a quantitative method to measure emergences in artificial societies is a meaningful and challenging task. This article mainly concentrates upon three kinds of emergences in artificial societies, including emergence of attribution, emergence of behavior, and emergence of structure. Based on information entropy, three metrics have been proposed to measure emergences in a quantitative way. Meanwhile, the correctness of these metrics has been verified through three case studies (the spread of an infectious influenza, a dynamic microblog network, and a flock of birds with several experimental simulations on the Netlogo platform. These experimental results confirm that these metrics increase with the rising degree of emergences. In addition, this article also has discussed the limitations and extended applications of these metrics.
Using complexity metrics with R-R intervals and BPM heart rate measures
Wallot, Sebastian; Fusaroli, Riccardo; Tylén, Kristian; Jegindø, Else-Marie
2013-01-01
Lately, growing attention in the health sciences has been paid to the dynamics of heart rate as indicator of impending failures and for prognoses. Likewise, in social and cognitive sciences, heart rate is increasingly employed as a measure of arousal, emotional engagement and as a marker of interpersonal coordination. However, there is no consensus about which measurements and analytical tools are most appropriate in mapping the temporal dynamics of heart rate and quite different metrics are ...
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. PMID:28278243
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.
What are we assessing when we measure food security? A compendium and review of current metrics.
Jones, Andrew D; Ngure, Francis M; Pelto, Gretel; Young, Sera L
2013-09-01
The appropriate measurement of food security is critical for targeting food and economic aid; supporting early famine warning and global monitoring systems; evaluating nutrition, health, and development programs; and informing government policy across many sectors. This important work is complicated by the multiple approaches and tools for assessing food security. In response, we have prepared a compendium and review of food security assessment tools in which we review issues of terminology, measurement, and validation. We begin by describing the evolving definition of food security and use this discussion to frame a review of the current landscape of measurement tools available for assessing food security. We critically assess the purpose/s of these tools, the domains of food security assessed by each, the conceptualizations of food security that underpin each metric, as well as the approaches that have been used to validate these metrics. Specifically, we describe measurement tools that 1) provide national-level estimates of food security, 2) inform global monitoring and early warning systems, 3) assess household food access and acquisition, and 4) measure food consumption and utilization. After describing a number of outstanding measurement challenges that might be addressed in future research, we conclude by offering suggestions to guide the selection of appropriate food security metrics.
Analysis of reliability metrics and quality enhancement measures in current density imaging.
Foomany, F H; Beheshti, M; Magtibay, K; Masse, S; Foltz, W; Sevaptsidis, E; Lai, P; Jaffray, D A; Krishnan, S; Nanthakumar, K; Umapathy, K
2013-01-01
Low frequency current density imaging (LFCDI) is a magnetic resonance imaging (MRI) technique which enables calculation of current pathways within the medium of study. The induced current produces a magnetic flux which presents itself in phase images obtained through MRI scanning. A class of LFCDI challenges arises from the subject rotation requirement, which calls for reliability analysis metrics and specific image registration techniques. In this study these challenges are formulated and in light of proposed discussions, the reliability analysis of calculation of current pathways in a designed phantom and a pig heart is presented. The current passed is measured with less than 5% error for phantom, using CDI method. It is shown that Gauss's law for magnetism can be treated as reliability metric in matching the images in two orientations. For the phantom and pig heart the usefulness of image registration for mitigation of rotation errors is demonstrated. The reliability metric provides a good representation of the degree of correspondence between images in two orientations for phantom and pig heart. In our CDI experiments this metric produced values of 95% and 26%, for phantom, and 88% and 75% for pig heart, for mismatch rotations of 0 and 20 degrees respectively.
The role of metrics and measurements in a software intensive total quality management environment
Daniels, Charles B.
1992-01-01
Paramax Space Systems began its mission as a member of the Rockwell Space Operations Company (RSOC) team which was the successful bidder on a massive operations consolidation contract for the Mission Operations Directorate (MOD) at JSC. The contract awarded to the team was the Space Transportation System Operations Contract (STSOC). Our initial challenge was to accept responsibility for a very large, highly complex and fragmented collection of software from eleven different contractors and transform it into a coherent, operational baseline. Concurrently, we had to integrate a diverse group of people from eleven different companies into a single, cohesive team. Paramax executives recognized the absolute necessity to develop a business culture based on the concept of employee involvement to execute and improve the complex process of our new environment. Our executives clearly understood that management needed to set the example and lead the way to quality improvement. The total quality management policy and the metrics used in this endeavor are presented.
Using Complexity Metrics With R-R Intervals and BPM Heart Rate Measures
Wallot, Sebastian; Fusaroli, Riccardo; Tylén, Kristian
2013-01-01
Lately, growing attention in the health sciences has been paid to the dynamics of heart rate as indicator of impending failures and for prognoses. Likewise, in social and cognitive sciences, heart rate is increasingly employed as a measure of arousal, emotional engagement and as a marker...... of interpersonal coordination. However, there is no consensus about which measurements and analytical tools are most appropriate in mapping the temporal dynamics of heart rate and quite different metrics are reported in the literature. As complexity metrics of heart rate variability depend critically......-of-concept, we employ a simple rest-exercise-rest task and show that non-linear statistics – fractal (DFA) and recurrence (RQA) analyses – reveal information about heart beat activity above and beyond the simple level of heart rate. Non-linear statistics unveil sustained post-exercise effects on heart rate...
Mr. Narendra Pal Singh Rathore Prof. Ravindra Gupta
2011-10-01
Full Text Available A large numbers of metrics have been proposed for measuring properties of object-oriented software such as size, inheritance, cohesion and coupling. The coupling metrics presented in this paper exploring the difference between inheritance and interface programming. This paper presents a measurement to measure coupling between object (CBO, number of associations between classes (NASSocC, number of dependencies in metric (NDepIN , number of dependencies out metric (NDepOut and Number of children (NOC in object oriented programming. A measurement is done for C# inheritance and interface programs. The metric values of class inheritance and interface prove which program is good to use and beneficial for C# developers.
Complexity metric as a complement to measurement based IMRT/VMAT patient-specific QA
Götstedt, J.; Karlsson Hauer, A.; Bäck, A.
2015-01-01
IMRT/VMAT treatment plans contain treatment fields with MLC openings of various size and shape. Clinical dose calculation algorithms show limitations in calculating the correct dose in small and irregular parts of a MLC opening which leads to differences between the planned and delivered dose distributions. The patient-specific IMRT QA is often designed to compare planned and measured dose distributions and is therefore heavily dependent on the measurement equipment and the evaluation method. The purpose of this study is to develop a complexity metric based on shape and size of MLC openings that correlates to the dose differences between planned and delivered 3D dose distributions. Different MLC openings are measured and evaluated and used to determine a penalty function to steer the complexity metric and make the complexity scores correlate to dose difference pass rates. Results of this initial study show that a correlation was found between complexity scores and dose difference pass rates for static fields with varied complexity. Preliminary results also show that the complexity metric can distinguish clinical IMRT fields with higher complexity.
Four Dimensional Trace Space Measurement
Hernandez, M.
2005-02-10
Future high energy colliders and FELs (Free Electron Lasers) such as the proposed LCLS (Linac Coherent Light Source) at SLAC require high brightness electron beams. In general a high brightness electron beam will contain a large number of electrons that occupy a short longitudinal duration, can be focused to a small transverse area while having small transverse divergences. Therefore the beam must have a high peak current and occupy small areas in transverse phase space and so have small transverse emittances. Additionally the beam should propagate at high energy and have a low energy spread to reduce chromatic effects. The requirements of the LCLS for example are pulses which contain 10{sup 10} electrons in a temporal duration of 10 ps FWHM with projected normalized transverse emittances of 1{pi} mm mrad[1]. Currently the most promising method of producing such a beam is the RF photoinjector. The GTF (Gun Test Facility) at SLAC was constructed to produce and characterize laser and electron beams which fulfill the LCLS requirements. Emittance measurements of the electron beam at the GTF contain evidence of strong coupling between the transverse dimensions of the beam. This thesis explores the effects of this coupling on the determination of the projected emittances of the electron beam. In the presence of such a coupling the projected normalized emittance is no longer a conserved quantity. The conserved quantity is the normalized full four dimensional phase space occupied by the beam. A method to determine the presence and evaluate the strength of the coupling in emittance measurements made in the laboratory is developed. A method to calculate the four dimensional volume the beam occupies in phase space using quantities available in the laboratory environment is also developed. Results of measurements made of the electron beam at the GTF that demonstrate these concepts are presented and discussed.
Magnolia Tilca
2014-10-01
Full Text Available The aim of this paper is to study the existence of the solution for the overlapping generations model, using fixed point theorems in metric spaces endowed with a graph. The overlapping generations model has been introduced and developed by Maurice Allais (1947, Paul Samuelson (1958, Peter Diamond (1965 and so on. The present paper treats the case presented by Edmond (2008 in (Edmond, 2008 for a continuous time. The theorem of existence of the solution for the prices fixed point problem derived from the overlapping generations model gives an approximation of the solution via the graph theory. The tools employed in this study are based on applications of the Jachymski fixed point theorem on metric spaces endowed with a graph (Jachymski, 2008
Nicola Dioguardi; Fabio Grizzi; Barbara Franceschini; Paola Bossi; Carlo Russo
2006-01-01
AIM: To provide the accurate alternative metrical means of monitoring the effects of new antiviral drugs on the reversal of newly formed collagen.METHODS: Digitized histological biopsy sections taken from 209 patients with chronic C virus hepatitis with different grade of fibrosis or cirrhosis, were measured by means of a new, rapid, user-friendly, fully computeraided method based on the international system meter rectified using fractal principles.RESULTS: The following were described: geometric perimeter, area and wrinkledness of fibrosis; the collation of the Knodell, Sheuer, Ishak and METAVIR scores with fractal-rectified metric measurements; the meaning of the physical composition of fibrosis in relation to the magnitude of collagen islets; the intra- and inter-biopsy sample variability of these parameters; the "staging"of biopsy sections indicating the pathway covered by fibrosis formation towards its maximum known value;the quantitative liver tissue architectural changes with the Hurst exponent.CONCLUSION: Our model provides the first metrical evaluations of the geometric properties of fibrosis and the quantitative architectural changes of the liver tissue.The representativeness of histological sections of the whole liver is also discussed in the light of the results obtained with the Hurst coefficient.
Obtaining the Knowledge of a Server Performance from Non-Intrusively Measurable Metrics
Satoru Ohta
2016-04-01
Full Text Available Most network services are provided by server computers. To provide these services with good quality, the server performance must be managed adequately. For the server management, the performance information is commonly obtained from the operating system (OS and hardware of the managed computer. However, this method has a disadvantage. If the performance is degraded by excessive load or hardware faults, it becomes difficult to collect and transmit information. Thus, it is necessary to obtain the information without interfering with the server’s OS and hardware. This paper investigates a technique that utilizes non-intrusively measureable metrics that are obtained through passive traffic monitoring and electric currents monitored by the sensors attached to the power supply. However, these metrics do not directly represent the performance experienced by users. Hence, it is necessary to discover the complicated function that maps the metrics to the true performance information. To discover this function from the measured samples, a machine learning technique based on a decision tree is examined. The technique is important because it is applicable to the power management of server clusters and the immigration control of virtual servers
Daza, Maicol A Ochoa
2011-01-01
We introduce and develop the theory of metric sheaves. A metric sheaf $\\A$ is defined on a topological space $X$ such that each fiber is a metric model. We describe the construction of the generic model as the quotient space of the sheaf through an appropriate filter. Semantics in this model is completely controlled and understood by the forcing rules in the sheaf.
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.
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.
Yu Wen WANG; Jian ZHANG; Yun An CUI
2012-01-01
Let X,Y be Banach spaces and M be a linear subspace in X × Y ={{x,y}|x ∈ X,y ∈ Y}.We may view M as a multi-valued linear operator from X to Y by taking M(x) ={y|{x,y} ∈ M}.In this paper,we give several criteria for a single-valued operator from Y to X to be the metric generalized inverse of the multi-valued linear operator M.The principal tool in this paper is also the generalized orthogonal decomposition theorem in Banach spaces.
Block-based test data adequacy measurement criteria and test complexity metrics
陈卫东; 杨建军; 叶澄清; 潘云鹤
2002-01-01
On the basis of software testing tools we developed for progrmnming languages, we firstly present a new control flowgraph model based on block. In view of the notion of block, we extend the traditional program-based software test data adequacy measurement criteria, and empirically analyze the subsume relation between these measurement criteria. Then, we define four test complexity metrics based on block. They are J-complexity 0; J-complexity 1 ; J-complexity 1 + ; J-complexity 2. Finally, we show the Kiviat diagram that makes software quality visible.
Block-based test data adequacy measurement criteria and test complexity metrics
无
2002-01-01
On the basis of software testing tools we developed for programming languages, we firstly present a new control flowgraph model based on block. In view of the notion of block, we extend the traditional program-based software test data adequacy measurement criteria, and empirically analyze the subsume relation between these measurement criteria. Then, we define four test complexity metrics based on block. They are J-complexity 0; J-complexity 1; J-complexity 1 +; J-complexity 2. Finally, we show the Kiviat diagram that makes software quality visible.
Bahadur Zada, Mian; Sarwar, Muhammad; Radenović, Stojan
2017-01-01
In this article, we apply common fixed point results in incomplete metric spaces to examine the existence of a unique common solution for the following systems of Urysohn integral equations and Volterra-Hammerstein integral equations, respectively: [Formula: see text] where [Formula: see text]; [Formula: see text] and [Formula: see text], [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], u, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], [Formula: see text], are real-valued measurable functions both in s and r on [Formula: see text].
On the metric of the space of states in a modified QCD
de Oca, Alejandro Cabo Montes
2013-01-01
The form of the resulting Feynman propagators in a proposed local and gauge invariant QCD for massive fermions suggests the existence of indefinite metric associated to quark states, a property that might relate it with the known Lee-Wick theories. Thus, the nature of the asymptotic free quark states in the theory is investigated here by quantizing the quadratic part of the quark action. As opposite to the case in the standard QCD, the free theory does not show Hamiltonian constraints. The propagation modes include a family of massless waves and a complementary set of massive oscillations. The theory can be quantized in a way that the massive modes show positive metric and the massless ones exhibit negative norms. It is remarked that, since QCD is expected to not exhibit gluon or quark asymptotic states, the presence of negative metric massless modes does not constitute a definite drawback of the theory. In addition, the fact that the positive metric quark states are massive, seems to be a good feature of the...
A Coupled Fixed Point Theorem for Geraghty Contractions in Partially Ordered Metric Spaces
K.P.R. Sastry
2014-07-01
Full Text Available In this paper we establish results on the existence and uniqueness of coupled fixed points of Geraghty contraction on a partially ordered set with a metric, with the continuity of the altering distance function dropped. Our results are improvements over the results of GVR Babu and P.Subhashini [3].
Lanczos spintensor for the Robinson-Trautman metrics of the vacuum space and Einstein-Maxwell fields
Gaftoi, V; Morales, J.; Ovando, G.; Pena, J. J. [Mexico city, Univ. Autonoma Metropolitana-Azcapotzalco (Mexico). Dept. de Ciencias Basicas. Area de Fisica
1998-10-01
Using the Newman-Penrose formalism, are obtained the {Omega}{sub r} projections of the Lanczos spintensor over the null tetrad for the Robinson-Trautman (RT) solutions of the vacuum space and Einstein-Maxwell fields. Specifically, the authors are concerned with the Weyl-Lanczos relationships for the II, III and D Petrov`s type of the RT afore-mentioned metrics. The presented approach considers the most general case of the functions P(x{sup 1}, x{sup 2}, u) and H(x{sup 1}, x{sup 2}, r, u), that characterize the metrics, resulting in a procedure by far simpler than equivalent methods that use spinors and tensors in order to determine the K{sub ijr} Lanczos spintensor.
Vildan Ozturk
2017-04-01
Full Text Available In this paper, we consider and generalize recent b-(E.A-property results in [11] via the concepts of C-class functions in b- metric spaces. A example is given to support the result.
Reza Ezzati
2013-02-01
Full Text Available In this paper, we prove a general form of a fixed point theorem with contractive-like mapping defined by altering function. We also present its application on study of existence and uniqueness of solution of fuzzy initial value problems in fuzzy partial metric spaces. In order to do this, we recall some fixed point theorems in partial metric spaces either crisp or fuzzy and use these theorems to prove ours.
Reza Ezzati; Maryam Bagherian
2013-01-01
In this paper, we prove a general form of a fixed point theorem with contractive-like mapping defined by altering function. We also present its application on study of existence and uniqueness of solution of fuzzy initial value problems in fuzzy partial metric spaces. In order to do this, we recall some fixed point theorems in partial metric spaces either crisp or fuzzy and use these theorems to prove ours.
Measuring reliability under epistemic uncertainty:Review on non-probabilistic reliability metrics
Kang Rui; Zhang Qingyuan; Zeng Zhiguo; Enrico Zio; Li Xiaoyang
2016-01-01
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 reli-ability 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.
Vector Spaces of Non-measurable Functions
Francisco J. GARC(I)A-PACHECO; Juan B. SEOANE-SEP(U)LVEDA
2006-01-01
We show that there exists an infinite dimensional vector space every non-zero element of which is a non-measurable function. Moreover, this vector space can be chosen to be closed and to have dimensionβ for any cardinalityβ. Some techniques involving measure theory and density characters of Banach spaces are used.
Manish Jain
2014-01-01
Full Text Available The object of this paper is to establish the existence and uniqueness of coupled fixed points under a (φ, ψ-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012 and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006, and Luong and Thuan (2011. The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.
Several applications of the theory of random conjugate spaces to measurability problems
2007-01-01
The central purpose of this paper is to illustrate that combining the recently developed theory of random conjugate spaces and the deep theory of Banach spaces can, indeed, solve some difficult measurability problems which occur in the recent study of the Lebesgue (or more general, Orlicz)-Bochner function spaces as well as in a slightly different way in the study of the random functional analysis but for which the measurable selection theorems currently available are not applicable. It is important that this paper provides a new method of studying a large class of the measurability problems, namely first converting the measurability problems to the abstract existence problems in the random metric theory and then combining the random metric theory and the relative theory of classical spaces so that the measurability problems can be eventually solved. The new method is based on the deep development of the random metric theory as well as on the subtle combination of the random metric theory with classical space theory.
Götstedt, Julia [Department of Radiation Physics, University of Gothenburg, Göteborg 413 45 (Sweden); Karlsson Hauer, Anna; Bäck, Anna, E-mail: anna.back@vgregion.se [Department of Therapeutic Radiation Physics, Sahlgrenska University Hospital, Göteborg 413 45 (Sweden)
2015-07-15
Purpose: Complexity metrics have been suggested as a complement to measurement-based quality assurance for intensity modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT). However, these metrics have not yet been sufficiently validated. This study develops and evaluates new aperture-based complexity metrics in the context of static multileaf collimator (MLC) openings and compares them to previously published metrics. Methods: This study develops the converted aperture metric and the edge area metric. The converted aperture metric is based on small and irregular parts within the MLC opening that are quantified as measured distances between MLC leaves. The edge area metric is based on the relative size of the region around the edges defined by the MLC. Another metric suggested in this study is the circumference/area ratio. Earlier defined aperture-based complexity metrics—the modulation complexity score, the edge metric, the ratio monitor units (MU)/Gy, the aperture area, and the aperture irregularity—are compared to the newly proposed metrics. A set of small and irregular static MLC openings are created which simulate individual IMRT/VMAT control points of various complexities. These are measured with both an amorphous silicon electronic portal imaging device and EBT3 film. The differences between calculated and measured dose distributions are evaluated using a pixel-by-pixel comparison with two global dose difference criteria of 3% and 5%. The extent of the dose differences, expressed in terms of pass rate, is used as a measure of the complexity of the MLC openings and used for the evaluation of the metrics compared in this study. The different complexity scores are calculated for each created static MLC opening. The correlation between the calculated complexity scores and the extent of the dose differences (pass rate) are analyzed in scatter plots and using Pearson’s r-values. Results: The complexity scores calculated by the edge
Prognostic Performance Metrics
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...
Applying Metric Regularity to Compute Condition measure of Smoothing Algorithm for Matrix Games
Mordukhovich, Boris; Roshchina, Vera
2010-01-01
We develop an approach of variational analysis and generalized differentiation to conditioning issues for two-person zero-sum matrix games. Our major results establish precise relationships between a certain condition measure of the smoothing first-order algorithm proposed in [A. Gilpin, J. Pe\\~na and T. Sandholm, First-order algorithm with O(ln(1/\\epsilon)) convergence for \\epsilon-equilibrium in two-person zero-sum games, in Proc. 23rd Nat. Conf. Art. Intel. (AAAI), 2008, pp. 75-82] and the exact bound of metric regularity for an associated set-valued mapping. In this way we compute the aforementioned condition measure in terms of the initial matrix game data.
Local Morrey and Campanato Spaces on Quasimetric Measure Spaces
Krzysztof Stempak
2014-01-01
Full Text Available We define and investigate generalized local Morrey spaces and generalized local Campanato spaces, within a context of a general quasimetric measure space. The locality is manifested here by a restriction to a subfamily of involved balls. The structural properties of these spaces and the maximal operators associated to them are studied. In numerous remarks, we relate the developed theory, mostly in the “global” case, to the cases existing in the literature. We also suggest a coherent theory of generalized Morrey and Campanato spaces on open proper subsets of Rn.
Semenov, Yuri S; Novozhilov, Artem S
2016-05-01
A two-valued fitness landscape is introduced for the classical Eigen's quasispecies model. This fitness landscape can be considered as a direct generalization of the so-called single- or sharply peaked landscape. A general, non-permutation invariant quasispecies model is studied, and therefore the dimension of the problem is [Formula: see text], where N is the sequence length. It is shown that if the fitness function is equal to [Formula: see text] on a G-orbit A and is equal to w elsewhere, then the mean population fitness can be found as the largest root of an algebraic equation of degree at most [Formula: see text]. Here G is an arbitrary isometry group acting on the metric space of sequences of zeroes and ones of the length N with the Hamming distance. An explicit form of this exact algebraic equation is given in terms of the spherical growth function of the G-orbit A. Motivated by the analysis of the two-valued fitness landscapes, an abstract generalization of Eigen's model is introduced such that the sequences are identified with the points of a finite metric space X together with a group of isometries acting transitively on X. In particular, a simplicial analog of the original quasispecies model is discussed, which can be considered as a mathematical model of the switching of the antigenic variants for some bacteria.
Using Complexity Metrics With R-R Intervals and BPM Heart Rate Measures
Sebastian eWallot
2013-08-01
Full Text Available Lately, growing attention in the health sciences has been paid to the dynamics of heart rate as indicator of impending failures and for prognoses. Likewise, in social and cognitive sciences, heart rate is increasingly employed as a measure of arousal, emotional engagement and as a marker of interpersonal coordination. However, there is no consensus about which measurements and analytical tools are most appropriate in mapping the temporal dynamics of heart rate and quite different metrics are reported in the literature. As complexity metrics of heart rate variability depend critically on variability of the data, different choices regarding the kind of measures can have a substantial impact on the results. In this article we compare linear and non-linear statistics on two prominent types of heart beat data, beat-to-beat intervals (R-R interval and beats-per-minute (BPM. As a proof-of-concept, we employ a simple rest-exercise-rest task and show that non-linear statistics – fractal (DFA and recurrence (RQA analyses – reveal information about heart beat activity above and beyond the simple level of heart rate. Non-linear statistics unveil sustained post-exercise effects on heart rate dynamics, but their power to do so critically depends on the type data that is employed: While R-R intervals are very susceptible to nonlinear analyses, the success of nonlinear methods for BPM data critically depends on their construction. Generally, ‘oversampled’ BPM time-series can be recommended as they retain most of the information about nonlinear aspects of heart beat dynamics.
Using complexity metrics with R-R intervals and BPM heart rate measures.
Wallot, Sebastian; Fusaroli, Riccardo; Tylén, Kristian; Jegindø, Else-Marie
2013-01-01
Lately, growing attention in the health sciences has been paid to the dynamics of heart rate as indicator of impending failures and for prognoses. Likewise, in social and cognitive sciences, heart rate is increasingly employed as a measure of arousal, emotional engagement and as a marker of interpersonal coordination. However, there is no consensus about which measurements and analytical tools are most appropriate in mapping the temporal dynamics of heart rate and quite different metrics are reported in the literature. As complexity metrics of heart rate variability depend critically on variability of the data, different choices regarding the kind of measures can have a substantial impact on the results. In this article we compare linear and non-linear statistics on two prominent types of heart beat data, beat-to-beat intervals (R-R interval) and beats-per-min (BPM). As a proof-of-concept, we employ a simple rest-exercise-rest task and show that non-linear statistics-fractal (DFA) and recurrence (RQA) analyses-reveal information about heart beat activity above and beyond the simple level of heart rate. Non-linear statistics unveil sustained post-exercise effects on heart rate dynamics, but their power to do so critically depends on the type data that is employed: While R-R intervals are very susceptible to non-linear analyses, the success of non-linear methods for BPM data critically depends on their construction. Generally, "oversampled" BPM time-series can be recommended as they retain most of the information about non-linear aspects of heart beat dynamics.
TIME-SPACE CONCEPT FOR PRECISION MEASUREMENT
LIU Xiaokang; PENG Donglin; ZHU Ge; WANG Xianquan
2008-01-01
The transformation between time and space is discussed. To improve real-time response speed of intelligent measuring system, the concept of exchanging program execution time with more circuitry is presented working in cycle mode. Displacement measuring by magnification is achieved with period measurement by magnification. To change the condition that traditional precision measurement depends on machining precision greatly, the concept of measuring space with time and theory of time-space coordinate transformation are proposed. Guided by the idea of measuring space with time, differential frequency measurement system and time grating displacement sensor are developed based on the proposed novel methods. And high-precision measurement is achieved without high-precision manufacture, which embeds the remarkable characteristics of low cost but high precision to the devices. Experiment and test results conform the validity of the proposed time-space concept.
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
A City and National Metric measuring Isolation from the Global Market for Food Security Assessment
Brown, Molly E.; Silver, Kirk Coleman; Rajagopalan, Krishnan
2013-01-01
The World Bank has invested in infrastructure in developing countries for decades. This investment aims to reduce the isolation of markets, reducing both seasonality and variability in food availability and food prices. Here we combine city market price data, global distance to port, and country infrastructure data to create a new Isolation Index for countries and cities around the world. Our index quantifies the isolation of a city from the global market. We demonstrate that an index built at the country level can be applied at a sub-national level to quantify city isolation. In doing so, we offer policy makers with an alternative metric to assess food insecurity. We compare our isolation index with other indices and economic data found in the literature.We show that our Index measures economic isolation regardless of economic stability using correlation and analysis
Fan, Ya-Jing; Cao, Huai-Xin; Meng, Hui-Xian; Chen, Liang
2016-12-01
The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg's uncertainty relation and Schrödinger's uncertainty relation. In this paper, we prove a Schrödinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, U_ρ ^{(g,f)}(A)U_ρ ^{(g,f)}(B)≥ f(0)^2l/k| Corr_ρ ^{s(g,f)}(A,B)| ^2 for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix ρ . As applications, we derive some new uncertainty relations for Wigner-Yanase skew information and Wigner-Yanase-Dyson skew information.
Fan, Ya-Jing; Cao, Huai-Xin; Meng, Hui-Xian; Chen, Liang
2016-09-01
The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg's uncertainty relation and Schrödinger's uncertainty relation. In this paper, we prove a Schrödinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, U_ρ ^{(g,f)}(A)U_ρ ^{(g,f)}(B)≥ f(0)^2l/k| {Corr}_ρ ^{s(g,f)}(A,B)| ^2 for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix ρ . As applications, we derive some new uncertainty relations for Wigner-Yanase skew information and Wigner-Yanase-Dyson skew information.
Measuring solar reflectance Part I: Defining a metric that accurately predicts solar heat gain
Levinson, Ronnen; Akbari, Hashem; Berdahl, Paul
2010-05-14
Solar reflectance can vary with the spectral and angular distributions of incident sunlight, which in turn depend on surface orientation, solar position and atmospheric conditions. A widely used solar reflectance metric based on the ASTM Standard E891 beam-normal solar spectral irradiance underestimates the solar heat gain of a spectrally selective 'cool colored' surface because this irradiance contains a greater fraction of near-infrared light than typically found in ordinary (unconcentrated) global sunlight. At mainland U.S. latitudes, this metric RE891BN can underestimate the annual peak solar heat gain of a typical roof or pavement (slope {le} 5:12 [23{sup o}]) by as much as 89 W m{sup -2}, and underestimate its peak surface temperature by up to 5 K. Using R{sub E891BN} to characterize roofs in a building energy simulation can exaggerate the economic value N of annual cool-roof net energy savings by as much as 23%. We define clear-sky air mass one global horizontal ('AM1GH') solar reflectance R{sub g,0}, a simple and easily measured property that more accurately predicts solar heat gain. R{sub g,0} predicts the annual peak solar heat gain of a roof or pavement to within 2 W m{sup -2}, and overestimates N by no more than 3%. R{sub g,0} is well suited to rating the solar reflectances of roofs, pavements and walls. We show in Part II that R{sub g,0} can be easily and accurately measured with a pyranometer, a solar spectrophotometer or version 6 of the Solar Spectrum Reflectometer.
刘民; 李法朝; 吴澄
2003-01-01
Measuring the difference between fuzzy numbers is often needed in many fuzzy optimizationproblems such as manufacturing system production line scheduling with uncertainty environments. In thispaper, based on the distance function of plane R2 and the level importance function, we establish theUID-metric and LPID-metric of measuring the difference between fuzzy numbers, and discuss the basicproperties of UID-metric and LPID-metric, and prove that fuzzy number spaces are metric spaces aboutUID-metric and LPID-metric if and only if the level importance function /(λ) ≠ 0 almost everywhere on [0,1]. Further, we discuss the convergence, separability and completeness of UID-metric and LPID-metricbased on the norms of plane R2. Finally, we analyze the characteristics of UID-metric and LPID-metric bysome application examples.
Yongjie Piao∗
2015-01-01
A classΦof 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying aφi-quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained.Our main results generalize and improve many same type common fixed point theorems in references.
Internal space charge measurement of materials in a space environment
Griseri, V.; Fukunaga, K.; Maeno, T.; Payan, D.; Laurent, C.; Levy, L.
2003-09-01
The charging/discharging effect produced by space environment on space vehicles are known but not fully identified yet. Experiments performed in laboratory in vacuum chamber that simulates spatial environment and the most realistic charge condition occurring in space have been developed in the last past forty years. A very small Pulse Electro-Acoustic space charge detection unit (mini-PEA) that can be mounted in a vacuum chamber, to measure internal space charges of materials in-situ during the irradiation has been developed. Several materials used in spatial environment such as Teflon®, and Kapton ® films on addition to PMMA films have been studied. The comparison and the good agreement between measured and calculated depth of penetration for electrons of given energy depending on the material nature contribute in the validation of the detection system and encourage us for further studies and development.
Output Measures and Library Space Planning.
Lushington, Nolan
1987-01-01
Draws some initial connections between library performance measures and library space planning and collection management. Output measure surveys are suggested for establishing hierarchies of use and appropriate design of environments for housing the collection. Four references are listed. (MES)
Quevedo, Hernando
2016-01-01
We review the problem of describing the gravitational field of compact stars in general relativity. We focus on the deviations from spherical symmetry which are expected to be due to rotation and to the natural deformations of mass distributions. We assume that the relativistic quadrupole moment takes into account these deviations, and consider the class of axisymmetric static and stationary quadrupolar metrics which satisfy Einstein's equations in empty space and in the presence of matter represented by a perfect fluid. We formulate the physical conditions that must be satisfied for a particular spacetime metric to describe the gravitational field of compact stars. We present a brief review of the main static and axisymmetric exact solutions of Einstein's vacuum equations, satisfying all the physical conditions. We discuss how to derive particular stationary and axisymmetric solutions with quadrupolar properties by using the solution generating techniques which correspond either to Lie symmetries and B\\"acku...
Geometric Methods for ATR: Shape Spaces, Metrics, Object/Image Relations, and Shapelets
2007-09-30
been collaborating with Ms. Olga Mendoza, a young researcher at AFRL, Wright -Patterson AFB, who has performed additional tests of the algorithms, and... modulo the action of a certain group of transformations on Rn , n = 2,3, and give global coordinates on the shape space, (2) give necessary and...r points in R" modulo the action of the group of affine transformations. These spaces would then represent the distinct objects and images independent
Fixed and periodic points in the probabilistic normed and metric spaces
Ghaemi, M.B. [Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288, Qazvin (Iran, Islamic Republic of) and Faculty of Mathematics, Iran University of Science and Technology, Tehran (Iran, Islamic Republic of)]. E-mail: M-Ghaemi@sbu.ac.ir; Razani, Abdolrahman [Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288, Qazvin (Iran, Islamic Republic of) and Department of Mathematics, Faculty of Science, Imam Khomeini International University, P.O. Box 34194-288, Qazvin (Iran, Islamic Republic of)]. E-mail: razani@ikiu.ac.ir
2006-06-15
In this paper, a fixed point theorem is proved, i.e., if A is a C-contraction in the Menger space (S,F) and E-bar S be such that A(E)-bar is compact, then A has a fixed point. In addition, under the same condition, the existence of a periodic point of A is proved. Finally, a fixed point theorem in probabilistic normed spaces is proved.
A Metric Smorgasbord: All You Can Measure for $9.99.
Kansky, Bob; Olson, Melfried
Presented is a set of metric education materials developed over a five-year period by the Science and Mathematics Teaching Center (SMTC) at the University of Wyoming. It is called a "Metric Smorgasbord" because it is a set of materials which have considerable variety, were planned to appear to a broad range of instructional tastes, and permit…
Blecher, David P
2012-01-01
The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces, operator systems, operator algebras, and so on), in terms which are purely linear-metric, by which we mean that they only use the vector space structure of the space and its matrix norms. In the last part we give some characterizations of operator algebras (which are not linear-metric in our strict sense described in the paper).
Measuring inbreeding and inbreeding depression on pig growth from pedigree or SNP-derived metrics.
Silió, L; Rodríguez, M C; Fernández, A; Barragán, C; Benítez, R; Óvilo, C; Fernández, A I
2013-10-01
Multilocus homozygosity, measured as the proportion of the autosomal genome in homozygous genotypes or in runs of homozygosity, was compared with the respective pedigree inbreeding coefficients in 64 Iberian pigs genotyped using the Porcine SNP60 Beadchip. Pigs were sampled from a set of experimental animals with a large inbreeding variation born in a closed strain with a completely recorded multi-generation genealogy. Individual inbreeding coefficients calculated from pedigree were strongly correlated with the different SNP-derived metrics of homozygosity (r = 0.814-0.919). However, unequal correlations between molecular and pedigree inbreeding were observed at chromosomal level being mainly dependent on the number of SNPs and on the correlation between heterozygosities measured across different loci. A panel of 192 SNPs of intermediate frequencies was selected for genotyping 322 piglets to test inbreeding depression on postweaning growth performance (daily gain and weight at 90 days). The negative effects on these traits of homozygosities calculated from the genotypes of 168 quality-checked SNPs were similar to those of inbreeding coefficients. The results support that few hundreds of SNPs may be useful for measuring inbreeding and inbreeding depression, when the population structure or the mating system causes a large variance of inbreeding. © 2013 Blackwell Verlag GmbH.
Measuring segregation: an activity space approach.
Wong, David W S; Shaw, Shih-Lung
2011-06-01
While the literature clearly acknowledges that individuals may experience different levels of segregation across their various socio-geographical spaces, most measures of segregation are intended to be used in the residential space. Using spatially aggregated data to evaluate segregation in the residential space has been the norm and thus individual's segregation experiences in other socio-geographical spaces are often de-emphasized or ignored. This paper attempts to provide a more comprehensive approach in evaluating segregation beyond the residential space. The entire activity spaces of individuals are taken into account with individuals serving as the building blocks of the analysis. The measurement principle is based upon the exposure dimension of segregation. The proposed measure reflects the exposure of individuals of a referenced group in a neighborhood to the populations of other groups that are found within the activity spaces of individuals in the referenced group. Using the travel diary data collected from the tri-county area in southeast Florida and the imputed racial-ethnic data, this paper demonstrates how the proposed segregation measurement approach goes beyond just measuring population distribution patterns in the residential space and can provide a more comprehensive evaluation of segregation by considering various socio-geographical spaces.
Jamal, Sameerah
In this paper, we study the geometric properties of generators for the Klein-Gordon equation on classes of space-time homogeneous Gödel-type metrics. Our analysis complements the study involving the “Symmetries of geodesic motion in Gödel-type spacetimes” by U. Camci (J. Cosmol. Astropart. Phys., doi:10.1088/1475-7516/2014/07/002). These symmetries or Killing vectors (KVs) are used to construct potential functions admitted by the Klein-Gordon equation. The criteria for the potential function originates from three primary sources, viz. through generators that are identically the Killing algebra, or with the KV fields that are recast into linear combinations and third, real subalgebras within the Killing algebra. This leads to a classification of the (1 + 3) Klein-Gordon equation according to the catalogue of infinitesimal Lie and Noether point symmetries admitted. A comprehensive list of group invariant functions is provided and their application to analytic solutions is discussed.
Spaces and maps of idempotent measures
Zarichnyi, Mikhail M [Ivan Franko National University of L' viv, L' viv (Ukraine)
2010-06-23
We prove that the weak* topologization of the set of all idempotent measures (Maslov measures) on compact Hausdorff spaces defines a functor on the category Comp of compact Hausdorff spaces, and this functor is normal in the sense of E. V. Shchepin; in particular, it has many properties in common with the probability measure functor and the hyperspace functor. Moreover, we establish that this functor defines a monad in the category Comp, and prove that the idempotent measure monad contains the hyperspace monad as a submonad. For the space of idempotent measures there is an analogue of the Milyutin map (that is, of a continuous map of compact Hausdorff spaces which admits a regular averaging operator for spaces of continuous functions). Using the assertion of the existence of Milyutin maps for idempotent measures, we prove that the idempotent measure functor is open, that is, it preserves the class of open surjective maps. We also prove that, in contrast to the case of probability measure spaces, the correspondence assigning to any pair of idempotent measures the set of measures on their product which have the given marginals is not continuous.
Kutbi Marwan Amin
2016-01-01
Full Text Available The aim of this paper is to introduce the concept of a new nonlinear multi-valued mapping so called weakly (α, ψ, ξ-contractive mapping and prove fixed point results for such mappings in metric spaces. Our results unify, generalize and complement various results from the literature. We give some examples which support our main results while previous results in literature are not applicable. Also, we analyze the existence of fixed points for mappings satisfying a general contractive inequality of integral type. Many fixed point results for multi-valued mappings in metric spaces endowed with an arbitrary binary relation and metric spaces endowed with graph are given here to illustrate the results in this paper.
Four dimensional trace space measurement
Hernández, M E; Winick, Herman; Smith, T
2003-01-01
Future high energy colliders and FELs (Free Electron Lasers) such as the proposed LCLS (Linac Coherent Light Source) at SLAC require high brightness electron beams. In general a high brightness electron beam will contain a large number of electrons that occupy a short longitudinal duration, can be focused to a small transverse area while having small transverse divergences. Therefore the beam must have a high peak current and occupy small areas in transverse phase space and so have small transverse emittances. Additionally the beam should propagate at high energy and have a low energy spread to reduce chromatic effects. The requirements of the LCLS for example are pulses which contain 1010 electrons in a temporal duration of 10 ps FWHM with projected normalized transverse emittances of 1π mm mrad. Currently the most promising method of producing such a beam is the RF photoinjector. The GTF (Gun Test Facility) at SLAC was constructed to produce and characterize laser and electron beams which fulfill the...
NASA science publications have used the metric system of measurement since 1970. Although NASA has maintained a metric use policy since 1979, practical constraints have restricted actual use of metric units. In 1988, an amendment to the Metric Conversion Act of 1975 required the Federal Government to adopt the metric system except where impractical. In response to Public Law 100-418 and Executive Order 12770, NASA revised its metric use policy and developed this Metric Transition Plan. NASA's goal is to use the metric system for program development and functional support activities to the greatest practical extent by the end of 1995. The introduction of the metric system into new flight programs will determine the pace of the metric transition. Transition of institutional capabilities and support functions will be phased to enable use of the metric system in flight program development and operations. Externally oriented elements of this plan will introduce and actively support use of the metric system in education, public information, and small business programs. The plan also establishes a procedure for evaluating and approving waivers and exceptions to the required use of the metric system for new programs. Coordination with other Federal agencies and departments (through the Interagency Council on Metric Policy) and industry (directly and through professional societies and interest groups) will identify sources of external support and minimize duplication of effort.
Measure Theory in Noncommutative Spaces
Steven Lord
2010-09-01
Full Text Available The integral in noncommutative geometry (NCG involves a non-standard trace called a Dixmier trace. The geometric origins of this integral are well known. From a measure-theoretic view, however, the formulation contains several difficulties. We review results concerning the technical features of the integral in NCG and some outstanding problems in this area. The review is aimed for the general user of NCG.
Improved structural similarity metric for the visible quality measurement of images
Lee, Daeho; Lim, Sungsoo
2016-11-01
The visible quality assessment of images is important to evaluate the performance of image processing methods such as image correction, compressing, and enhancement. The structural similarity is widely used to determine the visible quality; however, existing structural similarity metrics cannot correctly assess the perceived human visibility of images that have been slightly geometrically transformed or images that have undergone significant regional distortion. We propose an improved structural similarity metric that is more close to human visible evaluation. Compared with the existing metrics, the proposed method can more correctly evaluate the similarity between an original image and various distorted images.
度量空间中高维索引结构回顾%Review of High Dimensional Index Structures in Metric Spaces
刘芳洁; 董道国; 薛向阳
2003-01-01
Fast searches and query operations in high dimensional databases require efficient index structures. Amonga variety of index structures, the index structures in metric spaces are very useful. They can be used in an extensivefield, such as searching for protein molecular chains with certain sequences in Computational Biology and matching agiven strings fuzzily in Text Retrieval. In this paper, the features of index structures in metric spaces are analyzedand subsequently a further classification is given to these index structures. Finally, some representative index struc-tures are introduced in detail.
Dirac Hamiltonian and Reissner-Nordstrom Metric: Coulomb Interaction in Curved Space-Time
Noble, J H
2016-01-01
We investigate the spin-1/2 relativistic quantum dynamics in the curved space-time generated by a central massive charged object (black hole). This necessitates a study of the coupling of a Dirac particle to the Reissner-Nordstrom space-time geometry and the simultaneous covariant coupling to the central electrostatic field. The relativistic Dirac Hamiltonian for the Reissner-Nordstrom geometry is derived. A Foldy-Wouthuysen transformation reveals the presence of gravitational, and electro-gravitational spin-orbit coupling terms which generalize the Fokker precession terms found for the Dirac-Schwarzschild Hamiltonian, and other electro-gravitational correction terms to the potential proportional to alpha^n G, where alpha is the fine-structure constant, and G is the gravitational coupling constant. The particle-antiparticle symmetry found for the Dirac-Schwarzschild geometry (and for other geometries which do not include electromagnetic interactions) is shown to be explicitly broken due to the electrostatic c...
Associations between multiple green space measures and birth weight across two US cities.
Cusack, Leanne; Larkin, Andrew; Carozza, Susan E; Hystad, Perry
2017-09-01
Several measures of green space exposure have been used in epidemiological research, but their relevance to health, and representation of exposure pathways, remains unclear. Here we examine the relationships between multiple urban green space metrics and associations with term birth weight across two diverse US cities. We used Vital Statistics data to create a birth cohort from 2005 to 2009 in the cities of Portland, Oregon (n = 90,265) and Austin, Texas (n = 88,807). These cities have similar green space levels but very different population and contextual characteristics. Green space metrics derived from mother's full residential address using multiple buffer distances (50-1000m) included: Landsat Normalized Difference Vegetation Index (NDVI), % tree cover, % green space, % street tree buffering, and access to parks (using US EPA EnviroAtlas Data). Correlation between green space metrics were assessed and mixed models were used to determine associations with term birth weight, controlling for a comprehensive set of individual and neighborhood factors. City-specific models were run to determine how contextual and population differences affected green space associations with birth weight. We observed moderate to high degrees of correlation between different green space metrics (except park access), with similar patterns between cities. Unadjusted associations demonstrated consistent protective effects of NDVI, % green space, % tree cover, and % street tree buffering for most buffer sizes on birth weight; however, in fully adjusted models most metrics were no longer statistically significant and no clear patterns remained. For example, in Austin the difference in birth weight for the highest versus lowest quartile of % green space within 50m was 38.3g (95% CI: 30.4, 46.1) in unadjusted and -1.5g (98% CI: -8.8, 6.3) in adjusted models compared to 55.7g (95%CI: 47.9, -63.6) and 12.9g (95% CI: 4.4, 21.4) in Portland. Maternal race, ethnicity and education had the
Ren, Jingzheng; Sovacool, Benjamin
2014-01-01
Various metrics exist for energy security assessment along with a diffuse array of different strategies for improving national performance. These independent and interacted metrics overlap, however, and are rarely considered systematically. The objective of this study is to translate often subjec...... and affordability dimensions of energy security are most impactful to a nation's overall energy security, and that the promotion of renewable energy and diversification are compelling national energy security strategies, both for China and other countries.......Various metrics exist for energy security assessment along with a diffuse array of different strategies for improving national performance. These independent and interacted metrics overlap, however, and are rarely considered systematically. The objective of this study is to translate often...... a DEMATEL (Fuzzy Decision-making Trial and Evaluation Laboratory) methodology to analyze collected data, reveal cause-effect relationships, and prioritize energy security strategies. To apply our theoretical results in practice, we include a brief case study of China. We conclude that the availability...
Kerzner, Harold
2013-01-01
Today, with the growth of complex projects, stakeholder involvement in projects, advances in computer technology for dashboard designs, metrics, and key performance indicators for project management have become an important focus. This Second Edition of the bestselling book walks readers through everything from the basics of project management metrics and key performance indicators to establishing targets and using dashboards to monitor performance. The content is aligned with PMI's PMBOK Guide and stresses "value" as the main focal point.
Design based Object-Oriented Metrics to Measure Coupling and Cohesion
PREETI GULIA; Dr. RAJENDER SINGH CHHILLAR
2011-01-01
The object oriented design and object oriented development environment are currently popular in software organizations due to the object oriented programming languages. As the object oriented technology enters into software organizations, it has created new challenges for the companies which used only product metrics as atool for monitoring, controlling and maintaining the software product. This paper presents the new object oriented metrics namely for coupling of class by counting the number...
Yu, Yi-Kuo
2007-02-01
We construct a metric measure among weight matrices that are commonly used in non-interacting statistical physics systems, computational biology problems, as well as in general applications such as hidden Markov models. The metric distance between two weight matrices is obtained via aligning the matrices and thus can be evaluated by dynamic programming. Capable of allowing reverse complements in distance evaluation, this metric accommodates both gapless and gapped alignments between two weight matrices. The distance statistics among random motifs is also studied. We find that the average square distance and its standard error grow with different powers of motif length, and the normalized square distance follows a Gaussian distribution for large motif lengths.
Measuring the intangibles: a metrics for the economic complexity of countries and products.
Cristelli, Matthieu; Gabrielli, Andrea; Tacchella, Andrea; Caldarelli, Guido; Pietronero, Luciano
2013-01-01
We investigate a recent methodology we have proposed to extract valuable information on the competitiveness of countries and complexity of products from trade data. Standard economic theories predict a high level of specialization of countries in specific industrial sectors. However, a direct analysis of the official databases of exported products by all countries shows that the actual situation is very different. Countries commonly considered as developed ones are extremely diversified, exporting a large variety of products from very simple to very complex. At the same time countries generally considered as less developed export only the products also exported by the majority of countries. This situation calls for the introduction of a non-monetary and non-income-based measure for country economy complexity which uncovers the hidden potential for development and growth. The statistical approach we present here consists of coupled non-linear maps relating the competitiveness/fitness of countries to the complexity of their products. The fixed point of this transformation defines a metrics for the fitness of countries and the complexity of products. We argue that the key point to properly extract the economic information is the non-linearity of the map which is necessary to bound the complexity of products by the fitness of the less competitive countries exporting them. We present a detailed comparison of the results of this approach directly with those of the Method of Reflections by Hidalgo and Hausmann, showing the better performance of our method and a more solid economic, scientific and consistent foundation.
Health outcomes in diabetics measured with Minnesota Community Measurement quality metrics
Takahashi PY
2014-12-01
Full Text Available Paul Y Takahashi,1 Jennifer L St Sauver,2 Lila J Finney Rutten,2 Robert M Jacobson,3 Debra J Jacobson,2 Michaela E McGree,2 Jon O Ebbert1 1Department of Internal Medicine, Division of Primary Care Internal Medicine, 2Department of Health Sciences Research, Mayo Clinic Robert D and Patricia E Kern Center for the Science of Health Care Delivery, 3Department of Pediatric and Adolescent Medicine, Division of Community Pediatrics, Mayo Clinic, Rochester, MN, USA Objective: Our objective was to understand the relationship between optimal diabetes control, as defined by Minnesota Community Measurement (MCM, and adverse health outcomes including emergency department (ED visits, hospitalizations, 30-day rehospitalization, intensive care unit (ICU stay, and mortality. Patients and methods: In 2009, we conducted a retrospective cohort study of empaneled Employee and Community Health patients with diabetes mellitus. We followed patients from 1 September 2009 until 30 June 2011 for hospitalization and until 5 January 2014 for mortality. Optimal control of diabetes mellitus was defined as achieving the following three measures: low-density lipoprotein (LDL cholesterol <100 mg/mL, blood pressure <140/90 mmHg, and hemoglobin A1c <8%. Using the electronic medical record, we assessed hospitalizations, ED visits, ICU stays, 30-day rehospitalizations, and mortality. The chi-square or Wilcoxon rank-sum tests were used to compare those with and without optimal control. We used Cox proportional hazard models to estimate the associations between optimal diabetes mellitus status and each outcome. Results: We identified 5,731 empaneled patients with diabetes mellitus; 2,842 (49.6% were in the optimal control category. After adjustment, we observed that non-optimally controlled patients had higher risks for hospitalization (hazard ratio [HR] 1.11; 95% confidence interval [CI] 1.00–1.23, ED visits (HR 1.15; 95% CI 1.06–1.25, and mortality (HR 1.29; 95% CI 1.09–1
Salvagnini, Elena [UZ Gasthuisberg, Medical Imaging Research Center and Department of Radiology, Herestraat 49, B-3000 Leuven, Belgium and SCK-CEN, Boeretang 200, B-2400 Mol (Belgium); Bosmans, Hilde; Marshall, Nicholas W. [UZ Gasthuisberg, Medical Imaging Research Center and Department of Radiology, Herestraat 49, B-3000 Leuven (Belgium); Struelens, Lara [SCK-CEN, Boeretang 200, B-2400 Mol (Belgium)
2013-10-15
Purpose: The aim of this paper was to illustrate the value of the new metric effective detective quantum efficiency (eDQE) in relation to more established measures in the optimization process of two digital mammography systems. The following metrics were included for comparison against eDQE: detective quantum efficiency (DQE) of the detector, signal difference to noise ratio (SdNR), and detectability index (d′) calculated using a standard nonprewhitened observer with eye filter.Methods: The two systems investigated were the Siemens MAMMOMAT Inspiration and the Hologic Selenia Dimensions. The presampling modulation transfer function (MTF) required for the eDQE was measured using two geometries: a geometry containing scattered radiation and a low scatter geometry. The eDQE, SdNR, and d′ were measured for poly(methyl methacrylate) (PMMA) thicknesses of 20, 40, 60, and 70 mm, with and without the antiscatter grid and for a selection of clinically relevant target/filter (T/F) combinations. Figures of merit (FOMs) were then formed from SdNR and d′ using the mean glandular dose as the factor to express detriment. Detector DQE was measured at energies covering the range of typical clinically used spectra.Results: The MTF measured in the presence of scattered radiation showed a large drop at low spatial frequency compared to the low scatter method and led to a corresponding reduction in eDQE. The eDQE for the Siemens system at 1 mm{sup −1} ranged between 0.15 and 0.27, depending on T/F and grid setting. For the Hologic system, eDQE at 1 mm{sup −1} varied from 0.15 to 0.32, again depending on T/F and grid setting. The eDQE results for both systems showed that the grid increased the system efficiency for PMMA thicknesses of 40 mm and above but showed only small sensitivity to T/F setting. While results of the SdNR and d′ based FOMs confirmed the eDQE grid position results, they were also more specific in terms of T/F selection. For the Siemens system at 20 mm PMMA
Salvagnini, Elena; Bosmans, Hilde; Struelens, Lara; Marshall, Nicholas W
2013-10-01
The aim of this paper was to illustrate the value of the new metric effective detective quantum efficiency (eDQE) in relation to more established measures in the optimization process of two digital mammography systems. The following metrics were included for comparison against eDQE: detective quantum efficiency (DQE) of the detector, signal difference to noise ratio (SdNR), and detectability index (d') calculated using a standard nonprewhitened observer with eye filter. The two systems investigated were the Siemens MAMMOMAT Inspiration and the Hologic Selenia Dimensions. The presampling modulation transfer function (MTF) required for the eDQE was measured using two geometries: a geometry containing scattered radiation and a low scatter geometry. The eDQE, SdNR, and d' were measured for poly(methyl methacrylate) (PMMA) thicknesses of 20, 40, 60, and 70 mm, with and without the antiscatter grid and for a selection of clinically relevant target/filter (T/F) combinations. Figures of merit (FOMs) were then formed from SdNR and d' using the mean glandular dose as the factor to express detriment. Detector DQE was measured at energies covering the range of typical clinically used spectra. The MTF measured in the presence of scattered radiation showed a large drop at low spatial frequency compared to the low scatter method and led to a corresponding reduction in eDQE. The eDQE for the Siemens system at 1 mm(-1) ranged between 0.15 and 0.27, depending on T/F and grid setting. For the Hologic system, eDQE at 1 mm(-1) varied from 0.15 to 0.32, again depending on T/F and grid setting. The eDQE results for both systems showed that the grid increased the system efficiency for PMMA thicknesses of 40 mm and above but showed only small sensitivity to T/F setting. While results of the SdNR and d' based FOMs confirmed the eDQE grid position results, they were also more specific in terms of T/F selection. For the Siemens system at 20 mm PMMA, the FOMs indicated Mo/Mo (grid out) as
Hadjisolomou, Stavros P.; El-Haddad, George
2017-01-01
Coleoid cephalopods (squid, octopus, and sepia) are renowned for their elaborate body patterning capabilities, which are employed for camouflage or communication. The specific chromatic appearance of a cephalopod, at any given moment, is a direct result of the combined action of their intradermal pigmented chromatophore organs and reflecting cells. Therefore, a lot can be learned about the cephalopod coloration system by video recording and analyzing the activation of individual chromatophores in time. The fact that adult cephalopods have small chromatophores, up to several hundred thousand in number, makes measurement and analysis over several seconds a difficult task. However, current advancements in videography enable high-resolution and high framerate recording, which can be used to record chromatophore activity in more detail and accuracy in both space and time domains. In turn, the additional pixel information and extra frames per video from such recordings result in large video files of several gigabytes, even when the recording spans only few minutes. We created a software plugin, “SpotMetrics,” that can automatically analyze high resolution, high framerate video of chromatophore organ activation in time. This image analysis software can track hundreds of individual chromatophores over several hundred frames to provide measurements of size and color. This software may also be used to measure differences in chromatophore activation during different behaviors which will contribute to our understanding of the cephalopod sensorimotor integration system. In addition, this software can potentially be utilized to detect numbers of round objects and size changes in time, such as eye pupil size or number of bacteria in a sample. Thus, we are making this software plugin freely available as open-source because we believe it will be of benefit to other colleagues both in the cephalopod biology field and also within other disciplines. PMID:28298896
Hadjisolomou, Stavros P; El-Haddad, George
2017-01-01
Coleoid cephalopods (squid, octopus, and sepia) are renowned for their elaborate body patterning capabilities, which are employed for camouflage or communication. The specific chromatic appearance of a cephalopod, at any given moment, is a direct result of the combined action of their intradermal pigmented chromatophore organs and reflecting cells. Therefore, a lot can be learned about the cephalopod coloration system by video recording and analyzing the activation of individual chromatophores in time. The fact that adult cephalopods have small chromatophores, up to several hundred thousand in number, makes measurement and analysis over several seconds a difficult task. However, current advancements in videography enable high-resolution and high framerate recording, which can be used to record chromatophore activity in more detail and accuracy in both space and time domains. In turn, the additional pixel information and extra frames per video from such recordings result in large video files of several gigabytes, even when the recording spans only few minutes. We created a software plugin, "SpotMetrics," that can automatically analyze high resolution, high framerate video of chromatophore organ activation in time. This image analysis software can track hundreds of individual chromatophores over several hundred frames to provide measurements of size and color. This software may also be used to measure differences in chromatophore activation during different behaviors which will contribute to our understanding of the cephalopod sensorimotor integration system. In addition, this software can potentially be utilized to detect numbers of round objects and size changes in time, such as eye pupil size or number of bacteria in a sample. Thus, we are making this software plugin freely available as open-source because we believe it will be of benefit to other colleagues both in the cephalopod biology field and also within other disciplines.
Common Fixed Points for Asymptotic Pointwise Nonexpansive Mappings in Metric and Banach Spaces
P. Pasom
2012-01-01
Full Text Available Let C be a nonempty bounded closed convex subset of a complete CAT(0 space X. We prove that the common fixed point set of any commuting family of asymptotic pointwise nonexpansive mappings on C is nonempty closed and convex. We also show that, under some suitable conditions, the sequence {xk}k=1∞ defined by xk+1=(1-tmkxk⊕tmkTmnky(m-1k, y(m-1k=(1-t(m-1kxk⊕t(m-1kTm-1nky(m-2k,y(m-2k=(1-t(m-2kxk⊕t(m-2kTm-2nky(m-3k,…,y2k=(1-t2kxk⊕t2kT2nky1k,y1k=(1-t1kxk⊕t1kT1nky0k,y0k=xk, k∈N, converges to a common fixed point of T1,T2,…,Tm where they are asymptotic pointwise nonexpansive mappings on C, {tik}k=1∞ are sequences in [0,1] for all i=1,2,…,m, and {nk} is an increasing sequence of natural numbers. The related results for uniformly convex Banach spaces are also included.
Wette, Karl
2016-01-01
All-sky searches for gravitational-wave pulsars are generally limited in sensitivity by the finite availability of computing resources. Semicoherent searches are a common method of maximizing search sensitivity given a fixed computing budget. The work of Wette and Prix [Phys. Rev. D 88, 123005 (2013)] and Wette [Phys. Rev. D 92, 082003 (2015)] developed a semicoherent search method which uses metrics to construct the banks of pulsar signal templates needed to search the parameter space of interest. In this work we extend the range of validity of the parameter-space metrics using an empirically-derived relationship between the resolution (or mismatch) of the template banks and the mismatch of the overall search. This work has important consequences for the optimization of metric-based semicoherent searches at fixed computing cost.
Sequence-covering cs -images of Metric Spaces%度量空间的序列复盖cs-映象
刘贵方
2005-01-01
借助某些紧可数网,建立了度量空间的序列复盖cs-映象的一些特征.%In this paper, the characterizations of metric spaces under some sequence-covering (compact-covering) cs-mappings is established by means of certain kind of compact-countable networks.
Sharp, P. M.; D'Amico, I.
2016-02-01
We consider a model system of two electrons confined in a two-dimensional harmonic oscillator potential, with the electrons interacting via an α / r2 potential, and subject to a magnetic field applied perpendicular to the plane of confinement. Our results show that variations in the strength of the electron-electron interaction generate a "band structure" in ground state metric spaces, which shares many characteristics with those generated as a result of varying the confinement potential. In particular, the metric spaces for wavefunctions, particle densities, and paramagnetic current densities all exhibit distinct "bands" and "gaps". The behavior of the polar angle of the bands also shares traits with that obtained by varying the confinement potential, but the behavior of the arc lengths of the bands on the metric space spheres can be seen to be different for the two cases and opposite for a large range of angular momentum values. The findings here and in Refs. [1,2] demonstrate that the "band structure" that arises in ground state metric spaces when a magnetic field is applied is a robust feature.
Mustafa, Zead; Jaradat, Mohammed M M; Ansari, Arslan Hojat; Popović, Branislav Z; Jaradat, Husein M
2016-01-01
In this paper, by using the C-class functions and a new approach we present some coincidence point results for four mappings satisfying generalized [Formula: see text]-weakly contractive condition in the setting of ordered b-metric spaces. Also, an application and example are given to support our results.
Fixed point theorems in interval-valued metric spaces%区间值度量空间中的不动点定理
陈桂秀; 李生刚; 赵虎
2013-01-01
This paper studies a special kind of fuzzy metric ρ , called interval-valued metric. The operations of interval number (such as addition subtraction multiplication divition)are given in related references, the subtraction operation of interval num-ber is redefined, and the corresponding inequality properties are obtained. Then the definition of interval-valued metric is given. Some related conception in interval-valued metric space are introduced, such as convergent sequence, Cauchy sequence and completeness etc, and the fixed point theorem and common fixed point theorem in interval-valued metric space are presented.% 研究了一种特殊的模糊度量ρ，称为区间值度量。区间数的运算(如加减乘除运算)在相关文献中已有定义，对区间数的减法运算进行新的定义，得到相应的不等式性质，接着给出了区间值度量的定义；介绍了区间值度量空间中相关的定义，如收敛序列、Cauchy 序列以及完备性等；讨论了区间值度量空间中的不动点定理和公共不动点定理。
What Are We Assessing When We Measure Food Security? A Compendium and Review of Current Metrics12
Jones, Andrew D.; Ngure, Francis M.; Pelto, Gretel; Young, Sera L.
2013-01-01
The appropriate measurement of food security is critical for targeting food and economic aid; supporting early famine warning and global monitoring systems; evaluating nutrition, health, and development programs; and informing government policy across many sectors. This important work is complicated by the multiple approaches and tools for assessing food security. In response, we have prepared a compendium and review of food security assessment tools in which we review issues of terminology, measurement, and validation. We begin by describing the evolving definition of food security and use this discussion to frame a review of the current landscape of measurement tools available for assessing food security. We critically assess the purpose/s of these tools, the domains of food security assessed by each, the conceptualizations of food security that underpin each metric, as well as the approaches that have been used to validate these metrics. Specifically, we describe measurement tools that 1) provide national-level estimates of food security, 2) inform global monitoring and early warning systems, 3) assess household food access and acquisition, and 4) measure food consumption and utilization. After describing a number of outstanding measurement challenges that might be addressed in future research, we conclude by offering suggestions to guide the selection of appropriate food security metrics. PMID:24038241
Space debris measurement program at Phillips Laboratory
Dao, Phan D.; Mcnutt, Ross T.
1992-01-01
Ground-based optical sensing was identified as a technique for measuring space debris complementary to radar in the critical debris size range of 1 to 10 cm. The Phillips Laboratory is building a staring optical sensor for space debris measurement and considering search and track optical measurement at additional sites. The staring sensor is implemented in collaboration with Wright Laboratory using the 2.5 m telescope at Wright Patterson AFB, Dayton, Ohio. The search and track sensor is designed to detect and track orbital debris in tasked orbits. A progress report and a discussion of sensor performance and search and track strategies will be given.
Kerzner, Harold
2017-01-01
With the growth of complex projects, stakeholder involvement, and advancements in visual-based technology, metrics and KPIs (key performance indicators) are key factors in evaluating project performance. Dashboard reporting systems provide accessible project performance data, and sharing this vital data in a concise and consistent manner is a key communication responsibility of all project managers. This 3rd edition of Kerzner’s groundbreaking work includes the following updates: new sections on processing dashboard information, portfolio management PMO and metrics, and BI tool flexibility. PPT decks by chapter and a test bank will be available for use in seminar presentations and courses.
Vossos, Spyridon; Vossos, Elias
2016-08-01
closed LSTT is reduced, if one RIO has small velocity wrt another RIO. Thus, we have infinite number of closed LSTTs, each one with the corresponding SR theory. In case that we relate accelerated observers with variable metric of spacetime, we have the case of General Relativity (GR). For being that clear, we produce a generalized Schwarzschild metric, which is in accordance with any SR based on this closed complex LSTT and Einstein equations. The application of this kind of transformations to the SR and GR is obvious. But, the results may be applied to any linear space of dimension four endowed with steady or variable metric, whose elements (four- vectors) have spatial part (vector) with Euclidean metric.
Measuring gravitational effects on antimatter in space
Piacentino, Giovanni Maria; Venanzoni, Graziano
2016-01-01
We propose an experimental test of the gravitational interaction with antimatter by measuring the branching fraction of the CP~violating decay $K_\\mathrm{L} \\to \\pi^{+} \\pi^{-}$ in space. We show that at the altitude of the International Space Station, gravitational effects may change the level of CP~violation such that a 5$\\sigma$ discrimination may be obtained by collecting the $K_\\mathrm{L}$ produced by the cosmic proton flux within a few years.
王国俊
2000-01-01
Valuation spaces with respect to diverse implication operators are investigated in a unified way where the Lebesgue measure is a commonly used measure, and it is proved that all the logic formulas are measurable functions with respect to popularly used implication operations. The concept of t-(α-tautology) is introduced and rules of generalized modus ponens (MP) and hypothetic syllogism (HS) are established in the sense of semantics. The concept of truth degree of a logic formula is introduced and rules of integral MP and integral HS are proposed. Finally, a kind of pseudo-metric is introduced to the set consisting of all logic formulas by establishing a universal logical metric space, making it possible to develop a new type of approximate reasoning arise.
Exact Protein Structure Classification Using the Maximum Contact Map Overlap Metric
Wohlers, Inken; Le Boudic-Jamin, Mathilde; Djidjev, Hristo; Klau, Gunnar; Andonov, Rumen
2014-01-01
In this work we propose a new distance measure for compar-ing two protein structures based on their contact map representations. We show that our novel measure, which we refer to as the maximum contact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein representations. Having a metric in that space allows to avoid pairwise comparisons on the entire database and thus to significantly accelerate exploring the protein space compared to no-metric spaces. We...
Metric Entropy of Nonautonomous Dynamical Systems
Kawan Christoph
2014-01-01
Full Text Available We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence (Xn; μn of probability spaces and a sequence of measurable maps fn : Xn → Xn+1 with fnμn = μn+1. This notion generalizes the classical concept of metric entropy established by Kolmogorov and Sinai, and is related via a variational inequality to the topological entropy of nonautonomous systems as defined by Kolyada, Misiurewicz, and Snoha. Moreover, it shares several properties with the classical notion of metric entropy. In particular, invariance with respect to appropriately defined isomorphisms, a power rule, and a Rokhlin-type inequality are proved
Backes, Claudia; Paton, Keith R; Hanlon, Damien; Yuan, Shengjun; Katsnelson, Mikhail I; Houston, James; Smith, Ronan J; McCloskey, David; Donegan, John F; Coleman, Jonathan N
2016-02-21
Liquid phase exfoliation is a powerful and scalable technique to produce defect-free mono- and few-layer graphene. However, samples are typically polydisperse and control over size and thickness is challenging. Notably, high throughput techniques to measure size and thickness are lacking. In this work, we have measured the extinction, absorption, scattering and Raman spectra for liquid phase exfoliated graphene nanosheets of various lateral sizes (90 ≤ 〈L〉 ≤ 810 nm) and thicknesses (2.7 ≤ 〈N〉 ≤ 10.4). We found all spectra to show well-defined dependences on nanosheet dimensions. Measurements of extinction and absorption spectra of nanosheet dispersions showed both peak position and spectral shape to vary with nanosheet thickness in a manner consistent with theoretical calculations. This allows the development of empirical metrics to extract the mean thickness of liquid dispersed nanosheets from an extinction (or absorption) spectrum. While the scattering spectra depended on nanosheet length, poor signal to noise ratios made the resultant length metric unreliable. By analyzing Raman spectra measured on graphene nanosheet networks, we found both the D/G intensity ratio and the width of the G-band to scale with mean nanosheet length allowing us to establish quantitative relationships. In addition, we elucidate the variation of 2D/G band intensities and 2D-band shape with the mean nanosheet thickness, allowing us to establish quantitative metrics for mean nanosheet thickness from Raman spectra.
Metric diffusion along foliations
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.
Space-time measures for subluminal and superluminal motions
Calvo-Mozo, Benjam\\'\\in
2014-01-01
In present work we examine the implications on both, space-time measures and causal structure, of a generalization of the local causality postulate by asserting its validity to all motion regimes, the subluminal and superluminal ones. The new principle implies the existence of a denumerable set of metrical null cone speeds, \\{$c_k\\}$, where $c_1$ is the speed of light in vacuum, and $c_k/c \\simeq \\epsilon^{-k+1}$ for $k\\geq2$, where $\\epsilon^2$ is a tiny dimensionless constant which we introduce to prevent the divergence of the $x, t$ measures in Lorentz transformations, such that their generalization keeps $c_k$ invariant and as the top speed for every regime of motion. The non divergent factor $\\gamma_k$ equals $k\\epsilon^{-1}$ at speed $c_k$. We speak then of $k-$timelike and $k-$null intervals and of k-timelike and k-null paths on space-time, and construct a causal structure for each regime. We discuss also the possible transition of a material particle from the subluminal to the first superluminal regim...
Space-time framework of internal measurement
Matsuno, Koichiro
1998-07-01
Measurement internal to material bodies is ubiquitous. The internal observer has its own local space-time framework that enables the observer to distinguish, even to a slightest degree, those material bodies fallen into that framework. Internal measurement proceeding among the internal observers come to negotiate a construction of more encompassing local framework of space and time. The construction takes place through friction among the internal observers. Emergent phenomena are related to an occurrence of enlarging the local space-time framework through the frictional negotiation among the material participants serving as the internal observers. Unless such a negotiation is obtained, the internal observers would have to move around in the local space-time frameworks of their own that are mutually incommensurable. Enhancement of material organization as demonstrated in biological evolutionary processes manifests an inexhaustible negotiation for enlarging the local space-time framework available to the internal observers. In contrast, Newtonian space-time framework, that remains absolute and all encompassing, is an asymptote at which no further emergent phenomena could be expected. It is thus ironical to expect something to emerge within the framework of Newtonian absolute space and time. Instead of being a complex and organized configuration of interaction to appear within the global space-time framework, emergent phenomena are a consequence of negotiation among the local space-time frameworks available to internal measurement. Most indicative of the negotiation of local space-time frameworks is emergence of a conscious self grounding upon the reflexive nature of perceptions, that is, a self-consciousness in short, that certainly goes beyond the Kantian transcendental subject. Accordingly, a synthetic discourse on securing consciousness upon the ground of self-consciousness can be developed, though linguistic exposition of consciousness upon self
V-index: a novel metric to measure virtuosity of academics
Ferrara, Emilio
2012-01-01
In this paper, we propose the V-index (or, Virtuosity index) as a novel metric to assess the scientific virtuosity of academics. This index can be applied to researchers and journals as well. In particular, we show that the V-index fills the gap of h-index and similar metrics in considering the self-citations of authors or journals. The paper provides with three real-world examples: in the first, we evaluate the research impact of the most productive scientists in Computer Science (according to DBLP); in the second, we assess the virtuosity of the journals ranked in the "Computer Science Applications" section of SCImago; in the last, we apply V-index for the assessment of the 2011 research activity of 130 countries all over the world.
Measuring success : metrics that link supply chain management to aircraft readiness
McDoniel, Patrick S.; Balestreri, William G.
2002-01-01
Approved for public release; distribution is unlimited. This thesis evaluates and analyzes current strategic management planning methods that develop performance metrics linking supply chain management to aircraft readiness. Our primary focus is the Marine Aviation Logistics Squadron. Utilizing the Logistics Management Institute's DoD Supply Chain Implementation Guide and adapted SCOR model, we applied the six step process for developing a strategic logistics management plan for implementi...
Enterprise Sustainment Metrics
The Air Force sustainment enterprise does not have metrics that . . . adequately measure key sustainment parameters, according to the 2011 National...standardized and do not contribute to the overall assessment of the sustainment enterprise . This paper explores the development of a single metric...is not feasible. To answer the question does the sustainment enterprise provide cost-effective readiness for a weapon system, a suite of metrics is
Common Fixed Point Theorems in Uniformly Convex Metric Space%一致凸度量空间的公共不动点定理
曾秀华; 邓磊
2015-01-01
利用一致凸度量空间中的凸性模和自映象对的次相容性，讨论了一类4个自映象的公共不动点的存在性和唯一性问题，得到了一个公共不动点定理。该结果改进和推广了近期的相关结果。%Using the sub‐compatibility of convex modulus and self‐mapping pair in uniformly convex metric spaces ,we discuss the existence and uniqueness of some common fixed points with four self‐mappings in this paper .A new common fixed point theorem is obtained ,which largely improves and extends some re‐lated results that have been published recently in uniformly convex metric spaces .
度量空间的紧覆盖π的（P）映像%Compact-covering π-（P）-images of Metric Spaces
蔡长勇; 李进金
2011-01-01
This paper establishes an internal characterization of compact-covering π-（P）-images of metric spaces.Namely we show that X is a compact-covering π-（P）-image of a metric space if and only if it has a point-star network consisting of compact-finite-partiti%本文建立了度量空间的紧覆盖π的（P）映像的内在特征,即证明了X是度量空间的紧覆盖π的（P）映射下的像当且仅当X具有性质（P）的紧有限分解的点星网.
$C^3$-index: A PageRank based multi-faceted metric for authors' performance measurement
Pradhan, Dinesh; Paul, Partha Sarathi; Maheswari, Umesh; Nandi, Subrata; Chakraborty, Tanmoy
2016-01-01
Ranking scientific authors is an important but challenging task, mostly due to the dynamic nature of the evolving scientific publications. The basic indicators of an author's productivity and impact are still the number of publications and the citation count (leading to the popular metrics such as h-index, g-index etc.). H-index and its popular variants are mostly effective in ranking highly-cited authors, thus fail to resolve ties while ranking medium-cited and low-cited authors who are majo...
Spears, B K; Glenzer, S; Edwards, M J; Brandon, S; Clark, D; Town, R; Cerjan, C; Dylla-Spears, R; Mapoles, E; Munro, D; Salmonson, J; Sepke, S; Weber, S; Hatchett, S; Haan, S; Springer, P; Moses, E; Mapoles, E; Munro, D; Salmonson, J; Sepke, S
2011-12-16
The National Ignition Campaign (NIC) uses non-igniting 'THD' capsules to study and optimize the hydrodynamic assembly of the fuel without burn. These capsules are designed to simultaneously reduce DT neutron yield and to maintain hydrodynamic similarity with the DT ignition capsule. We will discuss nominal THD performance and the associated experimental observables. We will show the results of large ensembles of numerical simulations of THD and DT implosions and their simulated diagnostic outputs. These simulations cover a broad range of both nominal and off nominal implosions. We will focus on the development of an experimental implosion performance metric called the experimental ignition threshold factor (ITFX). We will discuss the relationship between ITFX and other integrated performance metrics, including the ignition threshold factor (ITF), the generalized Lawson criterion (GLC), and the hot spot pressure (HSP). We will then consider the experimental results of the recent NIC THD campaign. We will show that we can observe the key quantities for producing a measured ITFX and for inferring the other performance metrics. We will discuss trends in the experimental data, improvement in ITFX, and briefly the upcoming tuning campaign aimed at taking the next steps in performance improvement on the path to ignition on NIF.
Manish Jain
2013-01-01
Full Text Available We establish the existence and uniqueness of coupled common fixed point for symmetric (φ,ψ-contractive mappings in the framework of ordered G-metric spaces. Present work extends, generalize, and enrich the recent results of Choudhury and Maity (2011, Nashine (2012, and Mohiuddine and Alotaibi (2012, thereby, weakening the involved contractive conditions. Our theoretical results are accompanied by suitable examples and an application to integral equations.
Space object tracking with delayed measurements
Chen, Huimin; Shen, Dan; Chen, Genshe; Blasch, Erik; Pham, Khanh
2010-04-01
This paper is concerned with the nonlinear filtering problem for tracking a space object with possibly delayed measurements. In a distributed dynamic sensing environment, due to limited communication bandwidth and long distances between the earth and the satellites, it is possible for sensor reports to be delayed when the tracking filter receives them. Such delays can be complete (the full observation vector is delayed) or partial (part of the observation vector is delayed), and with deterministic or random time lag. We propose an approximate approach to incorporate delayed measurements without reprocessing the old measurements at the tracking filter. We describe the optimal and suboptimal algorithms for filter update with delayed measurements in an orbital trajectory estimation problem without clutter. Then we extend the work to a single object tracking under clutter where probabilistic data association filter (PDAF) is used to replace the recursive linear minimum means square error (LMMSE) filter and delayed measurements with arbitrary lags are be handled without reprocessing the old measurements. Finally, we demonstrate the proposed algorithms in realistic space object tracking scenarios using the NASA General Mission Analysis Tool (GMAT).
Knowledge Metrics of Brand Equity: Critical Measure of Brand Attachment and Brand Attitude Strength
Arslan Rafi
2011-11-01
Full Text Available The purpose of this study is to identify factors that can positively influence brand attachment and brand attitude strength. Brand creation through an effective marketing strategy is necessary for creation of unique associations in the customer’s memory. Customer’s attitude, awareness and association towards the brand are primarily focused while evaluating performance of a brand, before designing the marketing strategies and subsequent evaluation of the progress. In this research, literature establishes a direct and significant effect of Knowledge metrics of the Brand equity, i.e., Brand Awareness and Brand Association, on creation of Brand Attachment and Brand Attitude Strength and this factor becomes more effectual while introducing and promoting new brands. Finding of this research imply that for achieving desirable outcome through creation of Brand attachment and Brand Attitude Strength n the target audience and for designing more effective and fruitful strategies, managers and policy makers should pay more focus on creating strong Knowledge metrics amongst the target audience.
Hofer's metrics and boundary depth
Usher, Michael
2011-01-01
We show that if (M,\\omega) is a closed symplectic manifold which admits a nontrivial Hamiltonian vector field all of whose contractible closed orbits are constant, then Hofer's metric on the group of Hamiltonian diffeomorphisms of (M,\\omega) has infinite diameter, and indeed admits infinite-dimensional quasi-isometrically embedded normed vector spaces. A similar conclusion applies to Hofer's metric on various spaces of Lagrangian submanifolds, including those Hamiltonian-isotopic to the diagonal in M x M when M satisfies the above dynamical condition. To prove this, we use the properties of a Floer-theoretic quantity called the boundary depth, which measures the nontriviality of the boundary operator on the Floer complex in a way that encodes robust symplectic-topological information.
Clariana, Roy B.; Engelmann, Tanja; Yu, Wu
2013-01-01
Problem solving likely involves at least two broad stages, problem space representation and then problem solution (Newell and Simon, Human problem solving, 1972). The metric centrality that Freeman ("Social Networks" 1:215-239, 1978) implemented in social network analysis is offered here as a potential measure of both. This development research…
Measuring distance “as the horse runs”: Cross-scale comparison of terrain-based metrics
Buttenfield, Barbara P.; Ghandehari, M; Leyk, S; Stanislawski, Larry V.; Brantley, M E; Qiang, Yi
2016-01-01
Distance metrics play significant roles in spatial modeling tasks, such as flood inundation (Tucker and Hancock 2010), stream extraction (Stanislawski et al. 2015), power line routing (Kiessling et al. 2003) and analysis of surface pollutants such as nitrogen (Harms et al. 2009). Avalanche risk is based on slope, aspect, and curvature, all directly computed from distance metrics (Gutiérrez 2012). Distance metrics anchor variogram analysis, kernel estimation, and spatial interpolation (Cressie 1993). Several approaches are employed to measure distance. Planar metrics measure straight line distance between two points (“as the crow flies”) and are simple and intuitive, but suffer from uncertainties. Planar metrics assume that Digital Elevation Model (DEM) pixels are rigid and flat, as tiny facets of ceramic tile approximating a continuous terrain surface. In truth, terrain can bend, twist and undulate within each pixel.Work with Light Detection and Ranging (lidar) data or High Resolution Topography to achieve precise measurements present challenges, as filtering can eliminate or distort significant features (Passalacqua et al. 2015). The current availability of lidar data is far from comprehensive in developed nations, and non-existent in many rural and undeveloped regions. Notwithstanding computational advances, distance estimation on DEMs has never been systematically assessed, due to assumptions that improvements are so small that surface adjustment is unwarranted. For individual pixels inaccuracies may be small, but additive effects can propagate dramatically, especially in regional models (e.g., disaster evacuation) or global models (e.g., sea level rise) where pixels span dozens to hundreds of kilometers (Usery et al 2003). Such models are increasingly common, lending compelling reasons to understand shortcomings in the use of planar distance metrics. Researchers have studied curvature-based terrain modeling. Jenny et al. (2011) use curvature to generate
Deep space experiment to measure $G$
Feldman, Michael R; Schubert, Gerald; Trimble, Virginia; Kopeikin, Sergei; Lämmerzahl, Claus
2016-01-01
Responding to calls from the National Science Foundation (NSF) for new proposals to measure the gravitational constant $G$, we offer an interesting experiment in deep space employing the classic gravity train mechanism. Our setup requires three bodies: a larger layered solid sphere with a cylindrical hole through its center, a much smaller retroreflector which will undergo harmonic motion within the hole and a host spacecraft with laser ranging capabilities to measure round trip light-times to the retroreflector but ultimately separated a significant distance away from the sphere-retroreflector apparatus. Measurements of the period of oscillation of the retroreflector in terms of host spacecraft clock time using existing technology could give determinations of $G$ nearly three orders of magnitude more accurate than current measurements here on Earth. However, significant engineering advances in the release mechanism of the apparatus from the host spacecraft will likely be necessary. Issues with regard to the ...
Deusiano Florêncio dos Reis
2017-01-01
Full Text Available Generally, aquatic communities reflect the effects of anthropogenic changes such as deforestation or organic pollution. The Cerrado stands among the most threatened ecosystems by human activities in Brazil. In order to evaluate the ecological integrity of the streams in a preserved watershed in the Northern Cerrado biome corresponding to a mosaic of ecosystems in transition to the Amazonia biome in Brazil, biological metrics related to diversity, structure, and sensitivity of aquatic macroinvertebrates were calculated. Sampling included collections along stretches of 200 m of nine streams and measurements of abiotic variables (temperature, electrical conductivity, pH, total dissolved solids, dissolved oxygen, and discharge and the Index of Habitat Integrity (HII. The values of the abiotic variables and the HII indicated that most of the streams have good ecological integrity, due to high oxygen levels and low concentrations of dissolved solids and electric conductivity. Two streams showed altered HII scores mainly related to small dams for recreational and domestic use, use of Cerrado natural pasture for cattle raising, and spot deforestation in bathing areas. However, this finding is not reflected in the biological metrics that were used. Considering all nine streams, only two showed satisfactory ecological quality (measured by Biological Monitoring Working Party (BMWP, total richness, and EPT (Ephemeroptera, Plecoptera, and Trichoptera richness, only one of which had a low HII score. These results indicate that punctual measures of abiotic parameters do not reveal the long-term impacts of anthropic activities in these streams, including related fire management of pasture that annually alters the vegetation matrix and may act as a disturbance for the macroinvertebrate communities. Due to this, biomonitoring of low order streams in Cerrado ecosystems of the Northern Central Brazil by different biotic metrics and also physical attributes of the
dos Reis, Deusiano Florêncio; Salazar, Ayala Eduardo; Machado, Mayana Mendes Dias; Couceiro, Sheyla Regina Marques; de Morais, Paula Benevides
2017-01-01
Generally, aquatic communities reflect the effects of anthropogenic changes such as deforestation or organic pollution. The Cerrado stands among the most threatened ecosystems by human activities in Brazil. In order to evaluate the ecological integrity of the streams in a preserved watershed in the Northern Cerrado biome corresponding to a mosaic of ecosystems in transition to the Amazonia biome in Brazil, biological metrics related to diversity, structure, and sensitivity of aquatic macroinvertebrates were calculated. Sampling included collections along stretches of 200 m of nine streams and measurements of abiotic variables (temperature, electrical conductivity, pH, total dissolved solids, dissolved oxygen, and discharge) and the Index of Habitat Integrity (HII). The values of the abiotic variables and the HII indicated that most of the streams have good ecological integrity, due to high oxygen levels and low concentrations of dissolved solids and electric conductivity. Two streams showed altered HII scores mainly related to small dams for recreational and domestic use, use of Cerrado natural pasture for cattle raising, and spot deforestation in bathing areas. However, this finding is not reflected in the biological metrics that were used. Considering all nine streams, only two showed satisfactory ecological quality (measured by Biological Monitoring Working Party (BMWP), total richness, and EPT (Ephemeroptera, Plecoptera, and Trichoptera) richness), only one of which had a low HII score. These results indicate that punctual measures of abiotic parameters do not reveal the long-term impacts of anthropic activities in these streams, including related fire management of pasture that annually alters the vegetation matrix and may act as a disturbance for the macroinvertebrate communities. Due to this, biomonitoring of low order streams in Cerrado ecosystems of the Northern Central Brazil by different biotic metrics and also physical attributes of the riparian zone
Mirko Spiroski
2016-06-01
Conclusion: It is necessary to accept top twenty Macedonian biomedical scientists as an example of new metric that uses citation rates to measure influence at the article level, rather than qualification of the best Macedonian biomedical scientists.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of students interested in transportation, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational terminology,…
Metrics for Food Distribution.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of students interested in food distribution, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational…
Space weather monitoring with neutron monitor measurements
Steigies, Christian [Christian-Albrechts-Universitaet zu Kiel (Germany)
2013-07-01
Space Weather affects many areas of the modern society, advance knowledge about space weather events is important to protect personnel and infrastructure. Cosmic Rays (CR) measurements by ground-based Neutron Monitors are influenced by Coronal Mass Ejections (CME), the intensity of the ever present Cosmic Rays is reduced in a Forbush decrease (Fd). In the case of very energetic CMEs, the measured intensity can be significantly increased in a Ground Level Enhancement (GLE). By detecting the anisotropy of the CR environment, a CME can be detected hours before it arrives at Earth. During a GLE the high-energy particles from the Sun can be detected before the more abundant lower energy particles arrive at Earth, thus allowing to take protective measures. Since the beginning of the Neutron Monitor Database (NMDB) project, which has been started in 2008 with funding from the European Commission, real-time data from Neutron Monitors around the world has been made available through one web-portal. We have more than doubled the number of stations providing data since the start of the project to now over 30 stations. The effectiveness of the ALERT applications which are based on NMDB data has been shown by the recent GLE71. We present different applications through which the measurements and different data products are accessible.
Measurement and Analysis of Test Suite Volume Metrics for Regression Testing
S Raju
2014-01-01
Full Text Available Regression testing intends to ensure that a software applications works as specified after changes made to it during maintenance. It is an important phase in software development lifecycle. Regression testing is the re-execution of some subset of test cases that has already been executed. It is an expensive process used to detect defects due to regressions. Regression testing has been used to support software-testing activities and assure acquiring an appropriate quality through several versions of a software product during its development and maintenance. Regression testing assures the quality of modified applications. In this proposed work, a study and analysis of metrics related to test suite volume was undertaken. It was shown that the software under test needs more test cases after changes were made to it. A comparative analysis was performed for finding the change in test suite size before and after the regression test.
Detection and Measurement of Snowfall from Space
Elsa Cattani
2011-01-01
Full Text Available Snowfall detection and measurement represent highly difficult problems in modern hydrometeorology. Ground measurements are complicated due to detection technology limitations, snow drift and accumulation issues, and error definition. The snowfall detection from space is in turn affected by all detection limitations that characterize the measurement of rainfall with the addition of several complications, such as the indirect character of remote sensing precipitation estimation, the presence of frozen or snow-covered terrain, and the unknown vertical distribution of hydrometeors in the cloud column. Several methods for the retrieval of snowfall intensity from satellite have been proposed in recent times using passive and active sensors. No satisfactory answer to the general problem of quantitative snowfall intensity determination has been found to date, but several studies contribute to delineate a working framework for the future operational retrieval algorithms.
Degenerate pseudo-Riemannian metrics
Hervik, Sigbjorn; Yamamoto, Kei
2014-01-01
In this paper we study pseudo-Riemannian spaces with a degenerate curvature structure i.e. there exists a continuous family of metrics having identical polynomial curvature invariants. We approach this problem by utilising an idea coming from invariant theory. This involves the existence of a boost, the existence of this boost is assumed to extend to a neighbourhood. This approach proves to be very fruitful: It produces a class of metrics containing all known examples of degenerate metrics. To date, only Kundt and Walker metrics have been given, however, our study gives a plethora of examples showing that degenerate metrics extend beyond the Kundt and Walker examples. The approach also gives a useful criterion for a metric to be degenerate. Specifically, we use this to study the subclass of VSI and CSI metrics (i.e., spaces where polynomial curvature invariants are all vanishing or constants, respectively).
On the importance of metrics in practical applications
Joan-Gerard Camarena
2011-06-01
Full Text Available Students motivation for learning mathematical concepts can be increased when showing the usefulness of these concepts in practical problems. One important mathematical concept is the concept of metric space and, more related to the applications, the concept of metric function. In this work we aim to illustrate how important is to appropriately choose the metric when dealing with a practical problem. In particular, we focus on the problem of detection of noisy pixels in colour images. In this context, it is very important to appropriately measure the distances and similarities between the image pixels, which is done by means of an appropriate metric. We study the performance of different metrics, including recent fuzzy metrics, within a specific filter to show that it is indeed a critical choice to appropriately solve the task.
Proposing Metrics for Benchmarking Novel EEG Technologies Towards Real-World Measurements
Oliveira, Anderson S.; Schlink, Bryan R.; Hairston, W. David; König, Peter; Ferris, Daniel P.
2016-01-01
Recent advances in electroencephalographic (EEG) acquisition allow for recordings using wet and dry sensors during whole-body motion. The large variety of commercially available EEG systems contrasts with the lack of established methods for objectively describing their performance during whole-body motion. Therefore, the aim of this study was to introduce methods for benchmarking the suitability of new EEG technologies for that context. Subjects performed an auditory oddball task using three different EEG systems (Biosemi wet—BSM, Cognionics Wet—Cwet, Conionics Dry—Cdry). Nine subjects performed the oddball task while seated and walking on a treadmill. We calculated EEG epoch rejection rate, pre-stimulus noise (PSN), signal-to-noise ratio (SNR) and EEG amplitude variance across the P300 event window (CVERP) from a subset of 12 channels common to all systems. We also calculated test-retest reliability and the subject’s level of comfort while using each system. Our results showed that using the traditional 75 μV rejection threshold BSM and Cwet epoch rejection rates are ~25% and ~47% in the seated and walking conditions respectively. However, this threshold rejects ~63% of epochs for Cdry in the seated condition and excludes 100% of epochs for the majority of subjects during walking. BSM showed predominantly no statistical differences between seated and walking condition for all metrics, whereas Cwet showed increases in PSN and CVERP, as well as reduced SNR in the walking condition. Data quality from Cdry in seated conditions were predominantly inferior in comparison to the wet systems. Test-retest reliability was mostly moderate/good for these variables, especially in seated conditions. In addition, subjects felt less discomfort and were motivated for longer recording periods while using wet EEG systems in comparison to the dry system. The proposed method was successful in identifying differences across systems that are mostly caused by motion
Proposing Metrics for Benchmarking Novel EEG Technologies Towards Real-World Measurements.
Oliveira, Anderson S; Schlink, Bryan R; Hairston, W David; König, Peter; Ferris, Daniel P
2016-01-01
Recent advances in electroencephalographic (EEG) acquisition allow for recordings using wet and dry sensors during whole-body motion. The large variety of commercially available EEG systems contrasts with the lack of established methods for objectively describing their performance during whole-body motion. Therefore, the aim of this study was to introduce methods for benchmarking the suitability of new EEG technologies for that context. Subjects performed an auditory oddball task using three different EEG systems (Biosemi wet-BSM, Cognionics Wet-Cwet, Conionics Dry-Cdry). Nine subjects performed the oddball task while seated and walking on a treadmill. We calculated EEG epoch rejection rate, pre-stimulus noise (PSN), signal-to-noise ratio (SNR) and EEG amplitude variance across the P300 event window (CVERP) from a subset of 12 channels common to all systems. We also calculated test-retest reliability and the subject's level of comfort while using each system. Our results showed that using the traditional 75 μV rejection threshold BSM and Cwet epoch rejection rates are ~25% and ~47% in the seated and walking conditions respectively. However, this threshold rejects ~63% of epochs for Cdry in the seated condition and excludes 100% of epochs for the majority of subjects during walking. BSM showed predominantly no statistical differences between seated and walking condition for all metrics, whereas Cwet showed increases in PSN and CVERP, as well as reduced SNR in the walking condition. Data quality from Cdry in seated conditions were predominantly inferior in comparison to the wet systems. Test-retest reliability was mostly moderate/good for these variables, especially in seated conditions. In addition, subjects felt less discomfort and were motivated for longer recording periods while using wet EEG systems in comparison to the dry system. The proposed method was successful in identifying differences across systems that are mostly caused by motion-related artifacts and
Nyflot, MJ; Kusano, AS; Zeng, J; Carlson, JC; Novak, A; Sponseller, P; Jordan, L; Kane, G; Ford, EC [University of Washington, Seattle, WA (United States)
2014-06-15
Purpose: Interest in incident learning systems (ILS) for improving safety and quality in radiation oncology is growing, as evidenced by the upcoming release of the national ILS. However, an institution implementing such a system would benefit from quantitative metrics to evaluate performance and impact. We developed metrics to measure volume of reporting, severity of reported incidents, and changes in staff attitudes over time from implementation of our institutional ILS. Methods: We analyzed 2023 incidents from our departmental ILS from 2/2012–2/2014. Incidents were prospectively assigned a near-miss severity index (NMSI) at multidisciplinary review to evaluate the potential for error ranging from 0 to 4 (no harm to critical). Total incidents reported, unique users reporting, and average NMSI were evaluated over time. Additionally, departmental safety attitudes were assessed through a 26 point survey adapted from the AHRQ Hospital Survey on Patient Safety Culture before, 12 months, and 24 months after implementation of the incident learning system. Results: Participation in the ILS increased as demonstrated by total reports (approximately 2.12 additional reports/month) and unique users reporting (0.51 additional users reporting/month). Also, the average NMSI of reports trended lower over time, significantly decreasing after 12 months of reporting (p<0.001) but with no significant change at months 18 or 24. In survey data significant improvements were noted in many dimensions, including perceived barriers to reporting incidents such as concern of embarrassment (37% to 18%; p=0.02) as well as knowledge of what incidents to report, how to report them, and confidence that these reports were used to improve safety processes. Conclusion: Over a two-year period, our departmental ILS was used more frequently, incidents became less severe, and staff confidence in the system improved. The metrics used here may be useful for other institutions seeking to create or evaluate
Use of performance metrics for the measurement of universal coverage for maternal care in Mexico.
Serván-Mori, Edson; Contreras-Loya, David; Gomez-Dantés, Octavio; Nigenda, Gustavo; Sosa-Rubí, Sandra G; Lozano, Rafael
2017-01-20
This study provides evidence for those working in the maternal health metrics and health system performance fields, as well as those interested in achieving universal and effective health care coverage. Based on the perspective of continuity of health care and applying quasi-experimental methods to analyse the cross-sectional 2009 National Demographic Dynamics Survey (n = 14 414 women), we estimated the middle-term effects of Mexico's new public health insurance scheme, Seguro Popular de Salud (SPS) (vs women without health insurance) on seven indicators related to maternal health care (according to official guidelines): (a) access to skilled antenatal care (ANC); (b) timely ANC; (c) frequent ANC; (d) adequate content of ANC; (e) institutional delivery; (f) postnatal consultation and (g) access to standardized comprehensive antenatal and postnatal care (or the intersection of the seven process indicators). Our results show that 94% of all pregnancies were attended by trained health personnel. However, comprehensive access to ANC declines steeply in both groups as we move along the maternal healthcare continuum. The percentage of institutional deliveries providing timely, frequent and adequate content of ANC reached 70% among SPS women (vs 64.7% in the uninsured), and only 57.4% of SPS-affiliated women received standardized comprehensive care (vs 53.7% in the uninsured group). In Mexico, access to comprehensive antenatal and postnatal care as defined by Mexican guidelines (in accordance to WHO recommendations) is far from optimal. Even though a positive influence of SPS on maternal care was documented, important challenges still remain. Our results identified key bottlenecks of the maternal healthcare continuum that should be addressed by policy makers through a combination of supply side interventions and interventions directed to social determinants of access to health care.
Holographic Spherically Symmetric Metrics
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.
Barreira, Tiago V; Harrington, Deirdre M; Katzmarzyk, Peter T
2014-01-01
To determine whether relationships exist between accelerometer-measured moderate-to-vigorous physical activity (MVPA) and other cardiovascular (CV) health metrics in a large sample. Data from the 2003-2006 National Health and Nutrition Examination Survey (NHANES) collected from January 1, 2003, through December 31, 2006, were used. Overall, 3454 nonpregnant adults 20 years or older who fasted for 6 hours or longer, with valid accelerometer data and with CV health metrics, were included in the study. Blood pressure (BP), body mass index (BMI), smoking status, diet, fasting plasma glucose level, and total cholesterol level were defined as ideal, intermediate, and poor on the basis of American Heart Association criteria. Results were weighted to account for sampling design, oversampling, and nonresponse. Significant increasing linear trends in mean daily MVPA were observed across CV health levels for BMI, BP, and fasting plasma glucose (Pfasting plasma glucose level had significantly lower mean daily MVPA than individuals at the ideal levels (Pphysical activity in the overall definition of ideal CV health. Copyright © 2014 Mayo Foundation for Medical Education and Research. Published by Elsevier Inc. All rights reserved.
Measurement of Phase Coherence in Space Turbulence
Belmont, G.; Panis, J.; Rezeau, L.; Sahraoui, F.
2008-12-01
In many space plasmas such as Magnetosheath, intense magnetic fluctuations are permanently observed, with power law spectra. Assuming these fluctuations belong to some kind of turbulence, which can legitimately be suspected, spectra are clearly not sufficient to characterize it. Is this turbulence made of non linear "phase-coherent" structures, like in the classical Kolmogorov image, or is it made of incoherent waves as in weak turbulence? Is it homogeneous in space and scales or is it intermittent? " Many methods allow analyzing the statistical properties of turbulence, and the results obtained by tools such as structure functions or wavelets are of course influenced by all these properties, such providing indirect information about them. But few of them are specifically dedicated to the study of phase coherence so that the consequences that can be inferred from them are generally not univocal for this point of view. We will review those few tools existing in the literature that allow measuring more directly the phase coherence and present a new method, called "phase gradient analysis", which we are presently developing for this analysis. Preliminary results of this new tool will be presented.
K. P. R. Sastry
2013-03-01
Full Text Available In this paper, we obtain sufficient conditions for the existence of unique point of coincidence for a pair of self maps on a cone metric space satisfying certain control conditions. These results improve the fixed point theorem of Razani.et.al.[8] imposing conditions such as the cone is a lattice or lattice ordered semigroup and introducing two new control functions namely B. C. control function and S.B.C control function. An open problem is also given at the end for further investigation.
Balvín, Radek
2013-01-01
With growing amount of data produced by users on social media the need of extraction of relevant data for marketing, research and other uses grows as well. The bachelor thesis named "Social media metrics" presents the issues of monitoring, measurement and metrics of social media. In the research part it also maps and captures the present Czech practice in measurement and monitoring of social media. I also rate the use of social media monitoring tools and usual methods of social media measurem...
Measuring the report card: the validity of pay-for-performance metrics in orthopedic surgery.
Bhattacharyya, Timothy; Freiberg, Andrew A; Mehta, Priyesh; Katz, Jeffrey Neil; Ferris, Timothy
2009-01-01
To assess the validity of performance measures used in a nationwide pay-for-performance (P4P) project on hip and knee replacement, we analyzed hospital performance data from a Medicare P4P initiative and compared them to publicly available outcomes data. Overall, the ability to measure hospital quality was poor. A hospital's ranking on the composite score was primarily determined by process measures. A higher composite quality score was not associated with lower rates of complications or mortality. The current Medicare P4P quality measure has limited validity because of poor discrimination, lack of measure balance, and lack of correlation with important clinical outcomes.
Relationship of lenghts and angles in the classical logic metric space%经典逻辑度量空间中的边角关系
胡明娣; 楼志刚
2011-01-01
Aim To investigate the intrinsic structure of the classical logic metric space, discuss the structure of equilateral triangles and related properties. Methods The metric function proposed in quantitative logic was used as basic tool to develop computations. Results It is proved that there are some special graphs like Equilateral polygons and right triangles in the classical logic metric space. It is proved that there does not exist any equilateral triangle with length of 2/3 or more than 2/3, but there exist abundance of equilateral triangles with length arbitrarily close to 2/3. There exists an isometric reflexion transform and parallel trnsform which preserve the character of the equilateral triangle unchanged on the Lindenbaum algebras. Lastly, it is proved that, in the classical logic metric space, the values of cosine of an inside angle of a triangle constituted by three logic formulaes is dense in the unit interval [ 0,1 ], i.e. , the degree of the inside angles of triangles is dense in [ 0, π/2 ]. Conclusion In the classi cal logic metric space, there exist abundance of equilateral triangles with length arbitrarily close to 2/3 but there cloesn't exist any equilateral triangle with length of 2/3 or more than 2/3, and, both of the reflexion transform and the parallel transform can preserve the character of the equilateral triangle and the right triangle unchanged. The above conclusions lay the foundation for the studying of the basic structure of the classical logical metric space.%目的 研究逻辑度量空间的内蕴结构,讨论其中三角形的结构及相关性质.方法 利用计量逻辑学理论中建立的距离函数进行计算.结果 首先证明了在经典逻辑度量空间([F(S)],p)中存在等边多边形,直角三角形等特殊图形.其次证明了不存在边长大于或等于2/3的等边三角形,但存在边长可任意接近2/3的等边三角形.同时证明了Lindenbaum代数上的反射变换(u)*和平移变换ηG保持等边三
Zexia Huang; Heping Wang
2015-01-01
In this paper, we study optimal recovery (reconstruction) of functions on the sphere in the average case setting.We obtain the asymptotic orders of average sampling numbers of a Sobolev space on the sphere with a Gaussian measure in the Lq(Sd−1) metric for 1≤q≤∞, and show that some worst-case asymptotically optimal algorithms are also asymptotically optimal in the average case setting in the Lq(Sd−1) metric for 1≤q≤∞.
2012-11-01
As the old 'publish or perish' adage is brought into question, additional research-impact indices, known as altmetrics, are offering new evaluation alternatives. But such metrics may need to adjust to the evolution of science publishing.
Space filling in the World Trade Web: measures and null models
Ruzzenenti, Franco; Garlaschelli, Diego; Basosi, Riccardo
2012-01-01
It is here proposed global and local, bynary and weighted measures of space filling, to detect the degree of stretching of a network within its embedding space. Measures are normalized indexes that vary from zero - a maximally shrunk network, to one -a maximally expanded network. We evaluated the indexes according to three different null models an propose an unbiased measure of network filling, suitable for confrontation of different (cross sectional) embedded networks or historical trends of the same network. We further develop a local measure of filling and thereby of vertex assortativity. Finally, we showed that in the WTW metric distances seem to have determined the links' allocation more than the present null models tend to have predicted and that this burden upon links has been changing in time. However, surprisingly, our analysis seems to indicate that during globalization the WTW expanded merely because of topology and contrary to expectations it actually shrunk.
Automatic Classification of Protein Structure Using the Maximum Contact Map Overlap Metric
Andonov, R.; Djidjev, H.; Klau, G.W.; Le Boudic-Jamin, M.; Wohlers, I.
2015-01-01
In this work, we propose a new distance measure for comparing two protein structures based on their contact map representations. We show that our novel measure, which we refer to as the maximum contact map overlap (max-CMO) metric, satisfies all properties of a metric on the space of protein represe
Kaat, Aaron J; Schalet, Benjamin D; Rutsohn, Joshua; Jensen, Roxanne E; Cella, David
2017-09-08
Measuring patient-reported outcomes (PROs) is becoming an integral component of quality improvement initiatives, clinical care, and research studies in cancer, including comparative effectiveness research. However, the number of PROs limits comparability across studies. Herein, the authors attempted to link the Functional Assessment of Cancer Therapy-General Physical Well-Being (FACT-G PWB) subscale with the Patient-Reported Outcomes Measurement Information System (PROMIS) Physical Function (PF) calibrated item bank. The also sought to augment a subset of the conceptually most similar FACT-G PWB items with PROMIS PF items to improve the linking. Baseline data from 5506 participants in the Measuring Your Health (MY-Health) study were used to identify the optimal items for linking FACT-G PWB with PROMIS PF. A mixed methods approach identified the optimal items for creating the 5-item FACT/PROMIS-PF5 scale. Both the linked and augmented relationships were cross-validated using the follow-up MY-Health data. A 5-item FACT-G PWB item subset was found to be optimal for linking with PROMIS PF. In addition, a 2-item subset, including only items that were conceptually very similar to the PROMIS item bank content, were augmented with 3 PROMIS PF items. This new FACT/PROMIS-PF5 provided superior score recovery. The PROMIS PF metric allows for the evaluation of the extent to which similar questionnaires can be linked and therefore expressed on the same metric. These results allow for the aggregation of existing data and provide an optimal measure for future studies wishing to use the FACT yet also report on the PROMIS PF metric. Cancer 2017. © 2017 American Cancer Society. © 2017 American Cancer Society.
Kilbourne, Amy M.; Farmer Teh, Carrie; Welsh, Deborah; Pincus, Harold Alan; Lasky, Elaine; Perron, Brian; Bauer, Mark S
2010-01-01
Objective We implemented a set of processes of care measures for bipolar disorder that reflect psychosocial, patient preference, and continuum of care approaches to mental health, and examined whether veterans with bipolar disorder receive care concordant with these practices. Method Data from medical record reviews were used to assess key processes of care for 433 VA mental health outpatients with bipolar disorder. Both composite and individual processes of care measures were ope...
Carney, Timothy Jay; Shea, Christopher Michael
2017-01-01
Public health informatics is an evolving domain in which practices constantly change to meet the demands of a highly complex public health and healthcare delivery system. Given the emergence of various concepts, such as learning health systems, smart health systems, and adaptive complex health systems, health informatics professionals would benefit from a common set of measures and capabilities to inform our modeling, measuring, and managing of health system "smartness." Here, we introduce the concepts of organizational complexity, problem/issue complexity, and situational awareness as three codependent drivers of smart public health systems characteristics. We also propose seven smart public health systems measures and capabilities that are important in a public health informatics professional's toolkit.
Measuring Success: Metrics that Link Supply Chain Management to Aircraft Readiness
2002-09-01
systems also do not provide broad or detailed calculations of supply chain response time. If a MALS wishes to measure Supply Chain Response Time, it...Summary and Cockpit Chart Graphic (from Ref. 30) 114 30 tmdl wuc3 creqs oreqs new tdays sfill acwt tier_1% wrt difm wra_bcm_pc bcm_pc bcm1_pc
R&D performance measurement: more than choosing a set of metrics
Kerssens-van Drongelen, I.C.; Bilderbeek, J.
1999-01-01
In this article the results are presented of an empirical study focusing on the effectiveness of R&D performance measurement practices in the Netherlands. First, a theoretical examination of the subject ‘R&D performance measurement’ is given within the context of performance control. A distinction
Geometry of manifolds with area metric: Multi-metric backgrounds
Schuller, Frederic P. [Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo N2L 2Y5 (Canada) and Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, A. Postal 70-543, Mexico D.F. 04510 (Mexico)]. E-mail: fschuller@perimeterinstitute.ca; Wohlfarth, Mattias N.R. [II. Institut fuer Theoretische Physik, Universitaet Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)]. E-mail: mattias.wohlfarth@desy.de
2006-07-24
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings, and is considerably more general than Lorentzian geometry. Our construction of geometrically relevant objects, such as an area metric compatible connection and derived tensors, makes essential use of a decomposition theorem due to Gilkey, whereby we generate the area metric from a finite collection of metrics. Employing curvature invariants for multi-metric backgrounds we devise a class of gravity theories with inherently stringy character, and discuss gauge matter actions.
Amaya L Bustinduy
2011-07-01
Full Text Available To date, there has been no standardized approach to the assessment of aerobic fitness among children who harbor parasites. In quantifying the disability associated with individual or multiple chronic infections, accurate measures of physical fitness are important metrics. This is because exercise intolerance, as seen with anemia and many other chronic disorders, reflects the body's inability to maintain adequate oxygen supply (VO(2 max to the motor tissues, which is frequently linked to reduced quality-of-life in terms of physical and job performance. The objective of our study was to examine the associations between polyparasitism, anemia, and reduced fitness in a high risk Kenyan population using novel implementation of the 20-meter shuttle run test (20mSRT, a well-standardized, low-technology physical fitness test.Four villages in coastal Kenya were surveyed during 2009-2010. Children 5-18 years were tested for infection with Schistosoma haematobium (Sh, malaria, filaria, and geohelminth infections by standard methods. After anthropometric and hemoglobin testing, fitness was assessed with the 20 mSRT. The 20 mSRT proved easy to perform, requiring only minimal staff training. Parasitology revealed high prevalence of single and multiple parasitic infections in all villages, with Sh being the most common (25-62%. Anemia prevalence was 45-58%. Using multiply-adjusted linear modeling that accounted for household clustering, decreased aerobic capacity was significantly associated with anemia, stunting, and wasting, with some gender differences.The 20 mSRT, which has excellent correlation with VO(2, is a highly feasible fitness test for low-resource settings. Our results indicate impaired fitness is common in areas endemic for parasites, where, at least in part, low fitness scores are likely to result from anemia and stunting associated with chronic infection. The 20 mSRT should be used as a common metric to quantify physical fitness and compare sub
Charlton, Bruce G
2007-01-01
The Nobel prize for medicine or physiology, the Lasker award for clinical medicine, and the Gairdner international award are given to individuals for their role in developing theories, technologies and discoveries which have changed the direction of biomedical science. These distinctions have been used to develop an NLG metric to measure research performance and trends in 'revolutionary' biomedical science with the aim of identifying the premier revolutionary science research institutions and nations from 1992-2006. I have previously argued that the number of Nobel laureates in the biomedical field should be expanded to about nine per year and the NLG metric attempts to predict the possible results of such an expansion. One hundred and nineteen NLG prizes and awards were made during the past fifteen years (about eight per year) when overlapping awards had been removed. Eighty-five were won by the USA, revealing a massive domination in revolutionary biomedical science by this nation; the UK was second with sixteen awards; Canada had five, Australia four and Germany three. The USA had twelve elite centres of revolutionary biomedical science, with University of Washington at Seattle and MIT in first position with six awards and prizes each; Rockefeller University and Caltech were jointly second placed with five. Surprisingly, Harvard University--which many people rank as the premier world research centre--failed to reach the threshold of three prizes and awards, and was not included in the elite list. The University of Oxford, UK, was the only institution outside of the USA which featured as a significant centre of revolutionary biomedical science. Long-term success at the highest level of revolutionary biomedical science (and probably other sciences) probably requires a sufficiently large number of individually-successful large institutions in open competition with one another--as in the USA. If this model cannot be replicated within smaller nations, then it implies
Space Particle Hazard Measurement and Modeling
2016-09-01
launch in 2012. Key Publication: • [54] ISO Standard 11221 Space Systems – Space Solar Panels – Spacecraft Charging Induced - Electrostatic...plasma [71]. Completed charge testing on 3 solar panel cover glass replacement candidates developed by the Advanced Space Power program in AFRL/RVS...of Lifetimes Against Pitch Angle Diffusion, J. Atmos. Solar -Terr. Phys., 71, 1647, doi:10.1016/j.jastp.2008.07.004, 2009. [18] Meredith, N. P., et
Microcomputer-based tests for repeated-measures: Metric properties and predictive validities
Kennedy, Robert S.; Baltzley, Dennis R.; Dunlap, William P.; Wilkes, Robert L.; Kuntz, Lois-Ann
1989-01-01
A menu of psychomotor and mental acuity tests were refined. Field applications of such a battery are, for example, a study of the effects of toxic agents or exotic environments on performance readiness, or the determination of fitness for duty. The key requirement of these tasks is that they be suitable for repeated-measures applications, and so questions of stability and reliability are a continuing, central focus of this work. After the initial (practice) session, seven replications of 14 microcomputer-based performance tests (32 measures) were completed by 37 subjects. Each test in the battery had previously been shown to stabilize in less than five 90-second administrations and to possess retest reliabilities greater than r = 0.707 for three minutes of testing. However, all the tests had never been administered together as a battery and they had never been self-administered. In order to provide predictive validity for intelligence measurement, the Wechsler Adult Intelligence Scale-Revised and the Wonderlic Personnel Test were obtained on the same subjects.
Kilbourne, Amy M.; Farmer, Carrie; Welsh, Deborah; Pincus, Harold Alan; Lasky, Elaine; Perron, Brian; Bauer, Mark S.
2011-01-01
Objective We implemented a set of processes of care measures for bipolar disorder that reflect psychosocial, patient preference, and continuum of care approaches to mental health, and examined whether veterans with bipolar disorder receive care concordant with these practices. Method Data from medical record reviews were used to assess key processes of care for 433 VA mental health outpatients with bipolar disorder. Both composite and individual processes of care measures were operationalized. Results Based on composite measures, 17% had documented assessment of psychiatric symptoms (e.g., psychotic, hallucinatory), 28% had documented patient treatment preferences (e.g., reasons for treatment discontinuation), 56% had documented substance abuse and psychiatric comorbidity assessment, and 62% had documentation of adequate cardiometabolic assessment. No-show visits were followed up 20% of the time and monitoring of weight gain was noted in only 54% of the patient charts. In multivariate analyses, history of homelessness (OR=1.61; 95% CI=1.05-2.46) and nonwhite race (OR=1.74; 95%CI=1.02-2.98) were associated with documentation of psychiatric symptoms and comorbidities, respectively. Conclusions Only half of patients diagnosed with bipolar disorder received care in accordance with clinical practice guidelines. High quality treatment of bipolar disorder includes not only adherence to treatment guidelines but also patient-centered care processes. PMID:21112457
Learning Sequence Neighbourhood Metrics
Bayer, Justin; van der Smagt, Patrick
2011-01-01
Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector space of arbitrary dimensionality. Subsequently, the resulting features are meaningful and can be used for visualization or nearest neighbour classification in linear time. This kind of metric learning for sequential data enables the use of algorithms tailored towards fixed length vector spaces such as R^n.
Douglas, M R; Lukic, S; Reinbacher, R; Douglas, Michael R.; Karp, Robert L.; Lukic, Sergio; Reinbacher, Rene
2006-01-01
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.
Vortices as degenerate metrics
Baptista, J M
2012-01-01
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as degenerate hermitian metrics that satisfy a certain curvature equation. Using this viewpoint, we rephrase standard results about vortices and make some new observations. We note the existence of a conceptually simple, non-linear rule for superposing vortex solutions, and we describe the natural behaviour of the L^2-metric on the moduli space upon certain restrictions.
Canonical metrics on complex manifold
YAU Shing-Tung
2008-01-01
@@ Complex manifolds are topological spaces that are covered by coordinate charts where the Coordinate changes are given by holomorphic transformations. For example, Riemann surfaces are one dimensional complex manifolds. In order to understand complex manifolds, it is useful to introduce metrics that are compatible with the complex structure. In general, we should have a pair (M, ds2M) where ds2M is the metric. The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries. Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Canonical metrics on complex manifold
YAU; Shing-Tung(Yau; S.-T.)
2008-01-01
Complex manifolds are topological spaces that are covered by coordinate charts where the coordinate changes are given by holomorphic transformations.For example,Riemann surfaces are one dimensional complex manifolds.In order to understand complex manifolds,it is useful to introduce metrics that are compatible with the complex structure.In general,we should have a pair(M,ds~2_M)where ds~2_M is the metric.The metric is said to be canonical if any biholomorphisms of the complex manifolds are automatically isometries.Such metrics can naturally be used to describe invariants of the complex structures of the manifold.
Schultz, Benjamin G.; Stevens, Catherine J.; Keller, Peter E.; Tillmann, Barbara
2013-01-01
Implicit learning (IL) occurs unconsciously and without intention. Perceptual fluency is the ease of processing elicited by previous exposure to a stimulus. It has been assumed that perceptual fluency is associated with IL. However, the role of perceptual fluency following IL has not been investigated in temporal pattern learning. Two experiments by Schultz, Stevens, Keller, and Tillmann demonstrated the IL of auditory temporal patterns using a serial reaction-time task and a generation task based on the process dissociation procedure. The generation task demonstrated that learning was implicit in both experiments via motor fluency, that is, the inability to suppress learned information. With the aim to disentangle conscious and unconscious processes, we analyze unreported recognition data associated with the Schultz et al. experiments using the sequence identification measurement model. The model assumes that perceptual fluency reflects unconscious processes and IL. For Experiment 1, the model indicated that conscious and unconscious processes contributed to recognition of temporal patterns, but that unconscious processes had a greater influence on recognition than conscious processes. In the model implementation of Experiment 2, there was equal contribution of conscious and unconscious processes in the recognition of temporal patterns. As Schultz et al. demonstrated IL in both experiments using a generation task, and the conditions reported here in Experiments 1 and 2 were identical, two explanations are offered for the discrepancy in model and behavioral results based on the two tasks: 1) perceptual fluency may not be necessary to infer IL, or 2) conscious control over implicitly learned information may vary as a function of perceptual fluency and motor fluency. PMID:24086461
Benjamin G Schultz
Full Text Available Implicit learning (IL occurs unconsciously and without intention. Perceptual fluency is the ease of processing elicited by previous exposure to a stimulus. It has been assumed that perceptual fluency is associated with IL. However, the role of perceptual fluency following IL has not been investigated in temporal pattern learning. Two experiments by Schultz, Stevens, Keller, and Tillmann demonstrated the IL of auditory temporal patterns using a serial reaction-time task and a generation task based on the process dissociation procedure. The generation task demonstrated that learning was implicit in both experiments via motor fluency, that is, the inability to suppress learned information. With the aim to disentangle conscious and unconscious processes, we analyze unreported recognition data associated with the Schultz et al. experiments using the sequence identification measurement model. The model assumes that perceptual fluency reflects unconscious processes and IL. For Experiment 1, the model indicated that conscious and unconscious processes contributed to recognition of temporal patterns, but that unconscious processes had a greater influence on recognition than conscious processes. In the model implementation of Experiment 2, there was equal contribution of conscious and unconscious processes in the recognition of temporal patterns. As Schultz et al. demonstrated IL in both experiments using a generation task, and the conditions reported here in Experiments 1 and 2 were identical, two explanations are offered for the discrepancy in model and behavioral results based on the two tasks: 1 perceptual fluency may not be necessary to infer IL, or 2 conscious control over implicitly learned information may vary as a function of perceptual fluency and motor fluency.
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.
Frank H Durgin
2012-06-01
Full Text Available Athletes often give more accurate estimates of egocentric distance along the ground than do non-athletes. To explore whether cognitive calibration was accompanied by perceptual change, athletes and non-athletes made verbal height and distance estimates and also did a perceptual matching task between perceived egocentric distances and frontal vertical extents. Both groups were well calibrated for height estimation for poles viewed frontally, but athletes were much better calibrated at estimating longer egocentric distances (which are systematically underestimated by non-athletes. Athletes were more likely to have learned specific units of ground distance from relevant sports contexts. Both groups reported using human height as a metric for vertical extent. For non-athletes, verbal underestimation of ground distance corresponded to predictions based on perceptual matches between egocentric distances and vertical extents in conjunction with human-height-based verbal estimates of vertical extents. For athletes, the verbal scaling of egocentric distances of 10 m or more was more accurate and was not predicted by their egocentric distance matches to vertical extents.
Phantom metrics with Killing spinors
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.
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.
Measuring Intrinsic Curvature of Space with Electromagnetism
Mabin, Mason; Becker, Maria; Batelaan, Herman
2016-01-01
The concept of curved space is not readily observable in everyday life. The educational movie "Sphereland" attempts to illuminate the idea. The main character, a hexagon, has to go to great lengths to prove that her world is in fact curved. We present an experiment that demonstrates a new way to determine if a two-dimensional surface,…
Meanwell, Nicholas A
2016-04-18
-based application. In this review, after describing the background literature behind the derivation of efficiency metrics and approaches to assessing compound aesthetics, synopses of some recent practical application in lead optimization campaigns are presented. However, molecules that fall into space beyond that associated with traditional drug-like properties are an important part of the current and future landscape, exemplified by the summary of direct acting hepatitis C virus NS3 and NS5A inhibitors that have transformed clinical therapy for this chronic disease. While drug development in nontraditional drug-like space is more challenging and the rules for compound quality will be different with much still to be understood, careful and disciplined drug design practices will be an essential element of success.
Rainbow metric from quantum gravity
Assaniousssi, Mehdi; Lewandowski, Jerzy
2014-01-01
In this letter, we describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model. This idea is based on QFT on a quantum space-time. Under general assumptions, we discover that the quantum space-time on which the field propagates can be replaced by a classical space-time, whose metric depends explicitly on the energy of the field: as shown by an analysis of dispersion relations, quanta of different energy propagate on different metrics, similar to photons in a refractive material (hence the name "rainbow" used in the literature). In deriving this result, we do not consider any specific theory of quantum gravity: the qualitative behavior of high-energy particles on quantum space-time relies only on the assumption that the quantum space-time is described by a wave-function $\\Psi_o$ in a Hilbert space $\\mathcal{H}_G$.
Jackson, Brian A; Faith, Kay Sullivan
2013-02-01
Although significant progress has been made in measuring public health emergency preparedness, system-level performance measures are lacking. This report examines a potential approach to such measures for Strategic National Stockpile (SNS) operations. We adapted an engineering analytic technique used to assess the reliability of technological systems-failure mode and effects analysis-to assess preparedness. That technique, which includes systematic mapping of the response system and identification of possible breakdowns that affect performance, provides a path to use data from existing SNS assessment tools to estimate likely future performance of the system overall. Systems models of SNS operations were constructed and failure mode analyses were performed for each component. Linking data from existing assessments, including the technical assistance review and functional drills, to reliability assessment was demonstrated using publicly available information. The use of failure mode and effects estimates to assess overall response system reliability was demonstrated with a simple simulation example. Reliability analysis appears an attractive way to integrate information from the substantial investment in detailed assessments for stockpile delivery and dispensing to provide a view of likely future response performance.
Partial Reflection Spaced Antenna Wind Measurements
Fraser, G. J.
1984-01-01
The nature of partially reflecting (PR) irregularities is briefly reviewed and the techniques used in the PR spaced antenna method are discussed. The radars addressed use frequencies in the 2 to 6 MHz range operate in a pulse mode at vertical incidence. Radar system parameters including receiver dynamic range, coherent and incoherent detection, and post detection filtering are examined. Finally, data system parameters and real time analysis techniques are discussed.
Horowitz, Ariel I.; Moomaw, William R.; Liptzin, Daniel; Gramig, Benjamin M.; Reeling, Carson; Meyer, Johanna; Hurley, Kathleen
2016-06-01
Human alteration of the nitrogen cycle exceeds the safe planetary boundary for the use of reactive nitrogen (Nr). We complement global analysis by analyzing regional mass flows and the relative consequences of multiple chemical forms of Nr as they ‘cascade’ through multiple environmental media. The goals of this paper are (1) to identify the amounts of Nr that flow through a specific nitrogen rich region, (2) develop multiple metrics to characterize and compare multiple forms of Nr and the different damages that they cause, and (3) to use these metrics to assess the most societally acceptable and cost effective means for addressing the many dimensions of Nr damage. This paper uses a multiple metrics approach that in addition to mass flows considers economic damage, health and mitigation costs and qualitative damages to evaluate options for mitigating Nr flows in California’s San Joaquin Valley (SJV). Most analysis focuses attention on agricultural Nr because it is the largest flow in terms of mass. In contrast, the multiple metrics approach identifies mobile source Nr emissions as creating the most economic and health damage in the SJV. Emissions of Nr from mobile sources are smaller than those from crop agriculture and dairy in the SJV, but the benefits of abatement are greater because of reduced health impacts from air pollution, and abatement costs are lower. Our findings illustrate the benefit of a comprehensive multiple metrics approach to Nr management.
Engineering performance metrics
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.
Velocity-space sensitivity of neutron spectrometry measurements
Jacobsen, Asger Schou; Salewski, Mirko; Eriksson, J.;
2015-01-01
Neutron emission spectrometry (NES) measures the energies of neutrons produced in fusion reactions. Here we present velocity-space weight functions for NES and neutron yield measurements. Weight functions show the sensitivity as well as the accessible regions in velocity space for a given range...
Measuring Voting Power in Convex Policy Spaces
Sascha Kurz
2014-03-01
Full Text Available Classical power index analysis considers the individual’s ability to influence the aggregated group decision by changing its own vote, where all decisions and votes are assumed to be binary. In many practical applications we have more options than either “yes” or “no”. Here we generalize three important power indices to continuous convex policy spaces. This allows the analysis of a collection of economic problems like, e.g., tax rates or spending that otherwise would not be covered in binary models.
MEASURING ECONOMIC GROWTH FROM OUTER SPACE
Henderson, J. Vernon; Storeygard, Adam; Weil, David N.
2013-01-01
GDP growth is often measured poorly for countries and rarely measured at all for cities or subnational regions. We propose a readily available proxy: satellite data on lights at night. We develop a statistical framework that uses lights growth to augment existing income growth measures, under the assumption that measurement error in using observed light as an indicator of income is uncorrelated with measurement error in national income accounts. For countries with good national income accounts data, information on growth of lights is of marginal value in estimating the true growth rate of income, while for countries with the worst national income accounts, the optimal estimate of true income growth is a composite with roughly equal weights. Among poor-data countries, our new estimate of average annual growth differs by as much as 3 percentage points from official data. Lights data also allow for measurement of income growth in sub- and supranational regions. As an application, we examine growth in Sub Saharan African regions over the last 17 years. We find that real incomes in non-coastal areas have grown faster by 1/3 of an annual percentage point than coastal areas; non-malarial areas have grown faster than malarial ones by 1/3 to 2/3 annual percent points; and primate city regions have grown no faster than hinterland areas. Such applications point toward a research program in which “empirical growth” need no longer be synonymous with “national income accounts.” PMID:25067841
Measuring Intrinsic Curvature of Space with Electromagnetism
Mabin, Mason; Becker, Maria; Batelaan, Herman
2016-10-01
The concept of curved space is not readily observable in everyday life. The educational movie "Sphereland" attempts to illuminate the idea. The main character, a hexagon, has to go to great lengths to prove that her world is in fact curved. We present an experiment that demonstrates a new way to determine if a two-dimensional surface, the 2-sphere, is curved. The behavior of an electric field, placed on a spherical surface, is shown to be related to the intrinsic Gaussian curvature. This approach allows students to gain some understanding of Einstein's theory of general relativity, which relates the curvature of spacetime to the presence of mass and energy. Additionally, an opportunity is provided to investigate the dimensionality of Gauss's law.
1991-07-01
March 1979, pp. 121-128. Gorla, Narasimhaiah, Alan C. Benander, and Barbara A. Benander, "Debugging Effort Estimation Using Software Metrics", IEEE...Society, IEEE Guide for the Use of IEEE Standard Dictionary of Measures to Produce Reliable Software, IEEE Std 982.2-1988, June 1989. Jones, Capers
A field study on a 50-ha alfalfa (Medicago sativa L.) irrigated field was conducted to investigate the performance of the remote sensing (RS) based Mapping EvapoTranspiration at high Resolution with Internalized Calibration (METRIC) model in the estimation of evapotranspiration (ET) under the arid c...
Hussain, Husniza; Khalid, Norhayati Mustafa; Selamat, Rusidah; Wan Nazaimoon, Wan Mohamud
2013-09-01
The urinary iodine micromethod (UIMM) is a modification of the conventional method and its performance needs evaluation. UIMM performance was evaluated using the method validation and 2008 Iodine Deficiency Disorders survey data obtained from four urinary iodine (UI) laboratories. Method acceptability tests and Sigma quality metrics were determined using total allowable errors (TEas) set by two external quality assurance (EQA) providers. UIMM obeyed various method acceptability test criteria with some discrepancies at low concentrations. Method validation data calculated against the UI Quality Program (TUIQP) TEas showed that the Sigma metrics were at 2.75, 1.80, and 3.80 for 51±15.50 µg/L, 108±32.40 µg/L, and 149±38.60 µg/L UI, respectively. External quality control (EQC) data showed that the performance of the laboratories was within Sigma metrics of 0.85-1.12, 1.57-4.36, and 1.46-4.98 at 46.91±7.05 µg/L, 135.14±13.53 µg/L, and 238.58±17.90 µg/L, respectively. No laboratory showed a calculated total error (TEcalc)Sigma metrics at all concentrations. Only one laboratory had TEcalc
DeGroff, F. A.
2016-12-01
Anthropogenic changes to non-anthropogenic carbon fluxes are a primary driver of climate change. There currently exists no comprehensive metric to measure and value anthropogenic changes in carbon flux between all states of carbon. Focusing on atmospheric carbon emissions as a measure of anthropogenic activity on the environment ignores the fungible characteristics of carbon that are crucial in both the biosphere and the worldwide economy. Focusing on a single form of inorganic carbon as a proxy metric for the plethora of anthropogenic activity and carbon compounds will prove inadequate, convoluted, and unmanageable. A broader, more basic metric is needed to capture the entirety of carbon activity, particularly in an economic, profit-driven environment. We propose a new metric to measure changes in the temporal distance of any form or state of carbon from one state to another. Such a metric would be especially useful to measure the temporal distance of carbon from sinks such as the atmosphere or oceans. The effect of changes in carbon flux as a result of any human activity can be measured by the difference between the anthropogenic and non-anthropogenic temporal distance. The change in the temporal distance is a measure of the climate change potential much like voltage is a measure of electrical potential. The integral of the climate change potential is proportional to the anthropogenic climate change. We also propose a logarithmic vector scale for carbon quality, cq, as a measure of anthropogenic changes in carbon flux. The distance between the cq vector starting and ending temporal distances represents the change in cq. A base-10 logarithmic scale would allow the addition and subtraction of exponents to calculate changes in cq. As anthropogenic activity changes the temporal distance of carbon, the change in cq is measured as: cq = ß ( log10 [mean carbon temporal distance] ) where ß represents the carbon price coefficient for a particular country. For any
Visible Counterterrorism Measures in Urban Spaces
Dalgaard-Nielsen, Anja; Laisen, Jesper; Wandorf, Charlotte
2014-01-01
factors impacting positively or negatively on the feelings of safety of Danish citizens, when being in a crowded place. Surprisingly, the response to security measures like fences, cameras, and uniformed guards was positive. More visible security apparently reinforced feelings of safety. This article...
Orbiting Space Debris: Dangers, Measurement and Mitigation
1992-06-01
sure how many undetectable particles the fragmentation of a satellite creates. Actual ground-based tesis have been conducted in an attempt to...conducted by the Jet Propulsion Laboratory lo measure the presence of 0.2 lo 0.5 cm and 0.5 to 2 cm sized debris. The Areclbo radar in Puerto Rico
Induced measures in the space of mixed quantum states
Zyczkowski, Karol [Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warsaw, Poland and Instytut Fizyki, Uniwersytet Jagiellonski, Crakow (Poland)). E-mail: karol@cft.edu.pl; Sommers, Hans-Juergen [Fachbereich Physik, Universitaet-Gesamthochschule Essen, Essen (Germany)). E-mail: sommers@next30.theo-phys.uni-essen.de
2001-09-07
We analyse several product measures in the space of mixed quantum states. In particular, we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a NxK composite system, induces a unique measure in the space of NxN mixed states (or in the space of KxK mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of NxN pure states behaves as lnN-1/2. (author)
Induced measures in the space of mixed quantum states
Zyczkowski, K; Zyczkowski, Karol; Sommers, Hans-Juergen
2001-01-01
We analyze several product measures in the space of mixed quantum states. In particular we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure on the set of all pure states of a N x K composite system, induces a unique measure in the space of N x N mixed states (or in the space of K x K mixed states, if the reduction takes place with respect to the first subsystem). For K=N the induced measure is equal to the Hilbert-Schmidt measure, which is shown to coincide with the measure induced by singular values of non-Hermitian random Gaussian matrices pertaining to the Ginibre ensemble. We compute several averages with respect to this measure and show that the mean entanglement of $N \\times N$ pure states behaves as lnN-1/2.
Measuring Forest Height and Biomass from Space
Agueh, Temilola Elisabeth Fato
2013-01-01
Talk about doing earth science at NASA and how what we do is focus on the biosphere- that is the living portion of the earth.In particular, we are interested in looking at forests-quantifying deforestation, regrowth, change in general and helping develop new cutting-edge technologies and instruments to be able to measure these changes in land use, land cover and quality more accurately.
Metrics for Hard Goods Merchandising.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of students interested in hard goods merchandising, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational…
Metrics for Soft Goods Merchandising.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of students interested in soft goods merchandising, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational…
Conversion to the Metric System
Crunkilton, John C.; Lee, Jasper S.
1974-01-01
The authors discuss background information about the metric system and explore the effect of metrication of agriculture in areas such as equipment calibration, chemical measurement, and marketing of agricultural products. Suggestions are given for possible leadership roles and approaches that agricultural education might take in converting to the…
Metric Supplement to Technical Drawing.
Henschel, Mark
This manual is intended for use in training persons whose vocations involve technical drawing to use the metric system of measurement. It could be used in a short course designed for that purpose or for individual study. The manual begins with a brief discussion of the rationale for conversion to the metric system. It then provides a…
夏顺友
2013-01-01
利用抽象凸空间满足的H0条件和紧集的有限覆盖及与之相应的单位分解构造标准单纯形上的连续映射,从而由Brouwer不动点定理证明了抽象凸锥度量空间上具有邻域抽象凸值的锥度量上半连续集值映射的一个锥度量逼近连续选择定理,并由此得到具有邻域抽象凸值的锥度量上半连续集值映射的一个不动点定理,然后将此不动点定理应用于博弈论,通过构造锥度量上半连续最优反应集值映射得到抽象凸锥度量策略空间上的n人非合作广义博弈Nash平衡的一个存在性结果.%Constructing a continuity map on standard simplex by using H0 condition of abstract convex space and the partition of unity subordinate to the finite covering of a compact set,a cone metric approximate continuity selection for cone metric upper semi-continuous set-valued maps in abstract convex cone metric spaces is proved by employing Brouwer fixed point theorem.Then a fixed point theorem for cone metric upper semi-continuous maps is derived.As an application,constructing cone metric upper semi-continuous best reflect map,the existence of Nash equilibrium of n-person non-cooperative generalized game with abstract convex cone metric strategy space is proved.
Emittance Measurements of Space Charge Dominated Electron Beam.
2014-09-26
measurement 2,3 have been introduced in the past, especially in particle accelerator physics. In free space, the envelope of a non -neutral charged...density no and thickness 2d is located on the y-axis. Let us assume that the velocity space distribution is a Maxwellian with a temperature T and the beam
Candelas, Philip; McOrist, Jock
2016-01-01
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 alpha', 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 Ka...
Measuring Conflict Functions in Generalized Power Space
HU Lifang; GUAN Xin; DENG Yong; HAN Deqiang; HE You
2011-01-01
One of the most important open issues is that the classical conflict coefficient in D-S evidence theory (DST) cannot correctly determine the conflict degree between two pieces of evidence.This drawback greatly limits the use of DST in real application systems.Early researches mainly focused on the improvement of Dempster's rule of combination (DRC).However, the current research shows it is very important to define new conflict coefficients to determine the conflict degree between two or more pieces of evidence.The evidential sources of information are considered in this work and the definition of a conflict measure function (CMF) is proposed for selecting some useful CMFs in the next fusion work when sources are available at each instant.Firstly, the definition and theorems of CMF are put forward.Secondly, some typical CMFs are extended and then new CMFs are put forward.Finally, experiments illustrate that the CMF based on Jousselme and its similar ones are the best suited ones.
[The condition of crowding and spacing. Measuring or estimation?].
Reukers, H A; Kuijpers-Jagtman, A M; van 't Hof, M A
1994-10-01
Two methods for the assessment of the amount of crowding or spacing (measuring and assessment by eye) are compared. Both methods are well comparable and reproducible. Assessment by eye has the practical advantage that it takes considerable less time.
H\\"older continuity for Trudinger's equation in measure spaces
Kuusi, Tuomo; Siljander, Juhana; Urbano, José Miguel
2011-01-01
We complete the study of the regularity for Trudinger's equation by proving that weak solutions are H\\"older continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincar\\'e inequality. The proof uses the Harnack inequality and intrinsic scaling.
WSN-Based Space Charge Density Measurement System.
Deng, Dawei; Yuan, Haiwen; Lv, Jianxun; Ju, Yong
2017-01-01
It is generally acknowledged that high voltage direct current (HVDC) transmission line endures the drawback of large area, because of which the utilization of cable for space charge density monitoring system is of inconvenience. Compared with the traditional communication network, wireless sensor network (WSN) shows advantages in small volume, high flexibility and strong self-organization, thereby presenting great potential in solving the problem. Additionally, WSN is more suitable for the construction of distributed space charge density monitoring system as it has longer distance and higher mobility. A distributed wireless system is designed for collecting and monitoring the space charge density under HVDC transmission lines, which has been widely applied in both Chinese state grid HVDC test base and power transmission projects. Experimental results of the measuring system demonstrated its adaptability in the complex electromagnetic environment under the transmission lines and the ability in realizing accurate, flexible, and stable demands for the measurement of space charge density.
OPEN PUBLIC SPACE ATTRIBUTES AND CATEGORIES – COMPLEXITY AND MEASURABILITY
Ljiljana Čavić
2014-12-01
Full Text Available Within the field of architectural and urban research, this work addresses the complexity of contemporary public space, both in a conceptual and concrete sense. It aims at systematizing spatial attributes and their categories and discussing spatial complexity and measurability, all this in order to reach a more comprehensive understanding, description and analysis of public space. Our aim is to improve everyday usage of open public space and we acknowledged users as its crucial factor. There are numerous investigations on the complex urban and architectural reality of public space that recognise importance of users. However, we did not find any that would holistically account for what users find essential in public space. Based on the incompleteness of existing approaches on open public space and the importance of users for their success, this paper proposes a user-orientated approach. Through an initial survey directed to users, we collected the most important aspects of public spaces in the way that contemporary humans see them. The gathered data is analysed and coded into spatial attributes from which their role in the complexity of open public space and measurability are discussed. The work results in an inventory of attributes that users find salient in public spaces. It does not discuss their qualitative values or contribution in generating spatial realities. It aims to define them clearly so that any further logical argumentation on open space concerning users may be solidly constructed. Finally, through categorisation of attributes it proposes the disciplinary levels necessary for the analysis of complex urban-architectural reality
Reproducibility of graph metrics in fMRI networks
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.
SMOS: The Challenging Sea Surface Salinity Measurement From Space
Font, Jordi; Camps, Adriano; Borges, A; Martin-Neira, Manuel; Boutin, Jacqueline; Reul, Nicolas; Kerr, Yann; Hahne, A.; Mecklenburg, Suzanne
2010-01-01
Soil Moisture and Ocean Salinity, European Space Agency, is the first satellite mission addressing the challenge of measuring sea surface salinity from space. It uses an L-band microwave interferometric radiometer with aperture synthesis (MIRAS) that generates brightness temperature images, from which both geophysical variables are computed. The retrieval of salinity requires very demanding performances of the instrument in terms of calibration and stability. This paper highlights the importa...
Space camera optical axis pointing precision measurement system
Chen, Gang; Meng, Fanbo; Yang, Zijun; Guo, Yubo; Ye, Dong
2016-01-01
In order to realize the space camera which on satellite optical axis pointing precision measurement, a monocular vision measurement system based on object-image conjugate is established. In this system the algorithms such as object-image conjugate vision models and point by point calibration method are applied and have been verified. First, the space camera axis controller projects a laser beam to the standard screen for simulating the space camera's optical axis. The laser beam form a target point and has been captured by monocular vision camera. Then the two-dimensional coordinates of the target points on the screen are calculated by a new vision measurement model which based on a looking-up and matching table, the table has been generated by object-image conjugate algorithm through point by point calibration. Finally, compare the calculation of coordinates offered by measurement system with the theory of coordinate offered by optical axis controller, the optical axis pointing precision can be evaluated. Experimental results indicate that the absolute precision of measurement system up to 0.15mm in 2m×2m FOV. This measurement system overcome the nonlinear distortion near the edge of the FOV and can meet the requirement of space camera's optical axis high precision measurement and evaluation.
Metrics for Finite Markov Decision Processes
Ferns, Norman; Panangaden, Prakash; Precup, Doina
2012-01-01
We present metrics for measuring the similarity of states in a finite Markov decision process (MDP). The formulation of our metrics is based on the notion of bisimulation for MDPs, with an aim towards solving discounted infinite horizon reinforcement learning tasks. Such metrics can be used to aggregate states, as well as to better structure other value function approximators (e.g., memory-based or nearest-neighbor approximators). We provide bounds that relate our metric distances to the opti...
On-line phase space measurement with kicker excitation
Dietrich, J.; Maier, R.; Mohos, I.
1998-12-01
A new method for on-line phase space measurements with kicker excitation at COSY was developed. The position data were measured using the analog output of two beam position monitors (BPMs) and directly monitored on a digital storage oscilloscope with an external clock (bunch-synchronous sampling). Nonlinear behavior of the proton beam was visible as well as were resonance islands. Typical measurements are presented.
Cryogenic Thermal Conductivity Measurements on Candidate Materials for Space Missions
Tuttle, JIm; Canavan, Ed; Jahromi, Amir
2017-01-01
Spacecraft and instruments on space missions are built using a wide variety of carefully-chosen materials. In addition to having mechanical properties appropriate for surviving the launch environment, these materials generally must have thermal conductivity values which meet specific requirements in their operating temperature ranges. Space missions commonly propose to include materials for which the thermal conductivity is not well known at cryogenic temperatures. We developed a test facility in 2004 at NASAs Goddard Space Flight Center to measure material thermal conductivity at temperatures between 4 and 300 Kelvin, and we have characterized many candidate materials since then. The measurement technique is not extremely complex, but proper care to details of the setup, data acquisition and data reduction is necessary for high precision and accuracy. We describe the thermal conductivity measurement process and present results for several materials.
Heat kernel measures on random surfaces
Klevtsov, Semyon
2015-01-01
The heat kernel on the symmetric space of positive definite Hermitian matrices is used to endow the spaces of Bergman metrics of degree k on a Riemann surface M with a family of probability measures depending on a choice of the background metric. Under a certain matrix-metric correspondence, each positive definite Hermitian matrix corresponds to a Kahler metric on M. The one and two point functions of the random metric are calculated in a variety of limits as k and t tend to infinity. In the limit when the time t goes to infinity the fluctuations of the random metric around the background metric are the same as the fluctuations of random zeros of holomorphic sections. This is due to the fact that the random zeros form the boundary of the space of Bergman metrics.
Munasinghe, L.; Jun, T.; Rind, D. H.
2012-01-01
Consensus on global warming is the result of multiple and varying lines of evidence, and one key ramification is the increase in frequency of extreme climate events including record high temperatures. Here we develop a metric- called "record equivalent draws" (RED)-based on record high (low) temperature observations, and show that changes in RED approximate changes in the likelihood of extreme high (low) temperatures. Since we also show that this metric is independent of the specifics of the underlying temperature distributions, RED estimates can be aggregated across different climates to provide a genuinely global assessment of climate change. Using data on monthly average temperatures across the global landmass we find that the frequency of extreme high temperatures increased 10-fold between the first three decades of the last century (1900-1929) and the most recent decade (1999-2008). A more disaggregated analysis shows that the increase in frequency of extreme high temperatures is greater in the tropics than in higher latitudes, a pattern that is not indicated by changes in mean temperature. Our RED estimates also suggest concurrent increases in the frequency of both extreme high and extreme low temperatures during 2002-2008, a period when we observe a plateauing of global mean temperature. Using daily extreme temperature observations, we find that the frequency of extreme high temperatures is greater in the daily minimum temperature time-series compared to the daily maximum temperature time-series. There is no such observable difference in the frequency of extreme low temperatures between the daily minimum and daily maximum.
Security Metrics in Industrial Control Systems
Collier, Zachary A; Ganin, Alexander A; Kott, Alex; Linkov, Igor
2015-01-01
Risk is the best known and perhaps the best studied example within a much broader class of cyber security metrics. However, risk is not the only possible cyber security metric. Other metrics such as resilience can exist and could be potentially very valuable to defenders of ICS systems. Often, metrics are defined as measurable properties of a system that quantify the degree to which objectives of the system are achieved. Metrics can provide cyber defenders of an ICS with critical insights regarding the system. Metrics are generally acquired by analyzing relevant attributes of that system. In terms of cyber security metrics, ICSs tend to have unique features: in many cases, these systems are older technologies that were designed for functionality rather than security. They are also extremely diverse systems that have different requirements and objectives. Therefore, metrics for ICSs must be tailored to a diverse group of systems with many features and perform many different functions. In this chapter, we first...
Metric adjusted skew information
Hansen, Frank
2008-01-01
establish a connection between the geometrical formulation of quantum statistics as proposed by Chentsov and Morozova and measures of quantum information as introduced by Wigner and Yanase and extended in this article. We show that the set of normalized Morozova-Chentsov functions describing the possible...... quantum statistics is a Bauer simplex and determine its extreme points. We determine a particularly simple skew information, the "¿-skew information," parametrized by a ¿ ¿ (0, 1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations.......We extend the concept of Wigner-Yanase-Dyson skew information to something we call "metric adjusted skew information" (of a state with respect to a conserved observable). This "skew information" is intended to be a non-negative quantity bounded by the variance (of an observable in a state...
Linda Bennett
2013-07-01
Full Text Available Continuing purchase of AHSS resources is threatened more by library budget squeezes than that of STM resources. Librarians must justify all expenditure, but quantitative metrical analysis to assess the value to the institution of journals and specialized research databases for AHSS subjects can be inconclusive; often the number of recorded transactions is lower than for STM, as the resource may be relevant to a smaller number of users. This paper draws on a literature review and extensive primary research, including a survey of 570 librarians and academics across the Anglophone countries, findings from focus group meetings and the analysis of user behaviour at a UK university before and after the installation of the Summon discovery system. It concludes that providing a new approach to metrics can help to develop resources strategies that meet changing user needs; and that usage statistics can be complemented with supplementary ROI measures to make them more meaningful.
Recent measurements for hadrontherapy and space radiation: nuclear physics.
Miller, J
2001-01-01
The particles and energies commonly used for hadron therapy overlap the low end of the charge and energy range of greatest interest for space radiation applications, Z=1-26 and approximately 100-1000 MeV/nucleon. It has been known for some time that the nuclear interactions of the incident ions must be taken into account both in treatment planning and in understanding and addressing the effects of galactic cosmic ray ions on humans in space. Until relatively recently, most of the studies of nuclear fragmentation and transport in matter were driven by the interests of the nuclear physics and later, the hadron therapy communities. However, the experimental and theoretical methods and the accelerator facilities developed for use in heavy ion nuclear physics are directly applicable to radiotherapy and space radiation studies. I will briefly review relevant data taken recently at various accelerators, and discuss the implications of the measurements for radiotherapy, radiobiology and space radiation research.
Recent measurements for hadrontherapy and space radiation: nuclear physics
Miller, J.
2001-01-01
The particles and energies commonly used for hadron therapy overlap the low end of the charge and energy range of greatest interest for space radiation applications, Z=1-26 and approximately 100-1000 MeV/nucleon. It has been known for some time that the nuclear interactions of the incident ions must be taken into account both in treatment planning and in understanding and addressing the effects of galactic cosmic ray ions on humans in space. Until relatively recently, most of the studies of nuclear fragmentation and transport in matter were driven by the interests of the nuclear physics and later, the hadron therapy communities. However, the experimental and theoretical methods and the accelerator facilities developed for use in heavy ion nuclear physics are directly applicable to radiotherapy and space radiation studies. I will briefly review relevant data taken recently at various accelerators, and discuss the implications of the measurements for radiotherapy, radiobiology and space radiation research.
A Note on Discrete Einstein Metric
Ge, Huabin
2015-01-01
In this short note, we prove that the space of all admissible piecewise linear metrics parameterized by length square on a triangulated manifolds is a convex cone. We further study Regge's Einstein-Hilbert action and give a much more reasonable definition of discrete Einstein metric than our former version in \\cite{G}. Finally, we introduce a discrete Ricci flow for three dimensional triangulated manifolds, which is closely related to the existence of discrete Einstein metrics.
A unifying process capability metric
John Jay Flaig
2009-07-01
Full Text Available A new economic approach to process capability assessment is presented, which differs from the commonly used engineering metrics. The proposed metric consists of two economic capability measures – the expected profit and the variation in profit of the process. This dual economic metric offers a number of significant advantages over other engineering or economic metrics used in process capability analysis. First, it is easy to understand and communicate. Second, it is based on a measure of total system performance. Third, it unifies the fraction nonconforming approach and the expected loss approach. Fourth, it reflects the underlying interest of management in knowing the expected financial performance of a process and its potential variation.