Classroom reconstruction of the Schwarzschild metric
Kassner, Klaus
2015-01-01
A promising way to introduce general relativity in the classroom is to study the physical predictions that follow from 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 weak-field limit of the Schwarzschild metric with a minimum of relatively simple physical assumptions. Since this does not appear sufficient to arrive at a form of the metric useful for more than the most basic predictions (gravitational redshift), the determination of a single additional parameter from experiment is admitted. An attractive experimental candidate is the measurement of the perihelion precession of Mercury, because the result was already known before the completion of general relativity. It is sh...
The Planck Vacuum and the Schwarzschild Metrics
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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.
Eigentensors of the Lichnerowicz operator in Euclidean Schwarzschild metrics
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Martinez-Morales, J.L. [Instituto de Matematicas, Universidad Nacional Autonoma de Mexico, A. P. 273, Admon. de correos 3, C. P. 62251 Cuernavaca, Morelos (Mexico)
2006-09-01
Properties of the eigentensors of the Lichnerowicz Laplacian for the Euclidean Schwarzschild metric are discussed together with possible applications to the linear stability of higher-dimensional instantons. The main statement of the article is that any eigentensor of the Lichnerowicz operator in a Euclidean (possibly higher-dimensional) Schwarzschild metric is essentially singular at infinity. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Dust ball physics and the Schwarzschild metric
Kassner, Klaus
2016-01-01
A physics-first derivation of the Schwarzschild metric is given. Gravitation is described in terms of the effects of tidal forces (or of spacetime curvature) on the volume of a small ball of test particles (a dust ball), freely falling after all particles were at rest with respect to each other initially. The possibility to express Einstein's equation this way and some of its ramifications have been enjoyably discussed by Baez and Bunn [Am. J. Phys. 73, 644 (2005)]. Since the formulation avoids the use of tensors, neither advanced tensor calculus nor sophisticated differential geometry are needed in the calculation. The derivation is not lengthy and it has visual appeal, so it may be useful in teaching.
How to obtain the Schwarzschild metric before Einstein's field equations
Kassner, Klaus
2016-01-01
As is well-known, there is no way to derive the Schwarzschild metric on the basis of pre-general-relativistic physics alone, which means using only special relativity, the Einstein equivalence principle and the Newtonian limit. It is however possible to encode the additional physics needed in two reasonably plausible postulates allowing to deduce the exact Schwarzschild metric without invoking Einstein's field equations. Since these requirements are designed to apply to the spherically symmmetric case, their union is much less powerful than the postulates from which Einstein obtained his field equations. It is shown that the field equations imply the postulates given here but that the converse is not quite true. The approach provides a fairly fast calculation method for the Schwarzschild metric in arbitrary coordinates exhibiting stationarity.
Drude-Schwarzschild Metric and the Electrical Conductivity of Metals
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Silva P. R.
2014-07-01
Full Text Available Starting from a string with a length equal to the electron mean free path and having a unit cell equal to the Compton length of the electron, we construct a Schwarzschild-like metric. We found that this metric has a surface horizon with radius equal to the electron mean free path and its Bekenstein-like entropy is proportional to the number of squared unit cells contained in this spherical surface. The Hawking temperature is inversely proportional to the perimeter of the maximum circle of this sphere. Also, interesting analogies on some features of the particle physics are examined.
Quantum-mechanical corrections to the Schwarzschild black-hole metric
Bargueño, P.; Bravo Medina, S.; Nowakowski, M.; Batic, D.
2017-03-01
Motivated by quantum-mechanical corrections to the Newtonian potential, which can be translated into a {\\hbar} -correction to the g 00 component of the Schwarzschild metric, we construct a quantum-mechanically corrected metric assuming -g00=grr . We show how the Bekenstein black-hole entropy S receives its logarithmic contribution provided the quantum-mechanical corrections to the metric are negative. In this case the standard horizon at the Schwarzschild radius r S increases by small terms proportional to {\\hbar} and a remnant of the order of Planck mass emerges.
On the Ramifications of the Schwarzschild Space-Time Metric
Directory of Open Access Journals (Sweden)
Crothers S. J.
2005-04-01
Full Text Available In a previous paper I derived the general solution for the simple point-mass in a true Schwarzschild space. I extend that solution to the point-charge, the rotating point-mass, and the rotating point-charge, culminating in a single expression for the general solution for the point-mass in all its configurations when Λ = 0. The general exact solution is proved regular everywhere except at the arbitrary location of the source of the gravitational field. In no case does the black hole manifest. The conventional solutions giving rise to various black holes are shown to be inconsistent with General Relativity.
On the twin paradox in static spacetimes: I. Schwarzschild metric
Sokołowski, Leszek M.
2012-05-01
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.
On the twin paradox in static spacetimes: I. Schwarzschild metric
Sokolowski, Leszek M
2012-01-01
Motivated by a conjecture put forward by Abramowicz and Bajtlik we reconsider the twin paradox in static spacetimes. According to a well known theorem in Lorentzian geometry the longest timelike worldline between two given points is the unique geodesic line without points conjugate to the initial point on the segment joining the two points. We calculate the proper times for static twins, for twins moving on a circular orbit (if it is a geodesic) around a centre of symmetry and for twins travelling on outgoing and ingoing radial timelike geodesics. We show that the twins on the radial geodesic worldlines are always the oldest ones and we explicitly find the conjugate points (if they exist) outside the relevant segments. As it is of its own mathematical interest, we find general Jacobi vector fields on the geodesic lines under consideration. In the first part of the work we investigate Schwarzschild geometry.
Kokkotas, K. D.; Konoplya, R. A.; Zhidenko, A.
2017-09-01
Higher derivative extensions of Einstein gravity are important within the string theory approach to gravity and as alternative and effective theories of gravity. H. Lü, A. Perkins, C. Pope, and K. Stelle [Phys. Rev. Lett. 114, 171601 (2015), 10.1103/PhysRevLett.114.171601] found a numerical solution describing a spherically symmetric non-Schwarzschild asymptotically flat black hole in Einstein gravity with added higher derivative terms. Using the general and quickly convergent parametrization in terms of the continued fractions, we represent this numerical solution in the analytical form, which is accurate not only near the event horizon or far from the black hole, but in the whole space. Thereby, the obtained analytical form of the metric allows one to study easily all the further properties of the black hole, such as thermodynamics, Hawking radiation, particle motion, accretion, perturbations, stability, quasinormal spectrum, etc. Thus, the found analytical approximate representation can serve in the same way as an exact solution.
A comparative study of background flow geometries in Schwarzschild metric with shock
Tarafdar, Pratik
2016-01-01
We study the effects of discontinuity in general relativistic axially symmetric background fluid flow in the Schwarzschild metric. The discontinuities, or 'shocks', are incorporated using general relativistic Rankine-Hugoniot conditions. A general shock-invariant quantity is thus derived analytically for three distinct geometric configurations of the background fluid flow, viz., constant height discs, quasi-spherical discs and discs in hydrostatic equilibrium in the vertical direction. As already pointed out in our previous works, even identical initial conditions may lead to completely different phase-space behaviour of the stationary solutions for separate flow geometries. Hence it is then useful to investigate and compare the influence of geometric configuration of the flow described by various thermodynamic equations of state, on different important properties and manifestations of such physical discontinuities.
Merlin, Cesar
2014-01-01
We present a first numerical implementation of a new scheme by Pound et al. that enables the calculation of the gravitational self-force in Kerr spacetime from a reconstructed metric-perturbation in a radiation gauge. The numerical task of the metric reconstruction essentially reduces to solving the fully separable Teukolsky equation, rather than having to tackle the linearized Einstein's equations themselves. The method offers significant computational saving compared to existing methods in the Lorenz gauge, and we expect it to become a main workhorse for precision self-force calculations in the future. Here we implement the method for circular orbits on a Schwarzschild background, in order to illustrate its efficacy and accuracy. We use two independent methods for solving the Teukolsky equation, one based on a direct numerical integration, and the other on the analytical approach of Mano, Suzuki, and Takasugi. The relative accuracy of the output self-force is at least $10^{-7}$ using the first method, and a...
Tarafdar, Pratik; Majumdar, Archan S
2013-01-01
In black hole evaporation process, the mass of the hole anti-correlates with the Hawking temperature enabling us to infer that the smaller mass holes will have higher surface gravity. For analogue Hawking effects, however, the acoustic surface gravity is determined by the local value of the dynamical velocity of the stationary background fluid flow and the speed of propagation of the characteristic perturbation embedded in the background fluid, as well as their space derivatives evaluated along the direction normal to the acoustic horizon, respectively. The mass of the analogue system - whether classical or quantum - does not directly contribute to extremise the value of the associated acoustic surface gravity. For general relativistic axisymmetric background fluid flow in the Schwarzschild metric, we show that the initial boundary conditions describing such axisymmetrically accreting matter flow influence the maximization scheme of the acoustic surface gravity as well as the corresponding characteristic temp...
Vossos, Spyridon; Vossos, Elias
2017-12-01
Schwarzschild Metric is the first and the most important solution of Einstein vacuum field equations. This is associated with Lorentz metric of flat spacetime and produces the relativistic potential (Φ) and the field strength (g) outside a spherically symmetric mass or a non-rotating black hole. It has many applications such as gravitational red shift, the precession of Mercury’s orbit, Shapiro time delay etc. However, it is inefficient to explain the rotation curves in large galaxies and clusters of them, causing the necessity for dark matter. On the other hand, Modified Newtonian Dynamics (MOND) has already explained these rotation curves in many cases, using suitable interpolating function (μ) in Milgrom’s Law. In this presentation, we initially produce a Generalized Schwarzschild potential and the corresponding Metric of spacetime, in order to be in accordance with any isotropic metric of flat spacetime (including Galilean Metric of spacetime which is associated with Galilean Transformation of spacetime). From this Generalized Schwarzschild potential (Φ), we calculate the corresponding field strength (g), which is associated with the interpolating function (μ). In this way, a new relativistic potential is obtained (let us call 2nd Generalized Schwarzschild potential) which describes the gravitational interaction at any distance and for any metric of flat spacetime. Thus, not only the necessity for Dark Matter is eliminated, but also MOND becomes a pure Relativistic Theory of Gravitational Interaction. Then, we pass to the case of flat spacetime with Lorentz metric (Minkowski space), because the experimental data have been extracted using the Relativistic Doppler Shift and the gravitational red shift of Classic Relativity (CR). Thus, we Explain the Rotation Curves in Galaxies (e.g. NGC 3198) and Clusters of them as well as the Solar system, eliminating Dark Matter. This relativistic potential and the corresponding metric of spacetime have been obtained
Quantum corrected Schwarzschild thin-shell wormhole
Jusufi, Kimet
2016-01-01
Recently, Ali and Khalil (Nucl Phys B, 909, 173–185, 2016 ), based on Bohmian quantum mechanics, derived a quantum corrected version of the Schwarzschild metric. In this paper, we construct a quantum corrected Schwarzschild thin-shell wormhole (QSTSW) and investigate the stability of this wormhole. First we compute the surface stress at the wormhole throat by applying the Darmois–Israel formalism to the modified Schwarzschild metric and show that exotic matter is required at the throat to kee...
Linet, Bernard
2015-01-01
We present a complete analysis of the light rays within the linearized, weak-field approximation of a Schwarzschild-like metric describing the gravitational field of an isolated, spherically symmetric body. We prove in this context the existence of two time transfer functions and we obtain these functions in an exact closed-form. We are led to distinguish two regimes. In the first regime, the two time transfer functions correspond to rays which are confined in regions of spacetime where the weak-field approximation is valid. Such a regime occurs in gravitational lensing configurations with double images of a given source. We find the general expressions of the angular separation and the difference in light travel time between the two images. In the second regime, there exists only one time transfer function corresponding to a light ray remaining in a region of weak field. Performing a Taylor expansion of this function with respect to the gravitational constant, we obtain the Shapiro time delay completed by a ...
The Schwarzschild solution in the DGP model
Middleton, Chad; Siopsis, George
2003-01-01
We discuss the Schwarzschild solution in the Dvali-Gabadadze-Porrati (DGP) model. We obtain a perturbative expansion and find the explicit form of the lowest-order contribution. By keeping off-diagonal terms in the metric, we arrive at a perturbative expansion which is valid both far from and near the Schwarzschild radius. We calculate the lowest-order contribution explicitly and obtain the form of the metric both on the brane and in the bulk. As we approach the Schwarzschild radius, the pert...
Slowly rotating supercompact Schwarzschild stars
Posada, Camilo
2017-06-01
The Schwarzschild interior solution, or 'Schwarzschild star', which describes a spherically symmetric homogeneous mass with a constant energy density, shows a divergence in pressure when the radius of the star reaches the Schwarzschild-Buchdahl bound. Recently, Mazur and Mottola showed that this divergence is integrable through the Komar formula, inducing non-isotropic transverse stresses on a surface of some radius R0. When this radius approaches the Schwarzschild radius Rs = 2 M, the interior solution becomes one of negative pressure evoking a de Sitter space-time. This gravitational condensate star, or gravastar, is an alternative solution to the idea of a black hole as the ultimate state of gravitational collapse. Using Hartle's model to calculate equilibrium configurations of slowly rotating masses, we report results of surface and integral properties for a Schwarzschild star in the very little studied region Rs < R < (9/8)Rs. We found that in the gravastar limit, the angular velocity of the fluid relative to the local inertial frame tends to zero, indicating rigid rotation. Remarkably, the normalized moment of inertia I/MR2 and the mass quadrupole moment Q approach the corresponding values for the Kerr metric to second order in Ω. These results provide a solution to the problem of the source of a slowly rotating Kerr black hole.
Schwarzschild instanton in emergent gravity
Chanda, Sumanto; Guha, Partha; Roychowdhury, Raju
2017-09-01
In the bottom-up approach of emergent gravity, we attempt to find symplectic gauge fields emerging from Euclidean Schwarzschild instanton, which is studied as electromagnetism defined on the symplectic space (M,ω). Geometrical engineering with the emergent metric sets up the Seiberg-Witten map between commutative and non-commutative gauge fields, preparing the ground for the evaluation of topological invariants in terms of the underlying gauge theory quantities.
Doppleraj efikoj \\^ce Schwarzschild
Paiva, F M
2009-01-01
Motion of bodies and light rays are studied in the gravitational field of Schwarzschild. Several Doppler effects are described. ----- Movado de korpoj kaj lumo estas studitaj en gravita kampo de Schwarzschild. Pluraj Doppleraj efikoj estas priskribitaj.
Reconsidering Schwarzschild's original solution
Antoci, S; Liebscher, D. -E.
2001-01-01
We analyse the Schwarzschild solution in the context of the historical development of its present use, and explain the invariant definition of a singular surface at the Schwarzschild's radius, that can be applied to the Kerr-Newman solution too.
Radiation memory, boosted Schwarzschild spacetimes and supertranslations
Mädler, Thomas; Winicour, Jeffrey
2017-06-01
We investigate gravitational radiation memory and its corresponding effect on the asymptotic symmetries of a body whose exterior is a boosted Schwarzschild spacetime. First, in the context of linearized theory, we consider such a Schwarzschild body which is initially at rest, then goes through a radiative stage and finally emerges as a boosted Schwarzschild body. We show that the proper retarded solution of the exterior Schwarzschild spacetime for this process can be described in terms of the ingoing Kerr-Schild form of the Schwarzschild metric for both the initial and final states. An outgoing Kerr-Schild or time symmetric metric does not give the proper solution. The special property of Kerr-Schild metrics that their linearized and nonlinear forms are identical allows us to extend this result to processes in the nonlinear regime. We then discuss how the nonlinear memory effect, and its associated supertranslation, affect angular momentum conservation. Our approach provides a new framework for studying nonlinear aspects of the memory effect.
Quantum Corrected Schwarzschild Thin Shell Wormhole
Jusufi, Kimet
2016-01-01
Recently, Ali and Khalil \\cite{ahmed}, based on the Bohmian quantum mechanics derived a quantum corrected version of the Schwarzschild metric. In this paper, we construct a quantum corrected Schwarzschild thin shell wormhole (QSTSW) and investigate the stability of this wormhole. First we compute the surface stress at the wormhole throat by applying the Darmois-Israel formalism to the modified Schwarzschild metric and show that exotic matter is required at the throat to keep the wormhole stable. We then study the stability analysis of the wormhole by considering phantom-energy for the exotic matter, generalized Chaplygin gas (GCG), and the linearized stability analysis. It is argued that, quantum corrections can affect the stability domain of the wormhole.
Quantum corrected Schwarzschild thin-shell wormhole
Energy Technology Data Exchange (ETDEWEB)
Jusufi, Kimet [State University of Tetovo, Physics Department, Tetovo (Macedonia, The Former Yugoslav Republic of)
2016-11-15
Recently, Ali and Khalil (Nucl Phys B, 909, 173-185, 2016), based on Bohmian quantum mechanics, derived a quantum corrected version of the Schwarzschild metric. In this paper, we construct a quantum corrected Schwarzschild thin-shell wormhole (QSTSW) and investigate the stability of this wormhole. First we compute the surface stress at the wormhole throat by applying the Darmois-Israel formalism to the modified Schwarzschild metric and show that exotic matter is required at the throat to keep the wormhole stable. We then study the stability analysis of the wormhole by considering phantom-energy for the exotic matter, generalized Chaplygin gas (GCG), and the linearized stability analysis. It is argued that quantum corrections can affect the stability domain of the wormhole. (orig.)
On Quantum Deformation of the Schwarzschild Solution
Kazakov, D.I.; Solodukhin, S. N.
1993-01-01
We consider the deformation of the Schwarzschild solution in general relativity due to spherically symmetric quantum fluctuations of the metric and the matter fields. In this case, the 4D theory of gravity with Einstein action reduces to the effective two-dimensional dilaton gravity. We have found that the Schwarzschild singularity at $r=0$ is shifted to the finite radius $r_{min} \\sim r_{Pl}$, where the scalar curvature is finite, so that the space-time looks regular and consists of two asym...
Averaging Schwarzschild spacetime
Tegai, S. Ph.; Drobov, I. V.
2017-07-01
We tried to average the Schwarzschild solution for the gravitational point source by analogy with the same problem in Newtonian gravity or electrostatics. We expected to get a similar result, consisting of two parts: the smoothed interior part being a sphere filled with some matter content and an empty exterior part described by the original solution. We considered several variants of generally covariant averaging schemes. The averaging of the connection in the spirit of Zalaletdinov's macroscopic gravity gave unsatisfactory results. With the transport operators proposed in the literature it did not give the expected Schwarzschild solution in the exterior part of the averaged spacetime. We were able to construct a transport operator that preserves the Newtonian analogy for the outward region but such an operator does not have a clear geometrical meaning. In contrast, using the curvature as the primary averaged object instead of the connection does give the desired result for the exterior part of the problem in a fine way. However for the interior part, this curvature averaging does not work because the Schwarzschild curvature components diverge as 1 /r3 near the center and therefore are not integrable.
Analytical Solution Of Complete Schwarzschild\\'s Planetary Equation
African Journals Online (AJOL)
It is well known how to solve the Einstein\\'s planetary equation of motion by the method of successive approximation for the corresponding orbit solution. In this paper, we solve the complete schwarzschild\\'s planetary equation of motion by an exact analytical method. The result reveals that there are actually eight exact ...
The golden ratio in Schwarzschild-Kottler black holes
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Cruz, Norman [Universidad de Santiago de Chile, Departamento de Fisica, Facultad de Ciencia, Santiago 2 (Chile); Olivares, Marco [Universidad Diego Portales, Facultad de Ingenieria, Santiago (Chile); Villanueva, J.R. [Universidad de Valparaiso, Instituto de Fisica y Astronomia, Valparaiso (Chile)
2017-02-15
In this paper we show that the golden ratio is present in the Schwarzschild-Kottler metric. For null geodesics with maximal radial acceleration, the turning points of the orbits are in the golden ratio Φ = (√(5)-1)/2. This is a general result which is independent of the value and sign of the cosmological constant Λ. (orig.)
Gravitational field of Schwarzschild soliton
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Musavvir Ali
2015-01-01
Full Text Available The aim of this paper is to study the gravitational field of Schwarzschild soliton. Use of characteristic of λ-tensor is given to determine the kinds of gravitational fields. Through the cases of two and three dimension for Schwarzschild soliton, the Gaussian curvature is expressed in terms of eigen values of the characteristic equation.
Resolving the Schwarzschild singularity in both classic and quantum gravity
Zeng, Ding-fang
2017-01-01
The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zer...
Martin Schwarzschild (1912-1997)
Trimble, V.
1997-12-01
Martin Schwarzschild, the ASP Bruce Medalist for 1965, died on 10 April 1997. A refugee from Hitler's Germany who firmly embraced his adopted country, Schwarzschild not only solved a number of fundamental problems in stellar structure and evolution but also taught the rest of the astronomical community how to do so with his 1958 text, Structure and Evolution of the Stars. At about the time of his 1979 retirement, he turned to a completely different question of how to model spheroidal galaxies self-consistently and sent another generation of students and collaborators forward toward the still somewhat distant solution. It is impossible for anyone who ever interacted with Schwarzschild to remain entirely solemn when remembering him. (SECTION: Obituary)
Landau problem in the static schwarzschild universe
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A Jafari
2013-09-01
Full Text Available This paper considers the Landau problem in an elected static space time and the are erased levels shifts which are erased as a metric deviation from the Minkowski space time. This research is based on the Weber’s method. We try to rewrite the equation of motion of particles in the presence of the gravitational effects and consider the regions limited with the tangent spaces conditions. I t would be reasonable to assume the nonrelativistic particles with low speed. We show that due to the Weber’s method, the tangent space is always available. Another assumption of this article is time independent tangent space of Schwarzschild universe and use of Riemann’s normal coordinates.
Complete Schwarzschild\\'s planetary equation | Howusu | Journal of ...
African Journals Online (AJOL)
In this paper we derive the complete planetary equation from the Schwarzschild's equations of motion and compare it with the corresponding well-known planetary equation from the Schwarzchild's line element. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 265-268 ...
TRANSFER PANAS LUBANG HITAM SCHWARZSCHILD
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Y Tiandho
2015-07-01
Full Text Available Mekanika kuantum menunjukkan bahwa lubang hitam memiliki temperatur sebagai indikasi dapat mengemisikan partikel. Persamaan transfer panas secara general mengandung operator Laplacian yang sifatnya dipengaruhi oleh ruang. Kelengkungan ruang-waktu di daerah sekitar lubang hitam sangat besar sehingga operator Laplacian untuk menghitung distribusi temperaturnya merupakan Laplacian ruang lengkung. Persamaan Fourier untuk lubang hitam Schwarzschild bergantung pada jarak dan radius Schwarzschild. Pada keadaan tunak solusi dari komponen radius mengandung polinomial Legendre dan solusi dari komponen sudut ruang mengadung fungsi spherical harmonics. Untuk kasus dengan persamaan diferensial terhadap waktu bernilai konstan solusi menyimpulkan bahwa temperatur bertambah seiring waktu. Hasil yang telah didapatkan secara umum dapat digunakan untuk menentukan distribusi temperatur pada ruang lengkung akibat suatu objek bermassa M. Koreksi ini sekaligus menggambarkan peristiwa transfer panas dalam konteks relativitas umum.Quantum mechanics show that black hole has temperature that indicated that black hole can emit particles.<0} {0>Persamaan transfer panas secara general mengandung operator Laplacian yang sifatnya dipengaruhi oleh ruang.<}0{>Generally the heat transfer equation contains Laplacian operators that is influenced by space.<0} {0>Kelengkungan ruang-waktu di daerah sekitar lubang hitam sangat besar sehingga operator Laplacian untuk menghitung distribusi temperaturnya merupakan Laplacian ruang lengkung.<}0{>The space-time arch in the surrounding of black hole is very big so that Laplacian operators to calculate the temperature distribution is the arch space Laplacian.<0} {0>Persamaan Fourier untuk lubang hitam Schwarzschild bergantung pada jarak dan radius Schwarzschild.<}0{>Fourier equation for Schwarzschild black hole is depended on the distance and radius of Schwarzschild.<0} {0>Pada keadaan tunak solusi dari komponen radius mengandung polinomial
The Lemaitre-Schwarzschild problem revisited
Fuzfa, A.; Gérard, Jean-Marc; Lambert, Didier
2001-01-01
The Lemaitre and Schwarzschild analytical solutions for a relativistic spherical body of constant density are linked together through the use of the Weyl quadratic invariant. The critical radius for gravitational collapse of an incompressible fluid is shown to vary continuously from 9/8 of the Schwarzschild radius to the Schwarzschild radius itself while the internal pressures become locally anisotropic. Comment: Final version as accepted by GR&G (to appear in vol. 34, sept...
Augousti, A. T.; Gawelczyk, M.; Siwek, A.; Radosz, A.
2012-01-01
The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mother station (MS) is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are…
Exact Schwarzschild-de Sitter black holes in a family of massive gravity models
Nieuwenhuizen, T.M.
2011-01-01
The Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black hole metrics appear as exact solutions in the recently formulated massive gravity of de Rham, Gabadadze and Tolley, where the mass term sets the curvature scale. They occur within a two-parameter family of de Rham, Gabadadze and
Thermodynamics of Schwarzschild-Beltrami-de Sitter black hole
Liu, Hang; Meng, Xin-He
2017-09-01
In this paper, we investigate the thermodynamical properties of Schwarzschild-Beltrami-de Sitter (S-BdS) black hole introduced by Yan et al. in 2013 by introducing inertial Beltrami coordinates to traditional non-inertial Schwarzschild-de Sitter (S-dS) metric which is the exact static spherical symmetry solution of Einstein equation with a positive cosmological constant Λ. Based on this new metric, we compute entropy on all horizons and we give the entropy bound of the black hole. Hawking temperatures are calculated by considering a perturbation to entropy relations due to that the spacetime described by these inertial coordinates is no longer a stationary spacetime in which surface gravity related to Hawking temperature is defined well on killing horizon. We also get the Smarr relations and the first law of thermodynamics. We find that the S-BdS black hole seems to have similar thermodynamical properties to S-dS black hole in the comparison between their corresponding thermodynamical quantities, although the new black hole metric is described by inertial coordinates which exclude the effects of inertial force.
Geodesics of simultaneity in Schwarzschild
Paiva, F M
2010-01-01
Geodesic of simultaneity is a spacelike geodesic in which every pair of neighbour events are simultaneous ($g_{0\\mu}\\dd x^\\mu=0$). These geodesics are studied in the exterior region of \\Sch's metric.
Traversable Schwarzschild-like wormholes
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2017-11-01
In this paper we study relativistic static traversable wormhole solutions which are a slight generalization of Schwarzschild wormholes. In order to do this we assume a shape function with a linear dependence on the radial coordinate r. This linear shape function generates wormholes whose asymptotic spacetime is not flat: they are asymptotically locally flat, since in the asymptotic limit r → ∞ spacetimes exhibiting a solid angle deficit (or excess) are obtained. In particular, there exist wormholes which connect two asymptotically non-flat regions with a solid angle deficit. For these wormholes the size of their embeddings in a three-dimensional Euclidean space extends from the throat to infinity. A new phantom zero-tidal-force wormhole exhibiting such asymptotic is obtained. On the other hand, if a solid angle excess is present, the size of the wormhole embeddings depends on the amount of this angle excess, and the energy density is negative everywhere. We discuss the traversability conditions and study the impact of the β -parameter on the motion of a traveler when the wormhole throat is crossed. A description of the geodesic behavior for the wormholes obtained is also presented.
Quantum corrections to Schwarzschild black hole
Energy Technology Data Exchange (ETDEWEB)
Calmet, Xavier; El-Menoufi, Basem Kamal [University of Sussex, Department of Physics and Astronomy, Brighton (United Kingdom)
2017-04-15
Using effective field theory techniques, we compute quantum corrections to spherically symmetric solutions of Einstein's gravity and focus in particular on the Schwarzschild black hole. Quantum modifications are covariantly encoded in a non-local effective action. We work to quadratic order in curvatures simultaneously taking local and non-local corrections into account. Looking for solutions perturbatively close to that of classical general relativity, we find that an eternal Schwarzschild black hole remains a solution and receives no quantum corrections up to this order in the curvature expansion. In contrast, the field of a massive star receives corrections which are fully determined by the effective field theory. (orig.)
Properties of gravity near the Schwarzschild radius
Verozub, Leonid
2014-01-01
The radius of the observable region of the Universe is of the order of its Schwarzschild radius. Due to the spherical symmetry, this allows to check the properties of the gravitational force in the vicinity of the Schwarzschild radius by comparing the theoretical and observed Hubble diagram at high redshifts. This can be done in a simple model that fellows from projective-invariant equations of gravitation.This paper shows that the Hubble diagram up to $z=8$ testifies in favor of the specific...
Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime
Lim, Yen-Kheng
2016-01-01
An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter (SdS) spacetime and also the Mannheim-Kazanas (MK) metric of conformal Weyl gravity. From the exact solution, we obtain a small bending-angle approximation for a lens system where the source, lens and observer are co-aligned. This expansion improves previous calculations where we systematically avoid parameter ranges which correspond to non-existent null trajectories. The linear coefficient $\\gamma$ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by General Relativity for small $\\gamma$.
Exact gravitational lensing in conformal gravity and Schwarzschild-de Sitter spacetime
Lim, Yen-Kheng; Wang, Qing-hai
2017-01-01
An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the exact solution, we obtain a small-bending-angle approximation for a lens system where the source, lens, and observer are coaligned. This expansion improves previous calculations where we systematically avoid parameter ranges that correspond to nonexistent null trajectories. The linear coefficient γ characteristic to conformal gravity is shown to contribute enhanced deflection compared to the angle predicted by general relativity for small γ .
Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole
Directory of Open Access Journals (Sweden)
Alexis Larrañaga
2013-01-01
Full Text Available The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD. Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.
Schwarzschild Black Branes and Strings in higher-dimensional Brane Worlds
Kanti, Panagiota; Tamvakis, Kyriakos
2002-01-01
We consider branes embedded in spacetimes of codimension 1 and 2, with a warped metric tensor for the subspace parallel to the brane. We study a variety of brane-world solutions arising by introducing a Schwarzschild-like black hole metric on the brane and we investigate the properties of the corresponding higher-dimensional spacetime. We demonstrate that normalizable bulk modes lead to a vanishing flow of energy through the naked singularities. From this point of view, these singularities are harmless. (28 refs).
Directory of Open Access Journals (Sweden)
Sergio Mendoza
2009-01-01
Full Text Available We present heuristic arguments suggesting that if EM waves with wavelengths somewhat larger than the Schwarzschild radius of a black hole were fully absorbed by it, the second law of thermodynamics would be violated, under the Bekenstein interpretation of the area of a black hole as a measure of its entropy. Thus, entropy considerations make the well known fact that large wavelengths are only marginally absorbed by black holes, a natural consequence of thermodynamics. We also study numerically the ingoing radial propagation of a scalar field wave in a Schwarzschild metric, relaxing the standard assumption which leads to the eikonal equation, that the wave has zero spatial extent. We find that if these waves have wavelengths larger that the Schwarzschild radius, they are very substantially reflected, fully to numerical accuracy. Interestingly, this critical wavelength approximately coincides with the one derived from entropy considerations of the EM field, and is consistent with well known limit results of scattering in the Schwarzschild metric. The propagation speed is also calculated and seen to differ from the value c, for wavelengths larger than Rs, in the vicinity of Rs. As in all classical wave phenomena, whenever the wavelength is larger or comparable to the physical size of elements in the system, in this case changes in the metric, the zero extent Ã¢Â€Â™particleÃ¢Â€Â™ description fails, and the wave nature becomes apparent.
Schwarzschild-de Sitter spacetimes, McVittie coordinates, and trumpet geometries
Dennison, Kenneth A.; Baumgarte, Thomas W.
2017-12-01
Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated numerical studies of black holes in asymptotically de Sitter spacetimes. We derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter spacetimes by first generalizing the static maximal trumpet slicing of the Schwarzschild spacetime to static constant mean curvature trumpet slicings of Schwarzschild-de Sitter spacetimes. We then switch to a comoving isotropic radial coordinate which results in a coordinate system analogous to McVittie coordinates. At large distances from the black hole the resulting metric asymptotes to a Friedmann-Lemaître-Robertson-Walker metric with an exponentially-expanding scale factor. While McVittie coordinates have another asymptotically de Sitter end as the radial coordinate goes to zero, so that they generalize the notion of a "wormhole" geometry, our new coordinates approach a horizon-penetrating trumpet geometry in the same limit. Our analytical expressions clarify the role of time-dependence, boundary conditions and coordinate conditions for trumpet slices in a cosmological context, and provide a useful test for black hole simulations in asymptotically de Sitter spacetimes.
Thermodynamic stability of modified Schwarzschild-AdS black hole in rainbow gravity
Energy Technology Data Exchange (ETDEWEB)
Kim, Yong-Wan [Chonbuk National University, Research Institute of Physics and Chemistry, Jeonju (Korea, Republic of); Kim, Seung Kook [Seonam University, Department of Physical Therapy, Namwon (Korea, Republic of); Park, Young-Jai [Sogang University, Department of Physics, Seoul (Korea, Republic of)
2016-10-15
In this paper, we have extended the previous study of the thermodynamics and phase transition of the Schwarzschild black hole in the rainbow gravity to the Schwarzschild-AdS black hole where metric depends on the energy of a probe. Making use of the Heisenberg uncertainty principle and the modified dispersion relation, we have obtained the modified local Hawking temperature and thermodynamic quantities in an isothermal cavity. Moreover, we carry out the analysis of constant temperature slices of a black hole. As a result, we have shown that there also exists another Hawking-Page-like phase transition in which case a locally stable small black hole tunnels into a globally stable large black hole as well as the standard Hawking-Page phase transition from a hot flat space to a black hole. (orig.)
Bose–Einstein graviton condensate in a Schwarzschild black hole
Alfaro, Jorge; Espriu, Domènec; Gabbanelli, Luciano
2018-01-01
We analyze in detail a previous proposal by Dvali and Gómez that black holes could be treated as consisting of a Bose–Einstein condensate of gravitons. In order to do so we extend the Einstein–Hilbert action with a chemical potential-like term, thus placing ourselves in a grand-canonical ensemble. The form and characteristics of this chemical potential-like piece are discussed in some detail. We argue that the resulting equations of motion derived from the action could be interpreted as the Gross–Pitaevskii equation describing a graviton Bose–Einstein condensate trapped by the black hole gravitational field. After this, we proceed to expand the ensuring equations of motion up to second order around the classical Schwarzschild metric so that some non-linear terms in the metric fluctuation are kept. Next we search for solutions and, modulo some very plausible assumptions, we find out that the condensate vanishes outside the horizon but is non-zero in its interior. Inspired by a linearized approximation around the horizon we are able to find an exact solution for the mean-field wave function describing the graviton Bose–Einstein condensate in the black hole interior. After this, we can rederive some of the relations involving the number of gravitons N and the black hole characteristics along the lines suggested by Dvali and Gómez.
Statistical Entropy of Schwarzschild Black Holes
Englert, F
1998-01-01
The entropy of a seven dimensional Schwarzschild black hole of arbitrary large radius is obtained by a mapping onto a near extremal self-dual three-brane whose partition function can be evaluated. The three-brane arises from duality after submitting a neutral blackbrane, from which the Schwarzschild black hole can be obtained by compactification, to an infinite boost in non compact eleven dimensional space-time and then to a Kaluza-Klein compactification. This limit can be defined in precise terms and yields the Beckenstein-Hawking value up to a factor of order one which can be set to be exactly one with the extra assumption of keeping only transverse brane excitations. The method can be generalized to five and four dimensional black holes.
Quantum correlator outside a Schwarzschild black hole
Directory of Open Access Journals (Sweden)
Claudia Buss
2018-01-01
Full Text Available We calculate the quantum correlator in Schwarzschild black hole space–time. We perform the calculation for a scalar field in three different quantum states: Boulware, Unruh and Hartle–Hawking, and for points along a timelike circular geodesic. The results show that the correlator presents a global fourfold singularity structure, which is state-independent. Our results also show the different correlations in the three different quantum states arising in-between the singularities.
Quantum correlator outside a Schwarzschild black hole
Buss, Claudia; Casals, Marc
2018-01-01
We calculate the quantum correlator in Schwarzschild black hole space-time. We perform the calculation for a scalar field in three different quantum states: Boulware, Unruh and Hartle-Hawking, and for points along a timelike circular geodesic. The results show that the correlator presents a global fourfold singularity structure, which is state-independent. Our results also show the different correlations in the three different quantum states arising in-between the singularities.
Gravitino perturbations in Schwarzschild black holes
Piedra, Owen Pavel Fernández
2010-01-01
We consider the time evolution of massless gravitino perturbations in Schwarzschild black holes, and show that as in the case of fields of other values of spin, the evolution comes in three stages, after an initial outburst as a first stage, we observe the damped oscillations characteristic of the quasinormal ringing stage, followed by long time tails. Using the sixth order WKB method and Prony fitting of time domain data we determine the quasinormal frequencies. There is a good correspondenc...
Dirac Quasinormal modes of Schwarzschild black hole
Jing, Jiliang
2005-01-01
The quasinormal modes (QNMs) associated with the decay of Dirac field perturbation around a Schwarzschild black hole is investigated by using continued fraction and Hill-determinant approaches. It is shown that the fundamental quasinormal frequencies become evenly spaced for large angular quantum number and the spacing is given by $\\omega_{\\lambda+1}- \\omega_{\\lambda}=0.38490-0.00000i$. The angular quantum number has the surprising effect of increasing real part of the quasinormal frequencies...
Kundu, Prasun K.
2017-11-01
In a comment published several years ago in this journal, Mitra [J. Math. Phys. 50, 042502 (2009)] has claimed to prove that a neutral point particle in general relativity as described by the Schwarzschild metric must have zero gravitational mass, i.e., the mass parameter M0 of a Schwarzschild black hole necessarily vanishes. It is shown that the purported proof is incorrect. The error stems from a basic misunderstanding of the mathematical description of coordinate volume element in a differentiable manifold.
Schwarzschild black holes can wear scalar wigs.
Barranco, Juan; Bernal, Argelia; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Núñez, Darío; Sarbach, Olivier
2012-08-24
We study the evolution of a massive scalar field surrounding a Schwarzschild black hole and find configurations that can survive for arbitrarily long times, provided the black hole or the scalar field mass is small enough. In particular, both ultralight scalar field dark matter around supermassive black holes and axionlike scalar fields around primordial black holes can survive for cosmological times. Moreover, these results are quite generic in the sense that fairly arbitrary initial data evolve, at late times, as a combination of those long-lived configurations.
The solution of complete Schwarzschild's planetary equation with ...
African Journals Online (AJOL)
The Einstein's solution of the planetary equation of motion from Schwarzschild's line element is well known. In this paper, we solve the complete Schwarzschild's planetary equation with the method of successive approximation for the corresponding precession and compare the result with that from the line element.
Turning points of massive particles in Schwarzschild geometry
Polonyi, J.; Radosz, A.; Siwek, A.; Ostasiewicz, K.
2009-01-01
The stable geodesics in Schwarzschild geometry can not approach the center closer than the radius of the photon sphere, 3/2 times the Schwarzschild radius. In other words, massive particles moving along geodesics that cross the photon sphere do not escape, they fall into the black hole.
Resolving the Schwarzschild singularity in both classic and quantum gravity
Zeng, Ding-fang
2017-04-01
The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr-Sommerfield like ;orbital; quantisation assumption, we show that for each black hole of horizon radius rh, there are about e rh2/#x2113;pl 2 allowable eigen-energy-density profiles. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.
Resolving the Schwarzschild singularity in both classic and quantum gravity
Directory of Open Access Journals (Sweden)
Ding-fang Zeng
2017-04-01
Full Text Available The Schwarzschild singularity's resolution has key values in cracking the key mysteries related with black holes, the origin of their horizon entropy and the information missing puzzle involved in their evaporations. We provide in this work the general dynamic inner metric of collapsing stars with horizons and with non-trivial radial mass distributions. We find that static central singularities are not the final state of the system. Instead, the final state of the system is a periodically zero-cross breathing ball. Through 3+1 decomposed general relativity and its quantum formulation, we establish a functional Schrödinger equation controlling the micro-state of this breathing ball and show that, the system configuration with all the matter concentrating on the central point is not the unique eigen-energy-density solution. Using a Bohr–Sommerfield like “orbital” quantisation assumption, we show that for each black hole of horizon radius rh, there are about erh2/ℓpl2 allowable eigen-energy-density profiles. This naturally leads to physic interpretations for the micro-origin of horizon entropy, as well as solutions to the information missing puzzle involved in Hawking radiations.
Gravitino perturbations in Schwarzschild black holes
Piedra, Owen Pavel Fernández
2010-01-01
We consider the time evolution of massless gravitino perturbations in Schwarzschild black holes, and show that as in the case of fields of other values of spin, the evolution comes in three stages, after an initial outburst as a first stage, we observe the damped oscillations characteristic of the quasinormal ringing stage, followed by long time tails. Using the sixth order WKB method and Prony fitting of time domain data we determine the quasinormal frequencies. There is a good correspondence between the results obtained by the above two methods, and we obtain a considerable improvement with respect to the previously obtained third order WKB results. We also show that the response of a black hole depends crucially on the spin class of the perturbing field: the quality factor becomes a decreasing function of the spin for boson perturbations , whereas the opposite situation appears for fermion ones.
Counting Schwarzschild and Charged Black Holes
Energy Technology Data Exchange (ETDEWEB)
Rajaraman, Arvind
2003-05-23
We review the arguments that fundamental string states are in one to one correspondence with black hole states. We demonstrate the power of the assumption by showing that it implies that the statistical entropy of a wide class of nonextreme black holes occurring in string theory is proportional to the horizon area. However, the numerical coefficient relating the area and entropy only agrees with the Bekenstein-Hawking formula if the central charge of the string is six which does not correspond to any known string theory. Unlike the current D-brane methods the method used in this paper is applicable for the case of Schwarzschild and highly non-extreme charged black holes.
Al-Badawi, A.
2018-02-01
The Dirac equation is considered in a spacetime that represents a Schwarzschild metric coupled to a uniform external electromagnetic field. Due to the presence of electromagnetic field from the surroundings, the interaction with the spin-1/2 massive charged particle is considered. The equations of the spin-1/2 massive charged particle are separated into radial and angular equations by adopting the Newman-Penrose formalism. The angular equations obtained are similar to the Schwarzschild geometry. For the radial equations we manage to obtain the one dimensional Schrödinger-type wave equations with effective potentials. Finally, we study the behavior of the potentials by plotting them as a function of radial distance and expose the effect of the external parameter, charge and the frequency of the particle on them.
Quasinormal Modes of a Quantum-Corrected Schwarzschild Black ...
Indian Academy of Sciences (India)
corrected Schwarzschild black hole. The complex frequencies of the quasinormal modes are evaluated by the third-order WKB approximation. The numerical results obtained showed that the complex frequencies depend on the quantum ...
Stability of Schwarzschild singularity in non-local gravity
Calcagni, Gianluca; Modesto, Leonardo
2017-10-01
In a previous work, it was shown that all Ricci-flat spacetimes are exact solutions for a large class of non-local gravitational theories. Here we prove that, for a subclass of non-local theories, the Schwarzschild singularity is stable under linear perturbations. Thus, non-locality may be not enough to cure all the singularities of general relativity. Finally, we show that the Schwarzschild solution can be generated by the gravitational collapse of a thin shell of radiation.
Dynamics of particles around time conformal Schwarzschild black hole
Jawad, Abdul; Ali, Farhad; Shahzad, M. Umair; Abbas, G.
2016-11-01
In this work, we present the new technique for discussing the dynamical motion of neutral as well as charged particles in the absence/presence of a magnetic field around the time conformal Schwarzschild black hole. Initially, we find the numerical solutions of geodesics of the Schwarzschild black hole and the time conformal Schwarzschild black hole. We observe that the Schwarzschild spacetime admits the time conformal factor e^{ɛ f(t)}, where f( t) is an arbitrary function and ɛ is very small, which causes a perturbation in the spacetimes. This technique also re-scales the energy content of spacetime. We also investigate the thermal stability, horizons and energy conditions corresponding to time conformal Schwarzschild spacetime. Also, we examine the dynamics of a neutral and charged particle around a time conformal Schwarzschild black hole. We investigate the circumstances under which the particle can escape from the vicinity of a black hole after collision with another particle. We analyze the effective potential and effective force of a particle in the presence of a magnetic field with angular momentum graphically.
Caustic echoes from a Schwarzschild black hole
Zenginoğlu, Anıl
2012-01-01
We present the first numerical construction of the scalar Schwarzschild Green function in the time-domain, which reveals several universal features of wave propagation in black hole spacetimes. We demonstrate the trapping of energy near the photon sphere and confirm its exponential decay. The trapped wavefront propagates through caustics resulting in echoes that propagate to infinity. The arrival times and the decay rate of these caustic echoes are consistent with propagation along null geodesics and the large l-limit of quasinormal modes. We show that the four-fold singularity structure of the retarded Green function is due to the well-known action of a Hilbert transform on the trapped wavefront at caustics. A two-fold cycle is obtained for degenerate source-observer configurations along the caustic line, where the energy amplification increases with an inverse power of the scale of the source. Finally, we discuss the tail piece of the solution due to propagation within the light cone, up to and including nu...
Hawking radiation inside a Schwarzschild black hole
Hamilton, Andrew J S
2016-01-01
The boundary of any observer's spacetime is the boundary that divides what the observer can see from what they cannot see. The boundary of an observer's spacetime in the presence of a black hole is not the true (future event) horizon of the black hole, but rather the illusory horizon, the dimming, redshifting surface of the star that collapsed to the black hole long ago. The illusory horizon is the source of Hawking radiation seen by observers both outside and inside the true horizon. The perceived acceleration (gravity) on the illusory horizon sets the characteristic frequency scale of Hawking radiation, even if that acceleration varies dynamically, as it must do from the perspective of an infalling observer. The acceleration seen by a non-rotating free-faller both on the illusory horizon below and in the sky above is calculated for a Schwarzschild black hole. Remarkably, as an infaller approaches the singularity, the acceleration becomes isotropic, and diverging as a power law. The isotropic, power-law char...
Gravitino Perturbations in Schwarzschild Black Holes
Fernandez Piedra, Owen Pavel
We consider the time-evolution of massless gravitino perturbations in Schwarzschild black holes, and show that as in the case of fields of other values of spin, the evolution comes in three stages. After an initial outburst as a first stage, we observe the damped oscillations characteristic of the quasinormal ringing stage, followed by long time tails. Using the sixth-order WKB method and Prony fitting of time domain data we determine the quasinormal frequencies. There is a good correspondence between the results obtained by the above two methods, and we obtain a considerable improvement with respect to the previously obtained third-order WKB results. We also show that the response of a black hole depends crucially on the spin class of the perturbing field: the quality factor becomes a decreasing function of the spin for boson perturbations, whereas the opposite situation appears for fermion ones. With respect to the late-time behavior, we found numerical evidence of a faster decay of gravitino perturbations, a result in constrast with what is known for other neutral fields.
Geons and the quantum information metric
Sinamuli, Musema; Mann, Robert B.
2017-07-01
We investigate the proposed duality between a quantum information metric in a CFTd +1 and the volume of a maximum time slice in the dual AdSd +2 for topological geons. Examining the specific cases of Banados-Teitelboim-Zannelli (BTZ) black holes and planar Schwarzschild-anti-de Sitter black holes, along with their geon counterparts, we find that the proposed duality relation for geons is the same apart from a factor of 4. The information metric therefore provides a probe of the topology of the bulk spacetime.
1st Karl Schwarzschild Meeting on Gravitational Physics
Kaminski, Matthias; Mureika, Jonas; Bleicher, Marcus
2016-01-01
These proceedings collect the selected contributions of participants of the First Karl Schwarzschild Meeting on Gravitational Physics, held in Frankfurt, Germany to celebrate the 140th anniversary of Schwarzschild's birth. They are grouped into 4 main themes: I. The Life and Work of Karl Schwarzschild; II. Black Holes in Classical General Relativity, Numerical Relativity, Astrophysics, Cosmology, and Alternative Theories of Gravity; III. Black Holes in Quantum Gravity and String Theory; IV. Other Topics in Contemporary Gravitation. Inspired by the foundational principle ``By acknowledging the past, we open a route to the future", the week-long meeting, envisioned as a forum for exchange between scientists from all locations and levels of education, drew participants from 15 countries across 4 continents. In addition to plenary talks from leading researchers, a special focus on young talent was provided, a feature underlined by the Springer Prize for the best student and junior presentations.
Gravitational self-force effects on a point mass moving around a Schwarzschild black hole
Energy Technology Data Exchange (ETDEWEB)
Sago, Norichika [School of Mathematics, University of Southampton, University Road, Southampton, SO17 1BJ (United Kingdom)
2009-05-07
We consider the effects of the gravitational self-force on a point mass moving in a generic (eccentric) orbit around a Schwarzschild black hole. We developed a numerical code to solve the metric perturbation equations in the time domain, under the Lorenz gauge condition, and to implement the so-called 'mode sum' scheme to obtain the self-force. We use our numerical results to investigate both dissipative and conservative self-force effects on the particle's orbits. To check the consistency of our calculation, we (1) compare our results with independent calculations based on a different gauge, in the special case of a circular orbit (by considering gauge-invariant quantities); (2) derive the energy and angular momentum fluxes of emitted gravitational waves and compare with results from standard Teukolsky-based calculations.
Cardy-Verlinde Formula of Noncommutative Schwarzschild Black Hole
Directory of Open Access Journals (Sweden)
G. Abbas
2014-01-01
Full Text Available Few years ago, Setare (2006 has investigated the Cardy-Verlinde formula of noncommutative black hole obtained by noncommutativity of coordinates. In this paper, we apply the same procedure to a noncommutative black hole obtained by the coordinate coherent approach. The Cardy-Verlinde formula is entropy formula of conformal field theory in an arbitrary dimension. It relates the entropy of conformal field theory to its total energy and Casimir energy. In this paper, we have calculated the total energy and Casimir energy of noncommutative Schwarzschild black hole and have shown that entropy of noncommutative Schwarzschild black hole horizon can be expressed in terms of Cardy-Verlinde formula.
Stability of Schwarzschild singularity in non-local gravity
Directory of Open Access Journals (Sweden)
Gianluca Calcagni
2017-10-01
Full Text Available In a previous work, it was shown that all Ricci-flat spacetimes are exact solutions for a large class of non-local gravitational theories. Here we prove that, for a subclass of non-local theories, the Schwarzschild singularity is stable under linear perturbations. Thus, non-locality may be not enough to cure all the singularities of general relativity. Finally, we show that the Schwarzschild solution can be generated by the gravitational collapse of a thin shell of radiation.
Scalar wave scattering from Schwarzschild black holes in modified gravity
Sibandze, Dan B; Maharaj, Sunil D; Nzioki, Anne Marie; Dunsby, Peter K S
2016-01-01
We consider the scattering of gravitational waves off a Schwarzschild Black Hole in $f(R)$ gravity. We find that, while the reflection and transmission coefficients for tensor waves are the same as in General Relativity, a larger fraction of scalar waves are reflected compared to what one obtains for tensors. This may provide a novel observational signature for fourth order gravity.
Quasinormal Modes of a Quantum-Corrected Schwarzschild Black ...
Indian Academy of Sciences (India)
Chunyan Wang
2017-11-27
Nov 27, 2017 ... Abstract. In this work, we investigate the electromagnetic perturbation around a quantum-corrected. Schwarzschild black hole. The complex frequencies of the quasinormal modes are evaluated by the third- order WKB approximation. The numerical results obtained showed that the complex frequencies ...
Entropy Spectrum of Modified Schwarzschild Black Hole via an ...
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... Abstract. The entropy spectrum of a modified Schwarzschild black hole in the gravity's rainbow are investigated. By utilizing an action invariance of the black hole with the help of Bohr–Sommerfield quantization rule, the entropy spectrum for the modified black hole are calculated. The result of the equally ...
Schwarzschild models of the Sculptor dSph galaxy
Breddels, M. A.; Helmi, A.; van den Bosch, R. C. E.; van de Ven, G.; Battaglia, G.; Reyle, C; Robin, A; Schultheis, M
We have developed a spherically symmetric dynamical model of a dwarf spheroidal galaxy using the Schwarzschild method. This type of modelling yields constraints both on the total mass distribution (e.g. enclosed mass and scale radius) as well as on the orbital structure of the system modelled (e.g.
Entropy Spectrum of Modified Schwarzschild Black Hole via an ...
Indian Academy of Sciences (India)
526. Cheng-Zhou Liu where f1 and f2 are two energy functions and by this the present modified. Schwarzschild spacetime is endowed with Planck scale modifications. For the non-charged spherically static symmetric spacetime, the only dynamic degree freedom can be written as qr, the Hamilton's equation ˙r = dr dτ. = dHτ.
Gorbatenko, M. V.; Neznamov, V. P.
2012-06-01
Quantum-mechanical analysis show physical non-equivalence of the Schwarzschild metric, interdicting classical particles transitions through the "Events horizon" and metrics, allowing the transitiion through the gravitational radius (Eddington-Finkelstein metric,Penlevi-Gullstrand, Finkelstein-Lemaitre metric, Kruskal metric). In the first case stationary states for Dirac particles with real energies spectrum are possible, while in the second case only complex eigenvalues for the Dirac particles energies spectrum are possible. The results obtained could lead to revission of some representations of the standart Cosmological model, related with the Universe's evolution and with collapsars interaction with encountering media.
Gravitational redshifts in electromagnetic bursts occurring near Schwarzschild horizon
Karkowski, J
2003-01-01
It was suggested earlier that the gravitational redshift formula can be invalid when the effect of the backscattering is strong. It is demonstrated here numerically, for an exemplary electromagnetic pulse that is (i) initially located very close to the horizon of a Schwarzschild black hole and (ii) strongly backscattered, that a mean frequency does not obey the standard redshift formula. Redshifts appear to depend on the frequency and there manifests a backscatter-induced blueshift in the outgoing radiation.
Dynamical scalar hair formation around a Schwarzschild black hole
Benkel, Robert; Sotiriou, Thomas P.; Witek, Helvi
2016-12-01
Scalar fields coupled to the Gauss-Bonnet invariant evade the known no-hair theorems and have nontrivial configurations around black holes. We focus on a scalar field that couples linearly to the Gauss-Bonnet invariant and hence exhibits shift symmetry. We study its dynamical evolution and the formation of scalar hair in a Schwarzschild background. We show that the evolution eventually settles to the known static hairy solutions in the appropriate limit.
Akcay, Sarp
2010-01-01
Fast, reliable orbital evolutions of compact objects around massive black holes will be needed as input for gravitational wave search algorithms in the data stream generated by the planned Laser Interferometer Space Antenna (LISA). Currently, the state of the art is a time-domain code by [Phys. Rev. D{\\bf 81}, 084021, (2010)] that computes the gravitational self-force on a point-particle in an eccentric orbit around a Schwarzschild black hole. Currently, time-domain codes take up to a few days to compute just one point in parameter space. In a series of articles, we advocate the use of a frequency-domain approach to the problem of gravitational self-force (GSF) with the ultimate goal of orbital evolution in mind. Here, we compute the GSF for a particle in a circular orbit in Schwarzschild spacetime. We solve the linearized Einstein equations for the metric perturbation in Lorenz gauge. Our frequency-domain code reproduces the time-domain results for the GSF up to $\\sim 1000$ times faster for small orbital rad...
Bort, Nancy
2005-01-01
One of the most important review topics the author teaches in middle school is the use of metric measurement for problem solving and inquiry. For many years, she had students measuring various objects around the room using the tools of metric measurement. She dutifully taught hypothesizing, data collecting, and drawing conclusions. It was…
Accretion processes in magnetically and tidally perturbed Schwarzschild black holes
Kovács, Zoltán; Vasúth, Mátyás
2011-01-01
We study the accretion process in the region of the Preston-Poisson space-time describing a Schwarzschild black hole perturbed by asymptotically uniform magnetic field and axisymmetric tidal structures. We find that the accretion disk shrinks and the marginally stable orbit shifts towards the black hole with the perturbation. The radiation intensity of the accretion disk increases, while the radius where radiation is maximal remains unchanged. The spectrum is blue-shifted. Finally, the conversion efficiency of accreting mass into radiation is decreased by both the magnetic and the tidal perturbations.
Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
Barack, Leor
2010-01-01
We present a numerical code for calculating the local gravitational self-force acting on a pointlike particle in a generic (bound) geodesic orbit around a Schwarzschild black hole. The calculation is carried out in the Lorenz gauge: For a given geodesic orbit, we decompose the Lorenz-gauge metric perturbation equations (sourced by the delta-function particle) into tensorial harmonics, and solve for each harmonic using numerical evolution in the time domain (in 1+1 dimensions). The physical self-force along the orbit is then obtained via mode-sum regularization. The total self-force contains a dissipative piece as well as a conservative piece, and we describe a simple method for disentangling these two pieces in a time-domain framework. The dissipative component is responsible for the loss of orbital energy and angular momentum through gravitational radiation; as a test of our code we demonstrate that the work done by the dissipative component of the computed force is precisely balanced by the asymptotic fluxe...
Transformation Groups for a Schwarzschild-Type Geometry in f(R Gravity
Directory of Open Access Journals (Sweden)
Emre Dil
2016-01-01
Full Text Available We know that the Lorentz transformations are special relativistic coordinate transformations between inertial frames. What happens if we would like to find the coordinate transformations between noninertial reference frames? Noninertial frames are known to be accelerated frames with respect to an inertial frame. Therefore these should be considered in the framework of general relativity or its modified versions. We assume that the inertial frames are flat space-times and noninertial frames are curved space-times; then we investigate the deformation and coordinate transformation groups between a flat space-time and a curved space-time which is curved by a Schwarzschild-type black hole, in the framework of f(R gravity. We firstly study the deformation transformation groups by relating the metrics of the flat and curved space-times in spherical coordinates; after the deformation transformations we concentrate on the coordinate transformations. Later on, we investigate the same deformation and coordinate transformations in Cartesian coordinates. Finally we obtain two different sets of transformation groups for the spherical and Cartesian coordinates.
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
Gravitating discs around a Schwarzschild black hole: III
Semerak, O
2003-01-01
The properties of exact relativistic spacetimes of a Schwarzschild black hole surrounded by annular thin discs obtained by inversion of the first ten members of the counter-rotating Morgan-Morgan class are studied. Effects of the discs' own gravity are compared, in particular the induced deformation of the horizon and changes in the features of free circular motion in the disc plane. Within the plane of the two relevant parameters of the composite solution (relative disc mass and its inner radius), regions are specified where the discs satisfy basic physical requirements (energetic conditions and possibility, subluminality and stability of circular geodesics in terms of which they are interpreted). In contrast to the first inverted Morgan-Morgan disc, treated in previous papers, the 'higher' members of the family have to be placed farther and farther from the hole in order to remain stable when their mass is increased from zero.
Schwarzschild models of the Sculptor dSph galaxy
Directory of Open Access Journals (Sweden)
van de Ven G.
2012-02-01
Full Text Available We have developed a spherically symmetric dynamical model of a dwarf spheroidal galaxy using the Schwarzschild method. This type of modelling yields constraints both on the total mass distribution (e.g. enclosed mass and scale radius as well as on the orbital structure of the system modelled (e.g. velocity anisotropy. Therefore not only can we derive the dark matter content of these systems, but also explore possible formation scenarios. Here we present preliminary results for the Sculptor dSph. We find that the mass of Sculptor within 1 kpc is 8.5 × 107±0.05 M๏, its anisotropy profile is tangentially biased and slightly more isotropic near the center. For an NFW profile, the preferred concentration (~15 is compatible with cosmological models. Very cuspy density profiles (steeper than NFW are strongly disfavoured for Sculptor.
The Compton-Schwarzschild correspondence from extended de Broglie relations
Energy Technology Data Exchange (ETDEWEB)
Lake, Matthew J. [The Institute for Fundamental Study, “The Tah Poe Academia Institute' ,Naresuan University, Phitsanulok 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education,Bangkok 10400 (Thailand); Carr, Bernard [School of Physics and Astronomy, Queen Mary University of London,Mile End Road, London E1 4NS (United Kingdom)
2015-11-17
The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial gravity. In a mass-radius diagram, the two lines intersect near the Planck point (l{sub P},m{sub P}), where quantum gravity effects become significant. Since canonical (non-gravitational) quantum mechanics is based on the concept of wave-particle duality, encapsulated in the de Broglie relations, these relations should break down near (l{sub P},m{sub P}). It is unclear what physical interpretation can be given to quantum particles with energy E≫m{sub P}c{sup 2}, since they correspond to wavelengths λ≪l{sub P} or time periods τ≪t{sub P} in the standard theory. We therefore propose a correction to the standard de Broglie relations, which gives rise to a modified Schrödinger equation and a modified expression for the Compton wavelength, which may be extended into the region E≫m{sub P}c{sup 2}. For the proposed modification, we recover the expression for the Schwarzschild radius for E≫m{sub P}c{sup 2} and the usual Compton formula for E≪m{sub P}c{sup 2}. The sign of the inequality obtained from the uncertainty principle reverses at m≈m{sub P}, so that the Compton wavelength and event horizon size may be interpreted as minimum and maximum radii, respectively. We interpret the additional terms in the modified de Broglie relations as representing the self-gravitation of the wave packet.
The stable problem of the black-hole connected region in the Schwarzschild black hole
Tian, Guihua
2005-01-01
The stability of the Schwarzschild black hole is studied. Using the Painlev\\'{e} coordinate, our region can be defined as the black-hole-connected region(r>2m, see text) of the Schwarzschild black hole or the white-hole-connected region(r>2m, see text) of the Schwarzschild black hole. We study the stable problems of the black-hole-connected region. The conclusions are: (1) in the black-hole-connected region, the initially regular perturbation fields must have real frequency or complex frequen...
Null and timelike geodesics of the Schwarzschild black hole with string cloud background
Batool, Mahwish; Hussain, Ibrar
The trajectories of the time-like and null geodesics for radial and circular motion of the Schwarzschild black hole with string cloud background are investigated and compared with the Schwarzschild case without string clouds. It is found that in the presence of the string cloud parameter, the radius of the orbits is larger than the radius of the orbits in the case of the Schwarzschild black hole without string cloud parameter. Effective potential is calculated and it is observed that as the value of string cloud parameter increases the particle can more easily escape to infinity. Stability of the circular orbits is also discussed.
Transformation optics that mimics the system outside a Schwarzschild black hole
Chen, Huanyang; Miao, Rong-Xin; Li, Miao
2009-01-01
We applied the transformation optics to mimic a black hole of Schwarzschild form. Similar properties of photon sphere were also found numerically for the metamaterial black hole. Several reduced versions of the black hole systems were proposed for easier implementations.
The Compton-Schwarzschild correspondence from extended de Broglie relations
Lake, Matthew J
2015-01-01
The Compton wavelength gives the minimum radius within which the mass of a particle may be localized due to quantum effects, while the Schwarzschild radius gives the maximum radius within which the mass of a black hole may be localized due to classial gravity. In a mass-radius diagram, the two lines intersect near the Planck point $(l_P,m_P)$, where quantum gravity effects become significant. Since canonical (non-gravitational) quantum mechanics is based on the concept of wave-particle duality, encapsulated in the de Broglie relations, these relations should break down near $(l_P,m_P)$. It is unclear what physical interpretation can be given to quantum particles with energy $E \\gg m_Pc^2 $, since they correspond to wavelengths $\\lambda \\ll l_P$ or time periods $T \\ll t_P$ in the standard theory. We therefore propose a correction to the standard de Broglie relations, which gives rise to a modified Schr{\\" o}dinger equation and a modified expression for the Compton wavelength, which may be extended into the reg...
Features and stability analysis of non-Schwarzschild black hole in quadratic gravity
Energy Technology Data Exchange (ETDEWEB)
Cai, Yi-Fu [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy,University of Science and Technology of China, Chinese Academy of Sciences,Hefei, Anhui, 230026 (China); Department of Physics, McGill University,Montréal, Quebec, H3A 2T8 (Canada); School of Physical Sciences, University of Science and Technology of China,Hefei, Anhui, 230026 (China); Zhang, Hezi [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy,University of Science and Technology of China, Chinese Academy of Sciences,Hefei, Anhui, 230026 (China); School of Physical Sciences, University of Science and Technology of China,Hefei, Anhui, 230026 (China); Liu, Junyu [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy,University of Science and Technology of China, Chinese Academy of Sciences,Hefei, Anhui, 230026 (China); School of the Gifted Young, University of Science and Technology of China,Hefei, Anhui, 230026 (China); Cheng, Gong [CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy,University of Science and Technology of China, Chinese Academy of Sciences,Hefei, Anhui, 230026 (China); School of Physical Sciences, University of Science and Technology of China,Hefei, Anhui, 230026 (China); Wang, Min [Faculty of Materials and Energy, Southwest University,Chongqing, 400715 (China); CAS Key Laboratory for Research in Galaxies and Cosmology, Department of Astronomy,University of Science and Technology of China, Chinese Academy of Sciences,Hefei, Anhui, 230026 (China)
2016-01-19
Black holes are found to exist in gravitational theories with the presence of quadratic curvature terms and behave differently from the Schwarzschild solution. We present an exhaustive analysis for determining the quasinormal modes of a test scalar field propagating in a new class of black hole backgrounds in the case of pure Einstein-Weyl gravity. Our result shows that the field decay of quasinormal modes in such a non-Schwarzschild black hole behaves similarly to the Schwarzschild one, but the decay slope becomes much smoother due to the appearance of the Weyl tensor square in the background theory. We also analyze the frequencies of the quasinormal modes in order to characterize the properties of new back holes, and thus, if these modes can be the source of gravitational waves, the underlying theories may be testable in future gravitational wave experiments. We briefly comment on the issue of quantum (in)stability in this theory at linear order.
Khayrul, Hasan, M.; Sultana, Kausari; Shahjalal, Md.
2017-10-01
We probe the plausibility of weak equivalence principle for a circular motion at the radial distance of photon sphere of the Schwarzschild?(Anti-)de Sitter black hole. We switch the static Schwarzschild?(Anti-)de Sitter space-time to rotational by means of the transformation with constant angular velocity. The fiducial observers revolving along the trajectory of photon orbit of the Schwarzschild?(Anti-)de Sitter black hole are supposed to agree on the result of any physical experiment when their angular velocities are uniform, which give rise to the constancy in their accelerations, meaning the observers are equivalent. Our study, in contrast, finds that the observers do not measure similar results, claiming the invalidity of the principle of weak equivalence. However, the aim of our work is not to defy the principle absolutely, rather we focus our attention on the very cause for which the dispute arises, namely the rotational motion.
Alabama State Dept. of Education, Montgomery. Div. of Instructional Services.
Topics covered in the first part of this document include eight advantages of the metric system; a summary of metric instruction; the International System of Units (SI) style and usage; metric decimal tables; the metric system; and conversion tables. An alphabetized list of organizations which market metric materials for educators is provided with…
Effect of the Kerr Metric on Photosperic Radius Expansion in X Ray Burst
Kalita, S.; Barman, A.
2017-12-01
The main objective of this paper is to study general relativistic effects on the photospheric radius expansion during an X-ray burst. We examine how the Kerr metric causes a shift in the effective temperature and radiation flux with respect to the Schwarzschild values during mass accretion onto a neutron star or a black hole resulting in the X-ray burst. The spin of the compact object is used up to the maximal Kerr limit χ = 0.99 with different latitudes of accretion emission. The amplitude of temperature shift relative to the Schwarzschild case is found to be δ T/ T ≈ - (10-3 - 10-4) for the range χ = 0.1 - 0.99 at latitudes θ = 0o , 30o, 45o and 88o. The ratio of emission flux in the Kerr metric to that in the Schwarzschild metric, F(K)/F(S), is found to be less than unity. It goes up to a maximum of 0.9 for the lowest nonzero value of the spin parameter (i.e., 0.1). For the maximal Kerr limit, χ = 0.99 , it saturates near 0.8. This effect is more prominent towards the pole. This reduction in temperature and flux is found to be consistent with the absence of photospheric radius expansion in the X Ray burst LMXB 4U 1608-52, observed by NuSTAR. Although this is not uniquely ascribed to the metric, it is believed that the spacetime metric effect in the burst phenomena can be used as a probe for testing general relativity. Also, the shift in temperature or the radiation flux might have an observable signature in the element synthesis processes in such environments.
Interactive Visualization of a Thin Disc around a Schwarzschild Black Hole
Muller, Thomas; Frauendiener, Jorg
2012-01-01
In a first course in general relativity, the Schwarzschild spacetime is the most discussed analytic solution to Einstein's field equations. Unfortunately, there is rarely enough time to study the optical consequences of the bending of light for some advanced examples. In this paper, we present how the visual appearance of a thin disc around a…
Asymptotic description of a test particle around a Schwarzschild black hole
Rosales-Vera, Marco
2018-03-01
In this paper, the movement of a test particle around a Schwarzschild black hole is revisited. Using matched asymptotic expansions, approximate analytical expressions for the orbit of the test particle in the case of large eccentricity are found. The asymptotic solutions are compared with numerical and analytical results.
Rayimbaev, J. R.
2016-09-01
The motion of a magnetized particle orbiting around non-Schwarzschild black hole immersed in an external uniform magnetic field is considered. The influence of deformation parameter h to effective potential of the radial motion of the magnetized particle around non-Schwarzschild black hole using Hamilton-Jacobi formalism is studied. We have obtained numerical values of area Δ ρ where magnetized particles can move which is expanding (narrowing) due to the effect of the negative (positive) deformation. Finally, we have studied the collision of two particles (magnetized-neutral, magnetized-magnetized, magnetized-charged) in non-Schwarzschild spacetime and got the center-of-mass energy (E_{c.m}) for the particles. Moreover, we have found the capture radius (r_{cap}) - the distance from the central object to the point where particles collide and fall down to the central compact object. It is shown that non-Schwarzschild black holes could also act as particle accelerators with arbitrarily high center-of-mass energy.
Resonant scattering of light in a near-black-hole metric
Energy Technology Data Exchange (ETDEWEB)
Stadnik, Y.V.; Gossel, G.H.; Flambaum, V.V.; Berengut, J.C. [University of New South Wales, School of Physics, Sydney (Australia)
2013-11-15
We show that low-energy photon scattering from a body with radius R slightly larger than its Schwarzschild radius r{sub s} resembles black-hole absorption. This absorption occurs via capture resulting in one of the many long-lived, densely packed resonances that populate the continuum. The lifetimes and density of these meta-stable states tend to infinity in the limit r{sub s} {yields}R. We determine the energy-averaged cross section for particle capture into these resonances and show that it is equal to the absorption cross section for a Schwarzschild black hole. Thus a non-singular static metric may trap photons for arbitrarily long times, making it appear completely 'black' before the actual formation of a black hole. (orig.)
Weiss, Ittay
2012-01-01
A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and equivalent, axiomatization of metric space is given which is then generalized from a fresh point of view. Naturally arising examples from metric geometry are presented.
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.
Directory of Open Access Journals (Sweden)
Madjid Mirzavaziri
2010-11-01
Full Text Available In this paper we introduce the notion of an ℱ-metric, as a function valued distance mapping, on a set X and we investigate the theory of ℱ-metrics paces. We show that every metric space may be viewed as an F-metric space and every ℱ-metric space (X,δ can be regarded as a topological space (X,τδ. In addition, we prove that the category of the so-called extended F-metric spaces properly contains the category of metric spaces. We also introduce the concept of an `ℱ-metric space as a completion of an ℱ-metric space and, as an application to topology, we prove that each normal topological space is `ℱ-metrizable.
da Rocha, R.; Sobreiro, R. F.; Tomaz, A. A.
2017-12-01
Sound waves on a fluid stream, in a de Laval nozzle, are shown to correspond to quasinormal modes emitted by black holes that are physical solutions in a quadratic curvature gravity with cosmological constant. Sound waves patterns in transsonic regimes at a laboratory are employed here to provide experimental data regarding generalized theories of gravity, comprised by the exact de Sitter-like solution and a perturbative solution around the Schwarzschild-de Sitter standard solution as well. Using the classical tests of General Relativity to bound free parameters in these solutions, acoustic perturbations on fluid flows in nozzles are then regarded, to study quasinormal modes of these black holes solutions, providing deviations of the de Laval nozzle cross-sectional area, when compared to the Schwarzschild solution. The fluid sonic point in the nozzle, for sound waves in the fluid, is shown to implement the acoustic event horizon corresponding to quasinormal modes.
Slowly decaying resonances of massive scalar fields around Schwarzschild-de Sitter black holes
Toshmatov, Bobir; Stuchlík, Zdeněk
2017-07-01
We study in special limiting cases quasinormal modes of massive scalar fields in the Schwarzschild-de Sitter black hole backgrounds. We determine the lower limit on the mass parameter of the scalar field that allows the waves with quasinormal frequencies to propagate to infinity, showing that it depends on the spacetime parameters only. Then we discuss in the large multipole number limit quasinormal modes, whose frequencies can be directly related to the unstable circular photon geodesics. In the large scalar mass approximation, we demonstrate the new interesting phenomenon of slowly decaying resonances, that are strongly related to the maximum of the effective potential of the massive scalar field, which is located at the static radius of the Schwarzschild-de Sitter spacetimes, where the cosmic repulsion is just balanced by the black hole attraction.
Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity
Energy Technology Data Exchange (ETDEWEB)
Sibandze, Dan B.; Goswami, Rituparno; Maharaj, Sunil D.; Nzioki, Anne Marie [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, Private Bag X54001, Durban (South Africa); Dunsby, Peter K.S. [University of Cape Town, Department of Mathematics and Applied Mathematics and ACGC, Cape Town (South Africa)
2017-06-15
It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures of the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this paper we consider the perturbations of Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equation that governs these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Feng, Z.W.; Zu, X.T. [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Li, H.L. [University of Electronic Science and Technology of China, School of Physical Electronics, Chengdu (China); Shenyang Normal University, College of Physics Science and Technology, Shenyang (China); Yang, S.Z. [China West Normal University, Physics and Space Science College, Nanchong (China)
2016-04-15
We investigate the thermodynamics of Schwarzschild-Tangherlini black hole in the context of the generalized uncertainty principle (GUP). The corrections to the Hawking temperature, entropy and the heat capacity are obtained via the modified Hamilton-Jacobi equation. These modifications show that the GUP changes the evolution of the Schwarzschild-Tangherlini black hole. Specially, the GUP effect becomes susceptible when the radius or mass of the black hole approaches the order of Planck scale, it stops radiating and leads to a black hole remnant. Meanwhile, the Planck scale remnant can be confirmed through the analysis of the heat capacity. Those phenomena imply that the GUP may give a way to solve the information paradox. Besides, we also investigate the possibilities to observe the black hole at the Large Hadron Collider (LHC), and the results demonstrate that the black hole cannot be produced in the recent LHC. (orig.)
Ridho, Almizan
2017-01-01
130801028 Jika suatu bintang masif dengan massa M berbentuk bola, maka kita dapat menghitung radius bola yang mengungkung massa M tersebut. Kemudian untuk mengubah bintang masif tersebut menjadi lubang hitam kita harus mengubah radius ini menjadi sedemikian rupa. Radius yang menjadikan suatu bintang masif menjadi lubang hitam inilah yang kemudian dinamakan Radius Schwarzschild. Dengan demikian, kita juga dapat mendefinisikan lubang hitam sebagai suatu bintang masif bermassa M yang seluruh ...
Formation of the remnant close to Planck scale and the Schwarzschild black hole with global monopole
Li, Hui-Ling; Chen, Shuai-Ru
2017-10-01
In this paper, we use the generalized uncertainty principle (GUP) and quantum tunneling method to research the formation of the remnant from a Schwarzschild black hole with global monopole. Based on the corrected Hamilton-Jacobi equation, the corrections to the Hawking temperature, heat capacity and entropy are calculated. We not only find the remnant close to Planck scale by employing GUP, but also research the thermodynamic stability of the black hole remnant according to the phase transition and heat capacity.
Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
Damour, Thibault
2009-01-01
We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by ...
Real Scalar Field Scattering with Polynomial Approximation around Schwarzschild-de Sitter Black-hole
Liu, Molin; Liu, Hongya; Zhang, Jingfei; Yu, Fei
2008-01-01
As one of the fitting methods, the polynomial approximation is effective to process sophisticated problem. In this paper, we employ this approach to handle the scattering of scalar field around the Schwarzschild-de Sitter black-hole. The complex relationship between tortoise coordinate and radial coordinate is replaced by the approximate polynomial. The Schr$\\ddot{o}$dinger-like equation, the real boundary conditions and the polynomial approximation construct a full Sturm-Liouville type probl...
Wang, Mengjie; Herdeiro, Carlos; Jing, Jiliang
2017-11-01
We study Dirac quasinormal modes of Schwarzschild-anti-de Sitter (Schwarzschild-AdS) black holes, following the generic principle for allowed boundary conditions proposed in [M. Wang, C. Herdeiro, and M. O. P. Sampaio, Phys. Rev. D 92, 124006 (2015)., 10.1103/PhysRevD.92.124006]. After deriving the equations of motion for Dirac fields on the aforementioned background, we impose vanishing energy flux boundary conditions to solve these equations. We find a set of two Robin boundary conditions are allowed. These two boundary conditions are used to calculate Dirac normal modes on empty AdS and quasinormal modes on Schwarzschild-AdS black holes. In the former case, we recover the known normal modes of empty AdS; in the latter case, the two sets of Robin boundary conditions lead to two different branches of quasinormal modes. The impact on these modes of the black hole size, the angular momentum quantum number and the overtone number are discussed. Our results show that vanishing energy flux boundary conditions are a robust principle, applicable not only to bosonic fields but also to fermionic fields.
The non-integrability of the Zipoy-Voorhees metric
Lukes-Gerakopoulos, Georgios
2012-01-01
The low frequency gravitational wave detectors like eLISA/NGO will give us the opportunity to test whether the supermassive compact objects lying at the centers of galaxies are indeed Kerr black holes. A way to do such a test is to compare the gravitational wave signals with templates of perturbed black hole spacetimes, the so-called bumpy black hole spacetimes. The Zipoy-Voorhees (ZV) spacetime (known also as the $\\gamma$ spacetime) can be included in the bumpy black hole family, because it can be considered as a perturbation of the Schwarzschild spacetime background. Several authors have suggested that the ZV metric corresponds to an integrable system. Contrary to this integrability conjecture, in the present article it is shown by numerical examples that in general ZV belongs to the family of non-integrable systems.
Time-domain metric reconstruction for self-force applications
Barack, Leor; Giudice, Paco
2017-05-01
We present a new method for calculation of the gravitational self-force (GSF) in Kerr geometry, based on a time-domain reconstruction of the metric perturbation from curvature scalars. In this approach, the GSF is computed directly from a certain scalarlike self-potential that satisfies the time-domain Teukolsky equation on the Kerr background. The approach is computationally much cheaper than existing time-domain methods, which rely on a direct integration of the linearized Einstein's equations and are impaired by mode instabilities. At the same time, it retains the utility and flexibility of a time-domain treatment, allowing calculations for any type of orbit (including highly eccentric or unbound ones) and the possibility of self-consistently evolving the orbit under the effect of the GSF. Here we formulate our method, and present a first numerical application, for circular geodesic orbits in Schwarzschild geometry. We discuss further applications.
An explanation of the 'Pioneer effect' based on quasi-metric relativity
Østvang, D
2002-01-01
According to the so-called quasi-metric framework developed elsewhere, the cosmic expansion applies directly to gravitationally bound systems. This prediction has a number of observable consequences, none of which is in conflict with observation. In this paper, we compare test particle motion in the non-static gravitational field outside a spherically symmetric source (as predicted by a quasi-metric theory of gravity) to test particle motion in the Schwarzschild geometry. It is found that if one incorrectly uses the Schwarzschild geometry (to the relevant accuracy) to represent the non-static quasi-metric model, the largest errors result from the mismodelling of null paths. One consequence of this is that, using electromagnetic signals to track the motion of a non-relativistic particle results in the illusion that the particle is influenced by an anomalous acceleration of size cH (where H is the Hubble parameter) directed towards the observer. This result naturally explains the apparently anomalous force acti...
Metric Education and the Metrics Debate: A Perspective.
Chappelet, Jean Loup
A short history of the use of the metric system is given. The role of education in metrication is discussed. The metric activities of three groups of metrics advocates, the business community, private groups, and government agencies, are described. Arguments advanced by metric opponents are also included. The author compares the metric debate with…
Software Metrics Capability Evaluation Guide
National Research Council Canada - National Science Library
Budlong, Faye
1995-01-01
...: disseminating information regarding the U.S. Air Force Policy on software metrics, providing metrics information to the public through CrossTalk, conducting customer workshops in software metrics, guiding metrics technology adoption programs...
Metric diffusion along foliations
Walczak, Szymon M
2017-01-01
Up-to-date research in metric diffusion along compact foliations is presented in this book. Beginning with fundamentals from the optimal transportation theory and the theory of foliations; this book moves on to cover Wasserstein distance, Kantorovich Duality Theorem, and the metrization of the weak topology by the Wasserstein distance. Metric diffusion is defined, the topology of the metric space is studied and the limits of diffused metrics along compact foliations are discussed. Essentials on foliations, holonomy, heat diffusion, and compact foliations are detailed and vital technical lemmas are proved to aide understanding. Graduate students and researchers in geometry, topology and dynamics of foliations and laminations will find this supplement useful as it presents facts about the metric diffusion along non-compact foliation and provides a full description of the limit for metrics diffused along foliation with at least one compact leaf on the two dimensions.
Metric Independence of Vacuum and Force-Free Electromagnetic Fields.
Harte, Abraham I
2017-04-07
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well known to also be solutions in all spacetimes with conformally related metrics. This provides a sense in which electromagnetism alone cannot be used to measure certain aspects of geometry. We show that there is actually much more which cannot be so measured; relatively little of a spacetime's geometry is in fact imprinted in any particular electromagnetic field. This is demonstrated by finding a much larger class of metric transformations-involving five free functions-which preserve Maxwell solutions both in vacuum, without local currents, and also for the force-free electrodynamics associated with a tenuous plasma. One consequence of this is that many of the exact force-free fields which have previously been found around Schwarzschild and Kerr black holes are also solutions in appropriately identified flat backgrounds. As a more direct application, we use our metric transformations to write down a large class of electromagnetic waves which remain unchanged by a large class of gravitational waves propagating "in the same direction."
Metric Independence of Vacuum and Force-Free Electromagnetic Fields
Harte, Abraham I.
2017-04-01
Electromagnetic fields which solve the vacuum Maxwell equations in one spacetime are well known to also be solutions in all spacetimes with conformally related metrics. This provides a sense in which electromagnetism alone cannot be used to measure certain aspects of geometry. We show that there is actually much more which cannot be so measured; relatively little of a spacetime's geometry is in fact imprinted in any particular electromagnetic field. This is demonstrated by finding a much larger class of metric transformations—involving five free functions—which preserve Maxwell solutions both in vacuum, without local currents, and also for the force-free electrodynamics associated with a tenuous plasma. One consequence of this is that many of the exact force-free fields which have previously been found around Schwarzschild and Kerr black holes are also solutions in appropriately identified flat backgrounds. As a more direct application, we use our metric transformations to write down a large class of electromagnetic waves which remain unchanged by a large class of gravitational waves propagating "in the same direction."
Extended DBI massive gravity with generalized fiducial metric
Energy Technology Data Exchange (ETDEWEB)
Chullaphan, Tossaporn [The Institute for Fundamental Study, Naresuan University,Phitsanulok 65000 (Thailand); Department of Physics, Faculty of Science, Udon Thani Rajabhat University,Udon Thani 41000 (Thailand); Tannukij, Lunchakorn [Department of Physics, Faculty of Science, Mahidol University,Bangkok 10400 (Thailand); Wongjun, Pitayuth [The Institute for Fundamental Study, Naresuan University,Phitsanulok 65000 (Thailand); Thailand Center of Excellence in Physics, Ministry of Education,Bangkok 10400 (Thailand)
2015-06-05
We consider an extended model of DBI massive gravity by generalizing the fiducial metric to be an induced metric on the brane corresponding to a domain wall moving in five-dimensional Schwarzschild-Anti-de Sitter spacetime. The model admits all solutions of FLRW metric including flat, closed and open geometries while the original one does not. The background solutions can be divided into two branches namely self-accelerating branch and normal branch. For the self-accelerating branch, the graviton mass plays the role of cosmological constant to drive the late-time acceleration of the universe. It is found that the number degrees of freedom of gravitational sector is not correct similar to the original DBI massive gravity. There are only two propagating degrees of freedom from tensor modes. For normal branch, we restrict our attention to a particular class of the solutions which provides an accelerated expansion of the universe. It is found that the number of degrees of freedom in the model is correct. However, at least one of them is ghost degree of freedom which always present at small scale implying that the theory is not stable.
Calcaterra, Craig; Boldt, Axel; Green, Michael; Bleecker, David
2002-01-01
Coordinate systems are defined on general metric spaces with the purpose of generalizing vector fields on a manifold. Conversion formulae are available between metric and Cartesian coordinates on a Hilbert space. Nagumo's Invariance Theorem is invoked to prove the analogue of the classical Cauchy-Lipschitz Theorem for vector fields on a locally compact coordinatized space. A metric space version of Nagumo's Theorem is one consequence. Examples are given throughout.
-Metric Space: A Generalization
Directory of Open Access Journals (Sweden)
Farshid Khojasteh
2013-01-01
Full Text Available We introduce the notion of -metric as a generalization of a metric by replacing the triangle inequality with a more generalized inequality. We investigate the topology of the spaces induced by a -metric and present some essential properties of it. Further, we give characterization of well-known fixed point theorems, such as the Banach and Caristi types in the context of such spaces.
Software Metrics: Measuring Haskell
Ryder, Chris; Thompson, Simon
2005-01-01
Software metrics have been used in software engineering as a mechanism for assessing code quality and for targeting software development activities, such as testing or refactoring, at areas of a program that will most benefit from them. Haskell has many tools for software engineering, such as testing, debugging and refactoring tools, but software metrics have mostly been neglected. The work presented in this paper identifies a collection of software metrics for use with Haskell programs. Thes...
Intuitionistic fuzzy metric spaces
Energy Technology Data Exchange (ETDEWEB)
Park, Jin Han E-mail: jihpark@pknu.ac.kr
2004-12-01
Using the idea of intuitionistic fuzzy set due to Atanassov [Intuitionistic fuzzy sets. in: V. Sgurev (Ed.), VII ITKR's Session, Sofia June, 1983; Fuzzy Sets Syst. 20 (1986) 87], we define the notion of intuitionistic fuzzy metric spaces as a natural generalization of fuzzy metric spaces due to George and Veeramani [Fuzzy Sets Syst. 64 (1994) 395] and prove some known results of metric spaces including Baire's theorem and the Uniform limit theorem for intuitionistic fuzzy metric spaces.
Prognostic Performance Metrics
National Aeronautics and Space Administration — This chapter presents several performance metrics for offline evaluation of prognostics algorithms. A brief overview of different methods employed for performance...
Self-consistent orbital evolution of a particle around a Schwarzschild black hole.
Diener, Peter; Vega, Ian; Wardell, Barry; Detweiler, Steven
2012-05-11
The motion of a charged particle is influenced by the self-force arising from the particle's interaction with its own field. In a curved spacetime, this self-force depends on the entire past history of the particle and is difficult to evaluate. As a result, all existing self-force evaluations in curved spacetime are for particles moving along a fixed trajectory. Here, for the first time, we overcome this long-standing limitation and present fully self-consistent orbits and waveforms of a scalar charged particle around a Schwarzschild black hole.
Quasinormal Modes of a Quantum-Corrected Schwarzschild Black Hole for Electromagnetic Perturbation
Wang, Chunyan; Gao, Yajun; Ding, Wenbo; Yu, Qingxu
2017-12-01
In this work, we investigate the electromagnetic perturbation around a quantum-corrected Schwarzschild black hole. The complex frequencies of the quasinormal modes are evaluated by the third-order WKB approximation. The numerical results obtained showed that the complex frequencies depend on the quantum correction parameter a of a black hole, which the real parts and the magnitudes of the imaginary parts of quasinormal modes decrease with the increase in factor a. These conclusions show that the electromagnetic perturbation around the black hole oscillate and damp more slowly owing to the presence of the quantum correction parameter.
Barack, Leor; Sago, Norichika
2009-05-15
The innermost stable circular orbit (ISCO) of a test particle around a Schwarzschild black hole of mass M has (areal) radius r_{isco}=6MG/c;{2}. If the particle is endowed with mass micro(radius and frequency, at leading order in the mass ratio micro/M. We obtain, in the Lorenz gauge, Deltar_{isco}=-3.269(+/-0.003)microG/c;{2} and DeltaOmega_{isco}/Omega_{isco}=0.4870(+/-0.0006)micro/M. We discuss the implications of our result within the context of the extreme-mass-ratio binary inspiral problem.
The Metric Lens : Visualizing Metrics and Structure on Software Diagrams
Byelas, Heorhiy; Telea, Alexandru; Hassan, AE; Zaidman, A; DiPenta, M
2008-01-01
We present the metric lens, a new visualization of method-level code metrics atop UML class diagrams, which allows performing metric-metric and metric-structure correlations on large diagrams. Me demonstrate air interactive visualization tool in which users can quickly specify a wide palette of
Buliga, Marius
2011-01-01
This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into another. See arXiv:1103.6007 for the context.
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of cosmetology students, this instructional package on cosmetology is part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational terminology, measurement terms, and tools currently in use. Each of the…
Generalized bisimulation metrics
Chatzikokolakis, K.; Gebler, D.; Palamidessi, C.
2014-01-01
The bisimilarity pseudometric based on the Kantorovich lifting is one of the most popular metrics for probabilistic processes proposed in the literature. However, its application in verification is limited to linear properties. We propose a generalization of this metric which allows to deal with a
Surveillance Metrics Sensitivity Study
Energy Technology Data Exchange (ETDEWEB)
Bierbaum, R; Hamada, M; Robertson, A
2011-11-01
In September of 2009, a Tri-Lab team was formed to develop a set of metrics relating to the NNSA nuclear weapon surveillance program. The purpose of the metrics was to develop a more quantitative and/or qualitative metric(s) describing the results of realized or non-realized surveillance activities on our confidence in reporting reliability and assessing the stockpile. As a part of this effort, a statistical sub-team investigated various techniques and developed a complementary set of statistical metrics that could serve as a foundation for characterizing aspects of meeting the surveillance program objectives. The metrics are a combination of tolerance limit calculations and power calculations, intending to answer level-of-confidence type questions with respect to the ability to detect certain undesirable behaviors (catastrophic defects, margin insufficiency defects, and deviations from a model). Note that the metrics are not intended to gauge product performance but instead the adequacy of surveillance. This report gives a short description of four metrics types that were explored and the results of a sensitivity study conducted to investigate their behavior for various inputs. The results of the sensitivity study can be used to set the risk parameters that specify the level of stockpile problem that the surveillance program should be addressing.
Surveillance metrics sensitivity study.
Energy Technology Data Exchange (ETDEWEB)
Hamada, Michael S. (Los Alamos National Laboratory); Bierbaum, Rene Lynn; Robertson, Alix A. (Lawrence Livermore Laboratory)
2011-09-01
In September of 2009, a Tri-Lab team was formed to develop a set of metrics relating to the NNSA nuclear weapon surveillance program. The purpose of the metrics was to develop a more quantitative and/or qualitative metric(s) describing the results of realized or non-realized surveillance activities on our confidence in reporting reliability and assessing the stockpile. As a part of this effort, a statistical sub-team investigated various techniques and developed a complementary set of statistical metrics that could serve as a foundation for characterizing aspects of meeting the surveillance program objectives. The metrics are a combination of tolerance limit calculations and power calculations, intending to answer level-of-confidence type questions with respect to the ability to detect certain undesirable behaviors (catastrophic defects, margin insufficiency defects, and deviations from a model). Note that the metrics are not intended to gauge product performance but instead the adequacy of surveillance. This report gives a short description of four metrics types that were explored and the results of a sensitivity study conducted to investigate their behavior for various inputs. The results of the sensitivity study can be used to set the risk parameters that specify the level of stockpile problem that the surveillance program should be addressing.
Privacy Metrics and Boundaries
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
Cooper, Gloria S., Ed.; Magisos, Joel H., Ed.
Designed to meet the job-related metric measurement needs of students interested in transportation, this instructional package is one of five for the marketing and distribution cluster, part of a set of 55 packages for metric instruction in different occupations. The package is intended for students who already know the occupational terminology,…
Mishra, Subodha
2007-01-01
Using a single particle density distribution for a system of self-gravitating particles which ultimately forms a black hole, we from a condensed matter point of view derive the Schwarzschild radius and by including the quantum mechanical exchange energy we find a small correction to the Schwarzschild radius, which we designate as the skin of the black hole.
Rousselle, J.; Byrum, K.; Cameron, R.; Connaughton, V.; Errando, M.; Guarino, V.; Humensky, T.; Jenke, P.; Kieda, D.; Mukherjee, R.; Nieto, D.; Okumura, A.; Petrashyk, A; Vassiliev, V.
2015-01-01
We present the design and the status of procurement of the optical system of the prototype Schwarzschild-Couder telescope (pSCT), for which construction is scheduled to begin in fall at the Fred Lawrence Whipple Observatory in southern Arizona, USA. The Schwarzschild-Couder telescope is a candidate for the medium-sized telescopes of the Cherenkov Telescope Array, which utilizes imaging atmospheric Cherenkov techniques to observe gamma rays in the energy range of 60Gev-60TeV. The pSCT novel ap...
Papadopoulos, Demetrios B; Kokkotas, Kostas D; Stergioulas, Nikolaos
2015-01-01
We obtain an approximate solution for the motion of a charged particle around a Schwarzschild black hole immersed in a weak dipolar magnetic field. We focus on eccentric bound orbits in the equatorial plane of the Schwarzschild black hole and derive an analytic expression for the spectral distribution of the electromagnetic emission from a charged particle on such an orbit. Two sets of harmonic contributions appear, with specific frequency spacing. The expression can be written in compact form, if it is truncated up to the lowest order harmonic contributions.
Holographic Spherically Symmetric Metrics
Petri, Michael
The holographic principle (HP) conjectures, that the maximum number of degrees of freedom of any realistic physical system is proportional to the system's boundary area. The HP has its roots in the study of black holes. It has recently been applied to cosmological solutions. In this article we apply the HP to spherically symmetric static space-times. We find that any regular spherically symmetric object saturating the HP is subject to tight constraints on the (interior) metric, energy-density, temperature and entropy-density. Whenever gravity can be described by a metric theory, gravity is macroscopically scale invariant and the laws of thermodynamics hold locally and globally, the (interior) metric of a regular holographic object is uniquely determined up to a constant factor and the interior matter-state must follow well defined scaling relations. When the metric theory of gravity is general relativity, the interior matter has an overall string equation of state (EOS) and a unique total energy-density. Thus the holographic metric derived in this article can serve as simple interior 4D realization of Mathur's string fuzzball proposal. Some properties of the holographic metric and its possible experimental verification are discussed. The geodesics of the holographic metric describe an isotropically expanding (or contracting) universe with a nearly homogeneous matter-distribution within the local Hubble volume. Due to the overall string EOS the active gravitational mass-density is zero, resulting in a coasting expansion with Ht = 1, which is compatible with the recent GRB-data.
On analytic solutions of wave equations in regular coordinate systems on Schwarzschild background
Philipp, Dennis
2015-01-01
The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual Schwarzschild, Eddington-Finkelstein, Painleve-Gullstrand and Kruskal-Szekeres coordinates. In the first three cases, but not in the last one, it is possible to separate a harmonic time-dependence. Then the resulting radial equations belong to the class of confluent Heun equations, i.e., we can identify one irregular and two regular singularities. Using the generalized Riemann scheme we collect properties of all the singular points and construct analytic (local) solutions in terms of the standard confluent Heun function HeunC, Frobenius and asymptotic Thome series. We study the Eddington-Finkelstein case in detail and obtain a solution that is regular at the black hole horizon. This solution satisfies causal boundary conditions, i.e., it describes purely ingoing radiation at $r=2M$. ...
Perturbation of a Schwarzschild Black Hole Due to a Rotating Thin Disk
Čížek, P.; Semerák, O.
2017-09-01
Will, in 1974, treated the perturbation of a Schwarzschild black hole due to a slowly rotating, light, concentric thin ring by solving the perturbation equations in terms of a multipole expansion of the mass-and-rotation perturbation series. In the Schwarzschild background, his approach can be generalized to perturbation by a thin disk (which is more relevant astrophysically), but, due to rather bad convergence properties, the resulting expansions are not suitable for specific (numerical) computations. However, we show that Green’s functions, represented by Will’s result, can be expressed in closed form (without multipole expansion), which is more useful. In particular, they can be integrated out over the source (a thin disk in our case) to yield good converging series both for the gravitational potential and for the dragging angular velocity. The procedure is demonstrated, in the first perturbation order, on the simplest case of a constant-density disk, including the physical interpretation of the results in terms of a one-component perfect fluid or a two-component dust in a circular orbit about the central black hole. Free parameters are chosen in such a way that the resulting black hole has zero angular momentum but non-zero angular velocity, as it is just carried along by the dragging effect of the disk.
Proper temperature of the Schwarzschild AdS black hole revisited
Eune, Myungseok; Kim, Wontae
2017-10-01
The Unruh temperature calculated by using the global embedding of the Schwarzschild AdS spacetime into the Minkowski spacetime was identified with the local proper temperature; however, it became imaginary in a certain region outside the event horizon. So, the temperature was assumed to be zero of non-thermal radiation for that region. In this work, we revisit this issue in an exactly soluble two-dimensional Schwarzschild AdS black hole and present an alternative resolution to this problem in terms of the Tolman's procedure. However, the process appears to be non-trivial in the sense that the original procedure assuming the traceless energy-momentum tensor should be extended in such a way that it should cover the non-vanishing case of the energy-momentum tensor in the presence of the trace anomaly. Consequently, we show that the proper temperature turns out to be real everywhere outside the event horizon without any imaginary value, in particular, it vanishes at both the horizon and the asymptotic infinity.
Kanti, P.; Pappas, T.
2017-07-01
The absence of a true thermodynamical equilibrium for an observer located in the causal area of a Schwarzschild-de Sitter spacetime has repeatedly raised the question of the correct definition of its temperature. In this work, we consider five different temperatures for a higher-dimensional Schwarzschild-de Sitter black hole: the bare T0, the normalized TBH, and three effective ones given in terms of both the black-hole and cosmological horizon temperatures. We find that these five temperatures exhibit similarities but also significant differences in their behavior as the number of extra dimensions and the value of the cosmological constant are varied. We then investigate their effect on the energy emission spectra of Hawking radiation. We demonstrate that the radiation spectra for the normalized temperature TBH—proposed by Bousso and Hawking over twenty years ago—leads to the dominant emission curve, while the other temperatures either support a significant emission rate only in a specific Λ regime or have their emission rates globally suppressed. Finally, we compute the bulk-over-brane emissivity ratio and show that the use of different temperatures may lead to different conclusions regarding the brane or bulk dominance.
Recovering the mass profile and orbit anisotropy of mock dwarf galaxies with Schwarzschild modelling
Kowalczyk, Klaudia; Łokas, Ewa L.; Valluri, Monica
2017-10-01
We present a new study concerning the application of the Schwarzschild orbit superposition method to model spherical galaxies. The method aims to recover the mass and the orbit anisotropy parameter profiles of the objects using measurements of positions and line-of-sight velocities usually available for resolved stellar populations of dwarf galaxies in the Local Group. To test the reliability of the method, we used different sets of mock data extracted from four numerical realizations of dark matter haloes. The models shared the same density profile but differed in anisotropy profiles, covering a wide range of possibilities, from constant to increasing and decreasing with radius. The tests were done in two steps, first assuming that the mass profile of the dwarf is known and employing the method to retrieve the anisotropy only, and then varying also the mass distribution. We used two kinds of data samples: unrealistically large ones based on over 270 000 particles from the numerical realizations and small ones matching the amount of data available for the Fornax dwarf. For the large data samples, we recover both the mass and the anisotropy profiles with very high accuracy. For the realistically small ones, we also find a reasonably good agreement between the fitted and the input anisotropies, however the total density profiles can be significantly biased as a result of their oversensitivity to the available data. Our results therefore provide convincing evidence in favour of the applicability of the Schwarzschild method to break the mass-anisotropy degeneracy in dwarf galaxies.
(Non-adiabatic) string creation on nice slices in Schwarzschild black holes
Puhm, Andrea; Rojas, Francisco; Ugajin, Tomonori
2017-04-01
Nice slices have played a pivotal role in the discussion of the black hole information paradox as they avoid regions of strong spacetime curvature and yet smoothly cut through the infalling matter and the outgoing Hawking radiation, thus, justifying the use of low energy field theory. To avoid information loss it has been argued recently, however, that local effective field theory has to break down at the horizon. To assess the extent of this breakdown in a UV complete framework we study string-theoretic effects on nice slices in Schwarzschild black holes. Our purpose is two-fold. First, we use nice slices to address various open questions and caveats of [1] where it was argued that boost-enhanced non-adiabatic string-theoretic effects at the horizon could provide a dynamical mechanism for the firewall. Second, we identify two non-adiabatic effects on nice slices in Schwarzschild black holes: pair production of open strings near the horizon enhanced by the presence of the infinite tower of highly excited string states and a late-time non-adiabatic effect intrinsic to nice slices.
Lapiedra, Ramon
2016-01-01
The collapse of pressureless (dust) and non-homogeneous matter is analyzed under the following additional assumptions: spherical symmetry and existence of a spatially flat foliation of comoving 3-spaces (marginally bound collapse). The starting point is not, in this case, the integration of the Einstein equations from some suitable initial conditions. Instead, starting from the corresponding general exact solution of these equations, depending on two arbitrary functions of the radial coordinate, the fulfillment of the Lichnerowicz matching conditions of the interior collapsing metric and the exterior Schwarzschild one is ensured: the continuity of the metric and its first derivatives on the time-like hypersurface describing the evolution of the spherical 2-surface boundary of the collapsing cloud. The whole analytical family of resulting models is obtained and some of them are picked out as physical better models on the basis of the finite and stationary value of its {\\em intrinsic} energy.
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.
Dominici, Diego
2011-01-01
This work introduces a distance between natural numbers not based on their position on the real line but on their arithmetic properties. We prove some metric properties of this distance and consider a possible extension.
Balvín, Radek
2013-01-01
With growing amount of data produced by users on social media the need of extraction of relevant data for marketing, research and other uses grows as well. The bachelor thesis named "Social media metrics" presents the issues of monitoring, measurement and metrics of social media. In the research part it also maps and captures the present Czech practice in measurement and monitoring of social media. I also rate the use of social media monitoring tools and usual methods of social media measurem...
Energy Technology Data Exchange (ETDEWEB)
Madriz Aguilar, Jose Edgar; Reyes, Luz M.; Moreno, Claudia [Universidad de Guadalajara (UdG), Departamento de Matematicas, Centro Universitario de Ciencias Exactas e ingenierias (CUCEI), Guadalajara, Jalisco (Mexico); Bellini, Mauricio [Universidad Nacional de Mar del Plata (UNMdP), Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Funes 3350, C.P. 7600, Mar del Plata (Argentina); Consejo Nacional de Investigaciones Cientificas y Tecnicas (CONICET), Instituto de Investigaciones Fisicas de Mar del Plata (IFIMAR), Mar del Plata (Argentina)
2013-10-15
We develop a non-perturbative formalism for scalar metric fluctuations from a 5D extended version of general relativity in vacuum. In this work we concentrate our efforts on calculations valid on large cosmological scales, which are dominant during the inflationary phase of the universe. The resulting metric in this limit is obtained after implementing a planar coordinate transformation on a 5D Ricci-flat metric solution. We calculate the spectrum of these fluctuations with an effective 4D Schwarzschild-de Sitter spacetime on cosmological scales, which is obtained after we make a static foliation on the non-compact extra coordinate. Our results show how the squared metric fluctuations of the primordial universe become scale invariant with the inflationary expansion. (orig.)
From the Schwarzschild Anti-de Sitter Black Hole to the Conformal Field Theory
Directory of Open Access Journals (Sweden)
Akram Sadat Sefiedgar
2015-01-01
Full Text Available The emergence of the quantum gravitational effects in a very high energy regime necessitates some corrections to the thermodynamics of black holes. In this letter, we investigate a possible modification to the thermodynamics of Schwarzschild anti-de Sitter (SAdS black holes due to rainbow gravity model. Using the correspondence between a (d+1-dimensional SAdS black hole and a conformal filed theory in d-dimensional spacetime, one may find the corrections to the Cardy-Verlinde formula from the modified thermodynamics of the black hole. Furthermore, we show that the corrected Cardy-Verlinde formula can also be derived by redefining the Virasoro operator and the central charge.
Hawking radiation as tunneling in Schwarzschild anti-de Sitter black hole
Sefiedgar, A. S.; Ashrafinejad, A.
2017-08-01
The Hawking radiation from a (d+1) -dimensional Schwarzschild Anti-de Sitter (SAdS) black hole is investigated within rainbow gravity. Based on the method proposed by Kraus, Parikh and Wilczek, the Hawking radiation is considered as a tunneling process across the horizon. The emission rate of massless particles which are tunneling across the quantum-corrected horizon is calculated. Enforcing the energy conservation law leads to a dynamical geometry. Both the dynamical geometry and the quantum effects of space-time yield some corrections to the emission rate. The corrected radiation spectrum is not purely thermal. The emission rate is related to the changes of modified entropy in rainbow gravity and the corrected thermal spectrum may be consistent with an underlying unitary quantum theory. The correlations between emitted particles are also investigated in order to address the recovery of information.
Toward the construction of a medium size prototype Schwarzschild-Couder telescope for CTA
Rousselle, J.; Byrum, K.; Cameron, R.; Connaughton, V.; Errando, M.; Griffiths, S.; Guarino, V.; Humensky, T. B.; Jenke, P.; Kaaret, P.; Kieda, D.; Limon, M.; Mognet, I.; Mukherjee, R.; Nieto, D.; Okumura, A.; Peck, A.; Petrashyk, A.; Ribeiro, D.; Stevenson, B.; Vassiliev, V.; Yu, P.
2015-09-01
The construction of a prototype Schwarzschild-Couder telescope (pSCT) started in early June 2015 at the Fred Lawrence Whipple Observatory in Southern Arizona, as a candidate medium-sized telescope for the Cherenkov Telescope Array (CTA). Compared to current Davies-Cotton telescopes, this novel instrument with an aplanatic two-mirror optical system will offer a wider field-of-view and improved angular resolution. In addition, the reduced plate scale of the camera allows the use of highly-integrated photon detectors such as silicon photo multipliers. As part of CTA, this design has the potential to greatly improve the performance of the next generation ground-based observatory for very high-energy (E>60 GeV) gamma-ray astronomy. In this contribution we present the design and performance of both optical and alignment systems of the pSCT.
Accretion of a symmetry-breaking scalar field by a Schwarzschild black hole.
Traykova, Dina; Braden, Jonathan; Peiris, Hiranya V
2018-03-06
We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry-breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory.This article is part of the Theo Murphy meeting issue 'Higgs Cosmology'. © 2018 The Author(s).
General theories of linear gravitational perturbations to a Schwarzschild black hole
Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena
2018-02-01
We use the covariant formulation proposed by Tattersall, Lagos, and Ferreira [Phys. Rev. D 96, 064011 (2017), 10.1103/PhysRevD.96.064011] to analyze the structure of linear perturbations about a spherically symmetric background in different families of gravity theories, and hence study how quasinormal modes of perturbed black holes may be affected by modifications to general relativity. We restrict ourselves to single-tensor, scalar-tensor and vector-tensor diffeomorphism-invariant gravity models in a Schwarzschild black hole background. We show explicitly the full covariant form of the quadratic actions in such cases, which allow us to then analyze odd parity (axial) and even parity (polar) perturbations simultaneously in a straightforward manner.
Marginally Stable Circular Orbits in Schwarzschild Black Hole Surrounded by Quintessence Matter
Hussain, Ibrar
2016-01-01
Marginally stable circular orbits (MSCOs) of a massive test particle are investigated in the spacetime geometry of Schwarzschild black hole surrounded by quintessence. For that matter we consider three important scenarios where the equation of state parameter $\\omega_{q}$, has one of the following forms (i) $\\omega_q=-1$ (ii) $\\omega_q=-2/3$ and (iii) $\\omega_q= -1/3$. The existence of such marginally stable circular orbits in these scenarios depend on the range of normalization factor $\\alpha$. Briefly, we show that in the first case such orbits exist only if $0<\\alpha<4/16875$. Moreover in the second case which is a special Kiselev black hole it is found that MSCOs exist when the value of the normalization factor satisfy $0<\\alpha\\leq 0.00536165238$. In the last case the MSCOs are also shown to exist.
Schwarzschild-de Sitter spacetime: The role of temperature in the emission of Hawking radiation
Pappas, Thomas; Kanti, Panagiota
2017-12-01
We consider a Schwarzschild-de Sitter (SdS) black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.
Tripartite nonlocality for an open Dirac system in the background of Schwarzschild space–time
Ding, Zhi-Yong; Shi, Jia-Dong; Wu, Tao; He, Juan
2017-12-01
In this paper, the behavior of the tripartite nonlocality for a Dirac system in the background of Schwarzschild space–time is studied. It is shown that the nonlocality of the ultimate physical accessible state always decreases as the Hawking effect increases monotonically, which is independent of the number of particles located near the event horizon. Besides, the more particles there are located near the event horizon, the more difficult the violation of the Svetlichny inequality becomes. Furthermore, we investigate the property of these particles suffering from a non-Markovian environment, and derive that the nonlocality decreases quickly with the increasing decoherence time accompanied by damping revivals. To preserve tripartite nonlocality in the non-Markovian environment, we propose a scheme by means of prior weak measurement and post measurement reversal. It is worth noticing that the effect is better for larger measurement strengths, while it induces smaller success probability.
Energy Technology Data Exchange (ETDEWEB)
El-Menoufi, Basem Kamal [Department of Physics, University of Massachusetts,Amherst, MA 01003 (United States)
2016-05-05
In the context of effective field theory, we consider quantum gravity with minimally coupled massless particles. Fixing the background geometry to be of the Kerr-Schild type, we fully determine the one-loop effective action of the theory whose finite non-local part is induced by the long-distance portion of quantum loops. This is accomplished using the non-local expansion of the heat kernel in addition to a non-linear completion technique through which the effective action is expanded in gravitational curvatures. Via Euclidean methods, we identify a logarithmic correction to the Bekenstein-Hawking entropy of Schwarzschild black hole. Using dimensional transmutation the result is shown to exhibit an interesting interplay between the UV and IR properties of quantum gravity.
Accretion of a symmetry-breaking scalar field by a Schwarzschild black hole
Traykova, Dina; Braden, Jonathan; Peiris, Hiranya V.
2018-01-01
We simulate the behaviour of a Higgs-like field in the vicinity of a Schwarzschild black hole using a highly accurate numerical framework. We consider both the limit of the zero-temperature Higgs potential and a toy model for the time-dependent evolution of the potential when immersed in a slowly cooling radiation bath. Through these numerical investigations, we aim to improve our understanding of the non-equilibrium dynamics of a symmetry-breaking field (such as the Higgs) in the vicinity of a compact object such as a black hole. Understanding this dynamics may suggest new approaches for studying properties of scalar fields using black holes as a laboratory. This article is part of the Theo Murphy meeting issue `Higgs Cosmology'.
Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole
Rioseco, Paola
2016-01-01
We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole. To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime. The most general solution for the distribution function is given in terms of appropriate symplectic coordinates on the cotangent bundle, and the associated observables, including the particle current density and stress energy-momentum tensor, are determined. Next, we explore the case where the flow is steady-state and spherically symmetric. Assuming that in the asymptotic region the gas is described by an equilibrium distribution function, we determine the relevant parameters of the accretion flow as a function of the particle density and the temperature of the gas at infinity. In particular, we find that in the low temperature limit the tangential pressure at the horizon is about an order of magnitude larger than the radial one, showing explicitly that a collisionless gas, despite ex...
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.
von-Neumann stability and singularity resolution in loop quantized Schwarzschild black hole
Yonika, Alec; Khanna, Gaurav; Singh, Parampreet
2018-02-01
Though loop quantization of several spacetimes has exhibited existence of a bounce via an explicit evolution of states using numerical simulations, the question about the way central singularity is resolved in the black hole interior has remained open. The quantum Hamiltonian constraint in loop quantization turns out to be a finite difference equation whose stability is important to understand to gain insights on the viability of the underlying quantization and resulting physical implications. We take first steps towards addressing these issues for a loop quantization of the Schwarzschild interior recently given by Corichi and Singh. Von-Neumann stability analysis is performed using separability of solutions as well as a full two dimensional quantum difference equation. This results in a stability condition for black holes which have a very large mass compared to the Planck mass. For black holes of smaller masses evidence of numerical instability is found. In addition, stability analysis for macroscopic black holes leads to a constraint on the choice of the allowed states in numerical evolution. States which are not sharply peaked in accordance with this constraint result in instabilities. With the caveat of using kinematical norm, sharply peaked Gaussian states are evolved using the quantum difference equation and singularity resolution is obtained. A bounce is found for one of the triad variables, but for the other triad variable singularity resolution amounts to a non-singular passage through the zero volume. States are found to be peaked at the classical trajectory for a long time before and after the singularity resolution, and retain their semi-classical character across the zero volume. Our main result is that quantum bounce occurs in loop quantized Schwarzschild interior at least for macroscopic black holes. Instability of small black holes which can be a result of using kinematical norm nevertheless signifies the need of further understanding of the
Rigorous construction and Hadamard property of the Unruh state in Schwarzschild spacetime
Energy Technology Data Exchange (ETDEWEB)
Dappiaggi, Claudio; Pinamonti, Nicola [Hamburg Univ. (Germany). II. Inst. fuer Theoretische Physik; Moretti, Valter [Trento Univ., Povo (Italy). Dipt. di Matematica; Istituto Nazionale di Fisica Nucleare, Povo (Italy); Istituto Nazionale di Alta Matematica ' ' F. Severi' ' , GNFM, Sesto Fiorentino (Italy)
2009-07-15
The discovery of the radiation properties of black holes prompted the search for a natural candidate quantum ground state for a massless scalar field theory on Schwarzschild spacetime, here considered in the Eddington-Finkelstein representation. Among the several available proposals in the literature, an important physical role is played by the so-called Unruh state which is supposed to be appropriate to capture the physics of a black hole formed by spherically symmetric collapsing matter. Within this respect, we shall consider a massless Klein-Gordon field and we shall rigorously and globally construct such state, that is on the algebra of Weyl observables localised in the union of the static external region, the future event horizon and the non-static black hole region. Eventually, out of a careful use of microlocal techniques, we prove that the built state fulfils, where defined, the so-called Hadamard condition; hence, it is perturbatively stable, in other words realizing the natural candidate with which one could study purely quantum phenomena such as the role of the back reaction of Hawking's radiation. From a geometrical point of view, we shall make a profitable use of a bulk-to-boundary reconstruction technique which carefully exploits the Killing horizon structure as well as the conformal asymptotic behaviour of the underlying background. From an analytical point of view, our tools will range from Hoermander's theorem on propagation of singularities, results on the role of passive states, and a detailed use of the recently discovered peeling behaviour of the solutions of the wave equation in Schwarzschild spacetime. (orig.)
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.
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, choic...... 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.......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...
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...
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...
Directory of Open Access Journals (Sweden)
Kyril Tintarev
2007-05-01
Full Text Available The paper studies energy functionals on quasimetric spaces, defined by quadratic measure-valued Lagrangeans. This general model of medium, known as metric fractals, includes nested fractals and sub-Riemannian manifolds. In particular, the quadratic form of the Lagrangean satisfies Sobolev inequalities with the critical exponent determined by the (quasimetric homogeneous dimension, which is also involved in the asymptotic distribution of the form's eigenvalues. This paper verifies that the axioms of the metric fractal are preserved by space products, leading thus to examples of non-differentiable media of arbitrary intrinsic dimension.
The Noncommutative Ward Metric
Directory of Open Access Journals (Sweden)
Marco Maceda
2010-06-01
Full Text Available We analyze the moduli-space metric in the static nonabelian charge-two sector of the Moyal-deformed CP^1 sigma model in 1+2 dimensions. After carefully reviewing the commutative results of Ward and Ruback, the noncommutative Kähler potential is expanded in powers of dimensionless moduli. In two special cases we sum the perturbative series to analytic expressions. For any nonzero value of the noncommutativity parameter, the logarithmic singularity of the commutative metric is expelled from the origin of the moduli space and possibly altogether.
A Unification of $G$ -Metric, Partial Metric, and $b$ -Metric Spaces
Hussain, Nawab; Rezaei Roshan, Jamal; Parvaneh, Vahid; Latif, Abdul
2013-01-01
Using the concepts of $G$ -metric, partial metric, and $b$ -metric spaces, we define a new concept of generalized partial $b$ -metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.
Gower, John C.; Albers, Casper J.
2011-01-01
In canonical analysis with more variables than samples, it is shown that, as well as the usual canonical means in the range-space of the within-groups dispersion matrix, canonical means may be defined in its null space. In the range space we have the usual Mahalanobis metric; in the null space
Software Quality Assurance Metrics
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.
Ultrametricity and metric betweenness in tangent spaces to metric spaces
Dovgoshey, O.; Dordovskyi, D.
2009-01-01
The paper deals with pretangent spaces to general metric spaces. An ltrametricity criterion for pretangent spaces is found and it is closely related to the metric betweenness in the pretangent spaces.
Ng, Keith K.; Mann, Robert B.; Martín-Martínez, Eduardo
2017-10-01
The RP3 geon and the Schwarzschild black hole are two black hole spacetimes which differ only behind the event horizon. We show that the thermal Hawking radiation emanating from the two black holes contains nontrivial correlations, that these correlations contain information about their interiors, and demonstrate that a particle detector can recover these correlations. In this manner, a simple particle detector can determine the structure behind the event horizon of an eternal black hole.
NPScape Metric GIS Data - Housing
National Park Service, Department of the Interior — NPScape housing metrics are calculated using outputs from the Spatially Explicit Regional Growth Model. Metric GIS datasets are produced seamlessly for the United...
Metric adjusted skew information
DEFF Research Database (Denmark)
Hansen, Frank
2008-01-01
establish a connection between the geometrical formulation of quantum statistics as proposed by Chentsov and Morozova and measures of quantum information as introduced by Wigner and Yanase and extended in this article. We show that the set of normalized Morozova-Chentsov functions describing the possible...... quantum statistics is a Bauer simplex and determine its extreme points. We determine a particularly simple skew information, the "¿-skew information," parametrized by a ¿ ¿ (0, 1], and show that the convex cone this family generates coincides with the set of all metric adjusted skew informations.......We extend the concept of Wigner-Yanase-Dyson skew information to something we call "metric adjusted skew information" (of a state with respect to a conserved observable). This "skew information" is intended to be a non-negative quantity bounded by the variance (of an observable in a state...
Gurudu, Suryakanth R; Ramirez, Francisco C
2013-04-01
Endoscopy has evolved in the past 4 decades to become an important tool in the diagnosis and management of many digestive diseases. Greater focus on endoscopic quality has highlighted the need to ensure competency among endoscopists. A joint task force of the American College of Gastroenterology and the American Society for Gastrointestinal Endoscopy has proposed several quality metrics to establish competence and help define areas of continuous quality improvement. These metrics represent quality in endoscopy pertinent to pre-, intra-, and postprocedural periods. Quality in endoscopy is a dynamic and multidimensional process that requires continuous monitoring of several indicators and benchmarking with local and national standards. Institutions and practices should have a process in place for credentialing endoscopists and for the assessment of competence regarding individual endoscopic procedures.
Darling, Aaron E; Tritt, Andrew; Eisen, Jonathan A; Facciotti, Marc T
2011-10-01
High-throughput DNA sequencing technologies have spurred the development of numerous novel methods for genome assembly. With few exceptions, these algorithms are heuristic and require one or more parameters to be manually set by the user. One approach to parameter tuning involves assembling data from an organism with an available high-quality reference genome, and measuring assembly accuracy using some metrics. We developed a system to measure assembly quality under several scoring metrics, and to compare assembly quality across a variety of assemblers, sequence data types, and parameter choices. When used in conjunction with training data such as a high-quality reference genome and sequence reads from the same organism, our program can be used to manually identify an optimal sequencing and assembly strategy for de novo sequencing of related organisms. GPL source code and a usage tutorial is at http://ngopt.googlecode.com aarondarling@ucdavis.edu Supplementary data is available at Bioinformatics online.
Social media evaluation metrics
Ronalds Skulme; Valerijs Praude
2015-01-01
Background. There are many methods how specialists can evaluate return of online marketing activities. Most of the methods out there are designed for versatile use. But each online marketing tool has its own unique specific metrics that should be taken into account when measuring the return of marketing activities. Authors believe that the methods that are designed to evaluate online marketing activities should also be more specific. Hence authors believe that more specific online marketing r...
2016-03-02
COMID) and the Strongly Adaptive Online Learning (SAOL) framework proposed in [7]. 1.1 Related Work Linear Discriminant Analysis (LDA) and Principal... ensemble . 7 Algorithm 1 Strongly Adaptive Online Metric Learning 1: Initialize: w1(I) 2: for t = 1 to T do 3: Initialize new learner if needed. 4...the embeddings learned by static COMID for the category and sentiment clusterings respectively. Also shown are the 2- dimensional standard PCA
Monochromatic metrics are generalized Berwald
Bartelmeß, Nina; Matveev, Vladimir S.
2017-01-01
We show that monochromatic Finsler metrics, i.e., Finsler metrics such that each two tangent spaces are isomorphic as normed spaces, are generalized Berwald metrics, i.e., there exists an affine connection, possibly with torsion, that preserves the Finsler function
Spacetime Metrics from Gauge Potentials
Directory of Open Access Journals (Sweden)
Ettore Minguzzi
2014-03-01
Full Text Available I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2 (or the Lie algebra of quaternions. If the curvature of this potential vanishes, the metric reduces to a canonical curved background form reminiscent of the Friedmann S3 cosmological metric.
Implicit contractive mappings in modular metric and fuzzy metric spaces.
Hussain, N; Salimi, P
2014-01-01
The notion of modular metric spaces being a natural generalization of classical modulars over linear spaces like Lebesgue, Orlicz, Musielak-Orlicz, Lorentz, Orlicz-Lorentz, and Calderon-Lozanovskii spaces was recently introduced. In this paper we investigate the existence of fixed points of generalized α-admissible modular contractive mappings in modular metric spaces. As applications, we derive some new fixed point theorems in partially ordered modular metric spaces, Suzuki type fixed point theorems in modular metric spaces and new fixed point theorems for integral contractions. In last section, we develop an important relation between fuzzy metric and modular metric and deduce certain new fixed point results in triangular fuzzy metric spaces. Moreover, some examples are provided here to illustrate the usability of the obtained results.
Sironi, Giorgia
2017-09-01
At the beginning of XX century Karl Schwarzschild defined a method to design large-field aplanatic telescopes based on the use of two aspheric mirrors. The approach was then refined by Couder (1926) who, in order to correct for the astigmatic aberration, introduced a curvature of the focal plane. By the way, the realization of normal-incidence telescopes implementing the Schwarzschild aplanatic configuration has been historically limited by the lack of technological solutions to manufacture and test aspheric mirrors. On the other hand, the Schwarzschild solution was recovered for the realization of coma-free X-ray grazing incidence optics. Wolter-like grazing incidence systems are indeed free of spherical aberration, but still suffer from coma and higher order aberrations degrading the imaging capability for off-axis sources. The application of the Schwarzschild's solution to X-ray optics allowed Wolter to define an optical system that exactly obeys the Abbe sine condition, eliminating coma completely. Therefore these systems are named Wolter-Schwarzschild telescopes and have been used to implement wide-field X-ray telescopes like the ROSAT WFC and the SOHO X-ray telescope. Starting from this approach, a new class of X-ray optical system was proposed by Burrows, Burg and Giacconi assuming polynomials numerically optimized to get a flat field of view response and applied by Conconi to the wide field x-ray telescope (WFXT) design. The Schwarzschild-Couder solution has been recently re-discovered for the application to normal-incidence Cherenkov telescopes, thanks to the suggestion by Vassiliev and collaborators. The Italian Institute for Astrophysics (INAF) realized the first Cherenkov telescope based on the polynomial variation of the Schwarzschild configuration (the so-called ASTRI telescope). Its optical qualification was successfully completed in 2016, demonstrating the suitability of the Schwarzschild-like configuration for the Cherenkov astronomy requirements
Thermodynamics of the Schwarzschild-AdS Black Hole with a Minimal Length
Directory of Open Access Journals (Sweden)
Yan-Gang Miao
2017-01-01
Full Text Available Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the δ-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the δ-function and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the δ-function.
Hanada, Masanori; Miwa, Akitsugu; Nishimura, Jun; Takeuchi, Shingo
2009-05-08
In the string-gauge duality it is important to understand how the space-time geometry is encoded in gauge theory observables. We address this issue in the case of the D0-brane system at finite temperature T. Based on the duality, the temporal Wilson loop W in gauge theory is expected to contain the information of the Schwarzschild radius RSch of the dual black hole geometry as log(W)=RSch/(2pialpha'T). This translates to the power-law behavior log(W)=1.89(T/lambda 1/3)-3/5, where lambda is the 't Hooft coupling constant. We calculate the Wilson loop on the gauge theory side in the strongly coupled regime by performing Monte Carlo simulations of supersymmetric matrix quantum mechanics with 16 supercharges. The results reproduce the expected power-law behavior up to a constant shift, which is explainable as alpha' corrections on the gravity side. Our conclusion also demonstrates manifestly the fuzzball picture of black holes.
Holographic entanglement entropies for Schwarzschild and Reisner-Nordstr\\"om spacetimes
Sun, Yuan
2016-01-01
The holographic entanglement entropies (HEE) associated with four dimensional Schwarzschild and Reisner-Nordstr\\"om spacetimes are investigated. Unlike the cases of asymptotically AdS spacetimes for which the boundaries are always taken at (timelike) conformal infinities, we take the boundaries at either large but finite radial coordinate (far boundary) or very close to the black hole event horizons (near horizon boundary). The reason for such choices is that such boundaries are similar to the conformal infinity of AdS spacetime in that they are all timelike, so that there may be some hope to define dual systems with ordinary time evolution on such boundaries. Our results indicate that, in the case of far boundaries, the leading order contribution to the HEEs come from the background Minkowski spacetime, however, the next to leading order contribution which arises from the presence of the black holes is always proportional to the black hole mass, which constitutes a version of the first law of the HEE for asy...
Gravitational self-force in a Schwarzschild background and the effective one-body formalism
Damour, Thibault
2010-01-01
We discuss various ways in which the computation of conservative gravitational self-force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the effective one-body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass numerical relativity data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focusing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian expansions of various (EOB and GSF) functions at the fourth post-Newtonian level, and we analytically compute the first logarithm entering a certain, gauge-invariant “redshift” GSF function (defined along the sequence of circular orbits).
Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
Damour, Thibault
2009-01-01
We discuss various ways in which the computation of conservative Gravitational Self Force (GSF) effects on a point mass moving in a Schwarzschild background can inform us about the basic building blocks of the Effective One-Body (EOB) Hamiltonian. We display the information which can be extracted from the recently published GSF calculation of the first-GSF-order shift of the orbital frequency of the last stable circular orbit, and we combine this information with the one recently obtained by comparing the EOB formalism to high-accuracy numerical relativity (NR) data on coalescing binary black holes. The information coming from GSF data helps to break the degeneracy (among some EOB parameters) which was left after using comparable-mass NR data to constrain the EOB formalism. We suggest various ways of obtaining more information from GSF computations: either by studying eccentric orbits, or by focussing on a special zero-binding zoom-whirl orbit. We show that logarithmic terms start entering the post-Newtonian ...
A Unification of G-Metric, Partial Metric, and b-Metric Spaces
Directory of Open Access Journals (Sweden)
Nawab Hussain
2014-01-01
Full Text Available Using the concepts of G-metric, partial metric, and b-metric spaces, we define a new concept of generalized partial b-metric space. Topological and structural properties of the new space are investigated and certain fixed point theorems for contractive mappings in such spaces are obtained. Some examples are provided here to illustrate the usability of the obtained results.
Energy Technology Data Exchange (ETDEWEB)
Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.
2006-07-31
Relatively minor perturbations to a crystal structure can in some cases result in apparently large changes in symmetry. Changes in space group or even lattice can be induced by heavy metal or halide soaking (Dauter et al, 2001), flash freezing (Skrzypczak-Jankun et al, 1996), and Se-Met substitution (Poulsen et al, 2001). Relations between various space groups and lattices can provide insight in the underlying structural causes for the symmetry or lattice transformations. Furthermore, these relations can be useful in understanding twinning and how to efficiently solve two different but related crystal structures. Although (pseudo) symmetric properties of a certain combination of unit cell parameters and a space group are immediately obvious (such as a pseudo four-fold axis if a is approximately equal to b in an orthorhombic space group), other relations (e.g. Lehtio, et al, 2005) that are less obvious might be crucial to the understanding and detection of certain idiosyncrasies of experimental data. We have developed a set of tools that allows straightforward exploration of possible metric symmetry relations given unit cell parameters and a space group. The new iotbx.explore{_}metric{_}symmetry command produces an overview of the various relations between several possible point groups for a given lattice. Methods for finding relations between a pair of unit cells are also available. The tools described in this newsletter are part of the CCTBX libraries, which are included in the latest (versions July 2006 and up) PHENIX and CCI Apps distributions.
METRICS DEVELOPMENT FOR PATENTS
Directory of Open Access Journals (Sweden)
Daniela Francescato Veiga
Full Text Available Objective: To develop a proposal for metrics for patents to be applied in assessing the postgraduate programs of Medicine III - Capes. Methods: From the reading and analysis of the 2013 area documents of all the 48 areas of Capes, a proposal for metrics for patents was developed to be applied in Medicine III programs. Results: Except for the areas Biotechnology, Food Science, Biological Sciences III, Physical Education, Engineering I, III and IV and Interdisciplinary, most areas do not adopt a scoring system for patents. The proposal developed was based on the criteria of Biotechnology, with adaptations. In general, it will be valued, in ascending order, the deposit, the granting and licensing/production. It will also be assigned higher scores to patents registered abroad and whenever there is a participation of students. Conclusion: This proposal can be applied to the item Intellectual Production of the evaluation form, in subsection Technical Production/Patents. The percentage of 10% for academic programs and 40% for Masters Professionals should be maintained. The program will be scored as Very Good when it reaches 400 points or over; Good, between 200 and 399 points; Regular, between 71 and 199 points; Weak up to 70 points; Insufficient, no punctuation.
First optical validation of a Schwarzschild Couder telescope: the ASTRI SST-2M Cherenkov telescope
Giro, E.; Canestrari, R.; Sironi, G.; Antolini, E.; Conconi, P.; Fermino, C. E.; Gargano, C.; Rodeghiero, G.; Russo, F.; Scuderi, S.; Tosti, G.; Vassiliev, V.; Pareschi, G.
2017-12-01
Context. The Cherenkov Telescope Array (CTA) represents the most advanced facility designed for Cherenkov Astronomy. ASTRI SST-2M has been developed as a demonstrator for the Small Size Telescope in the context of the upcoming CTA. Its main innovation consists in the optical layout which implements the Schwarzschild-Couder configuration and is fully validated for the first time. The ASTRI SST-2M optical system represents the first qualified example of a two-mirror telescope for Cherenkov Astronomy. This configuration permits us to (i) maintain high optical quality across a large field of view; (ii) demagnify the plate scale; and (iii) exploit new technological solutions for focal plane sensors. Aims: The goal of the paper is to present the optical qualification of the ASTRI SST-2M telescope. The qualification has been obtained measuring the point spread function (PSF) sizes generated in the focal plane at various distances from the optical axis. These values have been compared with the performances expected by design. Methods: After an introduction on Gamma-ray Astronomy from the ground, the optical design of ASTRI SST-2M and how it has been implemented is discussed. Moreover, the description of the set-up used to qualify the telescope over the full field of view is shown. Results: We report the results of the first-light optical qualification. The required specification of a flat PSF of 10 arcmin in a large field of view ( 10°) has been demonstrated. These results validate the design specifications, opening a new scenario for Cherenkov Gamma-ray Astronomy and, in particular, for the detection of high-energy (5-300 TeV) gamma rays and wide-field observations with CTA.
Tomographic reconstruction of quantum metrics
Laudato, Marco; Marmo, Giuseppe; Mele, Fabio M.; Ventriglia, Franco; Vitale, Patrizia
2018-02-01
In the framework of quantum information geometry we investigate the relationship between monotone metric tensors uniquely defined on the space of quantum tomograms, once the tomographic scheme is chosen, and monotone quantum metrics on the space of quantum states, classified by operator monotone functions, according to the Petz classification theorem. We show that different metrics can be related through a change in the tomographic map and prove that there exists a bijective relation between monotone quantum metrics associated with different operator monotone functions. Such a bijective relation is uniquely defined in terms of solutions of a first order second degree differential equation for the parameters of the involved tomographic maps. We first exhibit an example of a non-linear tomographic map that connects a monotone metric with a new one, which is not monotone. Then we provide a second example where two monotone metrics are uniquely related through their tomographic parameters.
Metric Selection for Ecosystem Restoration
2013-06-01
1-11. Kiker, G .A., T. S. Bridges, A. Varghese, T. P. Seager, and I. Linkov. 2005. Application of multicriteria decision analysis in environmental...Presents two metric evaluation methods, screening and multi-criteria decision analysis . 5. Discusses metric application to ecosystem restoration...characterize project success. Metrics used in plan formulation can be quantified by modeling and analysis , or can be qualitative in nature, while
Implications of metric conversion.
Laros, R K
1980-11-01
The international scientific community is rapidly achieving conversion to the metric system, and the Système International (SI system) has been chosen for use by health scientists. Because the United States remains 1 of only 4 countries not now using part or all of the SI system, there is now a systematic effort toward rapid conversion. Although most of the SI system is not controversial, several SI units are highly so. Examples include joules instead of calories, pascals instead of millimeters of mercury, and moles per liter instead of milligrams per 100 milliliters. Obstetrician-gynecologists need to be familiar with the SI units and to voice their feelings about the various controversial units. There are decisions still to be made, and the time for discussion and advice is now.
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.
Metric-adjusted skew information
DEFF Research Database (Denmark)
Liang, Cai; Hansen, Frank
2010-01-01
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...... 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 information is a special case...... of (unbounded) metric-adjusted skew information....
Calamai, Simone; Petrecca, David; Zheng, Kai
2014-01-01
We study the geodesic equation for the Dirichlet (gradient) metric in the space of Kaehler potentials. We first solve the initial value problem for the geodesic equation of the combination metric, including the gradient metric. We then discuss a comparison theorem between it and the Calabi metric. As geometric motivation of the combination metric, we find that the Ebin metric restricted to the space of type II deformations of a Sasakian structure is the sum of the Calabi metric and the gradie...
Software metrics: Software quality metrics for distributed systems. [reliability engineering
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.
Zou, Li; Li, Fang-Yu; Li, Tao
2014-11-01
In this paper, we first deduce the Tolman-Oppenheimer-Volkoff (TOV) equations and Schwarzschild-de Sitter (SdS) constant-density interior solutions of perfect fluid spheres in hydrostatic equilibrium by the Einstein equations with a nonzero cosmological constant. The TOV equations and the spacetime properties of exact solutions inside uniform perfect fluid spheres with different spatial curvature and cosmological constants will be respectively analyzed in detail. Moreover, a brief comparison between the internal static solutions of the SdS type and the dynamical Einstein-Strauss-de Sitter (ESdS) vacuole spacetime is obtained.
Kim, Jinho; Garain, Sudip K.; Balsara, Dinshaw S.; Chakrabarti, Sandip K.
2017-11-01
We study time evolution of sub-Keplerian transonic accretion flows on to black holes using a general relativistic numerical simulation code. We perform simulations in Schwarzschild space-time. We first compare one-dimensional simulation results with theoretical results and validate the performance of our code. Next, we present results of axisymmetric, two-dimensional simulation of advective flows. We find that even in this case, for which no complete theoretical analysis is present in the literature, steady-state shock formation is possible.
Saha, T. T.
1984-01-01
An equation similar to the Abbe sine condition is derived for a Wolter type II telescope. This equation and the sine condition are then combined to produce a so called generalized sine condition. Using the law of reflection, Fermat's principle, the generalized sine condition, and simple geometry the surface equations for a Wolter type II telescope and an equivalent Wolter-Schwarzschild telescope are calculated. The performances of the telescopes are compared in terms of rms blur circle radius at the Gaussian focal plane and at best focus.
Extending cosmology: the metric approach
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
Separable metrics and radiating stars
Indian Academy of Sciences (India)
2016-12-14
Dec 14, 2016 ... and expanding spherically symmetric radiating star. We transform the junction condition to an ordinary differ- ential equation by making a separability assumption on the metric functions in the space–time variables. The condition of separability on the metric functions yields several new exact solutions.
Generalized metric spaces and mappings
Lin, Shou
2016-01-01
The idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.
Gibbons, Gary W.; Volkov, Mikhail S.
2017-05-01
We study solutions obtained via applying dualities and complexifications to the vacuum Weyl metrics generated by massive rods and by point masses. Rescaling them and extending to complex parameter values yields axially symmetric vacuum solutions containing singularities along circles that can be viewed as singular matter sources. These solutions have wormhole topology with several asymptotic regions interconnected by throats and their sources can be viewed as thin rings of negative tension encircling the throats. For a particular value of the ring tension the geometry becomes exactly flat although the topology remains non-trivial, so that the rings literally produce holes in flat space. To create a single ring wormhole of one metre radius one needs a negative energy equivalent to the mass of Jupiter. Further duality transformations dress the rings with the scalar field, either conventional or phantom. This gives rise to large classes of static, axially symmetric solutions, presumably including all previously known solutions for a gravity-coupled massless scalar field, as for example the spherically symmetric Bronnikov-Ellis wormholes with phantom scalar. The multi-wormholes contain infinite struts everywhere at the symmetry axes, apart from solutions with locally flat geometry.
Directory of Open Access Journals (Sweden)
R. da Rocha
2017-12-01
Full Text Available Sound waves on a fluid stream, in a de Laval nozzle, are shown to correspond to quasinormal modes emitted by black holes that are physical solutions in a quadratic curvature gravity with cosmological constant. Sound waves patterns in transsonic regimes at a laboratory are employed here to provide experimental data regarding generalized theories of gravity, comprised by the exact de Sitter-like solution and a perturbative solution around the Schwarzschildâde Sitter standard solution as well. Using the classical tests of General Relativity to bound free parameters in these solutions, acoustic perturbations on fluid flows in nozzles are then regarded, to study quasinormal modes of these black holes solutions, providing deviations of the de Laval nozzle cross-sectional area, when compared to the Schwarzschild solution. The fluid sonic point in the nozzle, for sound waves in the fluid, is shown to implement the acoustic event horizon corresponding to quasinormal modes. Keywords: Black holes, Fluid branes, Fluid dynamics, Quadratic curvature gravity, de Laval nozzle
Motion of a thin spherically symmetric Shell of Dust in the Schwarzschild field
Schmidt, H -J
2014-01-01
The equation of motion announced in the title was already deduced for the cases the inner metric being flat and the shell being negligibly small (test matter), using surface layers and geodesic trajectories resp. Here we derive the general equation of motion and solve it in closed form for the case of parabolic motion. Especially the motion near the horizon and near the singularity are examined.
Circular geodesics of naked singularities in the Kehagias-Sfetsos metric of Hořava's gravity
Vieira, Ronaldo S. S.; Schee, Jan; Kluźniak, Włodek; Stuchlík, Zdeněk; Abramowicz, Marek
2014-07-01
We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric of Hořava's gravity. For any value of the Hořava parameter ω, there are values of the gravitational mass M for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasistatic spherical fluid shell surrounded by an accretion disk, whose properties depend on the value of M, but are always very different from accretion disks familiar from the Kerr-metric solutions. The properties of the corresponding circular orbits are qualitatively similar to those of the Reissner-Nordström naked singularities. When event horizons are present, the orbits outside the Kehagias-Sfetsos black hole are qualitatively similar to those of the Schwarzschild metric.
METRICS DEVELOPMENT FOR PATENTS.
Veiga, Daniela Francescato; Ferreira, Lydia Masako
2015-01-01
To develop a proposal for metrics for patents to be applied in assessing the postgraduate programs of Medicine III - Capes. From the reading and analysis of the 2013 area documents of all the 48 areas of Capes, a proposal for metrics for patents was developed to be applied in Medicine III programs. Except for the areas Biotechnology, Food Science, Biological Sciences III, Physical Education, Engineering I, III and IV and Interdisciplinary, most areas do not adopt a scoring system for patents. The proposal developed was based on the criteria of Biotechnology, with adaptations. In general, it will be valued, in ascending order, the deposit, the granting and licensing/production. It will also be assigned higher scores to patents registered abroad and whenever there is a participation of students. This proposal can be applied to the item Intellectual Production of the evaluation form, in subsection Technical Production/Patents. The percentage of 10% for academic programs and 40% for Masters Professionals should be maintained. The program will be scored as Very Good when it reaches 400 points or over; Good, between 200 and 399 points; Regular, between 71 and 199 points; Weak up to 70 points; Insufficient, no punctuation. Desenvolver uma proposta de métricas para patentes a serem aplicadas na avaliação dos Programas de Pós-Graduação da Área Medicina III - Capes. A partir da leitura e análise dos documentos de área de 2013 de todas as 48 Áreas da Capes, desenvolveu-se uma proposta de métricas para patentes, a ser aplicada na avaliação dos programas da área. Constatou-se que, com exceção das áreas Biotecnologia, Ciência de Alimentos, Ciências Biológicas III, Educação Física, Engenharias I, III e IV e Interdisciplinar, a maioria não adota sistema de pontuação para patentes. A proposta desenvolvida baseou-se nos critérios da Biotecnologia, com adaptações. De uma forma geral, foi valorizado, em ordem crescente, o depósito, a concessão e o
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.
2008-01-01
As Global Positioning Satellite (GPS) applications become more prevalent for land- and air-based vehicles, GPS applications for space vehicles will also increase. The Applied Technology Directorate of Kennedy Space Center (KSC) has developed a lightweight, low-cost GPS Metric Tracking Unit (GMTU), the first of two steps in developing a lightweight, low-cost Space-Based Tracking and Command Subsystem (STACS) designed to meet Range Safety's link margin and latency requirements for vehicle command and telemetry data. The goals of STACS are to improve Range Safety operations and expand tracking capabilities for space vehicles. STACS will track the vehicle, receive commands, and send telemetry data through the space-based asset, which will dramatically reduce dependence on ground-based assets. The other step was the Low-Cost Tracking and Data Relay Satellite System (TDRSS) Transceiver (LCT2), developed by the Wallops Flight Facility (WFF), which allows the vehicle to communicate with a geosynchronous relay satellite. Although the GMTU and LCT2 were independently implemented and tested, the design collaboration of KSC and WFF engineers allowed GMTU and LCT2 to be integrated into one enclosure, leading to the final STACS. In operation, GMTU needs only a radio frequency (RF) input from a GPS antenna and outputs position and velocity data to the vehicle through a serial or pulse code modulation (PCM) interface. GMTU includes one commercial GPS receiver board and a custom board, the Command and Telemetry Processor (CTP) developed by KSC. The CTP design is based on a field-programmable gate array (FPGA) with embedded processors to support GPS functions.
Colonoscopy quality: metrics and implementation.
Calderwood, Audrey H; Jacobson, Brian C
2013-09-01
Colonoscopy is an excellent area for quality improvement because it is high volume, has significant associated risk and expense, and there is evidence that variability in its performance affects outcomes. The best end point for validation of quality metrics in colonoscopy is colorectal cancer incidence and mortality, but a more readily accessible metric is the adenoma detection rate. Fourteen quality metrics were proposed in 2006, and these are described in this article. Implementation of quality improvement initiatives involves rapid assessments and changes on an iterative basis, and can be done at the individual, group, or facility level. Copyright © 2013 Elsevier Inc. All rights reserved.
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.
On the topology of D-metric spaces and generation of D-metric spaces from metric spaces
S. V. R. Naidu; Rao, K. P. R.; N Srinivasa Rao
2004-01-01
An example of a D-metric space is given, in which D-metric convergence does not define a topology and in which a convergent sequence can have infinitely many limits. Certain methods for constructing D-metric spaces from a given metric space are developed and are used in constructing (1) an example of a D-metric space in which D-metric convergence defines a topology which is T1 but not Hausdorff, and (2) an example of a D-metric space in which D-metric convergence defines ...
Abodayeh, K.; Mlaiki, N.; T. Abdeljawad (Maraaba); Shatanawi, W.
2015-01-01
Very recently, Mehadi et al [M. Asadi, E. Karap{\\i}nar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on $M-$metric spaces] extended the partial metric spaces to the notion of $M-$metric spaces. In this article, we study some relations between partial metric spaces and $M-$metric spaces. Also, we generalize Caristi Kirki's Theorem from partial metric spaces to $M-$metric spaces, where we corrected some gaps in the proof of the main Theorem in E. Karap\\i n...
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)
Zimmerman, Marianna
1975-01-01
Describes a classroom activity which involved sixth grade students in a learning situation including making ice cream, safety procedures in a science laboratory, calibrating a thermometer, using metric units of volume and mass. (EB)
A unifying process capability metric
Directory of Open Access Journals (Sweden)
John Jay Flaig
2009-07-01
Full Text Available A new economic approach to process capability assessment is presented, which differs from the commonly used engineering metrics. The proposed metric consists of two economic capability measures – the expected profit and the variation in profit of the process. This dual economic metric offers a number of significant advantages over other engineering or economic metrics used in process capability analysis. First, it is easy to understand and communicate. Second, it is based on a measure of total system performance. Third, it unifies the fraction nonconforming approach and the expected loss approach. Fourth, it reflects the underlying interest of management in knowing the expected financial performance of a process and its potential variation.
Hyperbolic geometry for colour metrics.
Farup, Ivar
2014-05-19
It is well established from both colour difference and colour order perpectives that the colour space cannot be Euclidean. In spite of this, most colour spaces still in use today are Euclidean, and the best Euclidean colour metrics are performing comparably to state-of-the-art non-Euclidean metrics. In this paper, it is shown that a transformation from Euclidean to hyperbolic geometry (i.e., constant negative curvature) for the chromatic plane can significantly improve the performance of Euclidean colour metrics to the point where they are statistically significantly better than state-of-the-art non-Euclidean metrics on standard data sets. The resulting hyperbolic geometry nicely models both qualitatively and quantitatively the hue super-importance phenomenon observed in colour order systems.
Coverage Metrics for Model Checking
Penix, John; Visser, Willem; Norvig, Peter (Technical Monitor)
2001-01-01
When using model checking to verify programs in practice, it is not usually possible to achieve complete coverage of the system. In this position paper we describe ongoing research within the Automated Software Engineering group at NASA Ames on the use of test coverage metrics to measure partial coverage and provide heuristic guidance for program model checking. We are specifically interested in applying and developing coverage metrics for concurrent programs that might be used to support certification of next generation avionics software.
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.
Schwarzschildâde Sitter spacetime: The role of temperature in the emission of Hawking radiation
Directory of Open Access Journals (Sweden)
Thomas Pappas
2017-12-01
Full Text Available We consider a Schwarzschildâde Sitter (SdS black hole, and focus on the emission of massless scalar fields either minimally or non-minimally coupled to gravity. We use six different temperatures, two black-hole and four effective ones for the SdS spacetime, as the question of the proper temperature for such a background is still debated in the literature. We study their profiles under the variation of the cosmological constant, and derive the corresponding Hawking radiation spectra. We demonstrate that only few of these temperatures may support significant emission of radiation. We finally compute the total emissivities for each temperature, and show that the non-minimal coupling constant of the scalar field to gravity also affects the relative magnitudes of the energy emission rates.
The self-force on a non-minimally coupled static scalar charge outside a Schwarzschild black hole
Energy Technology Data Exchange (ETDEWEB)
Cho, Demian H J; Tsokaros, Antonios A; Wiseman, Alan G [Department of Physics, University of Wisconsin-Milwaukee, PO Box 413, Milwaukee, WI 53201 (United States)
2007-03-07
The finite part of the self-force on a static, non-minimally coupled scalar test charge outside a Schwarzschild black hole is zero. This result is determined from the work required to slowly raise or lower the charge through an infinitesimal distance. Unlike similar force calculations for minimally-coupled scalar charges or electric charges, we find that we must account for a flux of field energy that passes through the horizon and changes the mass and area of the black hole when the charge is displaced. This occurs even for an arbitrarily slow displacement of the non-minimally coupled scalar charge. For a positive coupling constant, the area of the hole increases when the charge is lowered and decreases when the charge is raised. The fact that the self-force vanishes for a static, non-minimally coupled scalar charge in Schwarzschild spacetime agrees with a simple prediction of the Quinn-Wald axioms. However, Zel'nikov and Frolov computed a non-vanishing self-force for a non-minimally coupled charge. Our method of calculation closely parallels the derivation of Zel'nikov and Frolov, and we show that their omission of this unusual flux is responsible for their (incorrect) result. When the flux is accounted for, the self-force vanishes. This correction eliminates a potential counter example to the Quinn-Wald axioms. The fact that the area of the black hole changes when the charge is displaced brings up two interesting questions that did not arise in similar calculations for static electric charges and minimally coupled scalar charges. (1) How can we reconcile a decrease in the area of the black hole horizon with the area theorem which concludes that {delta}Area{sub horizon} {>=} 0? The key hypothesis of the area theorem is that the stress-energy tensor must satisfy a null-energy condition T{sup {alpha}}{sup {beta}}l{sub {alpha}}l{sub {beta}} {>=} 0 for any null vector l{sub {alpha}}. We explicitly show that the stress-energy associated with a non
Conical Stream of the Two-Sided Jets in NGC 4261 over the Range of 103–109 Schwarzschild Radii
Directory of Open Access Journals (Sweden)
Satomi Nakahara
2016-12-01
Full Text Available We report the jet width profile of of the nearby ( ∼ 30 Mpc AGN NGC 4261 for both the approaching jet and the counter jet at radial distances ranging from ∼ 10 3 – 10 9 Schwarzschild radius ( R S from the central engine. Our Very Large Array (VLA and Very Long Baseline Array (VLBA observations reveal that the jets maintain a conical structure on both sides over the range 10 3 – 10 9 R S without any structural transition (i.e., parabolic to conical like in the approaching jet in M87. Thus, NGC 4261 will provide a unique opportunity to examine the conical jet hypothesis in blazars, while it may require some additional consideration on the acceleration and collimation process in AGN jets.
$P_{Z}(S)$-Metrics and $P_{Z}(S)$-Metric Spaces
Jafarpour-Golzari, Reza
2015-01-01
In this paper, we define notions of $P_{Z}(S)$-metric and $P_{Z}(S)$-metric space and we show that every $P_{Z}(S)$-metric Space, analogous to an ordinary metric space and generally, a $\\Lambda$-metric space, is a topological space, and in continuance, we show that from a topological point of view, some properties of $P_{Z}(S)$-metric spaces, and $\\Lambda$-metric spaces, have coordination.
Energy Technology Data Exchange (ETDEWEB)
Enqvist, Kari [Physics Department, University of Helsinki, and Helsinki Institute of Physics, FIN-00014 Helsinki (Finland); Koivisto, Tomi [Institute for Theoretical Physics and Spinoza Institute, Leuvenlaan 4, 3584 CE Utrecht (Netherlands); Rigopoulos, Gerasimos, E-mail: kari.enqvist@helsinki.fi, E-mail: T.S.Koivisto@astro.uio.no, E-mail: rigopoulos@physik.rwth-aachen.de [Institut für Theoretische Teilchenphysik und Kosmologie, RWTH Aachen University, D-52056 Aachen (Germany)
2012-05-01
We consider inflation within the context of what is arguably the simplest non-metric extension of Einstein gravity. There non-metricity is described by a single graviscalar field with a non-minimal kinetic coupling to the inflaton field Ψ, parameterized by a single parameter γ. There is a simple equivalent description in terms of a massless field and an inflaton with a modified potential. We discuss the implications of non-metricity for chaotic inflation and find that it significantly alters the inflaton dynamics for field values Ψ∼>M{sub P}/γ, dramatically changing the qualitative behaviour in this regime. In the equivalent single-field description this is described as a cuspy potential that forms of barrier beyond which the inflation becomes a ghost field. This imposes an upper bound on the possible number of e-folds. For the simplest chaotic inflation models, the spectral index and the tensor-to-scalar ratio receive small corrections dependent on the non-metricity parameter. We also argue that significant post-inflationary non-metricity may be generated.
DAML: domain adaptation metric learning.
Geng, Bo; Tao, Dacheng; Xu, Chao
2011-10-01
The state-of-the-art metric-learning algorithms cannot perform well for domain adaptation settings, such as cross-domain face recognition, image annotation, etc., because labeled data in the source domain and unlabeled ones in the target domain are drawn from different, but related distributions. In this paper, we propose the domain adaptation metric learning (DAML), by introducing a data-dependent regularization to the conventional metric learning in the reproducing kernel Hilbert space (RKHS). This data-dependent regularization resolves the distribution difference by minimizing the empirical maximum mean discrepancy between source and target domain data in RKHS. Theoretically, by using the empirical Rademacher complexity, we prove risk bounds for the nearest neighbor classifier that uses the metric learned by DAML. Practically, learning the metric in RKHS does not scale up well. Fortunately, we can prove that learning DAML in RKHS is equivalent to learning DAML in the space spanned by principal components of the kernel principle component analysis (KPCA). Thus, we can apply KPCA to select most important principal components to significantly reduce the time cost of DAML. We perform extensive experiments over four well-known face recognition datasets and a large-scale Web image annotation dataset for the cross-domain face recognition and image annotation tasks under various settings, and the results demonstrate the effectiveness of DAML. © 2011 IEEE
2010-01-01
... 7 Agriculture 12 2010-01-01 2010-01-01 false Metric units. 1794.4 Section 1794.4 Agriculture... (CONTINUED) ENVIRONMENTAL POLICIES AND PROCEDURES General § 1794.4 Metric units. RUS normally will prepare environmental documents using non-metric equivalents with one of the following two options; metric units in...
Lagrange Spaces with (γ,β-Metric
Directory of Open Access Journals (Sweden)
Suresh K. Shukla
2013-01-01
Full Text Available We study Lagrange spaces with (γ,β-metric, where γ is a cubic metric and β is a 1-form. We obtain fundamental metric tensor, its inverse, Euler-Lagrange equations, semispray coefficients, and canonical nonlinear connection for a Lagrange space endowed with a (γ,β-metric. Several other properties of such space are also discussed.
Metric spaces with unique pretangent spaces
Dovgoshey, Oleksiy; Abdullayev, Fahreddin; Kuchukaslan, Mehmet
2009-01-01
We find necessary and sufficient conditions under which an arbitrary metric space $X$ has a unique pretangent space at the marked point $a\\in X$. Key words: Metric spaces; Tangent spaces to metric spaces; Uniqueness of tangent metric spaces; Tangent space to the Cantor set.
Moduli spaces of riemannian metrics
Tuschmann, Wilderich
2015-01-01
This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.
Requirement Metrics for Risk Identification
Hammer, Theodore; Huffman, Lenore; Wilson, William; Rosenberg, Linda; Hyatt, Lawrence
1996-01-01
The Software Assurance Technology Center (SATC) is part of the Office of Mission Assurance of the Goddard Space Flight Center (GSFC). The SATC's mission is to assist National Aeronautics and Space Administration (NASA) projects to improve the quality of software which they acquire or develop. The SATC's efforts are currently focused on the development and use of metric methodologies and tools that identify and assess risks associated with software performance and scheduled delivery. This starts at the requirements phase, where the SATC, in conjunction with software projects at GSFC and other NASA centers is working to identify tools and metric methodologies to assist project managers in identifying and mitigating risks. This paper discusses requirement metrics currently being used at NASA in a collaborative effort between the SATC and the Quality Assurance Office at GSFC to utilize the information available through the application of requirements management tools.
Geodesics in Asymmetric Metric Spaces
Directory of Open Access Journals (Sweden)
Mennucci Andrea C. G.
2014-01-01
Full Text Available In a recent paper [17] we studied asymmetric metric spaces; in this context we studied the length of paths, introduced the class of run-continuous paths; and noted that there are different definitions of “length spaces” (also known as “path-metric spaces” or “intrinsic spaces”. In this paper we continue the analysis of asymmetric metric spaces.We propose possible definitions of completeness and (local compactness.We define the geodesics using as admissible paths the class of run-continuous paths.We define midpoints, convexity, and quasi-midpoints, but without assuming the space be intrinsic.We distinguish all along those results that need a stronger separation hypothesis. Eventually we discuss how the newly developed theory impacts the most important results, such as the existence of geodesics, and the renowned Hopf-Rinow (or Cohn-Vossen theorem.
Rainbow metric from quantum gravity
Directory of Open Access Journals (Sweden)
Mehdi Assanioussi
2015-12-01
Full Text Available In this Letter, we describe a general mechanism for emergence of a rainbow metric from a quantum cosmological model. This idea is based on QFT on a quantum spacetime. Under general assumptions, we discover that the quantum spacetime on which the field propagates can be replaced by a classical spacetime, whose metric depends explicitly on the energy of the field: as shown by an analysis of dispersion relations, quanta of different energy propagate on different metrics, similar to photons in a refractive material (hence the name “rainbow” used in the literature. In deriving this result, we do not consider any specific theory of quantum gravity: the qualitative behaviour of high-energy particles on quantum spacetime relies only on the assumption that the quantum spacetime is described by a wave-function Ψo in a Hilbert space HG.
Directory of Open Access Journals (Sweden)
Bessem Samet
2013-01-01
Full Text Available In 2005, Mustafa and Sims (2006 introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.
Probability measures on metric spaces
Parthasarathy, K R
2005-01-01
In this book, the author gives a cohesive account of the theory of probability measures on complete metric spaces (which is viewed as an alternative approach to the general theory of stochastic processes). After a general description of the basics of topology on the set of measures, the author discusses regularity, tightness, and perfectness of measures, properties of sampling distributions, and metrizability and compactness theorems. Next, he describes arithmetic properties of probability measures on metric groups and locally compact abelian groups. Covered in detail are notions such as decom
Thermodynamic Metrics and Optimal Paths
Energy Technology Data Exchange (ETDEWEB)
Sivak, David; Crooks, Gavin
2012-05-08
A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.
Metric structures of inviscid flows
Pasmanter, R A
1996-01-01
An intrinsic metric tensor, a flat connexion and the corresponding distance-like function are constructed in the configuration space formed by the velocity field {\\bf and} the thermodynamic variables of an inviscid fluid. The kinetic-energy norm is obtained as a limiting case; all physical quantities are Galilean invariant. Explicit expressions are given for the case of an ideal gas. The flat connexion is {\\bf not} metric-compatible. These results are achieved by applying the formalism of statistical manifolds \\cite{amari,otros} to the statistical mechanics of a moving fluid.
If d is super-metric, then d/(1+d) is super-metric
Warrens, Matthijs
2017-01-01
If a function d is metric, a well-known result is that d/(1 + d) is also metric. We consider m-ary analogs of the binary notion of semimetric, called hemi-metrics and super-metrics. The metrics are totally symmetric maps from Xm+1 into R≥0. It is shown that, if d is supermetric, then d/(1 + d) is
Warped products and Einstein metrics
Energy Technology Data Exchange (ETDEWEB)
Kim, Seongtag [Department of Mathematics Education, Inha University, Incheon 402-751 (Korea, Republic of)
2006-05-19
Warped product construction is an important method to produce a new metric with a base manifold and a fibre. We construct compact base manifolds with a positive scalar curvature which do not admit any non-trivial Einstein warped product, and noncompact complete base manifolds which do not admit any non-trivial Ricci-flat Einstein warped product. (letter to the editor)
Leading Gainful Employment Metric Reporting
Powers, Kristina; MacPherson, Derek
2016-01-01
This chapter will address the importance of intercampus involvement in reporting of gainful employment student-level data that will be used in the calculation of gainful employment metrics by the U.S. Department of Education. The authors will discuss why building relationships within the institution is critical for effective gainful employment…
Socio-technical security metrics
Gollmann, D.; Herley, C.; Koenig, V.; Pieters, W.; Sasse, M.A.
2015-01-01
Report from Dagstuhl seminar 14491. This report documents the program and the outcomes of Dagstuhl Seminar 14491 “Socio-Technical Security Metrics”. In the domain of safety, metrics inform many decisions, from the height of new dikes to the design of nuclear plants. We can state, for example, that
Modelling Software for Structure Metrics
van den Broek, P.M.; van den Berg, Klaas
In the approach to structural software metrics, software is modelled by means of flowgraphs. A tacit assumption in this approach is that the structure of a program is reflected by the structure of the flowgraph. When only the flow of control between commands is considered this assumption is valid;
Axiomatic Testing of Structure Metrics
van den Berg, Klaas; van den Broek, P.M.
1994-01-01
In this paper, axiomatic testing of software metrics is described. The testing is based on representation axioms from the measurement theory. In a case study, the axioms are given for the formal relational structure and the empirical relational structure. Two approaches of axiomatic testing are
Axiomatic Testing of Structure Metrics
van den Berg, Klaas; van den Broek, P.M.
In this paper, axiomatic testing of software metrics will be described. The testing is based on representation axioms from the measurement theory. In a case study, the axioms are given for the formal relational structure and the empirical relational structure. Two approaches of axiomatic testing are
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.
M. Deza; M. Laurent (Monique)
1997-01-01
htmlabstractCuts and metrics are well-known objects that arise - independently, but with many deep and fascinating connections - in diverse fields: in graph theory, combinatorial optimization, geometry of numbers, combinatorial matrix theory, statistical physics, VLSI design etc. This book offers a
Linear and Branching System Metrics
J., Hilston; de Alfaro, Luca; Faella, Marco; M.Z., Kwiatkowska; Telek, M.; Stoelinga, Mariëlle Ida Antoinette
We extend the classical system relations of trace inclusion, trace equivalence, simulation, and bisimulation to a quantitative setting in which propositions are interpreted not as boolean values, but as elements of arbitrary metric spaces. Trace inclusion and equivalence give rise to asymmetrical
Charged C-metric in conformal gravity
Lim, Yen-Kheng
2016-01-01
Using a C-metric-type ansatz, we obtain an exact solution to conformal gravity coupled to a Maxwell electromagnetic field. The solution resembles a C-metric spacetime carrying an electromagnetic charge. The metric is cast in a factorised form which allows us to study the domain structure of its static coordinate regions. This metric reduces to the well-known Mannheim-Kazanas metric under an appropriate limiting procedure, and also reduces to the (Anti-)de Sitter C-metric of Einstein gravity for a particular choice of parameters.
Sustainability Metrics: The San Luis Basin Project
Sustainability is about promoting humanly desirable dynamic regimes of the environment. Metrics: ecological footprint, net regional product, exergy, emergy, and Fisher Information. Adaptive management: (1) metrics assess problem, (2) specific problem identified, and (3) managemen...
Quality Metrics in Inpatient Neurology.
Dhand, Amar
2015-12-01
Quality of care in the context of inpatient neurology is the standard of performance by neurologists and the hospital system as measured against ideal models of care. There are growing regulatory pressures to define health care value through concrete quantifiable metrics linked to reimbursement. Theoretical models of quality acknowledge its multimodal character with quantitative and qualitative dimensions. For example, the Donabedian model distils quality as a phenomenon of three interconnected domains, structure-process-outcome, with each domain mutually influential. The actual measurement of quality may be implicit, as in peer review in morbidity and mortality rounds, or explicit, in which criteria are prespecified and systemized before assessment. As a practical contribution, in this article a set of candidate quality indicators for inpatient neurology based on an updated review of treatment guidelines is proposed. These quality indicators may serve as an initial blueprint for explicit quality metrics long overdue for inpatient neurology. Thieme Medical Publishers 333 Seventh Avenue, New York, NY 10001, USA.
Fuzzy polynucleotide spaces and metrics.
Nieto, Juan J; Torres, A; Georgiou, D N; Karakasidis, T E
2006-04-01
The study of genetic sequences is of great importance in biology and medicine. Mathematics is playing an important role in the study of genetic sequences and, generally, in bioinformatics. In this paper, we extend the work concerning the Fuzzy Polynucleotide Space (FPS) introduced in Torres, A., Nieto, J.J., 2003. The fuzzy polynucleotide Space: Basic properties. Bioinformatics 19(5); 587-592 and Nieto, J.J., Torres, A., Vazquez-Trasande, M.M. 2003. A metric space to study differences between polynucleotides. Appl. Math. Lett. 27:1289-1294: by studying distances between nucleotides and some complete genomes using several metrics. We also present new results concerning the notions of similarity, difference and equality between polynucleotides. The results are encouraging since they demonstrate how the notions of distance and similarity between polynucleotides in the FPS can be employed in the analysis of genetic material.
Quantum Metric of Classic Physics
Machusky, Eugene
2017-09-01
By methods of differential geometry and number theory the following has been established: All fundamental physical constants are the medians of quasi-harmonic functions of relative space and relative time. Basic quantum units are, in fact, the gradients of normal distribution of standing waves between the points of pulsating spherical spiral, which are determined only by functional bonds of transcendental numbers PI and E. Analytically obtained values of rotational speed, translational velocity, vibrational speed, background temperature and molar mass give the possibility to evaluate all basic quantum units with practically unlimited accuracy. Metric of quantum physics really is two-dimensional image of motion of waves in three-dimensional space. Standard physical model is correct, but SI metric system is insufficiently exact at submillimeter distances.
Multi-Metric Sustainability Analysis
Energy Technology Data Exchange (ETDEWEB)
Cowlin, Shannon [National Renewable Energy Lab. (NREL), Golden, CO (United States); Heimiller, Donna [National Renewable Energy Lab. (NREL), Golden, CO (United States); Macknick, Jordan [National Renewable Energy Lab. (NREL), Golden, CO (United States); Mann, Margaret [National Renewable Energy Lab. (NREL), Golden, CO (United States); Pless, Jacquelyn [National Renewable Energy Lab. (NREL), Golden, CO (United States); Munoz, David [Colorado School of Mines, Golden, CO (United States)
2014-12-01
A readily accessible framework that allows for evaluating impacts and comparing tradeoffs among factors in energy policy, expansion planning, and investment decision making is lacking. Recognizing this, the Joint Institute for Strategic Energy Analysis (JISEA) funded an exploration of multi-metric sustainability analysis (MMSA) to provide energy decision makers with a means to make more comprehensive comparisons of energy technologies. The resulting MMSA tool lets decision makers simultaneously compare technologies and potential deployment locations.
Relativistic electrons and magnetic fields of the M87 jet on the ∼10 Schwarzschild radii scale
Energy Technology Data Exchange (ETDEWEB)
Kino, M. [Korea Astronomy and Space Science Institute, 776 Daedukdae-ro, Yusong, Daejon 305-348 (Korea, Republic of); Takahara, F. [Department of Earth and Space Science, Osaka University, Toyonaka 560-0043 (Japan); Hada, K. [INAF—Istituto di Radioastronomia, via Gobetti 101, I-40129 Bologna (Italy); Doi, A. [Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency, 3-1-1 Yoshinodai, 229-8510 Sagamihara (Japan)
2014-05-01
We explore energy densities of the magnetic fields and relativistic electrons in the M87 jet. Since the radio core at the jet base is identical to the optically thick surface against synchrotron self-absorption (SSA), the observing frequency is identical to the SSA turnover frequency. As a first step, we assume the radio core has a simple uniform sphere geometry. Using the observed angular size of the radio core measured by the Very Long Baseline Array at 43 GHz, we estimate the energy densities of magnetic fields (U{sub B} ) and relativistic electrons (U{sub e} ) on the basis of the standard SSA formula. Imposing the condition that the Poynting power and kinetic power of relativistic electrons should be smaller than the total power of the jet, we find that (1) the allowed range of the magnetic field strength (B {sub tot}) is 1 G ≤ B {sub tot} ≤ 15 G and that (2) 1 × 10{sup –5} ≤ U{sub e} /U{sub B} ≤ 6 × 10{sup 2} holds. The uncertainty of U{sub e} /U{sub B} comes from the strong dependence on the angular size of the radio core and the minimum Lorentz factor of non-thermal electrons (γ {sub e,min}) in the core. It is still unsettled whether resultant energetics are consistent with either the magnetohydrodynamic jet or the kinetic power dominated jet even on the ∼10 Schwarzschild radii scale.
Otte, A N; Dickinson, H.; Funk, S.; Jogler, T.; Johnson, C.A.; Karn, P.; Meagher, K.; Naoya, H.; Nguyen, T.; Okumura, A.; Santander, M.; Sapozhnikov, L.; Stier, A.; Tajima, H.; Tibaldo, L.; Vandenbroucke, J.; Wakely, S.; Weinstein, A.; Williams, D.A.
2015-01-01
We present the development of a novel 11328 pixel silicon photomultiplier (SiPM) camera for use with a ground-based Cherenkov telescope with Schwarzschild-Couder optics as a possible medium-sized telescope for the Cherenkov Telescope Array (CTA). The finely pixelated camera samples air-shower images with more than twice the optical resolution of cameras that are used in current Cherenkov telescopes. Advantages of the higher resolution will be a better event reconstruction yielding improved background suppression and angular resolution of the reconstructed gamma-ray events, which is crucial in morphology studies of, for example, Galactic particle accelerators and the search for gamma-ray halos around extragalactic sources. Packing such a large number of pixels into an area of only half a square meter and having a fast readout directly attached to the back of the sensors is a challenging task. For the prototype camera development, SiPMs from Hamamatsu with through silicon via (TSV) technology are used. We give ...
Zakharov, Alexander F.
2018-01-01
Recently, Liu et al published a paper (2016 Class. Quantum Grav. 33 175014). In the abstract, the authors claimed as a key result of the paper that a particle sphere is found for the Schwarzschild black hole (BH), with its radius as a simple function of the particle velocity and proportional to the BH mass. Usually, if there are no references for the result it is assumed that the result was obtained originally in the paper; but this is not the case for the quoted paper. The concept of a particle sphere was introduced by Mielnik and Plebański (1962 Acta Phys. Pol. 21 239) and a simple derivation of the critical impact parameter was given in Zakharov A F (1988 Sov. Astron. 32 456 and Zakharov A F 1994 Class. Quantum Grav. 11 1027). We show that in slightly different notations, equation (17) for the critical impact parameter in Liu X et al (2016 Class. Quantum Grav. 33 175014) coincides with equation (12) in Zakharov (1994 Class. Quantum Grav. 11 1027) and with the corresponding equation (10.10) in Mielnik and Plebański (1962 Acta Phys. Pol. 21 239).
Kanti, P.; Pappas, T.; Pappas, N.
2014-12-01
In this paper, we consider the propagation of scalar particles in a higher-dimensional Schwarzschild-de Sitter black-hole spacetime, both on the brane and in the bulk. Our analysis applies for arbitrary partial modes and for both minimal and nonminimal coupling of the scalar field. A general expression for the greybody factor is analytically derived in each case, and its low-energy behavior is studied in detail. Its profile in terms of scalar properties (angular-momentum number and nonminimal coupling parameter) and spacetime properties (number of extra dimensions and cosmological constant) is thoroughly investigated. In contrast to previous studies, the effect of the cosmological constant is taken into account both close to and far away from the black-hole horizon. The dual role of the cosmological constant, that may act either as a helping agent to the emission of scalar particles or as a deterring effect depending on the value of the nonminimal coupling parameter, is also demonstrated.
Energy Technology Data Exchange (ETDEWEB)
He, Juan [School of Physics and Material Science, Anhui University, Hefei 230039 (China); School of Physics and Electronics Science, Fuyang Normal College, Fuyang 236037 (China); Xu, Shuai; Yu, Yang [School of Physics and Material Science, Anhui University, Hefei 230039 (China); Ye, Liu, E-mail: yeliu@ahu.edu.cn [School of Physics and Material Science, Anhui University, Hefei 230039 (China)
2015-01-05
We explore the performance of various correlation measures for open Dirac system with Hawking effect in Schwarzschild space–time. Our results indicate that the impact of Hawking effect on physical accessible entanglement is weaker than that of decoherence. For generalized amplitude damping (GAD) channel, the entanglement sudden death (ESD) is analyzed in detail, and the inequivalence of quantization for Dirac particles in the black hole and Kruskal space–time is verified via quantum discord measure. In addition, as an example for interpreting Bell non-locality, we study the GAD channel with Hawking effect. It can be noticed that there is a boundary line of Bell violation for physically accessible states. That is, quantum non-locality would disappear when Hawking temperature exceeds a certain value. This critical temperature increases as a decoherence parameter decreases. In the case of phase damping (PD) channel, the interaction between the particle and noise environment does not produce bipartite system–environment entanglement. Then we discuss entanglement distributions, and find that the reduced physically accessible entanglement can be redistributed to physical inaccessible region. At last, we extend our investigation to an N-qubit system, and obtain a universal expression of the physical accessible entanglement.
Barack, Leor
2011-01-01
We study conservative finite-mass corrections to the motion of a particle in a bound (eccentric) strong-field orbit around a Schwarzschild black hole. We assume the particle's mass $\\mu$ is much smaller than the black hole mass $M$, and explore post-geodesic corrections of $O(\\mu/M)$. Our analysis uses numerical data from a recently developed code that outputs the Lorenz-gauge gravitational self-force (GSF) acting on the particle along the eccentric geodesic. First, we calculate the $O(\\mu/M)$ conservative correction to the periastron advance of the orbit, as a function of the (gauge dependent) semi-latus rectum and eccentricity. A gauge-invariant description of the GSF precession effect is made possible in the circular-orbit limit, where we express the correction to the periastron advance as a function of the invariant azimuthal frequency. We compare this relation with results from fully nonlinear numerical-relativistic simulations. In order to obtain a gauge-invariant measure of the GSF effect for fully ecc...
Barack, Leor; Sago, Norichika
2010-01-01
Using a recently presented numerical code for calculating the Lorenz-gauge gravitational self-force (GSF), we compute the $O(m)$ conservative correction to the precession rate of the small-eccentricity orbits of a particle of mass $m$ moving around a Schwarzschild black hole of mass ${\\mathsf M}\\gg m$. Specifically, we study the gauge-invariant function $\\rho(x)$, where $\\rho$ is defined as the $O(m)$ part of the dimensionless ratio $(\\hat\\Omega_r/\\hat\\Omega_{\\varphi})^2$ between the squares of the radial and azimuthal frequencies of the orbit, and where $x=[Gc^{-3}({\\mathsf M}+m)\\hat\\Omega_{\\varphi}]^{2/3}$ is a gauge-invariant measure of the dimensionless gravitational potential (mass over radius) associated with the mean circular orbit. Our GSF computation of the function $\\rho(x)$ in the interval $0
Topology of soft cone metric spaces
Altintas, Ismet; Simsek, Dagistan; Taskopru, Kemal
2017-09-01
In Simsek's paper it was introduced a concept of soft cone metric space via soft elements and some fixed point theorems in soft cone metric space were provided. In this work, we examine topological structures such as open ball, soft neighbourhood and soft open set in soft metric spaces and their some properties, and prove that every soft cone metric space under some condition is a soft topological space according to elementary operations on soft sets.
The Metric of Quantum States Revisited
Pandya, Aalok; Nagawat, Ashok K.
2002-01-01
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised definition. The metric of quantum states in the configuration space and its possible geometrical framework is explored. Also, invariance of the metric of quantum states under local gauge transformations, coordinate transformations, and the relativistic transformat...
Object-Oriented Metrics Which Predict Maintainability
Li, Wei; Henry, Sallie M.
1993-01-01
Software metrics have been studied in the procedural paradigm as a quantitative means of assessing the software development process as well as the quality of software products. Several studies have validated that various metrics are useful indicators of maintenance effort in the procedural paradigm. However, software metrics have rarely been studied in the object oriented paradigm. Very few metrics have been proposed to measure object oriented systems, and the proposed ones have not been v...
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.
Congress Inches Away from Metric Conversion
Russell, Cristine
1974-01-01
Reasons are discussed concerning the House of Representatives' defeat in 1974 of a bill to establish a National Metric Conversion Board which would coordinate the process of voluntary conversion to the metric system a ten-year period. A brief history of the metric system in the United States is included. (DT)
Training Fundamentals Help Control Metric Conversion Cost
Hinkle, Peyton B.
1974-01-01
The increasing worldwide use of the metric system is leading the United States into abandoning the English system of measurement and undertaking the monumental task of converting to the metric system. Great Britain offers valuable training experience to the United States with their seven year lead into metrication. (DS)
Federal Government's Role in Metric Conversion
Barbrow, L. E.
1974-01-01
The coordinator for metric activities at the National Bureau of Standards views the primary responsibilities for metrication as resting in the private sector, but sees the Federal government assisting and coordinating the changeover. A National Metric Conversion Board will probably be created through legislation to coordinate the effort. (AG)
Context-dependent ATC complexity metric
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,
Metrics Made Easy: A Classroom Guide - 1978.
Blau, Sharon; And Others
This classroom guide for metric education included a brief rationale and history of metrics, a preliminary metric quiz, a symbol summary, and a list of recommended instructional materials. The guide is comprised primarily of four sections covering the topics of: weight, length, volume, and temperature. Each of these sections contains goals and…
Towards a catalog format for software metrics
Bouwers, E.; Visser, J.; Van Deursen, A.
2014-01-01
In the past two decades both the industry and the research community have proposed hundreds of metrics to track software projects, evaluate quality or estimate effort. Unfortunately, it is not always clear which metric works best in a particular context. Even worse, for some metrics there is little
Modeling and analysis of metrics databases
Paul, Raymond A.
1999-01-01
The main objective of this research is to propose a comprehensive framework for quality and risk management in software development process based on analysis and modeling of software metrics data. Existing software metrics work has focused mainly on the type of metrics tobe collected ...
Invariant Matsumoto metrics on homogeneous spaces
Salimi Moghaddam, H.R.
2014-01-01
In this paper we consider invariant Matsumoto metrics which are induced by invariant Riemannian metrics and invariant vector fields on homogeneous spaces, and then we give the flag curvature formula of them. Also we study the special cases of naturally reductive spaces and bi-invariant metrics. We end the article by giving some examples of geodesically complete Matsumoto spaces.
Quality metrics for sensor images
Ahumada, AL
1993-01-01
Methods are needed for evaluating the quality of augmented visual displays (AVID). Computational quality metrics will help summarize, interpolate, and extrapolate the results of human performance tests with displays. The FLM Vision group at NASA Ames has been developing computational models of visual processing and using them to develop computational metrics for similar problems. For example, display modeling systems use metrics for comparing proposed displays, halftoning optimizing methods use metrics to evaluate the difference between the halftone and the original, and image compression methods minimize the predicted visibility of compression artifacts. The visual discrimination models take as input two arbitrary images A and B and compute an estimate of the probability that a human observer will report that A is different from B. If A is an image that one desires to display and B is the actual displayed image, such an estimate can be regarded as an image quality metric reflecting how well B approximates A. There are additional complexities associated with the problem of evaluating the quality of radar and IR enhanced displays for AVID tasks. One important problem is the question of whether intruding obstacles are detectable in such displays. Although the discrimination model can handle detection situations by making B the original image A plus the intrusion, this detection model makes the inappropriate assumption that the observer knows where the intrusion will be. Effects of signal uncertainty need to be added to our models. A pilot needs to make decisions rapidly. The models need to predict not just the probability of a correct decision, but the probability of a correct decision by the time the decision needs to be made. That is, the models need to predict latency as well as accuracy. Luce and Green have generated models for auditory detection latencies. Similar models are needed for visual detection. Most image quality models are designed for static imagery
Crowdsourcing metrics of digital collections
Directory of Open Access Journals (Sweden)
Tuula Pääkkönen
2015-12-01
Full Text Available In the National Library of Finland (NLF there are millions of digitized newspaper and journal pages, which are openly available via the public website http://digi.kansalliskirjasto.fi. To serve users better, last year the front end was completely overhauled with its main aim in crowdsourcing features, e.g., by giving end-users the opportunity to create digital clippings and a personal scrapbook from the digital collections. But how can you know whether crowdsourcing has had an impact? How much crowdsourcing functionalities have been used so far? Did crowdsourcing work? In this paper the statistics and metrics of a recent crowdsourcing effort are analysed across the different digitized material types (newspapers, journals, ephemera. The subjects, categories and keywords given by the users are analysed to see which topics are the most appealing. Some notable public uses of the crowdsourced article clippings are highlighted. These metrics give us indications on how the end-users, based on their own interests, are investigating and using the digital collections. Therefore, the suggested metrics illustrate the versatility of the information needs of the users, varying from citizen science to research purposes. By analysing the user patterns, we can respond to the new needs of the users by making minor changes to accommodate the most active participants, while still making the service more approachable for those who are trying out the functionalities for the first time. Participation in the clippings and annotations can enrich the materials in unexpected ways and can possibly pave the way for opportunities of using crowdsourcing more also in research contexts. This creates more opportunities for the goals of open science since source data becomes available, making it possible for researchers to reach out to the general public for help. In the long term, utilizing, for example, text mining methods can allow these different end-user segments to
Some Equivalences between Cone $b$ -Metric Spaces and $b$ -Metric Spaces
Poom Kumam; Nguyen Dung; Vo Thi Le Hang
2013-01-01
We introduce a $b$ -metric on the cone $b$ -metric space and then prove some equivalences between them. As applications, we show that fixed point theorems on cone $b$ -metric spaces can be obtained from fixed point theorems on $b$ -metric spaces.
Web metrics for library and information professionals
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...
Adaptive Optics Metrics & QC Scheme
Girard, Julien H.
2017-09-01
"There are many Adaptive Optics (AO) fed instruments on Paranal and more to come. To monitor their performances and assess the quality of the scientific data, we have developed a scheme and a set of tools and metrics adapted to each flavour of AO and each data product. Our decisions to repeat observations or not depends heavily on this immediate quality control "zero" (QC0). Atmospheric parameters monitoring can also help predict performances . At the end of the chain, the user must be able to find the data that correspond to his/her needs. In Particular, we address the special case of SPHERE."
DEFF Research Database (Denmark)
Gravesen, Jens
2015-01-01
The space of colours is a fascinating space. It is a real vector space, but no matter what inner product you put on the space the resulting Euclidean distance does not correspond to human perception of difference between colours. In 1942 MacAdam performed the first experiments on colour matching...... and found the MacAdam ellipses which are often interpreted as defining the metric tensor at their centres. An important question is whether it is possible to define colour coordinates such that the Euclidean distance in these coordinates correspond to human perception. Using cubic splines to represent...
Sterken, C.; Dick, W. R.; Hamel, J.
2002-12-01
astronomers in his days, when his working place at Altona still belonged to the kingdom of Denmark. This paper is followed by a second one by the same author and deals with the correspondence of H. C. Schumacher and H C. Oersted (1777-1851) and shows how intense and diverse their cooperation was. In a subsequent paper, Wolfgang Kokott describes the role of the Astronomisches Jahrbuch (published from 1776 by the Royal Academy of Sciences at Berlin), a ranking international publication, with Bode's modest Berlin Observatory serving as a clearinghouse of information originating from virtually all European countries. "Karl Schwarzschild and the professionalisation of Astrophysics" is the title of Theodor Schmidt-Kaler's contribution and presents Schwarzschild's contributions to professionalization of astronomy: establishment of course lectures and a permanent astrophysical laboratory, a tight connection between teaching and research, stimulations and suggestions for astronomy at high school and for the formation of high school teachers, international organisation, and the planning of a southern observatory. Peter Habison describes the contribution of Leo de Ball (1853-1916, Director of the Kuffner Observatory in Vienna) to international astronomy. Internationalization in astronomy is also discussed in a following paper by Gudrun Wolfschmidt on the establishment of the Vereinigte Astronomische Gesellschaft, the international Astronomische Gesellschaft in 1863 and finally the International Astronomical Union in 1919. In the second but last paper of the book, Hilmar Duerbeck describes the history of the Chilean National Observatory, beginning with its origins out of Gilliss' US Naval Expedition to the Southern Hemisphere in 1849, over its directors Moesta, Vergara, Obrecht and Ristenpart, to the middle of the 20th century. The paper also includes the astronomical development at the Universidad Catolica and various international expeditions, which aimed at the observations of solar
Huang, ChunYu; Ma, Wen-chao; Wang, Dong; Ye, Liu
2018-01-01
In this work, the effect of Hawking radiation on the quantum Fisher information (QFI) of Dirac particles is investigated in the background of a Schwarzschild black hole. Interestingly, it has been verified that the QFI with respect to the weight parameter θ of a target state is always independent of the Hawking temperature T. This implies that if we encode the information on the weight parameter, then we can affirm that the corresponding accuracy of the parameter estimation will be immune to the Hawking effect. Besides, it reveals that the QFI with respect to the phase parameter φ exhibits a decay behavior with the increase in the Hawking temperature T and converges to a nonzero value in the limit of infinite Hawking temperature T. Remarkably, it turns out that the function F_φ on θ =π \\big /4 symmetry was broken by the influence of the Hawking radiation. Finally, we generalize the case of a three-qubit system to a case of a N-qubit system, i.e., |ψ > _{1,2,3,\\ldots ,N} =(cos θ | 0 > ^{⊗ N}+sin θ e^{iφ }| 1 > ^{⊗ N}) and obtain an interesting result: the number of particles in the initial state does not affect the QFI F_θ , nor the QFI F_φ . However, with the increasing number of particles located near the event horizon, F_φ will be affected by Hawking radiation to a large extent, while F_θ is still free from disturbance resulting from the Hawking effects.
Kowalczyk, Klaudia; Łokas, Ewa L.; Valluri, Monica
2018-02-01
In our previous work we confirmed the reliability of the spherically symmetric Schwarzschild orbit-superposition method to recover the mass and velocity anisotropy profiles of spherical dwarf galaxies. Here we investigate the effect of its application to intrinsically non-spherical objects. For this purpose we use a model of a dwarf spheroidal galaxy formed in a numerical simulation of a major merger of two disky dwarfs. The shape of the stellar component of the merger remnant is axisymmetric and prolate which allows us to identify and measure the bias caused by observing the spheroidal galaxy along different directions, especially the longest and shortest principal axis. The modelling is based on mock data generated from the remnant that are observationally available for dwarfs: projected positions and line-of-sight velocities of the stars. In order to obtain a reliable tool while keeping the number of parameters low we parametrize the total mass distribution as a radius-dependent mass-to-light ratio with just two free parameters we aim to constrain. Our study shows that if the total density profile is known, the true, radially increasing anisotropy profile can be well recovered for the observations along the longest axis whereas the data along the shortest axis lead to the inference an incorrect, isotropic model. On the other hand, if the density profile is derived from the method as well, the anisotropy is always underestimated but the total mass profile is well recovered for the data along the shortest axis whereas for the longest axis the mass content is overestimated.
Ribeiro, Deivid; Humensky, Brian; Nieto, Daniel; V Vassiliev Group in UCLA division of Astronomy and Astrophysics, P Kaaret Group at Iowa University Department of Physics and Astronomy, CTA Consortium
2016-01-01
The Cherenkov Telescope Array (CTA) is an international project for a next-generation ground-based gamma-ray observatory. CTA, conceived as an array of tens of imaging atmospheric Cherenkov telescopes, comprising small, medium and large-size telescopes, is aiming to improve on the sensitivity of current-generation experiments by an order of magnitude and provide energy coverage from 20 GeV to more than 300 TeV. The Schwarzschild-Couder design is a candidate 9-m diameter medium-sized telescope featuring a novel aplanatic two-mirror optical design capable of a wide field of view with significantly improved imaging resolution as compared to the traditional Davies-Cotton optical design. Achieving this imaging resolution imposes strict mirror alignment requirements that necessitate a sophisticated alignment system. This system uses a collection of position sensors between panels to determine the relative position of adjacent panels; each panel is mounted on a Stewart platform to allow motion control with six degrees of freedom, facilitating the alignment of the optical surface for the segmented primary and secondary mirrors. Alignments of the primary and secondary mirrors and the camera focal plane with respect to each other are performed utilizing a set of CCD cameras which image LEDs placed on the mirror panels to measure relative translation, and custom-built auto-collimators to measure relative tilt between the primary and secondary mirrors along the optical axis of the telescope. In this contribution we present the status of the development of the SC optical alignment system, soon to be materialized in a full-scale prototype SC medium-size telescope (pSCT) at the Fred Lawrence Whipple Observatory in southern Arizona.
Conversation level syntax similarity metric.
Boghrati, Reihane; Hoover, Joe; Johnson, Kate M; Garten, Justin; Dehghani, Morteza
2017-07-11
The syntax and semantics of human language can illuminate many individual psychological differences and important dimensions of social interaction. Accordingly, psychological and psycholinguistic research has begun incorporating sophisticated representations of semantic content to better understand the connection between word choice and psychological processes. In this work we introduce ConversAtion level Syntax SImilarity Metric (CASSIM), a novel method for calculating conversation-level syntax similarity. CASSIM estimates the syntax similarity between conversations by automatically generating syntactical representations of the sentences in conversation, estimating the structural differences between them, and calculating an optimized estimate of the conversation-level syntax similarity. After introducing and explaining this method, we report results from two method validation experiments (Study 1) and conduct a series of analyses with CASSIM to investigate syntax accommodation in social media discourse (Study 2). We run the same experiments using two well-known existing syntactic metrics, LSM and Coh-Metrix, and compare their results to CASSIM. Overall, our results indicate that CASSIM is able to reliably measure syntax similarity and to provide robust evidence of syntax accommodation within social media discourse.
Quality metrics for detailed clinical models.
Ahn, SunJu; Huff, Stanley M; Kim, Yoon; Kalra, Dipak
2013-05-01
To develop quality metrics for detailed clinical models (DCMs) and test their validity. Based on existing quality criteria which did not include formal metrics, we developed quality metrics by applying the ISO/IEC 9126 software quality evaluation model. The face and content validity of the initial quality metrics were assessed by 9 international experts. Content validity was defined as agreement by over 70% of the panelists. For eliciting opinions and achieving consensus of the panelists, a two round Delphi survey was conducted. Valid quality metrics were considered reliable if agreement between two evaluators' assessments of two example DCMs was over 0.60 in terms of the kappa coefficient. After reliability and validity were tested, the final DCM quality metrics were selected. According to the results of the reliability test, the degree of agreement was high (a kappa coefficient of 0.73). Based on the results of the reliability test, 8 quality evaluation domains and 29 quality metrics were finalized as DCM quality metrics. Quality metrics were validated by a panel of international DCM experts. Therefore, we expect that the metrics, which constitute essential qualitative and quantitative quality requirements for DCMs, can be used to support rational decision-making by DCM developers and clinical users. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.
Mapping the spacetime metric with GNSS: a preliminary study
Delva, P
2009-01-01
In order to do relativistic gravimetry one needs to define a system of null coordinates for a given constellation of satellites. We present here three methods in order to find the null coordinates of an event in a Schwarzschild geometry. We implement these three methods for the weak gravitational field of the Earth, compare their precision and time of computation.
Fast similarity search for learned metrics.
Kulis, Brian; Jain, Prateek; Grauman, Kristen
2009-12-01
We introduce a method that enables scalable similarity search for learned metrics. Given pairwise similarity and dissimilarity constraints between some examples, we learn a Mahalanobis distance function that captures the examples' underlying relationships well. To allow sublinear time similarity search under the learned metric, we show how to encode the learned metric parameterization into randomized locality-sensitive hash functions. We further formulate an indirect solution that enables metric learning and hashing for vector spaces whose high dimensionality makes it infeasible to learn an explicit transformation over the feature dimensions. We demonstrate the approach applied to a variety of image data sets, as well as a systems data set. The learned metrics improve accuracy relative to commonly used metric baselines, while our hashing construction enables efficient indexing with learned distances and very large databases.
Addazi, Andrea; Nojiri, Shin'ichi; Odintsov, Sergei
2017-06-01
We study the problem of a four-dimensional brane lying in the five-dimensional degenerate Schwarzschild-de Sitter (Nariai) black hole in five-dimensional F (R ) gravity. We show that there cannot exist the brane in the Nariai bulk space except for the case where the brane tension vanishes. We demonstrate that the five-dimensional Nariai bulk is unstable in a large region of the parameter space. In particular, the Nariai bulk can have classical (anti)evaporation instabilities. The bulk instability backreacts on the four-dimensional brane, in that case, the brane tension vanishes, and the unstable modes propagate in their world volume.
Metric implementation in U.S. construction.
Holland, Andrew J.
1997-01-01
Throughout the history of industrialization, people have been trying to develop a single system of measurement with a worldwide acceptance. Since its inception two centuries ago, the metric system has been gaining ground over the traditional "inch pound" system. Today, the United States remains as the sole user of the "inch pound" system of measurements. The pressure for unification into the metric system has been mounting. With the emergence of the "global economy," non metric products are b...
The definitive guide to IT service metrics
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.
The Kerr-Newman metric: A Review
Adamo, Tim
2014-01-01
The Kerr-Newman metric describes a very special rotating, charged mass and is the most general of the asymptotically flat stationary 'black hole' solutions to the Einstein-Maxwell equations of general relativity. We review the derivation of this metric from the Reissner-Nordstrom solution by means of a complex transformation algorithm and provide a brief overview of its basic geometric properties. We also include some discussion of interpretive issues, related metrics, and higher-dimensional analogues.
Particles and Strings in Degenerate Metric Spaces
Cabral, Luis A.; Rivelles, Victor O.
1999-01-01
We consider relativistic and non-relativistic particles and strings in spaces (or space-times) with a degenerate metric. We show that the resulting dynamics is described by a rich structure of constraints. All constraints are classified and the dynamics depends strongly on the parity of the difference between the dimension of the space (or space-time) and the rank of the degenerate metric. For a particular class of degenerate metrics we can identify the null eigenvectors of the metric with it...
Semantic Metrics for Object Oriented Design
Etzkorn, Lethe
2003-01-01
The purpose of this proposal is to research a new suite of object-oriented (OO) software metrics, called semantic metrics, that have the potential to help software engineers identify fragile, low quality code sections much earlier in the development cycle than is possible with traditional OO metrics. With earlier and better Fault detection, software maintenance will be less time consuming and expensive, and software reusability will be improved. Because it is less costly to correct faults found earlier than to correct faults found later in the software lifecycle, the overall cost of software development will be reduced. Semantic metrics can be derived from the knowledge base of a program understanding system. A program understanding system is designed to understand a software module. Once understanding is complete, the knowledge-base contains digested information about the software module. Various semantic metrics can be collected on the knowledge base. This new kind of metric measures domain complexity, or the relationship of the software to its application domain, rather than implementation complexity, which is what traditional software metrics measure. A semantic metric will thus map much more closely to qualities humans are interested in, such as cohesion and maintainability, than is possible using traditional metrics, that are calculated using only syntactic aspects of software.
Bounds for phylogenetic network space metrics.
Francis, Andrew; Huber, Katharina T; Moulton, Vincent; Wu, Taoyang
2018-04-01
Phylogenetic networks are a generalization of phylogenetic trees that allow for representation of reticulate evolution. Recently, a space of unrooted phylogenetic networks was introduced, where such a network is a connected graph in which every vertex has degree 1 or 3 and whose leaf-set is a fixed set X of taxa. This space, denoted [Formula: see text], is defined in terms of two operations on networks-the nearest neighbor interchange and triangle operations-which can be used to transform any network with leaf set X into any other network with that leaf set. In particular, it gives rise to a metric d on [Formula: see text] which is given by the smallest number of operations required to transform one network in [Formula: see text] into another in [Formula: see text]. The metric generalizes the well-known NNI-metric on phylogenetic trees which has been intensively studied in the literature. In this paper, we derive a bound for the metric d as well as a related metric [Formula: see text] which arises when restricting d to the subset of [Formula: see text] consisting of all networks with [Formula: see text] vertices, [Formula: see text]. We also introduce two new metrics on networks-the SPR and TBR metrics-which generalize the metrics on phylogenetic trees with the same name and give bounds for these new metrics. We expect our results to eventually have applications to the development and understanding of network search algorithms.
Simple emission metrics for climate impacts
Directory of Open Access Journals (Sweden)
B. Aamaas
2013-06-01
Full Text Available In the context of climate change, emissions of different species (e.g., carbon dioxide and methane are not directly comparable since they have different radiative efficiencies and lifetimes. Since comparisons via detailed climate models are computationally expensive and complex, emission metrics were developed to allow a simple and straightforward comparison of the estimated climate impacts of emissions of different species. Emission metrics are not unique and variety of different emission metrics has been proposed, with key choices being the climate impacts and time horizon to use for comparisons. In this paper, we present analytical expressions and describe how to calculate common emission metrics for different species. We include the climate metrics radiative forcing, integrated radiative forcing, temperature change and integrated temperature change in both absolute form and normalised to a reference gas. We consider pulse emissions, sustained emissions and emission scenarios. The species are separated into three types: CO2 which has a complex decay over time, species with a simple exponential decay, and ozone precursors (NOx, CO, VOC which indirectly effect climate via various chemical interactions. We also discuss deriving Impulse Response Functions, radiative efficiency, regional dependencies, consistency within and between metrics and uncertainties. We perform various applications to highlight key applications of emission metrics, which show that emissions of CO2 are important regardless of what metric and time horizon is used, but that the importance of short lived climate forcers varies greatly depending on the metric choices made. Further, the ranking of countries by emissions changes very little with different metrics despite large differences in metric values, except for the shortest time horizons (GWP20.
On an equivalence of the topology of algebraic cone metric spaces and metric spaces
Gamchi, Saeedeh Shamsi; Janfada, Mohammad; Niknam, Assadollah
2014-01-01
In this paper, we prove that the topology induced by algebraic cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e. any algebraic cone metric space is metrizable. Furthermore, the notion of algebraic cone normed space is introduced and also normability of the topology of this space is proved.
Fixed point theory in metric type spaces
Agarwal, Ravi P; O’Regan, Donal; Roldán-López-de-Hierro, Antonio Francisco
2015-01-01
Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise natur...
Cluster-based adaptive metric classification
Giotis, Ioannis; Petkov, Nicolai
2012-01-01
Introducing adaptive metric has been shown to improve the results of distance-based classification algorithms. Existing methods are often computationally intensive, either in the training or in the classification phase. We present a novel algorithm that we call Cluster-Based Adaptive Metric (CLAM)
Metric Conversion: Remedy or Rip-Off?
Schenck, John P.
1975-01-01
Opinions on metric conversion from seven large industrial organizations reflect inadequate evidence predicating conversion, no compelling need for conversion, opposition to hard conversion, lack of information about the financial and social costs of conversion, and feelings that metrics as the sole language of measurement will be regressive.…
Metric Conversion as a Planning Problem
Dieffenderfer, Richard A.
1974-01-01
A national survey of 200 vocational education leaders produced a status report on the efforts of States in developing metric education programs by determining the extent to which programs had been initiated, when programs were scheduled to begin, and when metric program development was expected to begin. (AG)
Discrete homology theory for metric spaces
H. Barcelo (Hélène); V. Capraro (Valerio); J. A. White; H. Barcelo (Hélène)
2014-01-01
htmlabstractWe define and study a notion of discrete homology theory for metric spaces. Instead of working with simplicial homology, our chain complexes are given by Lipschitz maps from an n n -dimensional cube to a fixed metric space. We prove that the resulting homology theory satisfies a
Using Metrics to Measure Contractor Performance
Engelbeck, R. Marshall
2004-01-01
Proceedings Paper (for Acquisition Research Program) This Project examines the use of metrics as a means to measure contractor performance. It is also designed to supplement the research being done on the ''Characteristics of Good Metrics for Performance Based Logistics (PBL)'' by Professors Ken Doerr and Ira Lewis along with Admiral Eaton. Acquisition Research Program
Fuzzy Set Field and Fuzzy Metric
Gebru Gebray; B. Krishna Reddy
2014-01-01
The notation of fuzzy set field is introduced. A fuzzy metric is redefined on fuzzy set field and on arbitrary fuzzy set in a field. The metric redefined is between fuzzy points and constitutes both fuzziness and crisp property of vector. In addition, a fuzzy magnitude of a fuzzy point in a field is defined.
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree (≥ 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system parameters, we ...
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.
Invariant metric for nonlinear symplectic maps
Indian Academy of Sciences (India)
Abstract. In this paper, we construct an invariant metric in the space of homogeneous polynomials of a given degree ( 3). The homogeneous polynomials specify a nonlinear symplectic map which in turn represents a Hamiltonian system. By minimizing the norm constructed out of this metric as a function of system ...
Quantitative metric theory of continued fractions
Indian Academy of Sciences (India)
Quantitative versions of the central results of the metric theory of contin- ued fractions were given primarily by C. ... Continued fractions; ergodic averages; metric theory of numbers. Mathematics Subject ... of subsets of X, a probability measure μ on the measurable space (X, β) and a measurable self-map T of X that is also ...
Group representations in indefinite metric spaces
van den Broek, P.M.; Denardo, G.; Ghirardi, G.; Weber, T.
1984-01-01
A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator eta leads to a projective representation U of G in V in terms of eta-unitary, eta-antiunitary, eta-pseudounitary, and eta-pseudoantiunitary operators. We investigate the restrictions which are put
Group representations in indefinite metric spaces
van den Broek, P.M.
A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator eta leads to a projective representation U of G in V in terms of eta-unitary, eta-antiunitary, eta-pseudounitary, and eta-pseudoantiunitary operators. We investigate the restrictions which are put
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.
Information metric from a linear sigma model.
Miyamoto, U; Yahikozawa, S
2012-05-01
The idea that a space-time metric emerges as a Fisher-Rao "information metric" of instanton moduli space has been examined in several field theories, such as the Yang-Mills theories and nonlinear σ models. In this paper, we report that the flat Euclidean or Minkowskian metric, rather than an anti-de Sitter metric that generically emerges from instanton moduli spaces, can be obtained as the Fisher-Rao metric from a nontrivial solution of the massive Klein-Gordon field (a linear σ model). This realization of the flat space from the simple field theory would be useful to investigate the ideas that relate the space-time geometry with the information geometry.
The metrics of science and technology
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...
Metrics for border management systems.
Energy Technology Data Exchange (ETDEWEB)
Duggan, Ruth Ann
2009-07-01
There are as many unique and disparate manifestations of border systems as there are borders to protect. Border Security is a highly complex system analysis problem with global, regional, national, sector, and border element dimensions for land, water, and air domains. The complexity increases with the multiple, and sometimes conflicting, missions for regulating the flow of people and goods across borders, while securing them for national security. These systems include frontier border surveillance, immigration management and customs functions that must operate in a variety of weather, terrain, operational conditions, cultural constraints, and geopolitical contexts. As part of a Laboratory Directed Research and Development Project 08-684 (Year 1), the team developed a reference framework to decompose this complex system into international/regional, national, and border elements levels covering customs, immigration, and border policing functions. This generalized architecture is relevant to both domestic and international borders. As part of year two of this project (09-1204), the team determined relevant relative measures to better understand border management performance. This paper describes those relative metrics and how they can be used to improve border management systems.
String Rearrangement Metrics: A Survey
Amir, Amihood; Levy, Avivit
A basic assumption in traditional pattern matching is that the order of the elements in the given input strings is correct, while the description of the content, i.e. the description of the elements, may be erroneous. Motivated by questions that arise in Text Editing, Computational Biology, Bit Torrent and Video on Demand, and Computer Architecture, a new pattern matching paradigm was recently proposed by [2]. In this model, the pattern content remains intact, but the relative positions may change. Several papers followed the initial definition of the new paradigm. Each paper revealed new aspects in the world of string rearrangement metrics. This new unified view has already proven itself by enabling the solution of an open problem of the mathematician Cayley from 1849. It also gave better insight to problems that were already studied in different and limited situations, such as the behavior of different cost functions, and enabled deriving results for cost functions that were not yet sufficiently analyzed by previous research. At this stage, a general understanding of this new model is beginning to coalesce. The aim of this survey is to present an overview of this recent new direction of research, the problems, the methodologies, and the state-of-the-art.
Families of quasi-pseudo-metrics generated by probabilistic quasi-pseudo-metric spaces
Directory of Open Access Journals (Sweden)
Mariusz T. Grabiec
2008-03-01
Full Text Available This paper contains a study of families of quasi-pseudo-metrics (the concept of a quasi-pseudo-metric was introduced by Wilson (1931 , Albert (1941 and Kelly (1963 generated by probabilistic quasi-pseudo-metric-spaces which are generalization of probabilistic metric space (PM-space shortly [2, 3, 4, 6]. The idea of PM-spaces was introduced by Menger (1942, 1951, Schweizer and Sklar (1983 and Serstnev (1965. Families of pseudo-metrics generated by PM-spaces and those generalizing PM-spaces have been described by Stevens (1968 and Nishiure (1970.
Foresters' Metric Conversions program (version 1.0). [Computer program
Jefferson A. Palmer
1999-01-01
The conversion of scientific measurements has become commonplace in the fields of - engineering, research, and forestry. Foresters? Metric Conversions is a Windows-based computer program that quickly converts user-defined measurements from English to metric and from metric to English. Foresters? Metric Conversions was derived from the publication "Metric...
Entropy of continuous maps on quasi-metric spaces
Sayyari, Y.; Molaei, M.; Moghayer, S.M.
2015-01-01
The category of metric spaces is a subcategory of quasi-metric spaces. In this paper the notion of entropy for the continuous maps of a quasi-metric space is extended via spanning and separated sets. Moreover, two metric spaces that are associated to a given quasi-metric space are introduced and the
Fuzzy Prokhorov metric on the set of probability measures
Repovš, D.; Savchenko, A.; Zarichnyi, M.
2011-01-01
We introduce a fuzzy metric on the set of probability measures on a fuzzy metric space. The construction is an analogue, in the realm of fuzzy metric spaces, of the Prokhorov metric on the set of probability measures on compact metric spaces.
Partial rectangular metric spaces and fixed point theorems.
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.
Fighter agility metrics. M.S. Thesis
Liefer, Randall K.
1990-01-01
Fighter flying qualities and combat capabilities are currently measured and compared in terms relating to vehicle energy, angular rates and sustained acceleration. Criteria based on these measurable quantities have evolved over the past several decades and are routinely used to design aircraft structures, aerodynamics, propulsion and control systems. While these criteria, or metrics, have the advantage of being well understood, easily verified and repeatable during test, they tend to measure the steady state capability of the aircraft and not its ability to transition quickly from one state to another. Proposed new metrics to assess fighter aircraft agility are collected and analyzed. A framework for classification of these new agility metrics is developed and applied. A complete set of transient agility metrics is evaluated with a high fidelity, nonlinear F-18 simulation. Test techniques and data reduction methods are proposed. A method of providing cuing information to the pilot during flight test is discussed. The sensitivity of longitudinal and lateral agility metrics to deviations from the pilot cues is studied in detail. The metrics are shown to be largely insensitive to reasonable deviations from the nominal test pilot commands. Instrumentation required to quantify agility via flight test is also considered. With one exception, each of the proposed new metrics may be measured with instrumentation currently available.
Robust Transfer Metric Learning for Image Classification.
Ding, Zhengming; Fu, Yun
2017-02-01
Metric learning has attracted increasing attention due to its critical role in image analysis and classification. Conventional metric learning always assumes that the training and test data are sampled from the same or similar distribution. However, to build an effective distance metric, we need abundant supervised knowledge (i.e., side/label information), which is generally inaccessible in practice, because of the expensive labeling cost. In this paper, we develop a robust transfer metric learning (RTML) framework to effectively assist the unlabeled target learning by transferring the knowledge from the well-labeled source domain. Specifically, RTML exploits knowledge transfer to mitigate the domain shift in two directions, i.e., sample space and feature space. In the sample space, domain-wise and class-wise adaption schemes are adopted to bridge the gap of marginal and conditional distribution disparities across two domains. In the feature space, our metric is built in a marginalized denoising fashion and low-rank constraint, which make it more robust to tackle noisy data in reality. Furthermore, we design an explicit rank constraint regularizer to replace the rank minimization NP-hard problem to guide the low-rank metric learning. Experimental results on several standard benchmarks demonstrate the effectiveness of our proposed RTML by comparing it with the state-of-the-art transfer learning and metric learning algorithms.
Launch Vehicle Production and Operations Cost Metrics
Watson, Michael D.; Neeley, James R.; Blackburn, Ruby F.
2014-01-01
Traditionally, launch vehicle cost has been evaluated based on $/Kg to orbit. This metric is calculated based on assumptions not typically met by a specific mission. These assumptions include the specified orbit whether Low Earth Orbit (LEO), Geostationary Earth Orbit (GEO), or both. The metric also assumes the payload utilizes the full lift mass of the launch vehicle, which is rarely true even with secondary payloads.1,2,3 Other approaches for cost metrics have been evaluated including unit cost of the launch vehicle and an approach to consider the full program production and operations costs.4 Unit cost considers the variable cost of the vehicle and the definition of variable costs are discussed. The full program production and operation costs include both the variable costs and the manufacturing base. This metric also distinguishes operations costs from production costs, including pre-flight operational testing. Operations costs also consider the costs of flight operations, including control center operation and maintenance. Each of these 3 cost metrics show different sensitivities to various aspects of launch vehicle cost drivers. The comparison of these metrics provides the strengths and weaknesses of each yielding an assessment useful for cost metric selection for launch vehicle programs.
More on fuzzy metric type spaces
Öner, Tarkan
2017-04-01
In this paper, we investigate the further properties of fuzzy metric type spaces introduced by Saadati [1]. We prove that a M-convergent sequence in a fuzzy metric type space has a unique limit. Later we show that for a fuzzy metric type space (X, M, *, K) if M is continuous with respect to the first (second) variable then M is continuous with respect to the second (first) variable and M-convergence are equivalent to convergence. Moreover, in such spaces open balls are open and closed balls are closed, therefore induced topology is Hausdorff, first countable, regular and metrizable.
Applying Sigma Metrics to Reduce Outliers.
Litten, Joseph
2017-03-01
Sigma metrics can be used to predict assay quality, allowing easy comparison of instrument quality and predicting which tests will require minimal quality control (QC) rules to monitor the performance of the method. A Six Sigma QC program can result in fewer controls and fewer QC failures for methods with a sigma metric of 5 or better. The higher the number of methods with a sigma metric of 5 or better, the lower the costs for reagents, supplies, and control material required to monitor the performance of the methods. Copyright © 2016 Elsevier Inc. All rights reserved.
Quantum chaos and operator fidelity metric
Giorda, Paolo; Zanardi, Paolo
2010-01-01
We show that the recently introduced operator fidelity metric provides a natural tool to investigate the crossover to quantum chaotic behavior. This metric is an information-theoretic measure of the global stability of a unitary evolution against perturbations. We use random matrix theory arguments to conjecture that the operator fidelity metric can be used to discriminate phases with regular behavior from quantum chaotic ones. A numerical study of the onset of chaotic in the Dicke model is given in order to support the conjecture.
Metrics Are Needed for Collaborative Software Development
Directory of Open Access Journals (Sweden)
Mojgan Mohtashami
2011-10-01
Full Text Available There is a need for metrics for inter-organizational collaborative software development projects, encompassing management and technical concerns. In particular, metrics are needed that are aimed at the collaborative aspect itself, such as readiness for collaboration, the quality and/or the costs and benefits of collaboration in a specific ongoing project. We suggest questions and directions for such metrics, spanning the full lifespan of a collaborative project, from considering the suitability of collaboration through evaluating ongoing projects to final evaluation of the collaboration.
Finite Metric Spaces of Strictly negative Type
DEFF Research Database (Denmark)
Hjorth, Poul G.
If a finite metric space is of strictly negative type then its transfinite diameter is uniquely realized by an infinite extent (“load vector''). Finite metric spaces that have this property include all trees, and all finite subspaces of Euclidean and Hyperbolic spaces. We prove that if the distance...... matrix of a finite metric space is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points....
Software metrics a rigorous and practical approach
Fenton, Norman
2014-01-01
A Framework for Managing, Measuring, and Predicting Attributes of Software Development Products and ProcessesReflecting the immense progress in the development and use of software metrics in the past decades, Software Metrics: A Rigorous and Practical Approach, Third Edition provides an up-to-date, accessible, and comprehensive introduction to software metrics. Like its popular predecessors, this third edition discusses important issues, explains essential concepts, and offers new approaches for tackling long-standing problems.New to the Third EditionThis edition contains new material relevant
Generalized Metric Spaces Do Not Have the Compatible Topology
Tomonari Suzuki
2014-01-01
We study generalized metric spaces, which were introduced by Branciari (2000). In particular, generalized metric spaces do not necessarily have the compatible topology. Also we prove a generalization of the Banach contraction principle in complete generalized metric spaces.
Learnometrics: Metrics for Learning Objects (Learnometrics: metrieken voor leerobjecten)
Ochoa, Xavier
2008-01-01
- Introduction - Quantitative Analysis of the Publication of Learning Objects - Quantiative Analysis of the Reuse of Learning Objects - Metadata Quality Metrics for Learning Objects - Relevance Ranking Metrics for Learning Objects - Metrics Service Architecture and Use Cases - Conclusions
New Gromov-Inspired Metrics on Phylogenetic Tree Space.
Liebscher, Volkmar
2018-03-01
We present a new class of metrics for unrooted phylogenetic X-trees inspired by the Gromov-Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or quadratic programming. They are robust under NNI operations, too. The local behaviour of the metrics shows that they are different from any previously introduced metrics. The performance of the metrics is briefly analysed on random weighted and unweighted trees as well as random caterpillars.
Steiner trees for fixed orientation metrics
DEFF Research Database (Denmark)
Brazil, Marcus; Zachariasen, Martin
2009-01-01
We consider the problem of constructing Steiner minimum trees for a metric defined by a polygonal unit circle (corresponding to s = 2 weighted legal orientations in the plane). A linear-time algorithm to enumerate all angle configurations for degree three Steiner points is given. We provide a sim...... metric generalises to the fixed orientation metric. Finally, we give an O(s n) time algorithm to compute a Steiner minimum tree for a given full Steiner topology with n terminal leaves.......We consider the problem of constructing Steiner minimum trees for a metric defined by a polygonal unit circle (corresponding to s = 2 weighted legal orientations in the plane). A linear-time algorithm to enumerate all angle configurations for degree three Steiner points is given. We provide...
Einstein metrics on tangent bundles of spheres
Energy Technology Data Exchange (ETDEWEB)
Dancer, Andrew S [Jesus College, Oxford University, Oxford OX1 3DW (United Kingdom); Strachan, Ian A B [Department of Mathematics, University of Hull, Hull HU6 7RX (United Kingdom)
2002-09-21
We give an elementary treatment of the existence of complete Kaehler-Einstein metrics with nonpositive Einstein constant and underlying manifold diffeomorphic to the tangent bundle of the (n+1)-sphere.
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.
How Metric Conversion Affects Administrative Practices
Straka, M. K.
1977-01-01
Changes necessary in the administrative activities of educational institutions following conversion to the metric system are outlined for secretarial practices, purchasing, internal reporting and forms, computer operations, travel, publications, buildings and plant, new buildings, sport facilities, and health services. (MF)
Metrics and Energy Landscapes in Irreversible Thermodynamics
Directory of Open Access Journals (Sweden)
Bjarne Andresen
2015-09-01
Full Text Available We describe how several metrics are possible in thermodynamic state space but that only one, Weinhold’s, has achieved widespread use. Lengths calculated based on this metric have been used to bound dissipation in finite-time (irreversible processes be they continuous or discrete, and described in the energy picture or the entropy picture. Examples are provided from thermodynamics of heat conversion processes as well as chemical reactions. Even losses in economics can be bounded using a thermodynamic type metric. An essential foundation for the metric is a complete equation of state including all extensive variables of the system; examples are given. Finally, the second law of thermodynamics imposes convexity on any equation of state, be it analytical or empirical.
NPScape Metric GIS Data - Conservation Status
National Park Service, Department of the Interior — NPScape conservation status metrics are calculated using data from the USGS Gap Analysis Program (PAD-US), World Protected Areas Database (WDPA), and National Marine...
Clean Cities Annual Metrics Report 2009 (Revised)
Energy Technology Data Exchange (ETDEWEB)
Johnson, C.
2011-08-01
Document provides Clean Cities coalition metrics about the use of alternative fuels; the deployment of alternative fuel vehicles, hybrid electric vehicles (HEVs), and idle reduction initiatives; fuel economy activities; and programs to reduce vehicle miles driven.
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.
Flight Crew State Monitoring Metrics Project
National Aeronautics and Space Administration — eSky will develop specific crew state metrics based on the timeliness, tempo and accuracy of pilot inputs required by the H-mode Flight Control System (HFCS)....
Hypermultiplet metric and D-instantons
Energy Technology Data Exchange (ETDEWEB)
Alexandrov, Sergei; Banerjee, Sibasish [Laboratoire Charles Coulomb UMR 5221, Université Montpellier 2,F-34095, Montpellier (France)
2015-02-27
We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kähler metric which is a non-trivial deformation of the local c-map. In the four-dimensional case corresponding to the universal hypermultiplet, our metric fits the Tod ansatz and provides an exact solution of the continuous Toda equation. We also analyze the fate of the curvature singularity of the perturbative metric by deriving an S-duality invariant equation which determines the singularity hypersurface after inclusion of the D(-1)-instanton effects.
Networks and centroid metrics for understanding football
African Journals Online (AJOL)
Gonçalo Dias
games. However, it seems that the centroid metric, supported only by the position ... displaying and measuring the interpersonal relationships established by the .... according to game venue (games played home or away), a histogram-based ...
Medicare Contracting - Redacted Benchmark Metric Reports
U.S. Department of Health & Human Services — The Centers for Medicare and Medicaid Services has compiled aggregate national benchmark cost and workload metrics using data submitted to CMS by the AB MACs and the...
Static and Dynamic Software Quality Metric Tools
Mayo, Kevin A.; Wake, Steven A.; Henry, Sallie M.
1990-01-01
The ability to detect and predict poor software quality is of major importance to software engineers, managers, and quality assurance organizations. Poor software quality leads to increased development costs and expensive maintenance. With so much attention on exacerbated budgetary constraints, a viable alternative is necessary. Software quality metrics are designed for this purpose. Metrics measure aspects of code or PDL representations, and can be collected and used throughout the life ...
Heterogeneous Multitask Metric Learning Across Multiple Domains.
Luo, Yong; Wen, Yonggang; Tao, Dacheng
2017-10-04
Distance metric learning plays a crucial role in diverse machine learning algorithms and applications. When the labeled information in a target domain is limited, transfer metric learning (TML) helps to learn the metric by leveraging the sufficient information from other related domains. Multitask metric learning (MTML), which can be regarded as a special case of TML, performs transfer across all related domains. Current TML tools usually assume that the same feature representation is exploited for different domains. However, in real-world applications, data may be drawn from heterogeneous domains. Heterogeneous transfer learning approaches can be adopted to remedy this drawback by deriving a metric from the learned transformation across different domains. However, they are often limited in that only two domains can be handled. To appropriately handle multiple domains, we develop a novel heterogeneous MTML (HMTML) framework. In HMTML, the metrics of all different domains are learned together. The transformations derived from the metrics are utilized to induce a common subspace, and the high-order covariance among the predictive structures of these domains is maximized in this subspace. There do exist a few heterogeneous transfer learning approaches that deal with multiple domains, but the high-order statistics (correlation information), which can only be exploited by simultaneously examining all domains, is ignored in these approaches. Compared with them, the proposed HMTML can effectively explore such high-order information, thus obtaining more reliable feature transformations and metrics. Effectiveness of our method is validated by the extensive and intensive experiments on text categorization, scene classification, and social image annotation.
A Laplacian on Metric Measure Spaces
DEFF Research Database (Denmark)
Kokkendorff, Simon Lyngby
2006-01-01
We introduce a Laplacian on a class of metric measure spaces via a direct pointwise mean value definition. Fundamental properties of this Laplacian, such as its symmetry as an operator on functions satisfying a Neumann or Dirichlet condition, are established.......We introduce a Laplacian on a class of metric measure spaces via a direct pointwise mean value definition. Fundamental properties of this Laplacian, such as its symmetry as an operator on functions satisfying a Neumann or Dirichlet condition, are established....
Constrained Metric Learning by Permutation Inducing Isometries.
Bosveld, Joel; Mahmood, Arif; Huynh, Du Q; Noakes, Lyle
2016-01-01
The choice of metric critically affects the performance of classification and clustering algorithms. Metric learning algorithms attempt to improve performance, by learning a more appropriate metric. Unfortunately, most of the current algorithms learn a distance function which is not invariant to rigid transformations of images. Therefore, the distances between two images and their rigidly transformed pair may differ, leading to inconsistent classification or clustering results. We propose to constrain the learned metric to be invariant to the geometry preserving transformations of images that induce permutations in the feature space. The constraint that these transformations are isometries of the metric ensures consistent results and improves accuracy. Our second contribution is a dimension reduction technique that is consistent with the isometry constraints. Our third contribution is the formulation of the isometry constrained logistic discriminant metric learning (IC-LDML) algorithm, by incorporating the isometry constraints within the objective function of the LDML algorithm. The proposed algorithm is compared with the existing techniques on the publicly available labeled faces in the wild, viewpoint-invariant pedestrian recognition, and Toy Cars data sets. The IC-LDML algorithm has outperformed existing techniques for the tasks of face recognition, person identification, and object classification by a significant margin.
Peano compactifications and property S metric spaces
Directory of Open Access Journals (Sweden)
R. F. Dickman
1980-01-01
Full Text Available Let (X,d denote a locally connected, connected separable metric space. We say the X is S-metrizable provided there is a topologically equivalent metric ρ on X such that (X,ρ has Property S, i.e. for any ϵ>0, X is the union of finitely many connected sets of ρ-diameter less than ϵ. It is well-known that S-metrizable spaces are locally connected and that if ρ is a Property S metric for X, then the usual metric completion (X˜,ρ˜ of (X,ρ is a compact, locally connected, connected metric space, i.e. (X˜,ρ˜ is a Peano compactification of (X,ρ. There are easily constructed examples of locally connected connected metric spaces which fail to be S-metrizable, however the author does not know of a non-S-metrizable space (X,d which has a Peano compactification. In this paper we conjecture that: If (P,ρ a Peano compactification of (X,ρ|X, X must be S-metrizable. Several (new necessary and sufficient for a space to be S-metrizable are given, together with an example of non-S-metrizable space which fails to have a Peano compactification.
Almost convex metrics and Peano compactifications
Directory of Open Access Journals (Sweden)
R. F. Dickman
1982-01-01
Full Text Available Let (X,d denote a locally connected, connected separable metric space. We say the X is S-metrizable provided there is a topologically equivalent metric ρ on X such that (X,ρ has Property S, i.e., for any ϵ>0, X is the union of finitely many connected sets of ρ-diameter less than ϵ. It is well-known that S-metrizable spaces are locally connected and that if ρ is a Property S metric for X, then the usual metric completion (X˜,ρ˜ of (X,ρ is a compact, locally connected, connected metric space; i.e., (X˜,ρ˜ is a Peano compactification of (X,ρ. In an earlier paper, the author conjectured that if a space (X,d has a Peano compactification, then it must be S-metrizable. In this paper, that conjecture is shown to be false; however, the connected spaces which have Peano compactificatons are shown to be exactly those having a totally bounded, almost convex metric. Several related results are given.
Energy Technology Data Exchange (ETDEWEB)
Wang, Mingzhi [Hunan Normal University, Department of Physics, Institute of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Chen, Songbai; Jing, Jiliang [Hunan Normal University, Department of Physics, Institute of Physics, Changsha, Hunan (China); Hunan Normal University, Key Laboratory of Low Dimensional Quantum Structures and Quantum Control of Ministry of Education, Changsha, Hunan (China); Hunan Normal University, Synergetic Innovation Center for Quantum Effects and Applications, Changsha, Hunan (China)
2017-04-15
We present firstly the equation of motion for a test scalar particle coupling to the Einstein tensor in the Schwarzschild-Melvin black hole spacetime through the short-wave approximation. Through analyzing Poincare sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram, we investigate the effects of the coupling parameter on the chaotic behavior of the particles. With the increase of the coupling strength, we find that the motion of the coupled particle for the chosen parameters becomes more regular and order for the negative couple constant. While, for the positive one, the motion of the coupled particles first undergoes a series of transitions betweens chaotic motion and regular motion and then falls into horizon or escapes to spatial infinity. Our results show that the coupling brings about richer effects for the motion of the particles. (orig.)
Pragmatic Metrics for Monitoring Science Data Centers
Moses, J. F.; Behnke, J.
2003-12-01
Science data metrics and their analysis are critical components to the end-to-end data and service flow for science data centers. The Earth Science Data and Information System Project has collected records of EOS science data archive, processing and distribution metrics from NASA's Distributed Active Archive Centers since 1996. The ESDIS Science Operations Office and the DAAC data centers have cooperated to develop a DAAC metrics reporting capability called the EOSDIS Data Gathering and Reporting Systems (EDGRS). This poster illustrates EDGRS processes and metrics data applications. EDGRS currently accesses detailed archive and distribution metrics from nine DAAC sites and transfers results to a centralized collection system on a routine basis. After automated quality checks the records are immediately made available through a web-based Graphic User Interface. Users can obtain standard graphs and prepare custom queries to generate specific reports for monitoring science data processing progress. Applications are illustrated that explore methods for performing data availability studies and performance analyses. Improvements are planned to support granule-level science data accounting and characterization of product distribution.
Evaluation Metrics for Biostatistical and Epidemiological Collaborations
Rubio, Doris McGartland; del Junco, Deborah J.; Bhore, Rafia; Lindsell, Christopher J.; Oster, Robert A.; Wittkowski, Knut M.; Welty, Leah J.; Li, Yi-Ju; DeMets, Dave
2011-01-01
Increasing demands for evidence-based medicine and for the translation of biomedical research into individual and public health benefit have been accompanied by the proliferation of special units that offer expertise in biostatistics, epidemiology, and research design (BERD) within academic health centers. Objective metrics that can be used to evaluate, track, and improve the performance of these BERD units are critical to their successful establishment and sustainable future. To develop a set of reliable but versatile metrics that can be adapted easily to different environments and evolving needs, we consulted with members of BERD units from the consortium of academic health centers funded by the Clinical and Translational Science Award Program of the National Institutes of Health. Through a systematic process of consensus building and document drafting, we formulated metrics that covered the three identified domains of BERD practices: the development and maintenance of collaborations with clinical and translational science investigators, the application of BERD-related methods to clinical and translational research, and the discovery of novel BERD-related methodologies. In this article, we describe the set of metrics and advocate their use for evaluating BERD practices. The routine application, comparison of findings across diverse BERD units, and ongoing refinement of the metrics will identify trends, facilitate meaningful changes, and ultimately enhance the contribution of BERD activities to biomedical research. PMID:21284015
Biomechanical metrics of aesthetic perception in dance.
Bronner, Shaw; Shippen, James
2015-12-01
The brain may be tuned to evaluate aesthetic perception through perceptual chunking when we observe the grace of the dancer. We modelled biomechanical metrics to explain biological determinants of aesthetic perception in dance. Eighteen expert (EXP) and intermediate (INT) dancers performed développé arabesque in three conditions: (1) slow tempo, (2) slow tempo with relevé, and (3) fast tempo. To compare biomechanical metrics of kinematic data, we calculated intra-excursion variability, principal component analysis (PCA), and dimensionless jerk for the gesture limb. Observers, all trained dancers, viewed motion capture stick figures of the trials and ranked each for aesthetic (1) proficiency and (2) movement smoothness. Statistical analyses included group by condition repeated-measures ANOVA for metric data; Mann-Whitney U rank and Friedman's rank tests for nonparametric rank data; Spearman's rho correlations to compare aesthetic rankings and metrics; and linear regression to examine which metric best quantified observers' aesthetic rankings, p chunking in which the brain combines sensory motor elements into integrated units of behaviour. In this representation, the chunk of information which is remembered, and to which the observer reacts, is the elemental mode shape of the motion rather than physical displacements. This suggests that reduction in redundant information to a simplistic dimensionality is related to the experienced observer's aesthetic perception.
Evaluation metrics for bone segmentation in ultrasound
Lougheed, Matthew; Fichtinger, Gabor; Ungi, Tamas
2015-03-01
Tracked ultrasound is a safe alternative to X-ray for imaging bones. The interpretation of bony structures is challenging as ultrasound has no specific intensity characteristic of bones. Several image segmentation algorithms have been devised to identify bony structures. We propose an open-source framework that would aid in the development and comparison of such algorithms by quantitatively measuring segmentation performance in the ultrasound images. True-positive and false-negative metrics used in the framework quantify algorithm performance based on correctly segmented bone and correctly segmented boneless regions. Ground-truth for these metrics are defined manually and along with the corresponding automatically segmented image are used for the performance analysis. Manually created ground truth tests were generated to verify the accuracy of the analysis. Further evaluation metrics for determining average performance per slide and standard deviation are considered. The metrics provide a means of evaluating accuracy of frames along the length of a volume. This would aid in assessing the accuracy of the volume itself and the approach to image acquisition (positioning and frequency of frame). The framework was implemented as an open-source module of the 3D Slicer platform. The ground truth tests verified that the framework correctly calculates the implemented metrics. The developed framework provides a convenient way to evaluate bone segmentation algorithms. The implementation fits in a widely used application for segmentation algorithm prototyping. Future algorithm development will benefit by monitoring the effects of adjustments to an algorithm in a standard evaluation framework.
Implementing the Data Center Energy Productivity Metric
Energy Technology Data Exchange (ETDEWEB)
Sego, Landon H.; Marquez, Andres; Rawson, Andrew; Cader, Tahir; Fox, Kevin M.; Gustafson, William I.; Mundy, Christopher J.
2012-10-01
As data centers proliferate in both size and number, their energy efficiency is becoming increasingly important. We discuss the properties of a number of the proposed metrics of energy efficiency and productivity. In particular, we focus on the Data Center Energy Productivity (DCeP) metric, which is the ratio of useful work produced by the data center to the energy consumed performing that work. We describe our approach for using DCeP as the principal outcome of a designed experiment using a highly instrumented, high performance computing data center. We found that DCeP was successful in clearly distinguishing between different operational states in the data center, thereby validating its utility as a metric for identifying configurations of hardware and software that would improve (or even maximize) energy productivity. We also discuss some of the challenges and benefits associated with implementing the DCeP metric, and we examine the efficacy of the metric in making comparisons within a data center and among data centers.
Models, Metrics, and Measurement in Developmental Psychology
Directory of Open Access Journals (Sweden)
Zachary Stein
2009-06-01
Full Text Available Developmental psychology is currently used to measure psychological phenomena and by some, to re-design communities. While we generally support these uses, we are concerned about quality control standards guiding the production of usable knowledge in the discipline. In order to address these issues precisely, we provide an overview of the discipline’s various facets. We distinguish between developmental models and developmental metrics and relate each to different types of quality-control devices. In our view, models are either explanatory or descriptive, and their quality is evaluated in terms of specific types of disciplinary discourse. Metrics are either calibrated measures or soft measures, and their quality is evaluated in terms of specific psychometric parameters. Following a discussion on how developmentalists make metrics, and on a variety of metrics that have been made, we discuss the two key psychometric quality-control parameters, validity and reliability. This sets the stage for a limited and exploratory literature review concerning the quality of a set of existing metrics. We reveal a conspicuous lack of psychometric rigor on the part of some of the most popular developmental approaches and invite remedies for this situation.
49 CFR 19.15 - Metric system of measurement.
2010-10-01
... Requirements § 19.15 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205), declares that the metric system is the preferred measurement... 49 Transportation 1 2010-10-01 2010-10-01 false Metric system of measurement. 19.15 Section 19.15...
43 CFR 12.915 - Metric system of measurement.
2010-10-01
... Requirements § 12.915 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement... 43 Public Lands: Interior 1 2010-10-01 2010-10-01 false Metric system of measurement. 12.915...
45 CFR 2543.15 - Metric system of measurement.
2010-10-01
...-PROFIT ORGANIZATIONS Pre-Award Requirements § 2543.15 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric... 45 Public Welfare 4 2010-10-01 2010-10-01 false Metric system of measurement. 2543.15 Section 2543...
29 CFR 95.15 - Metric system of measurement.
2010-07-01
... Requirements § 95.15 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205), declares that the metric system is the preferred measurement... 29 Labor 1 2010-07-01 2010-07-01 true Metric system of measurement. 95.15 Section 95.15 Labor...
22 CFR 518.15 - Metric system of measurement.
2010-04-01
... Pre-Award Requirements § 518.15 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205), declares that the metric system is the... 22 Foreign Relations 2 2010-04-01 2010-04-01 true Metric system of measurement. 518.15 Section 518...
34 CFR 74.15 - Metric system of measurement.
2010-07-01
... 34 Education 1 2010-07-01 2010-07-01 false Metric system of measurement. 74.15 Section 74.15... Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for U.S...
Metrizability of Cone Metric Spaces Via Renorming the Banach Spaces
Directory of Open Access Journals (Sweden)
Hossein Soleimani
2012-09-01
Full Text Available In this paper we show that by renorming an ordered Banach space, every cone $P$ can be converted to a normal cone with constant $K=1$ and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.
On Convergence of Fixed Points in Fuzzy Metric Spaces
Directory of Open Access Journals (Sweden)
Yonghong Shen
2013-01-01
Full Text Available We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.
NASA education briefs for the classroom. Metrics in space
1982-01-01
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.
Codes in W*-Metric Spaces: Theory and Examples
Bumgardner, Christopher J.
2011-01-01
We introduce a "W*"-metric space, which is a particular approach to non-commutative metric spaces where a "quantum metric" is defined on a von Neumann algebra. We generalize the notion of a quantum code and quantum error correction to the setting of finite dimensional "W*"-metric spaces, which includes codes and error correction for classical…
G-weak contraction in ordered cone rectangular metric spaces.
Malhotra, S K; Sharma, J B; Shukla, Satish
2013-01-01
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.
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.
Soft Cone Metric Spaces and Some Fixed Point Theorems
Altıntaş, İsmet; Taşköprü, Kemal
2016-01-01
This paper is an introduction to soft cone metric spaces. We define the concept of soft cone metric via soft element, investigate soft converges in soft cone metric spaces and prove some fixed point theorems for contractive mappings on soft cone metric spaces.
Robustness Metrics: Consolidating the multiple approaches to quantify Robustness
DEFF Research Database (Denmark)
Göhler, Simon Moritz; Eifler, Tobias; Howard, Thomas J.
2016-01-01
determined to be conceptually different from one another. The metrics were classified by their meaning and interpretation based on the types of information necessary to calculate the metrics. Four different classes were identified: 1) Sensitivity robustness metrics; 2) Size of feasible design space......, this ambiguity can have significant influence on the strategies used to combat variability, the way it is quantified and ultimately, the quality of the final design. In this contribution the literature for robustness metrics was systematically reviewed. From the 108 relevant publications found, 38 metrics were...... 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...
Enhanced Accident Tolerant LWR Fuels: Metrics Development
Energy Technology Data Exchange (ETDEWEB)
Shannon Bragg-Sitton; Lori Braase; Rose Montgomery; Chris Stanek; Robert Montgomery; Lance Snead; Larry Ott; Mike Billone
2013-09-01
The Department of Energy (DOE) Fuel Cycle Research and Development (FCRD) Advanced Fuels Campaign (AFC) is conducting research and development on enhanced Accident Tolerant Fuels (ATF) for light water reactors (LWRs). This mission emphasizes the development of novel fuel and cladding concepts to replace the current zirconium alloy-uranium dioxide (UO2) fuel system. The overall mission of the ATF research is to develop advanced fuels/cladding with improved performance, reliability and safety characteristics during normal operations and accident conditions, while minimizing waste generation. The initial effort will focus on implementation in operating reactors or reactors with design certifications. To initiate the development of quantitative metrics for ATR, a LWR Enhanced Accident Tolerant Fuels Metrics Development Workshop was held in October 2012 in Germantown, MD. This paper summarizes the outcome of that workshop and the current status of metrics development for LWR ATF.
SOCIAL METRICS APPLIED TO SMART TOURISM
Directory of Open Access Journals (Sweden)
O. Cervantes
2016-09-01
Full Text Available We present a strategy to make productive use of semantically-related social data, from a user-centered semantic network, in order to help users (tourists and citizens in general to discover cultural heritage, points of interest and available services in a smart city. This data can be used to personalize recommendations in a smart tourism application. Our approach is based on flow centrality metrics typically used in social network analysis: flow betweenness, flow closeness and eccentricity. These metrics are useful to discover relevant nodes within the network yielding nodes that can be interpreted as suggestions (venues or services to users. We describe the semantic network built on graph model, as well as social metrics algorithms used to produce recommendations. We also present challenges and results from a prototypical implementation applied to the case study of the City of Puebla, Mexico.
Rainbow Rindler metric and Unruh effect
Yadav, Gaurav; Majhi, Bibhas Ranjan
2016-01-01
The energy of a particle moving on a spacetime, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here we find the explicit expressions for the coordinate transformations from rainbow Minkowski spacetime to accelerated frame. The corresponding metric is also obtained which we call as rainbow-Rindler metric. So far we are aware of, no body has done it in a concrete manner. Here this is found from the first principle and hence all the parameters are properly identified. The advantage of this is that the calculated Unruh temperature is compatible with the Hawking temperature of the rainbow black hole horizon, obtained earlier. Since the accelerated frame has several importance in revealing various properties of gravity, we believe that the present result will not only fill that gap, but also help to explore different aspects of rainbow gravity paradigm.
Social Metrics Applied to Smart Tourism
Cervantes, O.; Gutiérrez, E.; Gutiérrez, F.; Sánchez, J. A.
2016-09-01
We present a strategy to make productive use of semantically-related social data, from a user-centered semantic network, in order to help users (tourists and citizens in general) to discover cultural heritage, points of interest and available services in a smart city. This data can be used to personalize recommendations in a smart tourism application. Our approach is based on flow centrality metrics typically used in social network analysis: flow betweenness, flow closeness and eccentricity. These metrics are useful to discover relevant nodes within the network yielding nodes that can be interpreted as suggestions (venues or services) to users. We describe the semantic network built on graph model, as well as social metrics algorithms used to produce recommendations. We also present challenges and results from a prototypical implementation applied to the case study of the City of Puebla, Mexico.
Landscape pattern metrics and regional assessment
O'Neill, R. V.; Riitters, K.H.; Wickham, J.D.; Jones, K.B.
1999-01-01
The combination of remote imagery data, geographic information systems software, and landscape ecology theory provides a unique basis for monitoring and assessing large-scale ecological systems. The unique feature of the work has been the need to develop and interpret quantitative measures of spatial pattern-the landscape indices. This article reviews what is known about the statistical properties of these pattern metrics and suggests some additional metrics based on island biogeography, percolation theory, hierarchy theory, and economic geography. Assessment applications of this approach have required interpreting the pattern metrics in terms of specific environmental endpoints, such as wildlife and water quality, and research into how to represent synergystic effects of many overlapping sources of stress.
Rainbow Rindler metric and Unruh effect
Yadav, Gaurav; Komal, Baby; Majhi, Bibhas Ranjan
2017-11-01
The energy of a particle moving on a space-time, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here, we find the explicit expressions for the coordinate transformations from rainbow Minkowski space-time to accelerated frame. The corresponding metric is also obtained which we call as rainbow Rindler metric. So far we are aware of that no body has done it in a concrete manner. Here, this is found from the first principle and hence all the parameters are properly identified. The advantage of this is that the calculated Unruh temperature is compatible with the Hawking temperature of the rainbow black hole horizon, obtained earlier. Since the accelerated frame has several importance in revealing various properties of gravity, we believe that the present result will not only fill that gap, but also help to explore different aspects of rainbow gravity paradigm.
Metrical and dynamical aspects in complex analysis
2017-01-01
The central theme of this reference book is the metric geometry of complex analysis in several variables. Bridging a gap in the current literature, the text focuses on the fine behavior of the Kobayashi metric of complex manifolds and its relationships to dynamical systems, hyperbolicity in the sense of Gromov and operator theory, all very active areas of research. The modern points of view expressed in these notes, collected here for the first time, will be of interest to academics working in the fields of several complex variables and metric geometry. The different topics are treated coherently and include expository presentations of the relevant tools, techniques and objects, which will be particularly useful for graduate and PhD students specializing in the area.
On the Plane Geometry with Generalized Absolute Value Metric
Directory of Open Access Journals (Sweden)
A. Bayar
2008-01-01
Full Text Available Metric spaces are among the most important widely studied topics in mathematics. In recent years, Mathematicians began to investigate using other metrics different from Euclidean metric. These metrics also find their place computer age in addition to their importance in geometry. In this paper, we consider the plane geometry with the generalized absolute value metric and define trigonometric functions and norm and then give a plane tiling example for engineers underlying Schwarz's inequality in this plane.
Feed efficiency metrics in growing pigs.
Calderón Díaz, J A; Berry, D P; Rebeiz, N; Metzler-Zebeli, B U; Magowan, E; Gardiner, G E; Lawlor, P G
2017-07-01
The objective of the present study was to quantify the interrelationships between different feed efficiency measures in growing pigs and characterize pigs divergent for a selection of these measures. The data set included data from 311 growing pigs between 42 and 91 d of age from 3 separate batches. Growth-related metrics available included midtest metabolic BW (BW), energy intake (EI), and ADG. Ratio efficiency traits included energy conversion ratio (ECR), Kleiber ratio (ADG/BW), relative growth rate (RGR), residual EI (REI), and residual daily gain (RDG). Residual intake and gain (RIG; i.e., a dual index of both REI and RDG) and residual midtest metabolic weight (RMW) were also calculated. Simple Pearson correlations were estimated between the growth and feed efficiency metrics. In litters with at least 3 pigs of each sex, pigs were separately stratified on each residual trait as high, medium, and low rank. Considerable interanimal variability existed in all metrics evaluated. Male pigs were superior to females for all metrics ( efficiency metrics improved as birth BW increased ( efficiency metrics were strong to moderate ( efficient) had lower EI and ECR and were superior for RIG ( efficient) had greater BW gain and better ECR ( Energy conversion ratio, REI, and RIG were superior ( efficient) compared with medium-RMW pigs. High-RIG pigs (i.e., more efficient) had lower EI ( efficiency traits investigated in this study were different from unity, indicating that each trait is depicting a different aspect of efficiency in pigs, although the moderate to strong correlations suggest that improvement in one trait would, on average, lead to improvements in the others. Pigs ranked as more efficient on residual traits such as REI consumed less energy for a similar BW gain, which would translate into an economic benefit for pig producers.
Interactive analysis of situational awareness metrics
Overby, Derek; Wall, Jim; Keyser, John
2012-01-01
Digital systems are employed to maintain situational awareness of people in various contexts including emergency response, disaster relief, and military operations. Because these systems are often operated in wireless environments and are used to support real-time decision making, the accuracy of the SA data provided is important to measure and evaluate in the development of new systems. Our work has been conducted in conjunction with analysts in the evaluation and performance comparison of different systems designed to provide a high degree of situational awareness in military operations. To this end, we defined temporal and spatial metrics for measuring the accuracy of the SA data provided by each system. In this paper we discuss the proposed temporal and spatial metrics for SA data and show how we provided these metrics in a linked coordinated multiple view environment that enabled the analysts we worked with to effectively perform several critical analysis tasks. The temporal metric is designed to help determine when network performance has a significant effect on SA data, and therefore identify specific time periods in which individuals were provided inaccurate position data for their peers. Temporal context can be used to determine the local or global nature of any SA data inaccuracy, and the spatial metric can then be used to identify geographic effects on network performance of the wireless system. We discuss the interactive software implementation of our metrics and show how this analysis capability enabled the analysts to evaluate the observed effects of network latency and system performance on SA data during an exercise.
Static spherical metrics: a geometrical approach
Tiwari, A. K.; Maharaj, S. D.; Narain, R.
2017-08-01
There exist several solution generating algorithms for static spherically symmetric metrics. Here we use the geometrical approach of Lie point symmetries to solve the condition of pressure isotropy by finding the associated five-dimensional Lie algebra of symmetry generators. For the non-Abelian subalgebras the underlying equation is solved to obtain a general solution. Contained within this class are vacuum models, constant density models, metrics with linear equations of state and the Buchdahl representation of the polytrope with index five. For a different particular symmetry generator the condition of pressure isotropy is transformed to a Riccati equation which admits particular solutions.
What Metrics Accurately Reflect Surgical Quality?
Ibrahim, Andrew M; Dimick, Justin B
2018-01-29
Surgeons are increasingly under pressure to measure and improve their quality. While there is broad consensus that we ought to track surgical quality, there is far less agreement about which metrics matter most. This article reviews the important statistical concepts of case mix and chance as they apply to understanding the observed wide variation in surgical quality. We then discuss the benefits and drawbacks of current measurement strategies through the framework of structure, process, and outcomes approaches. Finally, we describe emerging new metrics, such as video evaluation and network optimization, that are likely to take on an increasingly important role in the future of measuring surgical quality.
Enhancing U.S. Coast Guard Metrics
2015-01-01
1-m antenna , out to 20 nmi from shore, as part of the National Distress and Response System • percentage of cases in which “suitable” SAR resources...metric for effective coverage of reception of a 1-W signal from a 1-m antenna was deemed to have low feasibility. Potential Metrics Overall, we feel that...Department of State and the National Oceanic and Atmospheric Administration ( NOAA ), and must also ensure that the public—at least, the sector of the public
Stability and integration over Bergman metrics
Klevtsov, Semyon; Zelditch, Steve
2014-07-01
We study partition functions of random Bergman metrics, with the actions defined by a class of geometric functionals known as `stability functions'. We introduce a new stability invariant — the critical value of the coupling constant — defined as the minimal coupling constant for which the partition function converges. It measures the minimal degree of stability of geodesic rays in the space the Bergman metrics, with respect to the action. We calculate this critical value when the action is the ν-balancing energy, and show that on a Riemann surface of genus h.
Finsler generalization of the Tamm metric
Panzhenskii, V. I.; Surina, O. P.
2016-11-01
We study manifolds of the Finsler type whose tangent (pseudo-)Riemannian spaces are invariant under the (pseudo)orthogonal group. We construct the Cartan connection and study geodesics, extremals, and also motions. We establish that if the metric tensor of the space is a homogeneous tensor of the zeroth order with respect to the coordinates of the tangent vector, then the metric of the tangent space is realized on a cone of revolution. We describe the structure of geodesics on the cone as trajectories of motion of a free particle in a central field.
An equivalence of results in $C^*$-algebra valued b-metric and b-metric spaces
Directory of Open Access Journals (Sweden)
Nguyen Van Dung
2017-10-01
Full Text Available We construct a $b$-metric from a given $C^*$-algebra-valued $b$-metric and prove some equivalences between them. Then we show that not only fixed point results but also topological properties on $C^*$-algebra-valued $b$-metric spaces may be deduced from certain results in $b$-metric spaces. In particular, every $C^*$-algebra-valued $b$-metric space is metrizable.
Practical performance of tree comparison metrics.
Kuhner, Mary K; Yamato, Jon
2015-03-01
The phylogenetic literature contains numerous measures for assessing differences between two phylogenetic trees. Individual measures have been criticized on various grounds, but little is known about their comparative performance in typical applications. We evaluate the performance of nine tree distance measures on two tasks: 1) distinguishing trees separated by lesser versus greater numbers of recombinations, and 2) distinguishing trees inferred with lower versus higher quality data. We find that when the trees being compared are similar, measures that make use of branch lengths are superior, with the branch-length version of the Robinson-Foulds metric performing best. In contrast, for dissimilar trees topology-only measures are superior, with the Alignment metric of Nye et al. performing best. We also apply the measures to a mammalian dataset and observe that the best metric depends on whether branch-length information is of interest. We give practical recommendations for choosing a tree distance metric in different applications. © The Author(s) 2014. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. For Permissions, please email: journals.permissions@oup.com.
Vehicle Integrated Prognostic Reasoner (VIPR) Metric Report
Cornhill, Dennis; Bharadwaj, Raj; Mylaraswamy, Dinkar
2013-01-01
This document outlines a set of metrics for evaluating the diagnostic and prognostic schemes developed for the Vehicle Integrated Prognostic Reasoner (VIPR), a system-level reasoner that encompasses the multiple levels of large, complex systems such as those for aircraft and spacecraft. VIPR health managers are organized hierarchically and operate together to derive diagnostic and prognostic inferences from symptoms and conditions reported by a set of diagnostic and prognostic monitors. For layered reasoners such as VIPR, the overall performance cannot be evaluated by metrics solely directed toward timely detection and accuracy of estimation of the faults in individual components. Among other factors, overall vehicle reasoner performance is governed by the effectiveness of the communication schemes between monitors and reasoners in the architecture, and the ability to propagate and fuse relevant information to make accurate, consistent, and timely predictions at different levels of the reasoner hierarchy. We outline an extended set of diagnostic and prognostics metrics that can be broadly categorized as evaluation measures for diagnostic coverage, prognostic coverage, accuracy of inferences, latency in making inferences, computational cost, and sensitivity to different fault and degradation conditions. We report metrics from Monte Carlo experiments using two variations of an aircraft reference model that supported both flat and hierarchical reasoning.
Validation metrics for turbulent plasma transport
Energy Technology Data Exchange (ETDEWEB)
Holland, C., E-mail: chholland@ucsd.edu [Center for Energy Research, University of California, San Diego, La Jolla, California 92093-0417 (United States)
2016-06-15
Developing accurate models of plasma dynamics is essential for confident predictive modeling of current and future fusion devices. In modern computer science and engineering, formal verification and validation processes are used to assess model accuracy and establish confidence in the predictive capabilities of a given model. This paper provides an overview of the key guiding principles and best practices for the development of validation metrics, illustrated using examples from investigations of turbulent transport in magnetically confined plasmas. Particular emphasis is given to the importance of uncertainty quantification and its inclusion within the metrics, and the need for utilizing synthetic diagnostics to enable quantitatively meaningful comparisons between simulation and experiment. As a starting point, the structure of commonly used global transport model metrics and their limitations is reviewed. An alternate approach is then presented, which focuses upon comparisons of predicted local fluxes, fluctuations, and equilibrium gradients against observation. The utility of metrics based upon these comparisons is demonstrated by applying them to gyrokinetic predictions of turbulent transport in a variety of discharges performed on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], as part of a multi-year transport model validation activity.
Generalists, specialists and opportunists: niche metrics of ...
African Journals Online (AJOL)
There are distinct differences in the way in which Poicephalus parrots utilise food resources within their distributional range. Our study evaluated the niche metrics of all Poicephalus parrots studied thus far for evidence of linkages between body mass, distributional range and niche breadth. We calibrated the degree of ...
Metric Conversion and the School Shop
Jackman, Arthur A.
1976-01-01
Cost of metric conversion in school shops is examined, and the author categories all the shops in the school and gives useful information on which shops are the easiest to convert, which are most complicated, where resistance is most likely to be met, and where conversion is most urgent. The math department is seen as catalyst. (Editor/HD)
Metric Conversion: An Annotated Bibliography for Teachers.
National Education Association, Washington, DC.
This annotated bibliography was compiled to provide teachers with sources of information concerning the metric system. Articles of general interest concerning the reasons for change and experiences of others in implementing the change are included, as well as materials for practical use by teachers. Books and articles from current journals are…
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
... ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is constructed. It is used to derive Einstein's planetary equation of motion and photon equation of motion in the vicinity of the rotating homogeneous spherical mass.
Reuse metrics and measurement: A framework
Reifer, Donald J.
1990-01-01
The lessons learned and experience gleaned are described by those who have started to implement the reuse metrics and measurement framework used in controlling the development of common avionics and software for its affiliated aircraft programs. The framework was developed to permit the measurement of the long term cost/benefits resulting from the creation and use of Reusable Software Objects (RSOs). The framework also monitors the efficiency and effectiveness of the Software Reuse Library (SRL). The metrics and measurement framework is defined which was established to allow some determinations and findings to be made relative to software reuse. Seven criteria are discussed which were used to guide the establishment of the proposed reuse framework. Object recapture and creation metrics are explained along with their normalized use in effort, productivity, and quality determination. A single and multiple reuse instance version of a popular cost model is presented which uses these metrics and the measurement scheme proposed to predict the software effort and duration under various reuse assumptions. Studies in using this model to predict actuals taken from the RCI data base of over 1000 completed projects is discussed.
Metric semantics for true concurrent real time
Katoen, Joost P.; Baier, Christel; Latella, Diego
2001-01-01
This paper investigates the use of a complete metric space framework for providing denotational semantics to a real-time process algebra. The study is carried out in a non-interleaving setting and is based on a timed extension of Langerak's bundle event structures, a variant of Winskel's event
Metric semantics for true concurrent real time
Baier, Christel; Larsen, K.G.; Skyum, S.; Katoen, Joost P.; Latella, Diego; Winskel, G.
1998-01-01
This paper investigates the use of a complete metric space framework for providing denotational semantics to a real-time process algebra. The study is carried out in a non-interleaving setting and is based on a timed extension of Langerak's bundle event structures, a variant of Winskel's event
Calabi–Yau metrics and string compactification
Directory of Open Access Journals (Sweden)
Michael R. Douglas
2015-09-01
Full Text Available Yau proved an existence theorem for Ricci-flat Kähler metrics in the 1970s, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions from superstring theory.
Genetic basis of a cognitive complexity metric
Hansell, Narelle K; Halford, Graeme S; Andrews, Glenda; Shum, David H K; Harris, Sarah E; Davies, Gail; Franic, Sanja; Christoforou, Andrea; Zietsch, Brendan; Painter, Jodie; Medland, Sarah E; Ehli, Erik A; Davies, Gareth E; Steen, Vidar M; Lundervold, Astri J; Reinvang, Ivar; Montgomery, Grant W; Espeseth, Thomas; Hulshoff Pol, Hilleke E; Starr, John M; Martin, Nicholas G; Le Hellard, Stephanie; Boomsma, Dorret I; Deary, Ian J; Wright, Margaret J
2015-01-01
Relational complexity (RC) is a metric reflecting capacity limitation in relational processing. It plays a crucial role in higher cognitive processes and is an endophenotype for several disorders. However, the genetic underpinnings of complex relational processing have not been investigated. Using
Vestibular Influence on Auditory Metrical Interpretation
Phillips-Silver, J.; Trainor, L.J.
2008-01-01
When we move to music we feel the beat, and this feeling can shape the sound we hear. Previous studies have shown that when people listen to a metrically ambiguous rhythm pattern, moving the body on a certain beat-adults, by actively bouncing themselves in synchrony with the experimenter, and babies, by being bounced passively in the…
Click Model-Based Information Retrieval Metrics
Chuklin, A.; Serdyukov, P.; de Rijke, M.
2013-01-01
In recent years many models have been proposed that are aimed at predicting clicks of web search users. In addition, some information retrieval evaluation metrics have been built on top of a user model. In this paper we bring these two directions together and propose a common approach to converting
Enhancing Authentication Models Characteristic Metrics via ...
African Journals Online (AJOL)
Many choices exist for authenticating users into secure computing systems, yet users continue to lose confidence in the services of online and offline systems because of the increasing ... In this work, we derive the universal characteristic metrics set for authentication models based on security, usability and design issues.
Inferring feature relevances from metric learning
DEFF Research Database (Denmark)
Schulz, Alexander; Mokbel, Bassam; Biehl, Michael
2015-01-01
Powerful metric learning algorithms have been proposed in the last years which do not only greatly enhance the accuracy of distance-based classifiers and nearest neighbor database retrieval, but which also enable the interpretability of these operations by assigning explicit relevance weights to ...
Performance Metrics Research Project - Final Report
Energy Technology Data Exchange (ETDEWEB)
Deru, M.; Torcellini, P.
2005-10-01
NREL began work for DOE on this project to standardize the measurement and characterization of building energy performance. NREL's primary research objectives were to determine which performance metrics have greatest value for determining energy performance and to develop standard definitions and methods of measuring and reporting that performance.
Distance Metric Learning for Conditional Anomaly Detection.
Valko, Michal; Hauskrecht, Milos
2008-01-01
Anomaly detection methods can be very useful in identifying unusual or interesting patterns in data. A recently proposed conditional anomaly detection framework extends anomaly detection to the problem of identifying anomalous patterns on a subset of attributes in the data. The anomaly always depends (is conditioned) on the value of remaining attributes. The work presented in this paper focuses on instance-based methods for detecting conditional anomalies. The methods depend heavily on the distance metric that lets us identify examples in the dataset that are most critical for detecting the anomaly. To optimize the performance of the anomaly detection methods we explore and study metric learning methods. We evaluate the quality of our methods on the Pneumonia PORT dataset by detecting unusual admission decisions for patients with the community-acquired pneumonia. The results of our metric learning methods show an improved detection performance over standard distance metrics, which is very promising for building automated anomaly detection systems for variety of intelligent monitoring applications.
Standardised metrics for global surgical surveillance.
Weiser, Thomas G; Makary, Martin A; Haynes, Alex B; Dziekan, Gerald; Berry, William R; Gawande, Atul A
2009-09-26
Public health surveillance relies on standardised metrics to evaluate disease burden and health system performance. Such metrics have not been developed for surgical services despite increasing volume, substantial cost, and high rates of death and disability associated with surgery. The Safe Surgery Saves Lives initiative of WHO's Patient Safety Programme has developed standardised public health metrics for surgical care that are applicable worldwide. We assembled an international panel of experts to develop and define metrics for measuring the magnitude and effect of surgical care in a population, while taking into account economic feasibility and practicability. This panel recommended six measures for assessing surgical services at a national level: number of operating rooms, number of operations, number of accredited surgeons, number of accredited anaesthesia professionals, day-of-surgery death ratio, and postoperative in-hospital death ratio. We assessed the feasibility of gathering such statistics at eight diverse hospitals in eight countries and incorporated them into the WHO Guidelines for Safe Surgery, in which methods for data collection, analysis, and reporting are outlined.
Outsourced similarity search on metric data assets
DEFF Research Database (Denmark)
Yiu, Man Lung; Assent, Ira; Jensen, Christian Søndergaard
2012-01-01
This paper considers a cloud computing setting in which similarity querying of metric data is outsourced to a service provider. The data is to be revealed only to trusted users, not to the service provider or anyone else. Users query the server for the most similar data objects to a query example...
Metric propositional neighborhood logics on natural numbers
DEFF Research Database (Denmark)
Bresolin, Davide; Della Monica, Dario; Goranko, Valentin
2013-01-01
Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities referring, respectively, to an interval that is “met by” the current one and to an interval that “meets” the current one, plus an infinite set of length constraints, regarded as atomic propositions...
Assessing Software Quality Through Visualised Cohesion Metrics
Directory of Open Access Journals (Sweden)
Timothy Shih
2001-05-01
Full Text Available Cohesion is one of the most important factors for software quality as well as maintainability, reliability and reusability. Module cohesion is defined as a quality attribute that seeks for measuring the singleness of the purpose of a module. The module of poor quality can be a serious obstacle to the system quality. In order to design a good software quality, software managers and engineers need to introduce cohesion metrics to measure and produce desirable software. A highly cohesion software is thought to be a desirable constructing. In this paper, we propose a function-oriented cohesion metrics based on the analysis of live variables, live span and the visualization of processing element dependency graph. We give six typical cohesion examples to be measured as our experiments and justification. Therefore, a well-defined, well-normalized, well-visualized and well-experimented cohesion metrics is proposed to indicate and thus enhance software cohesion strength. Furthermore, this cohesion metrics can be easily incorporated with software CASE tool to help software engineers to improve software quality.
Strong ideal convergence in probabilistic metric spaces
Indian Academy of Sciences (India)
In the present paper we introduce the concepts of strongly ideal convergent sequence and strong ideal Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong ideal limit points and the strong ideal cluster points of a sequence in this ...
Strong ideal convergence in probabilistic metric spaces
Indian Academy of Sciences (India)
Abstract. In the present paper we introduce the concepts of strongly ideal convergent sequence and strong ideal Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong ideal limit points and the strong ideal cluster points of a ...
Metric Ricci Curvature for PL Manifolds
Directory of Open Access Journals (Sweden)
David Xianfeng Gu
2013-01-01
Full Text Available We introduce a metric notion of Ricci curvature for PL manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers theorem, for surfaces as well as for a large class of higher dimensional manifolds.
DIGITAL MARKETING: SUCCESS METRICS, FUTURE TRENDS
Preeti Kaushik
2017-01-01
Abstract – Business Marketing is one of the prospective which has been tremendously affected by digital world in last few years. Digital marketing refers to doing advertising through digital channels. This paper provides detailed study of metrics to measure success of digital marketing platform and glimpse of future of technologies by 2020.
Clean Cities 2011 Annual Metrics Report
Energy Technology Data Exchange (ETDEWEB)
Johnson, C.
2012-12-01
This report details the petroleum savings and vehicle emissions reductions achieved by the U.S. Department of Energy's Clean Cities program in 2011. The report also details other performance metrics, including the number of stakeholders in Clean Cities coalitions, outreach activities by coalitions and national laboratories, and alternative fuel vehicles deployed.
Clean Cities 2010 Annual Metrics Report
Energy Technology Data Exchange (ETDEWEB)
Johnson, C.
2012-10-01
This report details the petroleum savings and vehicle emissions reductions achieved by the U.S. Department of Energy's Clean Cities program in 2010. The report also details other performance metrics, including the number of stakeholders in Clean Cities coalitions, outreach activities by coalitions and national laboratories, and alternative fuel vehicles deployed.
Business model metrics : An open repository
Heikkila, M.; Bouwman, W.A.G.A.; Heikkila, J.; Solaimani, S.; Janssen, W.
2015-01-01
Development of successful business models has become a necessity in turbulent business environments, but compared to research on business modeling tools, attention to the role of metrics in designing business models in literature is limited. Building on existing approaches to business models and
A new universal colour image fidelity metric
Toet, A.; Lucassen, M.P.
2003-01-01
We extend a recently introduced universal grayscale image quality index to a newly developed perceptually decorrelated colour space. The resulting colour image fidelity metric quantifies the distortion of a processed colour image relative to its original version. We evaluated the new colour image
Alimov, A. R.
2017-07-01
In a broad class of finite-dimensional Banach spaces, we show that a closed set with lower semicontinuous metric projection is a strict sun, admits a continuous selection of the metric projection operator onto it, has contractible intersections with balls, and its (nonempty) intersection with any closed ball is a retract of this ball. For sets with continuous metric projection, a number of new results relating the solarity of such sets to the stability of the operator of best approximation are obtained. Bibliography 25 titles.
The implicit learning of metrical and non-metrical rhythms in blind and sighted adults
DEFF Research Database (Denmark)
Carrara-Augustenborg, Claudia; Schultz, Benjamin G.
2018-01-01
mechanisms, few have examined whether blind individuals show a learning advantage for auditory rhythms and whether learning can occur unintentionally and without awareness, that is, implicitly. We compared blind to sighted controls in their ability to implicitly learn metrical and nonmetrical auditory...... predictions; the blind group learned nonmetrical rhythms more readily than the sighted group but the blind group learned metrical rhythms less readily than the sighted group. Only the sighted group learned metrical rhythms more readily than nonmetrical rhythms. The blind group demonstrated awareness...
Weak partial metric spaces and some fixed point results
Directory of Open Access Journals (Sweden)
Ishak Altun
2012-10-01
Full Text Available The concept of partial metric p on a nonempty set X was introduced by Matthews. One of the most interesting properties of a partial metric is that p(x, x may not be zero for x e X. Also, each partial metric p on a nonempty set X generates a T0 topology on X. By omitting the small self-distance axiom of partial metric, Heckmann defined the weak partial metric space. In the present paper, we give some fixed point results on weak partial metric spaces.
Information metric on instanton moduli spaces in nonlinear sigma models.
Yahikozawa, Shigeaki
2004-02-01
We study the information metric on instanton moduli spaces in two-dimensional nonlinear sigma models. In the CP1 model, the information metric on the moduli space of one instanton with the topological charge Q=k(k > or =1) is a three-dimensional hyperbolic metric, which corresponds to Euclidean anti-de Sitter space-time metric in three dimensions, and the overall scale factor of the information metric is 4k(2)/3; this means that the sectional curvature is -3/4k(2). We also calculate the information metric in the CP2 model.
MetricMap: an embedding technique for processing distance-based queries in metric spaces.
Wang, Jason T L; Wang, Xiong; Shasha, Dennis; Zhang, Kaizhong
2005-10-01
In this paper, we present an embedding technique, called MetricMap, which is capable of estimating distances in a pseudometric space. Given a database of objects and a distance function for the objects, which is a pseudometric, we map the objects to vectors in a pseudo-Euclidean space with a reasonably low dimension while preserving the distance between two objects approximately. Such an embedding technique can be used as an approximate oracle to process a broad class of distance-based queries. It is also adaptable to data mining applications such as data clustering and classification. We present the theory underlying MetricMap and conduct experiments to compare MetricMap with other methods including MVP-tree and M-tree in processing the distance-based queries. Experimental results on both protein and RNA data show the good performance and the superiority of MetricMap over the other methods.
Baranski, Maciej; Passilly, Nicolas; Bargiel, Sylwester; Froehly, Luc; Gorecki, Christophe
2016-04-01
This paper presents the conception of a new micro-optical component fabricated within the wafer-level approach: a micromachined reflective objective, the so-called micro-Schwarzschild objective, characterized by superior optical performances than widespread microlenses. The system, made of two vertically integrated mirrors, works in transmission similarly as microlenses. While the specific geometric configuration of the two-mirrors allows elimination of most common optical aberrations, the reflective architecture provides inherent achromaticity. This paper presents in detail the optical design and analyzes fabrication tolerances. It also describes a fabrication flow chart based on silicon micromachining done at the wafer level that could allow production of thousands of such micro-optical devices within a single fabrication run. The realized prototype employs the two-step KOH etching process to generate the micromirror pairs followed by glass reflow for the secondary mirror generation and selective metallic deposition. Despite an insufficient mirror quality attributed to this specific silicon etching technique and highlighted by the reflective configuration, the objective fabrication in terms of alignment, bonding, and coating is shown as feasible.
Alvarez-Gaumé, Luís; Marino, M; Wadia, S R; Alvarez-Gaume, Luis; Basu, Pallab; Marino, Marcos; Wadia, Spenta R.
2006-01-01
In this paper we discuss the blackhole-string transition of the small Schwarzschild blackhole of $AdS_5 \\times S^5$ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak {\\it and} strong coupling, can be expressed entirely in terms of constant Polyakov lines which are $SU (N)$ matrices. In showing this we have taken into account that there are no Nambu-Goto modes associated with the fact that the 10 dimensional blackhole solution sits at a point in $S^5$. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order $N = \\infty$ phase transition with the blackhole-string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of $N^{-2/3}$. The $N = \\infty$ transition now becomes a smooth crossover in terms of a renormalized string c...
Energy Technology Data Exchange (ETDEWEB)
Xu, Shuai; Song, Xue-ke; Shi, Jia-dong; Ye, Liu, E-mail: yeliu@ahu.edu.cn
2014-06-02
In this Letter, we analytically explore the effect of the Hawking radiation on the quantum correlation and Bell non-locality for Dirac particles in the background of Schwarzschild black hole. It is shown that when the Hawking effect is almost nonexistent, corresponding to the case of an almost extreme black hole, the quantum properties of physically accessible state are the same for the initial situation. For finite Hawking temperature T, the accessible quantum correlation monotonously decreases along with increasing T owing to the thermal fields generated by the Hawking effect, and the accessible quantum non-locality will be disappeared when the Hawking temperature is more than a fixed value which increases with the parameter r of Werner state growing. Then we analyze the redistribution of quantum correlation, and find that for the case of the Hawking temperature being infinite, corresponding to the case of the black hole evaporating completely, the quantum correlation of physically accessible state is equal to the one of the inaccessible states. Moreover, due to the Pauli exclusion principle and the differences between Fermi–Dirac and Bose–Einstein statistics, for the Dirac fields the accessible classical correlation decreases with increase of the Hawking temperature, which is different for the scalar fields. For Bell non-locality, we also find that the quantum non-locality is always extinct for physically inaccessible states, and the strength of the non-locality decreases with enlarging intensity of Hawking effect when the non-locality is existent in physically accessible state.
Using a safety forecast model to calculate future safety metrics.
2017-05-01
This research sought to identify a process to improve long-range planning prioritization by using forecasted : safety metrics in place of the existing Utah Department of Transportation Safety Indexa metric based on historical : crash data. The res...
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.
Metric-Aware Secure Service Orchestration
Directory of Open Access Journals (Sweden)
Gabriele Costa
2012-12-01
Full Text Available Secure orchestration is an important concern in the internet of service. Next to providing the required functionality the composite services must also provide a reasonable level of security in order to protect sensitive data. Thus, the orchestrator has a need to check whether the complex service is able to satisfy certain properties. Some properties are expressed with metrics for precise definition of requirements. Thus, the problem is to analyse the values of metrics for a complex business process. In this paper we extend our previous work on analysis of secure orchestration with quantifiable properties. We show how to define, verify and enforce quantitative security requirements in one framework with other security properties. The proposed approach should help to select the most suitable service architecture and guarantee fulfilment of the declared security requirements.
A perceptual metric for photo retouching.
Kee, Eric; Farid, Hany
2011-12-13
In recent years, advertisers and magazine editors have been widely criticized for taking digital photo retouching to an extreme. Impossibly thin, tall, and wrinkle- and blemish-free models are routinely splashed onto billboards, advertisements, and magazine covers. The ubiquity of these unrealistic and highly idealized images has been linked to eating disorders and body image dissatisfaction in men, women, and children. In response, several countries have considered legislating the labeling of retouched photos. We describe a quantitative and perceptually meaningful metric of photo retouching. Photographs are rated on the degree to which they have been digitally altered by explicitly modeling and estimating geometric and photometric changes. This metric correlates well with perceptual judgments of photo retouching and can be used to objectively judge by how much a retouched photo has strayed from reality.
Data Complexity Metrics for XML Web Services
Directory of Open Access Journals (Sweden)
MISRA, S.
2009-06-01
Full Text Available Web services that are based on eXtensible Markup Language (XML technologies enable integration of diverse IT processes and systems and have been gaining extraordinary acceptance from the basic to the most complicated business and scientific processes. The maintainability is one of the important factors that affect the quality of the Web services that can be seen a kind of software project. The effective management of any type of software projects requires modelling, measurement, and quantification. This study presents a metric for the assessment of the quality of the Web services in terms of its maintainability. For this purpose we proposed a data complexity metric that can be evaluated by analyzing WSDL (Web Service Description Language documents used for describing Web services.
Metrics for measuring distances in configuration spaces.
Sadeghi, Ali; Ghasemi, S Alireza; Schaefer, Bastian; Mohr, Stephan; Lill, Markus A; Goedecker, Stefan
2013-11-14
In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices.
Finite Metric Spaces of Strictly Negative Type
DEFF Research Database (Denmark)
Hjorth, Poul; Lisonek, P.; Markvorsen, Steen
1998-01-01
We prove that, if a finite metric space is of strictly negative type, then its transfinite diameter is uniquely realized by the infinite extender (load vector). Finite metric spaces that have this property include all spaces on two, three, or four points, all trees, and all finite subspaces...... of Euclidean spaces. We prove that, if the distance matrix is both hypermetric and regular, then it is of strictly negative type. We show that the strictly negative type finite subspaces of spheres are precisely those which do not contain two pairs of antipodal points. In connection with an open problem raised...... by Kelly, we conjecture that all finite subspaces of hyperbolic spaces are hypermetric and regular, and hence of strictly negative type. (C) 1998 Elsevier Science Inc....
Machine Learning for ATLAS DDM Network Metrics
Lassnig, Mario; The ATLAS collaboration; Vamosi, Ralf
2016-01-01
The increasing volume of physics data is posing a critical challenge to the ATLAS experiment. In anticipation of high luminosity physics, automation of everyday data management tasks has become necessary. Previously many of these tasks required human decision-making and operation. Recent advances in hardware and software have made it possible to entrust more complicated duties to automated systems using models trained by machine learning algorithms. In this contribution we show results from our ongoing automation efforts. First, we describe our framework for distributed data management and network metrics, automatically extract and aggregate data, train models with various machine learning algorithms, and eventually score the resulting models and parameters. Second, we use these models to forecast metrics relevant for network-aware job scheduling and data brokering. We show the characteristics of the data and evaluate the forecasting accuracy of our models.
Primordial magnetic fields from metric perturbations
Maroto, A L
2001-01-01
We study the amplification of electromagnetic vacuum fluctuations induced by the evolution of scalar metric perturbations at the end of inflation. Such perturbations break the conformal invariance of Maxwell equations in Friedmann-Robertson-Walker backgrounds and allow the growth of magnetic fields on super-Hubble scales. We estimate the strength of the fields generated by this mechanism on galactic scales and compare the results with the present bounds on the galactic dynamo seed fields.
Agile Metrics: Progress Monitoring of Agile Contractors
2014-01-01
epic. The short timeframe is usually called an itera- tion or, in Scrum -based teams, a sprint; multiple iterations make up a release [Lapham 2011...9769 [Rawsthorne 2012] Rawsthorne, Dan. Monitoring Scrum Projects with AgileEVM and Earned Business Value Metrics (EBV). 2012. http...AgileEVM – Earned Value Manage- ment in Scrum Projects.” Presented at Agile2006, 23-28 July 2006. [USAF 2008] United States Air Force. United
Metric entropy in linear inverse scattering
Directory of Open Access Journals (Sweden)
M. A. Maisto
2016-09-01
Full Text Available The role of multiple views and/or multiple frequencies on the achievable performance in linear inverse scattering problems is addressed. To this end, the impact of views and frequencies on the Kolmogorov entropy measure is studied. This way the metric information that can be conveyed back from data to the unknown can be estimated. For the sake of simplicity, the study deals with strip scatterers and the cases of discrete angles of incidence and/or frequencies.
Anisotropic rectangular metric for polygonal surface remeshing
Pellenard, Bertrand
2013-06-18
We propose a new method for anisotropic polygonal surface remeshing. Our algorithm takes as input a surface triangle mesh. An anisotropic rectangular metric, defined at each triangle facet of the input mesh, is derived from both a user-specified normal-based tolerance error and the requirement to favor rectangle-shaped polygons. Our algorithm uses a greedy optimization procedure that adds, deletes and relocates generators so as to match two criteria related to partitioning and conformity.
Smart Grid Status and Metrics Report
Energy Technology Data Exchange (ETDEWEB)
Balducci, Patrick J. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Weimar, Mark R. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Kirkham, Harold [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)
2014-07-01
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. It measures 21 metrics to provide insight into the grid’s capacity to embody these characteristics. This report looks across a spectrum of smart grid concerns to measure the status of smart grid deployment and impacts.
Maximum Metric Spanning Tree made Byzantine Tolerant
Dubois, Swan; Masuzawa, Toshimitsu; Tixeuil, Sébastien
2011-01-01
Self-stabilization is a versatile approach to fault-tolerance since it permits a distributed system to recover from any transient fault that arbitrarily corrupts the contents of all memories in the system. Byzantine tolerance is an attractive feature of distributed systems that permits to cope with arbitrary malicious behaviors. This paper focus on systems that are both self-stabilizing and Byzantine tolerant. We consider the well known problem of constructing a maximum metric tree in this co...
Preserved Network Metrics across Translated Texts
Cabatbat, Josephine Jill T.; Monsanto, Jica P.; Tapang, Giovanni A.
2014-09-01
Co-occurrence language networks based on Bible translations and the Universal Declaration of Human Rights (UDHR) translations in different languages were constructed and compared with random text networks. Among the considered network metrics, the network size, N, the normalized betweenness centrality (BC), and the average k-nearest neighbors, knn, were found to be the most preserved across translations. Moreover, similar frequency distributions of co-occurring network motifs were observed for translated texts networks.
Economic metrics for wind energy projects
Wagner Sousa de Oliveira, Antonio Jorge Fernandes, Joaquim Jose Borges Gouveia
2011-01-01
This paper presents an overview of economic metrics for wind energy projects. The attractiveness of the proposed wind energy can vary considerably between evaluation of the private and public sector. The financing structure is very important influencing factor for the attractiveness of wind energy project. In many cases, the economic activities practiced by economic agents of financing the project in order to earn sufficient income to meet the investors‘ needs and other economic agents involv...
Quasinormal modes for the charged Vaidya metric
Energy Technology Data Exchange (ETDEWEB)
Chirenti, Cecilia [Centro de Matematica, Computacao e Cognicao, UFABC, 09210-170 Santo Andre, SP (Brazil); Saa, Alberto [Departamento de Matematica Aplicada, UNICAMP, 13083-859 Campinas, SP (Brazil)
2011-09-22
The scalar wave equation is considered in the background of a charged Vaidya metric in double null coordinates (u,v) describing a non-stationary charged black hole with varying mass m(v) and charge q(v). The resulting time-dependent quasinormal modes are presented and analyzed. We show, in particular, that it is possible to identify some signatures in the quasinormal frequencies from the creation of a naked singularity.
Evaluating and Estimating the WCET Criticality Metric
DEFF Research Database (Denmark)
Jordan, Alexander
2014-01-01
a programmer (or compiler) from targeting optimizations the right way. A possible resort is to use a metric that targets WCET and which can be efficiently computed for all code parts of a program. Similar to dynamic profiling techniques, which execute code with input that is typically expected...... are considered as standard WCET benchmarks. We furthermore demonstrate how the visualization of a Criticality-based profile can aid in the understanding of a program's worst-case behavior....
What can article-level metrics do for you?
Directory of Open Access Journals (Sweden)
Martin Fenner
2013-10-01
Full Text Available 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.
What can article-level metrics do for you?
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.
Metrics. [measurement for effective software development and management
Mcgarry, Frank
1991-01-01
A development status evaluation is presented for practical software performance measurement, or 'metrics', in which major innovations have recently occurred. Metrics address such aspects of software performance as whether a software project is on schedule, how many errors can be expected from it, whether the methodology being used is effective and the relative quality of the software employed. Metrics may be characterized as explicit, analytical, and subjective. Attention is given to the bases for standards and the conduct of metrics research.
Existing Model Metrics and Relations to Model Quality
Mohagheghi, Parastoo; Dehlen, Vegard
2009-01-01
This paper presents quality goals for models and provides a state-of-the-art analysis regarding model metrics. While model-based software development often requires assessing the quality of models at different abstraction and precision levels and developed for multiple purposes, existing work on model metrics do not reflect this need. Model size metrics are descriptive and may be used for comparing models but their relation to model quality is not welldefined. Code metrics are proposed to be ...
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 pointe...... metric spaces. - See more at: http://www.ams.org/journals/tran/2014-366-12/S0002-9947-2014-06010-8/#sthash.ullL9RMw.dpuf...
Decomposition-based transfer distance metric learning for image classification.
Luo, Yong; Liu, Tongliang; Tao, Dacheng; Xu, Chao
2014-09-01
Distance metric learning (DML) is a critical factor for image analysis and pattern recognition. To learn a robust distance metric for a target task, we need abundant side information (i.e., the similarity/dissimilarity pairwise constraints over the labeled data), which is usually unavailable in practice due to the high labeling cost. This paper considers the transfer learning setting by exploiting the large quantity of side information from certain related, but different source tasks to help with target metric learning (with only a little side information). The state-of-the-art metric learning algorithms usually fail in this setting because the data distributions of the source task and target task are often quite different. We address this problem by assuming that the target distance metric lies in the space spanned by the eigenvectors of the source metrics (or other randomly generated bases). The target metric is represented as a combination of the base metrics, which are computed using the decomposed components of the source metrics (or simply a set of random bases); we call the proposed method, decomposition-based transfer DML (DTDML). In particular, DTDML learns a sparse combination of the base metrics to construct the target metric by forcing the target metric to be close to an integration of the source metrics. The main advantage of the proposed method compared with existing transfer metric learning approaches is that we directly learn the base metric coefficients instead of the target metric. To this end, far fewer variables need to be learned. We therefore obtain more reliable solutions given the limited side information and the optimization tends to be faster. Experiments on the popular handwritten image (digit, letter) classification and challenge natural image annotation tasks demonstrate the effectiveness of the proposed method.
Image characterization metrics for muon tomography
Luo, Weidong; Lehovich, Andre; Anashkin, Edward; Bai, Chuanyong; Kindem, Joel; Sossong, Michael; Steiger, Matt
2014-05-01
Muon tomography uses naturally occurring cosmic rays to detect nuclear threats in containers. Currently there are no systematic image characterization metrics for muon tomography. We propose a set of image characterization methods to quantify the imaging performance of muon tomography. These methods include tests of spatial resolution, uniformity, contrast, signal to noise ratio (SNR) and vertical smearing. Simulated phantom data and analysis methods were developed to evaluate metric applicability. Spatial resolution was determined as the FWHM of the point spread functions in X, Y and Z axis for 2.5cm tungsten cubes. Uniformity was measured by drawing a volume of interest (VOI) within a large water phantom and defined as the standard deviation of voxel values divided by the mean voxel value. Contrast was defined as the peak signals of a set of tungsten cubes divided by the mean voxel value of the water background. SNR was defined as the peak signals of cubes divided by the standard deviation (noise) of the water background. Vertical smearing, i.e. vertical thickness blurring along the zenith axis for a set of 2 cm thick tungsten plates, was defined as the FWHM of vertical spread function for the plate. These image metrics provided a useful tool to quantify the basic imaging properties for muon tomography.
Models, Metrics, and Measurement in Developmental Psychology
Directory of Open Access Journals (Sweden)
Zachary Stein
2009-06-01
Full Text Available Developmental psychology is currently used to measure psychologicalphenomena and by some, to re-design communities. While we generally support theseuses, we are concerned about quality control standards guiding the production of usableknowledge in the discipline. In order to address these issues precisely, we provide anoverview of the discipline's various facets. We distinguish between developmentalmodels and developmental metrics and relate each to different types of quality-controldevices. In our view, models are either explanatory or descriptive, and their quality isevaluated in terms of specific types of disciplinary discourse. Metrics are eithercalibrated measures or soft measures, and their quality is evaluated in terms of specificpsychometric parameters. Following a discussion on how developmentalists makemetrics, and on a variety of metrics that have been made, we discuss the two keypsychometric quality-control parameters, validity and reliability. This sets the stage for alimited and exploratory literature review concerning the quality of a set of existingmetrics. We reveal a conspicuous lack of psychometric rigor on the part of some of themost popular developmental approaches and invite remedies for this situation.
A computational imaging target specific detectivity metric
Preece, Bradley L.; Nehmetallah, George
2017-05-01
Due to the large quantity of low-cost, high-speed computational processing available today, computational imaging (CI) systems are expected to have a major role for next generation multifunctional cameras. The purpose of this work is to quantify the performance of theses CI systems in a standardized manner. Due to the diversity of CI system designs that are available today or proposed in the near future, significant challenges in modeling and calculating a standardized detection signal-to-noise ratio (SNR) to measure the performance of these systems. In this paper, we developed a path forward for a standardized detectivity metric for CI systems. The detectivity metric is designed to evaluate the performance of a CI system searching for a specific known target or signal of interest, and is defined as the optimal linear matched filter SNR, similar to the Hotelling SNR, calculated in computational space with special considerations for standardization. Therefore, the detectivity metric is designed to be flexible, in order to handle various types of CI systems and specific targets, while keeping the complexity and assumptions of the systems to a minimum.
Metrics of the perception of body movement.
Giese, Martin A; Thornton, Ian; Edelman, Shimon
2008-07-28
Body movements are recognized with speed and precision, even from strongly impoverished stimuli. While cortical structures involved in biological motion recognition have been identified, the nature of the underlying perceptual representation remains largely unknown. We show that visual representations of complex body movements are characterized by perceptual spaces with well-defined metric properties. By multidimensional scaling, we reconstructed from similarity judgments the perceptual space configurations of stimulus sets generated by motion morphing. These configurations resemble the true stimulus configurations in the space of morphing weights. In addition, we found an even higher similarity between the perceptual metrics and the metrics of a physical space that was defined by distance measures between joint trajectories, which compute spatial trajectory differences after time alignment using a robust error norm. These outcomes were independent of the experimental paradigm for the assessment of perceived similarity (pairs-comparison vs. delayed match-to-sample) and of the method of stimulus presentation (point-light stimuli vs. stick figures). Our findings suggest that the visual perception of body motion is veridical and closely reflects physical similarities between joint trajectories. This implies that representations of form and motion share fundamental properties and places constraints on the computational mechanisms that support the recognition of biological motion patterns.
The Entropy-Based Quantum Metric
Directory of Open Access Journals (Sweden)
Roger Balian
2014-07-01
Full Text Available The von Neumann entropy S( D ^ generates in the space of quantum density matrices D ^ the Riemannian metric ds2 = −d2S( D ^ , which is physically founded and which characterises the amount of quantum information lost by mixing D ^ and D ^ + d D ^ . A rich geometric structure is thereby implemented in quantum mechanics. It includes a canonical mapping between the spaces of states and of observables, which involves the Legendre transform of S( D ^ . The Kubo scalar product is recovered within the space of observables. Applications are given to equilibrium and non equilibrium quantum statistical mechanics. There the formalism is specialised to the relevant space of observables and to the associated reduced states issued from the maximum entropy criterion, which result from the exact states through an orthogonal projection. Von Neumann’s entropy specialises into a relevant entropy. Comparison is made with other metrics. The Riemannian properties of the metric ds2 = −d2S( D ^ are derived. The curvature arises from the non-Abelian nature of quantum mechanics; its general expression and its explicit form for q-bits are given, as well as geodesics.
Experimental validation of navigation workload metrics
Energy Technology Data Exchange (ETDEWEB)
Schryver, J.C. [Oak Ridge National Lab., TN (United States); Wachtel, J.A. [Nuclear Regulatory Commission, Rockville, MD (United States). Office of Nuclear Regulatory Research
1994-04-01
Advanced digital computer display interfaces in the control room may increase operator workload. Workstation monitors provide limited display area, and information is represented in large-scale display networks. Display navigation may generate disorienting effects, require additional resources for window management, and increase memory and data integration requirements. Six ORNL employees participated in an experiment to validate proposed metrics of navigation workload in the advanced control room. The task environment was a display network consisting of 25 windows resembling a simplified Safety Parameter Display System for Pressurized Water Reactors. A repeated measures design with 3 within subjects factors was employed. The factors were task difficulty, navigation distance level, and a blocking factor. Participants were asked to monitor a single parameter or two parameters. Fourteen candidate metrics were tested. Analysis of variance of the modified task load index (MTLX) and rating subscales demonstrated substantial support for the claim that navigation of large-scale display networks can impose additional mental load. Primary and secondary task performance measures exhibited ceiling effects. Memory probes for these tasks were inadequate because they were recognition-based and coarse. Eye gaze measures were not validated, indicating a need for more refined data reduction algorithms. Strong positive correlations were found between MTLX and both navigation duration and standard deviation of pupil diameter. Further study and increased statistical power are required to validate objective navigation workload metrics.
Gentili, Claudio; Cristea, Ioana Alina; Ricciardi, Emiliano; Vanello, Nicola; Popita, Cristian; David, Daniel; Pietrini, Pietro
2017-06-01
Neuroticism is a complex personality trait encompassing diverse aspects. Notably, high levels of neuroticism are related to the onset of psychiatric conditions, including anxiety and mood disorders. Personality traits are stable individual features; therefore, they can be expected to be associated with stable neurobiological features, including the Brain Resting State (RS) activity as measured by fMRI. Several metrics have been used to describe RS properties, yielding rather inconsistent results. This inconsistency could be due to the fact that different metrics portray different RS signal properties and that these properties may be differently affected by neuroticism. To explore the distinct effects of neuroticism, we assessed several distinct metrics portraying different RS properties within the same population. Neuroticism was measured in 31 healthy subjects using the Zuckerman-Kuhlman Personality Questionnaire; RS was acquired by high-resolution fMRI. Using linear regression, we examined the modulatory effects of neuroticism on RS activity, as quantified by the Amplitude of low frequency fluctuations (ALFF, fALFF), regional homogeneity (REHO), Hurst Exponent (H), global connectivity (GC) and amygdalae functional connectivity. Neuroticism modulated the different metrics across a wide network of brain regions, including emotional regulatory, default mode and visual networks. Except for some similarities in key brain regions for emotional expression and regulation, neuroticism affected different metrics in different ways. Metrics more related to the measurement of regional intrinsic brain activity (fALFF, ALFF and REHO), or that provide a parsimonious index of integrated and segregated brain activity (HE), were more broadly modulated in regions related to emotions and their regulation. Metrics related to connectivity were modulated across a wider network of areas. Overall, these results show that neuroticism affects distinct aspects of brain resting state activity
Kahler-Einstein metrics, Bergman metrics, and higher alpha-invariants
Macbeth, Heather
The question of the existence of Kahler-Einstein metrics on a Kahler manifold M has been a subject of study for decades. The Kahler manifolds on which this question may be studied divide naturally into three types. For two of these types the question was long ago settled by Yau and Aubin. For the third type, Fano manifolds, the question is (despite great recent progress) open for many individual manifolds. In the first part of this thesis we define algebraic invariants Bm,k(M) of a Fano manifold M, which codify certain properties of M 's Bergman metrics. We prove a criterion (Theorem 1.1.1) in terms of these invariants Bm,k( M) for the existence of a Kahler-Einstein metric on M. The proof of Theorem 1.1.1 relies on Szekelyhidi's deep recent partial C0-estimate, and on a new family of estimates for Fano manifolds. We furthermore introduce a very general hypothesis on Bergman metrics, Conjecture 6.1.2, offering some partial results (Section 6.3) in evidence. Modulo this conjecture, we prove a variation of Theorem 1.1.1, which gives a criterion for the existence of a Kahler-Einstein metric on M in terms of the well-known alpha-invariants, alpha m,k(M). This result extends a theorem of Tian. The second part of this thesis concerns Riemannian manifolds more generally. We give a characterization (Theorem 1.2.1) of conformal classes realizing a compact manifold's Yamabe invariant. This characterization is the analogue of an observation of Nadirashvili for metrics realizing the maximal first eigenvalue, and of Fraser and Schoen for metrics realizing the maximal first Steklov eigenvalue.
A factor analysis of landscape pattern and structure metrics
Kurt H. Riitters; R.V. O' Neill; C.T. Hunsaker; James D. Wickham; D.H. Yankee; S.P. Timmins; K.B. Jones; B.L. Jackson
1995-01-01
Fifty-five metrics of landscape pattern and structure were calculated for 85 maps of land use and land cover. A multivariate factor analysis was used to identify the common axes (or dimensions) of pattern and structure which were measured by a reduced set of 26 metrics. The first six factors explained about 87% of the variation in the 26 landscape metrics. These...
7 CFR 51.2854 - Metric conversion table.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Metric conversion table. 51.2854 Section 51.2854 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards...) Metric Conversion Table § 51.2854 Metric conversion table. Inches Millimeters (mm) 1/8 3.2 1/4 6.4 3/8 9...
7 CFR 51.322 - Metric conversion table.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Metric conversion table. 51.322 Section 51.322 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards... STANDARDS) United States Standards for Grades of Apples Metric Conversion Table § 51.322 Metric conversion...
10 CFR 600.115 - Metric system of measurement.
2010-01-01
..., Hospitals, and Other Nonprofit Organizations Pre-Award Requirements § 600.115 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205... 10 Energy 4 2010-01-01 2010-01-01 false Metric system of measurement. 600.115 Section 600.115...
10 CFR 600.306 - Metric system of measurement.
2010-01-01
... Requirements for Grants and Cooperative Agreements With For-Profit Organizations General § 600.306 Metric system of measurement. (a) The Metric Conversion Act of 1975, as amended by the Omnibus Trade and... 10 Energy 4 2010-01-01 2010-01-01 false Metric system of measurement. 600.306 Section 600.306...
The Canadian Experience: Implications for Metric Conversion in Education.
Chalupsky, Albert B.; And Others
The findings of a study of metric conversion in Canada are reported, with special attention to its impact on education. Some 40 interviews with metric education leaders in 8 provinces, coupled with an extensive review of documents and correspondence with key individuals in metric conversion throughout Canada, served as the information source for…
7 CFR 51.653 - Metric conversion table.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Metric conversion table. 51.653 Section 51.653 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards..., and Arizona) Metric Conversion Table § 51.653 Metric conversion table. Inches Millimeters (mm) 1/4...
20 CFR 435.15 - Metric system of measurement.
2010-04-01
... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Metric system of measurement. 435.15 Section..., AND COMMERCIAL ORGANIZATIONS Pre-Award Requirements § 435.15 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the...
The Adult Conversion to Metrics: Is Education Enough?
Kundel, Susan E.
1979-01-01
The American College Testing Program sought to determine whether metric education for adult consumers would result in more positive attitudes to metric conversion. Examining preopinion, pretest, posttest, post-opinion, and background data, the researchers found that simply teaching adults how to use the metric system does not significantly affect…
7 CFR 51.914 - Metric conversion table.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Metric conversion table. 51.914 Section 51.914... STANDARDS) United States Standards for Grades of Table Grapes (European or Vinifera Type) 1 Metric Conversion Table § 51.914 Metric conversion table. Inches Millimeters (mm) 3/16 equals 12.7 9/16 equals 14.3...
7 CFR 3019.15 - Metric system of measurement.
2010-01-01
... HIGHER EDUCATION, HOSPITALS, AND OTHER NON-PROFIT ORGANIZATIONS Pre-Award Requirements § 3019.15 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act... 7 Agriculture 15 2010-01-01 2010-01-01 false Metric system of measurement. 3019.15 Section 3019.15...
7 CFR 51.714 - Metric conversion table.
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Metric conversion table. 51.714 Section 51.714 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards..., and Arizona) Metric Conversion Table § 51.714 Metric conversion table. Inches Millimeters (mm) 1/4...
15 CFR 14.15 - Metric system of measurement.
2010-01-01
... 15 Commerce and Foreign Trade 1 2010-01-01 2010-01-01 false Metric system of measurement. 14.15... COMMERCIAL ORGANIZATIONS Pre-Award Requirements § 14.15 Metric system of measurement. The Metric Conversion... system is the preferred measurement system for U.S. trade and commerce. The Act requires each Federal...
28 CFR 70.15 - Metric system of measurement.
2010-07-01
... 28 Judicial Administration 2 2010-07-01 2010-07-01 false Metric system of measurement. 70.15... AND OTHER NON-PROFIT ORGANIZATIONS Pre-Award Requirements § 70.15 Metric system of measurement. The... that the metric system is the preferred measurement system for U.S. trade and commerce. The Act...
2 CFR 215.15 - Metric system of measurement.
2010-01-01
... 2 Grants and Agreements 1 2010-01-01 2010-01-01 false Metric system of measurement. 215.15 Section... measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for U.S. trade and commerce. The Act...
32 CFR 32.15 - Metric system of measurement.
2010-07-01
... 32 National Defense 1 2010-07-01 2010-07-01 false Metric system of measurement. 32.15 Section 32..., HOSPITALS, AND OTHER NON-PROFIT ORGANIZATIONS Pre-Award Requirements § 32.15 Metric system of measurement...) declares that the metric system is the preferred measurement system for U.S. trade and commerce, and for...
45 CFR 74.15 - Metric system of measurement.
2010-10-01
... 45 Public Welfare 1 2010-10-01 2010-10-01 false Metric system of measurement. 74.15 Section 74.15... ORGANIZATIONS, AND COMMERCIAL ORGANIZATIONS Pre-Award Requirements § 74.15 Metric system of measurement. The... that the metric system is the preferred measurement system for U.S. trade and commerce. The Act...
32 CFR 22.530 - Metric system of measurement.
2010-07-01
... 32 National Defense 1 2010-07-01 2010-07-01 false Metric system of measurement. 22.530 Section 22... of measurement. (a) Statutory requirement. The Metric Conversion Act of 1975, as amended by the... CFR, 1991 Comp., p. 343), states that: (1) The metric system is the preferred measurement system for U...
22 CFR 226.15 - Metric system of measurement.
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Metric system of measurement. 226.15 Section....S. NON-GOVERNMENTAL ORGANIZATIONS Pre-award Requirements § 226.15 Metric system of measurement. (a...) declares that the metric system is the preferred measurement system for U.S. trade and commerce. (b...
40 CFR 30.15 - Metric system of measurement.
2010-07-01
... 40 Protection of Environment 1 2010-07-01 2010-07-01 false Metric system of measurement. 30.15... measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205), declares that the metric system is the preferred measurement system for U.S. trade and commerce. The Act...
36 CFR 1210.15 - Metric system of measurement.
2010-07-01
... 36 Parks, Forests, and Public Property 3 2010-07-01 2010-07-01 false Metric system of measurement... system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for U.S. trade and...
22 CFR 145.15 - Metric system of measurement.
2010-04-01
... 22 Foreign Relations 1 2010-04-01 2010-04-01 false Metric system of measurement. 145.15 Section... system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and Competitiveness Act (15 U.S.C. 205) declares that the metric system is the preferred measurement system for U.S. trade and...
An inheritance complexity metric for object-oriented code: A ...
Indian Academy of Sciences (India)
used in the literature as a means to evaluate the software engineering metrics. We applied our metric on ... metrics in the literature for measuring the complexity of operations in the method. Most of these ..... changing its representation because weights assigned to the class or the method cannot depend on the order or way ...
Term Based Comparison Metrics for Controlled and Uncontrolled Indexing Languages
Good, B. M.; Tennis, J. T.
2009-01-01
Introduction: We define a collection of metrics for describing and comparing sets of terms in controlled and uncontrolled indexing languages and then show how these metrics can be used to characterize a set of languages spanning folksonomies, ontologies and thesauri. Method: Metrics for term set characterization and comparison were identified and…
Fixed Point Theorems in Quaternion-Valued Metric Spaces
Directory of Open Access Journals (Sweden)
Ahmed El-Sayed Ahmed
2014-01-01
Full Text Available The aim of this paper is twofold. First, we introduce the concept of quaternion metric spaces which generalizes both real and complex metric spaces. Further, we establish some fixed point theorems in quaternion setting. Secondly, we prove a fixed point theorem in normal cone metric spaces for four self-maps satisfying a general contraction condition.
Tide or Tsunami? The Impact of Metrics on Scholarly Research
Bonnell, Andrew G.
2016-01-01
Australian universities are increasingly resorting to the use of journal metrics such as impact factors and ranking lists in appraisal and promotion processes, and are starting to set quantitative "performance expectations" which make use of such journal-based metrics. The widespread use and misuse of research metrics is leading to…
14 CFR 1274.206 - Metric Conversion Act.
2010-01-01
... 14 Aeronautics and Space 5 2010-01-01 2010-01-01 false Metric Conversion Act. 1274.206 Section 1274.206 Aeronautics and Space NATIONAL AERONAUTICS AND SPACE ADMINISTRATION COOPERATIVE AGREEMENTS WITH COMMERCIAL FIRMS Pre-Award Requirements § 1274.206 Metric Conversion Act. The Metric Conversion...
14 CFR 1260.115 - Metric system of measurement.
2010-01-01
... 14 Aeronautics and Space 5 2010-01-01 2010-01-01 false Metric system of measurement. 1260.115 Section 1260.115 Aeronautics and Space NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GRANTS AND....115 Metric system of measurement. The Metric Conversion Act, as amended by the Omnibus Trade and...
Tangent spaces to metric spaces and to their subspaces
Dovgoshey, O.
2009-01-01
We investigate a tangent space at a point of a general metric space and metric space valued derivatives. The conditions under which two different subspace of a metric space have isometric tangent spaces in a common point of these subspaces are completely determinated.
Meter Detection in Symbolic Music Using Inner Metric Analysis
de Haas, W.B.; Volk, A.
2016-01-01
In this paper we present PRIMA: a new model tailored to symbolic music that detects the meter and the first downbeat position of a piece. Given onset data, the metrical structure of a piece is interpreted using the Inner Metric Analysis (IMA) model. IMA identifies the strong and weak metrical
Understanding Acceptance of Software Metrics--A Developer Perspective
Umarji, Medha
2009-01-01
Software metrics are measures of software products and processes. Metrics are widely used by software organizations to help manage projects, improve product quality and increase efficiency of the software development process. However, metrics programs tend to have a high failure rate in organizations, and developer pushback is one of the sources…
On the completion of partial metric spaces | Van Dung | Quaestiones ...
African Journals Online (AJOL)
In this note, we give an example to answer affirmatively Ge-Lin's question on the completion of partial metric spaces [3, Question 1]. We also study some related results on the completion of a partial metric space. Keywords: Partial metric space, completion ...
Comparison of routing metrics for wireless mesh networks
CSIR Research Space (South Africa)
Nxumalo, SL
2011-09-01
Full Text Available A number of routing metrics exist in wireless networks. These routing metrics were originally designed for mobile ad hoc networks (MANETs). When Wireless Mesh Networks (WMNs) came into being, an idea of introducing and using these routing metrics...
A convergence theory for probabilistic metric spaces | Jäger ...
African Journals Online (AJOL)
We develop a theory of probabilistic convergence spaces based on Tardiff's neighbourhood systems for probabilistic metric spaces. We show that the resulting category is a topological universe and we characterize a subcategory that is isomorphic to the category of probabilistic metric spaces. Keywords: Probabilistic metric ...