Measuring fitness of Kenyan children with polyparasitic infections using the 20-meter shuttle run test as a morbidity metric.

Directory of Open Access Journals (Sweden)

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

FIT: Computer Program that Interactively Determines Polynomial Equations for Data which are a Function of Two Independent Variables

Science.gov (United States)

Arbuckle, P. D.; Sliwa, S. M.; Roy, M. L.; Tiffany, S. H.

1985-01-01

A computer program for interactively developing least-squares polynomial equations to fit user-supplied data is described. The program is characterized by the ability to compute the polynomial equations of a surface fit through data that are a function of two independent variables. The program utilizes the Langley Research Center graphics packages to display polynomial equation curves and data points, facilitating a qualitative evaluation of the effectiveness of the fit. An explanation of the fundamental principles and features of the program, as well as sample input and corresponding output, are included.

Parameter Search Algorithms for Microwave Radar-Based Breast Imaging: Focal Quality Metrics as Fitness Functions.

Science.gov (United States)

O'Loughlin, Declan; Oliveira, Bárbara L; Elahi, Muhammad Adnan; Glavin, Martin; Jones, Edward; Popović, Milica; O'Halloran, Martin

2017-12-06

Inaccurate estimation of average dielectric properties can have a tangible impact on microwave radar-based breast images. Despite this, recent patient imaging studies have used a fixed estimate although this is known to vary from patient to patient. Parameter search algorithms are a promising technique for estimating the average dielectric properties from the reconstructed microwave images themselves without additional hardware. In this work, qualities of accurately reconstructed images are identified from point spread functions. As the qualities of accurately reconstructed microwave images are similar to the qualities of focused microscopic and photographic images, this work proposes the use of focal quality metrics for average dielectric property estimation. The robustness of the parameter search is evaluated using experimental dielectrically heterogeneous phantoms on the three-dimensional volumetric image. Based on a very broad initial estimate of the average dielectric properties, this paper shows how these metrics can be used as suitable fitness functions in parameter search algorithms to reconstruct clear and focused microwave radar images.

Partner symmetries of the complex Monge-Ampere equation yield hyper-Kaehler metrics without continuous symmetries

International Nuclear Information System (INIS)

Malykh, A A; Nutku, Y; Sheftel, M B

2003-01-01

We extend the Mason-Newman Lax pair for the elliptic complex Monge-Ampere equation so that this equation itself emerges as an algebraic consequence. We regard the function in the extended Lax equations as a complex potential. Their differential compatibility condition coincides with the determining equation for the symmetries of the complex Monge-Ampere equation. We shall identify the real and imaginary parts of the potential, which we call partner symmetries, with the translational and dilatational symmetry characteristics, respectively. Then we choose the dilatational symmetry characteristic as the new unknown replacing the Kaehler potential. This directly leads to a Legendre transformation. Studying the integrability conditions of the Legendre-transformed system we arrive at a set of linear equations satisfied by a single real potential. This enables us to construct non-invariant solutions of the Legendre transform of the complex Monge-Ampere equation. Using these solutions we obtained explicit Legendre-transformed hyper-Kaehler metrics with a anti-self-dual Riemann curvature 2-form that admit no Killing vectors. They satisfy the Einstein field equations with Euclidean signature. We give the detailed derivation of the solution announced earlier and present a new solution with an added parameter. We compare our method of partner symmetries for finding non-invariant solutions to that of Dunajski and Mason who use 'hidden' symmetries for the same purpose

Hybrid metric-Palatini stars

Science.gov (United States)

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

2017-02-01

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

Goedel-type metrics in various dimensions

International Nuclear Information System (INIS)

Guerses, Metin; Karasu, Atalay; Sarioglu, Oezguer

2005-01-01

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

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

CERN Document Server

2012-01-01

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

Kerr metric in cosmological background

Energy Technology Data Exchange (ETDEWEB)

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

1977-06-01

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

Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models

Science.gov (United States)

Foldnes, Njal; Foss, Tron; Olsson, Ulf Henning

2012-01-01

The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…

Metric versus observable operator representation, higher spin models

Science.gov (United States)

Fring, Andreas; Frith, Thomas

2018-02-01

We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schrödinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the non-linear Ermakov-Pinney equation.

Fitting Lanchester Equations to the Battles of Kursk and Ardennes

OpenAIRE

Lucas, Thomas W.; Turkes, Turker

2004-01-01

The article of record as published may be found at http://dx.doi.org/10.1002/nav.10101 Lanchester equations and their extensions are widely used to calculate attrition in models of warfare. This paper examines how Lanchester models fit detailed daily data on the battles of Kursk and Ardennes. The data on Kursk, often called the greatest tank battle in history, was only recently made available. A new approach is used to find the optimal parameter values and gain an understanding...

The issue of statistical power for overall model fit in evaluating structural equation models

Directory of Open Access Journals (Sweden)

Richard HERMIDA

2015-06-01

Full Text Available Statistical power is an important concept for psychological research. However, examining the power of a structural equation model (SEM is rare in practice. This article provides an accessible review of the concept of statistical power for the Root Mean Square Error of Approximation (RMSEA index of overall model fit in structural equation modeling. By way of example, we examine the current state of power in the literature by reviewing studies in top Industrial-Organizational (I/O Psychology journals using SEMs. Results indicate that in many studies, power is very low, which implies acceptance of invalid models. Additionally, we examined methodological situations which may have an influence on statistical power of SEMs. Results showed that power varies significantly as a function of model type and whether or not the model is the main model for the study. Finally, results indicated that power is significantly related to model fit statistics used in evaluating SEMs. The results from this quantitative review imply that researchers should be more vigilant with respect to power in structural equation modeling. We therefore conclude by offering methodological best practices to increase confidence in the interpretation of structural equation modeling results with respect to statistical power issues.

Covariant Conformal Decomposition of Einstein Equations

Science.gov (United States)

Gourgoulhon, E.; Novak, J.

It has been shown1,2 that the usual 3+1 form of Einstein's equations may be ill-posed. This result has been previously observed in numerical simulations3,4. We present a 3+1 type formalism inspired by these works to decompose Einstein's equations. This decomposition is motivated by the aim of stable numerical implementation and resolution of the equations. We introduce the conformal 3-``metric'' (scaled by the determinant of the usual 3-metric) which is a tensor density of weight -2/3. The Einstein equations are then derived in terms of this ``metric'', of the conformal extrinsic curvature and in terms of the associated derivative. We also introduce a flat 3-metric (the asymptotic metric for isolated systems) and the associated derivative. Finally, the generalized Dirac gauge (introduced by Smarr and York5) is used in this formalism and some examples of formulation of Einstein's equations are shown.

Kerr metric in the deSitter background

International Nuclear Information System (INIS)

Vaidya, P.C.

1984-01-01

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

Indefinite metric fields and the renormalization group

International Nuclear Information System (INIS)

Sherry, T.N.

1976-11-01

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

Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm

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F. F. Ngwane

2015-01-01

Full Text Available We propose a block hybrid trigonometrically fitted (BHT method, whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs, including systems arising from the semidiscretization of hyperbolic Partial Differential Equations (PDEs, such as the Telegraph equation. The BHT is formulated from eight discrete hybrid formulas which are provided by a continuous two-step hybrid trigonometrically fitted method with two off-grid points. The BHT is implemented in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHT is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.

Generalization of Vaidya's radiation metric

Energy Technology Data Exchange (ETDEWEB)

Gleiser, R J; Kozameh, C N [Universidad Nacional de Cordoba (Argentina). Instituto de Matematica, Astronomia y Fisica

1981-11-01

In this paper it is shown that if Vaidya's radiation metric is considered from the point of view of kinetic theory in general relativity, the corresponding phase space distribution function can be generalized in a particular way. The new family of spherically symmetric radiation metrics obtained contains Vaidya's as a limiting situation. The Einstein field equations are solved in a ''comoving'' coordinate system. Two arbitrary functions of a single variable are introduced in the process of solving these equations. Particular examples considered are a stationary solution, a nonvacuum solution depending on a single parameter, and several limiting situations.

The Camassa-Holm equation as an incompressible Euler equation: A geometric point of view

Science.gov (United States)

Gallouët, Thomas; Vialard, François-Xavier

2018-04-01

The group of diffeomorphisms of a compact manifold endowed with the L2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently, several authors have extended optimal transport to the space of positive Radon measures where the Wasserstein-Fisher-Rao distance is a natural extension of the classical L2-Wasserstein distance. In this paper, we show a similar relation between this unbalanced optimal transport problem and the Hdiv right-invariant metric on the group of diffeomorphisms, which corresponds to the Camassa-Holm (CH) equation in one dimension. Geometrically, we present an isometric embedding of the group of diffeomorphisms endowed with this right-invariant metric in the automorphisms group of the fiber bundle of half densities endowed with an L2 type of cone metric. This leads to a new formulation of the (generalized) CH equation as a geodesic equation on an isotropy subgroup of this automorphisms group; On S1, solutions to the standard CH thus give radially 1-homogeneous solutions of the incompressible Euler equation on R2 which preserves a radial density that has a singularity at 0. An other application consists in proving that smooth solutions of the Euler-Arnold equation for the Hdiv right-invariant metric are length minimizing geodesics for sufficiently short times.

Long-range analysis of density fitting in extended systems

Science.gov (United States)

Varga, Scarontefan

Density fitting scheme is analyzed for the Coulomb problem in extended systems from the correctness of long-range behavior point of view. We show that for the correct cancellation of divergent long-range Coulomb terms it is crucial for the density fitting scheme to reproduce the overlap matrix exactly. It is demonstrated that from all possible fitting metric choices the Coulomb metric is the only one which inherently preserves the overlap matrix for infinite systems with translational periodicity. Moreover, we show that by a small additional effort any non-Coulomb metric fit can be made overlap-preserving as well. The problem is analyzed for both ordinary and Poisson basis set choices.

Factor structure of the Tomimatsu-Sato metrics

International Nuclear Information System (INIS)

Perjes, Z.

1989-02-01

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

Fisher information metrics for binary classifier evaluation and training

CERN Multimedia

CERN. Geneva

2018-01-01

Different evaluation metrics for binary classifiers are appropriate to different scientific domains and even to different problems within the same domain. This presentation focuses on the optimisation of event selection to minimise statistical errors in HEP parameter estimation, a problem that is best analysed in terms of the maximisation of Fisher information about the measured parameters. After describing a general formalism to derive evaluation metrics based on Fisher information, three more specific metrics are introduced for the measurements of signal cross sections in counting experiments (FIP1) or distribution fits (FIP2) and for the measurements of other parameters from distribution fits (FIP3). The FIP2 metric is particularly interesting because it can be derived from any ROC curve, provided that prevalence is also known. In addition to its relation to measurement errors when used as an evaluation criterion (which makes it more interesting that the ROC AUC), a further advantage of the FIP2 metric is ...

Fittings of unplasticized polyvinyl chloride (PVC-U), chlorinated polyvinyl chloride (PVC-C) or acrylonitrile/butadiene/styrene (ABS) with plain sockets for pipes under pressure - Dimensions of sockets - Metric series

CERN Document Server

International Organization for Standardization. Geneva

1985-01-01

Fittings of unplasticized polyvinyl chloride (PVC-U), chlorinated polyvinyl chloride (PVC-C) or acrylonitrile/butadiene/styrene (ABS) with plain sockets for pipes under pressure - Dimensions of sockets - Metric series

A differential equation for the asymptotic fitness distribution in the Bak-Sneppen model with five species.

Science.gov (United States)

Schlemm, Eckhard

2015-09-01

The Bak-Sneppen model is an abstract representation of a biological system that evolves according to the Darwinian principles of random mutation and selection. The species in the system are characterized by a numerical fitness value between zero and one. We show that in the case of five species the steady-state fitness distribution can be obtained as a solution to a linear differential equation of order five with hypergeometric coefficients. Similar representations for the asymptotic fitness distribution in larger systems may help pave the way towards a resolution of the question of whether or not, in the limit of infinitely many species, the fitness is asymptotically uniformly distributed on the interval [fc, 1] with fc ≳ 2/3. Copyright © 2015 Elsevier Inc. All rights reserved.

Symmetries and exact solutions of the nondiagonal Einstein-Rosen metrics

International Nuclear Information System (INIS)

Goyal, N; Gupta, R K

2012-01-01

We seek exact solutions of the nondiagonal Einstein-Rosen metrics. The method of Lie symmetry of differential equations is utilized to obtain new exact solutions of Einstein vacuum equations obtained from the nondiagonal Einstein-Rosen metric. Four cases arise depending on the nature of the Lie symmetry generator. In all cases, we find reductions in terms of ordinary differential equations and exact solutions of the nonlinear system of partial differential equations (PDEs) are derived. For this purpose, first we check the Painlevé property and then corresponding to the nonlinear system of PDEs, symmetries and exact solutions are obtained.

Phantom metrics with Killing spinors

Directory of Open Access Journals (Sweden)

W.A. Sabra

2015-11-01

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

Balanced metrics for vector bundles and polarised manifolds

DEFF Research Database (Denmark)

Garcia Fernandez, Mario; Ross, Julius

2012-01-01

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

A Kerr-NUT metric

International Nuclear Information System (INIS)

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

1976-01-01

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

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications

Science.gov (United States)

W. Hasan, W. Z.

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system’s modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model. PMID:29351554

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

Science.gov (United States)

Sabry, A H; W Hasan, W Z; Ab Kadir, M Z A; Radzi, M A M; Shafie, S

2018-01-01

The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF) algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Field data-based mathematical modeling by Bode equations and vector fitting algorithm for renewable energy applications.

Directory of Open Access Journals (Sweden)

A H Sabry

Full Text Available The power system always has several variations in its profile due to random load changes or environmental effects such as device switching effects when generating further transients. Thus, an accurate mathematical model is important because most system parameters vary with time. Curve modeling of power generation is a significant tool for evaluating system performance, monitoring and forecasting. Several numerical techniques compete to fit the curves of empirical data such as wind, solar, and demand power rates. This paper proposes a new modified methodology presented as a parametric technique to determine the system's modeling equations based on the Bode plot equations and the vector fitting (VF algorithm by fitting the experimental data points. The modification is derived from the familiar VF algorithm as a robust numerical method. This development increases the application range of the VF algorithm for modeling not only in the frequency domain but also for all power curves. Four case studies are addressed and compared with several common methods. From the minimal RMSE, the results show clear improvements in data fitting over other methods. The most powerful features of this method is the ability to model irregular or randomly shaped data and to be applied to any algorithms that estimating models using frequency-domain data to provide state-space or transfer function for the model.

Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern

Science.gov (United States)

Nassar, H.; Lebée, A.; Monasse, L.

2017-01-01

Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.

Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern.

Science.gov (United States)

Nassar, H; Lebée, A; Monasse, L

2017-01-01

Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.

Nonlinear metric perturbation enhancement of primordial gravitational waves.

Science.gov (United States)

Bastero-Gil, M; Macias-Pérez, J; Santos, D

2010-08-20

We present the evolution of the full set of Einstein equations during preheating after inflation. We study a generic supersymmetric model of hybrid inflation, integrating fields and metric fluctuations in a 3-dimensional lattice. We take initial conditions consistent with Einstein's constraint equations. The induced preheating of the metric fluctuations is not large enough to backreact onto the fields, but preheating of the scalar modes does affect the evolution of vector and tensor modes. In particular, they do enhance the induced stochastic background of gravitational waves during preheating, giving an energy density in general an order of magnitude larger than that obtained by evolving the tensor fluctuations in an homogeneous background metric. This enhancement can improve the expectations for detection by planned gravitational wave observatories.

Axisymmetric plasma equilibria in a Kerr metric

Science.gov (United States)

Elsässer, Klaus

2001-10-01

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

Principle of space existence and De Sitter metric

International Nuclear Information System (INIS)

Mal'tsev, V.K.

1990-01-01

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

A bridge role metric model for nodes in software networks.

Directory of Open Access Journals (Sweden)

Bo Li

Full Text Available A bridge role metric model is put forward in this paper. Compared with previous metric models, our solution of a large-scale object-oriented software system as a complex network is inherently more realistic. To acquire nodes and links in an undirected network, a new model that presents the crucial connectivity of a module or the hub instead of only centrality as in previous metric models is presented. Two previous metric models are described for comparison. In addition, it is obvious that the fitting curve between the Bre results and degrees can well be fitted by a power law. The model represents many realistic characteristics of actual software structures, and a hydropower simulation system is taken as an example. This paper makes additional contributions to an accurate understanding of module design of software systems and is expected to be beneficial to software engineering practices.

Holographic Spherically Symmetric Metrics

Science.gov (United States)

Petri, Michael

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

Self-dual metrics with self-dual Killing vectors

International Nuclear Information System (INIS)

Tod, K.P.; Ward, R.S.

1979-01-01

Twistor methods are used to derive a class of solutions to Einstein's vacuum equations, with anti-self dual Weyl tensor. In particular, all metrics with a Killing vector whose derivative is anti-self-dual and which admit a real positive-definite section are exhibited and shown to coincide with the metrics of Hawking. (author)

Correct Linearization of Einstein's Equations

Directory of Open Access Journals (Sweden)

Rabounski D.

2006-06-01

Full Text Available Regularly Einstein's equations can be reduced to a wave form (linearly dependent from the second derivatives of the space metric in the absence of gravitation, the space rotation and Christoffel's symbols. As shown here, the origin of the problem is that one uses the general covariant theory of measurement. Here the wave form of Einstein's equations is obtained in the terms of Zelmanov's chronometric invariants (physically observable projections on the observer's time line and spatial section. The obtained equations depend on solely the second derivatives even if gravitation, the space rotation and Christoffel's symbols. The correct linearization proves: the Einstein equations are completely compatible with weak waves of the metric.

Field equations for gravity quadratic in the curvature

International Nuclear Information System (INIS)

Rose, B.

1992-01-01

Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs

Classroom reconstruction of the Schwarzschild metric

OpenAIRE

Kassner, Klaus

2015-01-01

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

Energy functionals for Calabi-Yau metrics

International Nuclear Information System (INIS)

Headrick, M; Nassar, A

2013-01-01

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

Kerr-Newman metric in deSitter background

International Nuclear Information System (INIS)

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

1987-01-01

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

A Metric for Heterotic Moduli

Science.gov (United States)

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

2017-12-01

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

Dynamic field theory and equations of motion in cosmology

Energy Technology Data Exchange (ETDEWEB)

Kopeikin, Sergei M., E-mail: kopeikins@missouri.edu [Department of Physics and Astronomy, University of Missouri, 322 Physics Bldg., Columbia, MO 65211 (United States); Petrov, Alexander N., E-mail: alex.petrov55@gmail.com [Sternberg Astronomical Institute, Lomonosov Moscow State University, Universitetskij Prospect 13, Moscow 119992 (Russian Federation)

2014-11-15

We discuss a field-theoretical approach based on general-relativistic variational principle to derive the covariant field equations and hydrodynamic equations of motion of baryonic matter governed by cosmological perturbations of dark matter and dark energy. The action depends on the gravitational and matter Lagrangian. The gravitational Lagrangian depends on the metric tensor and its first and second derivatives. The matter Lagrangian includes dark matter, dark energy and the ordinary baryonic matter which plays the role of a bare perturbation. The total Lagrangian is expanded in an asymptotic Taylor series around the background cosmological manifold defined as a solution of Einstein’s equations in the form of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric tensor. The small parameter of the decomposition is the magnitude of the metric tensor perturbation. Each term of the series expansion is gauge-invariant and all of them together form a basis for the successive post-Friedmannian approximations around the background metric. The approximation scheme is covariant and the asymptotic nature of the Lagrangian decomposition does not require the post-Friedmannian perturbations to be small though computationally it works the most effectively when the perturbed metric is close enough to the background FLRW metric. The temporal evolution of the background metric is governed by dark matter and dark energy and we associate the large scale inhomogeneities in these two components as those generated by the primordial cosmological perturbations with an effective matter density contrast δρ/ρ≤1. The small scale inhomogeneities are generated by the condensations of baryonic matter considered as the bare perturbations of the background manifold that admits δρ/ρ≫1. Mathematically, the large scale perturbations are given by the homogeneous solution of the linearized field equations while the small scale perturbations are described by a particular solution of

Separable metrics and radiating stars

Indian Academy of Sciences (India)

We study the junction condition relating the pressure to heat flux at the boundary of an accelerating and expanding spherically symmetric radiating star. We transform the junction condition to an ordinary differential equation by making a separability assumption on the metric functions in the space–time variables.

Older driver fitness-to-drive evaluation using naturalistic driving data.

Science.gov (United States)

Guo, Feng; Fang, Youjia; Antin, Jonathan F

2015-09-01

As our driving population continues to age, it is becoming increasingly important to find a small set of easily administered fitness metrics that can meaningfully and reliably identify at-risk seniors requiring more in-depth evaluation of their driving skills and weaknesses. Sixty driver assessment metrics related to fitness-to-drive were examined for 20 seniors who were followed for a year using the naturalistic driving paradigm. Principal component analysis and negative binomial regression modeling approaches were used to develop parsimonious models relating the most highly predictive of the driver assessment metrics to the safety-related outcomes observed in the naturalistic driving data. This study provides important confirmation using naturalistic driving methods of the relationship between contrast sensitivity and crash-related events. The results of this study provide crucial information on the continuing journey to identify metrics and protocols that could be applied to determine seniors' fitness to drive. Published by Elsevier Ltd.

A Four-Stage Fifth-Order Trigonometrically Fitted Semi-Implicit Hybrid Method for Solving Second-Order Delay Differential Equations

Directory of Open Access Journals (Sweden)

Sufia Zulfa Ahmad

2016-01-01

Full Text Available We derived a two-step, four-stage, and fifth-order semi-implicit hybrid method which can be used for solving special second-order ordinary differential equations. The method is then trigonometrically fitted so that it is suitable for solving problems which are oscillatory in nature. The methods are then used for solving oscillatory delay differential equations. Numerical results clearly show the efficiency of the new method when compared to the existing explicit and implicit methods in the scientific literature.

Modeling nutrient in-stream processes at the watershed scale using Nutrient Spiralling metrics

Science.gov (United States)

Marcé, R.; Armengol, J.

2009-07-01

One of the fundamental problems of using large-scale biogeochemical models is the uncertainty involved in aggregating the components of fine-scale deterministic models in watershed applications, and in extrapolating the results of field-scale measurements to larger spatial scales. Although spatial or temporal lumping may reduce the problem, information obtained during fine-scale research may not apply to lumped categories. Thus, the use of knowledge gained through fine-scale studies to predict coarse-scale phenomena is not straightforward. In this study, we used the nutrient uptake metrics defined in the Nutrient Spiralling concept to formulate the equations governing total phosphorus in-stream fate in a deterministic, watershed-scale biogeochemical model. Once the model was calibrated, fitted phosphorus retention metrics where put in context of global patterns of phosphorus retention variability. For this purpose, we calculated power regressions between phosphorus retention metrics, streamflow, and phosphorus concentration in water using published data from 66 streams worldwide, including both pristine and nutrient enriched streams. Performance of the calibrated model confirmed that the Nutrient Spiralling formulation is a convenient simplification of the biogeochemical transformations involved in total phosphorus in-stream fate. Thus, this approach may be helpful even for customary deterministic applications working at short time steps. The calibrated phosphorus retention metrics were comparable to field estimates from the study watershed, and showed high coherence with global patterns of retention metrics from streams of the world. In this sense, the fitted phosphorus retention metrics were similar to field values measured in other nutrient enriched streams. Analysis of the bibliographical data supports the view that nutrient enriched streams have lower phosphorus retention efficiency than pristine streams, and that this efficiency loss is maintained in a wide

Cosmological implications of modified gravity induced by quantum metric fluctuations

Energy Technology Data Exchange (ETDEWEB)

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

2016-08-15

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

a tensor theory of gravitation in a curved metric on a flat background

International Nuclear Information System (INIS)

Drummond, J.E.

1979-01-01

A theory of gravity is proposed using a tensor potential for the field on a flat metric. This potential cannot be isolated by local observations, but some details can be deduced from measurements at a distance. The requirement that the field equations for the tensor potential shall be deducible from an action integral, that the action and field equations are gauge invariant, and, conversely, that the Lagrangian in the action integral can be integrated from the field equations leads to Einstein's field equations. The requirement that the field energy-momentum tensor exists leads to a constraint on the tensor potential. If the constraint is a differential gauge condition, then it can only be the Hilbert condition giving a unique background tensor, metric tensor and tensor potential. For a continuous field inside a solid sphere the metric must be homogeneous in the spatial coordinates, and the associated field energy-momentum tensor has properties consistent with Newtonian dynamics. (author)

Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

Science.gov (United States)

Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.

2017-07-01

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.

Wave equations on anti self dual (ASD) manifolds

Science.gov (United States)

Bashingwa, Jean-Juste; Kara, A. H.

2017-11-01

In this paper, we study and perform analyses of the wave equation on some manifolds with non diagonal metric g_{ij} which are of neutral signatures. These include the invariance properties, variational symmetries and conservation laws. In the recent past, wave equations on the standard (space time) Lorentzian manifolds have been performed but not on the manifolds from metrics of neutral signatures.

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

Science.gov (United States)

Aoki, Sinya; Yokoyama, Shuichi

2018-03-01

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

General heavenly equation governs anti-self-dual gravity

Energy Technology Data Exchange (ETDEWEB)

Malykh, A A [Department of Numerical Modelling, Russian State Hydrometeorlogical University, Malookhtinsky pr 98, 195196 St Petersburg (Russian Federation); Sheftel, M B, E-mail: andrei-malykh@mail.ru, E-mail: mikhail.sheftel@boun.edu.tr [Department of Physics, Bogazici University, 34342 Bebek, Istanbul (Turkey)

2011-04-15

We show that the general heavenly equation, suggested recently by Doubrov and Ferapontov (2010 arXiv:0910.3407v2 [math.DG]), governs anti-self-dual (ASD) gravity. We derive ASD Ricci-flat vacuum metric governed by the general heavenly equation, null tetrad and basis of 1-forms for this metric. We present algebraic exact solutions of the general heavenly equation as a set of zeros of homogeneous polynomials in independent and dependent variables. A real solution is obtained for the case of a neutral signature.

Fitting Nonlinear Ordinary Differential Equation Models with Random Effects and Unknown Initial Conditions Using the Stochastic Approximation Expectation-Maximization (SAEM) Algorithm.

Science.gov (United States)

Chow, Sy-Miin; Lu, Zhaohua; Sherwood, Andrew; Zhu, Hongtu

2016-03-01

The past decade has evidenced the increased prevalence of irregularly spaced longitudinal data in social sciences. Clearly lacking, however, are modeling tools that allow researchers to fit dynamic models to irregularly spaced data, particularly data that show nonlinearity and heterogeneity in dynamical structures. We consider the issue of fitting multivariate nonlinear differential equation models with random effects and unknown initial conditions to irregularly spaced data. A stochastic approximation expectation-maximization algorithm is proposed and its performance is evaluated using a benchmark nonlinear dynamical systems model, namely, the Van der Pol oscillator equations. The empirical utility of the proposed technique is illustrated using a set of 24-h ambulatory cardiovascular data from 168 men and women. Pertinent methodological challenges and unresolved issues are discussed.

Graph theory and the Virasoro master equation

International Nuclear Information System (INIS)

Obers, N.A.J.

1991-01-01

A brief history of affine Lie algebra, the Virasoro algebra and its culmination in the Virasoro master equation is given. By studying ansaetze of the master equation, the author obtains exact solutions and gains insight in the structure of large slices of affine-Virasoro space. He finds an isomorphism between the constructions in the ansatz SO(n) diag , which is a set of unitary, generically irrational affine-Virasoro constructions on SO(n), and the unlabeled graphs of order n. On the one hand, the conformal constructions, are classified by the graphs, while, conversely, a group-theoretic and conformal field-theoretic identification is obtained for every graph of graph theory. He also defines a class of magic Lie group bases in which the Virasoro master equation admits a simple metric ansatz {g metric }, whose structure is visible in the high-level expansion. When a magic basis is real on compact g, the corresponding g metric is a large system of unitary, generically irrational conformal field theories. Examples in this class include the graph-theory ansatz SO(n) diag in the Cartesian basis of SO(n), and the ansatz SU(n) metric in the Pauli-like basis of SU(n). Finally, he defines the 'sine-area graphs' of SU(n), which label the conformal field theories of SU(n) metric , and he notes that, in similar fashion, each magic basis of g defines a generalized graph theory on g which labels the conformal field theories of g metric

Fluids and vortex from constrained fluctuations around C-metric black holes

Science.gov (United States)

Hao, Xin; Wu, Bin; Zhao, Liu

2017-08-01

By foliating the four-dimensional C-metric black hole spacetime, we consider a kind of initial-value-like formulation of the vacuum Einstein's equation, the holographic initial data is a double consisting of the induced metric and the Brown-York energy momentum tensor on an arbitrary initial hypersurface. Then by perturbing the initial data that generates the background spacetime, it is shown that, in an appropriate limit, the fluctuation modes are governed by the continuity equation and the compressible Navier-Stokes equation which describe the momentum transport in non-relativistic viscous fluid on a flat Newtonian space. It turns out that the flat space fluid behaves as a pure vortex and the viscosity to entropy ratio is subjected to the black hole acceleration.

Gauge-invariant flow equation

Science.gov (United States)

Wetterich, C.

2018-06-01

We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

Curvature properties of four-dimensional Walker metrics

International Nuclear Information System (INIS)

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

2005-01-01

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

A study of the effects of grid non-orthogonality on the solution of shallow water equations in boundary-fitted coordinate systems

CERN Document Server

Sankaranarayanan, S

2003-01-01

In the present study, an existing two-dimensional boundary-fitted model [J. Hydraul. Eng.-ASCE 122 (9) (1996) 512] is used to study the effect of grid non-orthogonality on the solution of shallow water equations using boundary-fitted grids. The linearized two-dimensional shallow water equations are expressed in terms of the grid angle and aspect ratio. The truncation errors of the finite difference approximations used in the solution of the governing equations are shown to be dependent on the grid angle and the aspect ratio. The coefficient of the truncation error was shown to increase, with the decrease in the grid angle. The RMS errors in model predicted surface elevations and velocities for the case of seiching in a rectangular basin are found to increase gradually, as the grid resolution decreases from 174 to 80 gridpoints per wavelength or as the grid angle decreases from 90 deg. to 50 deg. and increases rather sharply for a grid angle of 30 deg. at grid resolutions less than 80 gridpoints per wavelength...

Heuristic extension of the Schwarzschild metric

International Nuclear Information System (INIS)

Espinosa, J.M.

1982-01-01

The Schwarzschild solution of Einstein's equations of gravitation has several singularities. It is known that the singularity at r = 2Gm/c 2 is only apparent, a result of the coordinates in which the solution was found. Paradoxical results occuring near the singularity show the system of coordinates is incomplete. We introduce a simple, two-dimensional metric with an apparent singularity that makes it incomplete. By a straightforward, heuristic procedure we extend and complete this simple metric. We then use the same procedure to give a heuristic derivation of the Kruskal system of coordinates, which is known to extend the Schwarzschild manifold past its apparent singularity and produce a complete manifold

Homogeneous axisymmetric model with a limitting stiff equation of state

International Nuclear Information System (INIS)

Korkina, M.P.; Martynenko, V.G.

1976-01-01

A solution is obtained for Einstein's equations in which all metric coefficients are time functions for a limiting stiff equation of the substance state. Thr solution describes a homogeneous cosmological model with cylindrical symmetry. It is shown that the same metrics can be induced by a massless scalar only time-dependent field. Analysis of this solution is presented

Four dimensional sigma model coupled to the metric tensor field

International Nuclear Information System (INIS)

Ghika, G.; Visinescu, M.

1980-02-01

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

A family of metric gravities

Science.gov (United States)

Shuler, Robert

2018-04-01

The goal of this paper is to take a completely fresh approach to metric gravity, in which the metric principle is strictly adhered to but its properties in local space-time are derived from conservation principles, not inferred from a global field equation. The global field strength variation then gains some flexibility, but only in the regime of very strong fields (2nd-order terms) whose measurement is now being contemplated. So doing provides a family of similar gravities, differing only in strong fields, which could be developed into meaningful verification targets for strong fields after the manner in which far-field variations were used in the 20th century. General Relativity (GR) is shown to be a member of the family and this is demonstrated by deriving the Schwarzschild metric exactly from a suitable field strength assumption. The method of doing so is interesting in itself because it involves only one differential equation rather than the usual four. Exact static symmetric field solutions are also given for one pedagogical alternative based on potential, and one theoretical alternative based on inertia, and the prospects of experimentally differentiating these are analyzed. Whether the method overturns the conventional wisdom that GR is the only metric theory of gravity and that alternatives must introduce additional interactions and fields is somewhat semantical, depending on whether one views the field strength assumption as a field and whether the assumption that produces GR is considered unique in some way. It is of course possible to have other fields, and the local space-time principle can be applied to field gravities which usually are weak-field approximations having only time dilation, giving them the spatial factor and promoting them to full metric theories. Though usually pedagogical, some of them are interesting from a quantum gravity perspective. Cases are noted where mass measurement errors, or distributions of dark matter, can cause one

Equation of state fits to the lower mantle and outer core

Science.gov (United States)

Butler, R.; Anderson, D. L.

1978-01-01

The lower mantle and outer core are subjected to tests for homogeneity and adiabaticity. An earth model is used which is based on the inversion of body waves and Q-corrected normal-mode data. Homogeneous regions are found at radii between 5125 and 4825 km, 4600 and 3850 km, and 3200 and 2200 km. The lower mantle and outer core are inhomogeneous on the whole and are only homogeneous in the above local regions. Finite-strain and atomistic equations of state are fit to the homogeneous regions. The apparent convergence of the finite-strain relations is examined to judge their applicability to a given region. In some cases the observed pressure derivatives of the elastic moduli are used as additional constraints. The effect of minor deviations from adiabaticity on the extrapolations is also considered. An ensemble of zero-pressure values of the density and seismic velocities are found for these regions. The range of extrapolated values from these several approaches provides a measure of uncertainties involved.

Linear Einstein equations and Kerr-Schild maps

International Nuclear Information System (INIS)

Gergely, Laszlo A

2002-01-01

We prove that given a solution of the Einstein equations g ab for the matter field T ab , an autoparallel null vector field l a and a solution (l a l c , T ac ) of the linearized Einstein equation on the given background, the Kerr-Schild metric g ac + λl a l c (λ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor T ac + λT ac + λ 2 l (a T c)b l b . The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed spacetime due to Guerses and Guersey

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

Directory of Open Access Journals (Sweden)

Andrei A. Malykh

2013-11-01

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

Weyl-Invariant Extension of the Metric-Affine Gravity

International Nuclear Information System (INIS)

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

2015-01-01

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

Yang–Mills equations on conformally connected torsion-free 4-manifolds with different signatures

Directory of Open Access Journals (Sweden)

Vyacheslav A. Luk'yanov

2017-12-01

Full Text Available In this paper we study spaces of conformal torsion-free connection of dimension 4 whose connection matrix satisfies the Yang–Mills equations. Here we generalize and strengthen the results obtained by us in previous articles, where the angular metric of these spaces had Minkowski signature. The generalization is that here we investigate the spaces of all possible metric signatures, and the enhancement is due to the fact that additional attention is paid to calculating the curvature matrix and establishing the properties of its components. It is shown that the Yang–Mills equations on 4-manifolds of conformal torsion-free connection for an arbitrary signature of the angular metric are reduced to Einstein's equations, Maxwell's equations and the equality of the Bach tensor of the angular metric and the energy-momentum tensor of the skew-symmetric charge tensor. It is proved that if the Weyl tensor is zero, the Yang–Mills equations have only self-dual or anti-self-dual solutions, i.e the curvature matrix of a conformal connection consists of self-dual or anti-self-dual external 2-forms. With the Minkowski signature (antiself-dual external 2-forms can only be zero. The components of the curvature matrix are calculated in the case when the angular metric of an arbitrary signature is Einstein, and the connection satisfies the Yang–Mills equations. In the Euclidean and pseudo-Euclidean 4-spaces we give some particular self-dual and anti-self-dual solutions of the Maxwell equations, to which all the Yang–Mills equations are reduced in this case.

Some applications on tangent bundle with Kaluza-Klein metric

Directory of Open Access Journals (Sweden)

Murat Altunbaş

2017-01-01

Full Text Available In this paper, differential equations of geodesics; parallelism, incompressibility and closeness conditions of the horizontal and complete lift of the vector fields are investigated with respect to Kaluza-Klein metric on tangent bundle.

Lie symmetries for systems of evolution equations

Science.gov (United States)

Paliathanasis, Andronikos; Tsamparlis, Michael

2018-01-01

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

Resources available for applying metrics in security and safety programming.

Science.gov (United States)

Luizzo, Anthony

2016-01-01

Incorporating metrics into security surveys has been championed as a better way of substantiating program-related effectiveness and expenditures. Although security surveys have been aroundfor well over 40 years, rarely, if ever, have metric-related strategies been part of the equation, the author says. In this article, he cites several published articles and research findings available to security professionals and their surveyors that may give them the expertise and confidence they need to make use of this valuable tool.

Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

Science.gov (United States)

Santa Vélez, Camilo; Enea Romano, Antonio

2018-05-01

Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

Metric preheating and limitations of linearized gravity

International Nuclear Information System (INIS)

Bassett, Bruce A.; Tamburini, Fabrizio; Kaiser, David I.; Maartens, Roy

1999-01-01

During the preheating era after inflation, resonant amplification of quantum field fluctuations takes place. Recently it has become clear that this must be accompanied by resonant amplification of scalar metric fluctuations, since the two are united by Einstein's equations. Furthermore, this 'metric preheating' enhances particle production, and leads to gravitational rescattering effects even at linear order. In multi-field models with strong preheating (q>>1), metric perturbations are driven non-linear, with the strongest amplification typically on super-Hubble scales (k→0). This amplification is causal, being due to the super-Hubble coherence of the inflaton condensate, and is accompanied by resonant growth of entropy perturbations. The amplification invalidates the use of the linearized Einstein field equations, irrespective of the amount of fine-tuning of the initial conditions. This has serious implications on all scales - from large-angle cosmic microwave background (CMB) anisotropies to primordial black holes. We investigate the (q,k) parameter space in a two-field model, and introduce the time to non-linearity, t nl , as the timescale for the breakdown of the linearized Einstein equations. t nl is a robust indicator of resonance behavior, showing the fine structure in q and k that one expects from a quasi-Floquet system, and we argue that t nl is a suitable generalization of the static Floquet index in an expanding universe. Backreaction effects are expected to shut down the linear resonances, but cannot remove the existing amplification, which threatens the viability of strong preheating when confronted with the CMB. Mode-mode coupling and turbulence tend to re-establish scale invariance, but this process is limited by causality and for small k the primordial scale invariance of the spectrum may be destroyed. We discuss ways to escape the above conclusions, including secondary phases of inflation and preheating solely to fermions. The exclusion principle

Measures of agreement between computation and experiment:validation metrics.

Energy Technology Data Exchange (ETDEWEB)

Barone, Matthew Franklin; Oberkampf, William Louis

2005-08-01

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

Modified Einstein and Navier–Stokes Equations

Science.gov (United States)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Modified Einstein and Navier-Stokes Equations

Science.gov (United States)

Bulyzhenkov, I. É.

2018-05-01

The appearance of inertial rest mass-energy is associated with the kinematic slowing-down of time and with the vortex state of the elementary massive space with zero integral of its kinetic and potential energies. An analog of the Einstein equation is found for moving densities of a non-empty metric space in the concept of the Einstein-Infeld material field. The vector consequences of this tensor equation for a metric medium of overlapping elementary carriers of continuous mass-energies allow us to modify the Navier-Stokes equation under inertial motion of the matter of the nonlocal field in the nonrelativistic limit. The nonlocality of massenergy generates kinematic accelerations of feedback to Newtonian acceleration, which impedes asymptotic divergence of energy fluxes. Stabilization of inertial media by dynamic Bernoulli pressure corresponds to nonlocal self-organization of Einstein-Infeld non-empty space and invalidates Newtonian localization of masses in empty space.

Multicomponent equations of state for electrolytes

DEFF Research Database (Denmark)

Lin, Yi; Thomsen, Kaj; Hemptinne, Jean-Charles de

2007-01-01

. The parameters in the equations of state were fitted to experimental data consisting of apparent molar volumes, osmotic coefficients, mean ionic activity coefficients, and solid-liquid equilibrium data. The results of the parameter fitting are presented. The ability of the equations of state to reproduce...

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

Science.gov (United States)

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

2018-04-01

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

Exact solutions of Einstein and Einstein-Maxwell equations in higher-dimensional spacetime

International Nuclear Information System (INIS)

Xu Dianyan; Beijing Univ., BJ

1988-01-01

The D-dimensional Schwarzschild-de Sitter metric and Reissner-Nordstrom-de-Sitter metric are derived directly by solving the Einstein and Einstein-Maxwell equations. The D-dimensional Kerr metric is rederived by using the complex coordinate transformation method and the D-dimensional Kerr-de Sitter metric is also given. The conjecture about the D-dimensional metric of a rotating charged mass is given at the end of this paper. (author)

General relativity: An erfc metric

Science.gov (United States)

Plamondon, Réjean

2018-06-01

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

Real-Time Exponential Curve Fits Using Discrete Calculus

Science.gov (United States)

Rowe, Geoffrey

2010-01-01

An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.

Some Remarks on Space-Time Decompositions, and Degenerate Metrics, in General Relativity

Science.gov (United States)

Bengtsson, Ingemar

Space-time decomposition of the Hilbert-Palatini action, written in a form which admits degenerate metrics, is considered. Simple numerology shows why D = 3 and 4 are singled out as admitting a simple phase space. The canonical structure of the degenerate sector turns out to be awkward. However, the real degenerate metrics obtained as solutions are the same as those that occur in Ashtekar's formulation of complex general relativity. An exact solution of Ashtekar's equations, with degenerate metric, shows that the manifestly four-dimensional form of the action, and its 3 + 1 form, are not quite equivalent.

General Eulerian formulation of the comoving-frame equation of radiative transfer

International Nuclear Information System (INIS)

Riffert, H.

1986-01-01

For a wide range of problems in radiation hydrodynamics the motion of the matter is best described in an Eulerian coordinate system, and here a comoving-frame equation of radiation transfer in such fixed coordinates is derived, using the radiation quantities measured in the comoving frame. The choice of coordinates is arbitrary, and the equation is given explicitly for an arbitrary diagonal metric, correct to all orders in v/c. All comoving frame equations derived earlier are included as special cases. An example is given for the case of a spherically symmetric flow in a Schwarzschild metric. 9 references

Landscape and flow metrics affecting the distribution of a federally-threatened fish: Improving management, model fit, and model transferability

Science.gov (United States)

Worthington, Thomas A.; Zhang, T.; Logue, Daniel R.; Mittelstet, Aaron R.; Brewer, Shannon K.

2016-01-01

Truncated distributions of pelagophilic fishes have been observed across the Great Plains of North America, with water use and landscape fragmentation implicated as contributing factors. Developing conservation strategies for these species is hindered by the existence of multiple competing flow regime hypotheses related to species persistence. Our primary study objective was to compare the predicted distributions of one pelagophil, the Arkansas River Shiner Notropis girardi, constructed using different flow regime metrics. Further, we investigated different approaches for improving temporal transferability of the species distribution model (SDM). We compared four hypotheses: mean annual flow (a baseline), the 75th percentile of daily flow, the number of zero-flow days, and the number of days above 55th percentile flows, to examine the relative importance of flows during the spawning period. Building on an earlier SDM, we added covariates that quantified wells in each catchment, point source discharges, and non-native species presence to a structured variable framework. We assessed the effects on model transferability and fit by reducing multicollinearity using Spearman’s rank correlations, variance inflation factors, and principal component analysis, as well as altering the regularization coefficient (β) within MaxEnt. The 75th percentile of daily flow was the most important flow metric related to structuring the species distribution. The number of wells and point source discharges were also highly ranked. At the default level of β, model transferability was improved using all methods to reduce collinearity; however, at higher levels of β, the correlation method performed best. Using β = 5 provided the best model transferability, while retaining the majority of variables that contributed 95% to the model. This study provides a workflow for improving model transferability and also presents water-management options that may be considered to improve the

Best Proximity Point Results in Complex Valued Metric Spaces

Directory of Open Access Journals (Sweden)

Binayak S. Choudhury

2014-01-01

complex valued metric spaces. We treat the problem as that of finding the global optimal solution of a fixed point equation although the exact solution does not in general exist. We also define and use the concept of P-property in such spaces. Our results are illustrated with examples.

Constraint propagation equations of the 3+1 decomposition of f(R) gravity

International Nuclear Information System (INIS)

Paschalidis, Vasileios; Shapiro, Stuart L; Halataei, Seyyed M H; Sawicki, Ignacy

2011-01-01

Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term (ω = 0). Using this equivalence and a 3+1 decomposition of the theory, it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (Hamiltonian and momentum) constraints. In this paper, we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.

Interior metric and ray-tracing map in the firework black-to-white hole transition

OpenAIRE

Rovelli, Carlo; Martin-Dussaud, Pierre

2018-01-01

The possibility that a black hole could tunnel into to white hole has recently received attention. Here we present a metric that improves the "firework" metric: it describes the entire process and solves the Einstein's equations everywhere except on a small transition surface that corresponds to the quantum tunneling. We compute the corresponding ray-tracing map from past infinity to future infinity explicitly.

Cosmology in massive gravity with effective composite metric

Energy Technology Data Exchange (ETDEWEB)

Heisenberg, Lavinia [Institute for Theoretical Studies, ETH Zurich Clausiusstrasse 47, 8092 Zurich (Switzerland); Refregier, Alexandre, E-mail: lavinia.heisenberg@eth-its.ethz.ch, E-mail: alexandre.refregier@phys.ethz.ch [Institute for Astronomy, Department of Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093, Zurich (Switzerland)

2016-09-01

This paper is dedicated to scrutinizing the cosmology in massive gravity. A matter field of the dark sector is coupled to an effective composite metric while a standard matter field couples to the dynamical metric in the usual way. For this purpose, we study the dynamical system of cosmological solutions by using phase analysis, which provides an overview of the class of cosmological solutions in this setup. This also permits us to study the critical points of the cosmological equations together with their stability. We show the presence of stable attractor de Sitter critical points relevant to the late-time cosmic acceleration. Furthermore, we study the tensor, vector and scalar perturbations in the presence of standard matter fields and obtain the conditions for the absence of ghost and gradient instabilities. Hence, massive gravity in the presence of the effective composite metric can accommodate interesting dark energy phenomenology, that can be observationally distinguished from the standard model according to the expansion history and cosmic growth.

A Fortran program for the numerical integration of the one-dimensional Schroedinger equation using exponential and Bessel fitting methods

International Nuclear Information System (INIS)

Cash, J.R.; Raptis, A.D.; Simos, T.E.

1990-01-01

An efficient algorithm is described for the accurate numerical integration of the one-dimensional Schroedinger equation. This algorithm uses a high-order, variable step Runge-Kutta like method in the region where the potential term dominates, and an exponential or Bessel fitted method in the asymptotic region. This approach can be used to compute scattering phase shifts in an efficient and reliable manner. A Fortran program which implements this algorithm is provided and some test results are given. (orig.)

A Family of Trigonometrically-fitted Partitioned Runge-Kutta Symplectic Methods

International Nuclear Information System (INIS)

Monovasilis, Th.; Kalogiratou, Z.; Simos, T. E.

2007-01-01

We are presenting a family of trigonometrically fitted partitioned Runge-Kutta symplectic methods of fourth order with six stages. The solution of the one dimensional time independent Schroedinger equation is considered by trigonometrically fitted symplectic integrators. The Schroedinger equation is first transformed into a Hamiltonian canonical equation. Numerical results are obtained for the one-dimensional harmonic oscillator and the exponential potential

Conformal gravity, the Einstein equations and spaces of complex null geodesics

Energy Technology Data Exchange (ETDEWEB)

Baston, R.J.; Mason, L.J.

1987-07-01

The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved.

Conformal gravity, the Einstein equations and spaces of complex null geodesics

International Nuclear Information System (INIS)

Baston, R.J.; Mason, L.J.

1987-01-01

The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved. (author)

The positive action conjecture and asymptotically euclidean metrics in quantum gravity

International Nuclear Information System (INIS)

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

1979-01-01

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

Spectral fitting method for the solution of time-dependent Schroedinger equations: Applications to atoms in intense laser fields

International Nuclear Information System (INIS)

Qiao Haoxue; Cai Qingyu; Rao Jianguo; Li Baiwen

2002-01-01

A spectral fitting method for solving the time-dependent Schroedinger equation has been developed and applied to the atom in intense laser fields. This method allows us to obtain a highly accurate time-dependent wave function with a contribution from the high-order term of Δt. Moreover, the time-dependent wave function is determined on a small number of discrete mesh points, thus making calculations simple and accurate. This method is illustrated by computing wave functions and harmonic generation spectra of a model atom in laser fields

Deduction of Einstein equation from homogeneity of Riemann spacetime

Science.gov (United States)

Ni, Jun

2012-03-01

The symmetry of spacetime translation leads to the energy-momentum conservation. However, the Lagrange depends on spacetime coordinates, which makes the symmetry of spacetime translation different with other symmetry invariant explicitly under symmetry transformation. We need an equation to guarantee the symmetry of spacetime translation. In this talk, I will show that the Einstein equation can be deduced purely from the general covariant principle and the homogeneity of spacetime in the frame of quantum field theory. The Einstein equation is shown to be the equation to guarantee the symmetry of spacetime translation. Gravity is an apparent force due to the curvature of spacetime resulted from the conservation of energy-momentum. In the action of quantum field, only electroweak-strong interactions appear with curved spacetime metric determined by the Einstein equation.. The general covariant principle and the homogeneity of spacetime are merged into one basic principle: Any Riemann spacetime metric guaranteeing the energy-momentum conservation are equivalent, which can be called as the conserved general covariant principle. [4pt] [1] Jun Ni, Chin. Phys. Lett. 28, 110401 (2011).

Metric reconstruction from Weyl scalars

Energy Technology Data Exchange (ETDEWEB)

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

2005-08-07

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

Metric reconstruction from Weyl scalars

International Nuclear Information System (INIS)

Whiting, Bernard F; Price, Larry R

2005-01-01

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

Human Performance Optimization Metrics: Consensus Findings, Gaps, and Recommendations for Future Research.

Science.gov (United States)

Nindl, Bradley C; Jaffin, Dianna P; Dretsch, Michael N; Cheuvront, Samuel N; Wesensten, Nancy J; Kent, Michael L; Grunberg, Neil E; Pierce, Joseph R; Barry, Erin S; Scott, Jonathan M; Young, Andrew J; OʼConnor, Francis G; Deuster, Patricia A

2015-11-01

Human performance optimization (HPO) is defined as "the process of applying knowledge, skills and emerging technologies to improve and preserve the capabilities of military members, and organizations to execute essential tasks." The lack of consensus for operationally relevant and standardized metrics that meet joint military requirements has been identified as the single most important gap for research and application of HPO. In 2013, the Consortium for Health and Military Performance hosted a meeting to develop a toolkit of standardized HPO metrics for use in military and civilian research, and potentially for field applications by commanders, units, and organizations. Performance was considered from a holistic perspective as being influenced by various behaviors and barriers. To accomplish the goal of developing a standardized toolkit, key metrics were identified and evaluated across a spectrum of domains that contribute to HPO: physical performance, nutritional status, psychological status, cognitive performance, environmental challenges, sleep, and pain. These domains were chosen based on relevant data with regard to performance enhancers and degraders. The specific objectives at this meeting were to (a) identify and evaluate current metrics for assessing human performance within selected domains; (b) prioritize metrics within each domain to establish a human performance assessment toolkit; and (c) identify scientific gaps and the needed research to more effectively assess human performance across domains. This article provides of a summary of 150 total HPO metrics across multiple domains that can be used as a starting point-the beginning of an HPO toolkit: physical fitness (29 metrics), nutrition (24 metrics), psychological status (36 metrics), cognitive performance (35 metrics), environment (12 metrics), sleep (9 metrics), and pain (5 metrics). These metrics can be particularly valuable as the military emphasizes a renewed interest in Human Dimension efforts

Parametrized post-Newtonian approximation and Rastall's gravitational field equations

International Nuclear Information System (INIS)

Smalley, L.L.

1978-01-01

The parametrized post-Newtonian (PPN) approximation is generalized to accomodate Rastall's modification of Einstein's theory of gravity, which allows nonzero divergence of the energy-momentum tensor. Rastall's theory is then shown to have consistent field equations, gauge conditions, and the correct Newtonian limit of the equations of motion. The PPN parameters are obtained and shown to agree experimentally with those for the Einstein theory. In light of the nonzero divergence condition, integral conservation laws are investigated and shown to yield conserved energy-momentum and angular-momentum. We conclude that the above generalization of metric theories, within the PPN framework, is a natural extension of the concept of metric theories

Monge-Ampere equations and tensorial functors

International Nuclear Information System (INIS)

Tunitsky, Dmitry V

2009-01-01

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

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

International Nuclear Information System (INIS)

Szereszewski, A; Sym, A

2015-01-01

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

On the Langevin equation for stochastic quantization of gravity

International Nuclear Information System (INIS)

Nakazawa, Naohito.

1989-10-01

We study the Langevin equation for stochastic quantization of gravity. By introducing two independent variables with a second-class constraint for the gravitational field, we formulate a pair of the Langevin equations for gravity which couples with white noises. After eliminating the multiplier field for the second-class constraint, we show that the equations leads to stochastic quantization of gravity including an unique superspace metric. (author)

A class of exact solutions to the Einstein field equations

International Nuclear Information System (INIS)

Goyal, Nisha; Gupta, R K

2012-01-01

The Einstein-Rosen metric is considered and a class of new exact solutions of the field equations for stationary axisymmetric Einstein-Maxwell fields is obtained. The Lie classical approach is applied to obtain exact solutions. By using the Lie classical method, we are able to derive symmetries that are used for reducing the coupled system of partial differential equations into ordinary differential equations. From reduced differential equations we have derived some new exact solutions of Einstein-Maxwell equations. (paper)

Generalized equations of gravitational field

International Nuclear Information System (INIS)

Stanyukovich, K.P.; Borisova, L.B.

1985-01-01

Equations for gravitational fields are obtained on the basis of a generalized Lagrangian Z=f(R) (R is the scalar curvature). Such an approach permits to take into account the evolution of a gravitation ''constant''. An expression for the force Fsub(i) versus the field variability is obtained. Conservation laws are formulated differing from the standard ones by the fact that in the right part of new equations the value Fsub(i) is present that goes to zero at an ultimate passage to the standard Einstein theory. An equation of state is derived for cosmological metrics for a particular case, f=bRsup(1+α) (b=const, α=const)

Scalar-flat Kaehler metrics with conformal Bianchi V symmetry

Energy Technology Data Exchange (ETDEWEB)

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

2011-06-21

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

Estimation of watershed-level distributed forest structure metrics relevant to hydrologic modeling using LiDAR and Landsat

Science.gov (United States)

Varhola, Andrés; Coops, Nicholas C.

2013-04-01

SummaryA detailed characterization of vegetation structure is fundamental for physically-based hydrologic models to simulate various processes that determine rates of snow accumulation and ablation, evapotranspiration and water dynamics. However, major efforts focused on developing complex equations to describe hydrologic processes as a function of vegetation structure at the plot level have not been accompanied by corresponding attempts to adequately extrapolate these metrics over the wider landscape in order to parameterize fully-distributed models. Recent advances in remote sensing technologies offer alternatives to overcome these difficulties and therefore improve our capacity to monitor vegetation and hydrologic processes extensively. Airborne Laser Scanning (ALS) stands out as the most promising tool to provide detailed, 3-dimensional representations of vegetation from which a wide array of structural metrics can be estimated. On the other hand, moderate scale optical remote sensing imagery such as Landsat Thematic Mapper (TM) offers the capacity to extrapolate these metrics across the landscape by virtue of its spatial and temporal resolutions. Here we correlate ALS-derived forest cover (FC), tree height (H), leaf area index (LAI) and sky view-factor (SVF) - the four main structural parameters used by hydrologic models - with a suite of spectral indices obtained from six spectral bands of a Landsat 5 TM image. Despite numerous sources of variation that affect the relationships between 2-dimensional spectral indices and three-dimensional structural metrics, models to predict FC, H, LAI and SVF with reasonable accuracy were developed. The extrapolation of these variables across a watershed in British Columbia severely affected by insect disturbance resulted in highly-detailed 30 m spatial resolution maps and frequency distributions consistent with the natural variation ranges of each metric - a major improvement compared to traditional approaches that use

Dirac equation for massive neutrinos in a Schwarzschild-de Sitter spacetime from a 5D vacuum

International Nuclear Information System (INIS)

Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

2011-01-01

Starting from a Dirac equation for massless neutrino in a 5D Ricci-flat background metric, we obtain the effective 4D equation for massive neutrino in a Schwarzschild-de Sitter (SdS) background metric from an extended SdS 5D Ricci-flat metric. We use the fact that the spin connection is defined to an accuracy of a vector, so that the covariant derivative of the spinor field is strongly dependent of the background geometry. We show that the mass of the neutrino can be induced from the extra space-like dimension.

Stochastic modeling of stock price process induced from the conjugate heat equation

Science.gov (United States)

Paeng, Seong-Hun

2015-02-01

Currency can be considered as a ruler for values of commodities. Then the price is the measured value by the ruler. We can suppose that inflation and variation of exchange rate are caused by variation of the scale of the ruler. In geometry, variation of the scale means that the metric is time-dependent. The conjugate heat equation is the modified heat equation which satisfies the heat conservation law for the time-dependent metric space. We propose a new model of stock prices by using the stochastic process whose transition probability is determined by the kernel of the conjugate heat equation. Our model of stock prices shows how the volatility term is affected by inflation and exchange rate. This model modifies the Black-Scholes equation in light of inflation and exchange rate.

Singularly perturbed hyperbolic problems on metric graphs: asymptotics of solutions

Directory of Open Access Journals (Sweden)

Golovaty Yuriy

2017-04-01

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

Sharp metric obstructions for quasi-Einstein metrics

Science.gov (United States)

Case, Jeffrey S.

2013-02-01

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

The Planck Vacuum and the Schwarzschild Metrics

Directory of Open Access Journals (Sweden)

Daywitt W. C.

2009-07-01

Full Text Available The Planck vacuum (PV is assumed to be the source of the visible universe. So under conditions of sufficient stress, there must exist a pathway through which energy from the PV can travel into this universe. Conversely, the passage of energy from the visible universe to the PV must also exist under the same stressful conditions. The following examines two versions of the Schwarzschild metric equation for compatability with this open-pathway idea.

Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method

Science.gov (United States)

Osetrin, Evgeny; Osetrin, Konstantin

2017-11-01

We consider space-time models with pure radiation, which admit integration of the eikonal equation by the method of separation of variables. For all types of these models, the equations of the energy-momentum conservation law are integrated. The resulting form of metric, energy density, and wave vectors of radiation as functions of metric for all types of spaces under consideration is presented. The solutions obtained can be used for any metric theories of gravitation.

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

International Nuclear Information System (INIS)

Reuter, Martin; Schollmeyer, Gregor M.

2016-01-01

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

Fitness function and nonunique solutions in x-ray reflectivity curve fitting: crosserror between surface roughness and mass density

International Nuclear Information System (INIS)

Tiilikainen, J; Bosund, V; Mattila, M; Hakkarainen, T; Sormunen, J; Lipsanen, H

2007-01-01

Nonunique solutions of the x-ray reflectivity (XRR) curve fitting problem were studied by modelling layer structures with neural networks and designing a fitness function to handle the nonidealities of measurements. Modelled atomic-layer-deposited aluminium oxide film structures were used in the simulations to calculate XRR curves based on Parratt's formalism. This approach reduced the dimensionality of the parameter space and allowed the use of fitness landscapes in the study of nonunique solutions. Fitness landscapes, where the height in a map represents the fitness value as a function of the process parameters, revealed tracks where the local fitness optima lie. The tracks were projected on the physical parameter space thus allowing the construction of the crosserror equation between weakly determined parameters, i.e. between the mass density and the surface roughness of a layer. The equation gives the minimum error for the other parameters which is a consequence of the nonuniqueness of the solution if noise is present. Furthermore, the existence of a possible unique solution in a certain parameter range was found to be dependent on the layer thickness and the signal-to-noise ratio

Dunajski–Tod equation and reductions of the generalized dispersionless 2DTL hierarchy

Energy Technology Data Exchange (ETDEWEB)

Bogdanov, L.V., E-mail: leonid@landau.ac.ru [L.D. Landau ITP RAS, Moscow (Russian Federation)

2012-10-01

We transfer the scheme for constructing differential reductions recently developed for the Manakov–Santini hierarchy to the case of the two-component generalization of dispersionless 2DTL hierarchy. We demonstrate that the equation arising as a result of the simplest reduction is equivalent (up to a Legendre type transformation) to the Dunajski–Tod equation, locally describing general ASD vacuum metric with conformal symmetry. We consider higher reductions and corresponding reduced hierarchies also. -- Highlights: ► We introduce a differential reduction for the two-component d2DTL equation. ► We demonstrate that it is connected with ASD vacuum metric with conformal symmetry. ► We construct higher reductions and the reduced hierarchies.

Generalized metric formulation of double field theory on group manifolds

International Nuclear Information System (INIS)

Blumenhagen, Ralph; Bosque, Pascal du; Hassler, Falk; Lüst, Dieter

2015-01-01

We rewrite the recently derived cubic action of Double Field Theory on group manifolds http://dx.doi.org/10.1007/JHEP02(2015)001 in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT WZW and of original DFT from tori is clarified. Furthermore, we show how to relate DFT WZW of the WZW background with the flux formulation of original DFT.

Metrics of a 'mole hole' against the Lobachevsky space background

International Nuclear Information System (INIS)

Tentyukov, M.N.

1994-01-01

'Classical' mole hole are the Euclidean metrics consisting of two large space regions connected by a throat. They are the instanton solutions of the Einstein equations. It is shown that for existence of mole holes in the general relativity theory it is required the energy-momentum tensor breaking energetic conditions. 9 refs., 7 figs

Cosmological transitions with changes in the signature of the metric

International Nuclear Information System (INIS)

Sakharov, A.D.

1984-01-01

It is conjectured that there exist states of the physical continuum which include regions with different signatures of the metric and that the observed Universe and an infinite number of other Universes arose as a result of quantum transitions with a change in the signature of the metric. The Lagrangian in such a theory must satisfy conditions of non-negativity in the regions with even signature. Signature here means the number of time coordinates. The induced gravitational Lagrangian in a conformally invariant theory of Kaluza-Klein type evidently satisfies this requirement and leads to effective equations of the gravitational theory of macroscopic space identical to the equations of the general theory of relativity. It is suggested that in our Universe there exist in addition to the observable (macroscopic) time dimension two or some other even number of compactified time dimensions. It is suggested that the formation of a Euclidean region in the center of a black hole or in the cosmological contraction of the Universe (if it is predetermined by the dynamics) is a possible outcome of gravitational collapse

A Comparison of Two-Stage Approaches for Fitting Nonlinear Ordinary Differential Equation Models with Mixed Effects.

Science.gov (United States)

Chow, Sy-Miin; Bendezú, Jason J; Cole, Pamela M; Ram, Nilam

2016-01-01

Several approaches exist for estimating the derivatives of observed data for model exploration purposes, including functional data analysis (FDA; Ramsay & Silverman, 2005 ), generalized local linear approximation (GLLA; Boker, Deboeck, Edler, & Peel, 2010 ), and generalized orthogonal local derivative approximation (GOLD; Deboeck, 2010 ). These derivative estimation procedures can be used in a two-stage process to fit mixed effects ordinary differential equation (ODE) models. While the performance and utility of these routines for estimating linear ODEs have been established, they have not yet been evaluated in the context of nonlinear ODEs with mixed effects. We compared properties of the GLLA and GOLD to an FDA-based two-stage approach denoted herein as functional ordinary differential equation with mixed effects (FODEmixed) in a Monte Carlo (MC) study using a nonlinear coupled oscillators model with mixed effects. Simulation results showed that overall, the FODEmixed outperformed both the GLLA and GOLD across all the embedding dimensions considered, but a novel use of a fourth-order GLLA approach combined with very high embedding dimensions yielded estimation results that almost paralleled those from the FODEmixed. We discuss the strengths and limitations of each approach and demonstrate how output from each stage of FODEmixed may be used to inform empirical modeling of young children's self-regulation.

Cosmology of hybrid metric-Palatini f(X)-gravity

International Nuclear Information System (INIS)

Capozziello, Salvatore; Harko, Tiberiu; Koivisto, Tomi S.; Lobo, Francisco S.N.; Olmo, Gonzalo J.

2013-01-01

A new class of modified theories of gravity, consisting of the superposition of the metric Einstein-Hilbert Lagrangian with an f(R) term constructed à la Palatini was proposed recently. The dynamically equivalent scalar-tensor representation of the model was also formulated, and it was shown that even if the scalar field is very light, the theory passes the Solar System observational constraints. Therefore the model predicts the existence of a long-range scalar field, modifying the cosmological and galactic dynamics. An explicit model that passes the local tests and leads to cosmic acceleration was also obtained. In the present work, it is shown that the theory can be also formulated in terms of the quantity X≡κ 2 T+R, where T and R are the traces of the stress-energy and Ricci tensors, respectively. The variable X represents the deviation with respect to the field equation trace of general relativity. The cosmological applications of this hybrid metric-Palatini gravitational theory are also explored, and cosmological solutions coming from the scalar-tensor representation of f(X)-gravity are presented. Criteria to obtain cosmic acceleration are discussed and the field equations are analyzed as a dynamical system. Several classes of dynamical cosmological solutions, depending on the functional form of the effective scalar field potential, describing both accelerating and decelerating Universes are explicitly obtained. Furthermore, the cosmological perturbation equations are derived and applied to uncover the nature of the propagating scalar degree of freedom and the signatures these models predict in the large-scale structure

$\\eta$-metric structures

OpenAIRE

Gaba, Yaé Ulrich

2017-01-01

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

Hermitian-Einstein metrics on holomorphic vector bundles over Hermitian manifolds

International Nuclear Information System (INIS)

Xi Zhang

2004-07-01

In this paper, we prove the long-time existence of the Hermitian-Einstein flow on a holomorphic vector bundle over a compact Hermitian (non-kaehler) manifold, and solve the Dirichlet problem for the Hermitian-Einstein equations. We also prove the existence of Hermitian-Einstein metrics for holomorphic vector bundles on a class of complete noncompact Hermitian manifolds. (author)

A Hamiltonian structure for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Torres del Castillo, G.F.

1991-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained (Author)

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

International Nuclear Information System (INIS)

Maeder, A.

1978-01-01

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

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

Science.gov (United States)

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

2018-03-01

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

Two-body Dirac equations for nucleon-nucleon scattering

International Nuclear Information System (INIS)

Liu Bin; Crater, Horace

2003-01-01

We investigate the nucleon-nucleon interaction by using the meson exchange model and the two-body Dirac equations of constraint dynamics. This approach to the two-body problem has been successfully tested for QED and QCD relativistic bound states. An important question we wish to address is whether or not the two-body nucleon-nucleon scattering problem can be reasonably described in this approach as well. This test involves a number of related problems. First we must reduce our two-body Dirac equations exactly to a Schroedinger-like equation in such a way that allows us to use techniques to solve them already developed for Schroedinger-like systems in nonrelativistic quantum mechanics. Related to this, we present a new derivation of Calogero's variable phase shift differential equation for coupled Schroedinger-like equations. Then we determine if the use of nine meson exchanges in our equations gives a reasonable fit to the experimental scattering phase shifts for n-p scattering. The data involve seven angular momentum states including the singlet states 1 S 0 , 1 P 1 , 1 D 2 and the triplet states 3 P 0 , 3 P 1 , 3 S 1 , 3 D 1 . Two models that we have tested give us a fairly good fit. The parameters obtained by fitting the n-p experimental scattering phase shift give a fairly good prediction for most of the p-p experimental scattering phase shifts examined (for the singlet states 1 S 0 , 1 D 2 and triplet states 3 P 0 , 3 P 1 ). Thus the two-body Dirac equations of constraint dynamics present us with a fit that encourages the exploration of a more realistic model. We outline generalizations of the meson exchange model for invariant potentials that may possibly improve the fit

Generalized metric formulation of double field theory on group manifolds

Energy Technology Data Exchange (ETDEWEB)

Blumenhagen, Ralph [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Bosque, Pascal du [Arnold-Sommerfeld-Center für Theoretische Physik,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); Hassler, Falk [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Lüst, Dieter [Max-Planck-Institut für Physik,Föhringer Ring 6, 80805 München (Germany); Arnold-Sommerfeld-Center für Theoretische Physik,Department für Physik, Ludwig-Maximilians-Universität München,Theresienstraße 37, 80333 München (Germany); CERN, PH-TH,1211 Geneva 23 (Switzerland)

2015-08-13

We rewrite the recently derived cubic action of Double Field Theory on group manifolds http://dx.doi.org/10.1007/JHEP02(2015)001 in terms of a generalized metric and extrapolate it to all orders in the fields. For the resulting action, we derive the field equations and state them in terms of a generalized curvature scalar and a generalized Ricci tensor. Compared to the generalized metric formulation of DFT derived from tori, all these quantities receive additional contributions related to the non-trivial background. It is shown that the action is invariant under its generalized diffeomorphisms and 2D-diffeomorphisms. Imposing additional constraints relating the background and fluctuations around it, the precise relation between the proposed generalized metric formulation of DFT{sub WZW} and of original DFT from tori is clarified. Furthermore, we show how to relate DFT{sub WZW} of the WZW background with the flux formulation of original DFT.

Fitted temperature-corrected Compton cross sections for Monte Carlo applications and a sampling distribution

International Nuclear Information System (INIS)

Wienke, B.R.; Devaney, J.J.; Lathrop, B.L.

1984-01-01

Simple temperature-corrected cross sections, which replace the static Klein-Nishina set in a one-to-one manner, are developed for Monte Carlo applications. The reduced set is obtained from a nonlinear least-squares fit to the exact photon-Maxwellian electron cross sections by using a Klein-Nishina-like formula as the fitting equation. Two parameters are sufficient, and accurate to two decimal places, to explicitly fit the exact cross sections over a range of 0 to 100 keV in electron temperature and 0 to 1 MeV in incident photon energy. Since the fit equations are Klein-Nishina-like, existing Monte Carlo code algorithms using the Klein-Nishina formula can be trivially modified to accommodate corrections for a moving Maxwellian electron background. The simple two parameter scheme and other fits are presented and discussed and comparisons with exact predictions are exhibited. The fits are made to the total photon-Maxwellian electron cross section and the fitting parameters can be consistently used in both the energy conservation equation for photon-electron scattering and the differential cross section, as they are presently sampled in Monte Carlo photonics applications. The fit equations are motivated in a very natural manner by the asymptotic expansion of the exact photon-Maxwellian effective cross-section kernel. A probability distribution is also obtained for the corrected set of equations

Solutions of the spin coefficient equations with nongeodesic eigenrays

International Nuclear Information System (INIS)

Kota, J.; Lukacs, B.; Perjes, Z.

1982-01-01

Among the many significant results obtained by spin coefficient techniques in general relativity, the exact integrals of gravitational equations have enjoyed particular attention. These integration procedures were first carried out with respect to a congruence of null geodesic curves. The authors show that spin coefficient equations can sometimes be exactly solved when the selected null congruence is nongeodesic. They derive metrics with this property and, among them, a new solution of the coupled Einstein-Maxwell equations. (Auth.)

Pediatric anthropometrics are inconsistent with current guidelines for assessing rider fit on all-terrain vehicles.

Science.gov (United States)

Bernard, Andrew C; Mullineaux, David R; Auxier, James T; Forman, Jennifer L; Shapiro, Robert; Pienkowski, David

2010-07-01

This study sought to establish objective anthropometric measures of fit or misfit for young riders on adult and youth-sized all-terrain vehicles and use these metrics to test the unproved historical reasoning that age alone is a sufficient measure of rider-ATV fit. Male children (6-11 years, n=8; and 12-15 years, n=11) were selected by convenience sampling. Rider-ATV fit was quantified by five measures adapted from published recommendations: (1) standing-seat clearance, (2) hand size, (3) foot vs. foot-brake position, (4) elbow angle, and (5) handlebar-to-knee distance. Youths aged 12-15 years fit the adult-sized ATV better than the ATV Safety Institute recommended age-appropriate youth model (63% of subjects fit all 5 measures on adult-sized ATV vs. 20% on youth-sized ATV). Youths aged 6-11 years fit poorly on ATVs of both sizes (0% fit all 5 parameters on the adult-sized ATV vs 12% on the youth-sized ATV). The ATV Safety Institute recommends rider-ATV fit according to age and engine displacement, but no objective data linking age or anthropometrics with ATV engine or frame size has been previously published. Age alone is a poor predictor of rider-ATV fit; the five metrics used offer an improvement compared to current recommendations. Copyright 2010 Elsevier Ltd. All rights reserved.

Variational boundary conditions based on the Nitsche method for fitted and unfitted isogeometric discretizations of the mechanically coupled Cahn-Hilliard equation

Science.gov (United States)

Zhao, Ying; Schillinger, Dominik; Xu, Bai-Xiang

2017-07-01

The primal variational formulation of the fourth-order Cahn-Hilliard equation requires C1-continuous finite element discretizations, e.g., in the context of isogeometric analysis. In this paper, we explore the variational imposition of essential boundary conditions that arise from the thermodynamic derivation of the Cahn-Hilliard equation in primal variables. Our formulation is based on the symmetric variant of Nitsche's method, does not introduce additional degrees of freedom and is shown to be variationally consistent. In contrast to strong enforcement, the new boundary condition formulation can be naturally applied to any mapped isogeometric parametrization of any polynomial degree. In addition, it preserves full accuracy, including higher-order rates of convergence, which we illustrate for boundary-fitted discretizations of several benchmark tests in one, two and three dimensions. Unfitted Cartesian B-spline meshes constitute an effective alternative to boundary-fitted isogeometric parametrizations for constructing C1-continuous discretizations, in particular for complex geometries. We combine our variational boundary condition formulation with unfitted Cartesian B-spline meshes and the finite cell method to simulate chemical phase segregation in a composite electrode. This example, involving coupling of chemical fields with mechanical stresses on complex domains and coupling of different materials across complex interfaces, demonstrates the flexibility of variational boundary conditions in the context of higher-order unfitted isogeometric discretizations.

Taming the nonlinearity of the Einstein equation.

Science.gov (United States)

Harte, Abraham I

2014-12-31

Many of the technical complications associated with the general theory of relativity ultimately stem from the nonlinearity of Einstein's equation. It is shown here that an appropriate choice of dynamical variables may be used to eliminate all such nonlinearities beyond a particular order: Both Landau-Lifshitz and tetrad formulations of Einstein's equation are obtained that involve only finite products of the unknowns and their derivatives. Considerable additional simplifications arise in physically interesting cases where metrics become approximately Kerr or, e.g., plane waves, suggesting that the variables described here can be used to efficiently reformulate perturbation theory in a variety of contexts. In all cases, these variables are shown to have simple geometrical interpretations that directly relate the local causal structure associated with the metric of interest to the causal structure associated with a prescribed background. A new method to search for exact solutions is outlined as well.

The metric and curvature properties of H-space

International Nuclear Information System (INIS)

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

1978-01-01

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

Remark on application of the Banach metric method to cosmology

International Nuclear Information System (INIS)

Szydlowski, M.; Heller, M.

1982-01-01

If the cosmological equations can be reduced to the form of a dynamic system, the space of all their solutions is a Banach space. The influence of different parameters on the dynamics of the world models can be easily studied by means of the Banach metric. The method is tested for the Friedman cosmological models perturbed by the bulk viscosity. (author)

Exact solutions of Einstein and Einstein-scalar equations in 2+1 dimensions

International Nuclear Information System (INIS)

Virbhadra, K.S.

1995-01-01

A nonstatic and circularly symmetric exact solution of the Einstein equations (with a cosmological constant Λ and null fluid) in 2 + 1 dimensions is given. This is a nonstatic generalization of the uncharged spinless Bandos Teitelboim Zanelli (BTZ) metric. For Λ = 0, spacetime is though not flat, the Kretschmann invariant vanishes. The energy, momentum, and power output for this metric are obtained. Further a static and circularly symmetric exact solution of the Einstein-massless scalar equations is given, which has a curvature singularity at r=0 and the scalar field diverges at r=0 as well as at infinity. (author). 12 refs

An improved nucleate boiling design equation

International Nuclear Information System (INIS)

Basu, D.K.; Pinder, K.L.

1976-01-01

The effect of varying ΔT, the primary variable, on the value of heat transfer coefficient (h) in nucleate boiling is discussed. The three-parameter quadratic equation, h=P 1 + P 2 (ΔT) + P 3 (ΔT) 2 (where the constants, P 1 ,P 2 ,P 3 are functions of pressure, liquid properties and surface properties of the heater) is suggested. Ten sets of data at atmospheric pressure from six different workers and two more sets for pressure variation have been tested. The above quadratic equation fits the experimental data better than the existing two-parameter power relation, h=C(ΔT)sup(n) (where C is constant). The values of the three coeffcients in the quadratic equations are dependent on pressure, liquid properties and surface properties. A generalized empirical equation has been derived, which fits the selected pressure data well. (author)

A variational principle giving gravitational 'superpotentials', the affine connection, Riemann tensor, and Einstein field equations

International Nuclear Information System (INIS)

Stachel, J.

1977-01-01

A first-order Lagrangian is given, from which follow the definitions of the fully covariant form of the Riemann tensor Rsub(μνkappalambda) in terms of the affine connection and metric; the definition of the affine connection in terms of the metric; the Einstein field equations; and the definition of a set of gravitational 'superpotentials' closely connected with the Komar conservation laws (Phys. Rev.; 113:934 (1959)). Substitution of the definition of the affine connection into this Lagrangian results in a second-order Lagrangian, from which follow the definition of the fully covariant Riemann tensor in terms of the metric, the Einstein equations, and the definition of the gravitational 'superpotentials'. (author)

Comparison of the Schrodinger and Salpeter equations

International Nuclear Information System (INIS)

Jacobs, S.; Olsson, M.G.

1985-01-01

A unified approach to the solution of the Schrodinger and spinless Salpeter equations is presented. Fits to heavy quark bound state energies using various potential models are employed to determine whether the Salpeter equation provides a better description of heavy quark systems than the Schrodinger equation

Einstein's equations of motion in the gravitational field of an oblate ...

African Journals Online (AJOL)

In an earlier paper we derived Einstein's geometrical gravitational field equations for the metric tensor due to an oblate spheroidal massive body. In this paper we derive the corresponding Einstein's equations of motion for a test particle of nonzero rest mass in the gravitational field exterior to a homogeneous oblate ...

The canonical equation of adaptive dynamics for life histories: from fitness-returns to selection gradients and Pontryagin's maximum principle.

Science.gov (United States)

Metz, Johan A Jacob; Staňková, Kateřina; Johansson, Jacob

2016-03-01

This paper should be read as addendum to Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013). Our goal is, using little more than high-school calculus, to (1) exhibit the form of the canonical equation of adaptive dynamics for classical life history problems, where the examples in Dieckmann et al. (J Theor Biol 241:370-389, 2006) and Parvinen et al. (J Math Biol 67: 509-533, 2013) are chosen such that they avoid a number of the problems that one gets in this most relevant of applications, (2) derive the fitness gradient occurring in the CE from simple fitness return arguments, (3) show explicitly that setting said fitness gradient equal to zero results in the classical marginal value principle from evolutionary ecology, (4) show that the latter in turn is equivalent to Pontryagin's maximum principle, a well known equivalence that however in the literature is given either ex cathedra or is proven with more advanced tools, (5) connect the classical optimisation arguments of life history theory a little better to real biology (Mendelian populations with separate sexes subject to an environmental feedback loop), (6) make a minor improvement to the form of the CE for the examples in Dieckmann et al. and Parvinen et al.

A Static Solution of Yang-Mills Equation on Anti-de Sitter Space

International Nuclear Information System (INIS)

Chen Li; Ren Xinan

2009-01-01

Since product metric on AdS space has played a very important role in Lorentz version of AdS/CFT correspondence, the Yang-Mills equation on AdS space with this metric is considered and a static solution is obtained in this paper, which helps to understand the AdS/CFT correspondence of Yang-Mills fields. (general)

Covariant field equations, gauge fields and conservation laws from Yang-Mills matrix models

International Nuclear Information System (INIS)

Steinacker, Harold

2009-01-01

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.

Evaluation of Vehicle-Based Crash Severity Metrics.

Science.gov (United States)

Tsoi, Ada H; Gabler, Hampton C

2015-01-01

Vehicle change in velocity (delta-v) is a widely used crash severity metric used to estimate occupant injury risk. Despite its widespread use, delta-v has several limitations. Of most concern, delta-v is a vehicle-based metric which does not consider the crash pulse or the performance of occupant restraints, e.g. seatbelts and airbags. Such criticisms have prompted the search for alternative impact severity metrics based upon vehicle kinematics. The purpose of this study was to assess the ability of the occupant impact velocity (OIV), acceleration severity index (ASI), vehicle pulse index (VPI), and maximum delta-v (delta-v) to predict serious injury in real world crashes. The study was based on the analysis of event data recorders (EDRs) downloaded from the National Automotive Sampling System / Crashworthiness Data System (NASS-CDS) 2000-2013 cases. All vehicles in the sample were GM passenger cars and light trucks involved in a frontal collision. Rollover crashes were excluded. Vehicles were restricted to single-event crashes that caused an airbag deployment. All EDR data were checked for a successful, completed recording of the event and that the crash pulse was complete. The maximum abbreviated injury scale (MAIS) was used to describe occupant injury outcome. Drivers were categorized into either non-seriously injured group (MAIS2-) or seriously injured group (MAIS3+), based on the severity of any injuries to the thorax, abdomen, and spine. ASI and OIV were calculated according to the Manual for Assessing Safety Hardware. VPI was calculated according to ISO/TR 12353-3, with vehicle-specific parameters determined from U.S. New Car Assessment Program crash tests. Using binary logistic regression, the cumulative probability of injury risk was determined for each metric and assessed for statistical significance, goodness-of-fit, and prediction accuracy. The dataset included 102,744 vehicles. A Wald chi-square test showed each vehicle-based crash severity metric

To Move More and Sit Less: Does Physical Activity/Fitness Knowledge Matter in Youth?

Science.gov (United States)

Chen, Senlin; Liu, Yang; Schaben, Jodee

2017-01-01

Purpose: The purpose of this study was to examine physical activity (PA)/fitness knowledge and its association with PA and sedentary behavior in youth. Method: Eighth grade students from five schools (N = 660) in a midwestern state completed a PE Metrics written test and the Youth Activity Profile to assess PA/fitness knowledge, PA (at school and…

Metric approach to quantum constraints

International Nuclear Information System (INIS)

Brody, Dorje C; Hughston, Lane P; Gustavsson, Anna C T

2009-01-01

A framework for deriving equations of motion for constrained quantum systems is introduced and a procedure for its implementation is outlined. In special cases, the proposed new method, which takes advantage of the fact that the space of pure states in quantum mechanics has both a symplectic structure and a metric structure, reduces to a quantum analogue of the Dirac theory of constraints in classical mechanics. Explicit examples involving spin-1/2 particles are worked out in detail: in the first example, our approach coincides with a quantum version of the Dirac formalism, while the second example illustrates how a situation that cannot be treated by Dirac's approach can nevertheless be dealt with in the present scheme.

Projection-iteration methods for solving nonlinear operator equations

International Nuclear Information System (INIS)

Nguyen Minh Chuong; Tran thi Lan Anh; Tran Quoc Binh

1989-09-01

In this paper, the authors investigate a nonlinear operator equation in uniformly convex Banach spaces as in metric spaces by using stationary and nonstationary generalized projection-iteration methods. Convergence theorems in the strong and weak sense were established. (author). 7 refs

Semantic metrics

OpenAIRE

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

2006-01-01

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

Stability properties of solutions to nonlinear models possessing a sign-undefined metric

International Nuclear Information System (INIS)

Barashenkov, I.V.

1983-01-01

Multicomponent field systems possessing a sign-undefined internal space metric, in particular models with a noncompact global invariance group are investigated. It is shown that the energy cannot have even a conditional relative minimum. It is demonstrated, nevertheless, that the corresponding nonlinear equations of motion are permitted to possess stable particle-like solutions

Metric modular spaces

CERN Document Server

Chistyakov, Vyacheslav

2015-01-01

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

Deriving Langevin equations in curved spacetime

International Nuclear Information System (INIS)

Ramos, Rudnei O.; Tavares, Romulo F.

2013-01-01

Full text: Warm inflation is an inflationary scenario where the interactions between the inflaton and other degrees of freedom are considered. The effective equation of motion for the inflaton is in general of the form of a Langevin equation, that includes both quantum and thermal effects and where these effects manifest in the form of dissipation and stochastic noise terms, which are related by a generalized fluctuation-dissipation relation. The dissipation term is related to the interactions of the inflaton with other degrees of freedom of the thermal bath that can be obtained from the appropriate Feynman propagators. As the inflaton evolves into an expanding metric, these effects have to be taken into account when calculating the Green functions and consequently the Feynman propagators. In this work we present the considerations that must be made to calculate the Green functions in curved space (expanding metric) and in the presence of radiation in order to proper derive the effective evolution of the inflaton in the warm-inflation scenario. (author)

Static Einstein--Maxwell field equations

International Nuclear Information System (INIS)

Das, A.

1979-01-01

The static Einstein--Maxwell field equations are investigated in the presence of both electric and magnetic fields. The sources or bodies are assumed to be of finite size and to not affect the connectivity of the associated space. Furthermore, electromagnetic and metric fields are assumed to have reasonable differentiabilities. It is then proved that the electric and magnetic field vectors are constant multiples of one another. Moreover, the static Einstein--Maxwell equations reduce to the static magnetovac case. If, furthermore, the variational derivation of the Einstein--Maxwell equations is assumed, then both the total electric and magnetic charge of each body must vanish. As a physical consequence it is pointed out that if a suspended magnet be electrically charged then it must experience a purely general relativistic torque

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-07-01

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

An analytical model of the HINT performance metric

Energy Technology Data Exchange (ETDEWEB)

Snell, Q.O.; Gustafson, J.L. [Scalable Computing Lab., Ames, IA (United States)

1996-10-01

The HINT benchmark was developed to provide a broad-spectrum metric for computers and to measure performance over the full range of memory sizes and time scales. We have extended our understanding of why HINT performance curves look the way they do and can now predict the curves using an analytical model based on simple hardware specifications as input parameters. Conversely, by fitting the experimental curves with the analytical model, hardware specifications such as memory performance can be inferred to provide insight into the nature of a given computer system.

The numerical simulation of convection delayed dominated diffusion equation

Directory of Open Access Journals (Sweden)

Mohan Kumar P. Murali

2016-01-01

Full Text Available In this paper, we propose a fitted numerical method for solving convection delayed dominated diffusion equation. A fitting factor is introduced and the model equation is discretized by cubic spline method. The error analysis is analyzed for the consider problem. The numerical examples are solved using the present method and compared the result with the exact solution.

Stability properties of solutions to nonlinear models possessing a sign-undefined metric

International Nuclear Information System (INIS)

Barashenkov, I.V.

1983-01-01

Multicomponent field systems possessing a sign-undefined internal space metric, in particular models with a noncompact global invariance group, are investigated. It is shown that the energy cannot have even a conditional relative minimum. It is demonstrated, nevertheless, that the corresponding nonlinear equations of motion are permitted to possess stable particle-like solutions. (Auth.)

Measuring floodplain spatial patterns using continuous surface metrics at multiple scales

Science.gov (United States)

Scown, Murray W.; Thoms, Martin C.; 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.

Fixed Points of Multivalued Contractive Mappings in Partial Metric Spaces

Directory of Open Access Journals (Sweden)

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.

On the hyperbolicity of Einstein's and other gauge field equations

International Nuclear Information System (INIS)

Friedrich, H.

1985-01-01

It is shown that Einstein's vacuum field equations (respectively the conformal vacuum field equations) in a frame formalism imply a symmetric hyperbolic system of ''reduce'' propagation equations for any choice of coordinate system and frame field (and conformal factor). Certain freely specifiable ''gauge source'' functions occurring in the reduced equations reflect the choice of gauge. Together with the initial data they determine the gauge uniquely. Their choice does not affect the isometry class (conformal class) of a solution of an initial value problem. By the same method symmetric hyperbolic propagation equations are obtained from other gauge field equations, irrespective of the gauge. Using the concept of source functions one finds that Einstein's field equation, considered as second order equations for the metric coefficients, are of wave equation type in any coordinate system. (orig.)

Using Patient Health Questionnaire-9 item parameters of a common metric resulted in similar depression scores compared to independent item response theory model reestimation.

Science.gov (United States)

Liegl, Gregor; Wahl, Inka; Berghöfer, Anne; Nolte, Sandra; Pieh, Christoph; Rose, Matthias; Fischer, Felix

2016-03-01

To investigate the validity of a common depression metric in independent samples. We applied a common metrics approach based on item-response theory for measuring depression to four German-speaking samples that completed the Patient Health Questionnaire (PHQ-9). We compared the PHQ item parameters reported for this common metric to reestimated item parameters that derived from fitting a generalized partial credit model solely to the PHQ-9 items. We calibrated the new model on the same scale as the common metric using two approaches (estimation with shifted prior and Stocking-Lord linking). By fitting a mixed-effects model and using Bland-Altman plots, we investigated the agreement between latent depression scores resulting from the different estimation models. We found different item parameters across samples and estimation methods. Although differences in latent depression scores between different estimation methods were statistically significant, these were clinically irrelevant. Our findings provide evidence that it is possible to estimate latent depression scores by using the item parameters from a common metric instead of reestimating and linking a model. The use of common metric parameters is simple, for example, using a Web application (http://www.common-metrics.org) and offers a long-term perspective to improve the comparability of patient-reported outcome measures. Copyright © 2016 Elsevier Inc. All rights reserved.

A Simple Metric for Determining Resolution in Optical, Ion, and Electron Microscope Images.

Science.gov (United States)

Curtin, Alexandra E; Skinner, Ryan; Sanders, Aric W

2015-06-01

A resolution metric intended for resolution analysis of arbitrary spatially calibrated images is presented. By fitting a simple sigmoidal function to pixel intensities across slices of an image taken perpendicular to light-dark edges, the mean distance over which the light-dark transition occurs can be determined. A fixed multiple of this characteristic distance is then reported as the image resolution. The prefactor is determined by analysis of scanning transmission electron microscope high-angle annular dark field images of Si. This metric has been applied to optical, scanning electron microscope, and helium ion microscope images. This method provides quantitative feedback about image resolution, independent of the tool on which the data were collected. In addition, our analysis provides a nonarbitrary and self-consistent framework that any end user can utilize to evaluate the resolution of multiple microscopes from any vendor using the same metric.

Covariant electrodynamics in linear media: Optical metric

Science.gov (United States)

Thompson, Robert T.

2018-03-01

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

Wave function of the Universe, preferred reference frame effects and metric signature transition

International Nuclear Information System (INIS)

Ghaffarnejad, Hossein

2015-01-01

Gravitational model of non-minimally coupled Brans Dicke (BD) scalar field 0 with dynamical unit time-like four vector field is used to study flat Robertson Walker (RW) cosmology in the presence of variable cosmological parameter V (ϕ) = Λϕ. Aim of the paper is to seek cosmological models which exhibit metric signature transition. The problem is studied in both classical and quantum cosmological approach with large values of BD parameter ω >> 1. Scale factor of RW metric is obtained as which describes nonsingular inflationary universe in Lorentzian signature sector. Euclidean signature sector of our solution describes a re-collapsing universe and is obtained from analytic continuation of the Lorentzian sector by exchanging . Dynamical vector field together with the BD scalar field are treated as fluid with time dependent barotropic index. They have regular (dark) matter dominance in the Euclidean (Lorentzian) sector. We solved Wheeler De Witt (WD) quantum wave equation of the cosmological system. Assuming a discrete non-zero ADM mass we obtained solutions of the WD equation as simple harmonic quantum Oscillator eigen functionals described by Hermite polynomials. Absolute values of these eigen functionals have nonzero values on the hypersurface in which metric field has signature degeneracy. Our eigen functionals describe nonzero probability of the space time with Lorentzian (Euclidean) signature for . Maximal probability corresponds to the ground state j = 0. (paper)

Baby universe metric equivalent to an interior black-hole metric

International Nuclear Information System (INIS)

Gonzalez-Diaz, P.F.

1991-01-01

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

Health-related physical fitness measures: reference values and reference equations for use in clinical practice.

Science.gov (United States)

Tveter, Anne Therese; Dagfinrud, Hanne; Moseng, Tuva; Holm, Inger

2014-07-01

To provide reference values and reference equations for frequently used clinical field tests of health-related physical fitness for use in clinical practice. Cross-sectional design. General community. Convenience sample of volunteers (N=370) between 18 and 90 years of age were recruited from a wide range of settings (ie, work sites, schools, community centers for older adults) and different geographic locations (ie, urban, suburban, rural) in southeastern Norway. Not applicable. The participants conducted 5 clinical field tests (6-minute walk test, stair test, 30-second sit-to-stand test, handgrip test, fingertip-to-floor test). The results of the field tests showed that performance remained unchanged until approximately 50 years of age; after that, performance deteriorated with increasing age. Grip strength (79%), meters walked in 6 minutes (60%), and seconds used on the stair test (59%) could be well predicted by age, sex, height, and weight in participants ≥50 years of age, whereas the performance on all tests was less well predicted in participants clinical practice. Copyright © 2014 American Congress of Rehabilitation Medicine. Published by Elsevier Inc. All rights reserved.

Standardized reporting of functioning information on ICF-based common metrics.

Science.gov (United States)

Prodinger, Birgit; Tennant, Alan; Stucki, Gerold

2018-02-01

In clinical practice and research a variety of clinical data collection tools are used to collect information on people's functioning for clinical practice and research and national health information systems. Reporting on ICF-based common metrics enables standardized documentation of functioning information in national health information systems. The objective of this methodological note on applying the ICF in rehabilitation is to demonstrate how to report functioning information collected with a data collection tool on ICF-based common metrics. We first specify the requirements for the standardized reporting of functioning information. Secondly, we introduce the methods needed for transforming functioning data to ICF-based common metrics. Finally, we provide an example. The requirements for standardized reporting are as follows: 1) having a common conceptual framework to enable content comparability between any health information; and 2) a measurement framework so that scores between two or more clinical data collection tools can be directly compared. The methods needed to achieve these requirements are the ICF Linking Rules and the Rasch measurement model. Using data collected incorporating the 36-item Short Form Health Survey (SF-36), the World Health Organization Disability Assessment Schedule 2.0 (WHODAS 2.0), and the Stroke Impact Scale 3.0 (SIS 3.0), the application of the standardized reporting based on common metrics is demonstrated. A subset of items from the three tools linked to common chapters of the ICF (d4 Mobility, d5 Self-care and d6 Domestic life), were entered as "super items" into the Rasch model. Good fit was achieved with no residual local dependency and a unidimensional metric. A transformation table allows for comparison between scales, and between a scale and the reporting common metric. Being able to report functioning information collected with commonly used clinical data collection tools with ICF-based common metrics enables clinicians

Ernst Equation and Riemann Surfaces: Analytical and Numerical Methods

International Nuclear Information System (INIS)

Ernst, Frederick J

2007-01-01

Shortly after Einstein published his general theory of relativity, the spherically symmetric solution of the vacuum field equations was discovered by Karl Schwarzschild, while Hermann Weyl showed that from any axisymmetric solution ψ of the Laplace equation ∇ 2 ψ = 0 (satisfying appropriate boundary conditions) the metric tensor of a static axisymmetric vacuum spacetime can be constructed. In particular, the Schwarzschild solution corresponds to a rather trivial solution of Laplace's equation expressed in terms of prolate spheroidal coordinates. It took about 45 years before Roy Kerr discovered what he called the 'rotating Schwarzschild solution', and an additional five years before I established that from any complex axisymmetric solution E of the nonlinear equation E∇ 2 E = ∇E·∇E (satisfying appropriate boundary conditions) the metric tensor of a stationary axisymmetric vacuum spacetime can be constructed. In particular, the Kerr solution corresponds to an extremely simple solution of this equation expressed in terms of prolate spheroidal coordinates. Ever more complicated solutions of this equation (using prolate spheroidal coordinates) were discovered by Tomimatsu and Sato, but for none of the associated spacetimes has a reasonable material source been suggested. What the present book describes are some of the heroic efforts that have been undertaken to construct physically significant spacetimes by solving the vacuum Ernst equation. Unfortunately, thus far, no one has made much progress extending the Ernst equation approach to facilitate the investigation of spacetime within a stationary axisymmetric material source, where, for example, the stress-energy tensor is that of a perfect fluid. However, in 1994, Meinel and Neugebauer had the novel idea of focusing attention upon global solutions such as the spacetime geometry associated with a rotating infinitely thin disk of dust, where the material source can be represented by discontinuities in the

Gravitational and electromagnetic potentials of the stationary Einstein-Maxwell field equations

International Nuclear Information System (INIS)

Jones, T.C.

1979-01-01

Associated with the stationary Einstein-Maxwell field equations is an infinite hierarchy of potentials. The basic characteristics of these potentials are examined in general and then in greater detail for the particular case of the Reissner-Nordstrom metric. Thier essential utility in the process of solution generation is elucidated, and the necessary equations for solution generation are developed. Appropriate generating functions, which contain the complete infinite hierarchy of potentials, are developed and analyzed. Particular attention is paid to the inherent gauge freedom of these generating functions. Two methods of solution generation, which yield asymptotically flat solutions in vacuum, are generalized to include electromagnetism. One method, using potentials consistent with the Harrison transformation and the Reissner-Nordstrom metric, is discussed in detail, and its resultant difficulties are explored

Trigonometric solutions of triangle equations. Simple Lie superalgebras

International Nuclear Information System (INIS)

Bazhanov, V.V.; Shadrikov, A.G.

1988-01-01

Trigonometric solutions of the graded triangle equation are constructed for the fundamental representations of all simple (nonexceptional) Lie superalgebras with nondegenerate metric. In Sec. 1, we introduce the concept of Z 2 graded spaces and give the basic definitions. In Sec. 2, we determine fundamental representations of the Lie superalgebras sl(mn) and osp(2rs) and give explicit realizations of the Coxeter automorphisms. In secs. 3 and 4, we give the trigonometric solutions of the graded triangle equation (quantum R matrices)

A Practitioners’ Perspective on Developmental Models, Metrics and Community

Directory of Open Access Journals (Sweden)

Chad Stewart

2009-12-01

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

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

Science.gov (United States)

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Some Fixed Point Results for Caristi Type Mappings in Modular Metric Spaces with an Application

Directory of Open Access Journals (Sweden)

Duran Turkoglu

2016-08-01

Full Text Available In this paper we give Caristi type fixed point theorem in complete modular metric spaces. Moreover we give a theorem which can be derived from Caristi type. Also an application for the bounded solution of funcional equations is investigated.

Properties of C-metric spaces

Science.gov (United States)

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

2017-09-01

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

Homothetic and conformal motions in spacelike slices of solutions of Einstein's equations

International Nuclear Information System (INIS)

Berger, B.K.

1976-01-01

Components of Killing's equation are used to obtain constraints satisfied in a spacelike hypersurface by the intrinsic metric and extrinsic curvature in the presence of a spacetime conformal motion for a solution of Einstein's equations. If the conformal motion is either a homothetic motion or a motion, it is shown that these Killing constraints are preserved by the Einstein evolution equations. It is then shown that the generator of the homothetic motion (homothetic Killing vector) can be constructed if the Killing constraints are satisfied by a set of initial data. It is shown that a homothetic motion in the intrinsic metric is a spacetime homothetic motion if the extrinsic curvature is transformed correctly under the spatial homothetic motion. Further restrictions on a proper conformal motion due to the fact that it is not identically a curvature collineation are obtained. Restrictions on the matter--stress--energy tensor are discussed. Examples are presented

Learning Low-Dimensional Metrics

OpenAIRE

Jain, Lalit; Mason, Blake; Nowak, Robert

2017-01-01

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

Weyl consistency conditions and a local renormalisation group equation for general renormalisable field theories

International Nuclear Information System (INIS)

Osborn, H.

1991-01-01

A local renormalisation group equation which realises infinitesimal Weyl rescalings of the metric and which is an extension of the usual Callan-Symanzik equation is described. In order to ensure that any local composite operators, with dimensions so that on addition to the basic lagrangian they preserve renormalisability, are well defined for arbitrarily many insertions into correlation functions the couplings are assumed to depend on χ. Local operators are then defined by functional differentiation with respect to the couplings just as the energy-momentum tensor is given by functional differentiation with respect to the metric. The local renormalisation group equation contains terms depending on derivatives of the couplings as well as the curvature tensor formed from the metric, constrained by power counting. Various consistency relations arising from the commutativity of Weyl transformations are derived, extending previous one-loop results for the trace anomaly to all orders. In two dimensions the relations give an alternative derivation of the c-theorem and similar extensions are obtained in four dimensions. The equations are applied in detail to general renormalisable σ-models in two dimensions. The Curci-Paffuti relation is derived without any commitment to a particular regularisation scheme and further equations used to construct an action for the vanishing of the β-functions are also obtained. The discussion is also extended to σ-models with a boundary, as appropriate for open strings, and relations for the additional β-functions present in such models are obtained. (orig.)

Variational mesh segmentation via quadric surface fitting

KAUST Repository

Yan, Dongming; Wang, Wen Ping; Liu, Yang; Yang, Zhouwang

2012-01-01

We present a new variational method for mesh segmentation by fitting quadric surfaces. Each component of the resulting segmentation is represented by a general quadric surface (including plane as a special case). A novel energy function is defined to evaluate the quality of the segmentation, which combines both L2 and L2 ,1 metrics from a triangle to a quadric surface. The Lloyd iteration is used to minimize the energy function, which repeatedly interleaves between mesh partition and quadric surface fitting. We also integrate feature-based and simplification-based techniques in the segmentation framework, which greatly improve the performance. The advantages of our algorithm are demonstrated by comparing with the state-of-the-art methods. © 2012 Elsevier Ltd. All rights reserved.

Variational mesh segmentation via quadric surface fitting

KAUST Repository

Yan, Dongming

2012-11-01

We present a new variational method for mesh segmentation by fitting quadric surfaces. Each component of the resulting segmentation is represented by a general quadric surface (including plane as a special case). A novel energy function is defined to evaluate the quality of the segmentation, which combines both L2 and L2 ,1 metrics from a triangle to a quadric surface. The Lloyd iteration is used to minimize the energy function, which repeatedly interleaves between mesh partition and quadric surface fitting. We also integrate feature-based and simplification-based techniques in the segmentation framework, which greatly improve the performance. The advantages of our algorithm are demonstrated by comparing with the state-of-the-art methods. © 2012 Elsevier Ltd. All rights reserved.

Relativistic gas in a Schwarzschild metric

International Nuclear Information System (INIS)

Kremer, Gilberto M

2013-01-01

A relativistic gas in a Schwarzschild metric is studied within the framework of a relativistic Boltzmann equation in the presence of gravitational fields, where Marle’s model for the collision operator of the Boltzmann equation is employed. The transport coefficients of the bulk and shear viscosities and thermal conductivity are determined from the Chapman–Enskog method. It is shown that the transport coefficients depend on the gravitational potential. Expressions for the transport coefficients in the presence of weak gravitational fields in the non-relativistic (low temperature) and ultra-relativistic (high temperature) limiting cases are given. Apart from the temperature gradient the heat flux has two relativistic terms. The first one, proposed by Eckart, is due to the inertia of energy and represents an isothermal heat flux when matter is accelerated. The other, suggested by Tolman, is proportional to the gravitational potential gradient and indicates that—in the absence of an acceleration field—a state of equilibrium of a relativistic gas in a gravitational field can be attained only if the temperature gradient is counterbalanced by a gravitational potential gradient. (paper)

A stochastic version of the Price equation reveals the interplay of deterministic and stochastic processes in evolution

Directory of Open Access Journals (Sweden)

Rice Sean H

2008-09-01

Full Text Available Abstract Background Evolution involves both deterministic and random processes, both of which are known to contribute to directional evolutionary change. A number of studies have shown that when fitness is treated as a random variable, meaning that each individual has a distribution of possible fitness values, then both the mean and variance of individual fitness distributions contribute to directional evolution. Unfortunately the most general mathematical description of evolution that we have, the Price equation, is derived under the assumption that both fitness and offspring phenotype are fixed values that are known exactly. The Price equation is thus poorly equipped to study an important class of evolutionary processes. Results I present a general equation for directional evolutionary change that incorporates both deterministic and stochastic processes and applies to any evolving system. This is essentially a stochastic version of the Price equation, but it is derived independently and contains terms with no analog in Price's formulation. This equation shows that the effects of selection are actually amplified by random variation in fitness. It also generalizes the known tendency of populations to be pulled towards phenotypes with minimum variance in fitness, and shows that this is matched by a tendency to be pulled towards phenotypes with maximum positive asymmetry in fitness. This equation also contains a term, having no analog in the Price equation, that captures cases in which the fitness of parents has a direct effect on the phenotype of their offspring. Conclusion Directional evolution is influenced by the entire distribution of individual fitness, not just the mean and variance. Though all moments of individuals' fitness distributions contribute to evolutionary change, the ways that they do so follow some general rules. These rules are invisible to the Price equation because it describes evolution retrospectively. An equally general

Metrics of quantum states

International Nuclear Information System (INIS)

Ma Zhihao; Chen Jingling

2011-01-01

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

A New Solution for Einstein Field Equation in General Relativity

Science.gov (United States)

Mousavi, Sadegh

2006-05-01

There are different solutions for Einstein field equation in general relativity that they have been proposed by different people the most important solutions are Schwarzchild, Reissner Nordstrom, Kerr and Kerr Newmam. However, each one of these solutions limited to special case. I've found a new solution for Einstein field equation which is more complete than all previous ones and this solution contains the previous solutions as its special forms. In this talk I will present my new metric for Einstein field equation and the Christofel symbols and Richi and Rieman tensor components for the new metric that I have calculated them by GR TENSOR software. As a result I will determine the actual movement of black holes which is different From Kerr black hole's movement. Finally this new solution predicts, existence of a new and constant field in the nature (that nobody can found it up to now), so in this talk I will introduce this new field and even I will calculate the amount of this field. SADEGH MOUSAVI, Amirkabir University of Technology.

Exact analytical solution of the convolution integral equation for a general profile fitting function and Gaussian detector kernel

International Nuclear Information System (INIS)

Garcia-Vicente, F.; Rodriguez, C.

2000-01-01

One of the most important aspects in the metrology of radiation fields is the problem of the measurement of dose profiles in regions where the dose gradient is large. In such zones, the 'detector size effect' may produce experimental measurements that do not correspond to reality. Mathematically it can be proved, under some general assumptions of spatial linearity, that the disturbance induced in the measurement by the effect of the finite size of the detector is equal to the convolution of the real profile with a representative kernel of the detector. In this work the exact relation between the measured profile and the real profile is shown, through the analytical resolution of the integral equation for a general type of profile fitting function using Gaussian convolution kernels. (author)

The Andersen aerobic fitness test

DEFF Research Database (Denmark)

Aadland, Eivind; Terum, Torkil; Mamen, Asgeir

2014-01-01

BACKGROUND: High aerobic fitness is consistently associated with a favorable metabolic risk profile in children. Direct measurement of peak oxygen consumption (VO2peak) is often not feasible, thus indirect tests such as the Andersen test are required in many settings. The present study seeks...... of agreement) were 26.7±125.2 m for test 2 vs. test 1 (pfit in the present sample; thus, we suggest a new equation: VO2peak = 23....... Researchers should be aware of the amount of noise in indirect tests that estimate aerobic fitness....

The collinearly-improved Balitsky–Kovchegov equation

Energy Technology Data Exchange (ETDEWEB)

Iancu, E.; Madrigal, J.D. [Institut de Physique Théorique, CEA Saclay, CNRS UMR 3681, F-91191 Gif-sur-Yvette (France); Mueller, A.H. [Department of Physics, Columbia University, New York, NY 10027 (United States); Soyez, G. [Institut de Physique Théorique, CEA Saclay, CNRS UMR 3681, F-91191 Gif-sur-Yvette (France); Triantafyllopoulos, D.N. [European Centre for Theoretical Studies in Nuclear Physics and Related Areas ECT* and Fondazione Bruno Kessler, Strada delle Tabarelle 286, I-38123 Villazzano (Italy)

2016-12-15

The high-energy evolution in perturbative QCD suffers from a severe lack-of-convergence problem, due to higher order corrections enhanced by double and single transverse logarithms. We resum double logarithms to all orders within the non-linear Balitsky-Kovchegov equation, by taking into account successive soft gluon emissions strongly ordered in lifetime. We further resum single logarithms generated by the first non-singular part of the splitting functions and by the one-loop running of the coupling. The resummed BK equation admits stable solutions, which are used to successfully fit the HERA data at small x for physically acceptable initial conditions and reasonable values of the fit parameters.

Dynamics in the Fitness-Income plane: Brazilian states vs World countries.

Science.gov (United States)

Operti, Felipe G; Pugliese, Emanuele; Andrade, José S; Pietronero, Luciano; Gabrielli, Andrea

2018-01-01

In this paper we introduce a novel algorithm, called Exogenous Fitness, to calculate the Fitness of subnational entities and we apply it to the states of Brazil. In the last decade, several indices were introduced to measure the competitiveness of countries by looking at the complexity of their export basket. Tacchella et al (2012) developed a non-monetary metric called Fitness. In this paper, after an overview about Brazil as a whole and the comparison with the other BRIC countries, we introduce a new methodology based on the Fitness algorithm, called Exogenous Fitness. Combining the results with the Gross Domestic Product per capita (GDPp), we look at the dynamics of the Brazilian states in the Fitness-Income plane. Two regimes are distinguishable: one with high predictability and the other with low predictability, showing a deep analogy with the heterogeneous dynamics of the World countries. Furthermore, we compare the ranking of the Brazilian states according to the Exogenous Fitness with the ranking obtained through two other techniques, namely Endogenous Fitness and Economic Complexity Index.

METRIC context unit architecture

Energy Technology Data Exchange (ETDEWEB)

Simpson, R.O.

1988-01-01

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

Pan tropical biomass equations for Mexico's dry forests

Directory of Open Access Journals (Sweden)

José Návar

2014-12-01

Full Text Available This study reports a set of robust regional M-tree allometric equations for Mexico's tropical dry forests and their application to a forest inventory dataset for the States of Durango and Sinaloa, Mexico. Calculated M data from 15 reported equations were fitted, applied and validated for regional and global models. Proposed theoretical models, empirically derived equations, as well as global and local reported equations were fitted and applied to calculated M-tree data using wood specific gravity, diameter at breast height, and top height as exogenous variables. Empirically-derived, computer-based equations assessed the M-tree evaluations slightly better than the theoretical, the global and the local models. However, the theoretical models projected compatible M-tree values and deserve further attention once wood specific gravity data are collected in the field. Using the best fit equation, mean M plot density values of 30, 41 and 35 Mg ha-1 were estimated from 57 plots (1,600 m² each, 217 plots (1,000 m² each and 166 plots (1,000 m² each in the tropical dry forests of the States of Durango, Tiniaquis and Vado Hondo (Sinaloa, respectively. The large sample size, the richness of the tested allometric models, the economic and ecological importance of this data-source, and the spatial coverage of these equations made this dataset uniquely useful for biomass, charcoal, and other bio-energy estimations, as well as for understanding the inherent heterogeneity of the stand-structure in dynamic tropical forest environments.

Analysis of Surface Plasmon Resonance Curves with a Novel Sigmoid-Asymmetric Fitting Algorithm

Directory of Open Access Journals (Sweden)

Daeho Jang

2015-09-01

Full Text Available The present study introduces a novel curve-fitting algorithm for surface plasmon resonance (SPR curves using a self-constructed, wedge-shaped beam type angular interrogation SPR spectroscopy technique. Previous fitting approaches such as asymmetric and polynomial equations are still unsatisfactory for analyzing full SPR curves and their use is limited to determining the resonance angle. In the present study, we developed a sigmoid-asymmetric equation that provides excellent curve-fitting for the whole SPR curve over a range of incident angles, including regions of the critical angle and resonance angle. Regardless of the bulk fluid type (i.e., water and air, the present sigmoid-asymmetric fitting exhibited nearly perfect matching with a full SPR curve, whereas the asymmetric and polynomial curve fitting methods did not. Because the present curve-fitting sigmoid-asymmetric equation can determine the critical angle as well as the resonance angle, the undesired effect caused by the bulk fluid refractive index was excluded by subtracting the critical angle from the resonance angle in real time. In conclusion, the proposed sigmoid-asymmetric curve-fitting algorithm for SPR curves is widely applicable to various SPR measurements, while excluding the effect of bulk fluids on the sensing layer.

Semiconservative quasispecies equations for polysomic genomes: The general case

Science.gov (United States)

Itan, Eran; Tannenbaum, Emmanuel

2010-06-01

This paper develops a formulation of the quasispecies equations appropriate for polysomic, semiconservatively replicating genomes. This paper is an extension of previous work on the subject, which considered the case of haploid genomes. Here, we develop a more general formulation of the quasispecies equations that is applicable to diploid and even polyploid genomes. Interestingly, with an appropriate classification of population fractions, we obtain a system of equations that is formally identical to the haploid case. As with the work for haploid genomes, we consider both random and immortal DNA strand chromosome segregation mechanisms. However, in contrast to the haploid case, we have found that an analytical solution for the mean fitness is considerably more difficult to obtain for the polyploid case. Accordingly, whereas for the haploid case we obtained expressions for the mean fitness for the case of an analog of the single-fitness-peak landscape for arbitrary lesion repair probabilities (thereby allowing for noncomplementary genomes), here we solve for the mean fitness for the restricted case of perfect lesion repair.

Scalar-metric quantum cosmology with Chaplygin gas and perfect fluid

Energy Technology Data Exchange (ETDEWEB)

Ghosh, Saumya; Panigrahi, Prasanta K. [Indian Institute of Science Education and Research Kolkata, Nadia, West Bengal (India); Gangopadhyay, Sunandan [Indian Institute of Science Education and Research Kolkata, Nadia, West Bengal (India); S.N. Bose National Centre for Basic Sciences, Kolkata (India)

2018-01-15

In this paper we consider the flat FRW cosmology with a scalar field coupled with the metric along with generalized Chaplygin gas and perfect fluid comprising the matter sector. We use the Schutz's formalism to deal with the generalized Chaplygin gas sector. The full theory is then quantized canonically using the Wheeler-DeWitt Hamiltonian formalism. We then solve the WD equation with appropriate boundary conditions. Then by defining a proper completeness relation for the self-adjointness of the WD equation we arrive at the wave packet for the universe. It is observed that the peak in the probability density gets affected due to both fluids in the matter sector, namely, the Chaplygin gas and perfect fluid. (orig.)

Closed string field theory: Quantum action and the Batalin-Vilkovsky master equation

International Nuclear Information System (INIS)

Zwiebach, B.

1993-01-01

The complete quantum theory of covariant closed strings is constructed in detail. The nonpolynomial action is defined by elementary vertices satisfying recursion relations that give rise to Jacobi-like identities for an infinite chain of string field products. The genus zero string field algebra is the homotopy Lie algebra L ∞ encoding the gauge symmetry of the classical theory. The higher genus algebraic structure implies the Batalin-Vilkovisky (BV) master equation and thus consistent BRST quantization of the quantum action. From the L ∞ algebra, and the BV equation on the off-shell state space we derive the L ∞ algebra, and the BV equation on physical states that were recently constructed in d=2 string theory. The string diagrams are surfaces with minimal area metrics, foliated by closed geodesics of length 2π. These metrics generalize quadratic differentials in that foliation bands can cross. The string vertices are succinctly characterized; they include the surfaces whose foliation bands are all of height smaller than 2π. (orig.)

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

Science.gov (United States)

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

2018-05-01

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

Nonlinear elliptic equations of the second order

CERN Document Server

Han, Qing

2016-01-01

Nonlinear elliptic differential equations are a diverse subject with important applications to the physical and social sciences and engineering. They also arise naturally in geometry. In particular, much of the progress in the area in the twentieth century was driven by geometric applications, from the Bernstein problem to the existence of Kähler-Einstein metrics. This book, designed as a textbook, provides a detailed discussion of the Dirichlet problems for quasilinear and fully nonlinear elliptic differential equations of the second order with an emphasis on mean curvature equations and on Monge-Ampère equations. It gives a user-friendly introduction to the theory of nonlinear elliptic equations with special attention given to basic results and the most important techniques. Rather than presenting the topics in their full generality, the book aims at providing self-contained, clear, and "elementary" proofs for results in important special cases. This book will serve as a valuable resource for graduate stu...

A sigmoidal fit for pressure-volume curves of idiopathic pulmonary fibrosis patients on mechanical ventilation: clinical implications

Directory of Open Access Journals (Sweden)

Juliana C. Ferreira

2011-01-01

Full Text Available OBJECTIVE: Respiratory pressure-volume curves fitted to exponential equations have been used to assess disease severity and prognosis in spontaneously breathing patients with idiopathic pulmonary fibrosis. Sigmoidal equations have been used to fit pressure-volume curves for mechanically ventilated patients but not for idiopathic pulmonary fibrosis patients. We compared a sigmoidal model and an exponential model to fit pressure-volume curves from mechanically ventilated patients with idiopathic pulmonary fibrosis. METHODS: Six idiopathic pulmonary fibrosis patients and five controls underwent inflation pressure-volume curves using the constant-flow technique during general anesthesia prior to open lung biopsy or thymectomy. We identified the lower and upper inflection points and fit the curves with an exponential equation, V = A-B.e-k.P, and a sigmoid equation, V = a+b/(1+e-(P-c/d. RESULTS: The mean lower inflection point for idiopathic pulmonary fibrosis patients was significantly higher (10.5 ± 5.7 cm H2O than that of controls (3.6 ± 2.4 cm H2O. The sigmoidal equation fit the pressure-volume curves of the fibrotic and control patients well, but the exponential equation fit the data well only when points below 50% of the inspiratory capacity were excluded. CONCLUSION: The elevated lower inflection point and the sigmoidal shape of the pressure-volume curves suggest that respiratory system compliance is decreased close to end-expiratory lung volume in idiopathic pulmonary fibrosis patients under general anesthesia and mechanical ventilation. The sigmoidal fit was superior to the exponential fit for inflation pressure-volume curves of anesthetized patients with idiopathic pulmonary fibrosis and could be useful for guiding mechanical ventilation during general anesthesia in this condition.

Low-memory iterative density fitting.

Science.gov (United States)

Grajciar, Lukáš

2015-07-30

A new low-memory modification of the density fitting approximation based on a combination of a continuous fast multipole method (CFMM) and a preconditioned conjugate gradient solver is presented. Iterative conjugate gradient solver uses preconditioners formed from blocks of the Coulomb metric matrix that decrease the number of iterations needed for convergence by up to one order of magnitude. The matrix-vector products needed within the iterative algorithm are calculated using CFMM, which evaluates them with the linear scaling memory requirements only. Compared with the standard density fitting implementation, up to 15-fold reduction of the memory requirements is achieved for the most efficient preconditioner at a cost of only 25% increase in computational time. The potential of the method is demonstrated by performing density functional theory calculations for zeolite fragment with 2592 atoms and 121,248 auxiliary basis functions on a single 12-core CPU workstation. © 2015 Wiley Periodicals, Inc.

The non-linear coupled spin 2-spin 3 Cotton equation in three dimensions

Energy Technology Data Exchange (ETDEWEB)

Linander, Hampus; Nilsson, Bengt E.W. [Department of Physics, Theoretical PhysicsChalmers University of Technology, S-412 96 Göteborg (Sweden)

2016-07-05

In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 “translation”, “Lorentz” and “dilatation”) properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.

Effects of metric hierarchy and rhyme predictability on word duration in The Cat in the Hat.

Science.gov (United States)

Breen, Mara

2018-05-01

Word durations convey many types of linguistic information, including intrinsic lexical features like length and frequency and contextual features like syntactic and semantic structure. The current study was designed to investigate whether hierarchical metric structure and rhyme predictability account for durational variation over and above other features in productions of a rhyming, metrically-regular children's book: The Cat in the Hat (Dr. Seuss, 1957). One-syllable word durations and inter-onset intervals were modeled as functions of segment number, lexical frequency, word class, syntactic structure, repetition, and font emphasis. Consistent with prior work, factors predicting longer word durations and inter-onset intervals included more phonemes, lower frequency, first mention, alignment with a syntactic boundary, and capitalization. A model parameter corresponding to metric grid height improved model fit of word durations and inter-onset intervals. Specifically, speakers realized five levels of metric hierarchy with inter-onset intervals such that interval duration increased linearly with increased height in the metric hierarchy. Conversely, speakers realized only three levels of metric hierarchy with word duration, demonstrating that they shortened the highly predictable rhyme resolutions. These results further understanding of the factors that affect spoken word duration, and demonstrate the myriad cues that children receive about linguistic structure from nursery rhymes. Copyright © 2018 Elsevier B.V. All rights reserved.

En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions

International Nuclear Information System (INIS)

Becker, D.; Reuter, M.

2014-01-01

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the

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

International Nuclear Information System (INIS)

Mielke, E.W.

1977-01-01

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

Numerical studies of rotational core collapse in axisymmetry using the conformally flat metric approach

International Nuclear Information System (INIS)

Dimmelmeier, H.; Font, J.A.; Mueller, E.

2001-01-01

The numerical simulation of hydrodynamic processes in general relativity is a highly complex problem. In order to reduce the complexity of the gravitational field equations, Wilson and coworkers have proposed an approximation scheme, where the 3-metric γ ij is chosen to be conformally flat. In this approximation the Einstein equations reduce to a set of 5 coupled elliptic equations. In this paper we present an axisymmetric general relativistic hydrodynamic code which utilizes this approach together with high-resolution shock-capturing schemes to solve the hydrodynamic equations. We report on tests and preliminary applications of the code to rotating neutron stars and supernova core collapse in axisymmetry. The code promises good applicability to handle a variety of relativistic astrophysical situations, and is prepared to provide information about gravitational radiation from rotating gravitational collapse. (author)

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

International Nuclear Information System (INIS)

Vacaru, Sergiu I.; Irwin, Klee

2017-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2017-01-15

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2016-11-25

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

Sewall Wright's equation Deltaq=(q(1-q) partial differentialw/ partial differentialq)/2w.

Science.gov (United States)

Edwards, A W

2000-02-01

An equation of Sewall Wright's expresses the change in the frequency of an allele under selection at a multiallelic locus as a function of the gradient of the mean fitness "surface" in the direction in which the relative proportions of the other alleles do not change. An attempt to derive this equation using conventional vector calculus shows that this description leads to a different equation and that the purported gradient in Wright's equation is not a gradient of the mean fitness surface except in the diallelic case, where the two equations are the same. It is further shown that if Fisher's angular transformation is applied to the diallelic case the genic variance is exactly equal to one-eighth of the square of the gradient of the mean fitness with respect to the transformed gene frequency. Copyright 2000 Academic Press.

Iterative solution of the Grad-Shafranov equation in symmetric magnetic coordinates

International Nuclear Information System (INIS)

Brambilla, Marco

2003-01-01

The inverse Grad-Shafranov equation for axisymmetric magnetohydrodynamic equilibria is reformulated in symmetric magnetic coordinates (in which magnetic field lines look 'straight', and the geometric toroidal angle is one of the coordinates). The poloidally averaged part of the equilibrium condition and Ampere law takes the form of two first-order ordinary differential equations, with the two arbitrary flux functions, pressure and force-free part of the current density, as sources. The condition for the coordinates to be flux coordinates, and the poloidally varying part of the equilibrium equation are similarly transformed into a set of first-order ordinary differential equations, with coefficients depending on the metric, and explicitly solved for the radial derivatives of the coefficients of the Fourier representation of the Cartesian coordinates in the poloidal angle. The derivation exploits the existence of Boozer-White coordinates, but does not require to find these coordinates explicitly; on the other hand, it offers a simple recipe to perform the transformation to Boozer-White coordinates, if required. Use of symmetric flux coordinates is advantageous for the formulation of many problems of equilibrium, stability, and wave propagation in tokamak plasmas, since these coordinates have the simplest metric of their class. It is also shown that in symmetric flux coordinates the Lagrangian equations of the drift motion of charged particles are automatically solved for the time derivatives, with right-hand sides closely related to the coefficients of the inverse Grad-Shafranov equation

Metric diffusion along foliations

CERN Document Server

Walczak, Szymon M

2017-01-01

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

MAGNETOHYDRODYNAMIC EQUATIONS (MHD GENERATION CODE

Directory of Open Access Journals (Sweden)

Francisco Frutos Alfaro

2017-04-01

Full Text Available A program to generate codes in Fortran and C of the full magnetohydrodynamic equations is shown. The program uses the free computer algebra system software REDUCE. This software has a package called EXCALC, which is an exterior calculus program. The advantage of this program is that it can be modified to include another complex metric or spacetime. The output of this program is modified by means of a LINUX script which creates a new REDUCE program to manipulate the magnetohydrodynamic equations to obtain a code that can be used as a seed for a magnetohydrodynamic code for numerical applications. As an example, we present part of the output of our programs for Cartesian coordinates and how to do the discretization.

A Contraction Fixed Point Theorem in Partially Ordered Metric Spaces and Application to Fractional Differential Equations

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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.

Fault Management Metrics

Science.gov (United States)

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

2017-01-01

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

Completion of a Dislocated Metric Space

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P. Sumati Kumari

2015-01-01

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

Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

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Zeki Kasap

2015-01-01

Full Text Available This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

An Introduction to Goodness of Fit for PMU Parameter Estimation

Energy Technology Data Exchange (ETDEWEB)

Riepnieks, Artis; Kirkham, Harold

2017-10-01

New results of measurements of phasor-like signals are presented based on our previous work on the topic. In this document an improved estimation method is described. The algorithm (which is realized in MATLAB software) is discussed. We examine the effect of noisy and distorted signals on the Goodness of Fit metric. The estimation method is shown to be performing very well with clean data and with a measurement window as short as a half a cycle and as few as 5 samples per cycle. The Goodness of Fit decreases predictably with added phase noise, and seems to be acceptable even with visible distortion in the signal. While the exact results we obtain are specific to our method of estimation, the Goodness of Fit method could be implemented in any phasor measurement unit.

Static Solutions of Einstein's Equations with Cylindrical Symmetry

Science.gov (United States)

Trendafilova, C. S.; Fulling, S. A.

2011-01-01

In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well-known cone solution, which is locally flat, but others in which the metric coefficients are powers of the radial coordinate and the spacetime is…

Fixed point results for contractions involving generalized altering distances in ordered metric spaces

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Samet Bessem

2011-01-01

Full Text Available Abstract In this article, we establish coincidence point and common fixed point theorems for mappings satisfying a contractive inequality which involves two generalized altering distance functions in ordered complete metric spaces. As application, we study the existence of a common solution to a system of integral equations. 2000 Mathematics subject classification. Primary 47H10, Secondary 54H25

The incompressible non-relativistic Navier-Stokes equation from gravity

International Nuclear Information System (INIS)

Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.

2009-01-01

We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

Remarks on G-Metric Spaces

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Bessem Samet

2013-01-01

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

Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations

International Nuclear Information System (INIS)

Mestdag, T; Crampin, M

2008-01-01

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

Weight of fitness deviation governs strict physical chaos in replicator dynamics

Science.gov (United States)

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation—a paradigm equation in evolutionary game dynamics—mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions—fixed points, periodic orbits, and chaotic trajectories—are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

On the axially symmetric non-rotating vacuum solutions of Rosen's equations

International Nuclear Information System (INIS)

Bozhkov, Y.

1990-10-01

It is shown that all axially symmetric nonrotating solutions of Rosen's field equations can be expressed in terms of two harmonic functions. It is also shown that the total energy of Rosen's metric is Mc 2 . (author). 8 refs

Variational solution of the loop equation in QCD

International Nuclear Information System (INIS)

Agishtein, M.E.; Migdal, A.A.

1988-01-01

A new technique for the large N loop equation of QCD is worked out. The Wilson loop W(C) is approximated by a Gaussian functional. The parameters are fitted to the loop equation, after which the equation is statisfied up to 0.2%. The resulting Wilson loop corresponds to linearly rising Regge trajectories. The problem of tachyon is still present, but it could be cured by iteration of the loop equation starting from this variational solution. (orig.)

Variational solution of the loop equation in QCD

International Nuclear Information System (INIS)

Agishtein, M.E.; Migdal, A.A.

1988-01-01

A new technique for the large N loop equation of QCD is worked out. The Wilson loop W(C) is approximated by a Gaussian functional. The parameters are fitted to the loop equation, after which the equation is satisfied up to 0.2%. The resulting Wilson loop corresponds to linearly rising Regge trajectories. The problem of tachyon is still present, but it could be cured by iteration of the loop equation starting from this variational solution

Metric-adjusted skew information

DEFF Research Database (Denmark)

Liang, Cai; Hansen, Frank

2010-01-01

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

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

Science.gov (United States)

Lehtonen, Jussi

2018-01-01

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

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

Science.gov (United States)

Post, J. V.

1981-01-01

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

The metric system: An introduction

Science.gov (United States)

Lumley, Susan M.

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

The metric system: An introduction

Energy Technology Data Exchange (ETDEWEB)

Lumley, S.M.

1995-05-01

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

A Hamiltonian functional for the linearized Einstein vacuum field equations

International Nuclear Information System (INIS)

Rosas-RodrIguez, R

2005-01-01

By considering the Einstein vacuum field equations linearized about the Minkowski metric, the evolution equations for the gauge-invariant quantities characterizing the gravitational field are written in a Hamiltonian form by using a conserved functional as Hamiltonian; this Hamiltonian is not the analog of the energy of the field. A Poisson bracket between functionals of the field, compatible with the constraints satisfied by the field variables, is obtained. The generator of spatial translations associated with such bracket is also obtained

Attack-Resistant Trust Metrics

Science.gov (United States)

Levien, Raph

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

Mapping Rubber Plantations and Natural Forests in Xishuangbanna (Southwest China Using Multi-Spectral Phenological Metrics from MODIS Time Series

Directory of Open Access Journals (Sweden)

Sebastian van der Linden

2013-05-01

Full Text Available We developed and evaluated a new approach for mapping rubber plantations and natural forests in one of Southeast Asia’s biodiversity hot spots, Xishuangbanna in China. We used a one-year annual time series of Moderate Resolution Imaging Spectroradiometer (MODIS, Enhanced Vegetation Index (EVI and short-wave infrared (SWIR reflectance data to develop phenological metrics. These phenological metrics were used to classify rubber plantations and forests with the Random Forest classification algorithm. We evaluated which key phenological characteristics were important to discriminate rubber plantations and natural forests by estimating the influence of each metric on the classification accuracy. As a benchmark, we compared the best classification with a classification based on the full, fitted time series data. Overall classification accuracies derived from EVI and SWIR time series alone were 64.4% and 67.9%, respectively. Combining the phenological metrics from EVI and SWIR time series improved the accuracy to 73.5%. Using the full, smoothed time series data instead of metrics derived from the time series improved the overall accuracy only slightly (1.3%, indicating that the phenological metrics were sufficient to explain the seasonal changes captured by the MODIS time series. The results demonstrate a promising utility of phenological metrics for mapping and monitoring rubber expansion with MODIS.

Global Attractivity Results for Mixed-Monotone Mappings in Partially Ordered Complete Metric Spaces

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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.

Symmetries of the dual metrics

International Nuclear Information System (INIS)

Baleanu, D.

1998-01-01

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

Sharp bounds for periodic solutions of Lipschitzian differential equations

International Nuclear Information System (INIS)

Zevin, A A

2009-01-01

A general system of Lipschitzian differential equations, containing simultaneously terms without delay and with arbitrary constant and time-varying delays, is considered. For the autonomous case, a lower bound for the period of nonconstant periodic solutions, expressed in the respective supremum Lipschitz constants, is found. For nonautonomous periodic equations, explicit upper bounds for the amplitudes and maximum derivatives of periodic solutions are obtained. For all n ≥ 2, the bounds do not depend on n and, in general, are different from that for n = 1. All the bounds are sharp; they are attained in linear differential equations with piece-wise constant deviating arguments. A relation between the obtained bounds and the sharp bounds in other metrics is established

Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation

Science.gov (United States)

Rahmani, Faramarz; Golshani, Mehdi

2018-01-01

One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space-time metric.

The evaporation of oil spills: prediction of equations using distillation data

International Nuclear Information System (INIS)

Fingas, M.

1997-01-01

The evaporative characteristics of 19 different crude oils and petroleum products were studied . Best-fit equation parameters were determined for percentage loss by time and absolute weight loss. Except in three cases, all oils were found to fit logarithmic curves. The equation constants were correlated with oil distillation data. Relationships enabling calculation of evaporation equations directly from distillation data have been developed. The high correlation of distillation data and evaporation data suggests that the two processes are analogous and that evaporation, like distillation, is largely governed by intrinsic oil properties rather than environmental properties such as boundary-layer factors

On the equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory

International Nuclear Information System (INIS)

Zhitnikov, V.V.; Ponomarev, V.N.

1986-01-01

An attempt is made to compare the solution of field equations, corresponding to quadratic equations for the fields (g μν , Γ μν α ) in gauge gravitation theory (GGT) with general relativity theory solutions. Without restrictions for a concrete type of metrics only solutions of equations, for which torsion turns to zero, are considered. Equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory is proved using the Newman-Penrose formalism

On some types of exact solutions of the Einstein equation. 2

International Nuclear Information System (INIS)

Obukhov, V.V.

1978-01-01

Several types of the Einstein spaces which can describe gravitational waves are investigated. When the solutions of the Einstein equations are found, additional conditions are imposed on the metrics under consideration. It is required: 1) that the spaces should admit the two-parametric Abelian group of motion; 2) that the wave coordinate system would be privileged; 3) that bicharacteristics of the Einstein equation would satisfy the harmonicity condition. The superposition of the enumerated conditions has made it possible to perform a complete integration of the Einstein equations. The solutions obtained are interpreted as the wave ones

Non-local PDEs with discrete state-dependent delays: Well-posedness in a metric space

Czech Academy of Sciences Publication Activity Database

Rezunenko, Oleksandr; Zagalak, Petr

2013-01-01

Roč. 33, č. 2 (2013), s. 819-835 ISSN 1078-0947 R&D Projects: GA ČR(CZ) GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Partial differential equations with delay s * well-posedness * metric space Subject RIV: BC - Control Systems Theory Impact factor: 0.923, year: 2013 http://library.utia.cas.cz/separaty/2012/AS/zagalak-0381969.pdf

Overview of journal metrics

Directory of Open Access Journals (Sweden)

Kihong Kim

2018-02-01

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

Picard-Fuchs equations and the moduli space of superconformal field theories

International Nuclear Information System (INIS)

Cadavid, A.C.; Ferrara, S.

1991-01-01

We derive simple techniques which allow us to relate Picard-Fuchs differential equations for the periods of holomorphic p-forms on certain complex manifolds, to their moduli space and its modular group (target space duality). For Calabi-Yau manifolds the special geometry of moduli space gives the Zamolodchikov metric and the Yukawa couplings in terms of the periods. For general N=2 superconformal theories these equations exactly determine perturbed correlation functions of the chiral rings of primary fields. (orig.)

Exponential-fitted methods for integrating stiff systems of ordinary differential equations: Applications to homogeneous gas-phase chemical kinetics

Science.gov (United States)

Pratt, D. T.

1984-01-01

Conventional algorithms for the numerical integration of ordinary differential equations (ODEs) are based on the use of polynomial functions as interpolants. However, the exact solutions of stiff ODEs behave like decaying exponential functions, which are poorly approximated by polynomials. An obvious choice of interpolant are the exponential functions themselves, or their low-order diagonal Pade (rational function) approximants. A number of explicit, A-stable, integration algorithms were derived from the use of a three-parameter exponential function as interpolant, and their relationship to low-order, polynomial-based and rational-function-based implicit and explicit methods were shown by examining their low-order diagonal Pade approximants. A robust implicit formula was derived by exponential fitting the trapezoidal rule. Application of these algorithms to integration of the ODEs governing homogenous, gas-phase chemical kinetics was demonstrated in a developmental code CREK1D, which compares favorably with the Gear-Hindmarsh code LSODE in spite of the use of a primitive stepsize control strategy.

Assessment and improvement of radiation oncology trainee contouring ability utilizing consensus-based penalty metrics

International Nuclear Information System (INIS)

Hallock, Abhirami; Read, Nancy; D'Souza, David

2012-01-01

The objective of this study was to develop and assess the feasibility of utilizing consensus-based penalty metrics for the purpose of critical structure and organ at risk (OAR) contouring quality assurance and improvement. A Delphi study was conducted to obtain consensus on contouring penalty metrics to assess trainee-generated OAR contours. Voxel-based penalty metric equations were used to score regions of discordance between trainee and expert contour sets. The utility of these penalty metric scores for objective feedback on contouring quality was assessed by using cases prepared for weekly radiation oncology radiation oncology trainee treatment planning rounds. In two Delphi rounds, six radiation oncology specialists reached agreement on clinical importance/impact and organ radiosensitivity as the two primary criteria for the creation of the Critical Structure Inter-comparison of Segmentation (CriSIS) penalty functions. Linear/quadratic penalty scoring functions (for over- and under-contouring) with one of four levels of severity (none, low, moderate and high) were assigned for each of 20 OARs in order to generate a CriSIS score when new OAR contours are compared with reference/expert standards. Six cases (central nervous system, head and neck, gastrointestinal, genitourinary, gynaecological and thoracic) then were used to validate 18 OAR metrics through comparison of trainee and expert contour sets using the consensus derived CriSIS functions. For 14 OARs, there was an improvement in CriSIS score post-educational intervention. The use of consensus-based contouring penalty metrics to provide quantitative information for contouring improvement is feasible.

Spectral representations of neutron-star equations of state

International Nuclear Information System (INIS)

Lindblom, Lee

2010-01-01

Methods are developed for constructing spectral representations of cold (barotropic) neutron-star equations of state. These representations are faithful in the sense that every physical equation of state has a representation of this type and conversely every such representation satisfies the minimal thermodynamic stability criteria required of any physical equation of state. These spectral representations are also efficient, in the sense that only a few spectral coefficients are generally required to represent neutron-star equations of state quiet accurately. This accuracy and efficiency is illustrated by constructing spectral fits to a large collection of 'realistic' neutron-star equations of state.

A non-iterative method for fitting decay curves with background

International Nuclear Information System (INIS)

Mukoyama, T.

1982-01-01

A non-iterative method for fitting a decay curve with background is presented. The sum of an exponential function and a constant term is linearized by the use of the difference equation and parameters are determined by the standard linear least-squares fitting. The validity of the present method has been tested against pseudo-experimental data. (orig.)

On the search for an appropriate metric for reaction time to suprathreshold increments and decrements.

Science.gov (United States)

Vassilev, Angel; Murzac, Adrian; Zlatkova, Margarita B; Anderson, Roger S

2009-03-01

Weber contrast, DeltaL/L, is a widely used contrast metric for aperiodic stimuli. Zele, Cao & Pokorny [Zele, A. J., Cao, D., & Pokorny, J. (2007). Threshold units: A correct metric for reaction time? Vision Research, 47, 608-611] found that neither Weber contrast nor its transform to detection-threshold units equates human reaction times in response to luminance increments and decrements under selective rod stimulation. Here we show that their rod reaction times are equated when plotted against the spatial luminance ratio between the stimulus and its background (L(max)/L(min), the larger and smaller of background and stimulus luminances). Similarly, reaction times to parafoveal S-cone selective increments and decrements from our previous studies [Murzac, A. (2004). A comparative study of the temporal characteristics of processing of S-cone incremental and decremental signals. PhD thesis, New Bulgarian University, Sofia, Murzac, A., & Vassilev, A. (2004). Reaction time to S-cone increments and decrements. In: 7th European conference on visual perception, Budapest, August 22-26. Perception, 33, 180 (Abstract).], are better described by the spatial luminance ratio than by Weber contrast. We assume that the type of stimulus detection by temporal (successive) luminance discrimination, by spatial (simultaneous) luminance discrimination or by both [Sperling, G., & Sondhi, M. M. (1968). Model for visual luminance discrimination and flicker detection. Journal of the Optical Society of America, 58, 1133-1145.] determines the appropriateness of one or other contrast metric for reaction time.

On the stationary Einstein-Maxwell-Klein-Gordon equations

International Nuclear Information System (INIS)

Gegenberg, J.D.

1981-05-01

The stationary Einstein-Maxwell-Klein-Gordon (EMKG) equations for interacting gravitational, electromagnetic and meson fields are examined. The theory is cast into the formalism of principal fiber bundles with a connection, wherein its relationship to current trends in theoretical physics is made manifest. The EMKG equations are shown to admit a Higgs-like mechanism for giving mass to the gauge field. A theorem specifying sufficient conditions for the stationarity of the spacetime metric to imply stationarity of the other fields is proved. By imposing additional constraints and symmetries, the EMKG equations are considerably simplified. An attempt is made to apply a solution-generation technique, and this meets with only partial success. Finally, a stationary but non-static solution is found, and the geometric and physical properties are discussed

Attractive electron-electron interactions within robust local fitting approximations.

Science.gov (United States)

Merlot, Patrick; Kjærgaard, Thomas; Helgaker, Trygve; Lindh, Roland; Aquilante, Francesco; Reine, Simen; Pedersen, Thomas Bondo

2013-06-30

An analysis of Dunlap's robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolution-of-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree-Fock and Kohn-Sham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. Copyright © 2013 Wiley Periodicals, Inc.

Comparison of machine learning techniques to predict all-cause mortality using fitness data: the Henry ford exercIse testing (FIT) project.

Science.gov (United States)

Sakr, Sherif; Elshawi, Radwa; Ahmed, Amjad M; Qureshi, Waqas T; Brawner, Clinton A; Keteyian, Steven J; Blaha, Michael J; Al-Mallah, Mouaz H

2017-12-19

Prior studies have demonstrated that cardiorespiratory fitness (CRF) is a strong marker of cardiovascular health. Machine learning (ML) can enhance the prediction of outcomes through classification techniques that classify the data into predetermined categories. The aim of this study is to present an evaluation and comparison of how machine learning techniques can be applied on medical records of cardiorespiratory fitness and how the various techniques differ in terms of capabilities of predicting medical outcomes (e.g. mortality). We use data of 34,212 patients free of known coronary artery disease or heart failure who underwent clinician-referred exercise treadmill stress testing at Henry Ford Health Systems Between 1991 and 2009 and had a complete 10-year follow-up. Seven machine learning classification techniques were evaluated: Decision Tree (DT), Support Vector Machine (SVM), Artificial Neural Networks (ANN), Naïve Bayesian Classifier (BC), Bayesian Network (BN), K-Nearest Neighbor (KNN) and Random Forest (RF). In order to handle the imbalanced dataset used, the Synthetic Minority Over-Sampling Technique (SMOTE) is used. Two set of experiments have been conducted with and without the SMOTE sampling technique. On average over different evaluation metrics, SVM Classifier has shown the lowest performance while other models like BN, BC and DT performed better. The RF classifier has shown the best performance (AUC = 0.97) among all models trained using the SMOTE sampling. The results show that various ML techniques can significantly vary in terms of its performance for the different evaluation metrics. It is also not necessarily that the more complex the ML model, the more prediction accuracy can be achieved. The prediction performance of all models trained with SMOTE is much better than the performance of models trained without SMOTE. The study shows the potential of machine learning methods for predicting all-cause mortality using cardiorespiratory fitness

Best-fitting prediction equations for basal metabolic rate: informing obesity interventions in diverse populations.

Science.gov (United States)

Sabounchi, N S; Rahmandad, H; Ammerman, A

2013-10-01

Basal metabolic rate (BMR) represents the largest component of total energy expenditure and is a major contributor to energy balance. Therefore, accurately estimating BMR is critical for developing rigorous obesity prevention and control strategies. Over the past several decades, numerous BMR formulas have been developed targeted to different population groups. A comprehensive literature search revealed 248 BMR estimation equations developed using diverse ranges of age, gender, race, fat-free mass, fat mass, height, waist-to-hip ratio, body mass index and weight. A subset of 47 studies included enough detail to allow for development of meta-regression equations. Utilizing these studies, meta-equations were developed targeted to 20 specific population groups. This review provides a comprehensive summary of available BMR equations and an estimate of their accuracy. An accompanying online BMR prediction tool (available at http://www.sdl.ise.vt.edu/tutorials.html) was developed to automatically estimate BMR based on the most appropriate equation after user-entry of individual age, race, gender and weight.

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

International Nuclear Information System (INIS)

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

1986-01-01

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

Einstein boundary conditions for the 3+1 Einstein equations

International Nuclear Information System (INIS)

Frittelli, Simonetta; Gomez, Roberto

2003-01-01

In the 3+1 framework of the Einstein equations for the case of a vanishing shift vector and arbitrary lapse, we calculate explicitly the four boundary equations arising from the vanishing of the projection of the Einstein tensor along the normal to the boundary surface of the initial-boundary value problem. Such conditions take the form of evolution equations along (as opposed to across) the boundary for certain components of the extrinsic curvature and for certain space derivatives of the three-metric. We argue that, in general, such boundary conditions do not follow necessarily from the evolution equations and the initial data, but need to be imposed on the boundary values of the fundamental variables. Using the Einstein-Christoffel formulation, which is strongly hyperbolic, we show how three of the boundary equations up to linear combinations should be used to prescribe the values of some incoming characteristic fields. Additionally, we show that the fourth one imposes conditions on some outgoing fields

Metric regularity and subdifferential calculus

International Nuclear Information System (INIS)

Ioffe, A D

2000-01-01

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

FC LSEI WNNLS, Least-Square Fitting Algorithms Using B Splines

International Nuclear Information System (INIS)

Hanson, R.J.; Haskell, K.H.

1989-01-01

1 - Description of problem or function: FC allows a user to fit dis- crete data, in a weighted least-squares sense, using piece-wise polynomial functions represented by B-Splines on a given set of knots. In addition to the least-squares fitting of the data, equality, inequality, and periodic constraints at a discrete, user-specified set of points can be imposed on the fitted curve or its derivatives. The subprograms LSEI and WNNLS solve the linearly-constrained least-squares problem. LSEI solves the class of problem with general inequality constraints, and, if requested, obtains a covariance matrix of the solution parameters. WNNLS solves the class of problem with non-negativity constraints. It is anticipated that most users will find LSEI suitable for their needs; however, users with inequalities that are single bounds on variables may wish to use WNNLS. 2 - Method of solution: The discrete data are fit by a linear combination of piece-wise polynomial curves which leads to a linear least-squares system of algebraic equations. Additional information is expressed as a discrete set of linear inequality and equality constraints on the fitted curve which leads to a linearly-constrained least-squares system of algebraic equations. The solution of this system is the main computational problem solved

Context-dependent ATC complexity metric

NARCIS (Netherlands)

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

2015-01-01

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

Einstein-Weyl spaces and dispersionless Kadomtsev-Petviashvili equation from Painleve I and II

International Nuclear Information System (INIS)

Dunajski, Maciej; Tod, Paul

2002-01-01

We present two constructions of new solutions to the dispersionless KP (dKP) equation arising from the first two Painleve transcendents. The first construction is a hodograph transformation based on Einstein-Weyl geometry, the generalized Nahm's equation and the isomonodromy problem. The second construction, motivated by the first, is a direct characterization of solutions to dKP which are constant on a central quadric. We show how the solutions to the dKP equations can be used to construct some three-dimensional Einstein-Weyl structures, and four-dimensional anti-self-dual null-Kaehler metrics

DLA Energy Biofuel Feedstock Metrics Study

Science.gov (United States)

2012-12-11

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

The Integration of Internal and External Training Load Metrics in Hurling

Directory of Open Access Journals (Sweden)

Malone Shane

2016-12-01

Full Text Available The current study aimed to assess the relationship between the hurling player’s fitness profile and integrated training load (TL metrics. Twenty-five hurling players performed treadmill testing for VO2max, the speed at blood lactate concentrations of 2 mmol•L-1 (vLT and 4 mmol•L-1 (vOBLA and the heart rate-blood lactate profile for calculation of individual training impulse (iTRIMP. The total distance (TD; m, high speed distance (HSD; m and sprint distance (SD; m covered were measured using GPS technology (4-Hz, VX Sport, Lower Hutt, New Zealand which allowed for the measurement of the external TL. The external TL was divided by the internal TL to form integration ratios. Pearson correlation analyses allowed for the assessment of the relationships between fitness measures and the ratios to performance during simulated match play. External measures of the TL alone showed limited correlations with fitness measures. Integrated TL ratios showed significant relationships with fitness measures in players. TD:iTRIMP was correlated with aerobic fitness measures VO2max (r = 0.524; p = 0.006; 95% CI: 0.224 to 0.754; large and vOBLA (r = 0.559; p = 0.003; 95% CI: 0.254 to 0.854; large. HSD:iTRIMP also correlated with aerobic markers for fitness vLT (r = 0.502; p = 0.009; 95% CI: 0.204 to 0.801; large; vOBLA (r = 0.407; p = 0.039; 95% CI: 0.024 to 0.644; moderate. Interestingly SD:iTRIMP also showed significant correlations with vLT (r = 0.611; p = 0.001; 95% CI: 0.324 to 0.754; large. The current study showed that TL ratios can provide practitioners with a measure of fitness as external performance alone showed limited relationships with aerobic fitness measures.

Symmetries of Taub-NUT dual metrics

International Nuclear Information System (INIS)

Baleanu, D.; Codoban, S.

1998-01-01

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

Metric learning

CERN Document Server

Bellet, Aurelien; Sebban, Marc

2015-01-01

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

Technical Privacy Metrics: a Systematic Survey

OpenAIRE

Wagner, Isabel; Eckhoff, David

2018-01-01

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

On Information Metrics for Spatial Coding.

Science.gov (United States)

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

2018-04-01

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

Generalized Painleve-Gullstrand metrics

Energy Technology Data Exchange (ETDEWEB)

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

2009-02-02

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

Gauge invariance and equations of motion for closed string modes

Directory of Open Access Journals (Sweden)

B. Sathiapalan

2014-12-01

Full Text Available We continue earlier discussions on loop variables and the exact renormalization group on the string world sheet for closed and open string backgrounds. The world sheet action with a UV regulator is written in a generally background covariant way by introducing a background metric. It is shown that the renormalization group gives background covariant equations of motion – this is the gauge invariance of the graviton. Interaction is written in terms of gauge invariant and generally covariant field strength tensors. The basic idea is to work in Riemann normal coordinates and covariantize the final equation. It turns out that the equations for massive modes are gauge invariant only if the space–time curvature of the (arbitrary background is zero. The exact RG equations give quadratic equations of motion for all the modes including the physical graviton. The level (2,2¯ massive field equations are used to illustrate the techniques. At this level there are mixed symmetry tensors. Gauge invariant interacting equations can be written down. In flat space an action can also be written for the free theory.

Scaled equation of state parameters for gases in the critical region

Science.gov (United States)

Sengers, J. M. H. L.; Greer, W. L.; Sengers, J. V.

1976-01-01

In the light of recent theoretical developments, the paper presents an accurate characterization of anomalous thermodynamic behavior of xenon, helium 4, helium 3, carbon dioxide, steam and oxygen in the critical region. This behavior is associated with long range fluctuations in the system and the physical properties depend primarily on a single variable, namely, the correlation length. A description of the thermodynamic behavior of fluids in terms of scaling laws is formulated, and the two successfully used scaled equations of state (NBS equation and Linear Model parametric equation) are compared. Methods for fitting both equations to experimental equation of state data are developed and formulated, and the optimum fit for each of the two scaled equations of the above gases are presented and the results are compared. By extending the experimental data for the above one-component fluids to partially miscible binary liquids, superfluid liquid helium, ferromagnets and solids exhibiting order-disorder transitions, the principle of universality is concluded. Finally by using this principle, the critical regions for nine additional fluids are described.

An equation for the dimensionless friction factor of consolidated ...

African Journals Online (AJOL)

An equation that relates the dimensionless friction factor of a porous medium its Reynolds number, during incompressible and compressible fluid flow through the medium is proposed. The equation is a curve fit of a graph drawn from the results of Ohirhian for water (liquid) and that of Akpokene for Nitrogen (gas) flow ...

Two classes of metric spaces

Directory of Open Access Journals (Sweden)

Isabel Garrido

2016-04-01

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

A mixed finite element method for nonlinear diffusion equations

KAUST Repository

Burger, Martin; Carrillo, José ; Wolfram, Marie-Therese

2010-01-01

We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.

Solution of the stationary vacuum equations of relativity for conformally flat 3-spaces

International Nuclear Information System (INIS)

Perjes, Z.; Lukacs, B.; Sebestyen, A.; Valentini, A.; Sparling, G.A.J.

1983-08-01

The solution of Einstein's vacuum gravitational equations for stationary space-times with a conformally flat 3-space is presented. There is no other solution of this problem than the Ehlers-rotation generalizations of the three conformastat space-times including the Schwarzschild metric. (author)

Isothermal equation of state of a lithium fluoride single crystal

Energy Technology Data Exchange (ETDEWEB)

Kim, K.Y.

1975-01-01

An isothermal equation of state of a LiF single crystal was determined from length change measurements of the specimen as a function of hydrostatic pressure up to approximately 7 kbars at 28 to 41/sup 0/C. The length change was measured with an accuracy of approximately 500 A by using a Fabry Perot type He--Ne laser interferometer for a 1-m long specimen at temperatures constant to less than 0.002/sup 0/C. Several two- and three-parameter equations of state were used in analyzing the measured pressure-volume data. The computer fit for each equation of state determines not only the value of its parameters but also the standard deviations associated with them and one dependent variable, either pressure or volume. With the parameters determined, the equations of state are extrapolated to approximately 5 megabars in order to see discrepancies. Using the Born model of ionic solids, two equations of state were derived both from a power law potential and from an exponential form for the repulsive energy of alkali metal halides and used to fit the pressure-volume data of a LiF single crystal. They are also extrapolated to approximately 5 megabars. The Birch's two-parameter equation and the Grover, Getting, and Kennedy equation are indistinguishable from the two equations of state derived from the Born model for pressures approximately equal to or less than 800 kbars within +-20 kbars. The above four equations of state also fit closely the Pagannone and Drickamer static compression data, the Christian shock wave data, and the Kormer et al. shock wave data. The isothermal bulk modulus and its first pressure derivative at atmospheric pressure and 28.83/sup 0/C are 664.5 +- 0.5 kbars and 5.40 +- 0.18, respectively, in close agreement with those values ultrasonically measured by R. A. Miller and C. S. Smith. (auth)

On characterizations of quasi-metric completeness

Energy Technology Data Exchange (ETDEWEB)

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

2017-07-01

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

Equation Discovery for Financial Forcasting in Context of Islamic Banking

Institute of Scientific and Technical Information of China (English)

Amer Alzaidi; Dimitar Kazakov

2010-01-01

This paper describes an equation discovery approach based on machine leamng using LAGdtAMGE as an equation discovery tool,with two sources of input,a dataset and model presented in context-free gammar.The approach is searching a large range of potential equations by a specific model.The parameters of the equation are fitted to find the best equations.The The experiments are illustratedwith commodity prices from the London Metal Exchange for the period of January-October 2009.The outputs of the experiments are a large number of equations;same of the equations display that the predicted rakes are following the market trends in perfect patterns.

Symmetries of the stationary Einstein--Maxwell equations. VI. Transformations which generate asymptotically flat spacetimes with arbitrary multipole moments

International Nuclear Information System (INIS)

Hoenselaers, C.; Kinnersley, W.; Xanthopoulos, B.C.

1979-01-01

A new series of transformations is presented for generating stationary axially symmetric asymptotically flat vacuum solutions of Einstein's equations. The application requires only algebraic manipulations to be performed. Several examples are given of new stationary axisymmetric solutions obtained in this way. It is conjectured that the transformations, applied to the genral Weyl metric, can be used to generate systematically all stationary metrics with axial symmetry

Midisuperspace-induced corrections to the Wheeler De Witt equation

International Nuclear Information System (INIS)

Mazzitelli, F.D.

1992-04-01

We consider the midisuperspace of four dimensional spherically symmetric metrics and the Kantowski-Sachs minisuperspace contained in it. We discuss the quantization of the midisuperspace using the fact that the dimensionally reduced Einstein Hilbert action becomes a scalar-tensor theory of gravity in two dimensions. We show that the covariant regularization procedure in the midisuperspace induces modifications into the minisuperspace Wheeler De Witt equation. (author). 8 refs

Engineering performance metrics

Science.gov (United States)

Delozier, R.; Snyder, N.

1993-03-01

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

Receptor binding kinetics equations: Derivation using the Laplace transform method.

Science.gov (United States)

Hoare, Sam R J

Measuring unlabeled ligand receptor binding kinetics is valuable in optimizing and understanding drug action. Unfortunately, deriving equations for estimating kinetic parameters is challenging because it involves calculus; integration can be a frustrating barrier to the pharmacologist seeking to measure simple rate parameters. Here, a well-known tool for simplifying the derivation, the Laplace transform, is applied to models of receptor-ligand interaction. The method transforms differential equations to a form in which simple algebra can be applied to solve for the variable of interest, for example the concentration of ligand-bound receptor. The goal is to provide instruction using familiar examples, to enable investigators familiar with handling equilibrium binding equations to derive kinetic equations for receptor-ligand interaction. First, the Laplace transform is used to derive the equations for association and dissociation of labeled ligand binding. Next, its use for unlabeled ligand kinetic equations is exemplified by a full derivation of the kinetics of competitive binding equation. Finally, new unlabeled ligand equations are derived using the Laplace transform. These equations incorporate a pre-incubation step with unlabeled or labeled ligand. Four equations for measuring unlabeled ligand kinetics were compared and the two new equations verified by comparison with numerical solution. Importantly, the equations have not been verified with experimental data because no such experiments are evident in the literature. Equations were formatted for use in the curve-fitting program GraphPad Prism 6.0 and fitted to simulated data. This description of the Laplace transform method will enable pharmacologists to derive kinetic equations for their model or experimental paradigm under study. Application of the transform will expand the set of equations available for the pharmacologist to measure unlabeled ligand binding kinetics, and for other time

Brand metrics that matter

NARCIS (Netherlands)

Muntinga, D.; Bernritter, S.

2017-01-01

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

Privacy Metrics and Boundaries

NARCIS (Netherlands)

L-F. Pau (Louis-François)

2005-01-01

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

Notes on Conservation Laws, Equations of Motion of Matter, and Particle Fields in Lorentzian and Teleparallel de Sitter Space-Time Structures

Directory of Open Access Journals (Sweden)

Waldyr A. Rodrigues

2016-01-01

Full Text Available We discuss the physics of interacting fields and particles living in a de Sitter Lorentzian manifold (dSLM, a submanifold of a 5-dimensional pseudo-Euclidean (5dPE equipped with a metric tensor inherited from the metric of the 5dPE space. The dSLM is naturally oriented and time oriented and is the arena used to study the energy-momentum conservation law and equations of motion for physical systems living there. Two distinct de Sitter space-time structures MdSL and MdSTP are introduced given dSLM, the first equipped with the Levi-Civita connection of its metric field and the second with a metric compatible parallel connection. Both connections are used only as mathematical devices. Thus, for example, MdSL is not supposed to be the model of any gravitational field in the General Relativity Theory (GRT. Misconceptions appearing in the literature concerning the motion of free particles in dSLM are clarified. Komar currents are introduced within Clifford bundle formalism permitting the presentation of Einstein equation as a Maxwell like equation and proving that in GRT there are infinitely many conserved currents. We prove that in GRT even when the appropriate Killing vector fields exist it is not possible to define a conserved energy-momentum covector as in special relativistic theories.

Computations of Wall Distances Based on Differential Equations

Science.gov (United States)

Tucker, Paul G.; Rumsey, Chris L.; Spalart, Philippe R.; Bartels, Robert E.; Biedron, Robert T.

2004-01-01

The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

Assessing precision, bias and sigma-metrics of 53 measurands of the Alinity ci system.

Science.gov (United States)

Westgard, Sten; Petrides, Victoria; Schneider, Sharon; Berman, Marvin; Herzogenrath, Jörg; Orzechowski, Anthony

2017-12-01

Assay performance is dependent on the accuracy and precision of a given method. These attributes can be combined into an analytical Sigma-metric, providing a simple value for laboratorians to use in evaluating a test method's capability to meet its analytical quality requirements. Sigma-metrics were determined for 37 clinical chemistry assays, 13 immunoassays, and 3 ICT methods on the Alinity ci system. Analytical Performance Specifications were defined for the assays, following a rationale of using CLIA goals first, then Ricos Desirable goals when CLIA did not regulate the method, and then other sources if the Ricos Desirable goal was unrealistic. A precision study was conducted at Abbott on each assay using the Alinity ci system following the CLSI EP05-A2 protocol. Bias was estimated following the CLSI EP09-A3 protocol using samples with concentrations spanning the assay's measuring interval tested in duplicate on the Alinity ci system and ARCHITECT c8000 and i2000 SR systems, where testing was also performed at Abbott. Using the regression model, the %bias was estimated at an important medical decisions point. Then the Sigma-metric was estimated for each assay and was plotted on a method decision chart. The Sigma-metric was calculated using the equation: Sigma-metric=(%TEa-|%bias|)/%CV. The Sigma-metrics and Normalized Method Decision charts demonstrate that a majority of the Alinity assays perform at least at five Sigma or higher, at or near critical medical decision levels. More than 90% of the assays performed at Five and Six Sigma. None performed below Three Sigma. Sigma-metrics plotted on Normalized Method Decision charts provide useful evaluations of performance. The majority of Alinity ci system assays had sigma values >5 and thus laboratories can expect excellent or world class performance. Laboratorians can use these tools as aids in choosing high-quality products, further contributing to the delivery of excellent quality healthcare for patients

Development of 1-Mile Walk Tests to Estimate Aerobic Fitness in Children

Science.gov (United States)

Sung, Hoyong; Collier, David N.; DuBose, Katrina D.; Kemble, C. David; Mahar, Matthew T.

2018-01-01

To examine the reliability and validity of 1-mile walk tests for estimation of aerobic fitness (VO[subscript 2max]) in 10- to 13-year-old children and to cross-validate previously published equations. Participants (n = 61) walked 1-mile on two different days. Self-reported physical activity, demographic variables, and aerobic fitness were used in…

Cyber threat metrics.

Energy Technology Data Exchange (ETDEWEB)

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

2012-03-01

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

Fixed point theory in metric type spaces

CERN Document Server

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

2015-01-01

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

Utility of ck metrics in predicting size of board-based software games

International Nuclear Information System (INIS)

Sabhat, N.; Azam, F.; Malik, A.A.

2017-01-01

Software size is one of the most important inputs of many software cost and effort estimation models. Early estimation of software plays an important role at the time of project inception. An accurate estimate of software size is, therefore, crucial for planning, managing, and controlling software development projects dealing with the development of software games. However, software size is unavailable during early phase of software development. This research determines the utility of CK (Chidamber and Kemerer) metrics, a well-known suite of object-oriented metrics, in estimating the size of software applications using the information from its UML (Unified Modeling Language) class diagram. This work focuses on a small subset dealing with board-based software games. Almost sixty games written using an object-oriented programming language are downloaded from open source repositories, analyzed and used to calibrate a regression-based size estimation model. Forward stepwise MLR (Multiple Linear Regression) is used for model fitting. The model thus obtained is assessed using a variety of accuracy measures such as MMRE (Mean Magnitude of Relative Error), Prediction of x(PRED(x)), MdMRE (Median of Relative Error) and validated using K-fold cross validation. The accuracy of this model is also compared with an existing model tailored for size estimation of board games. Based on a small subset of desktop games developed in various object-oriented languages, we obtained a model using CK metrics and forward stepwise multiple linear regression with reasonable estimation accuracy as indicated by the value of the coefficient of determination (R2 = 0.756).Comparison results indicate that the existing size estimation model outperforms the model derived using CK metrics in terms of accuracy of prediction. (author)

Deep Transfer Metric Learning.

Science.gov (United States)

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

2016-12-01

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

Applications of Multilevel Structural Equation Modeling to Cross-Cultural Research

Science.gov (United States)

Cheung, Mike W.-L.; Au, Kevin

2005-01-01

Multilevel structural equation modeling (MSEM) has been proposed as an extension to structural equation modeling for analyzing data with nested structure. We have begun to see a few applications in cross-cultural research in which MSEM fits well as the statistical model. However, given that cross-cultural studies can only afford collecting data…

Selected equation of state in the acentric factor system

International Nuclear Information System (INIS)

Schreiber, D.R.; Pitzer, K.S.

1988-06-01

A new equation of state in the acentric factor system is developed on the basis of high-precision data. The region in critical temperature T/sub r/, critical density P/sub r/ space is identified where there is good agreement as well as the regions of significant departures. The equation fits very well in the critical region. 10 refs., 6 figs., 3 tabs

Random-Effects Models for Meta-Analytic Structural Equation Modeling: Review, Issues, and Illustrations

Science.gov (United States)

Cheung, Mike W.-L.; Cheung, Shu Fai

2016-01-01

Meta-analytic structural equation modeling (MASEM) combines the techniques of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Both fixed-effects and random-effects models can be defined in MASEM.…

Inverse problems for random differential equations using the collage method for random contraction mappings

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Kunze, H. E.; La Torre, D.; Vrscay, E. R.

2009-01-01

In this paper we are concerned with differential equations with random coefficients which will be considered as random fixed point equations of the form T([omega],x([omega]))=x([omega]), [omega][set membership, variant][Omega]. Here T:[Omega]×X-->X is a random integral operator, is a probability space and X is a complete metric space. We consider the following inverse problem for such equations: Given a set of realizations of the fixed point of T (possibly the interpolations of different observational data sets), determine the operator T or the mean value of its random components, as appropriate. We solve the inverse problem for this class of equations by using the collage theorem for contraction mappings.

Regge calculus from discontinuous metrics

International Nuclear Information System (INIS)

Khatsymovsky, V.M.

2003-01-01

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

Numerical Calabi-Yau metrics

International Nuclear Information System (INIS)

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

2008-01-01

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

Analysis of equations of state for ICF

International Nuclear Information System (INIS)

Ogando, F.; Velarde, P.

1998-01-01

In the field of inertial confinement fusion (ICF), numerical simulation plays a very important role reproducing real results with a good accuracy. Once considered the needed simplificative approximations, it is obtained and equation system that has to be solved in a more or less complex way. Anyway these simulation codes have to fit the behaviour of real materials with the help of some flexible parameters. In the case of fluid dynamics, the key to fit the equation system to the real material behaviour are the equations of state (EOS) involved in the problem. This is why there is an actual need of using accurate data in order to obtain results that match the real behaviour of materials. Nowadays there are several available sources of real EOS data. These sources are based either in theoretical models fixed with experimental results or in analytical approximations to those models. In this article a comparative analysis is made between two of the most used EOS data sources in simulations. The aim of this work is to check the quality of these data that is commonly used and on which the accuracy of the results depend. (Author) 3 refs

Are Current Physical Match Performance Metrics in Elite Soccer Fit for Purpose or is the Adoption of an Integrated Approach Needed?

Science.gov (United States)

Bradley, Paul S; Ade, Jack D

2018-01-18

Time-motion analysis is a valuable data-collection technique used to quantify the physical match performance of elite soccer players. For over 40 years researchers have adopted a 'traditional' approach when evaluating match demands by simply reporting the distance covered or time spent along a motion continuum of walking through to sprinting. This methodology quantifies physical metrics in isolation without integrating other factors and this ultimately leads to a one-dimensional insight into match performance. Thus, this commentary proposes a novel 'integrated' approach that focuses on a sensitive physical metric such as high-intensity running but contextualizes this in relation to key tactical activities for each position and collectively for the team. In the example presented, the 'integrated' model clearly unveils the unique high-intensity profile that exists due to distinct tactical roles, rather than one-dimensional 'blind' distances produced by 'traditional' models. Intuitively this innovative concept may aid the coaches understanding of the physical performance in relation to the tactical roles and instructions given to the players. Additionally, it will enable practitioners to more effectively translate match metrics into training and testing protocols. This innovative model may well aid advances in other team sports that incorporate similar intermittent movements with tactical purpose. Evidence of the merits and application of this new concept are needed before the scientific community accepts this model as it may well add complexity to an area that conceivably needs simplicity.

Metrics for Evaluation of Student Models

Science.gov (United States)

Pelanek, Radek

2015-01-01

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

CRAPONE, Optical Model Potential Fit of Neutron Scattering Data

International Nuclear Information System (INIS)

Fabbri, F.; Fratamico, G.; Reffo, G.

2004-01-01

1 - Description of problem or function: Automatic search for local and non-local optical potential parameters for neutrons. Total, elastic, differential elastic cross sections, l=0 and l=1 strength functions and scattering length can be considered. 2 - Method of solution: A fitting procedure is applied to different sets of experimental data depending on the local or non-local approximation chosen. In the non-local approximation the fitting procedure can be simultaneously performed over the whole energy range. The best fit is obtained when a set of parameters is found where CHI 2 is at its minimum. The solution of the system equations is obtained by diagonalization of the matrix according to the Jacobi method

Random fixed point equations and inverse problems using "collage method" for contraction mappings

Science.gov (United States)

Kunze, H. E.; La Torre, D.; Vrscay, E. R.

2007-10-01

In this paper we are interested in the direct and inverse problems for the following class of random fixed point equations T(w,x(w))=x(w) where is a given operator, [Omega] is a probability space and X is a Polish metric space. The inverse problem is solved by recourse to the collage theorem for contractive maps. We then consider two applications: (i) random integral equations, and (ii) random iterated function systems with greyscale maps (RIFSM), for which noise is added to the classical IFSM.

On 0-Complete Partial Metric Spaces and Quantitative Fixed Point Techniques in Denotational Semantics

Directory of Open Access Journals (Sweden)

N. Shahzad

2013-01-01

Full Text Available In 1994, Matthews introduced the notion of partial metric space with the aim of providing a quantitative mathematical model suitable for program verification. Concretely, Matthews proved a partial metric version of the celebrated Banach fixed point theorem which has become an appropriate quantitative fixed point technique to capture the meaning of recursive denotational specifications in programming languages. In this paper we show that a few assumptions in statement of Matthews fixed point theorem can be relaxed in order to provide a quantitative fixed point technique useful to analyze the meaning of the aforementioned recursive denotational specifications in programming languages. In particular, we prove a new fixed point theorem for self-mappings between partial metric spaces in which the completeness has been replaced by 0-completeness and the contractive condition has been weakened in such a way that the new one best fits the requirements of practical problems in denotational semantics. Moreover, we provide examples that show that the hypothesis in the statement of our new result cannot be weakened. Finally, we show the potential applicability of the developed theory by means of analyzing a few concrete recursive denotational specifications, some of them admitting a unique meaning and others supporting multiple ones.

Issues in Benchmark Metric Selection

Science.gov (United States)

Crolotte, Alain

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

Duration of Postoperative Mechanical Ventilation as a Quality Metric for Pediatric Cardiac Surgical Programs.

Science.gov (United States)

Gaies, Michael; Werho, David K; Zhang, Wenying; Donohue, Janet E; Tabbutt, Sarah; Ghanayem, Nancy S; Scheurer, Mark A; Costello, John M; Gaynor, J William; Pasquali, Sara K; Dimick, Justin B; Banerjee, Mousumi; Schwartz, Steven M

2018-02-01

Few metrics exist to assess quality of care at pediatric cardiac surgical programs, limiting opportunities for benchmarking and quality improvement. Postoperative duration of mechanical ventilation (POMV) may be an important quality metric because of its association with complications and resource utilization. In this study we modelled case-mix-adjusted POMV duration and explored hospital performance across POMV metrics. This study used the Pediatric Cardiac Critical Care Consortium clinical registry to analyze 4,739 hospitalizations from 15 hospitals (October 2013 to August 2015). All patients admitted to pediatric cardiac intensive care units after an index cardiac operation were included. We fitted a model to predict duration of POMV accounting for patient characteristics. Robust estimates of SEs were obtained using bootstrap resampling. We created performance metrics based on observed-to-expected (O/E) POMV to compare hospitals. Overall, 3,108 patients (65.6%) received POMV; the remainder were extubated intraoperatively. Our model was well calibrated across groups; neonatal age had the largest effect on predicted POMV. These comparisons suggested clinically and statistically important variation in POMV duration across centers with a threefold difference observed in O/E ratios (0.6 to 1.7). We identified 1 hospital with better-than-expected and 3 hospitals with worse-than-expected performance (p < 0.05) based on the O/E ratio. We developed a novel case-mix-adjusted model to predict POMV duration after congenital heart operations. We report variation across hospitals on metrics of O/E duration of POMV that may be suitable for benchmarking quality of care. Identifying high-performing centers and practices that safely limit the duration of POMV could stimulate quality improvement efforts. Copyright © 2018 The Society of Thoracic Surgeons. Published by Elsevier Inc. All rights reserved.

Robustness of climate metrics under climate policy ambiguity

International Nuclear Information System (INIS)

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

2013-01-01

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

Data of NODDI diffusion metrics in the brain and computer simulation of hybrid diffusion imaging (HYDI acquisition scheme

Directory of Open Access Journals (Sweden)

Chandana Kodiweera

2016-06-01

Full Text Available This article provides NODDI diffusion metrics in the brains of 52 healthy participants and computer simulation data to support compatibility of hybrid diffusion imaging (HYDI, “Hybrid diffusion imaging” [1] acquisition scheme in fitting neurite orientation dispersion and density imaging (NODDI model, “NODDI: practical in vivo neurite orientation dispersion and density imaging of the human brain” [2]. HYDI is an extremely versatile diffusion magnetic resonance imaging (dMRI technique that enables various analyzes methods using a single diffusion dataset. One of the diffusion data analysis methods is the NODDI computation, which models the brain tissue with three compartments: fast isotropic diffusion (e.g., cerebrospinal fluid, anisotropic hindered diffusion (e.g., extracellular space, and anisotropic restricted diffusion (e.g., intracellular space. The NODDI model produces microstructural metrics in the developing brain, aging brain or human brain with neurologic disorders. The first dataset provided here are the means and standard deviations of NODDI metrics in 48 white matter region-of-interest (ROI averaging across 52 healthy participants. The second dataset provided here is the computer simulation with initial conditions guided by the first dataset as inputs and gold standard for model fitting. The computer simulation data provide a direct comparison of NODDI indices computed from the HYDI acquisition [1] to the NODDI indices computed from the originally proposed acquisition [2]. These data are related to the accompanying research article “Age Effects and Sex Differences in Human Brain White Matter of Young to Middle-Aged Adults: A DTI, NODDI, and q-Space Study” [3].

Web metrics for library and information professionals

CERN Document Server

Stuart, David

2014-01-01

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

Partial rectangular metric spaces and fixed point theorems.

Science.gov (United States)

Shukla, Satish

2014-01-01

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

Estimation of time- and state-dependent delays and other parameters in functional differential equations

Science.gov (United States)

Murphy, K. A.

1990-01-01

A parameter estimation algorithm is developed which can be used to estimate unknown time- or state-dependent delays and other parameters (e.g., initial condition) appearing within a nonlinear nonautonomous functional differential equation. The original infinite dimensional differential equation is approximated using linear splines, which are allowed to move with the variable delay. The variable delays are approximated using linear splines as well. The approximation scheme produces a system of ordinary differential equations with nice computational properties. The unknown parameters are estimated within the approximating systems by minimizing a least-squares fit-to-data criterion. Convergence theorems are proved for time-dependent delays and state-dependent delays within two classes, which say essentially that fitting the data by using approximations will, in the limit, provide a fit to the data using the original system. Numerical test examples are presented which illustrate the method for all types of delay.

Performance and scaling of locally-structured grid methods forpartial differential equations

Energy Technology Data Exchange (ETDEWEB)

Colella, Phillip; Bell, John; Keen, Noel; Ligocki, Terry; Lijewski, Michael; Van Straalen, Brian

2007-07-19

In this paper, we discuss some of the issues in obtaining high performance for block-structured adaptive mesh refinement software for partial differential equations. We show examples in which AMR scales to thousands of processors. We also discuss a number of metrics for performance and scalability that can provide a basis for understanding the advantages and disadvantages of this approach.

Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

Directory of Open Access Journals (Sweden)

Claudio Cremaschini

2017-07-01

Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.

Background metric in supergravity theories

International Nuclear Information System (INIS)

Yoneya, T.

1978-01-01

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

Daylight metrics and energy savings

Energy Technology Data Exchange (ETDEWEB)

Mardaljevic, John; Heschong, Lisa; Lee, Eleanor

2009-12-31

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

Families of null surfaces in the Minkowski tri dimensional space-time and its associated differential equations

International Nuclear Information System (INIS)

Silva O, G.; Garcia G, P.

2004-01-01

In this work we describe the procedure to obtain all the family of third order ordinary differential equations connected by a contact transformation such that in their spaces of solutions is defined a conformal three dimensional Minkowski metric. (Author)

A cautionary note on the use of information fit indexes in covariance structure modeling with means

NARCIS (Netherlands)

Wicherts, J.M.; Dolan, C.V.

2004-01-01

Information fit indexes such as Akaike Information Criterion, Consistent Akaike Information Criterion, Bayesian Information Criterion, and the expected cross validation index can be valuable in assessing the relative fit of structural equation models that differ regarding restrictiveness. In cases

Exponential and Bessel fitting methods for the numerical solution of the Schroedinger equation

International Nuclear Information System (INIS)

Raptis, A.D.; Cash, J.R.

1987-01-01

A new method is developed for the numerical integration of the one dimensional radial Schroedinger equation. This method involves using different integration formulae in different parts of the range of integration rather than using the same integration formula throughout. Two new integration formulae are derived, one which integrates Bessel and Neumann functions exactly and another which exactly integrates certain exponential functions. It is shown that, for large r, these new formulae are much more accurate than standard integration methods for the Schroedinger equation. The benefit of using this new approach is demonstrated by considering some numerical examples based on the Lennard-Jones potential. (orig.)

Prediction of cardiorespiratory fitness from self-reported data in elderly

Directory of Open Access Journals (Sweden)

Geraldo A Maranhao Neto

2017-12-01

Full Text Available Cardiorespiratory fitness (CRF is associated with several health outcomes. Some non-exercise equations are available for CRF estimation. However, little is known about the validation of these equations among elderly. The aim of this study was to exam the validity of non-exercise equations with self-reported information in elderly. Participants (n= 93 aged 60 to 91 years measured CRF using maximal cardiopulmonary exercise test. Five non-exercise equations were selected. Data included in the equations (age, sex, weight, height, body mass index, physical activity and smoking were self-reported. Coefficient of determination (R2 of linear regressions with laboratory-measured VO2 peak ranged from 0.04 to 0.64. The Bland-Altman plots showed higher agreement between achieved and predicted CRF obtained by Jackson and colleagues, and Wier and colleagues equations. On the other hand, the other equations showed lower agreement and overestimation. Our findings provide evidences that two non-exercise equations, previously developed, could be used on the prediction of CRF among elderly.

Enhancing the Equating of Item Difficulty Metrics: Estimation of Reference Distribution. Research Report. ETS RR-14-07

Science.gov (United States)

Ali, Usama S.; Walker, Michael E.

2014-01-01

Two methods are currently in use at Educational Testing Service (ETS) for equating observed item difficulty statistics. The first method involves the linear equating of item statistics in an observed sample to reference statistics on the same items. The second method, or the item response curve (IRC) method, involves the summation of conditional…

A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold

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Abimbola Abolarinwa

2014-08-01

Full Text Available In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.

Metrics for energy resilience

International Nuclear Information System (INIS)

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

2014-01-01

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

Allometric Equations for Estimating Biomass and Carbon Stocks in the Temperate Forests of North-Western Mexico

Directory of Open Access Journals (Sweden)

Benedicto Vargas-Larreta

2017-07-01

Full Text Available This paper presents new equations for estimating above-ground biomass (AGB and biomass components of seventeen forest species in the temperate forests of northwestern Mexico. A data set corresponding to 1336 destructively sampled oak and pine trees was used to fit the models. The generalized method of moments was used to simultaneously fit systems of equations for biomass components and AGB, to ensure additivity. In addition, the carbon content of each tree component was calculated by the dry combustion method, in a TOC analyser. The results of cross-validation indicated that the fitted equations accounted for on average 91%, 82%, 83% and 76% of the observed variance in stem wood and stem bark, branch and foliage biomass, respectively, whereas the total AGB equations explained on average 93% of the total observed variance in AGB. The inclusion of total height (h or diameter at breast height2 × total height (d2h as a predictor in the d-only based equations systems slightly improved estimates for stem wood, stem bark and total above-ground biomass, and greatly improved the estimates produced by the branch and foliage biomass equations. The predictive power of the proposed equations is higher than that of existing models for the study area. The fitted equations were used to estimate stand level AGB stocks from data on growing stock in 429 permanent sampling plots. Three machine-learning techniques were used to model the estimated stand level AGB and carbon contents; the selected models were used to map the AGB and carbon distributions in the study area, for which mean values of respectively 129.84 Mg ha−1 and 63.80 Mg ha−1 were obtained.

Family of electrovac colliding wave solutions of Einstein's equations

International Nuclear Information System (INIS)

Li, W.; Ernst, F.J.

1989-01-01

Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison [J. Math. Phys. 9, 1744 (1968)]. The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, Garcia, and Hauser (EGH) [J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)]. Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibanez, and Bruni [Phys. Rev. D 36, 1053 (1987)]. Among the electrovac solutions that are obtained is a charged version of the Nutku--Halil [Phys. Rev. Lett. 39, 1379 (1977)] metric that possesses an arbitrary complex charge parameter

The metrics of science and technology

CERN Document Server

Geisler, Eliezer

2000-01-01

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

Extending cosmology: the metric approach

OpenAIRE

Mendoza, S.

2012-01-01

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

Metrics, Media and Advertisers: Discussing Relationship

Directory of Open Access Journals (Sweden)

Marco Aurelio de Souza Rodrigues

2014-11-01

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

Measuring Information Security: Guidelines to Build Metrics

Science.gov (United States)

von Faber, Eberhard

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

Active Metric Learning for Supervised Classification

OpenAIRE

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

2018-01-01

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

Harmonic analysis, partial differential equations and applications in honor of Richard L. Wheeden

CERN Document Server

Franchi, Bruno; Lu, Guozhen; Perez, Carlos; Sawyer, Eric

2017-01-01

This is a collection of contributed papers by many eminent Harmonic Analysts and specialists of Partial Differential equations. The papers focus on weighted norm equalities for singular integrals, focusing wave equations, degenerate elliptic equations, Navier-Stokes flow in two dimensions and Poincare-Sobolev inequalities in the setting of metric spaces equipped with measures among others. Many topics considered in this volume stem from the interests of Richard L. Wheeden whose contributions to Potential Theory, singular integral theory and degenerate elliptic PDE theory this volume honors. Luis Caffarelli, Sagun Chanillo, Bruno Franchi, Cristian Guttierez, Xiaojun Huang, Carlos Kenig, Ermanno Lanconelli, Eric Sawyer and Alexander Volberg, are some of the many contributors to this volume. .

Observational constraints on scalar field models of dark energy with barotropic equation of state

International Nuclear Information System (INIS)

Sergijenko, Olga; Novosyadlyj, Bohdan; Durrer, Ruth

2011-01-01

We constrain the parameters of dynamical dark energy in the form of a classical or tachyonic scalar field with barotropic equation of state jointly with other cosmological parameters using the following datasets: the CMB power spectra from WMAP7, the baryon acoustic oscillations in the space distribution of galaxies from SDSS DR7, the power spectrum of luminous red galaxies from SDSS DR7 and the light curves of SN Ia from 2 different compilations: Union2 (SALT2 light curve fitting) and SDSS (SALT2 and MLCS2k2 light curve fittings). It has been found that the initial value of dark energy equation of state parameter is constrained very weakly by most of the data while the other cosmological parameters are well constrained: their likelihoods and posteriors are similar, their forms are close to Gaussian (or half-Gaussian) and the confidence ranges are narrow. The most reliable determinations of the best-fit value and 1σ confidence range for the initial value of the dark energy equation of state parameter are obtained from the combined datasets including SN Ia data from the full SDSS compilation with MLCS2k2 light curve fitting. In all such cases the best-fit value of this parameter is lower than the value of corresponding parameter for current epoch. Such dark energy loses its repulsive properties and in future the expansion of the Universe changes into contraction. We also perform a forecast for the Planck mock data and show that they narrow significantly the confidence ranges of cosmological parameters values, moreover, their combination with SN SDSS compilation with MLCS2k2 light curve fitting may exclude the fields with initial equation of state parameter > −0.1 at 2σ confidence level

Metric-independent measures for supersymmetric extended object theories on curved backgrounds

International Nuclear Information System (INIS)

Nishino, Hitoshi; Rajpoot, Subhash

2014-01-01

For Green–Schwarz superstring σ-model on curved backgrounds, we introduce a non-metric measure Φ≡ϵ ij ϵ IJ (∂ i φ I )(∂ j φ J ) with two scalars φ I (I=1,2) used in ‘Two-Measure Theory’ (TMT). As in the flat-background case, the string tension T=(2πα ′ ) −1 emerges as an integration constant for the A i -field equation. This mechanism is further generalized to supermembrane theory, and to super-p-brane theory, both on general curved backgrounds. This shows the universal applications of dynamical measure of TMT to general supersymmetric extended objects on general curved backgrounds

Multimetric indices: How many metrics?

Science.gov (United States)

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

Axisymmetric black holes allowing for separation of variables in the Klein-Gordon and Hamilton-Jacobi equations

Science.gov (United States)

Konoplya, R. A.; Stuchlík, Z.; Zhidenko, A.

2018-04-01

We determine the class of axisymmetric and asymptotically flat black-hole spacetimes for which the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables. The known Kerr, Kerr-Newman, Kerr-Sen and some other black-hole metrics in various theories of gravity are within the class of spacetimes described here. It is shown that although the black-hole metric in the Einstein-dilaton-Gauss-Bonnet theory does not allow for the separation of variables (at least in the considered coordinates), for a number of applications it can be effectively approximated by a metric within the above class. This gives us some hope that the class of spacetimes described here may be not only generic for the known solutions allowing for the separation of variables, but also a good approximation for a broader class of metrics, which does not admit such separation. Finally, the generic form of the axisymmetric metric is expanded in the radial direction in terms of the continued fractions and the connection with other black-hole parametrizations is discussed.

Metrics for Polyphonic Sound Event Detection

Directory of Open Access Journals (Sweden)

Annamaria Mesaros

2016-05-01

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

Robustness Metrics: Consolidating the multiple approaches to quantify Robustness

DEFF Research Database (Denmark)

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

2016-01-01

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

Common Metrics for Human-Robot Interaction

Science.gov (United States)

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

2006-01-01

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

An axisymmetric evolution code for the Einstein equations on hyperboloidal slices

International Nuclear Information System (INIS)

Rinne, Oliver

2010-01-01

We present the first stable dynamical numerical evolutions of the Einstein equations in terms of a conformally rescaled metric on hyperboloidal hypersurfaces extending to future null infinity. Axisymmetry is imposed in order to reduce the computational cost. The formulation is based on an earlier axisymmetric evolution scheme, adapted to time slices of constant mean curvature. Ideas from a previous study by Moncrief and the author are applied in order to regularize the formally singular evolution equations at future null infinity. Long-term stable and convergent evolutions of Schwarzschild spacetime are obtained, including a gravitational perturbation. The Bondi news function is evaluated at future null infinity.

Workshop summary: 'Integrating air quality and climate mitigation - is there a need for new metrics to support decision making?'

Science.gov (United States)

von Schneidemesser, E.; Schmale, J.; Van Aardenne, J.

2013-12-01

Air pollution and climate change are often treated at national and international level as separate problems under different regulatory or thematic frameworks and different policy departments. With air pollution and climate change being strongly linked with regard to their causes, effects and mitigation options, the integration of policies that steer air pollutant and greenhouse gas emission reductions might result in cost-efficient, more effective and thus more sustainable tackling of the two problems. To support informed decision making and to work towards an integrated air quality and climate change mitigation policy requires the identification, quantification and communication of present-day and potential future co-benefits and trade-offs. The identification of co-benefits and trade-offs requires the application of appropriate metrics that are well rooted in science, easy to understand and reflect the needs of policy, industry and the public for informed decision making. For the purpose of this workshop, metrics were loosely defined as a quantified measure of effect or impact used to inform decision-making and to evaluate mitigation measures. The workshop held on October 9 and 10 and co-organized between the European Environment Agency and the Institute for Advanced Sustainability Studies brought together representatives from science, policy, NGOs, and industry to discuss whether current available metrics are 'fit for purpose' or whether there is a need to develop alternative metrics or reassess the way current metrics are used and communicated. Based on the workshop outcome the presentation will (a) summarize the informational needs and current application of metrics by the end-users, who, depending on their field and area of operation might require health, policy, and/or economically relevant parameters at different scales, (b) provide an overview of the state of the science of currently used and newly developed metrics, and the scientific validity of these

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

OpenAIRE

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

2018-01-01

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

New exposure-based metric approach for evaluating O3 risk to North American aspen forests

International Nuclear Information System (INIS)

Percy, K.E.; Nosal, M.; Heilman, W.; Dann, T.; Sober, J.; Legge, A.H.; Karnosky, D.F.

2007-01-01

The United States and Canada currently use exposure-based metrics to protect vegetation from O 3 . Using 5 years (1999-2003) of co-measured O 3 , meteorology and growth response, we have developed exposure-based regression models that predict Populus tremuloides growth change within the North American ambient air quality context. The models comprised growing season fourth-highest daily maximum 8-h average O 3 concentration, growing degree days, and wind speed. They had high statistical significance, high goodness of fit, include 95% confidence intervals for tree growth change, and are simple to use. Averaged across a wide range of clonal sensitivity, historical 2001-2003 growth change over most of the 26 M ha P. tremuloides distribution was estimated to have ranged from no impact (0%) to strong negative impacts (-31%). With four aspen clones responding negatively (one responded positively) to O 3 , the growing season fourth-highest daily maximum 8-h average O 3 concentration performed much better than growing season SUM06, AOT40 or maximum 1 h average O 3 concentration metrics as a single indicator of aspen stem cross-sectional area growth. - A new exposure-based metric approach to predict O 3 risk to North American aspen forests has been developed

Applying the Nernst equation to simulate redox potential variations for biological nitrification and denitrification processes.

Science.gov (United States)

Chang, Cheng-Nan; Cheng, Hong-Bang; Chao, Allen C

2004-03-15

In this paper, various forms of Nernst equations have been developed based on the real stoichiometric relationship of biological nitrification and denitrification reactions. Instead of using the Nernst equation based on a one-to-one stoichiometric relation for the oxidizing and the reducing species, the basic Nernst equation is modified into slightly different forms. Each is suitable for simulating the redox potential (ORP) variation of a specific biological nitrification or denitrification process. Using the data published in the literature, the validity of these developed Nernst equations has been verified by close fits of the measured ORP data with the calculated ORP curve. The simulation results also indicate that if the biological process is simulated using an incorrect form of Nernst equation, the calculated ORP curve will not fit the measured data. Using these Nernst equations, the ORP value that corresponds to a predetermined degree of completion for the biochemical reaction can be calculated. Thus, these Nernst equations will enable a more efficient on-line control of the biological process.

Test of the FLRW Metric and Curvature with Strong Lens Time Delays

International Nuclear Information System (INIS)

Liao, Kai; Li, Zhengxiang; Wang, Guo-Jian; Fan, Xi-Long

2017-01-01

We present a new model-independent strategy for testing the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and constraining cosmic curvature, based on future time-delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the distance sum rule (DSR) and determining/constraining cosmic curvature. We propose an effective and efficient (redshift) evolution model for performing the former test, which allows us to concretely specify the violation criterion for the FLRW DSR. If the FLRW metric is consistent with the observations, then on the second level the cosmic curvature parameter will be constrained to ∼0.057 or ∼0.041 (1 σ ), depending on the availability of high-redshift supernovae, which is much more stringent than current model-independent techniques. We also show that the bias in the time-delay method might be well controlled, leading to robust results. The proposed method is a new independent tool for both testing the fundamental assumptions of homogeneity and isotropy in cosmology and for determining cosmic curvature. It is complementary to cosmic microwave background plus baryon acoustic oscillation analyses, which normally assume a cosmological model with dark energy domination in the late-time universe.

Test of the FLRW Metric and Curvature with Strong Lens Time Delays

Energy Technology Data Exchange (ETDEWEB)

Liao, Kai [School of Science, Wuhan University of Technology, Wuhan 430070 (China); Li, Zhengxiang; Wang, Guo-Jian [Department of Astronomy, Beijing Normal University, Beijing 100875 (China); Fan, Xi-Long, E-mail: liaokai@whut.edu.cn, E-mail: xilong.fan@glasgow.ac.uk [Department of Physics and Mechanical and Electrical Engineering, Hubei University of Education, Wuhan 430205 (China)

2017-04-20

We present a new model-independent strategy for testing the Friedmann–Lemaître–Robertson–Walker (FLRW) metric and constraining cosmic curvature, based on future time-delay measurements of strongly lensed quasar-elliptical galaxy systems from the Large Synoptic Survey Telescope and supernova observations from the Dark Energy Survey. The test only relies on geometric optics. It is independent of the energy contents of the universe and the validity of the Einstein equation on cosmological scales. The study comprises two levels: testing the FLRW metric through the distance sum rule (DSR) and determining/constraining cosmic curvature. We propose an effective and efficient (redshift) evolution model for performing the former test, which allows us to concretely specify the violation criterion for the FLRW DSR. If the FLRW metric is consistent with the observations, then on the second level the cosmic curvature parameter will be constrained to ∼0.057 or ∼0.041 (1 σ ), depending on the availability of high-redshift supernovae, which is much more stringent than current model-independent techniques. We also show that the bias in the time-delay method might be well controlled, leading to robust results. The proposed method is a new independent tool for both testing the fundamental assumptions of homogeneity and isotropy in cosmology and for determining cosmic curvature. It is complementary to cosmic microwave background plus baryon acoustic oscillation analyses, which normally assume a cosmological model with dark energy domination in the late-time universe.

Performance measurement systems, TQM, and multi-level firm performance: a person-organisation fit perspective

OpenAIRE

Wei, Jo-Ting; Chang, Yeun Wen; Zhang, Xiaoxiang; Wu, Hsin-Hung

2017-01-01

For firms implementing TQM, there is a need to redesign performance measurement systems (PMS). Innovated PMS ought to have measurement diversity in their structure with considering the spirit of TQM and emphasize the congruence of goals between employees and firms by adding the viewpoint of person-organisation fit (P-O fit). This paper adopts structural equation modeling (SEM) to examine Taiwanese manufacturing firms to study the association between the P-O fit of PMS and the implementation o...

ST-intuitionistic fuzzy metric space with properties

Science.gov (United States)

Arora, Sahil; Kumar, Tanuj

2017-07-01

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

Materials data base and design equations for the UCLA solid breeder blanket

International Nuclear Information System (INIS)

Sharafat, S.; Amodeo, R.; Ghoniem, N.M.

1986-02-01

The materials and properties investigated for this blanket study are listed. The phenomenological equations and mathematical fits for all materials and properties considered are given. Efforts to develop a swelling equation based on the few experimental data points available for breeder materials are described. The sintering phenomena for ceramics is investigated

Fitting Data to Model: Structural Equation Modeling Diagnosis Using Two Scatter Plots

Science.gov (United States)

Yuan, Ke-Hai; Hayashi, Kentaro

2010-01-01

This article introduces two simple scatter plots for model diagnosis in structural equation modeling. One plot contrasts a residual-based M-distance of the structural model with the M-distance for the factor score. It contains information on outliers, good leverage observations, bad leverage observations, and normal cases. The other plot contrasts…

Auxiliary basis expansions for large-scale electronic structure calculations.

Science.gov (United States)

Jung, Yousung; Sodt, Alex; Gill, Peter M W; Head-Gordon, Martin

2005-05-10

One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve divergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems.

Dirac equation in a de Sitter expansion for massive neutrinos from modern Kaluza-Klein theory

International Nuclear Information System (INIS)

Sánchez, Pablo Alejandro; Anabitarte, Mariano; Bellini, Mauricio

2012-01-01

Using the modern Kaluza-Klein theory of gravity (or the Induced Matter theory), we study the Dirac equation for massive neutrinos on a de Sitter background metric from a 5D Riemann-flat (and hence Ricci-flat) extended de Sitter metric, on which is defined the vacuum for test massless 1/2-spin neutral fields minimally coupled to gravity and free of any other interactions. We obtain that the effective 4D masses of the neutrinos can only take three possible values, which are related to the (static) foliation of the fifth and noncompact extra dimension.

Revisiting measurement invariance in intelligence testing in aging research: Evidence for almost complete metric invariance across age groups.

Science.gov (United States)

Sprague, Briana N; Hyun, Jinshil; Molenaar, Peter C M

2017-01-01

Invariance of intelligence across age is often assumed but infrequently explicitly tested. Horn and McArdle (1992) tested measurement invariance of intelligence, providing adequate model fit but might not consider all relevant aspects such as sub-test differences. The goal of the current paper is to explore age-related invariance of the WAIS-R using an alternative model that allows direct tests of age on WAIS-R subtests. Cross-sectional data on 940 participants aged 16-75 from the WAIS-R normative values were used. Subtests examined were information, comprehension, similarities, vocabulary, picture completion, block design, picture arrangement, and object assembly. The two intelligence factors considered were fluid and crystallized intelligence. Self-reported ages were divided into young (16-22, n = 300), adult (29-39, n = 275), middle (40-60, n = 205), and older (61-75, n = 160) adult groups. Results suggested partial metric invariance holds. Although most of the subtests reflected fluid and crystalized intelligence similarly across different ages, invariance did not hold for block design on fluid intelligence and picture arrangement on crystallized intelligence for older adults. Additionally, there was evidence of a correlated residual between information and vocabulary for the young adults only. This partial metric invariance model yielded acceptable model fit compared to previously-proposed invariance models of Horn and McArdle (1992). Almost complete metric invariance holds for a two-factor model of intelligence. Most of the subtests were invariant across age groups, suggesting little evidence for age-related bias in the WAIS-R. However, we did find unique relationships between two subtests and intelligence. Future studies should examine age-related differences in subtests when testing measurement invariance in intelligence.

General relativistic continuum mechanics and the post-Newtonian equations of motion

International Nuclear Information System (INIS)

Morrill, T.H.

1991-01-01

Aspects are examined of general relativistic continuum mechanics. Perfectly elastic materials are dealt with but not exclusively. The derivation of their equations of motion is emphasized, in the post-Newtonian approximation. A reformulation is presented based on the tetrad formalism, of Carter and Quintana's theory of general relativistic elastic continua. A field Lagrangian is derived describing perfect material media; show that the usual covariant conservations law for perfectly elastic media is fully equivalent to the Euler-Lagrange equations describing these same media; and further show that the equations of motion for such materials follow directly from Einstein's field equations. In addition, a version of this principle shows that the local mass density in curved space-time partially depends on the amount and distribution of mass energy in the entire universe and is related to the mass density that would occur if space-time were flat. The total Lagrangian was also expanded in an EIH (Einstein, Infeld, Hoffmann) series to obtain a total post-Newtonian Lagrangian. The results agree with those found by solving Einstein's equations for the metric coefficients and by deriving the post-Newtonian equations of motion from the covariant conservation law

Lagrangian derivation of the two coupled field equations in the Janus cosmological model

Science.gov (United States)

Petit, Jean-Pierre; D'Agostini, G.

2015-05-01

After a review citing the results obtained in previous articles introducing the Janus Cosmological Model, consisting of a set of two coupled field equations, where one metrics refers to the positive masses and the other to the negative masses, which explains the observed cosmic acceleration and the nature of dark energy, we present the Lagrangian derivation of the model.

Higher-order geodesic deviations applied to the Kerr metric

CERN Document Server

Colistete, R J; Kerner, R

2002-01-01

Starting with an exact and simple geodesic, we generate approximate geodesics by summing up higher-order geodesic deviations within a general relativistic setting, without using Newtonian and post-Newtonian approximations. We apply this method to the problem of closed orbital motion of test particles in the Kerr metric spacetime. With a simple circular orbit in the equatorial plane taken as the initial geodesic, we obtain finite eccentricity orbits in the form of Taylor series with the eccentricity playing the role of a small parameter. The explicit expressions of these higher-order geodesic deviations are derived using successive systems of linear equations with constant coefficients, whose solutions are of harmonic oscillator type. This scheme gives best results when applied to orbits with low eccentricities, but with arbitrary possible values of (GM/Rc sup 2).

Pragmatic security metrics applying metametrics to information security

CERN Document Server

Brotby, W Krag

2013-01-01

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

Defining a Progress Metric for CERT RMM Improvement

Science.gov (United States)

2017-09-14

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

IT Project Management Metrics

Directory of Open Access Journals (Sweden)

2007-01-01

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

Mass Customization Measurements Metrics

DEFF Research Database (Denmark)

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

2014-01-01

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

Metrical Phonology: German Sound System.

Science.gov (United States)

Tice, Bradley S.

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

Construction of Einstein-Sasaki metrics in D≥7

International Nuclear Information System (INIS)

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

2007-01-01

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

National Metrical Types in Nineteenth Century Art Song

Directory of Open Access Journals (Sweden)

Leigh VanHandel

2010-01-01

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

A Metric on Phylogenetic Tree Shapes.

Science.gov (United States)

Colijn, C; Plazzotta, G

2018-01-01

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

Software Quality Assurance Metrics

Science.gov (United States)

McRae, Kalindra A.

2004-01-01

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

A boundary-fitted staggered difference method for incompressible flow using Riemann geometry

International Nuclear Information System (INIS)

Koshizuka, Seiichi; Kondo, Shunsuke; Oka, Yoshiaki.

1990-01-01

A boundary-fitted staggered difference method (BFSDM) is investigated for incompressible flow in nuclear plants. BFSDM employs control cells for scalars, staggered location of velocity components, and integrated formulation of div=0. Governing equations are written as coordinate-free forms using Riemann geometry. Flow velocity is represented with contravariant physical components in the present method. Connection terms emerge as source terms in the coordinate-free governing equations. These terms are studied from the viewpoints of physical meaning, numerical stability, and conservative property. Some flows on a round or slant boundary are solved using boundary-fitted curvilinear (BFC) grids and rectangular grids to compare the present method and the rectangular-type (R-type) staggered difference method (SDM). Supercomputing of the present method, including vector processing, is also discussed compared with the R-type method. (author)

Tradeoffs in the design of health plan payment systems: Fit, power and balance.

Science.gov (United States)

Geruso, Michael; McGuire, Thomas G

2016-05-01

In many markets, including the new U.S. Marketplaces, health insurance plans are paid by risk-adjusted capitation, sometimes combined with reinsurance and other payment mechanisms. This paper proposes a framework for evaluating the de facto insurer incentives embedded in these complex payment systems. We discuss fit, power and balance, each of which addresses a distinct market failure in health insurance. We implement empirical metrics of fit, power, and balance in a study of Marketplace payment systems. Using data similar to that used to develop the Marketplace risk adjustment scheme, we quantify tradeoffs among the three classes of incentives. We show that an essential tradeoff arises between the goals of limiting costs and limiting cream skimming because risk adjustment, which is aimed at discouraging cream-skimming, weakens cost control incentives in practice. A simple reinsurance system scores better on our measures of fit, power and balance than the risk adjustment scheme in use in the Marketplaces. Copyright © 2016 Elsevier B.V. All rights reserved.

A one-step method for modelling longitudinal data with differential equations.

Science.gov (United States)

Hu, Yueqin; Treinen, Raymond

2018-04-06

Differential equation models are frequently used to describe non-linear trajectories of longitudinal data. This study proposes a new approach to estimate the parameters in differential equation models. Instead of estimating derivatives from the observed data first and then fitting a differential equation to the derivatives, our new approach directly fits the analytic solution of a differential equation to the observed data, and therefore simplifies the procedure and avoids bias from derivative estimations. A simulation study indicates that the analytic solutions of differential equations (ASDE) approach obtains unbiased estimates of parameters and their standard errors. Compared with other approaches that estimate derivatives first, ASDE has smaller standard error, larger statistical power and accurate Type I error. Although ASDE obtains biased estimation when the system has sudden phase change, the bias is not serious and a solution is also provided to solve the phase problem. The ASDE method is illustrated and applied to a two-week study on consumers' shopping behaviour after a sale promotion, and to a set of public data tracking participants' grammatical facial expression in sign language. R codes for ASDE, recommendations for sample size and starting values are provided. Limitations and several possible expansions of ASDE are also discussed. © 2018 The British Psychological Society.

Kinetic modeling and fitting software for interconnected reaction schemes: VisKin.

Science.gov (United States)

Zhang, Xuan; Andrews, Jared N; Pedersen, Steen E

2007-02-15

Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.

Degraded visual environment image/video quality metrics

Science.gov (United States)

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

2014-06-01

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

Problems which are well posed in a generalized sense with applications to the Einstein equations

International Nuclear Information System (INIS)

Kreiss, H-O; Winicour, J

2006-01-01

In the harmonic description of general relativity, the principal part of the Einstein equations reduces to a constrained system of ten curved space wave equations for the components of the spacetime metric. We use the pseudo- differential theory of systems which are strongly well posed in the generalized sense to establish the well posedness of constraint-preserving boundary conditions for this system when treated in a second-order differential form. The boundary conditions are of a generalized Sommerfeld type that is benevolent for numerical calculation

Perceived versus used workplace flexibility in Singapore: predicting work-family fit.

Science.gov (United States)

Jones, Blake L; Scoville, D Phillip; Hill, E Jeffrey; Childs, Geniel; Leishman, Joan M; Nally, Kathryn S

2008-10-01

This study examined the relationship of 2 types of workplace flexibility to work-family fit and work, personal, and marriage-family outcomes using data (N = 1,601) representative of employed persons in Singapore. We hypothesized that perceived and used workplace flexibility would be positively related to the study variables. Results derived from structural equation modeling revealed that perceived flexibility predicted work-family fit; however, used flexibility did not. Work-family fit related positively to each work, personal, and marriage-family outcome; however, workplace flexibility only predicted work and personal outcomes. Findings suggest work-family fit may be an important facilitating factor in the interface between work and family life, relating directly to marital satisfaction and satisfaction in other family relationships. Implications of these findings are discussed. Copyright 2008 APA, all rights reserved.

The Jacobi metric for timelike geodesics in static spacetimes

Science.gov (United States)

Gibbons, G. W.

2016-01-01

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

Relaxed metrics and indistinguishability operators: the relationship

Energy Technology Data Exchange (ETDEWEB)

Martin, J.

2017-07-01

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

Classification in medical images using adaptive metric k-NN

Science.gov (United States)

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

2010-03-01

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

Random-growth urban model with geographical fitness

Science.gov (United States)

Kii, Masanobu; Akimoto, Keigo; Doi, Kenji

2012-12-01

This paper formulates a random-growth urban model with a notion of geographical fitness. Using techniques of complex-network theory, we study our system as a type of preferential-attachment model with fitness, and we analyze its macro behavior to clarify the properties of the city-size distributions it predicts. First, restricting the geographical fitness to take positive values and using a continuum approach, we show that the city-size distributions predicted by our model asymptotically approach Pareto distributions with coefficients greater than unity. Then, allowing the geographical fitness to take negative values, we perform local coefficient analysis to show that the predicted city-size distributions can deviate from Pareto distributions, as is often observed in actual city-size distributions. As a result, the model we propose can generate a generic class of city-size distributions, including but not limited to Pareto distributions. For applications to city-population projections, our simple model requires randomness only when new cities are created, not during their subsequent growth. This property leads to smooth trajectories of city population growth, in contrast to other models using Gibrat’s law. In addition, a discrete form of our dynamical equations can be used to estimate past city populations based on present-day data; this fact allows quantitative assessment of the performance of our model. Further study is needed to determine appropriate formulas for the geographical fitness.

Ability of LANDSAT-8 Oli Derived Texture Metrics in Estimating Aboveground Carbon Stocks of Coppice Oak Forests

Science.gov (United States)

Safari, A.; Sohrabi, H.

2016-06-01

The role of forests as a reservoir for carbon has prompted the need for timely and reliable estimation of aboveground carbon stocks. Since measurement of aboveground carbon stocks of forests is a destructive, costly and time-consuming activity, aerial and satellite remote sensing techniques have gained many attentions in this field. Despite the fact that using aerial data for predicting aboveground carbon stocks has been proved as a highly accurate method, there are challenges related to high acquisition costs, small area coverage, and limited availability of these data. These challenges are more critical for non-commercial forests located in low-income countries. Landsat program provides repetitive acquisition of high-resolution multispectral data, which are freely available. The aim of this study was to assess the potential of multispectral Landsat 8 Operational Land Imager (OLI) derived texture metrics in quantifying aboveground carbon stocks of coppice Oak forests in Zagros Mountains, Iran. We used four different window sizes (3×3, 5×5, 7×7, and 9×9), and four different offsets ([0,1], [1,1], [1,0], and [1,-1]) to derive nine texture metrics (angular second moment, contrast, correlation, dissimilar, entropy, homogeneity, inverse difference, mean, and variance) from four bands (blue, green, red, and infrared). Totally, 124 sample plots in two different forests were measured and carbon was calculated using species-specific allometric models. Stepwise regression analysis was applied to estimate biomass from derived metrics. Results showed that, in general, larger size of window for deriving texture metrics resulted models with better fitting parameters. In addition, the correlation of the spectral bands for deriving texture metrics in regression models was ranked as b4>b3>b2>b5. The best offset was [1,-1]. Amongst the different metrics, mean and entropy were entered in most of the regression models. Overall, different models based on derived texture metrics

Measurable Control System Security through Ideal Driven Technical Metrics

Energy Technology Data Exchange (ETDEWEB)

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

2008-01-01

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

High Agreement was Obtained Across Scores from Multiple Equated Scales for Social Anxiety Disorder using Item Response Theory.

Science.gov (United States)

Sunderland, Matthew; Batterham, Philip; Calear, Alison; Carragher, Natacha; Baillie, Andrew; Slade, Tim

2018-04-10

There is no standardized approach to the measurement of social anxiety. Researchers and clinicians are faced with numerous self-report scales with varying strengths, weaknesses, and psychometric properties. The lack of standardization makes it difficult to compare scores across populations that utilise different scales. Item response theory offers one solution to this problem via equating different scales using an anchor scale to set a standardized metric. This study is the first to equate several scales for social anxiety disorder. Data from two samples (n=3,175 and n=1,052), recruited from the Australian community using online advertisements, were utilised to equate a network of 11 self-report social anxiety scales via a fixed parameter item calibration method. Comparisons between actual and equated scores for most of the scales indicted a high level of agreement with mean differences <0.10 (equivalent to a mean difference of less than one point on the standardized metric). This study demonstrates that scores from multiple scales that measure social anxiety can be converted to a common scale. Re-scoring observed scores to a common scale provides opportunities to combine research from multiple studies and ultimately better assess social anxiety in treatment and research settings. Copyright © 2018. Published by Elsevier Inc.

Experiential space is hardly metric

Czech Academy of Sciences Publication Activity Database

Šikl, Radovan; Šimeček, Michal; Lukavský, Jiří

2008-01-01

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

High resolution metric imaging payload

Science.gov (United States)

Delclaud, Y.

2017-11-01

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

Metric-like formalism for matter fields coupled to 3D higher spin gravity

Science.gov (United States)

Fujisawa, Ippei; Nakayama, Ryuichi

2014-12-01

The action integral for a matter system composed of 0- and 2-forms, C and Bμν, topologically coupled to 3D spin-3 gravity is considered first in the frame-like formalism. The field C satisfies an equation of motion, \\partial _{\\mu } \\, C+A_{\\mu } \\, C-C \\, \\bar{A}_{\\mu }=0, where Aμ and \\bar{A}_{\\mu } are the Chern-Simons gauge fields. With a suitable gauge fixing of a new local symmetry and diffeomorphism, only one component of Bμν, say Bϕr, remains non-vanishing and satisfies \\partial _{\\mu } \\, B_{\\phi r}+\\bar{A}_{\\mu } \\, B_{\\phi r}-B_{\\phi r} \\, A_{\\mu }=0. These equations are the same as those for 3D (free) Vasiliev scalars, C and \\tilde{C}. The spin connection is eliminated by solving the equation of motion for the total action, and it is shown that in the resulting metric-like formalism, (BC)2 interaction terms are induced because of the torsion. The world-volume components of the matter field, C0, Cμ and C(μν), are introduced by contracting the local-frame index of C with those of the inverse vielbeins, E_a^{\\mu } and E_a^{(\\mu \

Killing vector fields in three dimensions: a method to solve massive gravity field equations

Energy Technology Data Exchange (ETDEWEB)

Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)

2010-10-21

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

Smart Grid Status and Metrics Report Appendices

Energy Technology Data Exchange (ETDEWEB)

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

2014-07-01

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

Fitness consequences of social network position in a wild population of forked fungus beetles (Bolitotherus cornutus).

Science.gov (United States)

Formica, Vincent A; Wood, C W; Larsen, W B; Butterfield, R E; Augat, M E; Hougen, H Y; Brodie, E D

2012-01-01

Social networks describe the pattern of intraspecific interactions within a population. An individual's position in a social network often is expected to influence its fitness, but only a few studies have examined this relationship in natural populations. We investigated the fitness consequences of network position in a wild beetle population. Copulation success of male beetles positively covaried with strength (a measure of network centrality) and negatively covaried with clustering coefficient (CC) (a measure of cliquishness). Further analysis using mediation path models suggested that the activity level of individuals drove the relationships between strength and fitness almost entirely. In contrast, selection on CC was not explained by individual behaviours. Although our data suggest that social network position can experience strong sexual selection, it is also clear that the relationships between fitness and some network metrics merely reflect variation in individual-level behaviours. © 2011 The Authors. Journal of Evolutionary Biology © 2011 European Society For Evolutionary Biology.

Implications of Metric Choice for Common Applications of Readmission Metrics

OpenAIRE

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

2013-01-01

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

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

International Nuclear Information System (INIS)

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

2007-01-01

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P 2 . In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic

Spectrophotometric and pH-Metric Studies of Ce(III, Dy(III, Gd(III,Yb(III and Pr(III Metal Complexes with Rifampicin

Directory of Open Access Journals (Sweden)

A. N. Sonar

2011-01-01

Full Text Available The metal-ligand and proton-ligand stability constant of Ce(III, Dy(III, Gd(III,Yb(III and Pr(III metals with substituted heterocyclic drug (Rifampicin were determined at various ionic strength by pH metric titration. NaClO4 was used to maintain ionic strength of solution. The results obtained were extrapolated to the zero ionic strength using an equation with one individual parameter. The thermodynamic stability constant of the complexes were also calculated. The formation of complexes has been studied by Job’s method. The results obtained were of stability constants by pH metric method is confirmed by Job’s method.

Prognostic Performance Metrics

Data.gov (United States)

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

Metric dimensional reduction at singularities with implications to Quantum Gravity

International Nuclear Information System (INIS)

Stoica, Ovidiu Cristinel

2014-01-01

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

Adaptive metric kernel regression

DEFF Research Database (Denmark)

Goutte, Cyril; Larsen, Jan

2000-01-01

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

Non-existence of time-periodic solutions of the Dirac equation in a Reissner-Nordström black hole background

Science.gov (United States)

Finster, Felix; Smoller, Joel; Yau, Shing-Tung

2000-04-01

It is shown analytically that the Dirac equation has no normalizable, time-periodic solutions in a Reissner-Nordström black hole background; in particular, there are no static solutions of the Dirac equation in such a background metric. The physical interpretation is that Dirac particles can either disappear into the black hole or escape to infinity, but they cannot stay on a periodic orbit around the black hole.

An alternative to the breeder's and Lande's equations.

Science.gov (United States)

Houchmandzadeh, Bahram

2014-01-10

The breeder's equation is a cornerstone of quantitative genetics, widely used in evolutionary modeling. Noting the mean phenotype in parental, selected parents, and the progeny by E(Z0), E(ZW), and E(Z1), this equation relates response to selection R = E(Z1) - E(Z0) to the selection differential S = E(ZW) - E(Z0) through a simple proportionality relation R = h(2)S, where the heritability coefficient h(2) is a simple function of genotype and environment factors variance. The validity of this relation relies strongly on the normal (Gaussian) distribution of the parent genotype, which is an unobservable quantity and cannot be ascertained. In contrast, we show here that if the fitness (or selection) function is Gaussian with mean μ, an alternative, exact linear equation of the form R' = j(2)S' can be derived, regardless of the parental genotype distribution. Here R' = E(Z1) - μ and S' = E(ZW) - μ stand for the mean phenotypic lag with respect to the mean of the fitness function in the offspring and selected populations. The proportionality coefficient j(2) is a simple function of selection function and environment factors variance, but does not contain the genotype variance. To demonstrate this, we derive the exact functional relation between the mean phenotype in the selected and the offspring population and deduce all cases that lead to a linear relation between them. These results generalize naturally to the concept of G matrix and the multivariate Lande's equation Δ(z) = GP(-1)S. The linearity coefficient of the alternative equation are not changed by Gaussian selection.

Energy-Based Metrics for Arthroscopic Skills Assessment.

Science.gov (United States)

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

2017-08-05

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

A first course in structural equation modeling

CERN Document Server

Raykov, Tenko

2012-01-01

In this book, authors Tenko Raykov and George A. Marcoulides introduce students to the basics of structural equation modeling (SEM) through a conceptual, nonmathematical approach. For ease of understanding, the few mathematical formulas presented are used in a conceptual or illustrative nature, rather than a computational one.Featuring examples from EQS, LISREL, and Mplus, A First Course in Structural Equation Modeling is an excellent beginner's guide to learning how to set up input files to fit the most commonly used types of structural equation models with these programs. The basic ideas and methods for conducting SEM are independent of any particular software.Highlights of the Second Edition include: Review of latent change (growth) analysis models at an introductory level Coverage of the popular Mplus program Updated examples of LISREL and EQS A CD that contains all of the text's LISREL, EQS, and Mplus examples.A First Course in Structural Equation Modeling is intended as an introductory book for students...

Dynamical and geometric aspects of Hamilton-Jacobi and linearized Monge-Ampère equations VIASM 2016

CERN Document Server

Tran, Hung

2017-01-01

Consisting of two parts, the first part of this volume is an essentially self-contained exposition of the geometric aspects of local and global regularity theory for the Monge–Ampère and linearized Monge–Ampère equations. As an application, we solve the second boundary value problem of the prescribed affine mean curvature equation, which can be viewed as a coupling of the latter two equations. Of interest in its own right, the linearized Monge–Ampère equation also has deep connections and applications in analysis, fluid mechanics and geometry, including the semi-geostrophic equations in atmospheric flows, the affine maximal surface equation in affine geometry and the problem of finding Kahler metrics of constant scalar curvature in complex geometry. Among other topics, the second part provides a thorough exposition of the large time behavior and discounted approximation of Hamilton–Jacobi equations, which have received much attention in the last two decades, and a new approach to the subject, the n...

What can article-level metrics do for you?

Science.gov (United States)

Fenner, Martin

2013-10-01

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

About the possibility of a generalized metric

International Nuclear Information System (INIS)

Lukacs, B.; Ladik, J.

1991-10-01

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

Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory

International Nuclear Information System (INIS)

Janda, A.

2006-01-01

We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)

Stability by fixed point theory for functional differential equations

CERN Document Server

Burton, T A

2006-01-01

This book is the first general introduction to stability of ordinary and functional differential equations by means of fixed point techniques. It contains an extensive collection of new and classical examples worked in detail and presented in an elementary manner. Most of this text relies on three principles: a complete metric space, the contraction mapping principle, and an elementary variation of parameters formula. The material is highly accessible to upper-level undergraduate students in the mathematical sciences, as well as working biologists, chemists, economists, engineers, mathematicia

Stochastic reliability analysis using Fokker Planck equations

International Nuclear Information System (INIS)

Hari Prasad, M.; Rami Reddy, G.; Srividya, A.; Verma, A.K.

2011-01-01

The Fokker-Planck equation describes the time evolution of the probability density function of the velocity of a particle, and can be generalized to other observables as well. It is also known as the Kolmogorov forward equation (diffusion). Hence, for any process, which evolves with time, the probability density function as a function of time can be represented with Fokker-Planck equation. In stochastic reliability analysis one is more interested in finding out the reliability or failure probability of the components or structures as a function of time rather than instantaneous failure probabilities. In this analysis the variables are represented with random processes instead of random variables. A random processes can be either stationary or non stationary. If the random process is stationary then the failure probability doesn't change with time where as in the case of non stationary processes the failure probability changes with time. In the present paper Fokker Planck equations have been used to find out the probability density function of the non stationary random processes. In this paper a flow chart has been provided which describes step by step process for carrying out stochastic reliability analysis using Fokker-Planck equations. As a first step one has to identify the failure function as a function of random processes. Then one has to solve the Fokker-Planck equation for each random process. In this paper the Fokker-Planck equation has been solved by using Finite difference method. As a result one gets the probability density values of the random process in the sample space as well as time space. Later at each time step appropriate probability distribution has to be identified based on the available probability density values. For checking the better fitness of the data Kolmogorov-Smirnov Goodness of fit test has been performed. In this way one can find out the distribution of the random process at each time step. Once one has the probability distribution

Adaptive Metric Kernel Regression

DEFF Research Database (Denmark)

Goutte, Cyril; Larsen, Jan

1998-01-01

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

Ideal Based Cyber Security Technical Metrics for Control Systems

Energy Technology Data Exchange (ETDEWEB)

W. F. Boyer; M. A. McQueen

2007-10-01

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

THE ROLE OF ARTICLE LEVEL METRICS IN SCIENTIFIC PUBLISHING

Directory of Open Access Journals (Sweden)

Vladimir TRAJKOVSKI

2016-04-01

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

Characterising risk - aggregated metrics: radiation and noise

International Nuclear Information System (INIS)

Passchier, W.

1998-01-01

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

Predictive Temperature Equations for Three Sites at the Grand Canyon

Science.gov (United States)

McLaughlin, Katrina Marie Neitzel

Climate data collected at a number of automated weather stations were used to create a series of predictive equations spanning from December 2009 to May 2010 in order to better predict the temperatures along hiking trails within the Grand Canyon. The central focus of this project is how atmospheric variables interact and can be combined to predict the weather in the Grand Canyon at the Indian Gardens, Phantom Ranch, and Bright Angel sites. Through the use of statistical analysis software and data regression, predictive equations were determined. The predictive equations are simple or multivariable best fits that reflect the curvilinear nature of the data. With data analysis software curves resulting from the predictive equations were plotted along with the observed data. Each equation's reduced chi2 was determined to aid the visual examination of the predictive equations' ability to reproduce the observed data. From this information an equation or pair of equations was determined to be the best of the predictive equations. Although a best predictive equation for each month and season was determined for each site, future work may refine equations to result in a more accurate predictive equation.

Supplier selection using different metric functions

Directory of Open Access Journals (Sweden)

Omosigho S.E.

2015-01-01

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

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

Science.gov (United States)

2012-03-02

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

Regional Sustainability: The San Luis Basin Metrics Project

Science.gov (United States)

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

Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology

Science.gov (United States)

Elizaga Navascués, Beatriz; Martín de Blas, Daniel; Mena Marugán, Guillermo A.

2018-02-01

Loop quantum cosmology has recently been applied in order to extend the analysis of primordial perturbations to the Planck era and discuss the possible effects of quantum geometry on the cosmic microwave background. Two approaches to loop quantum cosmology with admissible ultraviolet behavior leading to predictions that are compatible with observations are the so-called hybrid and dressed metric approaches. In spite of their similarities and relations, we show in this work that the effective equations that they provide for the evolution of the tensor and scalar perturbations are somewhat different. When backreaction is neglected, the discrepancy appears only in the time-dependent mass term of the corresponding field equations. We explain the origin of this difference, arising from the distinct quantization procedures. Besides, given the privileged role that the big bounce plays in loop quantum cosmology, e.g. as a natural instant of time to set initial conditions for the perturbations, we also analyze the positivity of the time-dependent mass when this bounce occurs. We prove that the mass of the tensor perturbations is positive in the hybrid approach when the kinetic contribution to the energy density of the inflaton dominates over its potential, as well as for a considerably large sector of backgrounds around that situation, while this mass is always nonpositive in the dressed metric approach. Similar results are demonstrated for the scalar perturbations in a sector of background solutions that includes the kinetically dominated ones; namely, the mass then is positive for the hybrid approach, whereas it typically becomes negative in the dressed metric case. More precisely, this last statement is strictly valid when the potential is quadratic for values of the inflaton mass that are phenomenologically favored.

Feasibility study on the least square method for fitting non-Gaussian noise data

Science.gov (United States)

Xu, Wei; Chen, Wen; Liang, Yingjie

2018-02-01

This study is to investigate the feasibility of least square method in fitting non-Gaussian noise data. We add different levels of the two typical non-Gaussian noises, Lévy and stretched Gaussian noises, to exact value of the selected functions including linear equations, polynomial and exponential equations, and the maximum absolute and the mean square errors are calculated for the different cases. Lévy and stretched Gaussian distributions have many applications in fractional and fractal calculus. It is observed that the non-Gaussian noises are less accurately fitted than the Gaussian noise, but the stretched Gaussian cases appear to perform better than the Lévy noise cases. It is stressed that the least-squares method is inapplicable to the non-Gaussian noise cases when the noise level is larger than 5%.

An Equation of State for the Thermodynamic Properties of Cyclohexane

Energy Technology Data Exchange (ETDEWEB)

Zhou, Yong, E-mail: Yong.Zhou2@honeywell.com; Liu, Jun [Honeywell Integrated Technology China Co. Ltd., 430 Li Bing Road, Zhangjiang Hi-Tech Park, Shanghai 201203 (China); Penoncello, Steven G. [Center for Applied Thermodynamic Studies, College of Engineering, University of Idaho, Moscow, Idaho 83844 (United States); Lemmon, Eric W. [Applied Chemicals and Materials Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 (United States)

2014-12-15

An equation of state for cyclohexane has been developed using the Helmholtz energy as the fundamental property with independent variables of density and temperature. Multi-property fitting technology was used to fit the equation of state to data for pρT, heat capacities, sound speeds, virial coefficients, vapor pressures, and saturated densities. The equation of state was developed to conform to the Maxwell criteria for two-phase vapor-liquid equilibrium states, and is valid from the triple-point temperature to 700 K, with pressures up to 250 MPa and densities up to 10.3 mol dm{sup −3}. In general, the uncertainties (k = 2, indicating a level of confidence of 95%) in density for the equation of state are 0.1% (liquid and vapor) up to 500 K, and 0.2% above 500 K, with higher uncertainties within the critical region. Between 283 and 473 K with pressures lower than 30 MPa, the uncertainty is as low as 0.03% in density in the liquid phase. The uncertainties in the speed of sound are 0.2% between 283 and 323 K in the liquid, and 1% elsewhere. Other uncertainties are 0.05% in vapor pressure and 2% in heat capacities. The behavior of the equation of state is reasonable within the region of validity and at higher and lower temperatures and pressures. A detailed analysis has been performed in this article.

Probabilistic metric spaces

CERN Document Server

Schweizer, B

2005-01-01

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

Metric solution of a spinning mass

International Nuclear Information System (INIS)

Sato, H.

1982-01-01

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

Software architecture analysis tool : software architecture metrics collection

NARCIS (Netherlands)

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

2002-01-01

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

Generalized tolerance sensitivity and DEA metric sensitivity

OpenAIRE

Neralić, Luka; E. Wendell, Richard

2015-01-01

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

On Nakhleh's metric for reduced phylogenetic networks

OpenAIRE

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

2009-01-01

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

Generalized tolerance sensitivity and DEA metric sensitivity

Directory of Open Access Journals (Sweden)

Luka Neralić

2015-03-01

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

Social Media Metrics Importance and Usage Frequency in Latvia

Directory of Open Access Journals (Sweden)

Ronalds Skulme

2017-12-01

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

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

International Nuclear Information System (INIS)

Weiping Yin.

1990-03-01

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

Equations of motion according to the asymptotic post-Newtonian scheme for general relativity in the harmonic gauge

Science.gov (United States)

Arminjon, Mayeul

2005-10-01

The asymptotic scheme of post-Newtonian approximation defined for general relativity in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial metric, defining a family of weakly self-gravitating systems. We show that Weinberg’s (1972) expansion of the metric and his general expansion of the energy-momentum tensor T, as well as his expanded equations for the gravitational field and his general form of the expanded dynamical equations, apply naturally to this family. Then, following the asymptotic scheme, we derive the explicit form of the expansion of T for a perfect fluid, and the expanded fluid-dynamical equations. (These differ from those written by Weinberg.) By integrating these equations in the domain occupied by a body, we obtain a general form of the translational equations of motion for a 1PN perfect-fluid system in general relativity. To put them into a tractable form, we use an asymptotic framework for the separation parameter η, by defining a family of well-separated 1PN systems. We calculate all terms in the equations of motion up to the order η3 included. To calculate the 1PN correction part, we assume that the Newtonian motion of each body is a rigid one, and that the family is quasispherical, in the sense that in all bodies the inertia tensor comes close to being spherical as η→0. Apart from corrections that cancel for exact spherical symmetry, there is in the final equations of motion one additional term, as compared with the Lorentz-Droste (Einstein-Infeld-Hoffmann) acceleration. This term depends on the spin of the body and on its internal structure.

A new fitted operator finite difference method to solve systems of ...

African Journals Online (AJOL)

In recent years, fitted operator finite difference methods (FOFDMs) have been developed for numerous types of singularly perturbed ordinary differential equations. The construction of most of these methods differed though the final outcome remained similar. The most crucial aspect was how the difference operator was ...

Using Activity Metrics for DEVS Simulation Profiling

Directory of Open Access Journals (Sweden)

Muzy A.

2014-01-01

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

Tracker Performance Metric

National Research Council Canada - National Science Library

Olson, Teresa; Lee, Harry; Sanders, Johnnie

2002-01-01

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

Dirac equation in Kerr space-time

Energy Technology Data Exchange (ETDEWEB)

Iyer, B R; Kumar, Arvind [Bombay Univ. (India). Dept. of Physics

1976-06-01

The weak-field low-velocity approximation of Dirac equation in Kerr space-time is investigated. The interaction terms admit of an interpretation in terms of a 'dipole-dipole' interaction in addition to coupling of spin with the angular momentum of the rotating source. The gravitational gyro-factor for spin is identified. The charged case (Kerr-Newman) is studied using minimal prescription for electromagnetic coupling in the locally intertial frame and to the leading order the standard electromagnetic gyro-factor is retrieved. A first order perturbation calculation of the shift of the Schwarzchild energy level yields the main interesting result of this work: the anomalous Zeeman splitting of the energy level of a Dirac particle in Kerr metric.

Metrication: An economic wake-up call for US industry

Science.gov (United States)

Carver, G. P.

1993-03-01

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

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

OpenAIRE

Blair, D. E.

1990-01-01

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

Exergy metrication of radiant panel heating and cooling with heat pumps

International Nuclear Information System (INIS)

Kilkis, Birol

2012-01-01

Highlights: ► Rational Exergy Management Model analytically relates heat pumps and radiant panels. ► Heat pumps driven by wind energy perform better with radiantpanels. ► Better CO 2 mitigation is possible with wind turbine, heat pump, radiant panel combination. ► Energy savings and thermo-mechanical performance are directly linked to CO 2 emissions. - Abstract: Radiant panels are known to be energy efficient sensible heating and cooling systems and a suitable fit for low-exergy buildings. This paper points out the little known fact that this may not necessarily be true unless their low-exergy demand is matched with low-exergy waste and alternative energy resources. In order to further investigate and metricate this condition and shed more light on this issue for different types of energy resources and energy conversion systems coupled to radiant panels, a new engineering metric was developed. Using this metric, which is based on the Rational Exergy Management Model, true potential and benefits of radiant panels coupled to ground-source heat pumps were analyzed. Results provide a new perspective in identifying the actual benefits of heat pump technology in curbing CO 2 emissions and also refer to IEA Annex 49 findings for low-exergy buildings. Case studies regarding different scenarios are compared with a base case, which comprises a radiant panel system connected to a natural gas-fired condensing boiler in heating and a grid power-driven chiller in cooling. Results show that there is a substantial CO 2 emission reduction potential if radiant panels are optimally operated with ground-source heat pumps driven by renewable energy sources, or optimally matched with combined heat and power systems, preferably running on alternative fuels.

Hierarchical Bayesian modelling of mobility metrics for hazard model input calibration

Science.gov (United States)

Calder, Eliza; Ogburn, Sarah; Spiller, Elaine; Rutarindwa, Regis; Berger, Jim

2015-04-01

In this work we present a method to constrain flow mobility input parameters for pyroclastic flow models using hierarchical Bayes modeling of standard mobility metrics such as H/L and flow volume etc. The advantage of hierarchical modeling is that it can leverage the information in global dataset for a particular mobility metric in order to reduce the uncertainty in modeling of an individual volcano, especially important where individual volcanoes have only sparse datasets. We use compiled pyroclastic flow runout data from Colima, Merapi, Soufriere Hills, Unzen and Semeru volcanoes, presented in an open-source database FlowDat (https://vhub.org/groups/massflowdatabase). While the exact relationship between flow volume and friction varies somewhat between volcanoes, dome collapse flows originating from the same volcano exhibit similar mobility relationships. Instead of fitting separate regression models for each volcano dataset, we use a variation of the hierarchical linear model (Kass and Steffey, 1989). The model presents a hierarchical structure with two levels; all dome collapse flows and dome collapse flows at specific volcanoes. The hierarchical model allows us to assume that the flows at specific volcanoes share a common distribution of regression slopes, then solves for that distribution. We present comparisons of the 95% confidence intervals on the individual regression lines for the data set from each volcano as well as those obtained from the hierarchical model. The results clearly demonstrate the advantage of considering global datasets using this technique. The technique developed is demonstrated here for mobility metrics, but can be applied to many other global datasets of volcanic parameters. In particular, such methods can provide a means to better contain parameters for volcanoes for which we only have sparse data, a ubiquitous problem in volcanology.

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

International Nuclear Information System (INIS)

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

2003-01-01

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

Graev metrics on free products and HNN extensions

DEFF Research Database (Denmark)

Slutsky, Konstantin

2014-01-01

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

Automatic fitting of spiking neuron models to electrophysiological recordings

Directory of Open Access Journals (Sweden)

Cyrille Rossant

2010-03-01

Full Text Available Spiking models can accurately predict the spike trains produced by cortical neurons in response to somatically injected currents. Since the specific characteristics of the model depend on the neuron, a computational method is required to fit models to electrophysiological recordings. The fitting procedure can be very time consuming both in terms of computer simulations and in terms of code writing. We present algorithms to fit spiking models to electrophysiological data (time-varying input and spike trains that can run in parallel on graphics processing units (GPUs. The model fitting library is interfaced with Brian, a neural network simulator in Python. If a GPU is present it uses just-in-time compilation to translate model equations into optimized code. Arbitrary models can then be defined at script level and run on the graphics card. This tool can be used to obtain empirically validated spiking models of neurons in various systems. We demonstrate its use on public data from the INCF Quantitative Single-Neuron Modeling 2009 competition by comparing the performance of a number of neuron spiking models.

Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization

International Nuclear Information System (INIS)

Ohta, Nobuyoshi; Percacci, Roberto; Vacca, Gian Paolo

2016-01-01

We employ the exponential parametrization of the metric and a ''physical'' gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function f. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure. (orig.)

Interference-Fit Life Factors for Ball Bearings

Science.gov (United States)

Oswald, Fred B.; Zaretsky, Erwin V.; Poplawski, Joseph V.

2010-01-01

The effect of hoop stresses on the rolling-element fatigue life of angular-contact and deep-groove ball bearings was determined for common inner-ring interference fits at the ABEC-5 tolerance level. The analysis was applied to over 1150 bearing configurations and load cases. Hoop stresses were superimposed on the Hertzian principal stresses created by the applied bearing load to calculate the inner-race maximum shearing stress. The resulting fatigue life of the bearing was recalculated through a series of equations. The reduction in the fatigue life is presented as life factors that are applied to the unfactored bearing life. The life factors found in this study ranged from 1.00 (no life reduction)--where there was no net interface pressure--to a worst case of 0.38 (a 62-percent life reduction). For a given interference fit, the reduction in life is different for angular-contact and deep-groove ball bearings. Interference fits also affect the maximum Hertz stress-life relation. Experimental data of Czyzewski, showing the effect of interference fit on rolling-element fatigue life, were reanalyzed to determine the shear stress-life exponent. The Czyzewski data shear stress-life exponent c equals 8.77, compared with the assumed value of 9. Results are presented as tables and charts of life factors for angular-contact and deep-groove ball bearings with light, normal, and heavy loads and interference fits ranging from extremely light to extremely heavy.

Validation of Metrics for Collaborative Systems

OpenAIRE

Ion IVAN; Cristian CIUREA

2008-01-01

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

g-Weak Contraction in Ordered Cone Rectangular Metric Spaces

Directory of Open Access Journals (Sweden)

S. K. Malhotra

2013-01-01

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

Exponential Decay Metrics of Topical Tetracaine Hydrochloride Administration Describe Corneal Anesthesia Properties Mechanistically.

Science.gov (United States)

Ethington, Jason; Goldmeier, David; Gaynes, Bruce I

2017-03-01

To identify pharmacodynamic (PD) and pharmacokinetic (PK) metrics that aid in mechanistic understanding of dosage considerations for prolonged corneal anesthesia. A rabbit model using 0.5% tetracaine hydrochloride was used to induce corneal anesthesia in conjunction with Cochet-Bonnet anesthesiometry. Metrics were derived describing PD-PK parameters of the time-dependent domain of recovery in corneal sensitivity. Curve fitting used a 1-phase exponential dissociation paradigm assuming a 1-compartment PK model. Derivation of metrics including half-life and mean ligand residence time, tau (τ), was predicted by nonlinear regression. Bioavailability was determined by area under the curve of the dose-response relationship with varying drop volumes. Maximal corneal anesthesia maintained a plateau with a recovery inflection at the approximate time of predicted corneal drug half-life. PDs of recovery of corneal anesthesia were consistent with a first-order drug elimination rate. The mean ligand residence time (tau, τ) was 41.7 minutes, and half-life was 28.89 minutes. The mean estimated corneal elimination rate constant (ke) was 0.02402 minute. Duration of corneal anesthesia ranged from 55 to 58 minutes. There was no difference in time domain PD area under the curve between drop volumes. Use of a small drop volume of a topical anesthetic (as low as 11 μL) is bioequivalent to conventional drop size and seems to optimize dosing regiments with a little effect on ke. Prolongation of corneal anesthesia may therefore be best achieved with administration of small drop volumes at time intervals corresponding to the half-life of drug decay from the corneal compartment.

High-order shock-fitted detonation propagation in high explosives

Science.gov (United States)

Romick, Christopher M.; Aslam, Tariq D.

2017-03-01

A highly accurate numerical shock and material interface fitting scheme composed of fifth-order spatial and third- or fifth-order temporal discretizations is applied to the two-dimensional reactive Euler equations in both slab and axisymmetric geometries. High rates of convergence are not typically possible with shock-capturing methods as the Taylor series analysis breaks down in the vicinity of discontinuities. Furthermore, for typical high explosive (HE) simulations, the effects of material interfaces at the charge boundary can also cause significant computational errors. Fitting a computational boundary to both the shock front and material interface (i.e. streamline) alleviates the computational errors associated with captured shocks and thus opens up the possibility of high rates of convergence for multi-dimensional shock and detonation flows. Several verification tests, including a Sedov blast wave, a Zel'dovich-von Neumann-Döring (ZND) detonation wave, and Taylor-Maccoll supersonic flow over a cone, are utilized to demonstrate high rates of convergence to nontrivial shock and reaction flows. Comparisons to previously published shock-capturing multi-dimensional detonations in a polytropic fluid with a constant adiabatic exponent (PF-CAE) are made, demonstrating significantly lower computational error for the present shock and material interface fitting method. For an error on the order of 10 m /s, which is similar to that observed in experiments, shock-fitting offers a computational savings on the order of 1000. In addition, the behavior of the detonation phase speed is examined for several slab widths to evaluate the detonation performance of PBX 9501 while utilizing the Wescott-Stewart-Davis (WSD) model, which is commonly used in HE modeling. It is found that the thickness effect curve resulting from this equation of state and reaction model using published values is dramatically more steep than observed in recent experiments. Utilizing the present fitting

Depressive symptoms, perceived stress, self-efficacy, and outcome expectations: Predict fitness among adolescents with obesity.

Science.gov (United States)

Tulloch, Heather; Heenan, Adam; Sweet, Shane; Goldfield, Gary S; Kenny, Glen P; Alberga, Angela S; Sigal, Ronald J

2017-10-01

The objective of the present study was to test if outcome expectancy mediated the relationship between fitness and self-efficacy, perceived stress, and depressive symptoms.Adolescents with obesity ( n = 228) completed measures of perceived stress and depressive symptoms at baseline, self-efficacy and outcome expectancy at baseline and 3 months, and fitness at baseline and 6 months. Structural equation modeling was used to analyze the data. Results showed that self-efficacy was positively associated with fitness via outcome expectancies. For females, fewer depressive symptoms were linked to fitness via self-efficacy and outcome expectancies. Exercise interventions that enhance exercise self-efficacy, outcome expectancy, and reduce depressive symptoms may increase fitness.

Stability study of pre-stack seismic inversion based on the full Zoeppritz equation

Science.gov (United States)

Liang, Lifeng; Zhang, Hongbing; Guo, Qiang; Saeed, Wasif; Shang, Zuoping; Huang, Guojiao

2017-10-01

Pre-stack seismic inversion is highly important and complicated. Its result is non-unique, and the process is unstable because pre-stack seismic inversion is an ill-posed problem that simultaneously obtains the results of multiple parameters. Combining the full Zoeppritz equation and additional assumptions with edge-preserving regularization (EPR) can help mitigate the problem. To achieve this combination, we developed an inversion method by constructing a new objective function, which includes the EPR and the Markov random field. The method directly gains reflectivity R PP by the full Zoeppritz equation instead of its approximations and effectively controls the stability of simultaneous inversion by two additional assumptions: the sectional constant V S/V P and the generalized Gardner equation. Thus, the simultaneous inversion of multiple parameters is directed toward to V P, ΔL S (the fitting deviation of V S) and density, and the generalized Gardner equation is regarded as a constraint from which the fitting relationship is derived. We applied the fast simulated annealing algorithm to solve the nonlinear optimization problem. The test results on 2D synthetic data indicated that the stability of simultaneous inversion for V P, ΔL S and density is better than these for V P, V S, and density. The inverted result of density gradually worsens as the deviation ΔL D (the fitting deviation of the density) increases. Moreover, the inverted results were acceptable when using the fitting relationships with error, although they showed varying degrees of influence. We constructed time-varying and space-varying fitting relationships using the logging data in pre-stack inversion of the field seismic data. This improved the inverted results of the simultaneous inversion for complex geological models. Finally, the inverted results of the field data distinctly revealed more detailed information about the layers and matched well with the logging data along the wells over most

The equation of state of liquid Flibe

International Nuclear Information System (INIS)

Chen, Xiang M.; Schrock, V.E.; Peterson, P.F.

1991-01-01

Flibe (Li 2 BeF 4 ) is a candidate material for the liquid blanket in the HYLIFE-2 fusion reactor. The thermodynamic properties of the material are important for the study of thermohydraulic behavior of the concept design, including the compressible analysis of the blanket isochoric heating problem and resulting jet breakup. The equation of state provides the relationship between all the thermodynamic properties. Previously, a soft sphere model of liquid equation of state was used for describing a number of liquid metals. In this paper we have fitted the available experimental data for liquid Flibe with a modified soft sphere model. 5 refs

Mathematical analysis of partial differential equations modeling electrostatic MEMS

CERN Document Server

Esposito, Pierpaolo; Guo, Yujin

2010-01-01

Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing "electrostatically actuated" MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems-where the stationary MEMS models fit-are a well-developed

Probabilistic Forecasts of Solar Irradiance by Stochastic Differential Equations

DEFF Research Database (Denmark)

Iversen, Jan Emil Banning; Morales González, Juan Miguel; Møller, Jan Kloppenborg

2014-01-01

approach allows for characterizing both the interdependence structure of prediction errors of short-term solar irradiance and their predictive distribution. Three different stochastic differential equation models are first fitted to a training data set and subsequently evaluated on a one-year test set...... included in probabilistic forecasts may be paramount for decision makers to efficiently make use of this uncertain and variable generation. In this paper, a stochastic differential equation framework for modeling the uncertainty associated with the solar irradiance point forecast is proposed. This modeling...

The dynamics of metric-affine gravity

International Nuclear Information System (INIS)

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

2011-01-01

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

Solution of Wheeler-De Witt Equation, Potential Well and Tunnel Effect

International Nuclear Information System (INIS)

Huang Yongchang; Weng Gang

2005-01-01

This paper uses the relation of the cosmic scale factor and scalar field to solve Wheeler-De Witt equation, gives the tunnel effect of the cosmic scale factor a and quantum potential well of scalar field, and makes it fit with the physics of cosmic quantum birth. By solving Wheeler-De Witt equation we achieve a general probability distribution of the cosmic birth, and give the analysis of cosmic quantum birth.

The definitive guide to IT service metrics

CERN Document Server

McWhirter, Kurt

2012-01-01

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

Fitness landscape of the human immunodeficiency virus envelope protein that is targeted by antibodies

Science.gov (United States)

Louie, Raymond H. Y.; Kaczorowski, Kevin J.; Chakraborty, Arup K.; McKay, Matthew R.

2018-01-01

HIV is a highly mutable virus, and over 30 years after its discovery, a vaccine or cure is still not available. The isolation of broadly neutralizing antibodies (bnAbs) from HIV-infected patients has led to renewed hope for a prophylactic vaccine capable of combating the scourge of HIV. A major challenge is the design of immunogens and vaccination protocols that can elicit bnAbs that target regions of the virus’s spike proteins where the likelihood of mutational escape is low due to the high fitness cost of mutations. Related challenges include the choice of combinations of bnAbs for therapy. An accurate representation of viral fitness as a function of its protein sequences (a fitness landscape), with explicit accounting of the effects of coupling between mutations, could help address these challenges. We describe a computational approach that has allowed us to infer a fitness landscape for gp160, the HIV polyprotein that comprises the viral spike that is targeted by antibodies. We validate the inferred landscape through comparisons with experimental fitness measurements, and various other metrics. We show that an effective antibody that prevents immune escape must selectively bind to high escape cost residues that are surrounded by those where mutations incur a low fitness cost, motivating future applications of our landscape for immunogen design. PMID:29311326

MPFA algorithm for solving stokes-brinkman equations on quadrilateral grids

KAUST Repository

Iliev, Oleg; Kirsch, Ralf; Lakdawala, Zahra; Printsypar, Galina

2014-01-01

This work is concerned with the development of a robust and accurate numerical method for solving the Stokes-Brinkman system of equations, which describes a free fluid flow coupled with a flow in porous media. Quadrilateral boundary fitted grid

NASA education briefs for the classroom. Metrics in space

Science.gov (United States)

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

Reduction of the Poincare gauge field equations by means of a duality rotation

International Nuclear Information System (INIS)

Mielke, E.W.

1981-10-01

A rather general procedure is developed in order to reduce the two field equations of the Poincare gauge theory of gravity by a modified ansatz for the curvature tensor involving double duality. In the case of quasi-linear Lagrangians of the Yang-Mills type it is shown that non-trivial torsion solutions with duality properties necessarily ''live'' on an Einstein space as metrical background. (author)

Kernel-density estimation and approximate Bayesian computation for flexible epidemiological model fitting in Python.

Science.gov (United States)

Irvine, Michael A; Hollingsworth, T Déirdre

2018-05-26

Fitting complex models to epidemiological data is a challenging problem: methodologies can be inaccessible to all but specialists, there may be challenges in adequately describing uncertainty in model fitting, the complex models may take a long time to run, and it can be difficult to fully capture the heterogeneity in the data. We develop an adaptive approximate Bayesian computation scheme to fit a variety of epidemiologically relevant data with minimal hyper-parameter tuning by using an adaptive tolerance scheme. We implement a novel kernel density estimation scheme to capture both dispersed and multi-dimensional data, and directly compare this technique to standard Bayesian approaches. We then apply the procedure to a complex individual-based simulation of lymphatic filariasis, a human parasitic disease. The procedure and examples are released alongside this article as an open access library, with examples to aid researchers to rapidly fit models to data. This demonstrates that an adaptive ABC scheme with a general summary and distance metric is capable of performing model fitting for a variety of epidemiological data. It also does not require significant theoretical background to use and can be made accessible to the diverse epidemiological research community. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Enhancing Authentication Models Characteristic Metrics via ...

African Journals Online (AJOL)

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

Validation of Metrics for Collaborative Systems

Directory of Open Access Journals (Sweden)

Ion IVAN

2008-01-01

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

Equations of State and Phase Diagrams of Ammonia

Science.gov (United States)

Glasser, Leslie

2009-01-01

We present equations of state relating the phases and a three-dimensional phase diagram for ammonia with its solid, liquid, and vapor phases, based on fitted authentic experimental data and including recent information on the high-pressure solid phases. This presentation follows similar articles on carbon dioxide and water published in this…

Quantification of Dynamic Model Validation Metrics Using Uncertainty Propagation from Requirements

Science.gov (United States)