Instability of elliptic equations on compact Riemannian manifolds with non-negative Ricci curvature
Directory of Open Access Journals (Sweden)
Arnaldo S. Nascimento
2010-05-01
Full Text Available We prove the nonexistence of nonconstant local minimizers for a class of functionals, which typically appear in scalar two-phase field models, over smooth N-dimensional Riemannian manifolds without boundary and non-negative Ricci curvature. Conversely, for a class of surfaces possessing a simple closed geodesic along which the Gauss curvature is negative, we prove the existence of nonconstant local minimizers for the same class of functionals.
Scalar Curvature of a Causal Set
Benincasa, Dionigi M. T.; Dowker, Fay
2010-05-01
A one parameter family of retarded linear operators on scalar fields on causal sets is introduced. When the causal set is well approximated by 4 dimensional Minkowski spacetime, the operators are Lorentz invariant but nonlocal, are parametrized by the scale of the nonlocality, and approximate the continuum scalar D’Alembertian □ when acting on fields that vary slowly on the nonlocality scale. The same operators can be applied to scalar fields on causal sets which are well approximated by curved spacetimes in which case they approximate □-(1)/(2)R where R is the Ricci scalar curvature. This can used to define an approximately local action functional for causal sets.
Non-negative Ricci curvature on closed manifolds under Ricci flow
Maximo, Davi
2009-01-01
In this short note we show that non-negative Ricci curvature is not preserved under Ricci flow for closed manifolds of dimensions four and above, strengthening a previous result of Knopf in \\cite{K} for complete non-compact manifolds of bounded curvature. This brings down to four dimensions a similar result B\\"ohm and Wilking have for dimensions twelve and above, \\cite{BW}. Moreover, the manifolds constructed here are \\Kahler manifolds and relate to a question raised by Xiuxiong Chen in \\cite{XC}, \\cite{XCL}.
The Scalar Curvature of a Causal Set
Benincasa, Dionigi M T
2010-01-01
A one parameter family of retarded linear operators on scalar fields on causal sets is introduced. When the causal set is well-approximated by 4 dimensional Minkowski spacetime, the operators are Lorentz invariant but nonlocal, are parametrised by the scale of the nonlocality and approximate the continuum scalar D'Alembertian, $\\Box$, when acting on fields that vary slowly on the nonlocality scale. The same operators can be applied to scalar fields on causal sets which are well-approximated by curved spacetimes in which case they approximate $\\Box - {{1/2}}R$ where $R$ is the Ricci scalar curvature. This can used to define an approximately local action functional for causal sets.
Expanding solitons with non-negative curvature operator coming out of cones
Schulze, Felix
2010-01-01
We show that a Ricci flow of any complete Riemannian manifold without boundary with bounded non-negative curvature operator and non-zero asymptotic volume ratio exists for all time and has constant asymptotic volume ratio. We show that there is a limit solution, obtained by scaling down this solution at a fixed point in space, which is an expanding soliton coming out of the asymptotic cone at infinity.
Scalar Curvature for the Noncommutative Two Torus
Fathizadeh, Farzad
2011-01-01
We give a local expression for the {\\it scalar curvature} of the noncommutative two torus $ A_{\\theta} = C(\\mathbb{T}_{\\theta}^2)$ equipped with an arbitrary translation invariant complex structure and Weyl factor. This is achieved by evaluating the value of the (analytic continuation of the) {\\it spectral zeta functional} $\\zeta_a(s): = \\text{Trace}(a \\triangle^{-s})$ at $s=0$ as a linear functional in $a \\in C^{\\infty}(\\mathbb{T}_{\\theta}^2)$. A new, purely noncommutative, feature here is the appearance of the {\\it modular automorphism group} from the theory of type III factors and quantum statistical mechanics in the final formula for the curvature. This formula coincides with the formula that was recently obtained independently by Connes and Moscovici in their recent paper.
Scalar Curvature and Intrinsic Flat Convergence
Sormani, Christina
2016-01-01
Herein we present open problems and survey examples and theorems concerning sequences of Riemannian manifolds with uniform lower bounds on scalar curvature and their limit spaces. Examples of Gromov and of Ilmanen which naturally ought to have certain limit spaces do not converge with respect to smooth or Gromov-Hausdorff convergence. Thus we focus here on the notion of Intrinsic Flat convergence, developed jointly with Wenger. This notion has been applied successfully to study sequences that arise in General Relativity. Gromov has suggested it should be applied in other settings as well. We first review intrinsic flat convergence, its properties, and its compactness theorems, before presenting the applications and the open problems.
The scalar curvature problem on the four dimensional half sphere
Ben-Ayed, M; El-Mehdi, K
2003-01-01
In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the standard four dimensional half sphere. We provide an Euler-Hopf type criterion for a given function to be a scalar curvature for some metric conformal to the standard one. Our proof involves the study of critical points at infinity of the associated variational problem.
Total mean curvature, scalar curvature, and a variational analog of Brown-York mass
Mantoulidis, Christos
2016-01-01
Let $(\\Omega, g)$ be a compact Riemannian 3-manifold with nonnegative scalar curvature, and with a mean-convex boundary $\\Sigma$ which is topologically a 2-sphere. We demonstrate that the total mean curvature of $\\Sigma$ is bounded from above by a constant depending only on the induced metric on $\\Sigma$. As an application, we define a variational analog of the Brown-York quasi-local mass of $\\Sigma$ in $(\\Omega, g)$ without assuming that $\\Sigma$ has positive Gauss curvature. We also cast this discussion in the light of a natural variational problem on compact 3-manifolds with boundary and nonnegative scalar curvature.
Institute of Scientific and Technical Information of China (English)
Xiuxiong CHEN; Haozhao LI
2008-01-01
The authors show that the 2-non-negative traceless bisectional curvature is preserved along the K(a)hler-Ricci flow.The positivity of Ricci curvature is also preserved along the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature.As a corollary,the K(a)hler-Ricci flow with 2-non-negative traceless bisectional curvature will converge to a K(a)hler-Ricci soliton in the sense of Cheeger-Gromov-Hausdorff topology if complex dimension n≥3.
Estimates and Nonexistence of Solutions of the Scalar Curvature Equation on Noncompact Manifolds
Indian Academy of Sciences (India)
Zhang Zonglao
2005-08-01
This paper is to study the conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature. We derive some estimates and properties of supersolutions of the scalar curvature equation, and obtain some nonexistence results for complete solutions of scalar curvature equation.
Conformal couplings of a scalar field to higher curvature terms
Oliva, Julio
2011-01-01
We present a simple way of constructing conformal couplings of a scalar field to higher order Euler densities. This is done by constructing a four-rank tensor involving the curvature and derivatives of the field, which transforms covariantly under local Weyl rescalings. The equation of motion for the field, as well as its energy momentum tensor are shown to be of second order. The field equations for the spherically symmetric ansatz are integrated, and for generic non-homogeneous couplings, the solution is given in terms of a polynomial equation, in close analogy with Lovelock theories.
Measuring the Scalar Curvature with Clocks and Photons: Voronoi-Delaunay Lattices in Regge Calculus
McDonald, Jonathan R
2008-01-01
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a ...
On the scalar curvature for the noncommutative four torus
Fathizadeh, Farzad
2015-06-01
The scalar curvature for noncommutative four tori TΘ 4 , where their flat geometries are conformally perturbed by a Weyl factor, is computed by making the use of a noncommutative residue that involves integration over the 3-sphere. This method is more convenient since it does not require the rearrangement lemma and it is advantageous as it explains the simplicity of the final functions of one and two variables, which describe the curvature with the help of a modular automorphism. In particular, it readily allows to write the function of two variables as the sum of a finite difference and a finite product of the one variable function. The curvature formula is simplified for dilatons of the form sp, where s is a real parameter and p ∈ C ∞ ( TΘ 4 ) is an arbitrary projection, and it is observed that, in contrast to the two dimensional case studied by Connes and Moscovici, J. Am. Math. Soc. 27(3), 639-684 (2014), unbounded functions of the parameter s appear in the final formula. An explicit formula for the gradient of the analog of the Einstein-Hilbert action is also calculated.
Cones in the Euclidean space with vanishing scalar curvature
Directory of Open Access Journals (Sweden)
João Lucas M. Barbosa
2004-12-01
Full Text Available Given a hypersurface M on a unit sphere of the Euclidean space, we define the cone based on M as the set of half-lines issuing from the origin and passing through M. By assuming that the scalar curvature of the cone vanishes, we obtain conditions under which bounded domains of such cone are stable or unstable.Dada uma hipersuperfície M de uma esfera unitária do espaço euclidiano, definimos o cone sobre M como o conjunto das semi-retas que saem da origem e passam por M. Admitindo que a curvatura escalar de um dado cone é nula, estabelecemos condições para que os seus domínios limitados sejam estáveis ou instáveis.
Constant scalar curvature hypersurfaces in the extended Schwarzschild space-time
Pareja, M J
2006-01-01
In this paper we study the spherically symmetric constant scalar curvature hypersurfaces of the extended Schwarzschild space-time. Especially, we analyse the embedding equation and we find the family of solutions or slices that results varying a parameter "c" for fixed constant scalar curvature parameter and fixed time-translation parameter. The parameter "c" represents the amount of variation of volume of the 3-geometry during the 'time'-evolution.
Measuring the Scalar Curvature with Clocks and Photons: Voronoi-Delaunay Lattices in Regge Calculus
Miller, Warner; McDonald, Jonathan
2008-04-01
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe it is ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge Calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.
A geometric construction of the Riemann scalar curvature in Regge calculus
McDonald, Jonathan R.; Miller, Warner A.
2008-10-01
The Riemann scalar curvature plays a central role in Einstein's geometric theory of gravity. We describe a new geometric construction of this scalar curvature invariant at an event (vertex) in a discrete spacetime geometry. This allows one to constructively measure the scalar curvature using only clocks and photons. Given recent interest in discrete pre-geometric models of quantum gravity, we believe is it ever so important to reconstruct the curvature scalar with respect to a finite number of communicating observers. This derivation makes use of a new fundamental lattice cell built from elements inherited from both the original simplicial (Delaunay) spacetime and its circumcentric dual (Voronoi) lattice. The orthogonality properties between these two lattices yield an expression for the vertex-based scalar curvature which is strikingly similar to the corresponding hinge-based expression in Regge calculus (deficit angle per unit Voronoi dual area). In particular, we show that the scalar curvature is simply a vertex-based weighted average of deficits per weighted average of dual areas.
Spacetime Curvature in terms of Scalar Field Propagators
Saravani, Mehdi; Kempf, Achim
2015-01-01
We show how quantum fields can be used to measure the curvature of spacetime. In particular, we find that knowledge of the imprint that spacetime curvature leaves in the correlators of quantum fields suffices, in principle, to reconstruct the metric. We then consider the possibility that the quantum fields obey a natural ultraviolet cutoff, for example, at the Planck scale. We investigate how such a cutoff limits the spatial resolution with which curvature can be deduced from the properties of quantum fields. We find that the metric deduced from the quantum correlator exhibits a peculiar scaling behavior as the scale of the natural UV cutoff is approached.
Curvature Perturbation and Domain Wall Formation with Pseudo Scaling Scalar Dynamics
Ema, Yohei; Takimoto, Masahiro
2015-01-01
Cosmological dynamics of scalar field with a monomial potential $\\phi^{n}$ with a general background equation of state is revisited. It is known that if $n$ is smaller than a critical value, the scalar field exhibits a coherent oscillation and if $n$ is larger it obeys a scaling solution without oscillation. We study in detail the case where $n$ is equal to the critical value, and find a peculiar scalar dynamics which is neither oscillating nor scaling solution, and we call it a pseudo scaling solution. We also discuss cosmological implications of a pseudo scaling scalar dynamics, such as the curvature perturbation and the domain wall problem.
Khoury, Justin
2009-01-01
The universe can be made flat and smooth by undergoing a phase of ultra-slow (ekpyrotic) contraction with equation of state w >> 1, a condition that is achievable with a single, canonical scalar field and conventional general relativity. It has been argued, though, that another goal, generating scale-invariant density perturbations, requires at least two scalar fields and a two-step process that first produces entropy fluctuations and then converts them to curvature perturbations. In this paper, we exploit a loophole in the argument and introduce an ekpyrotic model based on a single, canonical scalar field that utilizes a purely "adiabatic mechanism" to generate nearly scale-invariant curvature fluctuations. The curvature perturbation tends to a constant at long wavelengths, indicating that the background evolution is a dynamical attractor. The resulting spectrum is slightly red with distinctive non-gaussian fluctuations.
Frame-Covariant Formulation of Inflation in Scalar-Curvature Theories
Burns, Daniel; Pilaftsis, Apostolos
2016-01-01
We develop a frame-covariant formulation of inflation in the slow-roll approximation by generalizing the inflationary attractor solution for scalar-curvature theories. Our formulation gives rise to new generalized forms for the potential slow-roll parameters, which enable us to examine the effect of conformal transformations and inflaton reparameterizations in scalar-curvature theories. We find that cosmological observables, such as the power spectrum, the spectral indices and their runnings, can be expressed in a concise manner in terms of the generalized potential slow-roll parameters which depend on the scalar-curvature coupling function, the inflaton wavefunction, and the inflaton potential. We show how the cosmological observables of inflation are frame-invariant in this generalized potential slow-roll formalism, as long as the end-of-inflation condition is appropriately extended to become frame-invariant as well. We then apply our formalism to specific scenarios, such as the induced gravity inflation, H...
Cosmological models with positive scalar spatial curvature and Λ>0
Ponce de Leon, J.
1987-12-01
Some exact spherically symmetric solutions of the Einstein field equations with Λ>0 and positive three-curvature are given. They have reasonable physical properties and represent universes which do not undergo inflation but have a non-de Sitter behaviour for large times. This paper extends some previous results in the literature. Permanent address: Apartado 2816, Caracas 1010-A, Venezuela.
Gravitomagnetism and the significance of the curvature scalar invariants
Costa, L Filipe O; Natário, José
2016-01-01
The curvature invariants have been subject of recent interest due to the debate concerning the notions of intrinsic/extrinsic frame-dragging, the use of the electromagnetic analogy in such classification, and the question of whether there is a fundamental difference between the gravitomagnetic field arising from the translational motion of the sources, detected with Lunar Laser Raging and in the observations of binary pulsars, and the gravitomagnetic field produced by the rotation of the Earth, detected in the LAGEOS Satellites data and by the Gravity Probe-B mission. In this work we clarify both the algebraic and physical meaning of the curvature invariants and their electromagnetic counterparts. The structure of the invariants of the astrophysical setups of interest is studied in detail, and its relationship with the gravitomagnetic effects is dissected. Finally, a new classification for intrinsic/extrinsic gravitomagnetism is put forth.
Bray, Hubert L
2009-01-01
In this thesis we describe how minimal surface techniques can be used to prove the Penrose inequality in general relativity for two classes of 3-manifolds. We also describe how a new volume comparison theorem involving scalar curvature for 3-manifolds follows from these same techniques.
Energy Technology Data Exchange (ETDEWEB)
Sakovich, Anna, E-mail: sakovich@math.kth.s [Institutionen foer Matematik, Kungliga Tekniska Hoegskolan, 100 44 Stockholm (Sweden)
2010-12-21
We follow the approach employed by Y Choquet-Bruhat, J Isenberg and D Pollack in the case of closed manifolds and establish existence and non-existence results for constant mean curvature solutions of the Einstein-scalar field constraint equations on asymptotically hyperbolic manifolds.
Intrinsic Dirac Behavior of Scalar Curvature in a Complex Weyl-Cartan Geometry
Rankin, J E
2011-01-01
The "spin-up" and "spin-down" projections of the second order, chiral form of Dirac Theory are shown to fit a superposition of forms predicted in an earlier classical, complex scalar gauge theory (April, 1992 Class. Quantum Grav.). In some sense, it appears to be possible to view the two component Dirac spinor as a single component, quaternionic, spacetime scalar. "Spin space" transformations become transformations of the internal quaternion basis. Essentially, quaternionic Dirac Theory projects into the complex plane neatly, where spin becomes related to the self-dual antisymmetric part of the metric. The correct Dirac eigenvalues and well-behaved eigenfunctions project intact into a pair of complex solutions for the scalar curvature in the earlier theory's Weyl-Cartan type geometry. Some estimates are made for predicted, interesting atomic and subatomic scale phenomena. A generalization of the complex geometric structure to allow quaternionic gauges and curvatures is sketched in an appendix, and appears to ...
Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature
Directory of Open Access Journals (Sweden)
Miguel Ángel García-Ariza
2014-12-01
Full Text Available In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying microscopic model of a thermodynamic system, which poses a limitation on the usefulness of Ruppeiner’s metric and conjecture. Finally, we address the problem of the choice of coordinates in black hole thermodynamics. We propose an alternative energy representation for Kerr-Newman black holes that mimics fully Weinhold’s approach. The corresponding Ruppeiner’s metrics become degenerate only at absolute zero and have non-vanishing scalar curvatures.
Second eigenvalue of a Jacobi operator of hypersurfaces with constant scalar curvature
Li, Haizhong
2010-01-01
Let $x:M\\to\\mathbb{S}^{n+1}(1)$ be an n-dimensional compact hypersurface with constant scalar curvature $n(n-1)r,~r\\geq 1$, in a unit sphere $\\mathbb{S}^{n+1}(1),~n\\geq 5$ and $J_s$ be the Jacobi operator of $M$. In \\cite{Cheng4}, Q. -M. Cheng studied the first eigenvalue of the Jacobi operator $J_s$ of the hypersurface with constant scalar curvature $n(n-1)r,r>1$ in $\\mathbb{S}^{n+1}(1)$. In \\cite{ABS}, L. J. Al\\'{\\i}as, A. Brasil and L. A. M. Sousa studied the first eigenvalue of $J_s$ of the hypersurface with constant scalar curvature $n(n-1)$ in $\\mathbb{S}^{n+1}(1),~n\\geq 3$. In this paper, we study the second eigenvalue of the Jacobi operator $J_s$ of $M$ and give an optimal upper bound for the second eigenvalue of $J_s$.
Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants
Tian, David Wenjie
2016-08-01
For a large class of scalar-tensor-like gravity whose action contains nonminimal couplings between a scalar field φ (x^α ) and generic curvature invariants R beyond the Ricci scalar R=R^α _{α }, we prove the covariant invariance of its field equation and confirm/prove the local energy-momentum conservation. These φ (x^α )- R coupling terms break the symmetry of diffeomorphism invariance under an active transformation, which implies that the solutions to the field equation should satisfy the consistency condition R ≡ 0 when φ (x^α ) is nondynamical and massless. Following this fact and based on the accelerated expansion of the observable Universe, we propose a primary test to check the viability of the modified gravity to be an effective dark energy, and a simplest example passing the test is the "Weyl/conformal dark energy".
Local energy-momentum conservation in scalar-tensor-like gravity with generic curvature invariants
Tian, David Wenjie
2015-01-01
For a large class of scalar-tensor-like modified gravity whose action contains nonminimal couplings between a scalar field $\\phi(x^\\alpha)$ and generic curvature invariants $\\mathcal{R}$ beyond the Ricci scalar $R=R^\\alpha_{\\;\\;\\alpha}$, we prove the covariant invariance of its field equation and confirm/prove the local energy-momentum conservation. These $\\phi(x^\\alpha)-\\mathcal{R}$ coupling terms break the symmetry of diffeomorphism invariance under a particle transformation, which implies that the solutions of the field equation should satisfy the consistency condition $\\mathcal{R}\\equiv 0$ when $\\phi(x^\\alpha)$ is nondynamical and massless. Following this fact and based on the accelerated expansion of the observable Universe, we propose a primary test to check the viability of the modified gravity to be an effective dark energy, and a simplest example passing the test is the "Weyl/conformal dark energy".
Morales, Manuel D.; Sarbach, Olivier
2017-02-01
Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field equations in which the outer boundary of the numerical grid is placed at null infinity. In this article, we numerically implement the tetrad-based approach presented by Bardeen, Sarbach, and Buchman [Phys. Rev. D 83, 104045 (2011), 10.1103/PhysRevD.83.104045] for a spherically symmetric, minimally coupled, self-gravitating scalar field. When this field is massless, the evolution system reduces to a regular, first-order symmetric hyperbolic system of equations for the conformally rescaled scalar field which is coupled to a set of singular elliptic constraints for the metric coefficients. We show how to solve this system based on a numerical finite-difference approximation, obtaining stable numerical evolutions for initial black hole configurations which are surrounded by a spherical shell of scalar field, part of which disperses to infinity and part of which is accreted by the black hole. As a nontrivial test, we study the tail decay of the scalar field along different curves, including one along the marginally trapped tube, one describing the world line of a timelike observer at a finite radius outside the horizon, and one corresponding to a generator of null infinity. Our results are in perfect agreement with the usual power-law decay discussed in previous work. This article also contains a detailed analysis for the asymptotic behavior and regularity of the lapse, conformal factor, extrinsic curvature and the Misner-Sharp mass function along constant mean curvature slices.
Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil
2012-10-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.
Bars, Itzhak; Steinhardt, Paul J; Turok, Neil
2012-01-01
We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null energy condition. There is a special subset of geodesically complete non-generic solutions which perform zero-size bounces without ever entering the antigravit...
Directory of Open Access Journals (Sweden)
T. Mardani
2005-06-01
Full Text Available In various statistical mechanical models, introduction of a metric into space of prameters gives a new perspective to the phase structure. In this paper, the scalar curvature R of this metric for a one dimensional four-state complex spin model is calculated. It is shown that this parameter has a similar behaviour to the Ising and Potts models.
Pashitskii, E A
2015-01-01
We suggest that the "Big Bang" may be a result of the first-order phase transition driven by changing scalar curvature of the 4D space-time in expanding cold Universe, filled with nonlinear scalar field $\\phi $ and neutral matter with equation of state $p=\
Analytic corrections to AdS by scalar matter and curvature squared term
Joshi, Lata Kh
2016-01-01
We revisit the background solution for scalar matter coupled higher derivative gravity originally reported in arXiv: 1409.8019[hep-th]. In this letter, we choose a convenient ansatz for metric which determines the first order perturbative corrections to scalar as well as geometry.
Belich, H; Paunov, R R
1999-01-01
By studying the {\\it internal} Riemannian geometry of the surfaces of constant negative scalar curvature, we obtain a natural map between the Liouville, and the sine-Gordon equations. First, considering isometric immersions into the Lobachevskian plane, we obtain an uniform expression for the general (locally defined) solution of both the equations. Second, we prove that there is a Lie-Bäcklund transformation interpolating between Liouville and sine-Gordon. Third, we use isometric immersions into the Lobachevskian plane to describe sine-Gordon N-solitons explicitly.
Yajima, Kohji
2015-01-01
We address the question of how one can modify the inflationary tensor spectrum without changing at all the successful predictions on the curvature perturbation. We show that this is indeed possible, and determine the two quadratic curvature corrections that are free from instabilities and affect only the tensor sector at the level of linear cosmological perturbations. Both of the two corrections can reduce the tensor amplitude, though one of them generates large non-Gaussianity of the curvature perturbation. It turns out that the other one corresponds to so-called Lorentz-violating Weyl gravity. In this latter case one can obtain as small as 65% of the standard tensor amplitude. Utilizing this effect we demonstrate that even power-law inflation can be within the 2$\\sigma$ contour of the Planck results.
Scalar-tensor cosmology with R^{-1} curvature correction by Noether Symmetry
Motavali, H; Jog, M Rowshan Almeh
2008-01-01
We discuss scalar-tensor cosmology with an extra $R^{-1}$ correction by the Noether Symmetry Approach. The existence of such a symmetry selects the forms of the coupling $\\omega(\\phi)$, of the potential $V(\\phi)$ and allows to obtain physically interesting exact cosmological solutions.
Morales, Manuel D
2016-01-01
Motivated by the goal for high accuracy modeling of gravitational radiation emitted by isolated systems, recently, there has been renewed interest in the numerical solution of the hyperboloidal initial value problem for Einstein's field equations in which the outer boundary of the numerical grid is placed at null infinity. In this article, we numerically implement the tetrad-based approach presented in [J.M. Bardeen, O. Sarbach, and L.T. Buchman, Phys. Rev. D 83, 104045 (2011)] for a spherically symmetric, minimally coupled, self-gravitating scalar field. When this field is massless, the evolution system reduces to a regular, first-order symmetric hyperbolic system of equations for the conformally rescaled scalar field which is coupled to a set of singular elliptic constraints for the metric coefficients. We show how to solve this system based on a numerical finite-difference approximation, obtaining stable numerical evolutions for initial black hole configurations which are surrounded by a spherical shell of...
Energy Technology Data Exchange (ETDEWEB)
Li, Changhong; Cheung, Yeuk-Kwan E., E-mail: chellifegood@gmail.com, E-mail: cheung@nju.edu.cn [Department of Physics, Nanjing University, 22 Hankou Road, Nanjing, 210093 China (China)
2014-07-01
We investigate the spectrum of cosmological perturbations in a bounce cosmos modeled by a scalar field coupled to the string tachyon field (CSTB cosmos). By explicit computation of its primordial spectral index we show the power spectrum of curvature perturbations, generated during the tachyon matter dominated contraction phase, to be nearly scale invariant. We propose a unified parameter space for a systematic study of inflationary and bounce cosmologies. The CSTB cosmos is dual-in Wands's sense-to slow-roll inflation as can be visualized with the aid of this parameter space. Guaranteed by the dynamical attractor behavior of the CSTB Cosmos, the scale invariance of its power spectrum is free of the fine-tuning problem, in contrast to the slow-roll inflation model.
Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere
Institute of Scientific and Technical Information of China (English)
Guo Xin WEI
2007-01-01
In this paper,we give a characterization of tori S1(√nr-2-n/nr)×Sn-1 (√n-2/nr)and Sm(√m/n)×Sn-m(√n-m/n).Our result extends the result due to Li (1996)on the condition that Mis an n-dimensional complete hypersurface in Sn+1 with two distinct principal curvatures.
Papadopoulos, Georgios O
2014-01-01
A classic, double problem with intriguing implications at the level of both applied differential geometry and theoretical physics is dealt with in this short work: Is there any criterion in order to decide whether a pseudo-Riemannian space can be locally described using curvature scalars solely? Also: In the case where such a description is impossible, does the Cartan-Karlhede algorithm constitute the only refuge? Surprisingly enough, the first question is susceptible of a very simple and elegant answer, while a naive scheme carries the ambition of providing (modulo specific restrictions) a negative answer to the second question. In order to avoid unnecessary complexity, the analysis is restricted to local rather than global considerations, without any loss of not only the generality but also the insights to the initial problem.
Günther, U; Bezerra, V; Romero, C; Guenther, Uwe; Zhuk, Alexander; Bezerra, Valdir; Romero, Carlos
2004-01-01
We study multidimensional gravitational models with scalar curvature nonlinearities of the type 1/R and R^4. It is assumed that the corresponding higher dimensional spacetime manifolds undergo a spontaneous compactification to manifolds with warped product structure. Special attention is paid to the stability of the extra-dimensional factor spaces. It is shown that for certain parameter regions the systems allow for a freezing stabilization of these spaces. In particular, we find for the 1/R model that configurations with stabilized extra dimensions do not provide a late-time acceleration (they are AdS), whereas the solution branch which allows for accelerated expansion (the dS branch) is incompatible with stabilized factor spaces. In the case of the R^4 model, we obtain that the stability region in parameter space depends on the total dimension D=dim(M) of the higher dimensional spacetime M. For D>8 the stability region consists of a single (absolutely stable) sector which is shielded from a conformal singul...
On affine non-negative matrix factorization
DEFF Research Database (Denmark)
Laurberg, Hans; Hansen, Lars Kai
2007-01-01
We generalize the non-negative matrix factorization (NMF) generative model to incorporate an explicit offset. Multiplicative estimation algorithms are provided for the resulting sparse affine NMF model. We show that the affine model has improved uniqueness properties and leads to more accurate...
Directory of Open Access Journals (Sweden)
Mohammed Larbi Labbi
2007-12-01
Full Text Available The $(2k$-th Gauss-Bonnet curvature is a generalization to higher dimensions of the $(2k$-dimensional Gauss-Bonnet integrand, it coincides with the usual scalar curvature for $k = 1$. The Gauss-Bonnet curvatures are used in theoretical physics to describe gravity in higher dimensional space times where they are known as the Lagrangian of Lovelock gravity, Gauss-Bonnet Gravity and Lanczos gravity. In this paper we present various aspects of these curvature invariants and review their variational properties. In particular, we discuss natural generalizations of the Yamabe problem, Einstein metrics and minimal submanifolds.
How quantum are non-negative wavefunctions?
Energy Technology Data Exchange (ETDEWEB)
Hastings, M. B. [Station Q, Microsoft Research, Santa Barbara, California 93106-6105, USA and Quantum Architectures and Computation Group, Microsoft Research, Redmond, Washington 98052 (United States)
2016-01-15
We consider wavefunctions which are non-negative in some tensor product basis. We study what possible teleportation can occur in such wavefunctions, giving a complete answer in some cases (when one system is a qubit) and partial answers elsewhere. We use this to show that a one-dimensional wavefunction which is non-negative and has zero correlation length can be written in a “coherent Gibbs state” form, as explained later. We conjecture that such holds in higher dimensions. Additionally, some results are provided on possible teleportation in general wavefunctions, explaining how Schmidt coefficients before measurement limit the possible Schmidt coefficients after measurement, and on the absence of a “generalized area law” [D. Aharonov et al., in Proceedings of Foundations of Computer Science (FOCS) (IEEE, 2014), p. 246; e-print arXiv.org:1410.0951] even for Hamiltonians with no sign problem. One of the motivations for this work is an attempt to prove a conjecture about ground state wavefunctions which have an “intrinsic” sign problem that cannot be removed by any quantum circuit. We show a weaker version of this, showing that the sign problem is intrinsic for commuting Hamiltonians in the same phase as the double semion model under the technical assumption that TQO-2 holds [S. Bravyi et al., J. Math. Phys. 51, 093512 (2010)].
Solving higher curvature gravity theories
Energy Technology Data Exchange (ETDEWEB)
Chakraborty, Sumanta [IUCAA, Pune (India); SenGupta, Soumitra [Indian Association for the Cultivation of Science, Theoretical Physics Department, Kolkata (India)
2016-10-15
Solving field equations in the context of higher curvature gravity theories is a formidable task. However, in many situations, e.g., in the context of f(R) theories, the higher curvature gravity action can be written as an Einstein-Hilbert action plus a scalar field action. We show that not only the action but the field equations derived from the action are also equivalent, provided the spacetime is regular. We also demonstrate that such an equivalence continues to hold even when the gravitational field equations are projected on a lower-dimensional hypersurface. We have further addressed explicit examples in which the solutions for Einstein-Hilbert and a scalar field system lead to solutions of the equivalent higher curvature theory. The same, but on the lower-dimensional hypersurface, has been illustrated in the reverse order as well. We conclude with a brief discussion on this technique of solving higher curvature field equations. (orig.)
Non-negative Matrix Factorization for Binary Data
DEFF Research Database (Denmark)
Larsen, Jacob Søgaard; Clemmensen, Line Katrine Harder
We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for analysing non-negative data is the Non-negative Matrix Factorization, though this is in......We propose the Logistic Non-negative Matrix Factorization for decomposition of binary data. Binary data are frequently generated in e.g. text analysis, sensory data, market basket data etc. A common method for analysing non-negative data is the Non-negative Matrix Factorization, though...
Sigma Models with Negative Curvature
Alonso, Rodrigo; Manohar, Aneesh V.
2016-01-01
We construct Higgs Effective Field Theory (HEFT) based on the scalar manifold H^n, which is a hyperbolic space of constant negative curvature. The Lagrangian has a non-compact O(n,1) global symmetry group, but it gives a unitary theory as long as only a compact subgroup of the global symmetry is gauged. Whether the HEFT manifold has positive or negative curvature can be tested by measuring the S-parameter, and the cross sections for longitudinal gauge boson and Higgs boson scattering, since the curvature (including its sign) determines deviations from Standard Model values.
BIFURCATION IN PRESCRIBED MEAN CURVATURE PROBLEM
Institute of Scientific and Technical Information of China (English)
马力
2002-01-01
This paper discusses the existence problem in the study of some partial differential equations. The author gets some bifurcation on the prescribed mean curvature problem on the unit ball, the scalar curvature problem on the n-sphere, and some field equations. The author gives some natural conditions such that the standard bifurcation or Thom-Mather theory can be used.
A Stringy (Holographic) Pomeron with Extrinsic Curvature
Qian, Yachao
2014-01-01
We model the soft pomeron in QCD using a scalar Polyakov string with extrinsic curvature in the bottom-up approach of holographic QCD. The overall dipole-dipole scattering amplitude in the soft pomeron kinematics is shown to be sensitive to the extrinsic curvature of the string for finite momentum transfer. The characteristics of the diffractive peak in the differential elastic $pp$ scattering are affected by a small extrinsic curvature of the string.
Self-Dual Manifolds with Positive Ricci Curvature
Lebrun, Claude; Nayatani, Shin; Nitta, Takashi
1994-01-01
We prove that the connected sums CP_2 # CP_2 and CP_2 # CP_2 # CP_2 admit self-dual metrics with positive Ricci curvature. Moreover, every self-dual metric of positive scalar curvature on CP_2 # CP_2 is conformal to a metric with positive Ricci curvature.
A Simons type formula for surfaces with parallel mean curvature
Fetcu, Dorel
2011-01-01
We prove a Simons type equation for non-minimal surfaces with parallel mean curvature vector (pmc surfaces) in $M^n(c)\\times\\mathbb{R}$, where $M^n(c)$ is an $n$-dimensional space form. Then, we use this equation in order to characterize complete non-minimal pmc surfaces with non-negative Gaussian curvature.
Vacuum polarization of a scalar field in wormhole spacetimes
Popov, A A; Popov, Arkadii A.; Sushkov, Sergey V.
2001-01-01
An analitical approximation of $$ for a scalar field in a static spherically symmetric wormhole spacetime is obtained. The scalar field is assumed to be both massive and massless, with an arbitrary coupling $\\xi$ to the scalar curvature, and in a zero temperature vacuum state.
Modular Curvature for Noncommutative Two-Tori
Connes, Alain
2011-01-01
Starting from the description of the conformal geometry of noncommutative 2-tori in the framework of modular spectral triples, we explicitly compute the local curvature functionals determined by the value at zero of the zeta functions affiliated with these spectral triples. We give a closed formula for the Ray-Singer analytic torsion in terms of the Dirichlet quadratic form and the generating function for Bernoulli numbers applied to the modular operator. The gradient of the Ray-Singer analytic torsion is then expressed in terms of these functionals, and yields the analogue of scalar curvature. Computing this gradient in two ways elucidates the meaning of the complicated two variable functions occurring in the formula for the scalar curvature. Moreover, the corresponding evolution equation for the metric produces the appropriate analogue of Ricci curvature. We prove the analogue of the classical result which asserts that in every conformal class the maximum value of the determinant of the Laplacian on metrics...
Curvature-Squared Cosmology In The First-Order Formalism
Shahid-Saless, Bahman
1993-01-01
Paper presents theoretical study of some of general-relativistic ramifications of gravitational-field energy density proportional to R - alpha R(exp 2) (where R is local scalar curvature of space-time and alpha is a constant).
Energy Technology Data Exchange (ETDEWEB)
Alonso, Rodrigo [Department of Physics, University of California at San Diego,La Jolla, CA 92093 (United States); Jenkins, Elizabeth E.; Manohar, Aneesh V. [Department of Physics, University of California at San Diego,La Jolla, CA 92093 (United States); CERN TH Division,CH-1211 Geneva 23 (Switzerland)
2016-08-17
The S-matrix of a quantum field theory is unchanged by field redefinitions, and so it only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold M is flat. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved M, since they parametrize deviations from the flat SM case. We show that the HEFT Lagrangian can be written in SMEFT form if and only if M has a SU(2){sub L}×U(1){sub Y} invariant fixed point. Experimental observables in HEFT depend on local geometric invariants of M such as sectional curvatures, which are of order 1/Λ{sup 2}, where Λ is the EFT scale. We give explicit expressions for these quantities in terms of the structure constants for a general G→H symmetry breaking pattern. The one-loop radiative correction in HEFT is determined using a covariant expansion which preserves manifest invariance of M under coordinate redefinitions. The formula for the radiative correction is simple when written in terms of the curvature of M and the gauge curvature field strengths. We also extend the CCWZ formalism to non-compact groups, and generalize the HEFT curvature computation to the case of multiple singlet scalar fields.
Sparse Non-negative Matrix Factor 2-D Deconvolution
DEFF Research Database (Denmark)
Mørup, Morten; Schmidt, Mikkel N.
2006-01-01
We introduce the non-negative matrix factor 2-D deconvolution (NMF2D) model, which decomposes a matrix into a 2-dimensional convolution of two factor matrices. This model is an extension of the non-negative matrix factor deconvolution (NMFD) recently introduced by Smaragdis (2004). We derive...... and prove the convergence of two algorithms for NMF2D based on minimizing the squared error and the Kullback-Leibler divergence respectively. Next, we introduce a sparse non-negative matrix factor 2-D deconvolution model that gives easy interpretable decompositions and devise two algorithms for computing...... this form of factorization. The developed algorithms have been used for source separation and music transcription....
Learning Hidden Markov Models using Non-Negative Matrix Factorization
Cybenko, George
2008-01-01
The Baum-Welsh algorithm together with its derivatives and variations has been the main technique for learning Hidden Markov Models (HMM) from observational data. We present an HMM learning algorithm based on the non-negative matrix factorization (NMF) of higher order Markovian statistics that is structurally different from the Baum-Welsh and its associated approaches. The described algorithm supports estimation of the number of recurrent states of an HMM and iterates the non-negative matrix factorization (NMF) algorithm to improve the learned HMM parameters. Numerical examples are provided as well.
NON-NEGATIVE RADIAL SOLUTION FOR AN ELLIPTIC EQUATION
Institute of Scientific and Technical Information of China (English)
Yang Guoying; Guo Zongming
2005-01-01
We study the structure and behavior of non-negative radial solution for the following elliptic equation △u = uv, x ∈ Rn with 0 ＜ v ＜ 1. We also obtain the detailed asymptotic expansion of u near infinity.
Algorithms for Sparse Non-negative Tucker Decompositions
DEFF Research Database (Denmark)
Mørup, Morten; Hansen, Lars Kai
2008-01-01
for Tucker decompositions when indeed the data and interactions can be considered non-negative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is the most appropriate for the data as well as to select the number of components by turning off excess components...
On the curvature of the present-day universe
Energy Technology Data Exchange (ETDEWEB)
Buchert, Thomas [Universite Lyon 1, Centre de Recherche Astrophysique de Lyon, CNRS UMR 5574, 9 avenue Charles Andre, F-69230 Saint-Genis-Laval (France); Carfora, Mauro [Dipartimento di Fisica Nucleare e Teorica, Universita degli Studi di Pavia, via A. Bassi 6, I-27100 Pavia (Italy)], E-mail: buchert@obs.univ-lyon1.fr, E-mail: mauro.carfora@pv.infn.it
2008-10-07
We discuss the effect of curvature and matter inhomogeneities on the averaged scalar curvature of the present-day universe. Motivated by studies of averaged inhomogeneous cosmologies, we contemplate on the question of whether it is sensible to assume that curvature averages out on some scale of homogeneity, as implied by the standard concordance model of cosmology, or whether the averaged scalar curvature can be largely negative today, as required for an explanation of dark energy from inhomogeneities. We confront both conjectures with a detailed analysis of the kinematical backreaction term and estimate its strength for a multi-scale inhomogeneous matter and curvature distribution. Our main result is a formula for the spatially averaged scalar curvature involving quantities that are all measurable on regional (i.e. up to 100 Mpc) scales. We propose strategies to quantitatively evaluate the formula, and pinpoint the assumptions implied by the conjecture of a small or zero averaged curvature. We reach the conclusion that the standard concordance model needs fine tuning in the sense of an assumed equipartition law for curvature in order to reconcile it with the estimated properties of the averaged physical space, whereas a negative averaged curvature is favoured, independent of the prior on the value of the cosmological constant.
Algorithms for Sparse Non-negative Tucker Decompositions
DEFF Research Database (Denmark)
Mørup, Morten; Hansen, Lars Kai
2008-01-01
There is a increasing interest in analysis of large scale multi-way data. The concept of multi-way data refers to arrays of data with more than two dimensions, i.e., taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions...... decompositions). To reduce ambiguities of this type of decomposition we develop updates that can impose sparseness in any combination of modalities, hence, proposed algorithms for sparse non-negative Tucker decompositions (SN-TUCKER). We demonstrate how the proposed algorithms are superior to existing algorithms...... for Tucker decompositions when indeed the data and interactions can be considered non-negative. We further illustrate how sparse coding can help identify what model (PARAFAC or Tucker) is the most appropriate for the data as well as to select the number of components by turning off excess components...
Wind Noise Reduction using Non-negative Sparse Coding
DEFF Research Database (Denmark)
Schmidt, Mikkel N.; Larsen, Jan; Hsiao, Fu-Tien
2007-01-01
We introduce a new speaker independent method for reducing wind noise in single-channel recordings of noisy speech. The method is based on non-negative sparse coding and relies on a wind noise dictionary which is estimated from an isolated noise recording. We estimate the parameters of the model...... and discuss their sensitivity. We then compare the algorithm with the classical spectral subtraction method and the Qualcomm-ICSI-OGI noise reduction method. We optimize the sound quality in terms of signal-to-noise ratio and provide results on a noisy speech recognition task....
Hierarchical subtask discovery with non-negative matrix factorization
CSIR Research Space (South Africa)
Earle, AC
2017-08-01
Full Text Available . Donoho, D. and Stodden, V. When does non-negative matrix factorization give a correct decomposition into parts? Proc. Advances in Neural Information Processing Systems 16, pp. 1141–1148, 2004. Hennequin, R., David, B., and Badeau, R. Beta-divergence as a... with Linearly Solvable Markov Decision Processes. arXiv, 2016. S¸ims¸ek, Ö. and Barto, A.S. Skill Characterization Based on Be- tweenness. Advances in Neural Information Processing Systems, pp. 1497–1504, 2009. Solway, A., Diuk, C., Córdova, N., Yee, D., Barto...
Representations of non-negative polynomials via critical ideals
Hiep, Dang Tuan
2011-01-01
This paper studies the representations of a non-negative polynomial $f$ on a non-compact semi-algebraic set $K$ modulo its critical ideal. Under the assumptions that the semi-algebraic set $K$ is regular and $f$ satisfies the boundary Hessian conditions (BHC) at each zero of $f$ in $K$, we show that $f$ can be represented as a sum of squares (SOS) of real polynomials modulo its critical ideal if $f\\ge 0$ on $K$. In particular, we focus on the polynomial ring $\\mathbb R[x]$.
Scalar field Hadamard renormalisation in $AdS_{n}$
Kent, Carl
2013-01-01
We outline an analytic method for computing the renormalised vacuum expectation value of the quadratic fluctuations and stress-energy tensor associated with a quantised scalar field propagating on $AdS_{n}$. Explicit results have been obtained using Hadamard renormalisation in the case of a massive neutral scalar field with arbitrary coupling to the curvature, for $n=2$ to $n=11$ inclusive.
Evolving extrinsic curvature and the cosmological constant problem
Capistrano, Abraão J. S.; Cabral, Luis A.
2016-10-01
The concept of smooth deformation of Riemannian manifolds associated with the extrinsic curvature is explained and applied to the Friedmann-Lemaître-Robertson-Walker cosmology. We show that such deformation can be derived from the Einstein-Hilbert-like dynamical principle may produce an observable effect in the sense of Noether. As a result, we show how the extrinsic curvature compensates both quantitative and qualitative differences between the cosmological constant Λ and the vacuum energy {ρ }{vac} obtaining the observed upper bound for the cosmological constant problem at electroweak scale. The topological characteristics of the extrinsic curvature are discussed showing that the produced extrinsic scalar curvature is an evolving dynamical quantity.
Baudoin, Fabrice
2012-01-01
By adapting some ideas of M. Ledoux \\cite{ledoux2}, \\cite{ledoux-stflour} and \\cite{Led} to a sub-Riemannian framework we study Sobolev, Poincar\\'e and isoperimetric inequalities associated to subelliptic diffusion operators that satisfy the generalized curvature dimension inequality that was introduced by F. Baudoin and N. Garofalo in \\cite{Bau2}. Our results apply in particular on all CR Sasakian manifolds whose horizontal Webster-Tanaka-Ricci curvature is non negative, all Carnot groups with step two, and wide subclasses of principal bundles over Riemannian manifolds whose Ricci curvature is non negative.
On the Riemann Curvature Operators in Randers Spaces
Rafie-Rad, M.
2013-05-01
The Riemann curvature in Riemann-Finsler geometry can be regarded as a collection of linear operators on the tangent spaces. The algebraic properties of these operators may be linked to the geometry and the topology of the underlying space. The principal curvatures of a Finsler space (M, F) at a point x are the eigenvalues of the Riemann curvature operator at x. They are real functions κ on the slit tangent manifold TM0. A principal curvature κ(x, y) is said to be isotropic (respectively, quadratic) if κ(x, y)/F(x, y) is a function of x only (respectively, κ(x, y) is quadratic with respect to y). On the other hand, the Randers metrics are the most popular and prominent metrics in pure and applied disciplines. Here, it is proved that if a Randers metric admits an isotropic principal curvature, then F is of isotropic S-curvature. The same result is also established for F to admit a quadratic principal curvature. These results extend Shen's verbal results about Randers metrics of scalar flag curvature K = K(x) as well as those Randers metrics with quadratic Riemann curvature operator. The Riemann curvature Rik may be broken into two operators Rik and Jik. The isotropic and quadratic principal curvature are characterized in terms of the eigenvalues of R and J.
Spherical gravitational curvature boundary-value problem
Šprlák, Michal; Novák, Pavel
2016-08-01
Values of scalar, vector and second-order tensor parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, the gravitational curvature tensor is decomposed into six parts which are expanded in terms of third-order tensor spherical harmonics. Secondly, gravitational curvature boundary-value problems defined for four combinations of the gravitational curvatures are formulated and solved in spectral and spatial domains. Thirdly, properties of the corresponding sub-integral kernels are investigated. The presented mathematical formulations reveal some important properties of the gravitational curvatures and extend the so-called Meissl scheme, i.e., an important theoretical framework that relates various parameters of the Earth's gravitational field.
Extrinsic Curvature Embedding Diagrams
Lu, J L
2003-01-01
Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\\it extrinsic} curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is {\\it embedded} in the higher dimensional curved space. Simple examples are given to illustrate the idea.
Alonso, Rodrigo; Manohar, Aneesh V
2016-01-01
The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold ${\\mathcal M}$ is flat. We explicitly compute the one-loop correction to scalar scattering in the SM written in non-linear Callan-Coleman-Wess-Zumino (CCWZ) form, where it has an infinite series of higher dimensional operators, and show that the $S$-matrix is finite. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved ${\\mathcal M}$, ...
Alonso, Rodrigo; Manohar, Aneesh V.
2016-01-01
The $S$-matrix of a quantum field theory is unchanged by field redefinitions, and so only depends on geometric quantities such as the curvature of field space. Whether the Higgs multiplet transforms linearly or non-linearly under electroweak symmetry is a subtle question since one can make a coordinate change to convert a field that transforms linearly into one that transforms non-linearly. Renormalizability of the Standard Model (SM) does not depend on the choice of scalar fields or whether the scalar fields transform linearly or non-linearly under the gauge group, but only on the geometric requirement that the scalar field manifold ${\\mathcal M}$ is flat. We explicitly compute the one-loop correction to scalar scattering in the SM written in non-linear Callan-Coleman-Wess-Zumino (CCWZ) form, where it has an infinite series of higher dimensional operators, and show that the $S$-matrix is finite. Standard Model Effective Field Theory (SMEFT) and Higgs Effective Field Theory (HEFT) have curved ${\\mathcal M}$, ...
Scalar hairy black holes and solitons in asymptotically flat spacetimes
Nucamendi, U; Nucamendi, Ulises; Salgado, Marcelo
2003-01-01
A numerical analysis shows that a class of scalar-tensor theories of gravity with a scalar field minimally and nonminimally coupled to the curvature allows static and spherically symmetric black hole solutions with scalar-field hair in asymptotically flat spacetimes. In the limit when the horizon radius of the black hole tends to zero, regular scalar solitons are found. The asymptotically flat solutions are obtained provided that the scalar potential $V(\\phi)$ of the theory is ``finetuned'' such that its local minimum is also a zero of the potential, the scalar field settling asymptotically at that minimum. The configurations, although unstable under spherically symmetric linear perturbations, are regular and thus can serve as counterexamples to the no-scalar-hair conjecture.
Riemann curvature of a boosted spacetime geometry
Battista, Emmanuele; Scudellaro, Paolo; Tramontano, Francesco
2014-01-01
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature through Dirac's delta distribution and its derivatives is numerically evaluated for this class of spacetimes. Eventually, the analysis of the Kteschmann invariant and the geodesic equation show that the spacetime possesses a scalar curvature singularity within a 3-sphere and it is possible to define what we here call boosted horizon, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. Thi...
Effective inhomogeneous inflation: curvature inhomogeneities of the Einstein vacuum
Energy Technology Data Exchange (ETDEWEB)
Buchert, Thomas [Universite Lyon 1, Centre de Recherche Astrophysique de Lyon, 9 Avenue Charles Andre, F-69230 Saint-Genis-Laval (France); Obadia, Nathaniel, E-mail: buchert@obs.univ-lyon1.fr, E-mail: nathaniel.obadia@ens-lyon.fr [Ecole Normale Superieure de Lyon, Centre de Recherche Astrophysique de Lyon, 46 Allee d' Italie, F-69364 Lyon Cedex 07 (France)
2011-08-21
We consider spatially averaged inhomogeneous universe models and argue that, already in the absence of sources, an effective scalar field arises through foliating and spatially averaging inhomogeneous geometrical curvature invariants of the Einstein vacuum. This scalar field (the 'morphon') acts as an inflaton, if we prescribe a potential of some generic form. We show that, for any initially negative average spatial curvature, the morphon is driven through an inflationary phase and leads-on average-to a spatially flat, homogeneous and isotropic universe model, providing initial conditions for pre-heating and, by the same mechanism, a possibly natural self-exit. (fast track communication)
Multiplicative algorithms for constrained non-negative matrix factorization
Peng, Chengbin
2012-12-01
Non-negative matrix factorization (NMF) provides the advantage of parts-based data representation through additive only combinations. It has been widely adopted in areas like item recommending, text mining, data clustering, speech denoising, etc. In this paper, we provide an algorithm that allows the factorization to have linear or approximatly linear constraints with respect to each factor. We prove that if the constraint function is linear, algorithms within our multiplicative framework will converge. This theory supports a large variety of equality and inequality constraints, and can facilitate application of NMF to a much larger domain. Taking the recommender system as an example, we demonstrate how a specialized weighted and constrained NMF algorithm can be developed to fit exactly for the problem, and the tests justify that our constraints improve the performance for both weighted and unweighted NMF algorithms under several different metrics. In particular, on the Movielens data with 94% of items, the Constrained NMF improves recall rate 3% compared to SVD50 and 45% compared to SVD150, which were reported as the best two in the top-N metric. © 2012 IEEE.
Noether Symmetry Approach for teleparallel-curvature cosmology
Capozziello, Salvatore; Myrzakulov, Ratbay
2014-01-01
We consider curvature-teleparallel $F(R,T)$ gravity, where the gravitational Lagrangian density is given by an arbitrary function of the Ricci scalar $R$ and the torsion scalar $T$. Using the Noether Symmetry Approach, we show that the functional form of the $F(R, T)$ function, can be determined by the presence of symmetries . Furthermore, we obtain exact solutions through to the presence of conserved quantities and the reduction of cosmological dynamical system. Example of particular cosmological models are considered.
Renormalization of the charged scalar field in curved space
Herman, R; Herman, Rhett; Hiscock, William A
1996-01-01
The DeWitt-Schwinger proper time point-splitting procedure is applied to a massive complex scalar field with arbitrary curvature coupling interacting with a classical electromagnetic field in a general curved spacetime. The scalar field current is found to have a linear divergence. The presence of the external background gauge field is found to modify the stress-energy tensor results of Christensen for the neutral scalar field by adding terms of the form (eF)^2 to the logarithmic counterterms. These results are shown to be expected from an analysis of the degree of divergence of scalar quantum electrodynamics.
One-loop quantum corrections to cosmological scalar field potentials
Arbey, A; Arbey, Alexandre; Mahmoudi, Farvah
2007-01-01
We study the loop corrections to potentials of complex or coupled real scalar fields used in cosmology to account for dark energy, dark matter or dark fluid. We show that the SUGRA quintessence and dark matter scalar field potentials are stable against the quantum fluctuations, and we propose solutions to the instability of the potentials of coupled quintessence and dark fluid scalar fields. We also find that a coupling to fermions is very restricted, unless this coupling has a structure which already exists in the scalar field potential or which can be compensated by higher order corrections. Finally, we study the influence of the curvature and kinetic term corrections.
Stability of Curvature Measures
Chazal, Frédéric; Lieutier, André; Thibert, Boris
2008-01-01
We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive $\\mu$-reach can be estimated by the same curvature measures of the offset of a compact set K' close to K in the Hausdorff sense. We show how these curvature measures can be computed for finite unions of balls. The curvature measures of the offset of a compact set with positive $\\mu$-reach can thus be approximated by the curvature measures of the offset of a point-cloud sample. These results can also be interpreted as a framework for an effective and robust notion of curvature.
Lasukov, V. V.
2012-06-01
It is shown that negative Scalars can claim to be the object referred to as black holes, therefore observation of black holes means observation of Scalars. In contrast to blackholes, negative Scalars contain no singularity inside. Negative Scalars can be observed from the effect of generation of ordinary matter by the Lemaître primordial atom.
Scalar field collapse with an exponential potential
Chakrabarti, Soumya
2017-02-01
An analogue of the Oppenheimer-Synder collapsing model is treated analytically, where the matter source is a scalar field with an exponential potential. An exact solution is derived followed by matching to a suitable exterior geometry, and an analysis of the visibility of the singularity. In some situations, the collapse indeed leads to a finite time curvature singularity, which is always hidden from the exterior by an apparent horizon.
Self-similar scalar field collapse
Banerjee, Narayan; Chakrabarti, Soumya
2017-01-01
A spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analyzed at the expense of a high degree of symmetry in the space-time, that of conformal flatness and self-similarity. Indeed collapsing models terminating into a curvature singularity can be obtained. The formation of black holes or the occurrence of naked singularities depends on the initial collapsing profiles.
(Curvature)^2-Terms for Supergravity in Three Dimension
Nishino, H; Nishino, Hitoshi; Rajpoot, Subhash
2006-01-01
We investigate the effect of (Curvature)^2-terms on N=1 and N=2 supergravity in three dimensions. We use the off-shell component fields (e_\\mu{}^m, \\psi_\\mu, S) for N=1 and (e_\\mu{}^m, \\psi_\\mu, \\psi_\\mu^*, A_\\mu, B, B^*) for N=2 supergravity. The S, A_\\mu and B are respectively a real scalar, a real vector and a complex scalar auxiliary fields. Both for N=1 and N=2, only two invariant actions for (Curvature)^2-terms exist, while only the actions with (Scalar Curvature)^2 are free of negative energy ghosts. Interestingly, the originally non-physical graviton and gravitino fields start propagating, together with the scalar field S for the N=1 case, or the complex scalar B and the longitudinal component \\partial_\\mu A^\\mu for N=2. These new propagating fields form two new physical massive supermultiplets of spins (1/2,0) with 2 x (1+1) degrees of freedom for the N=1 case, and two physical massive N=2 supermultiplets of spins (1/2,1/2,0,0) with 2 x (2+2) degrees of freedom for the N=2 case.
Forced hyperbolic mean curvature flow
Mao, Jing
2012-01-01
In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \\cite{klw,hdl}. For the first hyperbolic flow, as in \\cite{klw}, by using support function, we reduce it to a hyperbolic Monge-Amp$\\grave{\\rm{e}}$re equation successfully, leading to the short-time existence of the flow by the standard theory of hyperbolic partial differential equation. If the initial velocity is non-negative and the coefficient function of the forcing term is non-positive, we also show that there exists a class of initial velocities such that the solution of the flow exists only on a finite time interval $[0,T_{max})$, and the solution converges to a point or shocks and other propagating discontinuities are generated when $t\\rightarrow{T_{max}}$. These generalize the corresponding results in \\cite{klw}. For the second hyperbolic flow, as in \\cite{hdl}, we can prove the system of partial differential equations related to the flow is ...
... curvature of the penis after surgery or radiation treatment for prostate cancer. Peyronie's disease is uncommon. It affects men ages 40 to 60 and older. Curvature of the penis can occur along with Dupuytren's contracture . This is a cord-like thickening across the ...
DEFF Research Database (Denmark)
diffusion to volume growth. We are e.g. interested in obtaining precise bounds for mean exit times for Brownian motions and for isoperimetric inequalities. One way to obtain such bounds are via curvature controlled comparison with corresponding values in constant curvature spaces and in other tailor-made so...
Debus, J -D; Succi, S; Herrmann, H J
2015-01-01
By inspecting the effect of curvature on a moving fluid, we find that local sources of curvature not only exert inertial forces on the flow, but also generate viscous stresses as a result of the departure of streamlines from the idealized geodesic motion. The curvature-induced viscous forces are shown to cause an indirect and yet appreciable energy dissipation. As a consequence, the flow converges to a stationary equilibrium state solely by virtue of curvature-induced dissipation. In addition, we show that flow through randomly-curved media satisfies a non-linear transport law, resembling Darcy-Forchheimer's law, due to the viscous forces generated by the spatial curvature. It is further shown that the permeability can be characterized in terms of the average metric perturbation.
Odd Scalar Curvature in Anti-Poisson Geometry
Batalin, Igor A
2008-01-01
Recent works have revealed that the recipe for field-antifield quantization of Lagrangian gauge theories can be considerably relaxed when it comes to choosing a path integral measure \\rho if a zero-order term \
Riemann curvature of a boosted spacetime geometry
Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco
2016-10-01
The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.
Turzynski, Krzysztof
2014-01-01
We calculate the scalar spectral index n_s and the tensor-to-scalar ratio r in a class of recently proposed two-field no-scale models. We show that in order to obtain correct predictions it is crucial to include in the calculations the coupling between the curvature and the isocurvature perturbations induced by the noncanonical form of the kinetic terms. This coupling enhances the curvature perturbations and suppresses the resulting tensor-to-scalar ratio to the per mille level even for values of the slow-roll parameter epsilon~0.01.
Penile Curvature (Peyronie's Disease)
... use mechanical traction and vacuum devices aimed at stretching or bending the penis to reduce curvature. Surgery ... Communication Programs FAQs About NIDDK Meet the Director Offices & Divisions Staff Directory Budget & Legislative Information Advisory & Coordinating ...
Scalar field as a time variable during gravitational evolution
Nakonieczna, Anna
2015-01-01
Using a scalar field as an intrinsic 'clock' while investigating the dynamics of gravitational systems has been successfully pursued in various researches on the border between classical and quantum gravity. The objective of our research was to check explicitly whether the scalar field can serve as a time variable during dynamical evolution of the matter-geometry system, especially in regions of high curvature, which are essential from the perspective of quantum gravity. For this purpose, we analyzed a gravitational collapse of a self-interacting scalar field within the framework of general relativity. The obtained results indicated that the hypersurfaces of constant scalar field are spacelike in dynamical regions nearby the singularities formed during the investigated process. The scalar field values change monotonically in the areas, in which the constancy hypersurfaces are spacelike.
New scalar constraint operator for loop quantum gravity
Assanioussi, Mehdi; Mäkinen, Ilkka
2015-01-01
We present a concrete and explicit construction of a new scalar constraint operator for loop quantum gravity. The operator is defined on the recently introduced space of partially diffeomorphism invariant states, and this space is preserved by the action of the operator. To define the Euclidean part of the scalar constraint operator, we propose a specific regularization based on the idea of so-called "special" loops. The Lorentzian part of the quantum scalar constraint is merely the curvature operator that has been introduced in an earlier work. Due to the properties of the special loops assignment, the adjoint operator of the non-symmetric constraint operator is densely defined on the partially diffeomorphism invariant Hilbert space. This fact opens up the possibility of defining a symmetric scalar constraint operator as a suitable combination of the original operator and its adjoint. We also show that the algebra of the scalar constraint operators is anomaly free, and describe the structure of the kernel of...
Kleihaus, Burkhard; Yazadjiev, Stoytcho
2015-01-01
In the presence of a complex scalar field scalar-tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and ordinary hairy black holes. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn.
Tensor-multi-scalar theories: relativistic stars and 3+1 decomposition
Horbatsch, Michael; Gerosa, Davide; Pani, Paolo; Berti, Emanuele; Gualtieri, Leonardo; Sperhake, Ulrich
2015-01-01
Gravitational theories with multiple scalar fields coupled to the metric and each other - a natural extension of the well studied single-scalar-tensor theories - are interesting phenomenological frameworks to describe deviations from general relativity in the strong-field regime. In these theories, the N-tuple of scalar fields takes values in a coordinate patch of an N-dimensional Riemannian target-space manifold whose properties are poorly constrained by weak-field observations. Here we introduce for simplicity a non-trivial model with two scalar fields and a maximally symmetric target-space manifold. Within this model we present a preliminary investigation of spontaneous scalarization for relativistic, perfect fluid stellar models in spherical symmetry. We find that the scalarization threshold is determined by the eigenvalues of a symmetric scalar-matter coupling matrix, and that the properties of strongly scalarized stellar configurations additionally depend on the target-space curvature radius. In prepara...
Scalar self-force on static charge in a long throat
Popov, A.; Aslan, O.
2015-08-01
We compute the self-force on a scalar charge at rest in the space-time of long throat. We consider arbitrary values of the mass of the scalar field and the constant of nonminimal coupling of the scalar field to the curvature of space-time. We also show the coincidence of explicit calculations of self-force in the limit of large mass of the field with known results.
Approximate L0 constrained Non-negative Matrix and Tensor Factorization
DEFF Research Database (Denmark)
Mørup, Morten; Madsen, Kristoffer Hougaard; Hansen, Lars Kai
2008-01-01
Non-negative matrix factorization (NMF), i.e. V = WH where both V, W and H are non-negative has become a widely used blind source separation technique due to its part based representation. The NMF decomposition is not in general unique and a part based representation not guaranteed. However...... path for the L1 norm regularized least squares NMF for fixed W can be calculated at the cost of an ordinary least squares solution based on a modification of the Least Angle Regression and Selection (LARS) algorithm forming a non-negativity constrained LARS (NLARS). With the full regularization path...
On the conservation of second-order cosmological perturbations in a scalar field dominated universe
Vernizzi, F
2005-01-01
We discuss second-order cosmological perturbations on super-Hubble scales, in a scalar field dominated universe, such as during single field inflation. In this contest we show that the gauge-invariant curvature perturbations defined on the uniform density and comoving hypersurfaces coincide and that perturbations are adiabatic in the large scale limit. Since it has been recently shown that the uniform curvature perturbation is conserved on large scales if perturbations are adiabatic, we conclude that both the uniform and comoving curvature perturbations at second-order in a scalar field dominated universe are conserved.
Conformal-frame (in)dependence of cosmological observations in scalar-tensor theory
Energy Technology Data Exchange (ETDEWEB)
Chiba, Takeshi [Department of Physics, College of Humanities and Sciences, Nihon University, Tokyo 156-8550 (Japan); Yamaguchi, Masahide, E-mail: chiba@phys.chs.nihon-u.ac.jp, E-mail: gucci@phys.titech.ac.jp [Department of Physics, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)
2013-10-01
We provide the correspondence between the variables in the Jordan frame and those in the Einstein frame in scalar-tensor gravity and consider the frame-(in)dependence of the cosmological observables. In particular, we show that the cosmological observables/relations (redshift, luminosity distance, temperature anisotropies) are frame-independent. We also study the frame-dependence of curvature perturbations and find that the curvature perturbations are conformal invariant if the perturbation is adiabatic and the entropy perturbation between matter and the Brans-Dicke scalar is vanishing. The relation among various definitions of curvature perturbations in the both frames is also discussed, and the condition for the equivalence is clarified.
Non-negative matrix factorization and term structure of interest rates
Takada, Hellinton H.; Stern, Julio M.
2015-01-01
Non-Negative Matrix Factorization (NNMF) is a technique for dimensionality reduction with a wide variety of applications from text mining to identification of concentrations in chemistry. NNMF deals with non-negative data and results in non-negative factors and factor loadings. Consequently, it is a natural choice when studying the term structure of interest rates. In this paper, NNMF is applied to obtain factors from the term structure of interest rates and the procedure is compared with other very popular techniques: principal component analysis and Nelson-Siegel model. The NNMF approximation for the term structure of interest rates is better in terms of fitting. From a practitioner point of view, the NNMF factors and factor loadings obtained possess straightforward financial interpretations due to their non-negativeness.
Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition
Astakhov, S A; Kraskov, A; Grassberger, P; Astakhov, Sergey A.; St\\"ogbauer, Harald; Kraskov, Alexander; Grassberger, Peter
2006-01-01
We propose a simulated annealing algorithm (called SNICA for "stochastic non-negative independent component analysis") for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The de-mixing is based on a Metropolis type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM) The source codes of SNICA, MILCA and th...
Wolf, Joseph A
2010-01-01
This book is the sixth edition of the classic Spaces of Constant Curvature, first published in 1967, with the previous (fifth) edition published in 1984. It illustrates the high degree of interplay between group theory and geometry. The reader will benefit from the very concise treatments of riemannian and pseudo-riemannian manifolds and their curvatures, of the representation theory of finite groups, and of indications of recent progress in discrete subgroups of Lie groups. Part I is a brief introduction to differentiable manifolds, covering spaces, and riemannian and pseudo-riemannian geomet
Matos, T; Urena-Lopez, L A; Núñez, D
2001-01-01
This work is a review of the last results of research on the Scalar Field Dark Matter model of the Universe at cosmological and at galactic level. We present the complete solution to the scalar field cosmological scenario in which the dark matter is modeled by a scalar field $\\Phi$ with the scalar potential $V(\\Phi)=V_{0}(cosh {(\\lambda \\sqrt{\\kappa_{0}}\\Phi)}-1)$ and the dark energy is modeled by a scalar field $\\Psi$, endowed with the scalar potential $\\tilde{V}(\\Psi)= \\tilde{V_{0}}(\\sinh{(\\alpha \\sqrt{\\kappa_{0}}\\Psi)})^{\\beta}$, which together compose the 95% of the total matter energy in the Universe. The model presents successfully deals with the up to date cosmological observations, and is a good candidate to treat the dark matter problem at the galactic level.
Baryogenesis with Scalar Bilinears
Ma, E; Sarkar, U; Ma, Ernest; Raidal, Martti; Sarkar, Utpal
1999-01-01
We show that if a baryon asymmetry of the universe is generated through the out-of-equilibrium decays of heavy scalar bilinears coupling to two fermions of the minimal standard model, it is necessarily an asymmetry conserving $(B-L)$ which cannot survive past the electroweak phase transition because of sphalerons. We then show that a surviving $(B-L)$ asymmetry may be generated if the heavy scalars decay into two fermions, \\underline {and into two light scalars} (which may be detectable at hadron colliders). We list all possible such trilinear scalar interactions, and discuss how our new baryogenesis scenario may occur naturally in supersymmetric grand unified theories.
Energy Technology Data Exchange (ETDEWEB)
Kleihaus, Burkhard, E-mail: b.kleihaus@uni-oldenburg.de [Institut für Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany); Kunz, Jutta [Institut für Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany); Yazadjiev, Stoytcho [Department of Theoretical Physics, Faculty of Physics, Sofia University, Sofia 1164 (Bulgaria)
2015-05-11
In the presence of a complex scalar field scalar–tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and hairy black holes of General Relativity. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn.
Directory of Open Access Journals (Sweden)
Burkhard Kleihaus
2015-05-01
Full Text Available In the presence of a complex scalar field scalar–tensor theory allows for scalarized rotating hairy black holes. We exhibit the domain of existence for these scalarized black holes, which is bounded by scalarized rotating boson stars and hairy black holes of General Relativity. We discuss the global properties of these solutions. Like their counterparts in general relativity, their angular momentum may exceed the Kerr bound, and their ergosurfaces may consist of a sphere and a ring, i.e., form an ergo-Saturn.
Leonard, C Danielle; Allison, Rupert
2016-01-01
Current constraints on spatial curvature show that it is dynamically negligible: $|\\Omega_{\\rm K}| \\lesssim 5 \\times 10^{-3}$ (95% CL). Neglecting it as a cosmological parameter would be premature however, as more stringent constraints on $\\Omega_{\\rm K}$ at around the $10^{-4}$ level would offer valuable tests of eternal inflation models and probe novel large-scale structure phenomena. This precision also represents the "curvature floor", beyond which constraints cannot be meaningfully improved due to the cosmic variance of horizon-scale perturbations. In this paper, we discuss what future experiments will need to do in order to measure spatial curvature to this maximum accuracy. Our conservative forecasts show that the curvature floor is unreachable - by an order of magnitude - even with Stage IV experiments, unless strong assumptions are made about dark energy evolution and the optical depth to the CMB. We also discuss some of the novel problems that arise when attempting to constrain a global cosmological...
Curvature calculations with GEOCALC
Energy Technology Data Exchange (ETDEWEB)
Moussiaux, A.; Tombal, P.
1987-04-01
A new method for calculating the curvature tensor has been recently proposed by D. Hestenes. This method is a particular application of geometric calculus, which has been implemented in an algebraic programming language on the form of a package called GEOCALC. They show how to apply this package to the Schwarzchild case and they discuss the different results.
The curvature coordinate system
DEFF Research Database (Denmark)
Almegaard, Henrik
2007-01-01
hyperbolas. This means that when a plane orthogonal system of curves for which the vertices in a mesh always lie on a circle is mapped on a surface with positive Gaussian curvature using inverse mapping, and the mapped vertices are connected by straight lines, this network will form a faceted surface...
Scalar modes of the relic gravitons
Giovannini, Massimo
2015-01-01
In conformally flat background geometries the long wavelength gravitons can be described in the fluid approximation and they induce scalar fluctuations both during inflation and in the subsequent radiation-dominated epoch. While this effect is minute and suppressed for a de Sitter stage of expansion, the fluctuations of the energy-momentum pseudo-tensor of the graviton fluid lead to curvature perturbations that increase with time all along the post-inflationary evolution. An explicit calculation of these effects is presented for a standard thermal history and it is shown that the growth of the curvature perturbations caused by the long wavelength modes is approximately compensated by the slope of the power spectra of the energy density, pressure and anisotropic stress of the relic gravitons.
Scalar geons in Born-Infeld gravity
Afonso, V. I.; Olmo, Gonzalo J.; Rubiera-Garcia, D.
2017-08-01
The existence of static, spherically symmetric, self-gravitating scalar field solutions in the context of Born-Infeld gravity is explored. Upon a combination of analytical approximations and numerical methods, the equations for a free scalar field (without a potential term) are solved, verifying that the solutions recover the predictions of General Relativity far from the center but finding important new effects in the central regions. We find two classes of objects depending on the ratio between the Schwarzschild radius and a length scale associated to the Born-Infeld theory: massive solutions have a wormhole structure, with their throat at r≈ 2M, while for the lighter configurations the topology is Euclidean. The total energy density of these solutions exhibits a solitonic profile with a maximum peaked away from the center, and located at the throat whenever a wormhole exists. The geodesic structure and curvature invariants are analyzed for the various configurations considered.
Solar System Constraints on Scalar Tensor Theories with Non-Standard Action
Devi, N Chandrachani; Sen, Anjan A
2011-01-01
We compute the Parametrized Post-Newtonian (PPN) parameter,$\\gamma$, for scalar-tensor gravity theory when the action functional for the scalar field is a non-standard one, namely the Dirac-Born-Infeld (DBI) type action, used in the literature for a tachyon field. We investigate two different cases (Linear and conformal coupling) when the scalar field is non-minimally coupled to gravity via the scalar curvature. We find that the PPN parameter $\\gamma$, which measures the amount of space curvature per unit rest mass, becomes a function of the effective mass of the scalar field. We compare our result with the Solar system constraints obtained by the Cassini mission and derive the constraints on the model parameters.
Nicotri, Stefano
2009-01-01
A holographic description of scalar mesons is presented, in which two- and three-point functions are holographically reconstructed. Mass spectrum, decay constants, eigenfunctions and the coupling of the scalar states with two pseu- doscalars are found. A comparison of the results with current phenomenology is discussed.
Salgado, M; Nucamendi, U; Salgado, Marcelo; Sudarsky, Daniel; Nucamendi, Ulises
1998-01-01
We study in the physical frame the phenomenon of spontaneous scalarization that occurs in scalar-tensor theories of gravity for compact objects. We discuss the fact that the phenomenon occurs exactly in the regime where the Newtonian analysis indicates it should not. Finally we discuss the way the phenomenon depends on the equation of state used to describe the nuclear matter.
Kahler-Einstein and Kahler scalar flat supermanifolds
Ang, J P; Schulman, John
2016-01-01
Two results regarding K\\"ahler supermanifolds with potential $K=A+C\\theta\\bar\\theta$ are shown. First, if the supermanifold is K\\"ahler-Einstein, then its base (the supermanifold of one lower fermionic dimension and with K\\"ahler potential $A$) has constant scalar curvature. As a corollary, every constant scalar curvature K\\"ahler supermanifold has a unique superextension to a K\\"ahler-Einstein supermanifold of one higher fermionic dimension. Second, if the supermanifold is itself scalar flat, then its base satisfies the equation $$ \\phi^{\\bar ji}\\phi_{i\\bar j}=2\\Delta_0 S_0 + R_0^{\\bar ji}R_{0i\\bar j} - S_0^2, $$ where $\\Delta_0$ is the Laplace operator, $S_0$ is the scalar curvature, and $R_{0i\\bar j}$ is the Ricci tensor of the base, and $\\phi$ is some harmonic section on the base. Examples of bosonic manifolds satisfying the equation above are discussed.
Evolution of curvature perturbation in generalized gravity theories
Energy Technology Data Exchange (ETDEWEB)
Matsuda, Tomohiro, E-mail: matsuda@sit.ac.j [Laboratory of Physics, Saitama Institute of Technology, Fusaiji, Okabe-machi, Saitama 369-0293 (Japan)
2009-07-21
Using the cosmological perturbation theory in terms of the deltaN formalism, we find the simple formulation of the evolution of the curvature perturbation in generalized gravity theories. Compared with the standard gravity theory, a crucial difference appears in the end-boundary of the inflationary stage, which is due to the non-ideal form of the energy-momentum tensor that depends explicitly on the curvature scalar. Recent study shows that ultraviolet-complete quantum theory of gravity (Horava-Lifshitz gravity) can be approximated by using a generalized gravity action. Our paper may give an important step in understanding the evolution of the curvature perturbation during inflation, where the energy-momentum tensor may not be given by the ideal form due to the corrections from the fundamental theory.
Two-Dimensional Graphs Moving by Mean Curvature Flow
Institute of Scientific and Technical Information of China (English)
CHEN Jing Yi; LI Jia Yu; TIAN Gang
2002-01-01
A surface Σ is a graph in R4 if there is a unit constant 2-form ω on R4 such that initial surface, then the mean curvature flow has a global solution and the scaled surfaces converge to a self-similar solution. A surface ∑ is a graph in M1 × M2 where M1 and M2 are Riemann surfaces,surface with scalar curvature R, v0 ≥1/√2 on the initial surface, then the mean curvature flow has a global solution and it sub-converges to a minimal surface, if, in addition, R ≥ 0 it converges to a totally geodesic surface which is holomorphic.
Curvature Singularity in f(R) Theories of Gravity
Dutta, Koushik; Patel, Avani
2015-01-01
Although f(R) modifications of late time cosmology is successful in explaining present cosmic acceleration, it is very difficult to simultaneously satisfy the fifth-force constraint. Even when the fifth-force constraint is satisfied, the effective scalar degree of freedom may move to a point (close to its minima) in the field space where the Ricci scalar diverges. We elucidate this point further with a specific example of f(R) gravity that incorporates several viable f(R) gravity models in the literature. In particular, we show that the nonlinear evolution of the scalar field in pressureless contracting dust can easily lead to the curvature singularity, making this theory unviable.
Domain wall brane in squared curvature gravity
Liu, Yu-Xiao; Zhao, Zhen-Hua; Li, Hai-Tao
2011-01-01
We suggest a thick braneworld model in the squared curvature gravity theory. Despite the appearance of higher order derivatives, the localization of gravity and various bulk matter fields is shown to be possible. The existence of the normalizable gravitational zero mode indicates that our four-dimensional gravity is reproduced. In order to localize the chiral fermions on the brane, two types of coupling between the fermions and the brane forming scalar is introduced. The first coupling leads us to a Schr\\"odinger equation with a volcano potential, and the other a P\\"oschl-Teller potential. In both cases, the zero mode exists only for the left-hand fermions. Several massive KK states of the fermions can be trapped on the brane, either as resonant states or as bound states.
Forman curvature for complex networks
Sreejith, R. P.; Mohanraj, Karthikeyan; Jost, Jürgen; Saucan, Emil; Samal, Areejit
2016-06-01
We adapt Forman’s discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However, Forman curvature is uncorrelated with clustering coefficient in most networks. Importantly, we find that both model and real networks are vulnerable to targeted deletion of nodes with highly negative Forman curvature. Our results suggest that Forman curvature can be employed to gain novel insights on the organization of complex networks.
Cosmic string interactions induced by gauge and scalar fields
Kabat, Daniel
2012-01-01
We study the interaction between two parallel cosmic strings induced by gauge fields and by scalar fields with non-minimal couplings to curvature. For small deficit angles the gauge field behaves like a collection of non-minimal scalars with a specific value for the non-minimal coupling. We check this equivalence by computing the interaction energy between strings at first order in the deficit angles. This result provides another physical context for the "contact terms" which play an important role in the renormalization of black hole entropy due to a spin-1 field.
Observational Constraints on New Exact Inflationary Scalar-field Solutions
Barrow, John D
2016-01-01
An algorithm is used to generate new solutions of the scalar field equations in homogeneous and isotropic universes. Solutions can be found for pure scalar fields with various potentials in the absence and presence of spatial curvature and other perfect fluids. A series of generalisations of the Chaplygin gas and bulk viscous cosmological solutions for inflationary universes are found. We also show how the Hubble slow-roll parameters can be calculated using the solution algorithm and we compare these inflationary solutions with the observational data provided by the Planck 2015 collaboration in order to constraint and rule out some of these models.
Energy Technology Data Exchange (ETDEWEB)
Shapiro, Ilya L. [Universite de Geneve, Departement de Physique Theorique and Center for Astroparticle Physics, Geneva 4 (Switzerland); Universidade Federal de Juiz de Fora, Departamento de Fisica, ICE, Juiz de Fora, MG (Brazil); Tomsk State Pedagogical University, Tomsk (Russian Federation); Tomsk State University, Tomsk (Russian Federation); Morais Teixeira, Poliane de [Universidade Federal de Juiz de Fora, Departamento de Fisica, ICE, Juiz de Fora, MG (Brazil); SISSA, Trieste (Italy); Wipf, Andreas [Friedrich-Schiller-Universitaet, Theoretisch-Physikalisches-Institut, Jena (Germany)
2015-06-15
The running of the non-minimal parameter ξ of the interaction of the real scalar field and scalar curvature is explored within the non-perturbative setting of the functional renormalization group (RG). We establish the RG flow in curved space-time in the scalar field sector, in particular derive an equation for the non-minimal parameter. The RG trajectory is numerically explored for different sets of initial data. (orig.)
Non-negative matrix analysis in x-ray spectromicroscopy: choosing regularizers
Mak, Rachel; Wild, Stefan M.; Jacobsen, Chris
2016-01-01
In x-ray spectromicroscopy, a set of images can be acquired across an absorption edge to reveal chemical speciation. We previously described the use of non-negative matrix approximation methods for improved classification and analysis of these types of data. We present here an approach to find appropriate values of regularization parameters for this optimization approach. PMID:27041779
Efficient non-negative constrained model-based inversion in optoacoustic tomography
Ding, Lu; Luís Deán-Ben, X.; Lutzweiler, Christian; Razansky, Daniel; Ntziachristos, Vasilis
2015-09-01
The inversion accuracy in optoacoustic tomography depends on a number of parameters, including the number of detectors employed, discrete sampling issues or imperfectness of the forward model. These parameters result in ambiguities on the reconstructed image. A common ambiguity is the appearance of negative values, which have no physical meaning since optical absorption can only be higher or equal than zero. We investigate herein algorithms that impose non-negative constraints in model-based optoacoustic inversion. Several state-of-the-art non-negative constrained algorithms are analyzed. Furthermore, an algorithm based on the conjugate gradient method is introduced in this work. We are particularly interested in investigating whether positive restrictions lead to accurate solutions or drive the appearance of errors and artifacts. It is shown that the computational performance of non-negative constrained inversion is higher for the introduced algorithm than for the other algorithms, while yielding equivalent results. The experimental performance of this inversion procedure is then tested in phantoms and small animals, showing an improvement in image quality and quantitativeness with respect to the unconstrained approach. The study performed validates the use of non-negative constraints for improving image accuracy compared to unconstrained methods, while maintaining computational efficiency.
Existence of non-negative solutions for nonlinear equations in the semi-positone case
Directory of Open Access Journals (Sweden)
Naji Yebari
2006-09-01
Full Text Available Using the fibring method we prove the existence of non-negative solution of the p-Laplacian boundary value problem $-Delta_pu=lambda f(u$, for any $lambda >0$ on any regular bounded domain of $mathbb{R}^N$, in the special case $f(t=t^q-1$.
Non-negatively curved 5-manifolds with almost maximal symmetry rank
Galaz-Garcia, Fernando
2011-01-01
We show that a closed, simply-connected, non-negatively curved 5-manifold admitting an effective, isometric $T^2$ action is diffeomorphic to one of $S^5$, $S^3\\times S^2$, $S^3\\tilde{\\times} S^2$ (the non-trivial $S^3$-bundle over $S^2$) or the Wu manifold $SU(3)/SO(3)$.
Reduction of Non-stationary Noise using a Non-negative Latent Variable Decomposition
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard; Larsen, Jan
2008-01-01
We present a method for suppression of non-stationary noise in single channel recordings of speech. The method is based on a non-negative latent variable decomposition model for the speech and noise signals, learned directly from a noisy mixture. In non-speech regions an over complete basis...
The Magsat scalar magnetometer
Farthing, W. H.
1980-01-01
The Magsat scalar magnetometer is derived from optical pumping magnetometers flown on the orbiting geophysical observatories. The basic sensor, a cross-coupled arrangement of absorption cells, photodiodes, and amplifiers, oscillates at the Larmor frequency of atomic moments precessing about the ambient field direction. The Larmor frequency output is accumulated digitally and stored for transfer to the spacecraft telemetry stream. In orbit the instrument has met its principal objective of calibrating the vector magnetometer and providing scalar field data.
Spacetime compactification induced by scalars
Energy Technology Data Exchange (ETDEWEB)
Gell-Mann, M.; Zwiebach, B.
1984-07-05
It is shown that scalars of a nonlinear sigma model coupled to gravity can trigger spontaneous compactification of spacetime if the scalar manifold has an Einstein metric and the scalar self-coupling constant takes a specific value. The compactified space becomes isomorphic to the scalar manifold and the four-dimensional space has no cosmological term at the classical level.
3D FACE RECOGNITION FROM RANGE IMAGES BASED ON CURVATURE ANALYSIS
Directory of Open Access Journals (Sweden)
Suranjan Ganguly
2014-02-01
Full Text Available In this paper, we present a novel approach for three-dimensional face recognition by extracting the curvature maps from range images. There are four types of curvature maps: Gaussian, Mean, Maximum and Minimum curvature maps. These curvature maps are used as a feature for 3D face recognition purpose. The dimension of these feature vectors is reduced using Singular Value Decomposition (SVD technique. Now from calculated three components of SVD, the non-negative values of ‘S’ part of SVD is ranked and used as feature vector. In this proposed method, two pair-wise curvature computations are done. One is Mean, and Maximum curvature pair and another is Gaussian and Mean curvature pair. These are used to compare the result for better recognition rate. This automated 3D face recognition system is focused in different directions like, frontal pose with expression and illumination variation, frontal face along with registered face, only registered face and registered face from different pose orientation across X, Y and Z axes. 3D face images used for this research work are taken from FRAV3D database. The pose variation of 3D facial image is being registered to frontal pose by applying one to all registration technique then curvature mapping is applied on registered face images along with remaining frontal face images. For the classification and recognition purpose five layer feed-forward back propagation neural network classifiers is used, and the corresponding result is discussed in section 4.
Charged topological black hole with a conformally coupled scalar field
Martínez, C; Martinez, Cristian; Staforelli, Juan Pablo
2006-01-01
An exact four-dimensional electrically charged topological black hole solution with a conformal coupled self-interacting scalar field is shown. We consider a negative cosmological constant and a quartic self-interaction. According to the mass different causal structures appear, including an extremal black hole. In all cases, the asymptotic region is locally an anti-de Sitter spacetime and a curvature singularity at the origin is present. The scalar field is regular on and outside the event horizon, which is a surface of negative constant curvature. We study the thermodynamical properties for the non-extremal black hole in the grand canonical ensemble. The configurations are thermodynamically stable and do not present phase transitions. The entropy value differs from that which the area law dictates. The non-minimal coupling is responsible for that difference and it can be seen as a modification of the Newton's constant.
Forman curvature for directed networks
Sreejith, R P; Saucan, Emil; Samal, Areejit
2016-01-01
A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced the Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of Forman curvature in diverse model and real-world undirected networks revealed that this measure captures several aspects of the organization of complex undirected networks. However, many important real-world networks are inherently directed in nature, and the Forman curvature for undirected networks is unsuitable for analysis of such directed networks. Hence, we here extend the Forman curvature for undirected networks to the case of directed networks. The simple mathematical formula for the Forman curvature in directed networks elegantly incorporates node weights, edge weights and edge direction. By applying the Forman curvature for directed networks to a variety of model and real-world directed networks, we show that the measure can be used to characterize the structure of complex ...
Quantum probes of timelike naked singularity with scalar hair
Svitek, O.; Tahamtan, T.
2016-01-01
We study the curvature singularity resolution via quantum fields on a fixed background based on Klein--Gordon and Dirac equations for a static spacetime with a scalar field producing a timelike naked singularity. We show that both Klein--Gordon and Dirac quantum fields see this singularity. Subsequently we check the results by applying the maximal acceleration existence in Covariant Loop Quantum Gravity described recently and obtain the resolution of singularity. In the process we study the g...
Quantum probes of timelike naked singularity with scalar hair
Svítek, O
2016-01-01
We study the curvature singularity resolution via quantum fields on a fixed background based on Klein--Gordon and Dirac equations for a static spacetime with a scalar field producing a timelike naked singularity. We show that both Klein--Gordon and Dirac quantum fields see this singularity. Subsequently we check the results by applying the maximal acceleration existence in Covariant Loop Quantum Gravity described recently and obtain the resolution of singularity. In the process we study the geodesics in the spacetime.
Black holes and a scalar field in an expanding universe
Saida, Hiromi; Soda, Jiro
2000-12-01
We consider a model of an inhomogeneous universe with the presence of a massless scalar field, where the inhomogeneity is assumed to consist of many black holes. This model can be constructed by following Lindquist and Wheeler, which has already been investigated without the presence of a scalar field to show that an averaged scale factor coincides with that of the Friedmann model in Einstein gravity. In this paper we construct the inhomogeneous universe with a massless scalar field, where it is assumed that the averaged scale factor and scalar field are given by those of the Friedmann model including the scalar field. All of our calculations are carried out within the framework of Brans-Dicke gravity. In constructing the model of an inhomogeneous universe, we define the mass of a black hole in the Brans-Dicke expanding universe which is equivalent to the ADM mass in the epoch of the adiabatic time evolution of the mass, and obtain an equation relating our mass with the averaged scalar field and scale factor. We find that the mass has an adiabatic time dependence in a sufficiently late stage of the expansion of the universe; that is our mass is equivalent to the ADM mass. The other result is that its time dependence is qualitatively different according to the sign of the curvature of the universe: the mass increases (decelerating) in the closed universe case, is constant in the flat case and decreases (decelerating) in the open case. It is also noted that the mass in the Einstein frame depends on time. Our results that the mass has a time dependence should be retained even in the general scalar-tensor gravities with a scalar field potential. Furthermore, we discuss the relation of our model of the inhomogeneous universe to the uniqueness theorem of black hole spacetime and the gravitational memory effect of black holes in scalar-tensor gravities.
Pavlov, Yu V
2013-01-01
The problem is solved of describing scale factors of a homogeneous isotropic spaces-time such that the exact solution for the scalar field with a nonconformal coupling to curvature can be obtained from solutions for the conformally coupled field by redefining the mass and momentum. Explicit expressions for dependence of time from the large-scale factor are presented in the form of Abelian integrals in these cases. The exact solution for a scalar field with Gauss-Bonnet type coupling with curvature is received and it is shown that the corresponding nonconformal additions can dominate at the particles creation by gravitational field.
Technique for computing the PDFs and CDFs of non-negative infinitely divisible random variables
Veillette, Mark S
2010-01-01
We present a method for computing the PDF and CDF of a non-negative infinitely divisible random variable $X$. Our method uses the L\\'{e}vy-Khintchine representation of the Laplace transform $\\mathbb{E} e^{-\\lambda X} = e^{-\\phi(\\lambda)}$, where $\\phi$ is the Laplace exponent. We apply the Post-Widder method for Laplace transform inversion combined with a sequence convergence accelerator to obtain accurate results. We demonstrate this technique on several examples including the stable distribution, mixtures thereof, and integrals with respect to non-negative L\\'{e}vy processes. Software to implement this method is available from the authors and we illustrate its use at the end of the paper.
Single-channel source separation using non-negative matrix factorization
DEFF Research Database (Denmark)
Schmidt, Mikkel Nørgaard
, in which a number of methods for single-channel source separation based on non-negative matrix factorization are presented. In the papers, the methods are applied to separating audio signals such as speech and musical instruments and separating different types of tissue in chemical shift imaging.......Single-channel source separation problems occur when a number of sources emit signals that are mixed and recorded by a single sensor, and we are interested in estimating the original source signals based on the recorded mixture. This problem, which occurs in many sciences, is inherently under......-determined and its solution relies on making appropriate assumptions concerning the sources. This dissertation is concerned with model-based probabilistic single-channel source separation based on non-negative matrix factorization, and consists of two parts: i) three introductory chapters and ii) five published...
Non-negative submodular stochastic probing via stochastic contention resolution schemes
Adamczyk, Marek
2015-01-01
The abstract model of stochastic probing was presented by Gupta and Nagarajan (IPCO'13), and provides a unified view of a number of problems. Adamczyk, Sviridenko, Ward (STACS'14) gave better approximation for matroid environments and linear objectives. At the same time this method was easily extendable to settings, where the objective function was monotone submodular. However, the case of non-negative submodular function could not be handled by previous techniques. In this paper we address t...
Real-time detection of overlapping sound events with non-negative matrix factorization
Dessein, Arnaud; Cont, Arshia; Lemaitre, Guillaume
2013-01-01
International audience; In this paper, we investigate the problem of real-time detection of overlapping sound events by employing non-negative matrix factorization techniques. We consider a setup where audio streams arrive in real-time to the system and are decomposed onto a dictionary of event templates learned off-line prior to the decomposition. An important drawback of existing approaches in this context is the lack of controls on the decomposition. We propose and compare two provably con...
Supervised non-negative matrix factorization based latent semantic image indexing
Institute of Scientific and Technical Information of China (English)
Dong Liang; Jie Yang; Yuchou Chang
2006-01-01
@@ A novel latent semantic indexing (LSI) approach for content-based image retrieval is presented in this paper. Firstly, an extension of non-negative matrix factorization (NMF) to supervised initialization isdiscussed. Then, supervised NMF is used in LSI to find the relationships between low-level features and high-level semantics. The retrieved results are compared with other approaches and a good performance is obtained.
An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions
Directory of Open Access Journals (Sweden)
Tilak Bhattacharya
2001-06-01
Full Text Available We present an elementary proof of the Harnack inequality for non-negative viscosity supersolutions of $Delta_{infty}u=0$. This was originally proven by Lindqvist and Manfredi using sequences of solutions of the $p$-Laplacian. We work directly with the $Delta_{infty}$ operator using the distance function as a test function. We also provide simple proofs of the Liouville property, Hopf boundary point lemma and Lipschitz continuity.
Anisotropic cubic curvature couplings
Bailey, Quentin G
2016-01-01
To complement recent work on tests of spacetime symmetry in gravity, cubic curvature couplings are studied using an effective field theory description of spacetime-symmetry breaking. The associated mass dimension 8 coefficients for Lorentz violation studied do not result in any linearized gravity modifications and instead are revealed in the first nonlinear terms in an expansion of spacetime around a flat background. We consider effects on gravitational radiation through the energy loss of a binary system and we study two-body orbital perturbations using the post-Newtonian metric. Some effects depend on the internal structure of the source and test bodies, thereby breaking the Weak Equivalence Principle for self-gravitating bodies. These coefficients can be measured in solar-system tests, while binary-pulsar systems and short-range gravity tests are particularly sensitive.
Egorov, A I; Sushkov, Sergey V
2016-01-01
In 1921 Bach and Weyl derived the method of superposition to construct new axially symmetric vacuum solutions of General Relativity. In this paper we extend the Bach-Weyl approach to non-vacuum configurations with massless scalar fields. Considering a phantom scalar field with the negative kinetic energy, we construct a multi-wormhole solution describing an axially symmetric superposition of $N$ wormholes. The solution found is static, everywhere regular and has no event horizons. These features drastically tell the multi-wormhole configuration from other axially symmetric vacuum solutions which inevitably contain gravitationally inert singular structures, such as `struts' and `membranes', that keep the two bodies apart making a stable configuration. However, the multi-wormholes are static without any singular struts. Instead, the stationarity of the multi-wormhole configuration is provided by the phantom scalar field with the negative kinetic energy. Anther unusual property is that the multi-wormhole spaceti...
Higgs and gravitational scalar fields together induce Weyl gauge
Scholz, Erhard
2015-02-01
A common biquadratic potential for the Higgs field and an additional scalar field , non minimally coupled to gravity, is considered in a locally scale symmetric approach to standard model fields in curved spacetime. A common ground state of the two scalar fields exists and couples both fields to gravity, more precisely to Weyl geometric scalar curvature . In Einstein gauge (, often called "Einstein frame"), also is scaled to a constant. This condition makes perfect sense, even in the general case, in the Weyl geometric approach. There it has been called Weyl gauge, because it was first considered by Weyl in the different context of his original scale geometric theory of gravity of 1918. Now it may get new meaning as a combined effect of electroweak theory and gravity, and their common influence on atomic frequencies.
Higgs and gravitational scalar fields together induce Weyl gauge
Scholz, Erhard
2014-01-01
A common biquadratic potential for the Higgs field $h$ and an additional scalar field $\\phi$, non minimally coupled to gravity, is considered in locally scale symmetric approaches to standard model fields in curved spacetime. A common ground state of the two scalar fields exists and couples both fields to gravity, more precisely to scalar curvature $R$. In Einstein gauge ($\\phi = const$, often called "Einstein frame"), also $R$ is scaled to a constant. This condition makes perfect sense, even in the general case, in the Weyl geometric approach. There it has been called {\\em Weyl gauge}, because it was first considered by Weyl in the different context of his original scale geometric theory of gravity of 1918. Now it seems to get new meaning as a combined effect of electroweak theory and gravity, and their common influence on atomic frequencies.
Early time perturbations behaviour in scalar field cosmologies
Perrotta, F; Perrotta, Francesca; Baccigalupi, Carlo
1999-01-01
We consider the problem of the initial conditions and behaviour of the perturbations in scalar field cosmology with general potential. We use the general definition of adiabatic and isocurvature conditions to set the appropriate initial values for the perturbation in the scalar field and in the ordinary matter and radiation components. In both the cases of initial adiabaticity and isocurvature, we solve the Einstein and fluid equation at early times and on superhorizon scales to find the initial behaviour of the relevant quantities. In particular, in the isocurvature case, we consider models in which the initial perturbation arises from the matter as well as from the scalar field itself, provided that the initial value of the gauge invariant curvature is zero. We extend the standard code to include all these cases, and we show some results concerning the power spectrum of the cosmic microwave background temperature anisotropies. In particular, it turns out that the acoustic peaks follow opposite behaviours in...
Rejon-Barrera, Fernando
2015-01-01
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.
Energy Technology Data Exchange (ETDEWEB)
Rejon-Barrera, Fernando [Institute for Theoretical Physics, University of Amsterdam,Science Park 904, Postbus 94485, 1090 GL, Amsterdam (Netherlands); Robbins, Daniel [Department of Physics, Texas A& M University,TAMU 4242, College Station, TX 77843 (United States)
2016-01-22
We work out all of the details required for implementation of the conformal bootstrap program applied to the four-point function of two scalars and two vectors in an abstract conformal field theory in arbitrary dimension. This includes a review of which tensor structures make appearances, a construction of the projectors onto the required mixed symmetry representations, and a computation of the conformal blocks for all possible operators which can be exchanged. These blocks are presented as differential operators acting upon the previously known scalar conformal blocks. Finally, we set up the bootstrap equations which implement crossing symmetry. Special attention is given to the case of conserved vectors, where several simplifications occur.
On Nonlinear Higher Spin Curvature
Manvelyan, Ruben(Yerevan Physics Institute, Alikhanian Br. St. 2, Yerevan, 0036, Armenia); Mkrtchyan, Karapet; Rühl, Werner; Tovmasyan, Murad
2011-01-01
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider in detail the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the deWit-Freedman curvature.
On nonlinear higher spin curvature
Energy Technology Data Exchange (ETDEWEB)
Manvelyan, Ruben, E-mail: manvel@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Mkrtchyan, Karapet, E-mail: karapet@yerphi.a [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia); Ruehl, Werner, E-mail: ruehl@physik.uni-kl.d [Department of Physics, Erwin Schroedinger Strasse, Technical University of Kaiserslautern, Postfach 3049, 67653 Kaiserslautern (Germany); Tovmasyan, Murad, E-mail: mtovmasyan@ysu.a [Yerevan Physics Institute, Alikhanian Br. Str. 2, 0036 Yerevan (Armenia)
2011-05-09
We present the first nonlinear term of the higher spin curvature which is covariant with respect to deformed gauge transformations that are linear in the field. We consider the case of spin 3 after presenting spin 2 as an example, and then construct the general spin s quadratic term of the de Wit-Freedman curvature.
Environmental influences on DNA curvature
DEFF Research Database (Denmark)
Ussery, David; Higgins, C.F.; Bolshoy, A.
1999-01-01
DNA curvature plays an important role in many biological processes. To study environmentalinfluences on DNA curvature we compared the anomalous migration on polyacrylamide gels ofligation ladders of 11 specifically-designed oligonucleotides. At low temperatures (25 degreesC and below) most...... for DNAcurvature and for environmentally-sensitive DNA conformations in the regulation of geneexpression....
Scalar and Pseudoscalar Glueballs
Cheng, Hai-Yang
2009-01-01
We employ two simple and robust results to constrain the mixing matrix of the isosinglet scalar mesons $f_0(1710)$, $f_0(1500)$, $f_0(1370)$: one is the approximate SU(3) symmetry empirically observed in the scalar sector above 1 GeV and confirmed by lattice QCD, and the other is the scalar glueball mass at 1710 MeV in the quenched approximation. In the SU(3) symmetry limit, $f_0(1500)$ becomes a pure SU(3) octet and is degenerate with $a_0(1450)$, while $f_0(1370)$ is mainly an SU(3) singlet with a slight mixing with the scalar glueball which is the primary component of $f_0(1710)$. These features remain essentially unchanged even when SU(3) breaking is taken into account. The observed enhancement of $\\omega f_0(1710)$ production over $\\phi f_0(1710)$ in hadronic $J/\\psi$ decays and the copious $f_0(1710)$ production in radiative $J/\\psi$ decays lend further support to the prominent glueball nature of $f_0(1710)$. We deduce the mass of the pseudoscalar glueball $G$ from an $\\eta$-$\\eta'$-$G$ mixing formalism...
Scalar Field Cosmologies and the Initial Space-Time Singularity
Foster, S
1998-01-01
The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW space-time is analysed in detail using a dynamical systems approach which may readily be generalised to more complicated space-times. It is shown that for a very large and natural class of models a simple and regular past asymptotic structure exists. More specifically, there exists a family of solutions which is in continuous 1-1 correspondence with the exactly integrable massless scalar field cosmologies, this correspondence being realised by a unique asymptotic approximation. The set of solutions which do not fall into this class has measure zero. The significance of this result to the cosmological initial value problem is briefly discussed.
Exact solutions for scalar field cosmology in f(R) gravity
Maharaj, S D; Chervon, S V; Nikolaev, A V
2016-01-01
We look for exact solutions in scalar field cosmology. To achieve this we use $f(R)$ modified gravity with a scalar field and do not specify the the form of the $f(R)$ function. In particular, we study Friedmann universe assuming that acceleration of the scalar curvature is negligible. We first present solutions for special cases and then the general solution. Using initial conditions which represent the universe at the present epoch, we evaluated the constants of integration. This allows for the comparison of the scale factor in the new solutions with that of the $\\Lambda CDM$ solution, thereby affecting the age of the universe in $f(R)$ gravity.
Note on a specific subcases of Robinson-Trautman solution with scalar hair
Tahamtan, T
2016-01-01
Explicit Robinson-Trautman solution with minimally coupled free scalar field was derived and analyzed recently. It was shown that this solution possesses curvature singularity which is initially naked but later the horizon envelopes it. However this study concentrated on the general branch of the solution where all the free constants are nonzero. Interesting special cases arise when some of the parameters are set to zero. In most of these cases the scalar field is still present. One of the cases is a static solution which represents a parametric limit of Janis-Newman-Winicour scalar field spacetime.
Generating Ekpyrotic Curvature Perturbations Before the Big Bang
Lehners, J L; Steinhardt, P J; Turok, N G; Fadden, Paul Mc; Lehners, Jean-Luc; Steinhardt, Paul J.; Turok, Neil
2007-01-01
We analyze a general mechanism for producing a nearly scale-invariant spectrum of cosmological curvature perturbations during a contracting phase preceding a big bang, that can be entirely described using 4d effective field theory. The mechanism, based on first producing entropic perturbations and then converting them to curvature perturbations, can be naturally incorporated in cyclic and ekpyrotic models in which the big bang is modelled as a brane collision, as well as other types of cosmological models with a pre-big bang phase. We show that the correct perturbation amplitude can be obtained and that the scalar spectral tilt n tends to range from slightly blue to red, with 0.97 < n < 1.02 for the simplest models, a range compatible with current observations but shifted by a few per cent towards the blue compared to the prediction of the simplest, large-field inflationary models.
On the breakdown of the curvature perturbation $\\zeta$ during reheating
Algan, Merve Tarman; Kutluk, Emine Seyma
2015-01-01
It is known that in single scalar field inflationary models the standard curvature perturbation \\zeta, which is supposedly conserved at superhorizon scales, diverges during reheating at times d\\Phi/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge \\phi=0, where \\phi\\ denotes the inflaton perturbation, breaks down when d\\Phi/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of \\zeta\\ is ill posed mathematically. We solve this problem by introducing a family of smooth gauges that still eliminates the inflaton fluctuation \\phi\\ in the Hamiltonian formalism and gives a well behaved curvature perturbation \\zeta, which is now rigorously conserved at superhorizon scales. In the linearized theory, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for th...
The Ricci Curvature of Half-flat Manifolds
Ali, T; Ali, Tibra; Cleaver, Gerald B.
2007-01-01
We derive expressions for the Ricci curvature tensor and scalar in terms of intrinsic torsion classes of half-flat manifolds by exploiting the relationship between half-flat manifolds and non-compact $G_2$ holonomy manifolds. Our expressions are tested for Iwasawa and more general nilpotent manifolds. We also derive expressions, in the language of Calabi-Yau moduli spaces, for the torsion classes and the Ricci curvature of the \\emph{particular} half-flat manifolds that arise naturally via mirror symmetry in flux compactifications. Using these expressions we then derive a constraint on the K\\"ahler moduli space of type II string theory on these half-flat manifolds.
Generation of Curvature Perturbations with Extra Anisotropic Stress
Kojima, Kazuhiko; Mathews, Grant J
2009-01-01
We study the evolution of curvature perturbations and the cosmic microwave background (CMB) power spectrum in the presence of an hypothesized extra anisotropic stress in the early universe. Such extra anisotropic stress terms might arise, for example, from the presence of the dark radiation term in brane-world cosmology. For the first time we evolve the scalar modes of such perturbations before and after neutrino decoupling and analyze their effects on the CMB spectrum. A novel result of this work is that the cancellation of the neutrino and extra anisotropic stress could lead to a spectrum of residual curvature perturbations which by themselves could reproduce the observed CMB power spectrum. This possibility may be testable as it would generate non-Gaussian fluctuations which could be constrained by future observations of density fluctuations.
Kaluza-Klein Reduction of a Quadratic Curvature Model
Baskal, S
2010-01-01
Palatini variational principle is implemented on a five dimensional quadratic curvature gravity model, rendering two sets of equations which can be interpreted as the field equations and the stress-energy tensor. Unification of gravity with electromagnetism and the scalar dilaton field is achieved through the Kaluza-Klein dimensional reduction mechanism. The reduced curvature invariant, field equations and the stress-energy tensor in four dimensional spacetime are obtained. The structure of the interactions among the constituent fields is exhibited in detail. It is shown that the Lorentz force naturally emerges from the reduced field equations and the equations of the standard Kaluza-Klein theory is demonstrated to be intrinsically contained in this model.
Glauber theory and the quantum coherence of curvature inhomogeneities
Giovannini, Massimo
2016-01-01
The curvature inhomogeneities are systematically scrutinized in the framework of the Glauber approach. The amplified quantum fluctuations of the scalar and tensor modes of the geometry are shown to be first-order coherent while the interference of the corresponding intensities is larger than in the case of Bose-Einstein correlations. After showing that the degree of second-order coherence does not suffice to characterize unambiguously the curvature inhomogeneities, we argue that direct analyses of the degrees of third and fourth-order coherence are necessary to discriminate between different correlated states and to infer more reliably the statistical properties of the large-scale fluctuations. We speculate that the moments of the multiplicity distributions of the relic phonons might be observationally accessible thanks to new generations of instruments able to count the single photons of the Cosmic Microwave Background in the THz region.
Glauber theory and the quantum coherence of curvature inhomogeneities
Giovannini, Massimo
2017-02-01
The curvature inhomogeneities are systematically scrutinized in the framework of the Glauber approach. The amplified quantum fluctuations of the scalar and tensor modes of the geometry are shown to be first-order coherent while the interference of the corresponding intensities is larger than in the case of Bose–Einstein correlations. After showing that the degree of second-order coherence does not suffice to characterize unambiguously the curvature inhomogeneities, we argue that direct analyses of the degrees of third- and fourth-order coherence are necessary to discriminate between different correlated states and to infer more reliably the statistical properties of the large-scale fluctuations. We speculate that the moments of the multiplicity distributions of the relic phonons might be observationally accessible thanks to new generations of instruments able to count the single photons of the Cosmic Microwave Background in the THz region.
Inflation in non-minimal matter-curvature coupling theories
Gomes, Cláudio; Bertolami, Orfeu
2016-01-01
We study inflationary scenarios driven by a scalar field in the presence of a non-minimal coupling between matter and curvature. We show that the Friedmann equation can be significantly modified when the energy density during inflation exceeds a critical value determined by the non-minimal coupling, which in turn may considerably modify the spectrum of primordial perturbations and the inflationary dynamics. In particular, we show that these models are characterised by a consistency relation between the tensor-to-scalar ratio and the tensor spectral index that can differ significantly from the predictions of general relativity. We also give examples of observational predictions for some of the most commonly considered potentials and use the results of the Planck collaboration to set limits on the scale of the non-minimal coupling.
CURVATURE COMPUTATIONS OF 2-MANIFOLDS IN IRk
Institute of Scientific and Technical Information of China (English)
Guo-liang Xu; Chandrajit L. Bajaj
2003-01-01
In this paper, we provide simple and explicit formulas for computing Riemannian cur-vatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IRk with k ≥ 3.
Lectures on mean curvature flows
Zhu, Xi-Ping
2002-01-01
"Mean curvature flow" is a term that is used to describe the evolution of a hypersurface whose normal velocity is given by the mean curvature. In the simplest case of a convex closed curve on the plane, the properties of the mean curvature flow are described by Gage-Hamilton's theorem. This theorem states that under the mean curvature flow, the curve collapses to a point, and if the flow is diluted so that the enclosed area equals \\pi, the curve tends to the unit circle. In this book, the author gives a comprehensive account of fundamental results on singularities and the asymptotic behavior of mean curvature flows in higher dimensions. Among other topics, he considers in detail Huisken's theorem (a generalization of Gage-Hamilton's theorem to higher dimension), evolution of non-convex curves and hypersurfaces, and the classification of singularities of the mean curvature flow. Because of the importance of the mean curvature flow and its numerous applications in differential geometry and partial differential ...
Generalized Curvature-Matter Couplings in Modified Gravity
Directory of Open Access Journals (Sweden)
Tiberiu Harko
2014-07-01
Full Text Available In this work, we review a plethora of modified theories of gravity with generalized curvature-matter couplings. The explicit nonminimal couplings, for instance, between an arbitrary function of the scalar curvature R and the Lagrangian density of matter, induces a non-vanishing covariant derivative of the energy-momentum tensor, implying non-geodesic motion and, consequently, leads to the appearance of an extra force. Applied to the cosmological context, these curvature-matter couplings lead to interesting phenomenology, where one can obtain a unified description of the cosmological epochs. We also consider the possibility that the behavior of the galactic flat rotation curves can be explained in the framework of the curvature-matter coupling models, where the extra terms in the gravitational field equations modify the equations of motion of test particles and induce a supplementary gravitational interaction. In addition to this, these models are extremely useful for describing dark energy-dark matter interactions and for explaining the late-time cosmic acceleration.
Screening bulk curvature in the presence of large brane tension
Agarwal, Nishant; Khoury, Justin; Trodden, Mark
2011-01-01
We study a flat brane solution in an effective 5D action for cascading gravity and propose a mechanism to screen extrinsic curvature in the presence of a large tension on the brane. The screening mechanism leaves the bulk Riemann-flat, thus making it simpler to generalize large extra dimension dark energy models to higher codimensions. By studying an action with cubic interactions for the brane-bending scalar mode, we find that the perturbed action suffers from ghostlike instabilities for positive tension, whereas it can be made ghost-free for sufficiently small negative tension.
Inflation, bifurcations of nonlinear curvature Lagrangians and dark energy
Mielke, Eckehard W; Schunck, Franz E
2008-01-01
A possible equivalence of scalar dark matter, the inflaton, and modified gravity is analyzed. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different effective gravitational strength and cosmological constant. A swallow tail catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This `triple unification' may shed new light on the nature and large scale distribution not only of dark matter but also on `dark energy', regarded as an effective cosmological constant, and inflation.
EAU guidelines on penile curvature.
Hatzimouratidis, Konstantinos; Eardley, Ian; Giuliano, François; Hatzichristou, Dimitrios; Moncada, Ignacio; Salonia, Andrea; Vardi, Yoram; Wespes, Eric
2012-09-01
Penile curvature can be congenital or acquired. Acquired curvature is secondary due to La Peyronie (Peyronie's) disease. To provide clinical guidelines on the diagnosis and treatment of penile curvature. A systematic literature search on the epidemiology, diagnosis, and treatment of penile curvature was performed. Articles with the highest evidence available were selected and formed the basis for assigning levels of evidence and grades of recommendations. The pathogenesis of congenital penile curvature is unknown. Peyronie's disease is a poorly understood connective tissue disorder most commonly attributed to repetitive microvascular injury or trauma during intercourse. Diagnosis is based on medical and sexual histories, which are sufficient to establish the diagnosis. Physical examination includes assessment of palpable nodules and penile length. Curvature is best documented by a self-photograph or pharmacologically induced erection. The only treatment option for congenital penile curvature is surgery based on plication techniques. Conservative treatment for Peyronie's disease is associated with poor outcomes. Pharmacotherapy includes oral potassium para-aminobenzoate, intralesional treatment with verapamil, clostridial collagenase or interferon, topical verapamil gel, and iontophoresis with verapamil and dexamethasone. They can be efficacious in some patients, but none of these options carry a grade A recommendation. Steroids, vitamin E, and tamoxifen cannot be recommended. Extracorporeal shock wave treatment and penile traction devices may only be used to treat penile pain and reduce penile deformity, respectively. Surgery is indicated when Peyronie's disease is stable for at least 3 mo. Tunical shortening procedures, especially plication techniques, are the first treatment options. Tunical lengthening procedures are preferred in more severe curvatures or in complex deformities. Penile prosthesis implantation is recommended in patients with erectile dysfunction
Ascent sequences and upper triangular matrices containing non-negative integers
Dukes, Mark
2009-01-01
This paper presents a bijection between ascent sequences and upper triangular matrices whose non-negative entries are such that all rows and columns contain at least one non-zero entry. We show the equivalence of several natural statistics on these structures under this bijection and prove that some of these statistics are equidistributed. Several special classes of matrices are shown to have simple formulations in terms of ascent sequences. Binary matrices are shown to correspond to ascent sequences with no two adjacent entries the same. Bidiagonal matrices are shown to be related to order-consecutive set partitions and a simple condition on the ascent sequences generate this class.
Institute of Scientific and Technical Information of China (English)
Zheng Zhonglong; Yang Jie
2005-01-01
Many problems in image representation and classification involve some form of dimensionality reduction. Non-negative matrix factorization (NMF) is a recently proposed unsupervised procedure for learning spatially localized, parts-based subspace representation of objects. An improvement of the classical NMF by combining with Log-Gabor wavelets to enhance its part-based learning ability is presented. The new method with principal component analysis (PCA) and locally linear embedding (LLE) proposed recently in Science are compared. Finally, the new method to several real world datasets and achieve good performance in representation and classification is applied.
Fast Bayesian Non-Negative Matrix Factorisation and Tri-Factorisation
DEFF Research Database (Denmark)
Brouwer, Thomas; Frellsen, Jes; Liò, Pietro
We present a fast variational Bayesian algorithm for performing non-negative matrix factorisation and tri-factorisation. We show that our approach achieves faster convergence per iteration and timestep (wall-clock) than Gibbs sampling and non-probabilistic approaches, and do not require additional...... samples to estimate the posterior. We show that in particular for matrix tri-factorisation convergence is difficult, but our variational Bayesian approach offers a fast solution, allowing the tri-factorisation approach to be used more effectively....
Single-Channel Speech Separation using Sparse Non-Negative Matrix Factorization
DEFF Research Database (Denmark)
Schmidt, Mikkel N.; Olsson, Rasmus Kongsgaard
2007-01-01
We apply machine learning techniques to the problem of separating multiple speech sources from a single microphone recording. The method of choice is a sparse non-negative matrix factorization algorithm, which in an unsupervised manner can learn sparse representations of the data. This is applied...... to the learning of personalized dictionaries from a speech corpus, which in turn are used to separate the audio stream into its components. We show that computational savings can be achieved by segmenting the training data on a phoneme level. To split the data, a conventional speech recognizer is used...
Darkflation -- one scalar to rule them all?
Lalak, Zygmunt
2016-01-01
The problem of explaining both inflationary and dark matter physics in the framework of a minimal extension of the Standard Model was investigated. To this end, the Standard Model completed by a real scalar singlet playing a role of the dark matter candidate has been considered. We assumed both the dark matter field and the Higgs doublet to be nonminimally coupled to gravity. Using quantum field theory in curved spacetime we derived an effective action for the inflationary period and analyzed its consequences. We paid special attention to determination, by explicit calculations, of the form of coefficients controlling the higher-order in curvature gravitational terms. Their connection to the Standard Model coupling constants has been discussed.
Lax Triad Approach to Symmetries of Scalar Modified Kadomtsev–Petviashvili Hierarchy
Deng, Xiao; Chen, Kui; Zhang, Da-Jun
2017-02-01
By means of Lax triads we reconstruct isospectral and nonisospectral scalar modified Kadomtsev–Petviashvili (mKP) hierarchies. In this approach the argument y is treated as an independent variable which is independent of time parameters \\{{t}1,{t}2,\\ldots \\}. Consequently, the isospectral and nonisospectral scalar mKP flows can have clear zero curvature representations, which enables us to handle investigation of symmetries of the scalar isospectral mKP hierarchy as freely as for (1+1)-dimensional systems. As a result, we obtain Lie algebraic structures of the scalar mKP flows and construct symmetries for the scalar isospectral mKP hierarchy. Supported by the National Natural Science Foundation of China under Grant No. 11371241
Thermal Inflation with a Thermal Waterfall Scalar Field Coupled to a Light Spectator Scalar Field
Rumsey, Arron
2016-01-01
This thesis begins with an introduction to the state of the art of modern Cosmology. The field of Particle Cosmology is then introduced and explored, in particular with regard to the study of cosmological inflation. We then introduce a new model of Thermal Inflation, in which the mass of the thermal waterfall field responsible for the inflation is dependent on a light spectator scalar field. The model contains a variety of free parameters, two of which control the power of the coupling term and the non-renormalizable term. We use the $\\delta N$ formalism to investigate the "end of inflation" and modulated decay scenarios in turn to see whether they are able to produce the dominant contribution to the primordial curvature perturbation $\\zeta$. We constrain the model and then explore the parameter space. We explore key observational signatures, such as non-Gaussianity, the scalar spectral index and the running of the scalar spectral index. We find that for some regions of the parameter space, the ability of the...
SCALAR WAVES AND WIRELESS POWER
Directory of Open Access Journals (Sweden)
Trunev A. P.
2013-11-01
Full Text Available It is established that in the classical electrodynamics with Lorenz gauge there are solutions in the form of waves of scalar and vector potential at zero magnetic and electric field. It is shown that wave scalar and vector potential can interact with the substance, causing ionization of the atoms and molecules. The analogue of scalar waves in electrodynamics and sound waves in gas dynamics is discussed. Proposed technical application of the waves of scalar and vector potential similar to acoustic waves. Discusses Tesla invented electrical device capable of generating and receiving scalar waves
Online multi-modal robust non-negative dictionary learning for visual tracking.
Zhang, Xiang; Guan, Naiyang; Tao, Dacheng; Qiu, Xiaogang; Luo, Zhigang
2015-01-01
Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL) algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality.
Online multi-modal robust non-negative dictionary learning for visual tracking.
Directory of Open Access Journals (Sweden)
Xiang Zhang
Full Text Available Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality.
Hyperspectral Image Super-Resolution via Non-Negative Structured Sparse Representation.
Dong, Weisheng; Fu, Fazuo; Shi, Guangming; Cao, Xun; Wu, Jinjian; Li, Guangyu; Li, Guangyu
2016-05-01
Hyperspectral imaging has many applications from agriculture and astronomy to surveillance and mineralogy. However, it is often challenging to obtain high-resolution (HR) hyperspectral images using existing hyperspectral imaging techniques due to various hardware limitations. In this paper, we propose a new hyperspectral image super-resolution method from a low-resolution (LR) image and a HR reference image of the same scene. The estimation of the HR hyperspectral image is formulated as a joint estimation of the hyperspectral dictionary and the sparse codes based on the prior knowledge of the spatial-spectral sparsity of the hyperspectral image. The hyperspectral dictionary representing prototype reflectance spectra vectors of the scene is first learned from the input LR image. Specifically, an efficient non-negative dictionary learning algorithm using the block-coordinate descent optimization technique is proposed. Then, the sparse codes of the desired HR hyperspectral image with respect to learned hyperspectral basis are estimated from the pair of LR and HR reference images. To improve the accuracy of non-negative sparse coding, a clustering-based structured sparse coding method is proposed to exploit the spatial correlation among the learned sparse codes. The experimental results on both public datasets and real LR hypspectral images suggest that the proposed method substantially outperforms several existing HR hyperspectral image recovery techniques in the literature in terms of both objective quality metrics and computational efficiency.
Non-negative constraint for image-based breathing gating in ultrasound hepatic perfusion data
Wu, Kaizhi; Ding, Mingyue; Chen, Xi; Deng, Wenjie; Zhang, Zhijun
2015-12-01
Images acquired during free breathing using contrast enhanced ultrasound hepatic perfusion imaging exhibits a periodic motion pattern. It needs to be compensated for if a further accurate quantification of the hepatic perfusion analysis is to be executed. To reduce the impact of respiratory motion, image-based breathing gating algorithm was used to compensate the respiratory motion in contrast enhanced ultrasound. The algorithm contains three steps of which respiratory kinetics extracted, image subsequences determined and image subsequences registered. The basic performance of the algorithm was to extract the respiratory kinetics of the ultrasound hepatic perfusion image sequences accurately. In this paper, we treated the kinetics extracted model as a non-negative matrix factorization (NMF) problem. We extracted the respiratory kinetics of the ultrasound hepatic perfusion image sequences by non-negative matrix factorization (NMF). The technique involves using the NMF objective function to accurately extract respiratory kinetics. It was tested on simulative phantom and used to analyze 6 liver CEUS hepatic perfusion image sequences. The experimental results show the effectiveness of our proposed method in quantitative and qualitative.
Online Multi-Modal Robust Non-Negative Dictionary Learning for Visual Tracking
Zhang, Xiang; Guan, Naiyang; Tao, Dacheng; Qiu, Xiaogang; Luo, Zhigang
2015-01-01
Dictionary learning is a method of acquiring a collection of atoms for subsequent signal representation. Due to its excellent representation ability, dictionary learning has been widely applied in multimedia and computer vision. However, conventional dictionary learning algorithms fail to deal with multi-modal datasets. In this paper, we propose an online multi-modal robust non-negative dictionary learning (OMRNDL) algorithm to overcome this deficiency. Notably, OMRNDL casts visual tracking as a dictionary learning problem under the particle filter framework and captures the intrinsic knowledge about the target from multiple visual modalities, e.g., pixel intensity and texture information. To this end, OMRNDL adaptively learns an individual dictionary, i.e., template, for each modality from available frames, and then represents new particles over all the learned dictionaries by minimizing the fitting loss of data based on M-estimation. The resultant representation coefficient can be viewed as the common semantic representation of particles across multiple modalities, and can be utilized to track the target. OMRNDL incrementally learns the dictionary and the coefficient of each particle by using multiplicative update rules to respectively guarantee their non-negativity constraints. Experimental results on a popular challenging video benchmark validate the effectiveness of OMRNDL for visual tracking in both quantity and quality. PMID:25961715
Pavement crack detection combining non-negative feature with fast LoG in complex scene
Wang, Wanli; Zhang, Xiuhua; Hong, Hanyu
2015-12-01
Pavement crack detection is affected by much interference in the realistic situation, such as the shadow, road sign, oil stain, salt and pepper noise etc. Due to these unfavorable factors, the exist crack detection methods are difficult to distinguish the crack from background correctly. How to extract crack information effectively is the key problem to the road crack detection system. To solve this problem, a novel method for pavement crack detection based on combining non-negative feature with fast LoG is proposed. The two key novelties and benefits of this new approach are that 1) using image pixel gray value compensation to acquisit uniform image, and 2) combining non-negative feature with fast LoG to extract crack information. The image preprocessing results demonstrate that the method is indeed able to homogenize the crack image with more accurately compared to existing methods. A large number of experimental results demonstrate the proposed approach can detect the crack regions more correctly compared with traditional methods.
Directory of Open Access Journals (Sweden)
Chen Yidong
2011-10-01
Full Text Available Abstract Background Transcriptional regulation by transcription factor (TF controls the time and abundance of mRNA transcription. Due to the limitation of current proteomics technologies, large scale measurements of protein level activities of TFs is usually infeasible, making computational reconstruction of transcriptional regulatory network a difficult task. Results We proposed here a novel Bayesian non-negative factor model for TF mediated regulatory networks. Particularly, the non-negative TF activities and sample clustering effect are modeled as the factors from a Dirichlet process mixture of rectified Gaussian distributions, and the sparse regulatory coefficients are modeled as the loadings from a sparse distribution that constrains its sparsity using knowledge from database; meantime, a Gibbs sampling solution was developed to infer the underlying network structure and the unknown TF activities simultaneously. The developed approach has been applied to simulated system and breast cancer gene expression data. Result shows that, the proposed method was able to systematically uncover TF mediated transcriptional regulatory network structure, the regulatory coefficients, the TF protein level activities and the sample clustering effect. The regulation target prediction result is highly coordinated with the prior knowledge, and sample clustering result shows superior performance over previous molecular based clustering method. Conclusions The results demonstrated the validity and effectiveness of the proposed approach in reconstructing transcriptional networks mediated by TFs through simulated systems and real data.
Sharp maximal inequalities for the moments of martingales and non-negative submartingales
Osȩkowski, Adam
2012-01-01
In the paper we study sharp maximal inequalities for martingales and non-negative submartingales: if $f$, $g$ are martingales satisfying \\[|\\mathrm{d}g_n|\\leq|\\mathrm{d}f_n|,\\qquad n=0,1,2,...,\\] almost surely, then \\[\\Bigl\\|\\sup_{n\\geq0}|g_n|\\Bigr\\|_p\\leq p\\|f\\|_p,\\qquad p\\geq2,\\] and the inequality is sharp. Furthermore, if $\\alpha\\in[0,1]$, $f$ is a non-negative submartingale and $g$ satisfies \\[|\\mathrm{d}g_n|\\leq|\\mathrm{d}f_n|\\quad and\\quad |\\mathbb{E}(\\mathrm{d}g_{n+1}|\\mathcal {F}_n)|\\leq\\alpha\\mathbb{E}(\\mathrm{d}f_{n+1}|\\mathcal{F}_n),\\qquad n=0,1,2,...,\\] almost surely, then \\[\\Bigl\\|\\sup_{n\\geq0}|g_n|\\Bigr\\|_p\\leq(\\alpha+1)p\\|f\\|_p,\\qquad p\\geq2,\\] and the inequality is sharp. As an application, we establish related estimates for stochastic integrals and It\\^{o} processes. The inequalities strengthen the earlier classical results of Burkholder and Choi.
Aspect-Aided Dynamic Non-Negative Sparse Representation-Based Microwave Image Classification
Directory of Open Access Journals (Sweden)
Xinzheng Zhang
2016-09-01
Full Text Available Classification of target microwave images is an important application in much areas such as security, surveillance, etc. With respect to the task of microwave image classification, a recognition algorithm based on aspect-aided dynamic non-negative least square (ADNNLS sparse representation is proposed. Firstly, an aspect sector is determined, the center of which is the estimated aspect angle of the testing sample. The training samples in the aspect sector are divided into active atoms and inactive atoms by smooth self-representative learning. Secondly, for each testing sample, the corresponding active atoms are selected dynamically, thereby establishing dynamic dictionary. Thirdly, the testing sample is represented with ℓ 1 -regularized non-negative sparse representation under the corresponding dynamic dictionary. Finally, the class label of the testing sample is identified by use of the minimum reconstruction error. Verification of the proposed algorithm was conducted using the Moving and Stationary Target Acquisition and Recognition (MSTAR database which was acquired by synthetic aperture radar. Experiment results validated that the proposed approach was able to capture the local aspect characteristics of microwave images effectively, thereby improving the classification performance.
Non-negative matrix factorization by maximizing correntropy for cancer clustering
Wang, Jim Jing-Yan
2013-03-24
Background: Non-negative matrix factorization (NMF) has been shown to be a powerful tool for clustering gene expression data, which are widely used to classify cancers. NMF aims to find two non-negative matrices whose product closely approximates the original matrix. Traditional NMF methods minimize either the l2 norm or the Kullback-Leibler distance between the product of the two matrices and the original matrix. Correntropy was recently shown to be an effective similarity measurement due to its stability to outliers or noise.Results: We propose a maximum correntropy criterion (MCC)-based NMF method (NMF-MCC) for gene expression data-based cancer clustering. Instead of minimizing the l2 norm or the Kullback-Leibler distance, NMF-MCC maximizes the correntropy between the product of the two matrices and the original matrix. The optimization problem can be solved by an expectation conditional maximization algorithm.Conclusions: Extensive experiments on six cancer benchmark sets demonstrate that the proposed method is significantly more accurate than the state-of-the-art methods in cancer clustering. 2013 Wang et al.; licensee BioMed Central Ltd.
Semi-Supervised Projective Non-Negative Matrix Factorization for Cancer Classification.
Directory of Open Access Journals (Sweden)
Xiang Zhang
Full Text Available Advances in DNA microarray technologies have made gene expression profiles a significant candidate in identifying different types of cancers. Traditional learning-based cancer identification methods utilize labeled samples to train a classifier, but they are inconvenient for practical application because labels are quite expensive in the clinical cancer research community. This paper proposes a semi-supervised projective non-negative matrix factorization method (Semi-PNMF to learn an effective classifier from both labeled and unlabeled samples, thus boosting subsequent cancer classification performance. In particular, Semi-PNMF jointly learns a non-negative subspace from concatenated labeled and unlabeled samples and indicates classes by the positions of the maximum entries of their coefficients. Because Semi-PNMF incorporates statistical information from the large volume of unlabeled samples in the learned subspace, it can learn more representative subspaces and boost classification performance. We developed a multiplicative update rule (MUR to optimize Semi-PNMF and proved its convergence. The experimental results of cancer classification for two multiclass cancer gene expression profile datasets show that Semi-PNMF outperforms the representative methods.
DEFF Research Database (Denmark)
Sannino, Francesco
2016-01-01
We construct effective Lagrangians, and corresponding counting schemes, valid to describe the dynamics of the lowest lying large N stable massive composite state emerging in strongly coupled theories. The large N counting rules can now be employed when computing quantum corrections via an effective...... at the electroweak scale. To illustrate the formalism we consider the possibility that the Higgs emerges as: the lightest glueball of a new composite theory; the large N scalar meson in models of dynamical electroweak symmetry breaking; the large N pseudodilaton useful also for models of near-conformal dynamics....... For each of these realisations we determine the leading N corrections to the electroweak precision parameters. The results nicely elucidate the underlying large N dynamics and can be used to confront first principle lattice results featuring composite scalars with a systematic effective approach....
Directory of Open Access Journals (Sweden)
B.Karuna kumar
2009-09-01
Full Text Available Fingerprints are today the most widely used biometric features for personal identification. With the increasing usage of biometric systems the question arises naturally how to store and handle the acquired sensor data. Our algorithm for the digitized images is based on adaptive uniform scalar quantization of discrete wavelet transform sub band decomposition. This technique referred to as the wavelet scalar quantization method. The algorithm produces archival quality images at compression ratios of around 15 to 1 and will allow the current database of paper finger print cards to be replaced by digital imagery. A compliance testing program is also being implemented to ensure high standards of image quality and interchangeability of data between different implementations.
DEFF Research Database (Denmark)
Sannino, Francesco
2016-01-01
We construct effective Lagrangians, and corresponding counting schemes, valid to describe the dynamics of the lowest lying large N stable massive composite state emerging in strongly coupled theories. The large N counting rules can now be employed when computing quantum corrections via an effective...... at the electroweak scale. To illustrate the formalism we consider the possibility that the Higgs emerges as: the lightest glueball of a new composite theory; the large N scalar meson in models of dynamical electroweak symmetry breaking; the large N pseudodilaton useful also for models of near-conformal dynamics....... For each of these realisations we determine the leading N corrections to the electroweak precision parameters. The results nicely elucidate the underlying large N dynamics and can be used to confront first principle lattice results featuring composite scalars with a systematic effective approach....
Hadamard renormalized scalar field theory on anti-de Sitter space-time
Kent, Carl
2014-01-01
We consider a real massive free quantum scalar field with arbitrary curvature coupling on $n$-dimensional anti-de Sitter space-time. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for $n=2$ to $n=11$ inclusive.
Effects of Curvature on Dynamics
Dutta, Gautam
2010-01-01
In this article we discuss the effect of curvature on dynamics when a physical system moves adiabatically in a curved space. These effects give a way to measure the curvature of the space intrinsically without referring to higher dimensional space. Two interesting examples, the Foucault Pendulum and the perihelion shift of planetary orbits, are presented in a simple geometric way. A paper model is presented to see the perihelion shift.
Egorov, A. I.; Kashargin, P. E.; Sushkov, Sergey V.
2016-09-01
In 1921 Bach and Weyl derived the method of superposition to construct new axially symmetric vacuum solutions of general relativity. In this paper we extend the Bach-Weyl approach to non-vacuum configurations with massless scalar fields. Considering a phantom scalar field with the negative kinetic energy, we construct a multi-wormhole solution describing an axially symmetric superposition of N wormholes. The solution found is static, everywhere regular and has no event horizons. These features drastically tell the multi-wormhole configuration from other axially symmetric vacuum solutions which inevitably contain gravitationally inert singular structures, such as ‘struts’ and ‘membranes’, that keep the two bodies apart making a stable configuration. However, the multi-wormholes are static without any singular struts. Instead, the stationarity of the multi-wormhole configuration is provided by the phantom scalar field with the negative kinetic energy. Anther unusual property is that the multi-wormhole spacetime has a complicated topological structure. Namely, in the spacetime there exist 2 N asymptotically flat regions connected by throats.
Spatial curvature endgame: Reaching the limit of curvature determination
Leonard, C. Danielle; Bull, Philip; Allison, Rupert
2016-07-01
Current constraints on spatial curvature show that it is dynamically negligible: |ΩK|≲5 ×10-3 (95% C.L.). Neglecting it as a cosmological parameter would be premature however, as more stringent constraints on ΩK at around the 10-4 level would offer valuable tests of eternal inflation models and probe novel large-scale structure phenomena. This precision also represents the "curvature floor," beyond which constraints cannot be meaningfully improved due to the cosmic variance of horizon-scale perturbations. In this paper, we discuss what future experiments will need to do in order to measure spatial curvature to this maximum accuracy. Our conservative forecasts show that the curvature floor is unreachable—by an order of magnitude—even with Stage IV experiments, unless strong assumptions are made about dark energy evolution and the Λ CDM parameter values. We also discuss some of the novel problems that arise when attempting to constrain a global cosmological parameter like ΩK with such high precision. Measuring curvature down to this level would be an important validation of systematics characterization in high-precision cosmological analyses.
Cosmic acceleration from matter-curvature coupling
Zaregonbadi, Raziyeh; Farhoudi, Mehrdad
2016-10-01
We consider f( {R,T} ) modified theory of gravity in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We indicate that in this type of the theory, the coupling energy-momentum tensor is not conserved. However, we mainly focus on a particular model that matter is minimally coupled to the geometry in the metric formalism and wherein, its coupling energy-momentum tensor is also conserved. We obtain the corresponding Raychaudhuri dynamical equation that presents the evolution of the kinematic quantities. Then for the chosen model, we derive the behavior of the deceleration parameter, and show that the coupling term can lead to an acceleration phase after the matter dominated phase. On the other hand, the curvature of the universe corresponds with the deviation from parallelism in the geodesic motion. Thus, we also scrutinize the motion of the free test particles on their geodesics, and derive the geodesic deviation equation in this modified theory to study the accelerating universe within the spatially flat FLRW background. Actually, this equation gives the relative accelerations of adjacent particles as a measurable physical quantity, and provides an elegant tool to investigate the timelike and the null structures of spacetime geometries. Then, through the null deviation vector, we find the observer area-distance as a function of the redshift for the chosen model, and compare the results with the corresponding results obtained in the literature.
Discrete Curvature Theories and Applications
Sun, Xiang
2016-08-25
Discrete Di erential Geometry (DDG) concerns discrete counterparts of notions and methods in di erential geometry. This thesis deals with a core subject in DDG, discrete curvature theories on various types of polyhedral surfaces that are practically important for free-form architecture, sunlight-redirecting shading systems, and face recognition. Modeled as polyhedral surfaces, the shapes of free-form structures may have to satisfy di erent geometric or physical constraints. We study a combination of geometry and physics { the discrete surfaces that can stand on their own, as well as having proper shapes for the manufacture. These proper shapes, known as circular and conical meshes, are closely related to discrete principal curvatures. We study curvature theories that make such surfaces possible. Shading systems of freeform building skins are new types of energy-saving structures that can re-direct the sunlight. From these systems, discrete line congruences across polyhedral surfaces can be abstracted. We develop a new curvature theory for polyhedral surfaces equipped with normal congruences { a particular type of congruences de ned by linear interpolation of vertex normals. The main results are a discussion of various de nitions of normality, a detailed study of the geometry of such congruences, and a concept of curvatures and shape operators associated with the faces of a triangle mesh. These curvatures are compatible with both normal congruences and the Steiner formula. In addition to architecture, we consider the role of discrete curvatures in face recognition. We use geometric measure theory to introduce the notion of asymptotic cones associated with a singular subspace of a Riemannian manifold, which is an extension of the classical notion of asymptotic directions. We get a simple expression of these cones for polyhedral surfaces, as well as convergence and approximation theorems. We use the asymptotic cones as facial descriptors and demonstrate the
Detecting cells using non-negative matrix factorization on calcium imaging data.
Maruyama, Ryuichi; Maeda, Kazuma; Moroda, Hajime; Kato, Ichiro; Inoue, Masashi; Miyakawa, Hiroyoshi; Aonishi, Toru
2014-07-01
We propose a cell detection algorithm using non-negative matrix factorization (NMF) on Ca2+ imaging data. To apply NMF to Ca2+ imaging data, we use the bleaching line of the background fluorescence intensity as an a priori background constraint to make the NMF uniquely dissociate the background component from the image data. This constraint helps us to incorporate the effect of dye-bleaching and reduce the non-uniqueness of the solution. We demonstrate that in the case of noisy data, the NMF algorithm can detect cells more accurately than Mukamel's independent component analysis algorithm, a state-of-art method. We then apply the NMF algorithm to Ca2+ imaging data recorded on the local activities of subcellular structures of multiple cells in a wide area. We show that our method can decompose rapid transient components corresponding to somas and dendrites of many neurons, and furthermore, that it can decompose slow transient components probably corresponding to glial cells.
Convergence, Non-negativity and Stability of a New Milstein Scheme with Applications to Finance
Higham, Desmond J; Szpruch, Lukasz
2012-01-01
We propose and analyse a new Milstein type scheme for simulating stochastic differential equations (SDEs) with highly nonlinear coefficients. Our work is motivated by the need to justify multi-level Monte Carlo simulations for mean-reverting financial models with polynomial growth in the diffusion term. We introduce a double implicit Milstein scheme and show that it possesses desirable properties. It converges strongly and preserves non-negativity for a rich family of financial models and can reproduce linear and nonlinear stability behaviour of the underlying SDE without severe restriction on the time step. Although the scheme is implicit, we point out examples of financial models where an explicit formula for the solution to the scheme can be found.
Facial Expression Recognition via Non-Negative Least-Squares Sparse Coding
Directory of Open Access Journals (Sweden)
Ying Chen
2014-05-01
Full Text Available Sparse coding is an active research subject in signal processing, computer vision, and pattern recognition. A novel method of facial expression recognition via non-negative least squares (NNLS sparse coding is presented in this paper. The NNLS sparse coding is used to form a facial expression classifier. To testify the performance of the presented method, local binary patterns (LBP and the raw pixels are extracted for facial feature representation. Facial expression recognition experiments are conducted on the Japanese Female Facial Expression (JAFFE database. Compared with other widely used methods such as linear support vector machines (SVM, sparse representation-based classifier (SRC, nearest subspace classifier (NSC, K-nearest neighbor (KNN and radial basis function neural networks (RBFNN, the experiment results indicate that the presented NNLS method performs better than other used methods on facial expression recognition tasks.
Song Recommendation with Non-Negative Matrix Factorization and Graph Total Variation
Benzi, Kirell; Bresson, Xavier; Vandergheynst, Pierre
2016-01-01
This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, meta-data and social features. As we demonstrate, our hybrid recommendation system is very versatile and incorporates several well-known methods while outperforming them. Particularly, we show on real-world data that our model overcomes w.r.t. two evaluation metrics the recommendation of models solely based on low-rank information, graph-based information or a combination of both.
Joint cluster and non-negative least squares analysis for aerosol mass spectrum data
Energy Technology Data Exchange (ETDEWEB)
Zhang, T; Zhu, W [Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794-3600 (United States); McGraw, R [Environmental Sciences Department, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States)], E-mail: zhu@ams.sunysb.edu
2008-07-15
Aerosol mass spectrum (AMS) data contain hundreds of mass to charge ratios and their corresponding intensities from air collected through the mass spectrometer. The observations are usually taken sequentially in time to monitor the air composition, quality and temporal change in an area of interest. An important goal of AMS data analysis is to reduce the dimensionality of the original data yielding a small set of representing tracers for various atmospheric and climatic models. In this work, we present an approach to jointly apply the cluster analysis and the non-negative least squares method towards this goal. Application to a relevant study demonstrates the effectiveness of this new approach. Comparisons are made to other relevant multivariate statistical techniques including the principal component analysis and the positive matrix factorization method, and guidelines are provided.
Infinity Behavior of Bounded Subharmonic Functions on Ricci Non-negative Manifolds
Institute of Scientific and Technical Information of China (English)
Bao Qiang WU
2004-01-01
In this paper, we study the infinity behavior of the bounded subharmonic functions on a Ricci non-negative Riemannian manifold M. We first show that limr→∞r2/V(r) ∫B(r)△hdv = 0 if h is a bounded subharmonic function. If we further assume that the Laplacian decays pointwisely faster than quadratically we show that h approaches its supremun pointwisely at infinity, under certain auxiliary conditions on the volume growth of M. In particular, our result applies to the case when the Riemannian manifold has maximum volume growth. We also derive a representation formula in our paper, from which one can easily derive Yau's Liouville theorem on bounded harmonic functions.
Categorical dimensions of human odor descriptor space revealed by non-negative matrix factorization
Energy Technology Data Exchange (ETDEWEB)
Chennubhotla, Chakra [University of Pittsburgh School of Medicine, Pittsburgh PA; Castro, Jason [Bates College
2013-01-01
In contrast to most other sensory modalities, the basic perceptual dimensions of olfaction remain un- clear. Here, we use non-negative matrix factorization (NMF) - a dimensionality reduction technique - to uncover structure in a panel of odor profiles, with each odor defined as a point in multi-dimensional descriptor space. The properties of NMF are favorable for the analysis of such lexical and perceptual data, and lead to a high-dimensional account of odor space. We further provide evidence that odor di- mensions apply categorically. That is, odor space is not occupied homogenously, but rather in a discrete and intrinsically clustered manner. We discuss the potential implications of these results for the neural coding of odors, as well as for developing classifiers on larger datasets that may be useful for predicting perceptual qualities from chemical structures.
Park, Sang Ha; Lee, Seokjin; Sung, Koeng-Mo
Non-negative matrix factorization (NMF) is widely used for monaural musical sound source separation because of its efficiency and good performance. However, an additional clustering process is required because the musical sound mixture is separated into more signals than the number of musical tracks during NMF separation. In the conventional method, manual clustering or training-based clustering is performed with an additional learning process. Recently, a clustering algorithm based on the mel-frequency cepstrum coefficient (MFCC) was proposed for unsupervised clustering. However, MFCC clustering supplies limited information for clustering. In this paper, we propose various timbre features for unsupervised clustering and a clustering algorithm with these features. Simulation experiments are carried out using various musical sound mixtures. The results indicate that the proposed method improves clustering performance, as compared to conventional MFCC-based clustering.
Curvature tensors on distorted Killing horizons and their algebraic classification
Pravda, V
2005-01-01
We consider generic static spacetimes with Killing horizons and study properties of curvature tensors in the horizon limit. It is determined that the Weyl, Ricci, Riemann and Einstein tensors are algebraically special and mutually aligned on the horizon. It is also pointed out that results obtained in the tetrad adjusted to a static observer in general differ from those obtained in a free-falling frame. This is connected to the fact that a static observer becomes null on the horizon. It is also shown that finiteness of the Kretschmann scalar on the horizon is compatible with the divergence of the Weyl component $\\Psi_{3}$ or $\\Psi_{4}$ in the freely falling frame. Furthermore finiteness of $\\Psi_{4}$ is compatible with divergence of curvature invariants constructed from second derivatives of the Riemann tensor. We call the objects with finite Krestschmann scalar but infinite $\\Psi_{4}$ ``truly naked black holes''. In the (ultra)extremal versions of these objects the structure of the Einstein tensor on the hor...
Curvature and geodesic instabilities in a geometrical approach to the planar three-body problem
Krishnaswami, Govind S.; Senapati, Himalaya
2016-10-01
The Maupertuis principle allows us to regard classical trajectories as reparametrized geodesics of the Jacobi-Maupertuis (JM) metric on configuration space. We study this geodesic reformulation of the planar three-body problem with both Newtonian and attractive inverse-square potentials. The associated JM metrics possess translation and rotation isometries in addition to scaling isometries for the inverse-square potential with zero energy E. The geodesic flow on the full configuration space ℂ3 (with collision points excluded) leads to corresponding flows on its Riemannian quotients: the center of mass configuration space ℂ2 and shape space ℝ3 (as well as 𝕊3 and the shape sphere 𝕊2 for the inverse-square potential when E = 0). The corresponding Riemannian submersions are described explicitly in "Hopf" coordinates which are particularly adapted to the isometries. For equal masses subject to inverse-square potentials, Montgomery shows that the zero-energy "pair of pants" JM metric on the shape sphere is geodesically complete and has negative gaussian curvature except at Lagrange points. We extend this to a proof of boundedness and strict negativity of scalar curvatures everywhere on ℂ2, ℝ3, and 𝕊3 with collision points removed. Sectional curvatures are also found to be largely negative, indicating widespread geodesic instabilities. We obtain asymptotic metrics near collisions, show that scalar curvatures have finite limits, and observe that the geodesic reformulation "regularizes" pairwise and triple collisions on ℂ2 and its quotients for arbitrary masses and allowed energies. For the Newtonian potential with equal masses and zero energy, we find that the scalar curvature on ℂ2 is strictly negative though it could have either sign on ℝ3. However, unlike for the inverse-square potential, geodesics can encounter curvature singularities at collisions in finite geodesic time.
Model for a Universe described by a non-minimally coupled scalar field and interacting dark matter
Binder, J B
2006-01-01
In this work it is investigated the evolution of a Universe where a scalar field, non-minimally coupled to space-time curvature, plays the role of quintessence and drives the Universe to a present accelerated expansion. A non-relativistic dark matter constituent that interacts directly with dark energy is also considered, where the dark matter particle mass is assumed to be proportional to the value of the scalar field. Two models for dark matter pressure are considered: the usual one, pressureless, and another that comes from a thermodynamic theory and relates the pressure with the coupling between the scalar field and the curvature scalar. Although the model has a strong dependence on the initial conditions, it is shown that the mixture consisted of dark components plus baryonic matter and radiation can reproduce the expected red-shift behavior of the deceleration parameter, density parameters and luminosity distance.
Geometric scalar theory of gravity
Energy Technology Data Exchange (ETDEWEB)
Novello, M.; Bittencourt, E.; Goulart, E.; Salim, J.M.; Toniato, J.D. [Instituto de Cosmologia Relatividade Astrofisica ICRA - CBPF Rua Dr. Xavier Sigaud 150 - 22290-180 Rio de Janeiro - Brazil (Brazil); Moschella, U., E-mail: novello@cbpf.br, E-mail: eduhsb@cbpf.br, E-mail: Ugo.Moschella@uninsubria.it, E-mail: egoulart@cbpf.br, E-mail: jsalim@cbpf.br, E-mail: toniato@cbpf.br [Università degli Studi dell' Insubria - Dipartamento di Fisica e Matematica Via Valleggio 11 - 22100 Como - Italy (Italy)
2013-06-01
We present a geometric scalar theory of gravity. Our proposal will be described using the ''background field method'' introduced by Gupta, Feynman, Deser and others as a field theory formulation of general relativity. We analyze previous criticisms against scalar gravity and show how the present proposal avoids these difficulties. This concerns not only the theoretical complaints but also those related to observations. In particular, we show that the widespread belief of the conjecture that the source of scalar gravity must be the trace of the energy-momentum tensor — which is one of the main difficulties to couple gravity with electromagnetic phenomenon in previous models — does not apply to our geometric scalar theory. From the very beginning this is not a special relativistic scalar gravity. The adjective ''geometric'' pinpoints its similarity with general relativity: this is a metric theory of gravity. Some consequences of this new scalar theory are explored.
Reheating via a generalized non-minimal coupling of curvature to matter
Bertolami, Orfeu; Páramos, Jorge
2010-01-01
In this work one shows that a generalized non-minimal coupling between geometry and matter is compatible with Starobinsky inflation and leads to a successful process of preheating, a reheating scenario based on the production of massive particles via parametric resonance. The model naturally extends the usual preheating mechanism, which resorts to an {\\it ad-hoc} scalar curvature-dependent mass term for a scalar field $\\chi$, and also encompasses a previously studied preheating channel based upon a non-standard kinetic term.
Equi-Gaussian Curvature Folding
Indian Academy of Sciences (India)
E M El-Kholy; El-Said R Lashin; Salama N Daoud
2007-08-01
In this paper we introduce a new type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds. We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case of equi-Gaussian curvature foldings, $f:M→ P_n$, of an orientable surface onto a polygon $P_n$ we prove that (i) $f\\in\\mathcal{F}_{EG}(S^2)\\Leftrightarrow n=3$ (ii) $f\\in\\mathcal{F}_{EG}(T^2)\\Rightarrow n=4$ (iii) $f\\in\\mathcal{F}_{EG}(\\# 2T^2)\\Rightarrow n=5, 6$ and we generalize (iii) for $\\# nT^2$.
Frigerio, Michele; Riva, Francesco; Urbano, Alfredo
2012-01-01
We show that the dark matter (DM) could be a light composite scalar $\\eta$, emerging from a TeV-scale strongly-coupled sector as a pseudo Nambu-Goldstone boson (pNGB). Such state arises naturally in scenarios where the Higgs is also a composite pNGB, as in $O(6)/O(5)$ models, which are particularly predictive, since the low-energy interactions of $\\eta$ are determined by symmetry considerations. We identify the region of parameters where $\\eta$ has the required DM relic density, satisfying at the same time the constraints from Higgs searches at the LHC, as well as DM direct searches. Compositeness, in addition to justify the lightness of the scalars, can enhance the DM scattering rates and lead to an excellent discovery prospect for the near future. For a Higgs mass $m_h\\simeq 125$ GeV and a pNGB characteristic scale $f \\lesssim 1$ TeV, we find that the DM mass is either $m_\\eta \\simeq 50-70$ GeV, with DM annihilations driven by the Higgs resonance, or in the range 100-500 GeV, where the DM derivative interac...
Integral Menger curvature for surfaces
Strzelecki, Paweł; von der Mosel, Heiko
2009-01-01
We develop the concept of integral Menger curvature for a large class of nonsmooth surfaces. We prove uniform Ahlfors regularity and a $C^{1,\\lambda}$-a-priori bound for surfaces for which this functional is finite. In fact, it turns out that there is an explicit length scale $R>0$ which depends only on an upper bound $E$ for the integral Menger curvature $M_p(\\Sigma)$ and the integrability exponent $p$, and \\emph{not} on the surface $\\Sigma$ itself; below that scale, each surface with energy...
Instability in bacterial populations and the curvature tensor
Melgarejo, Augusto; Langoni, Laura; Ruscitti, Claudia
2016-09-01
In the geometry associated with equilibrium thermodynamics the scalar curvature Rs is a measure of the volume of correlation, and therefore the singularities of Rs indicates the system instabilities. We explore the use of a similar approach to study instabilities in non-equilibrium systems and we choose as a test example, a colony of bacteria. In this regard we follow the proposal made by Obata et al. of using the curvature tensor for studying system instabilities. Bacterial colonies are often found in nature in concentrated biofilms, or other colony types, which can grow into spectacular patterns visible under the microscope. For instance, it is known that a decrease of bacterial motility with density can promote separation into bulk phases of two coexisting densities; this is opposed to the logistic law for birth and death that allows only a single uniform density to be stable. Although this homogeneous configuration is stable in the absence of bacterial interactions, without logistic growth, a density-dependent swim speed v(ρ) leads to phase separation via a spinodal instability. Thus we relate the singularities in the curvature tensor R to the spinodal instability, that is the appearance of regions of different densities of bacteria.
Scalar field as a Bose-Einstein condensate?
Energy Technology Data Exchange (ETDEWEB)
Castellanos, Elías; Escamilla-Rivera, Celia [Mesoamerican Centre for Theoretical Physics (ICTP regional headquarters in Central America, the Caribbean and Mexico), Universidad Autónoma de Chiapas, Carretera Zapata Km. 4, Real del Bosque (Terán), 29040, Tuxtla Gutiérrez, Chiapas (Mexico); Macías, Alfredo [Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, A.P. 55-534, Mexico D.F. 09340 (Mexico); Núñez, Darío, E-mail: ecastellanos@mctp.mx, E-mail: cescamilla@mctp.mx, E-mail: amac@xanum.uam.mx, E-mail: nunez@nucleares.unam.mx [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Circuito Exterior C.U., A.P. 70-543, México D.F. 04510 (Mexico)
2014-11-01
We discuss the analogy between a classical scalar field with a self-interacting potential, in a curved spacetime described by a quasi-bounded state, and a trapped Bose-Einstein condensate. In this context, we compare the Klein-Gordon equation with the Gross-Pitaevskii equation. Moreover, the introduction of a curved background spacetime endows, in a natural way, an equivalence to the Gross-Pitaevskii equation with an explicit confinement potential. The curvature also induces a position dependent self-interaction parameter. We exploit this analogy by means of the Thomas-Fermi approximation, commonly used to describe the Bose-Einstein condensate, in order to analyze the quasi bound scalar field distribution surrounding a black hole.
Gauge Fields and Scalars in Rolling Tachyon Backgrounds
Energy Technology Data Exchange (ETDEWEB)
Thomas Mehen; Brian Wecht
2003-04-01
We investigate the dynamics of gauge and scalar fields on unstable D-branes with rolling tachyons. Assuming an FRW metric on the brane, we find a solution of the tachyon equation of motion which is valid for arbitrary tachyon potentials and scale factors. The equations of motion for a U(1) gauge field and a scalar field in this background are derived. These fields see an effective metric which differs from the original FRW metric. The field equations receive large corrections due to the curvature of the effective metric as well as the time variation of the gauge coupling. The equations of state for these fields resemble those of nonrelativistic matter rather than those of massless particles.
de Sitter symmetries and inflationary scalar-vector models
Directory of Open Access Journals (Sweden)
Juan P. Beltrán Almeida
2016-12-01
Full Text Available In this paper, we study the correspondence between a field theory in de Sitter space in D-dimensions and a dual conformal field theory in a euclidean space in (D − 1-dimensions. In particular, we investigate the form in which this correspondence is established for a system of interacting scalar and a vector fields propagating in de Sitter space. We analyze some necessary (but not sufficient conditions for which conformal symmetry is preserved in the dual theory in (D − 1-dimensions, making possible the establishment of the correspondence. The discussion that we address in this paper is framed on the context of inflationary cosmology. Thusly, the results obtained here pose some relevant possibilities of application to the calculation of the fields’s correlation functions and of the primordial curvature perturbation ζ, in inflationary models including coupled scalar and vector fields.
Evolution of curvature perturbations in a brane-world inflation at high-energies
Hiramatsu, T; Hiramatsu, Takashi; Koyama, Kazuya
2006-01-01
We study the evolution of scalar curvature perturbations in a brane-world inflation model in a 5D Anti-de Sitter spacetime. The inflaton perturbations are confined to a 4D brane but they are coupled to the 5D bulk metric perturbations. We numerically solve full coupled equations for the inflaton perturbations and the 5D metric perturbations. At high energies, the inflaton perturbations are strongly coupled to the bulk metric perurbations even on subhorizon scales, leading to the suppression of the amplitude of the comoving curvature perturbation at a horizon crossing with a particular choice of initial conditions. This indicates the need to qunatise the coupled brane-bulk system in a consistent way in order to define an initial vacuum state and calculate the spectrum of the scalar perturbations in a brane-world inflation.
Surface meshing with curvature convergence
Li, Huibin
2014-06-01
Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm. © 2014 IEEE.
Environmental influences on DNA curvature
DEFF Research Database (Denmark)
Ussery, David; Higgins, C.F.; Bolshoy, A.
1999-01-01
of the sequences exhibited a degree of anomalous migration. Increasedtemperature had a significant effect on the anomalous migration (curvature) of some sequencesbut limited effects on others; at 50 degrees C only 1 sequence migrated anomalously. Mg2+ hada strong influence on the migration of certain sequences...
Institute of Scientific and Technical Information of China (English)
Xiu-rui GENG; Lu-yan JI; Kang SUN
2016-01-01
Non-negative matrix factorization (NMF) has been widely used in mixture analysis for hyperspectral remote sensing. When used for spectral unmixing analysis, however, it has two main shortcomings: (1) since the dimensionality of hyperspectral data is usually very large, NMF tends to suffer from large computational complexity for the popular multiplicative iteration rule;(2) NMF is sensitive to noise (outliers), and thus the corrupted data will make the results of NMF meaningless. Although principal component analysis (PCA) can be used to mitigate these two problems, the transformed data will contain negative numbers, hindering the direct use of the multiplicative iteration rule of NMF. In this paper, we analyze the impact of PCA on NMF, and fi nd that multiplicative NMF can also be applicable to data after principal component transformation. Based on this conclusion, we present a method to perform NMF in the principal component space, named ‘principal component NMF’ (PCNMF). Experimental results show that PCNMF is both accurate and time-saving.
Robust and Non-Negative Collective Matrix Factorization for Text-to-Image Transfer Learning.
Yang, Liu; Jing, Liping; Ng, Michael K
2015-12-01
Heterogeneous transfer learning has recently gained much attention as a new machine learning paradigm in which the knowledge can be transferred from source domains to target domains in different feature spaces. Existing works usually assume that source domains can provide accurate and useful knowledge to be transferred to target domains for learning. In practice, there may be noise appearing in given source (text) and target (image) domains data, and thus, the performance of transfer learning can be seriously degraded. In this paper, we propose a robust and non-negative collective matrix factorization model to handle noise in text-to-image transfer learning, and make a reliable bridge to transfer accurate and useful knowledge from the text domain to the image domain. The proposed matrix factorization model can be solved by an efficient iterative method, and the convergence of the iterative method can be shown. Extensive experiments on real data sets suggest that the proposed model is able to effectively perform transfer learning in noisy text and image domains, and it is superior to the popular existing methods for text-to-image transfer learning.
Exploring Mixed Membership Stochastic Block Models via Non-negative Matrix Factorization
Peng, Chengbin
2014-12-01
Many real-world phenomena can be modeled by networks in which entities and connections are represented by nodes and edges respectively. When certain nodes are highly connected with each other, those nodes forms a cluster, which is called community in our context. It is usually assumed that each node belongs to one community only, but evidences in biology and social networks reveal that the communities often overlap with each other. In other words, one node can probably belong to multiple communities. In light of that, mixed membership stochastic block models (MMB) have been developed to model those networks with overlapping communities. Such a model contains three matrices: two incidence matrices indicating in and out connections and one probability matrix. When the probability of connections for nodes between communities are significantly small, the parameter inference problem to this model can be solved by a constrained non-negative matrix factorization (NMF) algorithm. In this paper, we explore the connection between the two models and propose an algorithm based on NMF to infer the parameters of MMB. The proposed algorithms can detect overlapping communities regardless of knowing or not the number of communities. Experiments show that our algorithm can achieve a better community detection performance than the traditional NMF algorithm. © 2014 IEEE.
Xi, Jianing; Li, Ao
2016-01-01
Recurrent copy number aberrations (RCNAs) in multiple cancer samples are strongly associated with tumorigenesis, and RCNA discovery is helpful to cancer research and treatment. Despite the emergence of numerous RCNA discovering methods, most of them are unable to detect RCNAs in complex patterns that are influenced by complicating factors including aberration in partial samples, co-existing of gains and losses and normal-like tumor samples. Here, we propose a novel computational method, called non-negative sparse singular value decomposition (NN-SSVD), to address the RCNA discovering problem in complex patterns. In NN-SSVD, the measurement of RCNA is based on the aberration frequency in a part of samples rather than all samples, which can circumvent the complexity of different RCNA patterns. We evaluate NN-SSVD on synthetic dataset by comparison on detection scores and Receiver Operating Characteristics curves, and the results show that NN-SSVD outperforms existing methods in RCNA discovery and demonstrate more robustness to RCNA complicating factors. Applying our approach on a breast cancer dataset, we successfully identify a number of genomic regions that are strongly correlated with previous studies, which harbor a bunch of known breast cancer associated genes.
Moschidis, Georgios
2016-01-01
The wave equation $\\square_{g_{M,a}}\\psi=0$ on subextremal Kerr spacetimes $(\\mathcal{M}_{M,a},g_{M,a})$, $0<|a|
Detecting heterogeneity in single-cell RNA-Seq data by non-negative matrix factorization
Zhu, Xun; Ching, Travers; Pan, Xinghua; Weissman, Sherman M.
2017-01-01
Single-cell RNA-Sequencing (scRNA-Seq) is a fast-evolving technology that enables the understanding of biological processes at an unprecedentedly high resolution. However, well-suited bioinformatics tools to analyze the data generated from this new technology are still lacking. Here we investigate the performance of non-negative matrix factorization (NMF) method to analyze a wide variety of scRNA-Seq datasets, ranging from mouse hematopoietic stem cells to human glioblastoma data. In comparison to other unsupervised clustering methods including K-means and hierarchical clustering, NMF has higher accuracy in separating similar groups in various datasets. We ranked genes by their importance scores (D-scores) in separating these groups, and discovered that NMF uniquely identifies genes expressed at intermediate levels as top-ranked genes. Finally, we show that in conjugation with the modularity detection method FEM, NMF reveals meaningful protein-protein interaction modules. In summary, we propose that NMF is a desirable method to analyze heterogeneous single-cell RNA-Seq data. The NMF based subpopulation detection package is available at: https://github.com/lanagarmire/NMFEM. PMID:28133571
A perturbation-based framework for link prediction via non-negative matrix factorization
Wang, Wenjun; Cai, Fei; Jiao, Pengfei; Pan, Lin
2016-12-01
Many link prediction methods have been developed to infer unobserved links or predict latent links based on the observed network structure. However, due to network noises and irregular links in real network, the performances of existed methods are usually limited. Considering random noises and irregular links, we propose a perturbation-based framework based on Non-negative Matrix Factorization to predict missing links. We first automatically determine the suitable number of latent features, which is inner rank in NMF, by Colibri method. Then, we perturb training set of a network by perturbation sets many times and get a series of perturbed networks. Finally, the common basis matrix and coefficients matrix of these perturbed networks are obtained via NMF and form similarity matrix of the network for link prediction. Experimental results on fifteen real networks show that the proposed framework has competitive performances compared with state-of-the-art link prediction methods. Correlations between the performances of different methods and the statistics of networks show that those methods with good precisions have similar consistence.
On bounded and unbounded dynamics of the Hamiltonian system for unified scalar field cosmology
Energy Technology Data Exchange (ETDEWEB)
Starkov, Konstantin E., E-mail: kstarkov@ipn.mx
2016-05-27
This paper is devoted to the research of global dynamics for the Hamiltonian system formed by the unified scalar field cosmology. We prove that this system possesses only unbounded dynamics in the space of negative curvature. It is found the invariant domain filled only by unbounded dynamics for the space with positive curvature. Further, we construct a set of polytopes depending on the Hamiltonian level surface that contain all compact invariant sets. Besides, one invariant two dimensional plane is described. Finally, we establish nonchaoticity of dynamics in one special case. - Highlights: • Unbounded dynamics is stated in case of negative curvature. • Domain with unbounded dynamics is got in case of positive curvature. • Localization polytope for compact invariant sets is computed. • One two dimensional invariant plane is described. • Nonchaotic dynamics is stated in one special case.
General second order scalar-tensor theory, self tuning, and the Fab Four
Charmousis, Christos; Padilla, Antonio; Saffin, Paul M
2011-01-01
Starting from the most general scalar-tensor theory with second order field equations in four dimensions, we establish the unique action that will allow for the existence of a consistent self-tuning mechanism on FLRW backgrounds, and show how it can be understood as a combination of just four base Lagrangians with an intriguing geometric structure dependent on the Ricci scalar, the Einstein tensor, the double dual of the Riemann tensor and the Gauss-Bonnet combination. Spacetime curvature can be screened from the net cosmological constant at any given moment because we allow the scalar field to break Poincar\\'e invariance on the self-tuning vacua, thereby evading the Weinberg no-go theorem. We show how the four arbitrary functions of the scalar field combine in an elegant way opening up the possibility of obtaining non-trivial cosmological solutions.
Energy Technology Data Exchange (ETDEWEB)
Hooft, G. t' [Institute for Theoretical Physics, Utrecht University, and Spinoza Institute, Postbus 8000, 3508 TA Utrecht (Netherlands); Isidori, G. [Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa (Italy); INFN, Laboratori Nazionali di Frascati, Via E.Fermi 40, 00044 Frascati (Italy); Maiani, L. [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , P.le A. Moro 2, 00185 Roma (Italy); INFN, Sezione di Roma ' La Sapienza' , P.le A. Moro 2, 00185 Roma (Italy); Polosa, A.D. [INFN, Sezione di Roma ' La Sapienza' , P.le A. Moro 2, 00185 Roma (Italy)], E-mail: antonio.polosa@cern.ch; Riquer, V. [INFN, Sezione di Roma ' La Sapienza' , P.le A. Moro 2, 00185 Roma (Italy)
2008-05-08
We discuss the effect of the instanton induced, six-fermion effective Lagrangian on the decays of the lightest scalar mesons in the diquark-antidiquark picture. This addition allows for a remarkably good description of light scalar meson decays. The same effective Lagrangian produces a mixing of the lightest scalars with the positive parity qq-bar states. Comparing with previous work where the qq-bar mesons are identified with the nonet at 1200-1700 MeV, we find that the mixing required to fit the mass spectrum is in good agreement with the instanton coupling obtained from light scalar decays. A coherent picture of scalar mesons as a mixture of tetraquark states (dominating in the lightest mesons) and heavy qq-bar states (dominating in the heavier mesons) emerges.
Electroweak Baryogenesis and Colored Scalars
Energy Technology Data Exchange (ETDEWEB)
Cohen, Timothy; /SLAC /Michigan U., MCTP; Pierce, Aaron; /Michigan U., MCTP
2012-02-15
We consider the 2-loop finite temperature effective potential for a Standard Model-like Higgs boson, allowing Higgs boson couplings to additional scalars. If the scalars transform under color, they contribute 2-loop diagrams to the effective potential that include gluons. These 2-loop effects are perhaps stronger than previously appreciated. For a Higgs boson mass of 115 GeV, they can increase the strength of the phase transition by as much as a factor of 3.5. It is this effect that is responsible for the survival of the tenuous electroweak baryogenesis window of the Minimal Supersymmetric Standard Model. We further illuminate the importance of these 2-loop diagrams by contrasting models with colored scalars to models with singlet scalars. We conclude that baryogenesis favors models with light colored scalars. This motivates searches for pair-produced di-jet resonances or jet(s) + = E{sub T}.
Slawski, Martin
2012-01-01
Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a necessity in such setting. Deviating from this paradigm, we show that non-negativity constraints on the regression coefficients may be similarly effective as explicit regularization. For a broad range of designs with Gram matrix having non-negative entries, we establish bounds on the $\\ell_2$-prediction error of non-negative least squares (NNLS) whose form qualitatively matches corresponding results for $\\ell_1$-regularization. Under slightly stronger conditions, it is established that NNLS followed by hard thresholding performs excellently in terms of support recovery of an (approximately) sparse target, in some cases improving over $\\ell_1$-regularization. A substantial advantage of NNLS over r...
Scalar and Asymptotic Scalar Derivatives Theory and Applications
Isac, George
2008-01-01
This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings and the non-gradient type monotonicity on Riemannian manifolds. Scalar and Asymptotic Derivatives: Theory and Applications also presents the material in relation to Euclidean spaces, Hilbert spaces, Banach spaces, Riemannian manifolds, and Hadamard manifolds. This book is
Functional biogeography of ocean microbes revealed through non-negative matrix factorization.
Directory of Open Access Journals (Sweden)
Xingpeng Jiang
Full Text Available The direct "metagenomic" sequencing of genomic material from complex assemblages of bacteria, archaea, viruses and microeukaryotes has yielded new insights into the structure of microbial communities. For example, analysis of metagenomic data has revealed the existence of previously unknown microbial taxa whose spatial distributions are limited by environmental conditions, ecological competition, and dispersal mechanisms. However, differences in genotypes that might lead biologists to designate two microbes as taxonomically distinct need not necessarily imply differences in ecological function. Hence, there is a growing need for large-scale analysis of the distribution of microbial function across habitats. Here, we present a framework for investigating the biogeography of microbial function by analyzing the distribution of protein families inferred from environmental sequence data across a global collection of sites. We map over 6,000,000 protein sequences from unassembled reads from the Global Ocean Survey dataset to [Formula: see text] protein families, generating a protein family relative abundance matrix that describes the distribution of each protein family across sites. We then use non-negative matrix factorization (NMF to approximate these protein family profiles as linear combinations of a small number of ecological components. Each component has a characteristic functional profile and site profile. Our approach identifies common functional signatures within several of the components. We use our method as a filter to estimate functional distance between sites, and find that an NMF-filtered measure of functional distance is more strongly correlated with environmental distance than a comparable PCA-filtered measure. We also find that functional distance is more strongly correlated with environmental distance than with geographic distance, in agreement with prior studies. We identify similar protein functions in several components and
Gene Ranking of RNA-Seq Data via Discriminant Non-Negative Matrix Factorization.
Jia, Zhilong; Zhang, Xiang; Guan, Naiyang; Bo, Xiaochen; Barnes, Michael R; Luo, Zhigang
2015-01-01
RNA-sequencing is rapidly becoming the method of choice for studying the full complexity of transcriptomes, however with increasing dimensionality, accurate gene ranking is becoming increasingly challenging. This paper proposes an accurate and sensitive gene ranking method that implements discriminant non-negative matrix factorization (DNMF) for RNA-seq data. To the best of our knowledge, this is the first work to explore the utility of DNMF for gene ranking. When incorporating Fisher's discriminant criteria and setting the reduced dimension as two, DNMF learns two factors to approximate the original gene expression data, abstracting the up-regulated or down-regulated metagene by using the sample label information. The first factor denotes all the genes' weights of two metagenes as the additive combination of all genes, while the second learned factor represents the expression values of two metagenes. In the gene ranking stage, all the genes are ranked as a descending sequence according to the differential values of the metagene weights. Leveraging the nature of NMF and Fisher's criterion, DNMF can robustly boost the gene ranking performance. The Area Under the Curve analysis of differential expression analysis on two benchmarking tests of four RNA-seq data sets with similar phenotypes showed that our proposed DNMF-based gene ranking method outperforms other widely used methods. Moreover, the Gene Set Enrichment Analysis also showed DNMF outweighs others. DNMF is also computationally efficient, substantially outperforming all other benchmarked methods. Consequently, we suggest DNMF is an effective method for the analysis of differential gene expression and gene ranking for RNA-seq data.
Finding Imaging Patterns of Structural Covariance via Non-Negative Matrix Factorization
Sotiras, Aristeidis; Resnick, Susan M.; Davatzikos, Christos
2015-01-01
In this paper, we investigate the use of Non-Negative Matrix Factorization (NNMF) for the analysis of structural neuroimaging data. The goal is to identify the brain regions that co-vary across individuals in a consistent way, hence potentially being part of underlying brain networks or otherwise influenced by underlying common mechanisms such as genetics and pathologies. NNMF offers a directly data-driven way of extracting relatively localized co-varying structural regions, thereby transcending limitations of Principal Component Analysis (PCA), Independent Component Analysis (ICA) and other related methods that tend to produce dispersed components of positive and negative loadings. In particular, leveraging upon the well known ability of NNMF to produce parts-based representations of image data, we derive decompositions that partition the brain into regions that vary in consistent ways across individuals. Importantly, these decompositions achieve dimensionality reduction via highly interpretable ways and generalize well to new data as shown via split-sample experiments. We empirically validate NNMF in two data sets: i) a Diffusion Tensor (DT) mouse brain development study, and ii) a structural Magnetic Resonance (sMR) study of human brain aging. We demonstrate the ability of NNMF to produce sparse parts-based representations of the data at various resolutions. These representations seem to follow what we know about the underlying functional organization of the brain and also capture some pathological processes. Moreover, we show that these low dimensional representations favorably compare to descriptions obtained with more commonly used matrix factorization methods like PCA and ICA. PMID:25497684
Non-negative Matrix Factorization as a Method for Studying Coronal Heating
Barnes, Will; Bradshaw, Stephen
2015-04-01
Many theoretical efforts have been made to model the response of coronal loops to nanoflare heating, but the theory has long suffered from a lack of direct observations. Nanoflares, originally proposed by Parker (1988), heat the corona through short, impulsive bursts of energy. Because of their short duration and comparatively low amplitude, emission signatures from nanoflare heating events are often difficult to detect. Past algorithms (e.g. Ugarte-Urra and Warren, 2014) for measuring the frequency of transient brightenings in active region cores have provided only a lower bound for such measurements. We present the use of non-negative matrix factorization (NMF) to analyze spectral data in active region cores in order to provide more accurate determinations of nanoflare heating properties. NMF, a matrix deconvolution technique, has a variety of applications , ranging from Raman spectroscopy to face recognition, but, to our knowledge, has not been applied in the field of solar physics. The strength of NMF lies in its ability to estimate sources (heating events) from measurements (observed spectral emission) without any knowledge of the mixing process (Cichocki et al., 2009). We apply our NMF algorithm to forward-modeled emission representative of that produced by nanoflare heating events in an active region core. The heating events are modeled using a state-of-the-art hydrodynamics code (Bradshaw and Cargill, 2013) and the emission and active regions are synthesized using advanced forward modeling and visualization software (Bradshaw and Klimchuk, 2011; Reep et al., 2013). From these active region visualizations, our NMF algorithm is then able to predict the heating event frequency and amplitudes. Improved methods of nanoflare detection will help to answer fundamental questions regarding the frequency of energy release in the solar corona and how the corona responds to such impulsive heating. Additionally, development of reliable, automated nanoflare detection
On mean curvatures in submanifolds geometry
Institute of Scientific and Technical Information of China (English)
2008-01-01
By using moving frame theory,first we introduce 2p-th mean curvatures and(2p+1)-th mean curvature vector fields for a submanifold.We then give an integral expression of them that characterizes them as mean values of symmetric functions of principle curvatures.Next we apply it to derive directly the celebrated Weyl-Gray tube formula in terms of integrals of the 2p-th mean curvatures and some Minkowski-type integral formulas.
The constraint equations for the Einstein-scalar field system on compact manifolds
Energy Technology Data Exchange (ETDEWEB)
Choquet-Bruhat, Yvonne [University of Paris VI, 4 place jussieu, 75005, Paris (France); Isenberg, James [Department of Mathematics, University of Oregon, Eugene, Oregon 97403-5203 (United States); Pollack, Daniel [Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195-4350 (United States)
2007-02-21
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed scalar curvature problem as special cases.
Cosmological model with dynamical curvature
Stichel, Peter C
2016-01-01
We generalize the recently introduced relativistic Lagrangian darkon fluid model (EPJ C (2015) 75:9) by starting with a self-gravitating geodesic fluid whose energy-momentum tensor is dust-like with a nontrivial energy flow. The corresponding covariant propagation and constraint equations are considered in a shear-free nonrelativistic limit whose analytic solutions determine the 1st-order relativistic correction to the spatial curvature. This leads to a cosmological model where the accelerated expansion of the Universe is driven by a time-dependent spatial curvature without the need for introducing any kind of dark energy. We derive the differential equation to be satisfied by the area distance for this model.
Spherically symmetric scalar field collapse
Indian Academy of Sciences (India)
Koyel Ganguly; Narayan Banerjee
2013-03-01
It is shown that a scalar field, minimally coupled to gravity, may have collapsing modes even when the energy condition is violated, that is, for ( + 3) < 0. This result may be useful in the investigation of the possible clustering of dark energy. All the examples dealt with have apparent horizons formed before the formation of singularity. The singularities formed are shell focussing in nature. The density of the scalar field distribution is seen to diverge at singularity. The Ricci scalar also diverges at the singularity. The interior spherically symmetric metric is matched with exterior Vaidya metric at the hypersurface and the appropriate junction conditions are obtained.
Quantum Complexity and Negative Curvature
Brown, Adam R; Zhao, Ying
2016-01-01
As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we show that the same pattern is exhibited by a much simpler system: classical geodesics on a compact two-dimensional geometry of uniform negative curvature. This striking parallel persists whether the system is allowed to evolve naturally or is perturbed from the outside.
Substrate curvature regulates cell migration
He, Xiuxiu; Jiang, Yi
2017-06-01
Cell migration is essential in many aspects of biology. Many basic migration processes, including adhesion, membrane protrusion and tension, cytoskeletal polymerization, and contraction, have to act in concert to regulate cell migration. At the same time, substrate topography modulates these processes. In this work, we study how substrate curvature at micrometer scale regulates cell motility. We have developed a 3D mechanical model of single cell migration and simulated migration on curved substrates with different curvatures. The simulation results show that cell migration is more persistent on concave surfaces than on convex surfaces. We have further calculated analytically the cell shape and protrusion force for cells on curved substrates. We have shown that while cells spread out more on convex surfaces than on concave ones, the protrusion force magnitude in the direction of migration is larger on concave surfaces than on convex ones. These results offer a novel biomechanical explanation to substrate curvature regulation of cell migration: geometric constrains bias the direction of the protrusion force and facilitates persistent migration on concave surfaces.
Pozdeeva, Ekaterina O; Toporensky, Alexey V; Vernov, Sergey Yu
2016-01-01
We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant.
A model for a non-minimally coupled scalar field interacting with dark matter
Binder, J B
2005-01-01
In this work we investigate the evolution of a Universe consisted of a scalar field, a dark matter field and non-interacting baryonic matter and radiation. The scalar field, which plays the role of dark energy, is non-minimally coupled to space-time curvature, and drives the Universe to a present accelerated expansion. The non-relativistic dark matter field interacts directly with the dark energy and has a pressure which follows from a thermodynamic theory. We show that this model can reproduce the expected behavior of the density parameters, deceleration parameter and luminosity distance.
Pozdeeva, Ekaterina O.; Skugoreva, Maria A.; Toporensky, Alexey V.; Vernov, Sergey Yu.
2016-12-01
We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaître-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant.
Roles of a coherent scalar field on the evolution of cosmic structures
Hwang, J
1997-01-01
A coherently oscillating scalar field, an axion as an example, is known to behave as a cold dark matter. The arguments were usually made in the Newtonian context. Ratra proved the case in relativistic context using the synchronous gauge. In this paper we present another proof based on a more suitable gauge choice, the uniform-curvature gauge, which fits the problem. By a proper time averaging the perturbed oscillating scalar field behaves as a cold dark matter on the relevant scales including the superhorizon scale.
Mean curvature 1 surfaces in hyperbolic 3-space with low total curvature. I
Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro
2004-01-01
A complete surface of constant mean curvature 1 (CMC-1) in hyperbolic 3- space with constant curvature $-1$ has two natural notions of ‘‘total curvature’’—one is the total absolute curvature which is the integral over the surface of the absolute value of the Gaussian curvature, and the other is the dual total absolute curvature which is the total absolute curvature of the dual CMC-1 surface. In this paper, we completely classify CMC-1 surfaces with dual total absolute curvature...
A hybrid-optimization method for large-scale non-negative full regualarization in image restoration
Guerrero, J.; Raydan, M.; Rojas, M.
2011-01-01
We describe a new hybrid-optimization method for solving the full-regularization problem of comput- ing both the regularization parameter and the corresponding regularized solution in 1-norm and 2-norm Tikhonov regularization with additional non-negativity constraints. The approach combines the simu
NMF-mGPU: non-negative matrix factorization on multi-GPU systems.
Mejía-Roa, Edgardo; Tabas-Madrid, Daniel; Setoain, Javier; García, Carlos; Tirado, Francisco; Pascual-Montano, Alberto
2015-02-13
In the last few years, the Non-negative Matrix Factorization ( NMF ) technique has gained a great interest among the Bioinformatics community, since it is able to extract interpretable parts from high-dimensional datasets. However, the computing time required to process large data matrices may become impractical, even for a parallel application running on a multiprocessors cluster. In this paper, we present NMF-mGPU, an efficient and easy-to-use implementation of the NMF algorithm that takes advantage of the high computing performance delivered by Graphics-Processing Units ( GPUs ). Driven by the ever-growing demands from the video-games industry, graphics cards usually provided in PCs and laptops have evolved from simple graphics-drawing platforms into high-performance programmable systems that can be used as coprocessors for linear-algebra operations. However, these devices may have a limited amount of on-board memory, which is not considered by other NMF implementations on GPU. NMF-mGPU is based on CUDA ( Compute Unified Device Architecture ), the NVIDIA's framework for GPU computing. On devices with low memory available, large input matrices are blockwise transferred from the system's main memory to the GPU's memory, and processed accordingly. In addition, NMF-mGPU has been explicitly optimized for the different CUDA architectures. Finally, platforms with multiple GPUs can be synchronized through MPI ( Message Passing Interface ). In a four-GPU system, this implementation is about 120 times faster than a single conventional processor, and more than four times faster than a single GPU device (i.e., a super-linear speedup). Applications of GPUs in Bioinformatics are getting more and more attention due to their outstanding performance when compared to traditional processors. In addition, their relatively low price represents a highly cost-effective alternative to conventional clusters. In life sciences, this results in an excellent opportunity to facilitate the
Inflation and the Higgs Scalar
Energy Technology Data Exchange (ETDEWEB)
Green, Dan [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
2014-12-05
This note makes a self-contained exposition of the basic facts of big bang cosmology as they relate to inflation. The fundamental problems with that model are then explored. A simple scalar model of inflation is evaluated which provides the solution of those problems and makes predictions which will soon be definitively tested. The possibility that the recently discovered fundamental Higgs scalar field drives inflation is explored.
Inflation and the Higgs Scalar
Green, Dan
2014-01-01
This note makes a self-contained exposition of the basic facts of big bang cosmology as they relate to inflation. The fundamental problems with that model are then explored. A quartic scalar potential model of inflation is evaluated which provides the solution of those problems and makes predictions which will soon be definitively tested. The possibility that the recently discovered fundamental Higgs scalar field drives inflation is explored.
Converting entropy to curvature perturbations after a cosmic bounce
Energy Technology Data Exchange (ETDEWEB)
Fertig, Angelika; Lehners, Jean-Luc; Mallwitz, Enno; Wilson-Ewing, Edward [Max Planck Institute for Gravitational Physics, Albert Einstein Institute,14476 Potsdam-Golm (Germany)
2016-10-04
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves.
Spin And Curvature In The Worldline Path Integral
Dilkes, F A
1999-01-01
Several aspects of worldline path-integrals are discussed in the context of quantum field theory. It is shown how “near-diagonal” elements of the Seeley-Gilkey coefficients can be computed both in the presence of an arbitrary Riemann metric, a gauge- potential and a scalar potential. These are connected with derivative expansions and ultraviolet properties of field theories. Recently resolved subtleties connected with curvature and curvilinear coordinate systems are taken into account and non-covariant terms in the worldline action are shown to be a necessary ingredient for a correct expansion. This is contrasted with the success of older formal methods. Rudimentary symbolic algebra is shown to be a practical tool for tracking the combinatorics of higher-order calculations. A significant generalization of the Parker-Toms conjecture and the form of the single-particle effective action in curved space results. Some aspects of spin are also considered and it is shown how the spinning particle...
Testing a non-minimal coupling between matter and curvature
Páramos, J
2011-01-01
One of the most interesting and current phenomenological extensions of General Relativity is the so-called $f (R)$ class of theories; a natural generalization of this includes an explicit non-minimal coupling between matter and curvature. The purpose of this work is to present a unified view of the applicability of the latter to various contexts, ranging from astrophysical matter distributions to a cosmological setting. Various results are discussed, including the impact of this non-minimal coupling in the choice of Lagrangian density, a mechanism to mimic galactic dark matter and a Cosmological Constant at a astrophysical scale, the possibility of accounting for the accelerated expansion of the Universe and modifications to post-inflationary reheating. The equivalence between a model exhibiting a non-minimal coupling and multi-scalar-theories is also discussed.
Higher Curvature Gravity in TeV-Scale Extra Dimensions
Energy Technology Data Exchange (ETDEWEB)
Rizzo, Thomas G.
2006-03-31
We begin a general exploration of the phenomenology of TeV-scale extra-dimensional models with gravitational actions that contain higher curvature terms. In particular, we examine how the classic collider signatures of the models of Arkani-Hamed, Dimopoulos and Dvali (missing energy and new dimension-8 contact interactions) and of Randall and Sundrum (TeV-scale graviton Kaluza-Klein resonances) are altered by these modifications to the usual Einstein-Hilbert action. We find that not only are the detailed signatures for these gravitationally induced processes altered but new contributions are found to arise due to the existence of additional scalar Kaluza-Klein states in the spectrum.
Higher-curvature Corrections to Holographic Entanglement with Momentum Relaxation
Tanhayi, M Reza
2016-01-01
We study the effects of Gauss-Bonnet corrections on entanglement entropy and mutual information in the holographic model with momentum relaxation. There are in fact two kinds of deformation in the states of conformal field theory in this model: the higher-curvature terms, which could address the low-energy quantum excitation corrections, and the deformation due to scalar fields, which are responsible for the momentum conservation breaking. We use holographic methods to obtain the corresponding changes due to these deformations in the finite and universal parts of entanglement entropy for strip geometry. Holographic calculation indicates that mutual and tripartite information undergo a transition beyond which they identically change their values. We find that the behavior of transition curves depends on the sign of the Gauss-Bonnet coupling $\\lambda$. The transition for $\\lambda>0$ takes place in larger separation of subsystems than that of $\\lambda<0$.
Converting entropy to curvature perturbations after a cosmic bounce
Fertig, Angelika; Mallwitz, Enno; Wilson-Ewing, Edward
2016-01-01
We study two-field bouncing cosmologies in which primordial perturbations are created in either an ekpyrotic or a matter-dominated contraction phase. We use a non-singular ghost condensate bounce model to follow the perturbations through the bounce into the expanding phase of the universe. In contrast to the adiabatic perturbations, which on large scales are conserved across the bounce, entropy perturbations can grow significantly during the bounce phase. If they are converted into adiabatic/curvature perturbations after the bounce, they typically form the dominant contribution to the observed temperature fluctuations in the microwave background, which can have several beneficial implications. For ekpyrotic models, this mechanism loosens the constraints on the amplitude of the ekpyrotic potential while naturally suppressing the intrinsic amount of non-Gaussianity. For matter bounce models, the mechanism amplifies the scalar perturbations compared to the associated primordial gravitational waves.
Thermodynamic curvature for attractive and repulsive intermolecular forces.
May, Helge-Otmar; Mausbach, Peter; Ruppeiner, George
2013-09-01
The thermodynamic curvature scalar R for the Lennard-Jones system is evaluated in phase space, including vapor, liquid, and solid state. We paid special attention to the investigation of R along vapor-liquid, liquid-solid, and vapor-solid equilibria. Because R is a measure of interaction strength, we traced out the line R=0 dividing the phase space into regions with effectively attractive (R0) interactions. Furthermore, we analyzed the dependence of R on the strength of attraction applying a perturbation ansatz proposed by Weeks-Chandler-Anderson. Our results show clearly a transition from R>0 (for poorly repulsive interaction) to R<0 when loading attraction in the intermolecular potential.
Bound to bounce: a coupled scalar-tachyon model for a smooth cyclic universe
Li, Changhong; Cheung, Yeuk-Kwan E
2011-01-01
We introduce a string-inspired model for a cyclic universe, utilizing the tachyon-scalar coupling as well as contribution from curvature in a closed universe. The universe undergoes a locked inflation stage after each bounce. Cycles of inflation, decelerating expansion, followed by contraction are made possible because of the negative contribution to effective energy density by the curvature term. No ghosts are ever generated at any point in the entire evolution of the universe. The minimum size of the universe is nonzero for generic initial values of the scalar field. The Null, Weak, and Dominant Energy Conditions are not violated at the bounce points, contrary to many bounce models previously proposed. And the Strong Energy Condition is satisfied in periods with tachyon matter domination.
Noncommutative double scalar fields in FRW cosmology as cosmical oscillators
Energy Technology Data Exchange (ETDEWEB)
Malekolkalami, Behrooz; Farhoudi, Mehrdad, E-mail: b_malekolkalami@sbu.ac.i, E-mail: m-farhoudi@sbu.ac.i [Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839 (Iran, Islamic Republic of)
2010-12-21
We investigate the effects caused by noncommutativity of the phase space generated by two scalar fields that have non-minimal conformal couplings to the background curvature in the FRW cosmology. We restrict deformation of the minisuperspace to noncommutativity between the scalar fields and between their canonical conjugate momenta. Then, the investigation is carried out by means of a comparative analysis of the mathematical properties (supplemented with some diagrams) of the time evolution of variables in a classical model and the wavefunction of the universe in a quantum perspective, both in the commutative and noncommutative frames. We find that the imposition of noncommutativity causes more ability in tuning time solutions of the scalar fields and, hence, has important implications in the evolution of the Universe. We find that the noncommutative parameter in the momenta sector is the only responsible parameter for the noncommutative effects in the spatially flat universes. A distinguishing feature of the noncommutative solutions of the scalar fields is that they can be simulated with the well-known three harmonic oscillators depending on three values of the spatial curvature, namely the free, forced and damped harmonic oscillators corresponding to the flat, closed and open universes, respectively. In this respect, we call them cosmical oscillators. In particular, in closed universes, when the noncommutative parameters are small, the cosmical oscillators have an analogous effect with the familiar beating effect in the sound phenomena. Some of the special solutions in the classical model and the allowed wavefunctions in the quantum model make bounds on the values of the noncommutative parameters. The existence of a non-zero constant potential (i.e. a cosmological constant) does not change time evolutions of the scalar fields, but modifies the scale factor. An interesting feature of the well-behaved solutions of the wavefunctions is that the functional form of
Braneworld Inflation with Induced Gravity and Curvature Effect
Institute of Scientific and Technical Information of China (English)
Kourosh Nozari; S.Shafizadeh
2011-01-01
We construct a general braneworld inflation scenario where the inflaton field evolves on the DGP brahe and curvature effects are taken into account via incorporation of the Gauss-Bonnet term in the bulk action. While induced gravity on the DGP brahe modifies the IR limit of general relativity, the Gauss-Bonnet term in the bulk action modifies the UV sector of the theory. In this setup, the dynamics of perturbations on the brahe are studied with details and some confrontation with recent observations are discussed. While the Einstein-Gauss-Bonnet inflation scenario favors only a red spectrum of the scalar perturbation, pure DGP and GBIG inflation models have the capacity to realize the blue spectrum too. In addition, the GBIG inflation scenario in the large field limit requires a smaller number of e-folds than other proposed scenarios in the same situation. For the tensor-to-scalar ratio, the GBIG inflation scenario gives a better 1fit with observationally supported value of R≈ 0.24.
Local vs. global temperature under a positive curvature condition
Sanders, Ko
2016-01-01
For a massless free scalar field in a globally hyperbolic space-time we compare the global temperature T, defined for the KMS states $\\omega^T$, with the local temperature $T_{\\omega}(x)$ introduced by Buchholz and Schlemmer. We prove the following claims: (1) Whenever $T_{\\omega^T}(x)$ is defined, it is a continuous, monotonically increasing function of T at every point x. (2) $T_{\\omega}(x)$ is defined when the space-time is ultra-static with compact Cauchy surface and non-trivial scalar curvature $R\\ge 0$, $\\omega$ is stationary and a few other assumptions are satisfied. Our proof of (2) relies on the positive mass theorem. We discuss the necessity of its assumptions, providing counter-examples in an ultra-static space-time with non-compact Cauchy surface and R<0 somewhere. We interpret the result in terms of a violation of the weak energy condition in the background space-time.
Sprlak, M.; Novak, P.; Pitonak, M.; Hamackova, E.
2015-12-01
Values of scalar, vectorial and second-order tensorial parameters of the Earth's gravitational field have been collected by various sensors in geodesy and geophysics. Such observables have been widely exploited in different parametrization methods for the gravitational field modelling. Moreover, theoretical aspects of these quantities have extensively been studied and are well understood. On the other hand, new sensors for observing gravitational curvatures, i.e., components of the third-order gravitational tensor, are currently under development. This fact may be documented by the terrestrial experiments Dulkyn and Magia, as well as by the proposal of the gravity-dedicated satellite mission called OPTIMA. As the gravitational curvatures represent new types of observables, their exploitation for modelling of the Earth's gravitational field is a subject of this study. Firstly, we derive integral transforms between the gravitational potential and gravitational curvatures, i.e., we find analytical solutions of the boundary value problems with gravitational curvatures as boundary conditions. Secondly, properties of the corresponding Green kernel functions are studied in the spatial and spectral domains. Thirdly, the correctness of the new analytical solutions is tested in a simulation study. The presented mathematical apparatus reveal important properties of the gravitational curvatures. It also extends the Meissl scheme, i.e., an important theoretical paradigm that relates various parameters of the Earth's gravitational field.
Kim, Hyo-Sil
2011-01-01
We study the motion-planning problem for a car-like robot whose turning radius is bounded from below by one and which is allowed to move in the forward direction only (Dubins car). For two robot configurations $\\sigma, \\sigma'$, let $\\ell(\\sigma, \\sigma')$ be the shortest bounded-curvature path from $\\sigma$ to $\\sigma'$. For $d \\geq 0$, let $\\ell(d)$ be the supremum of $\\ell(\\sigma, \\sigma')$, over all pairs $(\\sigma, \\sigma')$ that are at Euclidean distance $d$. We study the function $\\dub(d) = \\ell(d) - d$, which expresses the difference between the bounded-curvature path length and the Euclidean distance of its endpoints. We show that $\\dub(d)$ decreases monotonically from $\\dub(0) = 7\\pi/3$ to $\\dub(\\ds) = 2\\pi$, and is constant for $d \\geq \\ds$. Here $\\ds \\approx 1.5874$. We describe pairs of configurations that exhibit the worst-case of $\\dub(d)$ for every distance $d$.
DEFF Research Database (Denmark)
Nielsen, Søren Føns Vind; Mørup, Morten
2014-01-01
of the component matrices. We examine three gene expression prediction scenarios based on data missing at random, whole genes missing and whole areas missing within a subject. We find that the column-wise updating approach also known as HALS performs the most efficient when fitting the model. We further observe...... that the non-negativity constrained CP model is able to predict gene expressions better than predicting by the subject average when data is missing at random. When whole genes and whole areas are missing it is in general better to predict by subject averages. However, we find that when whole genes are missing...... missing in our problem. Our analysis is based on the non-negativity constrained Canonical Polyadic (CP) decomposition where we handle the missing data using marginalization considering three prominent alternating least squares procedures; multiplicative updates, column-wise, and row-wise updating...
Mirror with thermally controlled radius of curvature
Neil, George R.; Shinn, Michelle D.
2010-06-22
A radius of curvature controlled mirror for controlling precisely the focal point of a laser beam or other light beam. The radius of curvature controlled mirror provides nearly spherical distortion of the mirror in response to differential expansion between the front and rear surfaces of the mirror. The radius of curvature controlled mirror compensates for changes in other optical components due to heating or other physical changes. The radius of curvature controlled mirror includes an arrangement for adjusting the temperature of the front surface and separately adjusting the temperature of the rear surface to control the radius of curvature. The temperature adjustment arrangements can include cooling channels within the mirror body or convection of a gas upon the surface of the mirror. A control system controls the differential expansion between the front and rear surfaces to achieve the desired radius of curvature.
Challenging the Presence of Scalar Charge and Dipolar Radiation in Binary Pulsars
Yagi, Kent; Yunes, Nicolas
2016-01-01
Corrections to general relativity that introduce long-ranged scalar fields which are non-minimally coupled to curvature typically predict that neutron stars possess a non-trivial scalar field profile. An observer far from a star is most sensitive to the spherically-symmetric piece of this profile that decays linearly with the inverse of the distance, the so-called scalar charge, which is related to the emission of dipolar radiation from compact binaries. The presence of dipolar radiation has the potential to very strongly constrain extended theories of gravity. These facts may lead people to believe that gravitational theories with long-ranged scalar fields have already been constrained strongly from binary pulsar observations. Here we challenge this "lore" by investigating the decoupling limit of Gauss-Bonnet gravity as an example, in which the scalar field couples linearly to the Gauss-Bonnet density in the action. We prove a theorem that neutron stars in this theory cannot possess a scalar charge. Thus Gau...
S-curvature of isotropic Berwald metrics
Institute of Scientific and Technical Information of China (English)
Akbar TAYEBI; Mehdi RAFIE-RAD
2008-01-01
Isotropic Berwald metrics are as a generalization of Berwald metrics. Shen proved that every Berwald metric is of vanishing S-curvature. In this paper, we generalize this fact and prove that every isotropic Berwald metric is of isotropic S-curvature. Let F = α + β be a Randers metric of isotropic Berwald curvature. Then it corresponds to a conformal vector field through navigation representation.
Curvature and bubble convergence of harmonic maps
Kokarev, Gerasim
2010-01-01
We explore geometric aspects of bubble convergence for harmonic maps. More precisely, we show that the formation of bubbles is characterised by the local excess of curvature on the target manifold. We give a universal estimate for curvature concentration masses at each bubble point and show that there is no curvature loss in the necks. Our principal hypothesis is that the target manifold is Kaehler.
Curvatures for Parameter Subsets in Nonlinear Regression
1986-01-01
The relative curvature measures of nonlinearity proposed by Bates and Watts (1980) are extended to an arbitrary subset of the parameters in a normal, nonlinear regression model. In particular, the subset curvatures proposed indicate the validity of linearization-based approximate confidence intervals for single parameters. The derivation produces the original Bates-Watts measures directly from the likelihood function. When the intrinsic curvature is negligible, the Bates-Watts parameter-effec...
Reheating in tachyonic inflationary models: Effects on the large scale curvature perturbations
Energy Technology Data Exchange (ETDEWEB)
Jain, Rajeev Kumar, E-mail: rajeev.jain@unige.ch [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India); Chingangbam, Pravabati, E-mail: prava@iiap.res.in [Korea Institute for Advanced Study, 207-43 Cheongnyangni 2-dong, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of); Sriramkumar, L., E-mail: sriram@physics.iitm.ac.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India)
2011-11-11
We investigate the problem of perturbative reheating and its effects on the evolution of the curvature perturbations in tachyonic inflationary models. We derive the equations governing the evolution of the scalar perturbations for a system consisting of a tachyon and a perfect fluid. Assuming the perfect fluid to be radiation, we solve the coupled equations for the system numerically and study the evolution of the perturbations from the sub-Hubble to the super-Hubble scales. In particular, we analyze the effects of the transition from tachyon driven inflation to the radiation dominated epoch on the evolution of the large scale curvature and non-adiabatic pressure perturbations. We consider two different potentials to describe the tachyon and study the effects of two possible types of decay of the tachyon into radiation. We plot the spectrum of curvature perturbations at the end of inflation as well as at the early stages of the radiation dominated epoch. We find that reheating does not affect the amplitude of the curvature perturbations in any of these cases. These results corroborate similar conclusions that have been arrived at earlier based on the study of the evolution of the perturbations in the super-Hubble limit. We illustrate that, before the transition to the radiation dominated epoch, the relative non-adiabatic pressure perturbation between the tachyon and radiation decays in a fashion very similar to that of the intrinsic entropy perturbation associated with the tachyon. Moreover, we show that, after the transition, the relative non-adiabatic pressure perturbation dies down extremely rapidly during the early stages of the radiation dominated epoch. It is these behavior which ensure that the amplitude of the curvature perturbations remain unaffected during reheating. We also discuss the corresponding results for the popular chaotic inflation model in the case of the canonical scalar field.
Scalar transport by planktonic swarms
Martinez-Ortiz, Monica; Dabiri, John O.
2012-11-01
Nutrient and energy transport in the ocean is primarily governed by the action of physical phenomena. In previous studies it has been suggested that aquatic fauna may significantly contribute to this process through the action of the induced drift mechanism. In this investigation, the role of planktonic swarms as ecosystem engineers is assessed through the analysis of scalar transport within a stratified water column. The vertical migration of Artemia salina is controlled via luminescent signals on the top and bottom of the column. The scalar transport of fluorescent dye is visualized and quantified through planar laser induced fluorescence (PLIF). Preliminary results show that the vertical movement of these organisms enhances scalar transport relative to control cases in which only buoyancy forces and diffusion are present. Funded by the BSF program (2011553).
Semiclassical black hole in thermal equilibrium with a nonconformal scalar field
Anderson, Paul R.; Hiscock, William A.; Whitesell, Janet; York, James W., Jr.
1994-11-01
Analytic semiclassical corrections to the Schwarzschild metric are found perturbatively, to first order in ɛ=ħ/M2, for a quantized scalar field with an arbitrary curvature coupling. The approximation scheme developed by Anderson, Hiscock, and Samuel is used to provide approximate algebraic expressions for the components of the vacuum stress-energy tensor. The linearized Einstein equations are solved to find the metric perturbations caused by the quantized field. Microcanonical boundary conditions are imposed on a spherical wall enclosing the black hole. The various physical effects of the back reaction, and their dependence on the value of the curvature coupling, are discussed in detail. The perturbations are found most often to lower the temperature of the black hole. Requiring that the entropy of the system be increased by the quantized field results in upper and lower bounds on the value of the curvature coupling constant, -3.431<=ξ<=7/10.
Gravitational collapse of a homogeneous scalar field coupled kinematically to Einstein tensor
Koutsoumbas, George; Ntrekis, Konstantinos; Papantonopoulos, Eleftherios; Tsoukalas, Minas
2017-02-01
We study the gravitational collapse of a homogeneous time-dependent scalar field that, besides its coupling to curvature, is also kinematically coupled to the Einstein tensor. This coupling is a part of the Horndeski theory and we investigate its effect on the collapsing process. We find that the time required for the scalar field to collapse depends on the value of the derivative coupling and the singularity is protected by a horizon. Matching the internal solution with an external Schwarzschild-anti-de Sitter metric we show that a black hole is formed, while the weak energy condition is satisfied during the collapsing process. The scalar field takes on a finite value at the singularity.
$(2+1)$-dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory
Xu, Wei
2014-01-01
We obtain an exact static solution to Einstein-Power-Maxwell (EPM) theory in $(2+1)$ dimensional AdS spacetime, in which the scalar field couples to gravity in a non-minimal way. After considering the scalar potential, a stable system leads to a constraint on the power parameter $k$ of Maxwell field. The solution contains a curvature singularity at the origin and is non-conformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Especially for the cases with $k>1$, the lower bound is negative, thus there exist scalar black holes with negative mass. The null geodesics in this spacetime are also discussed in detail. They are divided into five models, which are made up of the cases with the following geodesic motions: no-allowed motion, the circular motion, the elliptic motion and the unbounded spiral motion.
Scalar spin of elementary fermions
Energy Technology Data Exchange (ETDEWEB)
Jourjine, A., E-mail: jourjine@pks.mpg.de
2014-01-20
We show that, using the experimentally observed values of CKM and PMNS mixing matrices, all known elementary fermions can be assigned a new quantum number, the scalar spin, in a unique way. This is achieved without introduction of new degrees of freedom. The assignment implies that tau-neutrino should be an anti-Dirac spinor, while mu–tau leptons and charm–top, strange–bottom quarks form Dirac–anti-Dirac scalar spin doublets. The electron and its neutrino remain as originally described by Dirac.
Buttazzo, Dario
2014-01-01
In the motivated hypothesis that the scalar bosons of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) be the lightest new particles around, a possible strategy to search for signs of the extra CP-even states is outlined. It is shown how the measurements of the couplings of the 126 GeV Higgs boson constrain the region of the physical parameters in a generic NMSSM which minimises the fine-tuning of the electroweak scale. We also determine the cross section for the production of a heavier CP-even scalar, together with its most relevant branching ratios.
Perfect Actions for Scalar Theories
Bietenholz, W
1998-01-01
We construct an optimally local perfect lattice action for free scalars of arbitrary mass, and truncate its couplings to a unit hypercube. Spectral and thermodynamic properties of this ``hypercube scalar'' are drastically improved compared to the standard action. We also discuss new variants of perfect actions, using anisotropic of triangular lattices, or applying new types of RGTs. Finally we add a $\\lambda \\phi^{4}$ term and address perfect lattice perturbation theory. We report on a lattice action for the anharmonic oscillator, which is perfect to $O(\\lambda)$.
Scalar strong interaction hadron theory
Hoh, Fang Chao
2015-01-01
The scalar strong interaction hadron theory, SSI, is a first principles' and nonlocal theory at quantum mechanical level that provides an alternative to low energy QCD and Higgs related part of the standard model. The quark-quark interaction is scalar rather than color-vectorial. A set of equations of motion for mesons and another set for baryons have been constructed. This book provides an account of the present state of a theory supposedly still at its early stage of development. This work will facilitate researchers interested in entering into this field and serve as a basis for possible future development of this theory.
Scalar mixing in isotropic turbulence
Kosály, George
1989-04-01
Eswaran and Pope [Phys. Fluids 31, 506 (1988)] performed direct numerical simulations to study the influence of the initial scalar integral length scale on mixing in stationary, isotropic turbulence. Their data demonstrate that both the decay rate and the shape of the rms versus time curve depend on the initial value of the scalar-to-velocity integral length-scale ratio. The present paper discusses modifications of the high Reynolds number theory of Corrsin [AIChE J. 10, 870 (1964)]. The predictions mirror the behavior found in the moderate Reynolds number simulations.
Higher curvature supergravity and cosmology
Energy Technology Data Exchange (ETDEWEB)
Ferrara, Sergio [Th-Ph Department, CERN, Geneva (Switzerland); U.C.L.A., Los Angeles, CA (United States); INFN - LNF, Frascati (Italy); Sagnotti, Augusto [Scuola Normale Superiore, Pisa (Italy); INFN, Pisa (Italy)
2016-04-15
In this contribution we describe dual higher-derivative formulations of some cosmological models based on supergravity. Work in this direction started with the R + R{sup 2} Starobinsky model, whose supersymmetric extension was derived in the late 80's and was recently revived in view of new CMB data. Models dual to higher-derivative theories are subject to more restrictions than their bosonic counterparts or standard supergravity. The three sections are devoted to a brief description of R + R{sup 2} supergravity, to a scale invariant R{sup 2} supergravity and to theories with a nilpotent curvature, whose duals describe non-linear realizations (in the form of a Volkov-Akulov constrained superfield) coupled to supergravity. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
On the Ricci Curvature of a Randers Metric of Isotropic S-curvature
Institute of Scientific and Technical Information of China (English)
Xiao Huan MO; Chang Tao YU
2008-01-01
We derive the integral inequality of a Randers metric with isotropic S-curvature in terms of its navigation representation. Using the obtained inequality we give some rigidity results under the condition of Ricci curvature. In particular, we show the following result: Assume that an n-dimensional compact Randers manifold (M, F)hasconstantS-curvature c.Then(M, F) must be Riemannian ifits Ricci curvature satisfies that Ric < - (n - 1)c2.
Asymptotic analysis of singular solutions of the scalar and mean curvature equations
Directory of Open Access Journals (Sweden)
Gonzalo García
2005-01-01
Full Text Available We show that positive solutions of a semilinear elliptic problem in the Sobolev critical exponent with Newmann conditions, related to conformal deformation of metrics in ℝ+n, are asymptotically symmetric in a neighborhood of the origin. As a consequence, we prove for a related problem of conformal deformation of metrics in ℝ+n that if a solution satisfies a Kazdan-Warner-type identity, then the conformal metric can be realized as a smooth metric on S+n.
A new extension of Hořava-Lifshitz gravity and curing pathologies of the scalar graviton
Moon, Taeyoon; Oh, Phillial; Park, Mu-In
2011-07-01
We consider an extension of the Hořava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free parameters which breaks local anisotropic Weyl symmetry but still preserves residual global Weyl symmetry. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity. With a constant scalar field background and particular choices of the parameters, it reduces to the Hořava-Lifshitz (HL) gravity, but any perturbation from these particular configurations produces some nontrivial extensions of HL gravity. The perturbation analysis of the new extended HL gravity in the Minkowski background shows that the pathological behaviors of scalar graviton, i.e., ghost or instability problem, and strong coupling problem do not emerge up to cubic order as well as quadratic order.
A New Extension of Ho\\v{r}ava-Lifshitz Gravity and Curing Pathologies of the Scalar Graviton
Moon, Taeyoon; Park, Mu-In
2011-01-01
We consider an extension of the Ho\\v{r}ava-Lifshitz gravity with extra conformal symmetry by introducing a scalar field with higher order curvature terms. Relaxing the exact local Weyl symmetry, we construct an action with three free parameters which breaks local anisotropic Weyl symmetry but still preserves residual global Weyl symmetry. At low energies, it reduces to a Lorentz-violating scalar-tensor gravity. With a constant scalar field background and particular choices of the parameters, it reduces to the Ho\\v{r}ava-Lifshitz (HL) gravity, but any perturbation from these particular configurations produces some non-trivial extensions of HL gravity. The perturbation analysis of the new extended HL gravity in the Minkowski background shows thatthe pathological behaviors of scalar graviton, i.e., ghost or instability problem, and strong coupling problem do not emerge up to cubic order as well as quadratic order.
The Hamiltonian formalism for scalar fields coupled to gravity in a cosmological background
Energy Technology Data Exchange (ETDEWEB)
Bernardini, A.E., E-mail: alexeb@ufscar.br; Bertolami, O., E-mail: orfeu.bertolami@fc.up.pt
2013-11-15
A novel routine to investigate the scalar fields in a cosmological context is discussed in the framework of the Hamiltonian formalism. Starting from the Einstein–Hilbert action coupled to a Lagrangian density that contains two components–one corresponding to a scalar field Lagrangian, L{sub ϕ}, and another that depends on the scale parameter, L{sub a}–one can identify a generalized Hamiltonian density from which first-order dynamical equations can be obtained. This set up corresponds to the dynamics of Friedmann–Robertson–Walker models in the presence of homogeneous fields embedded into a generalized cosmological background fluid in a system that evolves all together isentropically. Once the generalized Hamiltonian density is properly defined, the constraints on the gravity–matter–field system are straightforwardly obtained through the first-order Hamilton equations. The procedure is illustrated for three examples of cosmological interest for studies of the dark sector: real scalar fields, tachyonic fields and generalized Born–Infeld tachyonic fields. The inclusion of some isentropic fluid component into the Friedmann equation allows for identifying an exact correspondence between the dark sector underlying scalar field and an ordinary real scalar field dynamics. As a final issue, the Hamiltonian formulation is used to set the first-order dynamical equations through which one obtains the exact analytical description of the cosmological evolution of a generalized Chaplygin gas (GCG) with dustlike matter, radiation or curvature contributions. Model stability in terms of the square of the sound velocity, c{sub s}{sup 2}, cosmic acceleration, q, and conditions for inflation are discussed. -- Highlights: •The Hamiltonian formalism for scalar fields coupled to gravity in a cosmological background is constructed. •Real scalar, tachyonic and generalized Born–Infeld tachyonic-type fields are considered. •An extended formulation of the Hamilton
SCALAR AND VECTOR IN COMPULATION
Directory of Open Access Journals (Sweden)
Valery F. Ochkov
2013-01-01
Full Text Available The article deals with two fundamental data types – scalar and vector (array, without the ability of working with them one cannot solve using computer school or university tasks in mathematics, physics, chemistry and other technical training courses. Some fundamentals of teaching computer science at school and university are covered as well.
Scalar Calibration of Vector Magnetometers
DEFF Research Database (Denmark)
Merayo, José M.G.; Brauer, Peter; Primdahl, Fritz;
2000-01-01
The calibration parameters of a vector magnetometer are estimated only by the use of a scalar reference magnetometer. The method presented in this paper differs from those previously reported in its linearized parametrization. This allows the determination of three offsets or signals in the absence...
Scalar-Tensor Theory of Gravity and Generalized Second Law of Thermodynamics on the Event Horizon
Mazumder, Nairwita
2010-01-01
In blackhole physics, the second law of thermodynamics is generally valid whether the blackhole is a static or a non-static one. Considering the universe as a thermodynamical system the second law of blackhole dynamics extends to the non-negativity of the sum of the entropy of the matter and the horizon, known as generalized second law of thermodynamics(GSLT). Here, we have assumed the universe to be bounded by the event-horizon or filled with perfect fluid and holographic dark energy in two cases. Thus considering entropy to be an arbitrary function of the area of the event-horizon, we have tried to find the conditions and the restrictions over the scalar field and equation of state for the validity of the GSLT and both in quintessence-era and in phantom-era in scalar tensor theory.
Lattice QCD simulation of the Berry curvature
Yamamoto, Arata
2016-01-01
The Berry curvature is a fundamental concept describing topological order of quantum systems. While it can be analytically tractable in non-interacting systems, numerical simulations are necessary in interacting systems. We present a formulation to calculate the Berry curvature in lattice QCD.
Strong curvature effects in Neumann wave problems
DEFF Research Database (Denmark)
Willatzen, Morten; Pors, A.; Gravesen, Jens
2012-01-01
equation for a quantum-mechanical particle confined by infinite barriers relevant in semiconductor physics. With this in mind and the interest to tailor waveguides towards a desired spectrum and modal pattern structure in classical structures and nanostructures, it becomes increasingly important...... to understand the influence of curvature effects in waveguides. In this work, we demonstrate analytically strong curvature effects for the eigenvalue spectrum of the Helmholtz equation with Neumann boundary conditions in cases where the waveguide cross section is a circular sector. It is found that the linear......-in-curvature contribution originates from parity symmetry breaking of eigenstates in circular-sector tori and hence vanishes in a torus with a complete circular cross section. The same strong curvature effect is not present in waveguides subject to Dirichlet boundary conditions where curvature contributions contribute...
Importance of plan curvature in watershed modeling
Boll, J.; Ribail, J.; Zhao, M.
2016-12-01
A hillslope's hydrologic response to precipitation events is largely controlled by the topographic features of a given hillslope, specifically the profile and plan curvature. Many models simplify hillslope topography and ignore the curvature properties, and some use alternate measures such as a topographic index or the hillslope width function. Models that ignore curvature properties may be calibrated to produce the statistically acceptable integrated response of runoff at a watershed outlet, but incorporating these properties is necessary to model accurately hydrologic processes such as surface flow, erosion, subsurface lateral flow, location of runoff generation and drainage response. In this study, we evaluated the sensitivity of rainfall-runoff modelling to profile and plan curvature in two models. In the first model, the Water Erosion Prediction Project (WEPP) model, hillslope uses a representative width to the hillslope by dividing the drainage area by the average surface channel length. Profile curvature is preserved with a limited spatial resolution due to the number of overland flow elements. In the second model, the distributed Soil Moisture Routing (SMR) model, the geographic information system uses the D8 algorithm to capture profile and plan curvature. Sensitivity to topographic features was tested for three profile curvatures (convex, concave, straight) combined with three plan curvatures (diverging, converging, uniform) resulting in a total of nine hillslopes. Each hillslope was subjected to different rainfall events to detect threshold behavior for when topographic features cannot be ignored. Our findings indicate that concave and convex plan curvature need to be included when subsurface flow processes are the dominant flow process for surface flow runoff generation. We present thresholds for acceptable cases when profile and plan curvature can be simplified in larger spatial hydrologic units.
Scalar potentials out of canonical quantum cosmology
Guzman, W; Socorro, J; Urena-Lopez, L A
2005-01-01
Using canonical quantization of a flat FRW cosmological model containing a real scalar field $\\phi$ endowed with a scalar potential $V(\\phi)$, we are able to obtain exact and semiclassical solutions of the so called Wheeler-DeWitt equation for a particular family of scalar potentials. Some features of the solutions and their classical limit are discussed.
Galactic Collapse of Scalar Field Dark Matter
Alcubierre, M; Matos, T; Núñez, D; Urena-Lopez, L A; Wiederhold, P; Alcubierre, Miguel; Matos, Tonatiuh; Nunez, Dario; Wiederhold, Petra
2002-01-01
We present a scenario for galaxy formation based on the hypothesis of scalar field dark matter. We interpret galaxy formation through the collapse of a scalar field fluctuation. We find that a cosh potential for the self-interaction of the scalar field provides a reasonable scenario for galactic formation, which is in agreement with cosmological observations and phenomenological studies in galaxies.
Galactic Collapse of Scalar Field Dark Matter
2001-01-01
We present a scenario for galaxy formation based on the hypothesis of scalar field dark matter. We interpret galaxy formation through the collapse of a scalar field fluctuation. We find that a cosh potential for the self-interaction of the scalar field provides a reasonable scenario for galactic formation, which is in agreement with cosmological observations and phenomenological studies in galaxies.
Energy Technology Data Exchange (ETDEWEB)
Gao, Dengliang
2013-03-01
In 3D seismic interpretation, curvature is a popular attribute that depicts the geometry of seismic reflectors and has been widely used to detect faults in the subsurface; however, it provides only part of the solutions to subsurface structure analysis. This study extends the curvature algorithm to a new curvature gradient algorithm, and integrates both algorithms for fracture detection using a 3D seismic test data set over Teapot Dome (Wyoming). In fractured reservoirs at Teapot Dome known to be formed by tectonic folding and faulting, curvature helps define the crestal portion of the reservoirs that is associated with strong seismic amplitude and high oil productivity. In contrast, curvature gradient helps better define the regional northwest-trending and the cross-regional northeast-trending lineaments that are associated with weak seismic amplitude and low oil productivity. In concert with previous reports from image logs, cores, and outcrops, the current study based on an integrated seismic curvature and curvature gradient analysis suggests that curvature might help define areas of enhanced potential to form tensile fractures, whereas curvature gradient might help define zones of enhanced potential to develop shear fractures. In certain fractured reservoirs such as at Teapot Dome where faulting and fault-related folding contribute dominantly to the formation and evolution of fractures, curvature and curvature gradient attributes can be potentially applied to differentiate fracture mode, to predict fracture intensity and orientation, to detect fracture volume and connectivity, and to model fracture networks.
Scalar-Scalar, Scalar-Tensor, and Tensor-Tensor Correlators from Anisotropic Inflation
Gumrukcuoglu, A E; Peloso, Marco
2010-01-01
We compute the phenomenological signatures of a model (Watanabe et al' 09) of anisotropic inflation driven by a scalar and a vector field. The action for the vector is U(1) invariant, and the model is free of ghost instabilities. A suitable coupling of the scalar to the kinetic term of the vector allows for a slow roll evolution of the vector vev, and hence for a prolonged anisotropic expansion; this provides a counter example to the cosmic no hair conjecture. We compute the nonvanishing two point correlation functions between physical modes of the system, and express them in terms of power spectra with angular dependence. The anisotropy parameter g_* for the scalar-scalar spectrum (defined as in the Ackerman et al '07 parametrization) turns out to be negative in the simplest realization of the model, which, therefore, cannot account for the angular dependence emerged in some analyses of the WMAP data. A g_* of order -0.1 is achieved when the energy of the vector is about 6-7 orders of magnitude smaller than ...
DEFF Research Database (Denmark)
Nielsen, Søren Føns Vind; Mørup, Morten
2014-01-01
forms a promising framework for imputing missing values and characterizing gene expression in the human brain. However, care also has to be taken in particular when predicting the genetic expression levels at a whole region of the brain missing as our analysis indicates that this requires a substantial......Non-negative Tensor Factorization (NTF) has become a prominent tool for analyzing high dimensional multi-way structured data. In this paper we set out to analyze gene expression across brain regions in multiple subjects based on data from the Allen Human Brain Atlas [1] with more than 40 % data...
Matrix Representation in Quantum Mechanics with Non-Negative QDF in the Case of a Hydrogen-Like Atom
Zhidkov, E P; Lovetsky, K P; Tretiakov, N P
2002-01-01
The correspondence rules A(q,p)\\mapsto\\hat{A} of the orthodoxal quantum mechanics do not allow one to introduce into the theory the non-negative quantum distribution function F(q,p). The correspondence rules A(q,p)\\mapsto\\hat{O}(A) of Kuryshkin's quantum mechanics (QMK) do allow one to do it. Besides, the operators \\hat{O}(A) turn out to be \\hat{A} bounded and \\hat{A} small at infinity for all systems of auxiliary functions {\\varphi_k}. This allows one to realise canonical matrix representation of QMK to investigate its dependence on the systems of functions {\\varphi_k}.
DEFF Research Database (Denmark)
2014-01-01
Due to applications in areas such as diagnostics and environmental safety, detection of molecules at very low concentrations has attracted recent attention. A powerful tool for this is Surface Enhanced Raman Spectroscopy (SERS) where substrates form localized areas of electromagnetic “hot spots...... a Bayesian Non-negative Matrix Factorization (NMF) approach to identify locations of target molecules. The proposed method is able to successfully analyze the spectra and extract the target spectrum. A visualization of the loadings of the basis vector is created and the results show a clear SNR enhancement...
Equation of State of Gravitational Scalar-Torsion Mode
Tseng, Huan-Hsin; Geng, Chao-Qiang
2012-01-01
We investigate the equation of state (EoS) of the scalar-torsion mode in Poincar\\'{e} gauge theory of gravity. We concentrate on two cases with the constant curvature solution and positive kinetic energy, respectively. In the former, we find that the torsion EoS has different values in the various stages of the universe. In particular, it behaves like the radiation (matter) EoS of $w_r=1/3$ ($w_m=0$) in the radiation (matter) dominant epoch, while in the late time the torsion density is supportive for the accelerating universe. In the latter, our numerical analysis shows that in general the EoS has an asymptotic behavior in the high redshift regime, while it could cross the phantom divide line in the low redshift regime.
Extended Quintessence with non-minimally coupled phantom scalar field
Hrycyna, Orest
2007-01-01
We investigate evolutional paths of an extended quintessence with a non-minimally coupled phantom scalar field $\\psi$ to the Ricci curvature. The dynamical system methods are used to investigate typical regimes of dynamics at the late time. We demonstrate that there are two generic types of evolutional scenarios which approach the attractor (a focus or a node type critical point) in the phase space: the quasi-oscillatory and monotonic trajectories approach to the attractor which represents the FRW model with the cosmological constant. We demonstrate that dynamical system admits invariant two-dimensional submanifold and discussion which cosmological scenario is realised depends on behaviour of the system on the phase plane $(\\psi, \\psi')$. We formulate simple conditions on the value of coupling constant $\\xi$ for which trajectories tend to the focus in the phase plane and hence damping oscillations around the mysterious value w=-1. We describe this condition in terms of slow-roll parameters calculated at the c...
Darkflation-One scalar to rule them all?
Lalak, Zygmunt; Nakonieczny, Łukasz
2017-03-01
The problem of explaining both inflationary and dark matter physics in the framework of a minimal extension of the Standard Model was investigated. To this end, the Standard Model completed by a real scalar singlet playing a role of the dark matter candidate has been considered. We assumed both the dark matter field and the Higgs doublet to be nonminimally coupled to gravity. Using quantum field theory in curved spacetime we derived an effective action for the inflationary period and analyzed its consequences. In this approach, after integrating out both dark matter and Standard Model sectors we obtained the effective action expressed purely in terms of the gravitational field. We paid special attention to determination, by explicit calculations, of the form of coefficients controlling the higher-order in curvature gravitational terms. Their connection to the Standard Model coupling constants has been discussed.
Effective long wavelength scalar dynamics in de Sitter
Moss, Ian
2016-01-01
We discuss the effective infrared theory governing a light scalar's long wavelength dynamics in de Sitter spacetime. We show how the separation of scales around the physical curvature radius $k/a \\sim H$ can be performed consistently with a window function and how short wavelengths can be integrated out in the Schwinger-Keldysh path integral formalism. At leading order, and for time scales $\\Delta t \\gg H^{-1}$, this results in the well-known Starobinsky stochastic evolution. Our approach allows for the computation of quantum UV corrections, generating an effective potential on which the stochastic dynamics takes place, as well as the description of dynamics on spatial and temporal scales comparable to $H^{-1}$ and above. We further elaborate on the use of a Wigner function to evaluate the non-perturbative expectation values of field correlators and the stress-energy tensor of $\\phi$ within the stochastic formalism.
Warped-AdS3 black holes with scalar halo
Giribet, Gaston
2015-01-01
We construct a stretched (aka Warped) Anti-de Sitter black hole in 3 dimensions supported by a real scalar field configuration. The latter is regular everywhere outside and on the horizon. No hair theorems in 3 dimensions demand the matter to be coupled to the curvature in a non-minimal way; however, this coupling can still be of the Horndeski type, i.e. yielding second order field equations similar to those appearing in the context of Galileon theories. These Warped-Anti-de Sitter black holes exhibit interesting thermodynamical properties, such as finite Hawking temperature and entropy. We compute the black hole entropy in the gravity theory and speculate with the possibility of this to admit a microscopic description in terms of a dual (Warped) Conformal Field Theory. We also discuss the inner and outer black hole mechanics.
Cold black holes in scalar-tensor theories
Bronnikov, K A; Evangelista, R L; Fabris, J C
1997-01-01
We study the possible existence of black holes in scalar-tensor theories of gravity in four dimensions. Their existence is verified for anomalous versions of these theories, with a negative kinetic term in the Lagrangian. The Hawking temperature T_H of these holes is zero, while the horizon area is (in most cases) infinite. It is shown that an infinite value of T_H can occur only at a curvature singularity rather than a horizon. As a special case, the Brans-Dicke theory is studied in more detail, and two kinds of infinite-area black holes are revealed, with finite and infinite proper time needed for an infalling particle to reach the horizon.
Search for Scalar Leptons and Scalar Quarks at LEP
Achard, P; Aguilar-Benítez, M; Alcaraz, J; Alemanni, G; Allaby, James V; Aloisio, A; Alviggi, M G; Anderhub, H; Andreev, V P; Anselmo, F; Arefev, A; Azemoon, T; Aziz, T; Bagnaia, P; Bajo, A; Baksay, G; Baksay, L; Baldew, S V; Banerjee, S; Banerjee, Sw; Barczyk, A; Barillère, R; Bartalini, P; Basile, M; Batalova, N; Battiston, R; Bay, A; Becattini, F; Becker, U; Behner, F; Bellucci, L; Berbeco, R; Berdugo, J; Berges, P; Bertucci, B; Betev, B L; Biasini, M; Biglietti, M; Biland, A; Blaising, J J; Blyth, S C; Bobbink, Gerjan J; Böhm, A; Boldizsar, L; Borgia, B; Bottai, S; Bourilkov, D; Bourquin, Maurice; Braccini, S; Branson, J G; Brochu, F; Burger, J D; Burger, W J; Cai, X D; Capell, M; Cara Romeo, G; Carlino, G; Cartacci, A M; Casaus, J; Cavallari, F; Cavallo, N; Cecchi, C; Cerrada, M; Chamizo-Llatas, M; Chang, Y H; Chemarin, M; Chen, A; Chen, G; Chen, G M; Chen, H F; Chen, H S; Chiefari, G; Cifarelli, Luisa; Cindolo, F; Clare, I; Clare, R; Coignet, G; Colino, N; Costantini, S; de la Cruz, B; Cucciarelli, S; van Dalen, J A; De Asmundis, R; Déglon, P L; Debreczeni, J; Degré, A; Dehmelt, K; Deiters, K; Della Volpe, D; Delmeire, E; Denes, P; De Notaristefani, F; De Salvo, A; Diemoz, M; Dierckxsens, M; Dionisi, C; Dittmar, M; Doria, A; Dova, M T; Duchesneau, D; Duda, M; Echenard, B; Eline, A; El-Hage, A; El-Mamouni, H; Engler, A; Eppling, F J; Extermann, P; Falagán, M A; Falciano, S; Favara, A; Fay, J; Fedin, O; Felcini, M; Ferguson, T; Fesefeldt, H S; Fiandrini, E; Field, J H; Filthaut, F; Fisher, P H; Fisher, W; Fisk, I; Forconi, G; Freudenreich, Klaus; Furetta, C; Galaktionov, Yu; Ganguli, S N; García-Abia, P; Gataullin, M; Gentile, S; Giagu, S; Gong, Z F; Grenier, G; Grimm, O; Grünewald, M W; Guida, M; van Gulik, R; Gupta, V K; Gurtu, A; Gutay, L J; Haas, D; Hatzifotiadou, D; Hebbeker, T; Hervé, A; Hirschfelder, J; Hofer, H; Hohlmann, M; Holzner, G; Hou, S R; Hu, Y; Jin, B N; Jones, L W; de Jong, P; Josa-Mutuberria, I; Käfer, D; Kaur, M; Kienzle-Focacci, M N; Kim, J K; Kirkby, Jasper; Kittel, E W; Klimentov, A; König, A C; Kopal, M; Koutsenko, V F; Kräber, M H; Krämer, R W; Krüger, A; Kunin, A; Ladrón de Guevara, P; Laktineh, I; Landi, G; Lebeau, M; Lebedev, A; Lebrun, P; Lecomte, P; Lecoq, P; Le Coultre, P; Le Goff, J M; Leiste, R; Levtchenko, M; Levchenko, P M; Li, C; Likhoded, S; Lin, C H; Lin, W T; Linde, Frank L; Lista, L; Liu, Z A; Lohmann, W; Longo, E; Lü, Y S; Luci, C; Luminari, L; Lustermann, W; Ma Wen Gan; Malgeri, L; Malinin, A; Maña, C; Mans, J; Martin, J P; Marzano, F; Mazumdar, K; McNeil, R R; Mele, S; Merola, L; Meschini, M; Metzger, W J; Mihul, A; Milcent, H; Mirabelli, G; Mnich, J; Mohanty, G B; Muanza, G S; Muijs, A J M; Musicar, B; Musy, M; Nagy, S; Natale, S; Napolitano, M; Nessi-Tedaldi, F; Newman, H; Nisati, A; Novák, T; Nowak, H; Ofierzynski, R A; Organtini, G; Pal, I; Palomares, C; Paolucci, P; Paramatti, R; Passaleva, G; Patricelli, S; Paul, T; Pauluzzi, M; Paus, C; Pauss, Felicitas; Pedace, M; Pensotti, S; Perret-Gallix, D; Petersen, B; Piccolo, D; Pierella, F; Pioppi, M; Piroué, P A; Pistolesi, E; Plyaskin, V; Pohl, M; Pozhidaev, V; Pothier, J; Prokofev, D; Prokofiev, D O; Quartieri, J; Rahal-Callot, G; Rahaman, M A; Raics, P; Raja, N; Ramelli, R; Rancoita, P G; Ranieri, R; Raspereza, A V; Razis, P A; Ren, D; Rescigno, M; Reucroft, S; Riemann, S; Riles, K; Roe, B P; Romero, L; Rosca, A; Rosier-Lees, S; Roth, S; Rosenbleck, C; Rubio, J A; Ruggiero, G; Rykaczewski, H; Sakharov, A; Saremi, S; Sarkar, S; Salicio, J; Sánchez, E; Schäfer, C; Shchegelskii, V; Schopper, Herwig Franz; Schotanus, D J; Sciacca, C; Servoli, L; Shevchenko, S; Shivarov, N; Shoutko, V; Shumilov, E; Shvorob, A V; Son, D; Souga, C; Spillantini, P; Steuer, M; Stickland, D P; Stoyanov, B; Strässner, A; Sudhakar, K; Sultanov, G G; Sun, L Z; Sushkov, S; Suter, H; Swain, J D; Szillási, Z; Tang, X W; Tarjan, P; Tauscher, Ludwig; Taylor, L; Tellili, B; Teyssier, D; Timmermans, C; Ting, Samuel C C; Ting, S M; Tonwar, S C; Tóth, J; Tully, C; Tung, K L; Ulbricht, J; Valente, E; Van de Walle, R T; Vásquez, R; Veszpremi, V; Vesztergombi, G; Vetlitskii, I; Vicinanza, D; Viertel, Gert M; Villa, S; Vivargent, M; Vlachos, S; Vodopyanov, I; Vogel, H; Vogt, H; Vorobev, I; Vorobyov, A A; Wadhwa, M; Wang, Q; Wang, X L; Wang, Z M; Weber, M; Wienemann, P; Wilkens, H; Wynhoff, S; Xia, L; Xu, Z Z; Yamamoto, J; Yang, B Z; Yang, C G; Yang, H J; Yang, M; Yeh, S C; Zalite, A; Zalite, Yu; Zhang, Z P; Zhao, J; Zhu, G Y; Zhu, R Y; Zhuang, H L; Zichichi, A; Zimmermann, B; Zöller, M
2004-01-01
Scalar partners of quarks and leptons, predicted in supersymmetric models, are searched for in e^+e^- collisions at centre-of-mass energies between 192GeV and 209GeV at LEP. No evidence for any such particle is found in a data sample of 450 pb^-1. Upper limits on their production cross sections are set and lower limits on their masses are derived in the framework of the Minimal Supersymmetric Standard Model.
Curvature function and coarse graining
Díaz-Marín, Homero; Zapata, José A.
2010-12-01
A classic theorem in the theory of connections on principal fiber bundles states that the evaluation of all holonomy functions gives enough information to characterize the bundle structure (among those sharing the same structure group and base manifold) and the connection up to a bundle equivalence map. This result and other important properties of holonomy functions have encouraged their use as the primary ingredient for the construction of families of quantum gauge theories. However, in these applications often the set of holonomy functions used is a discrete proper subset of the set of holonomy functions needed for the characterization theorem to hold. We show that the evaluation of a discrete set of holonomy functions does not characterize the bundle and does not constrain the connection modulo gauge appropriately. We exhibit a discrete set of functions of the connection and prove that in the abelian case their evaluation characterizes the bundle structure (up to equivalence), and constrains the connection modulo gauge up to "local details" ignored when working at a given scale. The main ingredient is the Lie algebra valued curvature function F_S (A) defined below. It covers the holonomy function in the sense that exp {F_S (A)} = Hol(l= partial S, A).
Magnetophoretic Induction of Root Curvature
Hasenstein, Karl H.
1997-01-01
The last year of the grant period concerned the consolidation of previous experiments to ascertain that the theoretical premise apply not just to root but also to shoots. In addition, we verified that high gradient magnetic fields do not interfere with regular cellular activities. Previous results have established that: (1) intracellular magnetophoresis is possible; and (2) HGMF lead to root curvature. In order to investigate whether HGMF affect the assembly and/or organization of structural proteins, we examined the arrangement of microtubules in roots exposed to HGMF. The cytoskeletal investigations were performed with fomaldehyde-fixed, nonembedded tissue segments that were cut with a vibratome. Microtubules (MTs) were stained with rat anti-yeast tubulin (YOL 1/34) and DTAF-labeled antibody against rat IgG. Microfilaments (MFs) were visualized by incubation in rhodamine-labeled phalloidin. The distribution and arrangement of both components of the cytoskeleton were examined with a confocal microscope. Measurements of growth rates and graviresponse were done using a video-digitizer. Since HGMF repel diamagnetic substances including starch-filled amyloplasts and most The second aspect of the work includes studies of the effect of cytoskeletal inhibitors on MTs and MFs. The analysis of the effect of micotubular inhibitors on the auxin transport in roots showed that there is very little effect of MT-depolymerizing or stabilizing drugs on auxin transport. This is in line with observations that application of such drugs is not immediately affecting the graviresponsiveness of roots.
Programming curvature using origami tessellations
Dudte, Levi H.; Vouga, Etienne; Tachi, Tomohiro; Mahadevan, L.
2016-05-01
Origami describes rules for creating folded structures from patterns on a flat sheet, but does not prescribe how patterns can be designed to fit target shapes. Here, starting from the simplest periodic origami pattern that yields one-degree-of-freedom collapsible structures--we show that scale-independent elementary geometric constructions and constrained optimization algorithms can be used to determine spatially modulated patterns that yield approximations to given surfaces of constant or varying curvature. Paper models confirm the feasibility of our calculations. We also assess the difficulty of realizing these geometric structures by quantifying the energetic barrier that separates the metastable flat and folded states. Moreover, we characterize the trade-off between the accuracy to which the pattern conforms to the target surface, and the effort associated with creating finer folds. Our approach enables the tailoring of origami patterns to drape complex surfaces independent of absolute scale, as well as the quantification of the energetic and material cost of doing so.
The curvature of semidirect product groups associated with two-component Hunter-Saxton systems
Kohlmann, Martin
2011-06-01
In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its μ-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group Diff( S) with a space of scalar functions on S we show that both equations are locally well posed. The main result of this paper is that the sectional curvature associated with the 2HS is constant and positive and that 2µHS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in Escher et al (2011 J. Geom. Phys. 61 436-52).
The intrinsic curvature of thermodynamic potentials for black holes with critical points
Dolan, Brian P
2015-01-01
The geometry of thermodynamic state space is studied for asymptotically anti-de Sitter black holes in D-dimensional space times. Convexity of thermodynamic potentials and the analytic structure of the response functions is analysed. The thermodynamic potentials can be used to define a metric on the space of thermodynamic variables and two commonly used such metrics are the Weinhold metric, derived from the internal energy, and the Ruppeiner metric, derived from the entropy. The intrinsic curvature of these metrics is calculated for charged and for rotating black holes and it is shown that the curvature diverges when heat capacities diverge but, contrary to general expectations, the singularities in the Ricci scalars do not reflect the critical behaviour. When a cosmological constant is included as a state space variable it can be interpreted as a pressure and the thermodynamically conjugate variable as a thermodynamic volume. The geometry of the resulting extended thermodynamic state space is also studied, in...
The curvature of semidirect product groups associated with two-component Hunter-Saxton systems
Energy Technology Data Exchange (ETDEWEB)
Kohlmann, Martin, E-mail: kohlmann@ifam.uni-hannover.de [Institute for Applied Mathematics, University of Hannover, D-30167 Hannover (Germany)
2011-06-03
In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its {mu}-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group Diff(S) with a space of scalar functions on S we show that both equations are locally well posed. The main result of this paper is that the sectional curvature associated with the 2HS is constant and positive and that 2{mu}HS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in Escher et al (2011 J. Geom. Phys. 61 436-52).
Graviscalars from higher-dimensional metrics and curvature-Higgs mixing
Giudice, Gian Francesco; Wells, J D; Giudice, Gian F.; Rattazzi, Riccardo; Wells, James D.
2001-01-01
We investigate the properties of scalar fields arising from gravity propagating in extra dimensions. In the scenario of large extra dimensions, proposed by Arkani-Hamed, Dimopoulos and Dvali (1998), graviscalar Kaluza-Klein excitations are less important than the spin-2 counterparts in most processes. However, there are important exceptions. The Higgs boson can mix to these particles by coupling to the Ricci scalar. Because of the large number of states involved, this mixing leads, in practice, to a sizeable invisible width for the Higgs. In the Randall-Sundrum scenario, the only graviscalar is the radion. It can be produced copiously at hadron colliders by virtue of its enhanced coupling to two gluons through the trace anomaly of QCD. We study both the production and decay of the radion, and compare it to the Standard Model Higgs boson. Furthermore, we find that radion detectability depends crucially on the curvature-Higgs boson mixing parameter. (29 refs).
Soldea, Octavian; Elber, Gershon; Rivlin, Ehud
2006-02-01
This paper presents a method to globally segment volumetric images into regions that contain convex or concave (elliptic) iso-surfaces, planar or cylindrical (parabolic) iso-surfaces, and volumetric regions with saddle-like (hyperbolic) iso-surfaces, regardless of the value of the iso-surface level. The proposed scheme relies on a novel approach to globally compute, bound, and analyze the Gaussian and mean curvatures of an entire volumetric data set, using a trivariate B-spline volumetric representation. This scheme derives a new differential scalar field for a given volumetric scalar field, which could easily be adapted to other differential properties. Moreover, this scheme can set the basis for more precise and accurate segmentation of data sets targeting the identification of primitive parts. Since the proposed scheme employs piecewise continuous functions, it is precise and insensitive to aliasing.
Gravitational induced particle production through a nonminimal curvature-matter coupling
Harko, Tiberiu; Mimoso, José P; Pavón, Diego
2015-01-01
We consider the possibility of a gravitationally induced particle production through the mechanism of a nonminimal curvature-matter coupling. An interesting feature of this gravitational theory is that the divergence of the energy-momentum tensor is nonzero. As a first step in our study we reformulate the model in terms of an equivalent scalar-tensor theory, with two arbitrary potentials. By using the formalism of open thermodynamic systems, we interpret the energy balance equations in this gravitational theory from a thermodynamic point of view, as describing irreversible matter creation processes. The particle number creation rates, the creation pressure, and the entropy production rates are explicitly obtained as functions of the scalar field and its potentials, as well as of the matter Lagrangian. The temperature evolution laws of the newly created particles are also obtained. The cosmological implications of the model are briefly investigated, and it is shown that the late-time cosmic acceleration may be...
Pezzaglia, W M
1997-01-01
A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted to represent internal structure of matter (e.g. classical or quantum spin). The generalized Dirac operator must now include differentiation with respect to these higher order geometric coordinates. In a Riemann space, where the magnitude and rank of geometric objects are preserved under displacement, these new terms modify the geodesics. One possible physical interpretation is natural coupling of the classical spin to linear motion, providing a new derivation of the Papapetrou equations. A generalized curvature is proposed for the Clifford manifold in which the connection does not preserve the rank of a multivector under parallel transport, e.g. a vector may be ``rotated'' into a scalar.
Curvatures and potential of M-theory in D=4 with fluxes and twist
D'Auria, R; Trigiante, M
2005-01-01
We give the curvatures of the free differential algebra (FDA) of M--theory compactified to D=4 on a twisted seven--torus with the 4--form flux switched on. Two formulations are given, depending on whether the 1--form field strengths of the scalar fields (originating from the 3--form gauge field $\\hat{A}^{(3)}$) are included or not in the FDA. We also give the bosonic equations of motion and discuss at length the scalar potential which emerges in this type of compactifications. For flat groups we show the equivalence of this potential with a dual formulation of the theory which has the full $\\rE_{7(7)}$ symmetry.
On different curvatures of spheres in Funk geometry
Olin, Eugeny A
2011-01-01
We compute the series expansions for the normal curvatures of hyperspheres, the Finsler and Rund curvatures of circles in Funk geometry as the radii tend to infinity. These three curvatures are different at infinity in Funk geometry.
Constrained inflaton due to a complex scalar
Energy Technology Data Exchange (ETDEWEB)
Budhi, Romy H. S. [Physics Department, Gadjah Mada University,Yogyakarta 55281 (Indonesia); Institute for Theoretical Physics, Kanazawa University,Kanazawa 920-1192 (Japan); Kashiwase, Shoichi; Suematsu, Daijiro [Institute for Theoretical Physics, Kanazawa University,Kanazawa 920-1192 (Japan)
2015-09-14
We reexamine inflation due to a constrained inflaton in the model of a complex scalar. Inflaton evolves along a spiral-like valley of special scalar potential in the scalar field space just like single field inflation. Sub-Planckian inflaton can induce sufficient e-foldings because of a long slow-roll path. In a special limit, the scalar spectral index and the tensor-to-scalar ratio has equivalent expressions to the inflation with monomial potential φ{sup n}. The favorable values for them could be obtained by varying parameters in the potential. This model could be embedded in a certain radiative neutrino mass model.
Higher curvature effects in Arkani-Hamed-Dimopoulos-Dvali and Randall-Sundrum models
Indian Academy of Sciences (India)
T G Rizzo
2007-11-01
We explore the collider phenomenology of terascale extra-dimensional models with gravitational actions that contain higher curvature terms. In particular, we examine how the classic collider signatures of the models of Arkani-Hamed, Dimopoulos and Dvali (ADD) and of Randall and Sundrum (RS) are altered by these modifications to the usual Einstein-Hilbert (EH) action. Not only are the detailed signatures for gravitationally induced processes altered but new contributions are found to arise due to the existence of additional scalar Kaluza-Klein (KK) states in the spectrum.
Geometrical order-of-magnitude estimates for spatial curvature in realistic models of the Universe
Buchert, Thomas; van Elst, Henk; 10.1007/s10714-009-0828-4
2009-01-01
The thoughts expressed in this article are based on remarks made by J\\"urgen Ehlers at the Albert-Einstein-Institut, Golm, Germany in July 2007. The main objective of this article is to demonstrate, in terms of plausible order-of-magnitude estimates for geometrical scalars, the relevance of spatial curvature in realistic models of the Universe that describe the dynamics of structure formation since the epoch of matter-radiation decoupling. We introduce these estimates with a commentary on the use of a quasi-Newtonian metric form in this context.
Effects of curvature-Higgs coupling on electroweak fine-tuning
Energy Technology Data Exchange (ETDEWEB)
Demir, Durmuş Ali, E-mail: demir@physics.iztech.edu.tr
2014-06-02
It is shown that nonminimal coupling between the Standard Model (SM) Higgs field and spacetime curvature, present already at the renormalizable level, can be fine-tuned to stabilize the electroweak scale against power-law ultraviolet divergences. The nonminimal coupling acts as an extrinsic stabilizer with no effect on the loop structure of the SM, if gravity is classical. This novel fine-tuning scheme, which could also be interpreted within Sakharov's induced gravity approach, works neatly in extensions of the SM involving additional Higgs fields or singlet scalars.
Three-dimensional black holes with conformally coupled scalar and gauge fields
Cardenas, Marcela; Martinez, Cristian
2014-01-01
We consider three-dimensional gravity with negative cosmological constant in the presence of a scalar and an Abelian gauge field. Both fields are conformally coupled to gravity, the scalar field through a nonminimal coupling with the curvature and the gauge field by means of a Lagrangian given by a power of the Maxwell one. A sixth-power self-interaction potential, which does not spoil conformal invariance is also included in the action. Using a circularly symmetric ansatz, we obtain black hole solutions dressed with the scalar and gauge fields, which are regular on and outside the event horizon. These charged hairy black holes are asymptotically anti-de Sitter spacetimes. The mass and the electric charge are computed by using the Regge-Teitelboim Hamiltonian approach. If both leading and subleading terms of the asymptotic condition of the scalar field are present, a boundary condition that functionally relates them is required for determining the mass. Since the asymptotic form of the scalar field solution i...
Exact charged black-hole solutions in D-dimensional f(T) gravity: torsion vs curvature analysis
Capozziello, Salvatore; Saridakis, Emmanuel N; Vasquez, Yerko
2012-01-01
We extract exact charged black-hole solutions with flat transverse sections in the framework of D-dimensional Maxwell-f(T) gravity, and we analyze the singularities and horizons based on both torsion and curvature invariants. Interestingly enough, we find that in some particular solution subclasses there appear more singularities in the curvature scalars than in the torsion ones. This difference disappears in the uncharged case, or in the case where f(T) gravity becomes the usual linear-in-T teleparallel gravity, that is General Relativity. Curvature and torsion invariants behave very differently when matter fields are present, and thus f(R) gravity and f(T) gravity exhibit different features and cannot be directly re-casted each other.
Dai, Yimian; Wu, Yiquan; Song, Yu; Guo, Jun
2017-03-01
To further enhance the small targets and suppress the heavy clutters simultaneously, a robust non-negative infrared patch-image model via partial sum minimization of singular values is proposed. First, the intrinsic reason behind the undesirable performance of the state-of-the-art infrared patch-image (IPI) model when facing extremely complex backgrounds is analyzed. We point out that it lies in the mismatching of IPI model's implicit assumption of a large number of observations with the reality of deficient observations of strong edges. To fix this problem, instead of the nuclear norm, we adopt the partial sum of singular values to constrain the low-rank background patch-image, which could provide a more accurate background estimation and almost eliminate all the salient residuals in the decomposed target image. In addition, considering the fact that the infrared small target is always brighter than its adjacent background, we propose an additional non-negative constraint to the sparse target patch-image, which could not only wipe off more undesirable components ulteriorly but also accelerate the convergence rate. Finally, an algorithm based on inexact augmented Lagrange multiplier method is developed to solve the proposed model. A large number of experiments are conducted demonstrating that the proposed model has a significant improvement over the other nine competitive methods in terms of both clutter suppressing performance and convergence rate.
Wright, L.; Coddington, O.; Pilewskie, P.
2015-12-01
Current challenges in Earth remote sensing require improved instrument spectral resolution, spectral coverage, and radiometric accuracy. Hyperspectral instruments, deployed on both aircraft and spacecraft, are a growing class of Earth observing sensors designed to meet these challenges. They collect large amounts of spectral data, allowing thorough characterization of both atmospheric and surface properties. The higher accuracy and increased spectral and spatial resolutions of new imagers require new numerical approaches for processing imagery and separating surface and atmospheric signals. One potential approach is source separation, which allows us to determine the underlying physical causes of observed changes. Improved signal separation will allow hyperspectral instruments to better address key science questions relevant to climate change, including land-use changes, trends in clouds and atmospheric water vapor, and aerosol characteristics. In this work, we investigate a Non-negative Matrix Factorization (NMF) method for the separation of atmospheric and land surface signal sources. NMF offers marked benefits over other commonly employed techniques, including non-negativity, which avoids physically impossible results, and adaptability, which allows the method to be tailored to hyperspectral source separation. We adapt our NMF algorithm to distinguish between contributions from different physically distinct sources by introducing constraints on spectral and spatial variability and by using library spectra to inform separation. We evaluate our NMF algorithm with simulated hyperspectral images as well as hyperspectral imagery from several instruments including, the NASA Airborne Visible/Infrared Imaging Spectrometer (AVIRIS), NASA Hyperspectral Imager for the Coastal Ocean (HICO) and National Ecological Observatory Network (NEON) Imaging Spectrometer.
Right thoracic curvature in the normal spine
Directory of Open Access Journals (Sweden)
Masuda Keigo
2011-01-01
Full Text Available Abstract Background Trunk asymmetry and vertebral rotation, at times observed in the normal spine, resemble the characteristics of adolescent idiopathic scoliosis (AIS. Right thoracic curvature has also been reported in the normal spine. If it is determined that the features of right thoracic side curvature in the normal spine are the same as those observed in AIS, these findings might provide a basis for elucidating the etiology of this condition. For this reason, we investigated right thoracic curvature in the normal spine. Methods For normal spinal measurements, 1,200 patients who underwent a posteroanterior chest radiographs were evaluated. These consisted of 400 children (ages 4-9, 400 adolescents (ages 10-19 and 400 adults (ages 20-29, with each group comprised of both genders. The exclusion criteria were obvious chest and spinal diseases. As side curvature is minimal in normal spines and the range at which curvature is measured is difficult to ascertain, first the typical curvature range in scoliosis patients was determined and then the Cobb angle in normal spines was measured using the same range as the scoliosis curve, from T5 to T12. Right thoracic curvature was given a positive value. The curve pattern was organized in each collective three groups: neutral (from -1 degree to 1 degree, right (> +1 degree, and left ( Results In child group, Cobb angle in left was 120, in neutral was 125 and in right was 155. In adolescent group, Cobb angle in left was 70, in neutral was 114 and in right was 216. In adult group, Cobb angle in left was 46, in neutral was 102 and in right was 252. The curvature pattern shifts to the right side in the adolescent group (p Conclusions Based on standing chest radiographic measurements, a right thoracic curvature was observed in normal spines after adolescence.
Pavlov, Y V
2001-01-01
One derived expressions for the vacuum mean values of energy-momentum tensor of the scalar field with arbitrary relation to curvature in N-dimensional quasi-euclidean space-time for vacuum. One generalized n-wave procedure for multidimensional spaces. One calculated all counter-members for N=5 and for a conformal scalar field in N=6, 7. One determined the geometric structure of three first counter-members for N-dimensional spaces. All subtractions in 4-dimensional space-time and 3 first subtractions in multidimensional spaces are shown to correspond to renormalization of constants of priming and gravitational Lagrangian
CP violating scalar Dark Matter
Cordero-Cid, A; Keus, V; King, S F; Moretti, S; Rojas, D; Sokołowska, D
2016-01-01
We study an extension of the Standard Model (SM) in which two copies of the SM scalar $SU(2)$ doublet which do not acquire a Vacuum Expectation Value (VEV), and hence are \\textit{inert}, are added to the scalar sector. We allow for CP-violation in the \\textit{inert} sector, where the lightest \\textit{inert} state is protected from decaying to SM particles through the conservation of a $Z_2$ symmetry. The lightest neutral particle from the \\textit{inert} sector, which has a mixed CP-charge due to CP-violation, is hence a Dark Matter (DM) candidate. We discuss the new regions of DM relic density opened up by CP-violation, and compare our results to the CP-conserving limit and the Inert Doublet Model (IDM). We constrain the parameter space of the CP-violating model using recent results from the Large Hadron Collider (LHC) and DM direct and indirect detection experiments.
Scalar Glueball Mixing and Decay
Burakovsky, L; Burakovsky, Leonid; Page, Philip R.
1999-01-01
We provide the first explanation of the counter-intuitive scalar glueball couplings to pseudoscalar mesons found in lattice QCD and predict hitherto uncalculated decay modes. Significant a_1 pi and (pi pi)_S (pi pi)_S couplings are found. We demonstrate the equivalence of linear and quadratic mass matrices for glueball-quarkonium mixing. The equivalence of formalisms which deal with a glueball-quarkonium basis and only a quarkonium basis is demonstrated. We show that the f_0(1500) is not the heaviest state arising from glueball-quarkonium mixing for a glueball mass consistent with lattice QCD. The masses and couplings of scalar mesons, as well as their valence content, are calculated.
Scalar-tensor linear inflation
Artymowski, Michal
2016-01-01
We investigate two approaches to non minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for any form of the non-minimal coupling to gravity of the form of $f(\\varphi)R/2$; b) the particle physics approach, where we motivate the form of the Jordan frame potential by the loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced inflation, but instead of the Starobinsky attractor they lead to the linear inflation in the strong coupling limit.
Scalar-tensor linear inflation
Artymowski, Michał; Racioppi, Antonio
2017-04-01
We investigate two approaches to non-minimally coupled gravity theories which present linear inflation as attractor solution: a) the scalar-tensor theory approach, where we look for a scalar-tensor theory that would restore results of linear inflation in the strong coupling limit for a non-minimal coupling to gravity of the form of f(varphi)R/2; b) the particle physics approach, where we motivate the form of the Jordan frame potential by loop corrections to the inflaton field. In both cases the Jordan frame potentials are modifications of the induced gravity inflationary scenario, but instead of the Starobinsky attractor they lead to linear inflation in the strong coupling limit.
Scalar Fields in Particle Physics
Pedro, Leonardo
2016-01-01
Extending the scalar sector helps in studying the Higgs mechanism and some Standard Model problems. We implement the correspondence between the gauge-dependent elementary states and the non-perturbative non-abelian gauge-invariant asymptotic states, necessary to study the non-perturbative phenomenology of two-Higgs-doublet models. The Flavour and CP violation in experimental data follows a hierarchical pattern, accounted by the Standard Model. We define the Minimal Flavour Violation condition with six spurions in effective field theories, implying Flavour and CP violation entirely dependent on the fermion mixing matrices but independent of the fermion masses hierarchy; it is renormalization-group invariant. We study the phenomenology of renormalizable two-Higgs-doublet models which verify the defined condition as consequence of a symmetry; new light physical scalars, mediating Flavour Changing Neutral Currents, are allowed by flavour data without flavour coefficients beyond the Standard Model; we tested the m...
CP violating scalar Dark Matter
Energy Technology Data Exchange (ETDEWEB)
Cordero-Cid, A.; Hernández-Sánchez, J. [Instituto de Física and Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Apdo. Postal 542, C.P. 72570 Puebla (Mexico); Keus, V. [Department of Physics and Helsinki Institute of Physics, University of Helsinki, Gustaf Hallstromin katu 2, Helsinki, FIN-00014 (Finland); School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); King, S.F. [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Moretti, S. [School of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ (United Kingdom); Particle Physics Department, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX (United Kingdom); Rojas, D. [Instituto de Física and Facultad de Ciencias de la Electrónica, Benemérita Universidad Autónoma de Puebla, Apdo. Postal 542, C.P. 72570 Puebla (Mexico); Sokołowska, D. [Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw (Poland)
2016-12-05
We study an extension of the Standard Model (SM) in which two copies of the SM scalar SU(2) doublet which do not acquire a Vacuum Expectation Value (VEV), and hence are inert, are added to the scalar sector. We allow for CP-violation in the inert sector, where the lightest inert state is protected from decaying to SM particles through the conservation of a Z{sub 2} symmetry. The lightest neutral particle from the inert sector, which has a mixed CP-charge due to CP-violation, is hence a Dark Matter (DM) candidate. We discuss the new regions of DM relic density opened up by CP-violation, and compare our results to the CP-conserving limit and the Inert Doublet Model (IDM). We constrain the parameter space of the CP-violating model using recent results from the Large Hadron Collider (LHC) and DM direct and indirect detection experiments.
Scalar Trapping and Saxion Cosmology
Moroi, Takeo; Nakayama, Kazunori; Takimoto, Masahiro
2013-01-01
We study in detail the dynamics of a scalar field in thermal bath with symmetry breaking potential. In particular, we focus on the process of trapping of a scalar field at an enhanced symmetry point through the thermal/non-thermal particle production, taking into account the interactions of produced particles with the standard model particles. As an explicit example, we revisit the saxion dynamics with an initial amplitude much larger than the Peccei-Quinn scale and show that the saxion trapping phenomenon happens for the most cases and it often leads to thermal inflation. We also study the saxion dynamics after thermal inflation, and it is shown that thermal dissipation effect on the saxion can relax the axion overproduction problem from the saxion decay.
Variations on Slavnov's scalar product
Foda, O
2012-01-01
We consider the rational six-vertex model on an L-by-L lattice with domain wall boundary conditions and restrict N parallel-line rapidities, N < L/2, to satisfy length-L XXX spin-1/2 chain Bethe equations. We show that the partition function is an (L-2N)-parameter extension of Slavnov's scalar product of a Bethe eigenstate and a generic state, with N magnons each, on a length-L XXX spin-1/2 chain. Decoupling the extra parameters, we obtain a third determinant expression for the scalar product, where the first is due to Slavnov [1], and the second is due to Kostov and Matsuo [2]. We show that the new determinant is a discrete KP tau-function in the inhomogeneities, and consequently that tree-level N = 4 SYM structure constants that are known to be determinants, remain determinants at 1-loop level.
Scalar top study: Detector optimization
Indian Academy of Sciences (India)
C Milsténe; A Sopczak
2007-11-01
A vertex detector concept of the linear collider flavour identification (LCFI) collaboration, which studies pixel detectors for heavy quark flavour identification, has been implemented in simulations for -quark tagging in scalar top studies. The production and decay of scalar top quarks (stops) is particularly interesting for the development of the vertex detector as only two -quarks and missing energy (from undetected neutralinos) are produced for light stops. Previous studies investigated the vertex detector design in scenarios with large mass differences between stop and neutralino, corresponding to large visible energy in the detector. In this study we investigate the tagging performance dependence on the vertex detector design in a scenario with small visible energy for the international linear collider (ILC).
Abedi, Habib
2016-01-01
Multiple field models of inflation exhibit new features than single field models. In this work, we study the hierarchy of parameters based on Hubble expansion rate in curved field space and derive the system of flow equations that describe their evolution. Then we focus on obtaining derivatives of number of $e$-folds with respect to scalar fields during inflation and at hypersurface of the end of inflation.
Random scalar fields and hyperuniformity
Ma, Zheng; Torquato, Salvatore
2017-06-01
Disordered many-particle hyperuniform systems are exotic amorphous states of matter that lie between crystals and liquids. Hyperuniform systems have attracted recent attention because they are endowed with novel transport and optical properties. Recently, the hyperuniformity concept has been generalized to characterize two-phase media, scalar fields, and random vector fields. In this paper, we devise methods to explicitly construct hyperuniform scalar fields. Specifically, we analyze spatial patterns generated from Gaussian random fields, which have been used to model the microwave background radiation and heterogeneous materials, the Cahn-Hilliard equation for spinodal decomposition, and Swift-Hohenberg equations that have been used to model emergent pattern formation, including Rayleigh-Bénard convection. We show that the Gaussian random scalar fields can be constructed to be hyperuniform. We also numerically study the time evolution of spinodal decomposition patterns and demonstrate that they are hyperuniform in the scaling regime. Moreover, we find that labyrinth-like patterns generated by the Swift-Hohenberg equation are effectively hyperuniform. We show that thresholding (level-cutting) a hyperuniform Gaussian random field to produce a two-phase random medium tends to destroy the hyperuniformity of the progenitor scalar field. We then propose guidelines to achieve effectively hyperuniform two-phase media derived from thresholded non-Gaussian fields. Our investigation paves the way for new research directions to characterize the large-structure spatial patterns that arise in physics, chemistry, biology, and ecology. Moreover, our theoretical results are expected to guide experimentalists to synthesize new classes of hyperuniform materials with novel physical properties via coarsening processes and using state-of-the-art techniques, such as stereolithography and 3D printing.
Quantum gravity and scalar fields
Energy Technology Data Exchange (ETDEWEB)
Mackay, Paul T. [School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU (United Kingdom); Toms, David J., E-mail: d.j.toms@newcastle.ac.u [School of Mathematics and Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU (United Kingdom)
2010-02-15
In this Letter we consider the quantization of a scalar field coupled to gravity at one loop order. We investigate the divergences appearing in the mass (i.e. phi{sup 2}) term in the effective action. We use the Vilkovisky-DeWitt effective action technique which guarantees that the result is gauge invariant as well as gauge condition independent in contrast to traditional calculations. Our final result is to identify the complete pole part of the effective action.
Foda, O; Zuparic, M
2009-01-01
Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP tau function. This leads to a correspondence between the eigenstates and points on Sato's Grassmannian. Each of these points is a function of the rapidities of the corresponding eigenstate, the inhomogeneity variables of the spin chain and the crossing parameter.
Energy Technology Data Exchange (ETDEWEB)
Foda, O. [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)], E-mail: foda@ms.unimelb.edu.au; Wheeler, M. [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)], E-mail: mwheeler@ms.unimelb.edu.au; Zuparic, M. [Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010 (Australia)], E-mail: mzup@ms.unimelb.edu.au
2009-10-21
Using a Jacobi-Trudi-type identity, we show that the scalar product of a general state and a Bethe eigenstate in a finite-length XXZ spin-1/2 chain is (a restriction of) a KP {tau} function. This leads to a correspondence between the eigenstates and points on Sato's Grassmannian. Each of these points is a function of the rapidities of the corresponding eigenstate, the inhomogeneity variables of the spin chain and the crossing parameter.
Magnetic curvature effects on plasma interchange turbulence
Li, B.; Liao, X.; Sun, C. K.; Ou, W.; Liu, D.; Gui, G.; Wang, X. G.
2016-06-01
The magnetic curvature effects on plasma interchange turbulence and transport in the Z-pinch and dipole-like systems are explored with two-fluid global simulations. By comparing the transport levels in the systems with a different magnetic curvature, we show that the interchange-mode driven transport strongly depends on the magnetic geometry. For the system with large magnetic curvature, the pressure and density profiles are strongly peaked in a marginally stable state and the nonlinear evolution of interchange modes produces the global convective cells in the azimuthal direction, which lead to the low level of turbulent convective transport.
A new formula of the Gravitational Curvature for the prism
Grazia D'Urso, Maria
2017-04-01
Gravitational Curvatures (GC) are the components of the third-order gravitational tensor and physically represent the rate of change of the gravity gradient. While scalar, vector and second-order tensor quantities of the Earth's gravitational field have extensively been studied and their properties have been well understood [1], the first successful terrestrial measurements of the third-order vertical gravitational gradients have been recently performed in [2] by atom interferometry sensors in laboratory environment. Possible benefits of the airborne third-order gravitational gradients for exploration geophysics are discussed in [3] while Brieden et al. (2010) [4] have proposed a new satellite mission called OPTical Interferometry for global Mass change detection from space (OPTIMA) sensing the third-order gravitational gradients in space. Moreover, exploitation of GC for modelling the Earth's gravitational field has been object of recent studies [5-7]. We extend the approach presented by the author in previous papers [8-10] by evaluating the algebraic expression of the third-order gravitational tensor for a prism. Comparisons with previous results [11-12] are also included. [1] Freeden W, Schreiner M (2009) Spherical functions of mathematical geosciences. A scalar, vectorial, and tensorial setup. In: Advances in geophysical and environmental mechanics and mathematics. Springer, Berlin [2] Rosi G, Cacciapuoti L, Sorrentino F, Menchetti M, Prevedelli M, Tino GM (2015) Measurements of the gravity-field curvature by atom interferometry. Phys Rev Lett 114:013001 [3] Di Francesco D, Meyer T, Christensen A, FitzGerald D (2009) Gravity gradiometry - today and tomorrow. In: 11th SAGA Biennial technical meeting and exhibition, 13-18 September 2009, Switzerland, pp 80-83 [4] Brieden P, Müller J, Flury J, Heinzel G (2010) The mission OPTIMA - novelties and benefit. In: Geotechnologien science report No. 17, Potsdam, pp 134-139 [5] Šprlák M, Novák P (2015) Integral
Scalar mesostatic field with regard for gravitational effects
Fisher, I Z
1948-01-01
(Foreword by translator.) The aim of present translation is to clarify the historically important question who was the pioneer in obtaining of exact static solutions of Einstein equations minimally coupled with scalar field. Usually, people cite the works by Janis, Newman, Winicour (Phys. Rev. Lett. 20 (1968) 878) and others authors whereas it is clear that JNW rediscovered (in other coordinates) the Fisher's solution which was obtained 20 years before, in 1947. Regrettably, up to now I continue to meet many papers (even very fresh ones) whose authors evidently do not know about the Fisher's work, so I try to remove this gap by virtue of present translation and putting it into the LANL e-print archive. (Original Abstract.) It is considered the scalar mesostatic field of a point source with the regard for spacetime curvature caused by this field. For the field with $\\mass = 0$ the exact solution of Einstein equations was obtained. It was demonstrated that at small distance from a source the gravitational effec...
A simplified approach to general scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Bloomfield, Jolyon, E-mail: jkb84@cornell.edu [Center for Radiophysics and Space Research, Cornell University, Ithaca, New York, 14853 (United States)
2013-12-01
The most general covariant action describing gravity coupled to a scalar field with only second order equations of motion, Horndeski's theory (also known as ''Generalized Galileons''), provides an all-encompassing model in which single scalar dark energy models may be constrained. However, the generality of the model makes it cumbersome to manipulate. In this paper, we demonstrate that when considering linear perturbations about a Friedmann-Robertson-Walker background, the theory is completely specified by only six functions of time, two of which are constrained by the background evolution. We utilise the ideas of the Effective Field Theory of Inflation/Dark Energy to explicitly construct these six functions of time in terms of the free functions appearing in Horndeski's theory. These results are used to investigate the behavior of the theory in the quasistatic approximation. We find that only four functions of time are required to completely specify the linear behavior of the theory in this limit, which can further be reduced if the background evolution is fixed. This presents a significantly reduced parameter space from the original presentation of Horndeski's theory, giving hope to the possibility of constraining the parameter space. This work provides a cross-check for previous work on linear perturbations in this theory, and also generalizes it to include spatial curvature.
Curvature constraints from Large Scale Structure
Di Dio, Enea; Raccanelli, Alvise; Durrer, Ruth; Kamionkowski, Marc; Lesgourgues, Julien
2016-01-01
We modified the CLASS code in order to include relativistic galaxy number counts in spatially curved geometries; we present the formalism and study the effect of relativistic corrections on spatial curvature. The new version of the code is now publicly available. Using a Fisher matrix analysis, we investigate how measurements of the spatial curvature parameter $\\Omega_K$ with future galaxy surveys are affected by relativistic effects, which influence observations of the large scale galaxy distribution. These effects include contributions from cosmic magnification, Doppler terms and terms involving the gravitational potential. As an application, we consider angle and redshift dependent power spectra, which are especially well suited for model independent cosmological constraints. We compute our results for a representative deep, wide and spectroscopic survey, and our results show the impact of relativistic corrections on the spatial curvature parameter estimation. We show that constraints on the curvature para...
Generalized Strong Curvature Singularities and Cosmic Censorship
Rudnicki, W; Kondracki, W
2002-01-01
A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.
Curvature of Indoor Sensor Network: Clustering Coefficient
Directory of Open Access Journals (Sweden)
2009-03-01
Full Text Available We investigate the geometric properties of the communication graph in realistic low-power wireless networks. In particular, we explore the concept of the curvature of a wireless network via the clustering coefficient. Clustering coefficient analysis is a computationally simplified, semilocal approach, which nevertheless captures such a large-scale feature as congestion in the underlying network. The clustering coefficient concept is applied to three cases of indoor sensor networks, under varying thresholds on the link packet reception rate (PRR. A transition from positive curvature (“meshed” network to negative curvature (“core concentric” network is observed by increasing the threshold. Even though this paper deals with network curvature per se, we nevertheless expand on the underlying congestion motivation, propose several new concepts (network inertia and centroid, and finally we argue that greedy routing on a virtual positively curved network achieves load balancing on the physical network.
Holomorphic curvature of complex Finsler submanifolds
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Let M be a complex n-dimensional manifold endowed with a strongly pseudoconvex complex Finsler metric F. Let M be a complex m-dimensional submanifold of M, which is endowed with the induced complex Finsler metric F. Let D be the complex Rund connection associated with (M, F). We prove that (a) the holomorphic curvature of the induced complex linear connection on (M, F) and the holomorphic curvature of the intrinsic complex Rund connection ～* on (M, F) coincide; (b) the holomorphic curvature of ～* does not exceed the holomorphic curvature of D; (c) (M, F) is totally geodesic in (M, F) if and only if a suitable contraction of the second fundamental form B(·, ·) of (M, F) vanishes, i.e., B(χ, ι) = 0. Our proofs are mainly based on the Gauss, Codazzi and Ricci equations for (M, F).
Cosmological Attractor Models and Higher Curvature Supergravity
Cecotti, Sergio
2014-01-01
We study cosmological $\\alpha$-attractors in superconformal/supergravity models, where $\\alpha$ is related to the geometry of the moduli space. For $\\alpha=1$ attractors \\cite{Kallosh:2013hoa} we present a generalization of the previously known manifestly superconformal higher curvature supergravity model \\cite{Cecotti:1987sa}. The relevant standard 2-derivative supergravity with a minimum of two chiral multiplets is shown to be dual to a 4-derivative higher curvature supergravity, where in general one of the chiral superfields is traded for a curvature superfield. There is a degenerate case when both matter superfields become non-dynamical and there is only a chiral curvature superfield, pure higher derivative supergravity. Generic $\\alpha$-models \\cite{Kallosh:2013yoa} interpolate between the attractor point at $\\alpha=0$ and generic chaotic inflation models at large $\\alpha$, in the limit when the inflaton moduli space becomes flat. They have higher derivative duals with the same number of matter fields as...
Higher Curvature Supergravity, Supersymmetry Breaking and Inflation
Ferrara, Sergio
2014-01-01
In these lectures, after a short introduction to cosmology, we discuss the supergravity embedding of higher curvature models of inflation. The supergravity description of such models is presented for the two different formulations of minimal supergravity.
Curvature Gradient Driving Droplets in Fast Motion
Lv, Cunjing; Yin, Yajun; Tseng, Fan-gang; Zheng, Quanshui
2011-01-01
Earlier works found out spontaneous directional motion of liquid droplets on hydrophilic conical surfaces, however, not hydrophobic case. Here we show that droplets on any surface may take place spontaneous directional motion without considering contact angle property. The driving force is found to be proportional to the curvature gradient of the surface. Fast motion can be lead at surfaces with small curvature radii. The above discovery can help to create more effective transportation technology of droplets, and better understand some observed natural phenomena.
GDP growth and the yield curvature
DEFF Research Database (Denmark)
Møller, Stig Vinther
2014-01-01
This paper examines the forecastability of GDP growth using information from the term structure of yields. In contrast to previous studies, the paper shows that the curvature of the yield curve contributes with much more forecasting power than the slope of yield curve. The yield curvature also...... predicts bond returns, implying a common element to time-variation in expected bond returns and expected GDP growth....
Gravity localization in non-minimally coupled scalar thick braneworlds with a Gauss-Bonnet term
Energy Technology Data Exchange (ETDEWEB)
Malagon-Morejon, D; Quiros, I [Division de Ciencias e IngenierIa de la Universidad de Guanajuato, A.P. 150, 37150, Leon, Guanajuato (Mexico); Herrera-Aguilar, A, E-mail: malagon@ifm.umich.mx, E-mail: herrera@ifm.umich.mx, E-mail: iquiros@fisica.ugto.mx
2011-04-01
We consider a warped five-dimensional thick braneworld with a four-dimensional Poincare invariant space-time in the framework of scalar matter non-minimally coupled to gravity plus a Gauss-Bonnet term in the bulk. Scalar field and higher curvature corrections to the background equations as well as the perturbed equations are shown. A relationship between 4-dimensional and 5-dimensional Planck masses is studied in general terms. By imposing finiteness of the 4-dimensional Planck mass and regularity of the geometry, the localization properties of the tensor modes of the first order perturbed geometry are analized for an important class of solutions motivated by models with scalar fields which are minimally coupled to gravity. In order to study the gravity localization properties for this model, the normalizability condition for the lowest level of the tensor fluctuations is analized. We see that for the class of solutions examined, gravity in 4 dimensions is recovered if the curvature invariants are regular and Planck masses are finite.
Nonadditive Compositional Curvature Energetics of Lipid Bilayers
Sodt, A. J.; Venable, R. M.; Lyman, E.; Pastor, R. W.
2016-09-01
The unique properties of the individual lipids that compose biological membranes together determine the energetics of the surface. The energetics of the surface, in turn, govern the formation of membrane structures and membrane reshaping processes, and thus they will underlie cellular-scale models of viral fusion, vesicle-dependent transport, and lateral organization relevant to signaling. The spontaneous curvature, to the best of our knowledge, is always assumed to be additive. We describe observations from simulations of unexpected nonadditive compositional curvature energetics of two lipids essential to the plasma membrane: sphingomyelin and cholesterol. A model is developed that connects molecular interactions to curvature stress, and which explains the role of local composition. Cholesterol is shown to lower the number of effective Kuhn segments of saturated acyl chains, reducing lateral pressure below the neutral surface of bending and favoring positive curvature. The effect is not observed for unsaturated (flexible) acyl chains. Likewise, hydrogen bonding between sphingomyelin lipids leads to positive curvature, but only at sufficient concentration, below which the lipid prefers negative curvature.
Soelter, Jan; Schumacher, Jan; Spors, Hartwig; Schmuker, Michael
2014-09-01
Segmentation of functional parts in image series of functional activity is a common problem in neuroscience. Here we apply regularized non-negative matrix factorization (rNMF) to extract glomeruli in intrinsic optical signal (IOS) images of the olfactory bulb. Regularization allows us to incorporate prior knowledge about the spatio-temporal characteristics of glomerular signals. We demonstrate how to identify suitable regularization parameters on a surrogate dataset. With appropriate regularization segmentation by rNMF is more resilient to noise and requires fewer observations than conventional spatial independent component analysis (sICA). We validate our approach in experimental data using anatomical outlines of glomeruli obtained by 2-photon imaging of resting synapto-pHluorin fluorescence. Taken together, we show that rNMF provides a straightforward method for problem tailored source separation that enables reliable automatic segmentation of functional neural images, with particular benefit in situations with low signal-to-noise ratio as in IOS imaging.
DEFF Research Database (Denmark)
Mørup, Morten; Hansen, Lars Kai; Parnas, Josef;
2006-01-01
generalized to a parallel factor (PARAFAC) model to form a non-negative multi-way factorization (NMWF). While the NMF can examine subject specific activities the NMWF can effectively extract the most similar activities across subjects and or conditions. The methods are tested on a proprioceptive stimulus...... consisting of a weight change in a handheld load. While somatosensory gamma oscillations have previously only been evoked by electrical stimuli we hypothesized that a natural proprioceptive stimulus also would be able to evoke gamma oscillations. ITPC maxima were determined by visual inspection...... contralateral to stimulus side and additionally an unexpected 20Hz activity slightly lateralized in the frontal central region. Consequently, also proprioceptive stimuli are able to elicit evoked gamma activity....
Two pitfalls of BOLD fMRI magnitude-based neuroimage analysis: non-negativity and edge effect.
Chen, Zikuan; Calhoun, Vince D
2011-08-15
BOLD fMRI is accepted as a noninvasive imaging modality for neuroimaging and brain mapping. A BOLD fMRI dataset consists of magnitude and phase components. Currently, only the magnitude is used for neuroimage analysis. In this paper, we show that the fMRI-magnitude-based neuroimage analysis may suffer two pitfalls: one is that the magnitude is non-negative and cannot differentiate positive from negative BOLD activity; the other is an edge effect that may manifest as an edge enhancement or a spatial interior dip artifact at a local uniform BOLD region. We demonstrate these pitfalls via numeric simulations using a BOLD fMRI model and also via a phantom experiment. We also propose a solution by making use of the fMRI phase image, the counterpart of the fMRI magnitude.
Gauvin, Laetitia; Cattuto, Ciro
2014-01-01
The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computationa...
Directory of Open Access Journals (Sweden)
Sujoy Roy
2017-08-01
Full Text Available In this study, we developed and evaluated a novel text-mining approach, using non-negative tensor factorization (NTF, to simultaneously extract and functionally annotate transcriptional modules consisting of sets of genes, transcription factors (TFs, and terms from MEDLINE abstracts. A sparse 3-mode term × gene × TF tensor was constructed that contained weighted frequencies of 106,895 terms in 26,781 abstracts shared among 7,695 genes and 994 TFs. The tensor was decomposed into sub-tensors using non-negative tensor factorization (NTF across 16 different approximation ranks. Dominant entries of each of 2,861 sub-tensors were extracted to form term–gene–TF annotated transcriptional modules (ATMs. More than 94% of the ATMs were found to be enriched in at least one KEGG pathway or GO category, suggesting that the ATMs are functionally relevant. One advantage of this method is that it can discover potentially new gene–TF associations from the literature. Using a set of microarray and ChIP-Seq datasets as gold standard, we show that the precision of our method for predicting gene–TF associations is significantly higher than chance. In addition, we demonstrate that the terms in each ATM can be used to suggest new GO classifications to genes and TFs. Taken together, our results indicate that NTF is useful for simultaneous extraction and functional annotation of transcriptional regulatory networks from unstructured text, as well as for literature based discovery. A web tool called Transcriptional Regulatory Modules Extracted from Literature (TREMEL, available at http://binf1.memphis.edu/tremel, was built to enable browsing and searching of ATMs.
Directory of Open Access Journals (Sweden)
Laetitia Gauvin
Full Text Available The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule.
Yun, Younghee; Jung, Wonmo; Kim, Hyunho; Jang, Bo-Hyoung; Kim, Min-Hee; Noh, Jiseong; Ko, Seong-Gyu; Choi, Inhwa
2017-08-01
Syndrome differentiation (SD) results in a diagnostic conclusion based on a cluster of concurrent symptoms and signs, including pulse form and tongue color. In Korea, there is a strong interest in the standardization of Traditional Medicine (TM). In order to standardize TM treatment, standardization of SD should be given priority. The aim of this study was to explore the SD, or symptom clusters, of patients with atopic dermatitis (AD) using non-negative factorization methods and k-means clustering analysis. We screened 80 patients and enrolled 73 eligible patients. One TM dermatologist evaluated the symptoms/signs using an existing clinical dataset from patients with AD. This dataset was designed to collect 15 dermatologic and 18 systemic symptoms/signs associated with AD. Non-negative matrix factorization was used to decompose the original data into a matrix with three features and a weight matrix. The point of intersection of the three coordinates from each patient was placed in three-dimensional space. With five clusters, the silhouette score reached 0.484, and this was the best silhouette score obtained from two to nine clusters. Patients were clustered according to the varying severity of concurrent symptoms/signs. Through the distribution of the null hypothesis generated by 10,000 permutation tests, we found significant cluster-specific symptoms/signs from the confidence intervals in the upper and lower 2.5% of the distribution. Patients in each cluster showed differences in symptoms/signs and severity. In a clinical situation, SD and treatment are based on the practitioners' observations and clinical experience. SD, identified through informatics, can contribute to development of standardized, objective, and consistent SD for each disease. Copyright © 2017. Published by Elsevier Ltd.
Gauvin, Laetitia; Panisson, André; Cattuto, Ciro
2014-01-01
The increasing availability of temporal network data is calling for more research on extracting and characterizing mesoscopic structures in temporal networks and on relating such structure to specific functions or properties of the system. An outstanding challenge is the extension of the results achieved for static networks to time-varying networks, where the topological structure of the system and the temporal activity patterns of its components are intertwined. Here we investigate the use of a latent factor decomposition technique, non-negative tensor factorization, to extract the community-activity structure of temporal networks. The method is intrinsically temporal and allows to simultaneously identify communities and to track their activity over time. We represent the time-varying adjacency matrix of a temporal network as a three-way tensor and approximate this tensor as a sum of terms that can be interpreted as communities of nodes with an associated activity time series. We summarize known computational techniques for tensor decomposition and discuss some quality metrics that can be used to tune the complexity of the factorized representation. We subsequently apply tensor factorization to a temporal network for which a ground truth is available for both the community structure and the temporal activity patterns. The data we use describe the social interactions of students in a school, the associations between students and school classes, and the spatio-temporal trajectories of students over time. We show that non-negative tensor factorization is capable of recovering the class structure with high accuracy. In particular, the extracted tensor components can be validated either as known school classes, or in terms of correlated activity patterns, i.e., of spatial and temporal coincidences that are determined by the known school activity schedule.
Semiclassical thermodynamics of scalar fields
Bessa, A; Fraga, E S; Gelis, François
2007-01-01
We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time, with spatially independent boundary conditions. Field fluctuations -- both field deviations around these classical solutions, and fluctuations of the boundary value of the fields -- are resummed in a Gaussian approximation. In our final expression for the partition function, this resummation is reduced to solving certain ordinary differential equations. Moreover, we show that it is renormalizable with the usual 1-loop counterterms.
Entropic quantization of scalar fields
Energy Technology Data Exchange (ETDEWEB)
Ipek, Selman; Caticha, Ariel [Department of Physics, University at Albany-SUNY, Albany, NY 12222 (United States)
2015-01-13
Entropic Dynamics is an information-based framework that seeks to derive the laws of physics as an application of the methods of entropic inference. The dynamics is derived by maximizing an entropy subject to constraints that represent the physically relevant information that the motion is continuous and non-dissipative. Here we focus on the quantum theory of scalar fields. We provide an entropic derivation of Hamiltonian dynamics and using concepts from information geometry derive the standard quantum field theory in the Schrödinger representation.
Renormalizability and the Scalar Field
Sastry, R R
1999-01-01
The infinite dimensional generalization of the quantum mechanics of extended objects, namely, the quantum field theory of extended objects is presented. The paradigm example studied in this paper is the Euclidean scalar field with a found to be finite when the virtual particle intermediate states are characterized by fuzzy particles instead of ordinary pointlike particles. Causality, Lorentz invariance, and unitarity (verified up to fourth order in the coupling constant) are preserved in the theory. In addition, the Kallen-Lehmann spectral representation for the propagator is discussed.
Bruckmann, Falk
2016-01-01
We study scalar QCD at nonzero density in the strong coupling limit. It has a sign problem which looks structurally similar to the one in QCD. We show first data for the reweighting factor. After introducing dual variables by integrating out the SU(3) gauge links, we find that at least 3 flavors are needed for a nontrivial dependence on the chemical potential. In this dual representation there is no sign problem remaining. The dual variables are partially constrained, thus we propose to use a hybrid approach for the updates: For unconstrained variables local updates can be used, while for constrained variables using updates based on the worm algorithm is more promising.
Late Time Acceleration From Matter-Curvature Coupling
Zaregonbadi, Raziyeh
2015-01-01
We consider f(R,T) modified theory of gravity, in which, in general, the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the energy-momentum tensor. We mainly focus on a particular model wherein matter is minimally coupled to the geometry in the metric formalism. In this type of the theory, the coupling energy-momentum tensor is not conserved; it determines the appearance of an extra force acting on the particles, and can cause the late time acceleration in the evolution of the universe. To check such a kind of effect, we obtain the corresponding Raychaudhuri dynamical equation that gives the evolution of the kinematic quantities. Then for the chosen model, we derive the behavior of the deceleration parameter, and show that the coupling term can cover the dynamic of the universe in the late time accelerating phase. On the other hand, the curvature of the universe corresponds with the deviation from parallelism in the geodesic motion. Thus, we also scrutinize the...
Scalar excursions in large-eddy simulations
Matheou, Georgios; Dimotakis, Paul E.
2016-12-01
The range of values of scalar fields in turbulent flows is bounded by their boundary values, for passive scalars, and by a combination of boundary values, reaction rates, phase changes, etc., for active scalars. The current investigation focuses on the local conservation of passive scalar concentration fields and the ability of the large-eddy simulation (LES) method to observe the boundedness of passive scalar concentrations. In practice, as a result of numerical artifacts, this fundamental constraint is often violated with scalars exhibiting unphysical excursions. The present study characterizes passive-scalar excursions in LES of a shear flow and examines methods for diagnosis and assesment of the problem. The analysis of scalar-excursion statistics provides support of the main hypothesis of the current study that unphysical scalar excursions in LES result from dispersive errors of the convection-term discretization where the subgrid-scale model (SGS) provides insufficient dissipation to produce a sufficiently smooth scalar field. In the LES runs three parameters are varied: the discretization of the convection terms, the SGS model, and grid resolution. Unphysical scalar excursions decrease as the order of accuracy of non-dissipative schemes is increased, but the improvement rate decreases with increasing order of accuracy. Two SGS models are examined, the stretched-vortex and a constant-coefficient Smagorinsky. Scalar excursions strongly depend on the SGS model. The excursions are significantly reduced when the characteristic SGS scale is set to double the grid spacing in runs with the stretched-vortex model. The maximum excursion and volume fraction of excursions outside boundary values show opposite trends with respect to resolution. The maximum unphysical excursions increase as resolution increases, whereas the volume fraction decreases. The reason for the increase in the maximum excursion is statistical and traceable to the number of grid points (sample size
Rubakov, V
2010-01-01
We consider Friedberg-Lee-Sirlin Q-balls in a (3+1)-dimensional model with vanishing scalar potential of one of the fields. The Q-ball is stabilized by the gradient energy of this field and carries scalar charge, over and beyond the global charge. The latter property is inherent also in a model with the scalar potential that does not vanish in some finite field region near the origin.
Unified Dark Matter Scalar Field Models
Directory of Open Access Journals (Sweden)
Daniele Bertacca
2010-01-01
of a single scalar field accounts for a unified description of the Dark Matter and Dark Energy sectors, dubbed Unified Dark Matter (UDM models. In this framework, we consider the general Lagrangian of -essence, which allows to find solutions around which the scalar field describes the desired mixture of Dark Matter and Dark Energy. We also discuss static and spherically symmetric solutions of Einstein's equations for a scalar field with noncanonical kinetic term, in connection with galactic halo rotation curves.
Galactic collapse of scalar field dark matter
Energy Technology Data Exchange (ETDEWEB)
Alcubierre, Miguel [Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, D-14476 Golm (Germany); Guzman, F Siddhartha [Max-Planck-Institut fuer Gravitationsphysik, Am Muehlenberg 1, D-14476 Golm (Germany); Matos, Tonatiuh [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, AP 14-740, 07000 Mexico, DF (Mexico); Nunez, Dario [Centre for Gravitational Physics and Geometry, Penn State University, University Park, PA 16802 (United States); Urena-Lopez, L Arturo [Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, AP 14-740, 07000 Mexico, DF (Mexico); Wiederhold, Petra [Departamento de Control Automatico, Centro de Investigacion y de Estudios Avanzados del IPN, AP 14-740, 07000 Mexico, DF (Mexico)
2002-10-07
We present a scenario for core galaxy formation based on the hypothesis of scalar field dark matter. We interpret galaxy formation through the collapse of a scalar field fluctuation. We find that a cosh potential for the self-interaction of the scalar field provides a reasonable scenario for the formation of a galactic core plus a remnant halo, which is in agreement with cosmological observations and phenomenological studies in galaxies.
Strong curvature effects in Neumann wave problems
Willatzen, M.; Pors, A.; Gravesen, J.
2012-08-01
Waveguide phenomena play a major role in basic sciences and engineering. The Helmholtz equation is the governing equation for the electric field in electromagnetic wave propagation and the acoustic pressure in the study of pressure dynamics. The Schrödinger equation simplifies to the Helmholtz equation for a quantum-mechanical particle confined by infinite barriers relevant in semiconductor physics. With this in mind and the interest to tailor waveguides towards a desired spectrum and modal pattern structure in classical structures and nanostructures, it becomes increasingly important to understand the influence of curvature effects in waveguides. In this work, we demonstrate analytically strong curvature effects for the eigenvalue spectrum of the Helmholtz equation with Neumann boundary conditions in cases where the waveguide cross section is a circular sector. It is found that the linear-in-curvature contribution originates from parity symmetry breaking of eigenstates in circular-sector tori and hence vanishes in a torus with a complete circular cross section. The same strong curvature effect is not present in waveguides subject to Dirichlet boundary conditions where curvature contributions contribute to second-order in the curvature only. We demonstrate this finding by considering wave propagation in a circular-sector torus corresponding to Neumann and Dirichlet boundary conditions, respectively. Results for relative eigenfrequency shifts and modes are determined and compared with three-dimensional finite element method results. Good agreement is found between the present analytical method using a combination of differential geometry with perturbation theory and finite element results for a large range of curvature ratios.
Strong curvature effects in Neumann wave problems
Energy Technology Data Exchange (ETDEWEB)
Willatzen, M.; Pors, A. [Mads Clausen Institute, University of Southern Denmark, Alsion 2, DK-6400 Sonderborg (Denmark); Gravesen, J. [Department of Mathematics, Technical University of Denmark, Matematiktorvet, DK-2800 Kgs. Lyngby (Denmark)
2012-08-15
Waveguide phenomena play a major role in basic sciences and engineering. The Helmholtz equation is the governing equation for the electric field in electromagnetic wave propagation and the acoustic pressure in the study of pressure dynamics. The Schroedinger equation simplifies to the Helmholtz equation for a quantum-mechanical particle confined by infinite barriers relevant in semiconductor physics. With this in mind and the interest to tailor waveguides towards a desired spectrum and modal pattern structure in classical structures and nanostructures, it becomes increasingly important to understand the influence of curvature effects in waveguides. In this work, we demonstrate analytically strong curvature effects for the eigenvalue spectrum of the Helmholtz equation with Neumann boundary conditions in cases where the waveguide cross section is a circular sector. It is found that the linear-in-curvature contribution originates from parity symmetry breaking of eigenstates in circular-sector tori and hence vanishes in a torus with a complete circular cross section. The same strong curvature effect is not present in waveguides subject to Dirichlet boundary conditions where curvature contributions contribute to second-order in the curvature only. We demonstrate this finding by considering wave propagation in a circular-sector torus corresponding to Neumann and Dirichlet boundary conditions, respectively. Results for relative eigenfrequency shifts and modes are determined and compared with three-dimensional finite element method results. Good agreement is found between the present analytical method using a combination of differential geometry with perturbation theory and finite element results for a large range of curvature ratios.
Low energy constraints and scalar leptoquarks⋆
Directory of Open Access Journals (Sweden)
Fajfer Svjetlana
2014-01-01
Full Text Available The presence of a colored weak doublet scalar state with mass below 1 TeV can provide an explanation of the observed branching ratios in B → D(∗τντ decays. Constraints coming from Z → bb̄, muon g − 2, lepton flavor violating decays are derived. The colored scalar is accommodated within 45 representation of SU(5 group of unification. We show that presence of color scalar can improve mass relations in the up-type quark sector mass. Impact of the colored scalar embedding in 45-dimensional representation of SU(5 on low-energy phenomenology is also presented.
Two loop scalar bilinears for inflationary SQED
Energy Technology Data Exchange (ETDEWEB)
Prokopec, T [Institute for Theoretical Physics and Spinoza Institute, Utrecht University Leuvenlaan 4, Postbus 80.195, 3508 TD Utrecht (Netherlands); Tsamis, N C [Department of Physics, University of Crete GR-710 03 Heraklion, Hellas (Greece); Woodard, R P [Department of Physics, University of Florida Gainesville, FL 32611 (United States)
2007-01-07
We evaluate the one- and two-loop contributions to the expectation values of two coincident and gauge invariant scalar bilinears in the theory of massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. One of these bilinears is the product of two covariantly differentiated scalars, the other is the product of two undifferentiated scalars. The computations are done using dimensional regularization and the Schwinger-Keldysh formalism. Our results are in perfect agreement with the stochastic predictions at this order.
CSW rules for a massive scalar
DEFF Research Database (Denmark)
Boels, Rutger Herman; Schwinn, Christian
2008-01-01
We derive the analog of the Cachazo-Svrcek-Witten (CSW) diagrammatic Feynman rules for four-dimensional Yang-Mills gauge theory coupled to a massive colored scalar. The mass term is shown to give rise to a new tower of vertices in addition to the CSW vertices for massless scalars in non-supersymm......We derive the analog of the Cachazo-Svrcek-Witten (CSW) diagrammatic Feynman rules for four-dimensional Yang-Mills gauge theory coupled to a massive colored scalar. The mass term is shown to give rise to a new tower of vertices in addition to the CSW vertices for massless scalars in non...
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.
Schwarzschild black holes can wear scalar wigs
Barranco, Juan; Degollado, Juan Carlos; Diez-Tejedor, Alberto; Megevand, Miguel; Alcubierre, Miguel; Núñez, Darío; Sarbach, Olivier
2012-01-01
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 ultra-light scalar field dark matter around supermassive black holes and axion-like 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 evolves, at late times, as a combination of those long-lived configurations.
Visualization of scalar topology for structural enhancement
Energy Technology Data Exchange (ETDEWEB)
Bajaj, C.L.; Pascucci, V.; Schikore, D.R.
1998-09-22
Scalar fields arise in every scientific application. Existing scalar visualization techniques require that the user infer the global scalar structure from what is frequently an insufficient display of information. We present a visualization technique which numerically detects the structure at all scales, removing from the user the responsibility of extracting information implicit in the data, and presenting the structure explicitly for analysis. We further demonstrate how scalar topology detection proves useful for correct visualization and image processing applications such as image co-registration, isocontouring, and mesh compression.
Scalar Field (Wave) Dark Matter
Matos, T
2016-01-01
Recent high-quality observations of dwarf and low surface brightness (LSB) galaxies have shown that their dark matter (DM) halos prefer flat central density profiles. On the other hand the standard cold dark matter model simulations predict a more cuspy behavior. Feedback from star formation has been widely used to reconcile simulations with observations, this might be successful in field dwarf galaxies but its success in low mass galaxies remains uncertain. One model that have received much attention is the scalar field dark matter model. Here the dark matter is a self-interacting ultra light scalar field that forms a cosmological Bose-Einstein condensate, a mass of $10^{-22}$eV/c$^2$ is consistent with flat density profiles in the centers of dwarf spheroidal galaxies, reduces the abundance of small halos, might account for the rotation curves even to large radii in spiral galaxies and has an early galaxy formation. The next generation of telescopes will provide better constraints to the model that will help...
Measuring Berry curvature with quantum Monte Carlo
Kolodrubetz, Michael
2014-01-01
The Berry curvature and its descendant, the Berry phase, play an important role in quantum mechanics. They can be used to understand the Aharonov-Bohm effect, define topological Chern numbers, and generally to investigate the geometric properties of a quantum ground state manifold. While Berry curvature has been well-studied in the regimes of few-body physics and non-interacting particles, its use in the regime of strong interactions is hindered by the lack of numerical methods to solve it. In this paper we fill this gap by implementing a quantum Monte Carlo method to solve for the Berry curvature, based on interpreting Berry curvature as a leading correction to imaginary time ramps. We demonstrate our algorithm using the transverse-field Ising model in one and two dimensions, the latter of which is non-integrable. Despite the fact that the Berry curvature gives information about the phase of the wave function, we show that our algorithm has no sign or phase problem for standard sign-problem-free Hamiltonians...
Burko, L M; Beetle, C; Burko, Lior M.; Baumgarte, Thomas W.; Beetle, Christopher
2006-01-01
Beetle and Burko recently introduced a background--independent scalar curvature invariant for general relativity that carries information only about the gravitational radiation in generic spacetimes, in cases where such radiation is incontrovertibly defined. In this paper we adopt a formalism that only uses spatial data as they are used in numerical relativity and compute the Beetle--Burko radiation scalar for a number of analytical examples, specifically linearized Einstein--Rosen cylindrical waves, linearized quadrupole waves, the Kerr spacetime, Bowen--York initial data, and the Kasner spacetime. These examples illustrate how the Beetle--Burko radiation scalar can be used to examine the gravitational wave content of numerically generated spacetimes, and how it may provide a useful diagnostic for initial data sets.
Rossman, Wayne; Umehara, Masaaki; Yamada, Kotaro
2001-01-01
We survey our recent results on classifying complete constant mean curvature 1 (CMC-1) surfaces in hyperbolic 3-space with low total curvature. There are two natural notions of "total curvature"-- one is the total absolute curvature which is the integral over the surface of the absolute value of the Gaussian curvature, and the other is the dual total absolute curvature which is the total absolute curvature of the dual CMC-1 surface. Here we discuss results on both notions (proven in two other...
Investigations of the torque anomaly in an annular sector. I. Global calculations, scalar case
Milton, Kimball A; Parashar, Prachi; Abalo, E K; Fulling, Stephen A; Bouas, Jeffrey D; Carter, Hamilton; Kirsten, Klaus
2013-01-01
In an attempt to understand a recently discovered torque anomaly in quantum field theory with boundaries, we calculate the Casimir energy and torque of a scalar field subject to Dirichlet boundary conditions on an annular sector defined by two coaxial cylinders intercut by two planes through the axis. In this model the particularly troublesome divergence at the cylinder axis does not appear, but new divergences associated with the curved boundaries are introduced. All the divergences associated with the volume, the surface area, the corners, and the curvature are regulated by point separation either in the direction of the axis of the cylinder or in the (Euclidean) time; the full divergence structure is isolated, and the remaining finite energy and torque are extracted. Formally, only the regulator based on axis splitting yields the expected balance between energy and torque. Because of the logarithmic curvature divergences, there is an ambiguity in the linear dependence of the energy on the wedge angle; if t...
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
Singh, Parampreet
2013-01-01
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaitre-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaitre-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
Radiation Like Scalar Field and Gauge Fields in Cosmology for a theory with Dynamical Time
Benisty, David
2016-01-01
Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spacial curvature of the universe. This is because only such $ k=0 $ radiation solutions poses a homothetic Killimg vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved space time, and there are no deviations from standard gauge filed equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang Mills equations, for more general space times.
Mass hierarchies and non-decoupling in multi-scalar field dynamics
Achúcarro, Ana; Hardeman, Sjoerd; Palma, Gonzalo A; Patil, Subodh P
2010-01-01
In this work we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Non-trivial imprints of the `heavy' directions arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the low energy effective theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the trajectory can still have a profound influence on the perturbations as modes parallel to the trajectory mix with those normal to the trajectory if the trajectory turns sharply enough. These effects could be important during inflation, which could lead to detectable effects in upcoming observations.
Radiation-like scalar field and gauge fields in cosmology for a theory with dynamical time
Benisty, David; Guendelman, E. I.
2016-09-01
Cosmological solutions with a scalar field behaving as radiation are obtained, in the context of gravitational theory with dynamical time. The solution requires the spacial curvature of the universe k, to be zero, unlike the standard radiation solutions, which do not impose any constraint on the spatial curvature of the universe. This is because only such k = 0 radiation solutions pose a homothetic Killing vector. This kind of theory can be used to generalize electromagnetism and other gauge theories, in curved spacetime, and there are no deviations from standard gauge field equation (like Maxwell equations) in the case there exist a conformal Killing vector. But there could be departures from Maxwell and Yang-Mills equations, for more general spacetimes.
The global rotating scalar field vacuum on anti-de Sitter space–time
Directory of Open Access Journals (Sweden)
Carl Kent
2015-01-01
Full Text Available We consider the definition of the global vacuum state of a quantum scalar field on n-dimensional anti-de Sitter space–time as seen by an observer rotating about the polar axis. Since positive (or negative frequency scalar field modes must have positive (or negative Klein–Gordon norm respectively, we find that the only sensible choice of positive frequency corresponds to positive frequency as seen by a static observer. This means that the global rotating vacuum is identical to the global nonrotating vacuum. For n≥4, if the angular velocity of the rotating observer is smaller than the inverse of the anti-de Sitter radius of curvature, then modes with positive Klein–Gordon norm also have positive frequency as seen by the rotating observer. We comment on the implications of this result for the construction of global rotating thermal states.
The rotating scalar field vacuum on anti-de Sitter space-time
Kent, Carl
2015-01-01
We consider the definition of the vacuum state of a quantum scalar field on $n$-dimensional anti-de Sitter space-time as seen by an observer rotating about the polar axis. Since positive (or negative) frequency scalar field modes must have positive (or negative) Klein-Gordon norm respectively, we find that the only sensible choice of positive frequency corresponds to positive frequency as seen by a static observer. This means that the rotating vacuum is identical to the nonrotating vacuum. If the angular velocity of the rotating observer is smaller than the inverse of the anti-de Sitter radius of curvature, then modes with positive Klein-Gordon norm also have positive frequency as seen by the rotating observer. We comment on the implications of this result for the construction of rotating thermal states.
Scalar fields in multidimensional gravity. No-hair and other no-go theorems
Bronnikov, K A; Michtchenko, A V
2003-01-01
Global properties of static, spherically symmetric configurations of scalar fields of sigma-model type with arbitrary potentials are studied in $D$ dimensions, including space-times containing multiple internal factor spaces. The latter are assumed to be Einstein spaces, not necessarily Ricci-flat, and the potential $V$ includes contributions from their curvatures. The following results generalize those known in four dimensions: (A) a no-hair theorem: in case $V\\geq 0$, an asymptotically flat black hole cannot have varying scalar fields or moduli fields outside the event horizon; (B) nonexistence of particlelike solutions in models with $V\\geq 0$; (C) nonexistence of wormholes under very general conditions; (D) a restriction on possible global causal structures (represented by Carter-Penrose diagrams). The list of structures in all models under consideration is the same as is known for vacuum with a cosmological constant in general relativity: Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild--de...
Evolution of geodesic congruences in a gravitationally collapsing scalar field background
Shaikh, Rajibul; DasGupta, Anirvan
2014-01-01
The evolution of timelike and null geodesic congruences in a non-static, inhomogeneous spacetime representing the gravitational collapse of a massless scalar field, is investigated in detail. We show explicitly how the initial values of the expansion, rotation and shear of a congruence, as well as the spacetime curvature along the congruence, influence the evolution and focusing of trajectories in different ways. The role of initial conditions on the focusing time is explored and highlighted. In certain specific cases, the expansion scalar is found to exhibit a finite jump (from negative to positive value) before focusing. The issue of singularity formation and the effect of the central inhomogeneity in the spacetime, on the evolution of the kinematic variables, is discussed. In summary, our analysis does seem to throw some light on how a family of trajectories evolve in a specific model of gravitational collapse.
Evolution of cosmological perturbations in a stage dominated by an oscillatory scalar field
Kodama, H; Kodama, Hideo; Hamazaki, Takashi
1996-01-01
In the investigation of the evolution of cosmological perturbations in inflationary universe models the behavior of perturbations during the reheating stage is the most unclear point. In particular in the early reheating phase in which a rapidly oscillating scalar field dominates the energy density, the behavior of perturbations is not known well because their evolution equation expressed in terms of the curvature perturbation becomes singular. In this paper it is shown that in spite of this singular behavior of the evolution equation the Bardeen parameter stays constant in a good accuracy during this stage for superhorizon-scale perturbations except for a sequence of negligibly short intervals around the zero points of the time derivative of the scalar field. This justifies the conventional formula relating the amplitudes of quantum fluctuations during inflation and those of adiabatic perturbations at horizon crossing in the Friedmann stage, except for possible corrections produced by the energy transfer fro...
$Om$ diagnostic applied to scalar field models and slowing down of cosmic acceleration
Shahalam, M; Agarwal, Abhineet
2015-01-01
We apply the $Om$ diagnostic to models for dark energy based on scalar fields. In case of the power law potentials, we demonstrate the possibility of slowing down the expansion of the Universe around the present epoch for a specific range in the parameter space. For these models, we also examine the issues concerning the age of Universe. We use the $Om$ diagnostic to distinguish the $\\Lambda$CDM model from non minimally coupled scalar field, phantom field and generic quintessence models. Our study shows that the $Om$ has zero, positive and negative curvatures for $\\Lambda$CDM, phantom and quintessence models respectively. We use an integrated data base (SN+Hubble+BAO+CMB) for bservational analysis and demonstrate that $Om$ is a useful diagnostic to apply to observational data.
Local thermal behaviour of a massive scalar field near a reflecting wall
De Lorenci, V A; Moreira, E S
2014-01-01
The mean square fluctuation and the expectation value of the stress-energy-momentum tensor of a neutral massive scalar field at finite temperature are determined near an infinite plane Dirichlet wall. The flat background has an arbitrary number of dimensions and the field is arbitrarily coupled to the vanishing curvature. It is shown that, unlike vacuum contributions, thermal contributions are free from boundary divergences. The study reveals a local version of dimensional reduction, namely, corrections to familiar blackbody expressions are linear in the temperature, with the corresponding coefficients given only in terms of vacuum expectation values in a background with one less dimension. It is shown that such corrections are "classical" (i.e., not dependent on Planck's constant) only if the scalar field is massless.
Dark energy, curvature and cosmic coincidence
Franca, U
2006-01-01
The fact that the energy densities of dark energy and matter are similar currently, known as the coincidence problem, is one of the main unsolved problems of cosmology. We present here a phenomenological model in which a spatial curvature of the universe can lead to a transition in the present epoch from a matter dominated universe to a scaling dark energy dominance in a very natural way. In particular, we show that if the exponential potential of the dark energy field depends linearly on the spatial curvature density of a closed universe, the observed values of some cosmological parameters can be obtained assuming acceptable values for the present spatial curvature of the universe, and without fine tuning in the only parameter of the model. We also comment on possible variations of this model.
On the curvature effect of thin membranes
Wang, Duo; Jiao, Xiangmin; Conley, Rebecca; Glimm, James
2013-01-01
We investigate the curvature effect of a thin, curved elastic interface that separates two subdomains and exerts a pressure due to a curvature effect. This pressure, which we refer to as interface pressure, is similar to the surface tension in fluid mechanics. It is important in some applications, such as the canopy of parachutes, biological membranes of cells, balloons, airbags, etc., as it partially balances a pressure jump between the two sides of an interface. In this paper, we show that the interface pressure is equal to the trace of the matrix product of the curvature tensor and the Cauchy stress tensor in the tangent plane. We derive the theory for interfaces in both 2-D and 3-D, and present numerical discretizations for computing the quality over triangulated surfaces.
Total positive curvature of circular DNA
DEFF Research Database (Denmark)
Bohr, Jakob; Olsen, Kasper Wibeck
2013-01-01
molecules, e.g., plasmids, it is shown to have implications for the total positive curvature integral. For small circular micro-DNAs it follows as a consequence of Fenchel's inequality that there must exist a minimum length for the circular plasmids to be double stranded. It also follows that all circular...... micro-DNAs longer than the minimum length must be concave, a result that is consistent with typical atomic force microscopy images of plasmids. Predictions for the total positive curvature of circular micro-DNAs are given as a function of length, and comparisons with circular DNAs from the literature......The properties of double-stranded DNA and other chiral molecules depend on the local geometry, i.e., on curvature and torsion, yet the paths of closed chain molecules are globally restricted by topology. When both of these characteristics are to be incorporated in the description of circular chain...
Extrinsic and intrinsic curvatures in thermodynamic geometry
Energy Technology Data Exchange (ETDEWEB)
Hosseini Mansoori, Seyed Ali, E-mail: shossein@bu.edu [Department of Physics, Boston University, 590 Commonwealth Ave., Boston, MA 02215 (United States); Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Mirza, Behrouz, E-mail: b.mirza@cc.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Sharifian, Elham, E-mail: e.sharifian@ph.iut.ac.ir [Department of Physics, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of)
2016-08-10
We investigate the intrinsic and extrinsic curvatures of a certain hypersurface in thermodynamic geometry of a physical system and show that they contain useful thermodynamic information. For an anti-Reissner–Nordström-(A)de Sitter black hole (Phantom), the extrinsic curvature of a constant Q hypersurface has the same sign as the heat capacity around the phase transition points. The intrinsic curvature of the hypersurface can also be divergent at the critical points but has no information about the sign of the heat capacity. Our study explains the consistent relationship holding between the thermodynamic geometry of the KN-AdS black holes and those of the RN (J-zero hypersurface) and Kerr black holes (Q-zero hypersurface) ones [1]. This approach can easily be generalized to an arbitrary thermodynamic system.
Gaussian Curvature on Hyperelliptic Riemann Surfaces
Indian Academy of Sciences (India)
Abel Castorena
2014-05-01
Let be a compact Riemann surface of genus $g ≥ 1, _1,\\ldots,_g$ be a basis of holomorphic 1-forms on and let $H=(h_{ij})^g_{i,j=1}$ be a positive definite Hermitian matrix. It is well known that the metric defined as $ds_H^2=\\sum^g_{i,j=1}h_{ij}_i\\otimes \\overline{_j}$ is a K\\"a hler metric on of non-positive curvature. Let $K_H:C→ \\mathbb{R}$ be the Gaussian curvature of this metric. When is hyperelliptic we show that the hyperelliptic Weierstrass points are non-degenerated critical points of $K_H$ of Morse index +2. In the particular case when is the × identity matrix, we give a criteria to find local minima for $K_H$ and we give examples of hyperelliptic curves where the curvature function $K_H$ is a Morse function.
Integrating curvature: from Umlaufsatz to J^+ invariant
Lanzat, Sergei
2011-01-01
Hopf's Umlaufsatz relates the total curvature of a closed immersed plane curve to its rotation number. While the curvature of a curve changes under local deformations, its integral over a closed curve is invariant under regular homotopies. A natural question is whether one can find some non-trivial densities on a curve, such that the corresponding integrals are (possibly after some corrections) also invariant under regular homotopies of the curve in the class of generic immersions. We construct a family of such densities using indices of points relative to the curve. This family depends on a formal parameter q and may be considered as a quantization of the total curvature. The linear term in the Taylor expansion at q=1 coincides, up to a normalization, with Arnold's J^+ invariant. This leads to an integral expression for J^+.
Anisotropic membrane curvature sensing by antibacterial peptides
Gómez-Llobregat, Jordi; Lindén, Martin
2014-01-01
Many proteins and peptides have an intrinsic capacity to sense and induce membrane curvature, and play crucial roles for organizing and remodeling cell membranes. However, the molecular driving forces behind these processes are not well understood. Here, we describe a new approach to study curvature sensing, by simulating the direction-dependent interactions of single molecules with a buckled lipid bilayer. We analyze three antimicrobial peptides, a class of membrane-associated molecules that specifically target and destabilize bacterial membranes, and find qualitatively different sensing characteristics that would be difficult to resolve with other methods. These findings provide new insights into the microscopic mechanisms of antimicrobial peptides, which might aid the development of new antibiotics. Our approach is generally applicable to a wide range of curvature sensing molecules, and our results provide strong motivation to develop new experimental methods to track position and orientation of membrane p...
Anomalous Coupling Between Topological Defects and Curvature
Vitelli, Vincenzo; Turner, Ari M.
2004-11-01
We investigate a counterintuitive geometric interaction between defects and curvature in thin layers of superfluids, superconductors, and liquid crystals deposited on curved surfaces. Each defect feels a geometric potential whose functional form is determined only by the shape of the surface, but whose sign and strength depend on the transformation properties of the order parameter. For superfluids and superconductors, the strength of this interaction is proportional to the square of the charge and causes all defects to be repelled (attracted) by regions of positive (negative) Gaussian curvature. For liquid crystals in the one elastic constant approximation, charges between 0 and 4π are attracted by regions of positive curvature while all other charges are repelled.
Cosmic curvature from de Sitter equilibrium cosmology.
Albrecht, Andreas
2011-10-01
I show that the de Sitter equilibrium cosmology generically predicts observable levels of curvature in the Universe today. The predicted value of the curvature, Ω(k), depends only on the ratio of the density of nonrelativistic matter to cosmological constant density ρ(m)(0)/ρ(Λ) and the value of the curvature from the initial bubble that starts the inflation, Ω(k)(B). The result is independent of the scale of inflation, the shape of the potential during inflation, and many other details of the cosmology. Future cosmological measurements of ρ(m)(0)/ρ(Λ) and Ω(k) will open up a window on the very beginning of our Universe and offer an opportunity to support or falsify the de Sitter equilibrium cosmology.
(2+1)-Dimensional charged black holes with scalar hair in Einstein-Power-Maxwell Theory
Xu, Wei; Zou, De-Cheng
2017-06-01
In (2+1)-dimensional AdS spacetime, we obtain new exact black hole solutions, including two different models (power parameter k=1 and k≠1), in the Einstein-Power-Maxwell (EPM) theory with nonminimally coupled scalar field. For the charged hairy black hole with k≠1, we find that the solution contains a curvature singularity at the origin and is nonconformally flat. The horizon structures are identified, which indicates the physically acceptable lower bound of mass in according to the existence of black hole solutions. Later, the null geodesic equations for photon around this charged hairy black hole are also discussed in detail.
Scalar-Tensor Quintessence with a linear potential: Avoiding the Big Crunch cosmic doomsday
Lykkas, A
2015-01-01
All quintessence potentials that are either monotonic or have a minimum at negative values of the potential, generically predict a future collapse of the scale factor to a "doomsday" singularity. We show that this doomsday is generically avoided in models with a proper non-minimal coupling of the quintessence scalar field to the curvature scalar $R$. For simplicity we consider linear quintessence potential $V=-s\\phi$ and linear non-minimal coupling $F=1-\\lambda \\phi$. However our result is generic and is due to the fact that the non-minimal coupling modifies the effective potential that determines the dynamics of the scalar field. Thus for each positive value of the parameter $s$ we find a critical value $\\lambda_{crit}(s)$ such that for $\\lambda>\\lambda_{crit}(s)$ the negative potential energy does not dominate the universe and the cosmic doomsday Big Crunch singularity is avoided because the scalar field eventually rolls up its potential. We find that $\\lambda_{crit}(s)$ increases approximately linearly wit...
The constraint equations for the Einstein-scalar field system on compact manifolds
Choquet-Bruhat, Y; Pollack, D; Choquet-Bruhat, Yvonne; Isenberg, James; Pollack, Daniel
2006-01-01
We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new conformal invariant, which is sensitive to the presence of the initial data for the scalar field, we are able to divide the set of free conformal data into subclasses depending on the possible signs for the coefficients of terms in the resulting Einstein-scalar field Lichnerowicz equation. For many of these subclasses we determine whether or not a solution exists. In contrast to other well studied field theories, there are certain cases, depending on the mean curvature and the potential of the scalar field, for which we are unable to resolve the question of existence of a solution. We consider this system in such generality so as to include the vacuum constraint equations with an arbitrary cosmological constant, the Yamabe equation and even (all cases of) the prescribed sca...
Spherically symmetric scalar vacuum no-go theorems, black holes and solitons
Bronnikov, K A
2001-01-01
We prove some theorems characterizing the global properties of static, spherically symmetric configurations of a self-gravitating real scalar field in general relativity (GR) in various dimensions, with an arbitrary potential $V$, not necessarily positive-definite. The results are extended to sigma models, scalar-tensor and curvature-nonlinear theories of gravity. We show that the list of all possible types of space-time causal structure in the models under study is the same as for a constant scalar field, namely, Minkowski (or AdS), Schwarzschild, de Sitter and Schwarzschild - de Sitter, and all horizons are simple. In particular, these theories do not admit regular black holes with any asymptotics. Some special features of (2+1)D gravity are revealed. We give examples of two types of asymptotically flat configurations with positive mass in GR, admitted by the above theorems: (i) a black hole with nontrivial ``scalar hair'' and (ii) a particlelike solution with a regular centre; in both cases, the potential ...
Weakly dynamic dark energy via metric-scalar couplings with torsion
Sur, Sourav
2016-01-01
We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the pseudo-trace of the latter provides a mass term for the scalar field in the effective action. In the equivalent scalar-tensor framework, we find explicit cosmological solutions suitable for describing dark energy in both Einstein and Jordan frames. We demand the dynamical evolution of the dark energy to be weak enough, so that the present-day values of the cosmological parameters could be estimated keeping them within the confidence limits set for the standard $\\L$CDM model from recent observations. For such estimates, we examine the variations of the effective matter density and the dark energy equation of state over different redshift ranges. In spite of being weakly dynamic, the dark energy component here differs significantly from the cosmological constant, both in characterist...
Einstein Gravity and Beyond: Aspects of Higher-Curvature Gravity and Black Holes
Chatterjee, Saugata
This thesis explores the different aspects of higher curvature gravity. The "membrane paradigm" of black holes in Einstein gravity is extended to black holes in f(R) gravity and it is shown that the higher curvature effects of f( R) gravity causes the membrane fluid to become non-Newtonian. Next a modification of the null energy condition in gravity is provided. The purpose of the null energy condition is to filter out ill-behaved theories containing ghosts. Conformal transformations, which are simple redefinitions of the spacetime, introduces serious violations of the null energy condition. This violation is shown to be spurious and a prescription for obtaining a modified null energy condition, based on the universality of the second law of thermodynamics, is provided. The thermodynamic properties of the black holes are further explored using merger of extremal black holes whose horizon entropy has topological contributions coming from the higher curvature Gauss-Bonnet term. The analysis refutes the prevalent belief in the literature that the second law of black hole thermodynamics is violated in the presence of the Gauss-Bonnet term in four dimensions. Subsequently a specific class of higher derivative scalar field theories called the galileons are obtained from a Kaluza-Klein reduction of Gauss-Bonnet gravity. Galileons are null energy condition violating theories which lead to violations of the second law of thermodynamics of black holes. These higher derivative scalar field theories which are non-minimally coupled to gravity required the development of a generalized method for obtaining the equations of motion. Utilizing this generalized method, it is shown that the inclusion of the Gauss-Bonnet term made the theory of gravity to become higher derivative, which makes it difficult to make any statements about the connection between the violation of the second law of thermodynamics and the galileon fields.
Hypersurfaces of constant curvature in Hyperbolic space
Guan, Bo
2010-01-01
We show that for a very general and natural class of curvature functions, the problem of finding a complete strictly convex hypersurface satisfying f({\\kappa}) = {\\sigma} over (0,1) with a prescribed asymptotic boundary {\\Gamma} at infinity has at least one solution which is a "vertical graph" over the interior (or the exterior) of {\\Gamma}. There is uniqueness for a certain subclass of these curvature functions and as {\\sigma} varies between 0 and 1, these hypersurfaces foliate the two components of the complement of the hyperbolic convex hull of {\\Gamma}.
Fingerprint Feature Extraction Based on Macroscopic Curvature
Institute of Scientific and Technical Information of China (English)
Zhang Xiong; He Gui-ming; Zhang Yun
2003-01-01
In the Automatic Fingerprint Identification System (AFIS), extracting the feature of fingerprint is very important. The local curvature of ridges of fingerprint is irregular, so people have the barrier to effectively extract the fingerprint curve features to describe fingerprint. This article proposes a novel algorithm; it embraces information of few nearby fingerprint ridges to extract a new characteristic which can describe the curvature feature of fingerprint. Experimental results show the algorithm is feasible, and the characteristics extracted by it can clearly show the inner macroscopic curve properties of fingerprint. The result also shows that this kind of characteristic is robust to noise and pollution.
Fingerprint Feature Extraction Based on Macroscopic Curvature
Institute of Scientific and Technical Information of China (English)
Zhang; Xiong; He; Gui-Ming; 等
2003-01-01
In the Automatic Fingerprint Identification System(AFIS), extracting the feature of fingerprint is very important. The local curvature of ridges of fingerprint is irregular, so people have the barrier to effectively extract the fingerprint curve features to describe fingerprint. This article proposes a novel algorithm; it embraces information of few nearby fingerprint ridges to extract a new characterstic which can describe the curvature feature of fingerprint. Experimental results show the algorithm is feasible, and the characteristics extracted by it can clearly show the inner macroscopic curve properties of fingerprint. The result also shows that this kind of characteristic is robust to noise and pollution.
Anomalous coupling of scalars to gauge fields
Energy Technology Data Exchange (ETDEWEB)
Brax, Philippe [CEA, IPhT, CNRS, URA 2306, Gif-sur-Yvette (France). Inst. de Physique Theorique; Burrage, Clare [Geneve Univ. (Switzerland). Dept. de Physique Theorique; Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Davis, Anne-Christine [Centre for Mathematical Sciences, Cambridge (United Kingdom). Dept. of Applied Mathematics and Theoretical Physics; Seery, David [Sussex Univ., Brighton (United Kingdom). Dept. of Physics and Astronomy; Weltman, Amanda [Cape Town Univ., Rondebosch (South Africa). Astronomy, Cosmology and Gravity Centre
2010-10-15
We study the transformation properties of a scalar-tensor theory, coupled to fermions, under the Weyl rescaling associated with a transition from the Jordan to the Einstein frame. We give a simple derivation of the corresponding modification to the gauge couplings. After changing frames, this gives rise to a direct coupling between the scalar and the gauge fields. (orig.)
Optimal Regularizing Effect for Scalar Conservation Laws
Golse, François
2011-01-01
We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.
New type scalar fields for cosmic acceleration
Energy Technology Data Exchange (ETDEWEB)
Kehagias, A; Pakis, S [Department of Physics, National Technical University of Athens, GR-15773, Zografou, Athens (Greece)
2007-05-15
We present a model where a non-conventional scalar field may act like dark energy and leads to cosmic acceleration. The latter is driven by an appropriate field configuration, which result in an effective cosmological constant. The potential role of such a scalar in the cosmological constant problem is also discussed.
Dynamical and statistical effects of the intrinsic curvature of internal space of molecules.
Teramoto, Hiroshi; Takatsuka, Kazuo
2005-02-15
The Hamilton dynamics of a molecule in a translationally and/or rotationally symmetric field is kept rigorously constrained in its phase space. The relevant dynamical laws should therefore be extracted from these constrained motions. An internal space that is induced by a projection of such a limited phase space onto configuration space is an intrinsically curved space even for a system of zero total angular momentum. In this paper we discuss the general effects of this curvedness on dynamics and structures of molecules in such a manner that is invariant with respect to the selection of coordinates. It is shown that the regular coordinate originally defined by Riemann is particularly useful to expose the curvature correction to the dynamics and statistical properties of molecules. These effects are significant both qualitatively and quantitatively and are studied in two aspects. One is the direct effect on dynamics: A trajectory receives a Lorentz-like force from the curved space as though it was placed in a magnetic field. The well-known problem of the trapping phenomenon at the transition state is analyzed from this point of view. By showing that the trapping force is explicitly described in terms of the curvature of the internal space, we clarify that the physical origin of the trapped motion is indeed originated from the curvature of the internal space and hence is not dependent of the selection of coordinate system. The other aspect is the effect of phase space volume arising from the curvedness: We formulate a general expression of the curvature correction of the classical density of states and extract its physical significance in the molecular geometry along with reaction rate in terms of the scalar curvature and volume loss (gain) due to the curvature. The transition state theory is reformulated from this point of view and it is applied to the structural transition of linear chain molecules in the so-called dihedral angle model. It is shown that the
Devarajan, Karthik; Cheung, Vincent C.K.
2017-01-01
Non-negative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two nonnegative matrices, W and H where V ~ WH. It has been successfully applied in the analysis and interpretation of large-scale data arising in neuroscience, computational biology and natural language processing, among other areas. A distinctive feature of NMF is its nonnegativity constraints that allow only additive linear combinations of the data, thus enabling it to learn parts that have distinct physical representations in reality. In this paper, we describe an information-theoretic approach to NMF for signal-dependent noise based on the generalized inverse Gaussian model. Specifically, we propose three novel algorithms in this setting, each based on multiplicative updates and prove monotonicity of updates using the EM algorithm. In addition, we develop algorithm-specific measures to evaluate their goodness-of-fit on data. Our methods are demonstrated using experimental data from electromyography studies as well as simulated data in the extraction of muscle synergies, and compared with existing algorithms for signal-dependent noise. PMID:24684448
Ju, Bin; Qian, Yuntao; Ye, Minchao; Ni, Rong; Zhu, Chenxi
2015-01-01
Predicting what items will be selected by a target user in the future is an important function for recommendation systems. Matrix factorization techniques have been shown to achieve good performance on temporal rating-type data, but little is known about temporal item selection data. In this paper, we developed a unified model that combines Multi-task Non-negative Matrix Factorization and Linear Dynamical Systems to capture the evolution of user preferences. Specifically, user and item features are projected into latent factor space by factoring co-occurrence matrices into a common basis item-factor matrix and multiple factor-user matrices. Moreover, we represented both within and between relationships of multiple factor-user matrices using a state transition matrix to capture the changes in user preferences over time. The experiments show that our proposed algorithm outperforms the other algorithms on two real datasets, which were extracted from Netflix movies and Last.fm music. Furthermore, our model provides a novel dynamic topic model for tracking the evolution of the behavior of a user over time.
Directory of Open Access Journals (Sweden)
Martin R L Paine
Full Text Available High-grade serous carcinoma (HGSC is the most common and deadliest form of ovarian cancer. Yet it is largely asymptomatic in its initial stages. Studying the origin and early progression of this disease is thus critical in identifying markers for early detection and screening purposes. Tissue-based mass spectrometry imaging (MSI can be employed as an unbiased way of examining localized metabolic changes between healthy and cancerous tissue directly, at the onset of disease. In this study, we describe MSI results from Dicer-Pten double-knockout (DKO mice, a mouse model faithfully reproducing the clinical nature of human HGSC. By using non-negative matrix factorization (NMF for the unsupervised analysis of desorption electrospray ionization (DESI datasets, tissue regions are segregated based on spectral components in an unbiased manner, with alterations related to HGSC highlighted. Results obtained by combining NMF with DESI-MSI revealed several metabolic species elevated in the tumor tissue and/or surrounding blood-filled cyst including ceramides, sphingomyelins, bilirubin, cholesterol sulfate, and various lysophospholipids. Multiple metabolites identified within the imaging study were also detected at altered levels within serum in a previous metabolomic study of the same mouse model. As an example workflow, features identified in this study were used to build an oPLS-DA model capable of discriminating between DKO mice with early-stage tumors and controls with up to 88% accuracy.
Kim, Jaeyeon; Bennett, Rachel V.; Parry, R. Mitchell; Gaul, David A.; Wang, May D.; Matzuk, Martin M.; Fernández, Facundo M.
2016-01-01
High-grade serous carcinoma (HGSC) is the most common and deadliest form of ovarian cancer. Yet it is largely asymptomatic in its initial stages. Studying the origin and early progression of this disease is thus critical in identifying markers for early detection and screening purposes. Tissue-based mass spectrometry imaging (MSI) can be employed as an unbiased way of examining localized metabolic changes between healthy and cancerous tissue directly, at the onset of disease. In this study, we describe MSI results from Dicer-Pten double-knockout (DKO) mice, a mouse model faithfully reproducing the clinical nature of human HGSC. By using non-negative matrix factorization (NMF) for the unsupervised analysis of desorption electrospray ionization (DESI) datasets, tissue regions are segregated based on spectral components in an unbiased manner, with alterations related to HGSC highlighted. Results obtained by combining NMF with DESI-MSI revealed several metabolic species elevated in the tumor tissue and/or surrounding blood-filled cyst including ceramides, sphingomyelins, bilirubin, cholesterol sulfate, and various lysophospholipids. Multiple metabolites identified within the imaging study were also detected at altered levels within serum in a previous metabolomic study of the same mouse model. As an example workflow, features identified in this study were used to build an oPLS-DA model capable of discriminating between DKO mice with early-stage tumors and controls with up to 88% accuracy. PMID:27159635
Modeling Polio Data Using the First Order Non-Negative Integer-Valued Autoregressive, INAR(1), Model
Vazifedan, Turaj; Shitan, Mahendran
Time series data may consists of counts, such as the number of road accidents, the number of patients in a certain hospital, the number of customers waiting for service at a certain time and etc. When the value of the observations are large it is usual to use Gaussian Autoregressive Moving Average (ARMA) process to model the time series. However if the observed counts are small, it is not appropriate to use ARMA process to model the observed phenomenon. In such cases we need to model the time series data by using Non-Negative Integer valued Autoregressive (INAR) process. The modeling of counts data is based on the binomial thinning operator. In this paper we illustrate the modeling of counts data using the monthly number of Poliomyelitis data in United States between January 1970 until December 1983. We applied the AR(1), Poisson regression model and INAR(1) model and the suitability of these models were assessed by using the Index of Agreement(I.A.). We found that INAR(1) model is more appropriate in the sense it had a better I.A. and it is natural since the data are counts.
Ghoraani, Behnaz
2016-12-01
Time-frequency (TF) representation has found wide use in many challenging signal processing tasks including classification, interference rejection, and retrieval. Advances in TF analysis methods have led to the development of powerful techniques, which use non-negative matrix factorization (NMF) to adaptively decompose the TF data into TF basis components and coefficients. In this paper, standard NMF is modified for TF data, such that the improved TF bases can be used for signal classification applications with overlapping classes and data retrieval. The new method, called jointly learnt NMF (JLNMF) method, identifies both distinct and shared TF bases and is able to use the decomposed bases to successfully retrieve and separate the class-specific information from data. The paper provides the framework of the proposed JLNMF cost function and proposes a projected gradient framework to solve for limit point stationarity solutions. The developed algorithm has been applied to a synthetic data retrieval experiment and epileptic spikes in EEG signals of infantile spasms and discrimination of pathological voice disorder. The experimental results verified that JLNMF successfully identified the class-specific information, thus enhancing data separation performance.
Ray, Sumanta; Maulik, Ujjwal
2016-12-20
Detecting perturbation in modular structure during HIV-1 disease progression is an important step to understand stage specific infection pattern of HIV-1 virus in human cell. In this article, we proposed a novel methodology on integration of multiple biological information to identify such disruption in human gene module during different stages of HIV-1 infection. We integrate three different biological information: gene expression information, protein-protein interaction information and gene ontology information in single gene meta-module, through non negative matrix factorization (NMF). As the identified metamodules inherit those information so, detecting perturbation of these, reflects the changes in expression pattern, in PPI structure and in functional similarity of genes during the infection progression. To integrate modules of different data sources into strong meta-modules, NMF based clustering is utilized here. Perturbation in meta-modular structure is identified by investigating the topological and intramodular properties and putting rank to those meta-modules using a rank aggregation algorithm. We have also analyzed the preservation structure of significant GO terms in which the human proteins of the meta-modules participate. Moreover, we have performed an analysis to show the change of coregulation pattern of identified transcription factors (TFs) over the HIV progression stages.
Directory of Open Access Journals (Sweden)
Bin Ju
Full Text Available Predicting what items will be selected by a target user in the future is an important function for recommendation systems. Matrix factorization techniques have been shown to achieve good performance on temporal rating-type data, but little is known about temporal item selection data. In this paper, we developed a unified model that combines Multi-task Non-negative Matrix Factorization and Linear Dynamical Systems to capture the evolution of user preferences. Specifically, user and item features are projected into latent factor space by factoring co-occurrence matrices into a common basis item-factor matrix and multiple factor-user matrices. Moreover, we represented both within and between relationships of multiple factor-user matrices using a state transition matrix to capture the changes in user preferences over time. The experiments show that our proposed algorithm outperforms the other algorithms on two real datasets, which were extracted from Netflix movies and Last.fm music. Furthermore, our model provides a novel dynamic topic model for tracking the evolution of the behavior of a user over time.
Non-linear curvature perturbation in multi-field inflation models with non-minimal coupling
Energy Technology Data Exchange (ETDEWEB)
White, Jonathan; Minamitsuji, Masato; Sasaki, Misao, E-mail: jwhite@yukawa.kyoto-u.ac.jp, E-mail: masato.minamitsuji@ist.utl.pt, E-mail: misao@yukawa.kyoto-u.ac.jp [Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502 (Japan)
2013-09-01
Using the δN formalism we consider the non-linear curvature perturbation in multi-field models of inflation with non-minimal coupling. In particular, we focus on the relation between the δN formalism as applied in the conformally related Jordan and Einstein frames. Exploiting results already known in the Einstein frame, we give expressions for the power spectrum, spectral tilt and non-gaussianity associated with the Jordan frame curvature perturbation. In the case that an adiabatic limit has not been reached, we find that in general these quantities differ from those associated with the Einstein frame curvature perturbation, and also confirm their equivalence in the absence of isocurvature modes. We then proceed to consider two analytically soluble examples, the first involving a non-minimally coupled 'spectator' field and the second being a non-minimally coupled extension of the multi-brid inflation model. In the first model we find that predictions can easily be brought into agreement with the recent Planck results, as the tensor-to-scalar ratio is generally small, the spectral tilt tuneable and the non-gaussianity suppressed. In the second model we find that predictions for all three parameters can differ substantially from those predicted in the minimally coupled case, and that the recent Planck results for the spectral tilt can be used to constrain the non-minimal coupling parameters.
Resummations in hot scalar electrodynamics
Krämmer, U; Schulz, H
1994-01-01
The gauge-boson sector of perturbative scalar electrodynamics is investigated in detail as a testing ground for resummation methods in hot gauge theories. It also serves as a simple non-trivial reference system for the non-Abelian gluon plasma. The complete next-to-leading order contributions to the polarization tensor are obtained within the resummation scheme of Braaten and Pisarski. The simpler scheme proposed recently by Arnold and Espinosa is shown to apply to static quantities only, whereas Braaten-Pisarski resummation turns out to need modification for collective phenomena close to the light-cone. Finally, a recently proposed resummation of quasi-particle damping contributions is assessed critically.
Discrete Scalar Quantum Field Theory
Gudder, Stan
2016-01-01
We begin with a description of spacetime by a 4-dimensional cubic lattice $\\sscript$. It follows from this framework that the the speed of light is the only nonzero instantaneous speed for a particle. The dual space $\\sscripthat$ corresponds to a cubic lattice of energy-momentum. This description implies that there is a discrete set of possible particle masses. We then define discrete scalar quantum fields on $\\sscript$. These fields are employed to define interaction Hamiltonians and scattering operators. Although the scattering operator $S$ cannot be computed exactly, approximations are possible. Whether $S$ is unitary is an unsolved problem. Besides the definitions of these operators, our main assumption is conservation of energy-momentum for a scattering process. This article concludes with various examples of perturbation approximations. These include simplified versions of electron-electron and electron-proton scattering as well as simple decay processes. We also define scattering cross-sections, decay ...
Gravity and the Tenacious Scalar Field
Brans, C H
1997-01-01
Scalar fields have had a long and controversial life in gravity theories, having progressed through many deaths and resurrections. The first scientific gravity theory, Newton's, was that of a scalar potential field, so it was natural for Einstein and others to consider the possibility of incorporating gravity into special relativity as a scalar theory. This effort, though fruitless in its original intent, nevertheless was useful in leading the way to Einstein's general relativity, a purely two-tensor field theory. However, a universally coupled scalar field again appeared, both in the context of Dirac's large number hypothesis and in five dimensional unified field theories as studied by Fierz, Jordan, and others. While later experimentation seems to indicate that if such a scalar exists its influence on solar system size interactions is negligible, other reincarnations have been proposed under the guise of dilatons in string theory and inflatons in cosmology. This paper presents a brief overview of this histo...
Slowly rotating neutron stars in scalar-tensor theories with a massive scalar field
Yazadjiev, Stoytcho S; Popchev, Dimitar
2016-01-01
In the scalar-tensor theories with a massive scalar field the coupling constants, and the coupling functions in general, which are observationally allowed, can differ significantly from those in the massless case. This fact naturally implies that the scalar-tensor neutron stars with a massive scalar field can have rather different structure and properties in comparison with their counterparts in the massless case and in general relativity. In the present paper we study slowly rotating neutron stars in scalar-tensor theories with a massive gravitational scalar. Two examples of scalar-tensor theories are examined - the first example is the massive Brans-Dicke theory and the second one is a massive scalar-tensor theory indistinguishable from general relativity in the weak field limit. In the later case we study the effect of the scalar field mass on the spontaneous scalarization of neutron stars. Our numerical results show that the inclusion of a mass term for the scalar field indeed changes the picture drastica...
A Lagrangian fluctuation-dissipation relation for scalar turbulence
Drivas, Theodore D
2016-01-01
An exact relation is derived between the dissipation of scalar fluctuations and the variance of the scalar inputs (due to initial scalar values, scalar sources, and boundary fluxes) as those are sampled by stochastic Lagrangian trajectories. Previous work on the Kraichnan (1968) model of turbulent scalar advection has shown that anomalous scalar dissipation, non-vanishing in the limit of vanishing viscosity and diffusivity, is in that model due to Lagrangian spontaneous stochasticity, or non-determinism of the Lagrangian particle trajectories in the limit. We here extend this result to scalars advected by any incompressible velocity field. For fluid flows in domains without walls (e.g. periodic boxes) and for insulating/impermeable walls with zero scalar fluxes, we prove that anomalous scalar dissipation and spontaneous stochasticity are completely equivalent. For flows with imposed scalar values or non-vanishing scalar fluxes at the walls, spontaneous stochasticity still implies anomalous scalar dissipation ...
Thin layer structure of dissipation rate of scalar turbulence
Institute of Scientific and Technical Information of China (English)
ZHOU; Haibing; (周海兵); CUI; Guixiang; (崔桂香); XU; Chunxiao; (许春晓); ZHANG; Zhaoshun; (张兆顺)
2003-01-01
The structure of scalar turbulence dissipation is studied by means of direct numerical simulation. It has been discovered that the scalar turbulence dissipation exhibits thin layer structure. Based on the analysis of transportation equation of scalar turbulence dissipation, we have investigated the effect of turbulent strains on the generation of scalar turbulence dissipation and found that fluctuating scalar gradients trend to the third principal direction of turbulent strains. Therefore the generation of the thin layer structure of scalar turbulence dissipation is well interpreted.
Timelike Constant Mean Curvature Surfaces with Singularities
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2014-01-01
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces at ...
Timelike Constant Mean Curvature Surfaces with Singularities
DEFF Research Database (Denmark)
Brander, David; Svensson, Martin
2014-01-01
We use integrable systems techniques to study the singularities of timelike non-minimal constant mean curvature (CMC) surfaces in the Lorentz–Minkowski 3-space. The singularities arise at the boundary of the Birkhoff big cell of the loop group involved. We examine the behavior of the surfaces...
Geometrical Constraint on Curvature with BAO experiments
Takada, Masahiro
2015-01-01
The spatial curvature ($K$ or $\\Omega_K$) is one of the most fundamental parameters of isotropic and homogeneous universe and has a close link to the physics of early universe. Combining the radial and angular diameter distances measured via the baryon acoustic oscillation (BAO) experiments allows us to unambiguously constrain the curvature. The method is primarily based on the metric theory, but not much on the theory of structure formation other than the existence of BAO scale and is free of any model of dark energy. In this paper, we estimate a best-achievable accuracy of constraining the curvature with the BAO experiments. We show that an all-sky, cosmic-variance-limited galaxy survey covering the universe up to $z>4$ enables a precise determination of the curvature to an accuracy of $\\sigma(\\Omega_K)\\simeq 10^{-3}$. When we assume a model of dark energy, either the cosmological constraint or the $(w_0,w_a)$-model, it can achieve a precision of $\\sigma(\\Omega_K)\\simeq \\mbox{a few}\\times 10^{-4}$. These fo...
Spinal curvature measurement by tracked ultrasound snapshots.
Ungi, Tamas; King, Franklin; Kempston, Michael; Keri, Zsuzsanna; Lasso, Andras; Mousavi, Parvin; Rudan, John; Borschneck, Daniel P; Fichtinger, Gabor
2014-02-01
Monitoring spinal curvature in adolescent kyphoscoliosis requires regular radiographic examinations; however, the applied ionizing radiation increases the risk of cancer. Ultrasound imaging is favored over radiography because it does not emit ionizing radiation. Therefore, we tested an ultrasound system for spinal curvature measurement, with the help of spatial tracking of the ultrasound transducer. Tracked ultrasound was used to localize vertebral transverse processes as landmarks along the spine to measure curvature angles. The method was tested in two scoliotic spine models by localizing the same landmarks using both ultrasound and radiographic imaging and comparing the angles obtained. A close correlation was found between tracked ultrasound and radiographic curvature measurements. Differences between results of the two methods were 1.27 ± 0.84° (average ± SD) in an adult model and 0.96 ± 0.87° in a pediatric model. Our results suggest that tracked ultrasound may become a more tolerable and more accessible alternative to radiographic spine monitoring in adolescent kyphoscoliosis.
Geodesic curvature driven surface microdomain formation.
Adkins, Melissa R; Zhou, Y C
2017-09-15
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Local surface orientation dominates haptic curvature discrimination
Wijntjes, M.W.A.; Sato, A.; Hayward, V.; Kappers, A.M.L.
2009-01-01
Prior studies have shown that local surface orientation is a dominant source of information for haptic curvature perception in static conditions. We show that this dominance holds for dynamic touch, just as was shown earlier for static touch. Using an apparatus specifically developed for this purpos
Einstein Hermitian Metrics of Positive Sectional Curvature
Koca, Caner
2011-01-01
In this paper we will prove that the only compact 4-manifold M with an Einstein metric of positive sectional curvature which is also hermitian with respect to some complex structure on M, is the complex projective plane CP^2, with its Fubini-Study metric.
Curvature controlled wetting in two dimensions
DEFF Research Database (Denmark)
Gil, Tamir; Mikheev, Lev V.
1995-01-01
. As the radius of the substrate r0→∞, the leading effect of the curvature is adding the Laplace pressure ΠL∝r0-1 to the pressure balance in the film. At temperatures and pressures under which the wetting is complete in planar geometry, Laplace pressure suppresses divergence of the mean thickness of the wetting...
Resolving curvature singularities in holomorphic gravity
Mantz, C.L.M.; Prokopec, T.
2011-01-01
We formulate a holomorphic theory of gravity and study how the holomorphy symmetry alters the two most important singular solutions of general relativity: black holes and cosmology. We show that typical observers (freely) falling into a holomorphic black hole do not encounter a curvature singularity
Geodesic curvature driven surface microdomain formation
Adkins, Melissa R.; Zhou, Y. C.
2017-09-01
Lipid bilayer membranes are not uniform and clusters of lipids in a more ordered state exist within the generally disorder lipid milieu of the membrane. These clusters of ordered lipids microdomains are now referred to as lipid rafts. Recent reports attribute the formation of these microdomains to the geometrical and molecular mechanical mismatch of lipids of different species on the boundary. Here we introduce the geodesic curvature to characterize the geometry of the domain boundary, and develop a geodesic curvature energy model to describe the formation of these microdomains as a result of energy minimization. Our model accepts the intrinsic geodesic curvature of any binary lipid mixture as an input, and will produce microdomains of the given geodesic curvature as demonstrated by three sets of numerical simulations. Our results are in contrast to the surface phase separation predicted by the classical surface Cahn-Hilliard equation, which tends to generate large domains as a result of the minimizing line tension. Our model provides a direct and quantified description of the structure inhomogeneity of lipid bilayer membrane, and can be coupled to the investigations of biological processes on membranes for which such inhomogeneity plays essential roles.
Change in corneal curvature induced by surgery
G. van Rij (Gabriel)
1987-01-01
textabstractThe first section deals with the mechanisms by which sutures, incisions and intracorneal contact lenses produce a change in corneal curvature. To clarify the mechanisms by which incisions and sutures produce astigmatism, we made incisions and placed sutures in the corneoscleral limbus of
Level-Slope-Curvature - Fact or Artefact?
R. Lord (Roger); A.A.J. Pelsser (Antoon)
2005-01-01
textabstractThe first three factors resulting from a principal components analysis of term structure data are in the literature typically interpreted as driving the level, slope and curvature of the term structure. Using slight generalisations of theorems from total positivity, we present sufficient
Jozwik, Kamila M; Kriegeskorte, Nikolaus; Mur, Marieke
2016-03-01
Object similarity, in brain representations and conscious perception, must reflect a combination of the visual appearance of the objects on the one hand and the categories the objects belong to on the other. Indeed, visual object features and category membership have each been shown to contribute to the object representation in human inferior temporal (IT) cortex, as well as to object-similarity judgments. However, the explanatory power of features and categories has not been directly compared. Here, we investigate whether the IT object representation and similarity judgments are best explained by a categorical or a feature-based model. We use rich models (>100 dimensions) generated by human observers for a set of 96 real-world object images. The categorical model consists of a hierarchically nested set of category labels (such as "human", "mammal", and "animal"). The feature-based model includes both object parts (such as "eye", "tail", and "handle") and other descriptive features (such as "circular", "green", and "stubbly"). We used non-negative least squares to fit the models to the brain representations (estimated from functional magnetic resonance imaging data) and to similarity judgments. Model performance was estimated on held-out images not used in fitting. Both models explained significant variance in IT and the amounts explained were not significantly different. The combined model did not explain significant additional IT variance, suggesting that it is the shared model variance (features correlated with categories, categories correlated with features) that best explains IT. The similarity judgments were almost fully explained by the categorical model, which explained significantly more variance than the feature-based model. The combined model did not explain significant additional variance in the similarity judgments. Our findings suggest that IT uses features that help to distinguish categories as stepping stones toward a semantic representation
Spinning particles in vacuum spacetimes of different curvature types
Semerák, O.; Šrámek, M.
2015-09-01
We consider the motion of spinning test particles with nonzero rest mass in the "pole-dipole" approximation, as described by the Mathisson-Papapetrou-Dixon (MPD) equations, and examine its properties in dependence on the spin supplementary condition added to close the system. In order to better understand the spin-curvature interaction, the MPD equation of motion is decomposed in the orthonormal tetrad whose time vector is given by the four-velocity Vμ chosen to fix the spin condition (the "reference observer") and the first spatial vector by the corresponding spin sμ; such projections do not contain the Weyl scalars Ψ0 and Ψ4 obtained in the associated Newman-Penrose (NP) null tetrad. One natural option of how to choose the remaining two spatial basis vectors is shown to follow "intrinsically" whenever Vμ has been chosen; it is realizable if the particle's four-velocity and four-momentum are not parallel. In order to see how the problem depends on the algebraic type of curvature, one first identifies the first vector of the NP tetrad kμ with the highest-multiplicity principal null direction of the Weyl tensor, and then sets Vμ so that kμ belong to the spin-bivector eigenplane. In spacetimes of any algebraic type but III, it is known to be possible to rotate the tetrads so as to become "transverse," namely so that Ψ1 and Ψ3 vanish. If the spin-bivector eigenplane could be made to coincide with the real-vector plane of any of such transverse frames, the spinning particle motion would consequently be fully determined by Ψ2 and the cosmological constant; however, this can be managed in exceptional cases only. Besides focusing on specific Petrov types, we derive several sets of useful relations that are valid generally and check whether/how the exercise simplifies for some specific types of motion. The particular option of having four-velocity parallel to four-momentum is advocated, and a natural resolution of nonuniqueness of the corresponding reference
Scalar Mixing In A Vortex Flow
Meunier, P.; Villermaux, E.; Leweke, T.
We present experimental and theoretical results on the evolution of a scalar blob em- bedded in the velocity field of one or two vortices, a configuration relevant to geo- physical mixing in particular. We first follow the evolution of the scalar in one vortex. The scalar blob rolls up into a spiral and then diffuses rapidly, much faster than in the absence of a vortex flow. A simple model predicts that the maximal scalar concentration decreases in time as t-3 , after a mixing time which scales like Pe1 /2 /3 (where Pe = /D is the Peclet number). This hyper-diffusion process is due to the coupled presence of stretching and diffusion, and is in good quantitative agreement with the experimental results. In contrast with this temporal variation of the scalar, the model predicts that the proba- bility distribution functions (PDF) of the scalar are almost stationnary. The agreement between experimental and theoretical PDF is excellent. Finally, we report on the evolution of the PDF of a scalar during the merging of two vortices and on the comparison law of the concentration PDF's associated with each vortices, both in laminar and turbulent situations.
Scalar cosmological perturbations from inflationary black holes
Energy Technology Data Exchange (ETDEWEB)
Prokopec, Tomislav; Reska, Paul, E-mail: t.prokopec@uu.nl, E-mail: p.m.reska@uu.nl [Spinoza Institute and Institute for Theoretical Physics, Utrecht University, Leuvenlaan 4, 3584 CE Utrecht (Netherlands)
2011-03-01
We study the correction to the scale invariant power spectrum of a scalar field on de Sitter space from small black holes that formed during a pre-inflationary matter dominated era. The formation probability of such black holes is estimated from primordial Gaussian density fluctuations. We determine the correction to the spectrum of scalar cosmological perturbations from the Keldysh propagator of a massless scalar field on Schwarzschild-de Sitter space. Our results suggest that the effect is strong enough to be tested — and possibly even ruled out — by observations.
Newtonian Collapse of Scalar Field Dark Matter
Guzman, F S
2003-01-01
In this letter, we develop a Newtonian approach to the collapse of galaxy fluctuations of scalar field dark matter under initial conditions inferred from simple assumptions. The full relativistic system, the so called Einstein-Klein-Gordon, is reduced to the Schr\\"odinger-Newton one in the weak field limit. The scaling symmetries of the SN equations are exploited to track the non-linear collapse of single scalar matter fluctuations. The results can be applied to both real and complex scalar fields.
Levin, A.; Rubakov, V.
We consider Friedberg-Lee-Sirlin Q-balls in a (3+1)-dimensional model with vanishing scalar potential of one of the fields. We show that, unlike in (2+1) and (1+1) dimensions, the Q-ball is stabilized by the gradient energy of this field and carries scalar charge, over and beyond the global charge. The latter property is also inherent in a model with the scalar potential that does not vanish in a finite field region near the origin.
Comment on "Scalar Einstein-Aether theory"
Jacobson, Ted; Speranza, Antony J.
2014-01-01
A recent paper studies a modification of Einstein-aether theory in which the aether vector is restricted, at the level of the action, to be the gradient of a scalar. In this comment we note that this scalar version of Einstein-aether theory is equivalent to the projectable version of the IR limit of Ho\\v{r}ava gravity when the potential for the scalar is constant. This provides a generally covariant formulation for projectable Ho\\v{r}ava gravity.
Oscillons in dilaton-scalar theories
Fodor, Gyula; Horváth, Zalán; Mezei, Márk
2009-01-01
It is shown by both analytical methods and numerical simulations that extremely long living spherically symmetric oscillons appear in virtually any real scalar field theory coupled to a massless dilaton (DS theories). In fact such ''dilatonic'' oscillons are already present in the simplest non-trivial DS theory -- a free massive scalar field coupled to the dilaton. It is shown that in analogy to the previously considered cases with a single nonlinear scalar field, in DS theories there are also time periodic quasibreathers (QB) associated to small amplitude oscillons. Exploiting the QB picture the radiation law of the small amplitude dilatonic oscillons is determined analytically.
Methods for Assessing Curvature and Interaction in Mixture Experiments
Energy Technology Data Exchange (ETDEWEB)
Piepel, Gregory F.(BATTELLE (PACIFIC NW LAB)); Hicks, Ruel D.(ASSOC WESTERN UNIVERSITY); Szychowski, Jeffrey M.(ASSOC WESTERN UNIVERSITY); Loeppky, Jason L.(ASSOC WESTERN UNIVERSITY)
2002-05-01
The terms curvature and interaction traditionally are not defined or used in the context of mixture experiments because curvature and interaction effects are partially confounded due to the mixture constrain that the component proportions sum to 1.
Laser triangulation measurements of scoliotic spine curvatures.
Čelan, Dušan; Jesenšek Papež, Breda; Poredoš, Primož; Možina, Janez
2015-01-01
The main purpose of this research was to develop a new method for differentiating between scoliotic and healthy subjects by analysing the curvatures of their spines in the cranio-caudal view. The study included 247 subjects with physiological curvatures of the spine and 28 subjects with clinically confirmed scoliosis. The curvature of the spine was determined by a computer analysis of the surface of the back, measured with a non-invasive, 3D, laser-triangulation system. The determined spinal curve was represented in the transversal plane, which is perpendicular to the line segment that was defined by the initial point and the end point of the spinal curve. This was achieved using a rotation matrix. The distances between the extreme points in the antero-posterior (AP) and left-right (LR) views were calculated in relation to the length of the spine as well as the quotient of these two values LR/AP. All the measured parameters were compared between the scoliotic and control groups using the Student's t-Test in case of normal data and Kruskal-Wallis test in case of non-normal data. Besides, a comprehensive diagram representing the distances between the extreme points in the AP and LR views was introduced, which clearly demonstrated the direction and the size of the thoracic and lumbar spinal curvatures for each individual subject. While the distances between the extreme points of the spine in the AP view were found to differ only slightly between the groups (p = 0.1), the distances between the LR extreme points were found to be significantly greater in the scoliosis group, compared to the control group (p < 0.001). The quotient LR/AP was statistically significantly different in both groups (p < 0.001). The main innovation of the presented method is the ability to differentiate a scoliotic subject from a healthy subject by assessing the curvature of the spine in the cranio-caudal view. Therefore, the proposed method could be useful for human posture
Exact and Approximate Quadratures for Curvature Tensor Estimation
Langer, Torsten; Belyaev, Alexander; Seidel, Hans-Peter; Greiner, Günther; Hornegger, Joachim; Niemann, Heinrich; Stamminger, Marc
2005-01-01
Accurate estimations of geometric properties of a surface from its discrete approximation are important for many computer graphics and geometric modeling applications. In this paper, we derive exact quadrature formulae for mean curvature, Gaussian curvature, and the Taubin integral representation of the curvature tensor. The exact quadratures are then used to obtain reliable estimates of the curvature tensor of a smooth surface approximated by a dense triangle me...
Owen, Robert; Chen, Yanbei; Kaplan, Jeffrey D; Lovelace, Geoffrey; Matthews, Keith D; Nichols, David A; Scheel, Mark A; Zhang, Fan; Zimmerman, Aaron; Thorne, Kip S
2010-01-01
When one splits spacetime into space plus time, the spacetime curvature (Weyl tensor) gets split into an "electric" part E_{jk} that describes tidal gravity and a "magnetic" part B_{jk} that describes differential dragging of inertial frames. We introduce tools for visualizing B_{jk} (frame-drag vortex lines, their vorticity, and vortexes) and E_{jk} (tidal tendex lines, their tendicity, and tendexes), and also visualizations of a black-hole horizon's (scalar) vorticity and tendicity. We use these tools to elucidate the nonlinear dynamics of curved spacetime in merging black-hole binaries.
Adaptive scalarization methods in multiobjective optimization
Eichfelder, Gabriele
2008-01-01
This book presents adaptive solution methods for multiobjective optimization problems based on parameter dependent scalarization approaches. Readers will benefit from the new adaptive methods and ideas for solving multiobjective optimization.
Exotic Material as Interactions Between Scalar Fields
Directory of Open Access Journals (Sweden)
Robertson G. A.
2006-04-01
Full Text Available Many theoretical papers refer to the need to create exotic materials with average negative energies for the formation of space propulsion anomalies such as "wormholes" and "warp drives". However, little hope is given for the existence of such material to resolve its creation for such use. From the standpoint that non-minimally coupled scalar fields to gravity appear to be the current direction mathematically. It is proposed that exotic material is really scalar field interactions. Within this paper the Ginzburg-Landau (GL scalar fields associated with superconductor junctions isinvestigated as a source for negative vacuum energy fluctuations, which could be used to study the interactions among energyfluctuations, cosmological scalar (i.e., Higgs fields, and gravity.
Entangled scalar and tensor fluctuations during inflation
Energy Technology Data Exchange (ETDEWEB)
Collins, Hael; Vardanyan, Tereza [Department of Physics, Carnegie Mellon University,5000 Forbes Avenue, Pittsburgh, Pennsylvania (United States)
2016-11-29
We show how the choice of an inflationary state that entangles scalar and tensor fluctuations affects the angular two-point correlation functions of the T, E, and B modes of the cosmic microwave background. The propagators for a state starting with some general quadratic entanglement are solved exactly, leading to predictions for the primordial scalar-scalar, tensor-tensor, and scalar-tensor power spectra. These power spectra are expressed in terms of general functions that describe the entangling structure of the initial state relative to the standard Bunch-Davies vacuum. We illustrate how such a state would modify the angular correlations in the CMB with a simple example where the initial state is a small perturbation away from the Bunch-Davies state. Because the state breaks some of the rotational symmetries, the angular power spectra no longer need be strictly diagonal.
Scalar Casimir effect between two concentric spheres
Ozcan, Mustafa
2012-01-01
The Casimir effect giving rise to an attractive force between the closely spaced two concentric spheres that confine the massless scalar field is calculated by using a direct mode summation with contour integration in the complex plane of eigenfrequencies. We devoleped a new approach appropriate for the calculation of the Casimir energy for spherical boundary conditions. The Casimir energy for a massless scalar field between the closely spaced two concentric spheres coincides with the Casimir energy of the parallel plates for a massless scalar field in the limit when the dimensionless parameter {\\eta}, ({\\eta}=((a-b)/(\\surd(ab))) where a (b) is inner (outer) radius of sphere), goes to zero. The efficiency of new approach is demonstrated by calculation of the Casimir energy for a massless scalar field between the closely spaced two concentric half spheres. PACS number(s): 03.70.+k, 12.20.DS, 11.10.Gh
Collineations of the curvature tensor in general relativity
Indian Academy of Sciences (India)
Rishi Kumar Tiwari
2005-07-01
Curvature collineations for the curvature tensor, constructed from a fundamental Bianchi Type-V metric, are studied. We are concerned with a symmetry property of space-time which is called curvature collineation, and we briefly discuss the physical and kinematical properties of the models.
Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity
Ponglertsakul, Supakchai; Winstanley, Elizabeth
2017-01-01
We study soliton and black hole solutions of Einstein charged scalar field theory in cavity. We examine the effect of introducing a scalar field mass on static, spherically symmetric solutions of the field equations. We focus particularly on the spaces of soliton and black hole solutions, as well as studying their stability under linear, spherically symmetric perturbations of the metric, electromagnetic field, and scalar field.
Effect of scalar field mass on gravitating charged scalar solitons and black holes in a cavity
Ponglertsakul, Supakchai
2016-01-01
We study soliton and black hole solutions of Einstein charged scalar field theory in cavity. We examine the effect of introducing a scalar field mass on static, spherically symmetric solutions of the field equations. We focus particularly on the spaces of soliton and black hole solutions, as well as studying their stability under linear, spherically symmetric perturbations of the metric, electromagnetic field, and scalar field.
On a curvature-statistics theorem
Energy Technology Data Exchange (ETDEWEB)
Calixto, M [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, Paseo Alfonso XIII 56, 30203 Cartagena (Spain); Aldaya, V [Instituto de Astrofisica de Andalucia, Apartado Postal 3004, 18080 Granada (Spain)], E-mail: Manuel.Calixto@upct.es
2008-08-15
The spin-statistics theorem in quantum field theory relates the spin of a particle to the statistics obeyed by that particle. Here we investigate an interesting correspondence or connection between curvature ({kappa} = {+-}1) and quantum statistics (Fermi-Dirac and Bose-Einstein, respectively). The interrelation between both concepts is established through vacuum coherent configurations of zero modes in quantum field theory on the compact O(3) and noncompact O(2; 1) (spatial) isometry subgroups of de Sitter and Anti de Sitter spaces, respectively. The high frequency limit, is retrieved as a (zero curvature) group contraction to the Newton-Hooke (harmonic oscillator) group. We also make some comments on the physical significance of the vacuum energy density and the cosmological constant problem.
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Space-time curvature and cosmology
Nurgaliev, I. S.; Ponomarev, V. N.
1982-10-01
The possibility is considered of obtaining a steady-state cosmological solution in the framework of the Einstein-Cartan theory. It is found that the Einstein-Cartan equations without the cosmological constant admit a solution in the form of the static de Sitter metric for a specific value of the spin-spin gravitational interaction constant, whose introduction is required by gauge theory. It is shown that the steady-state solution might serve as a model for the pre-Friedmann stage of the expansion of the universe, when the spin-curvature interaction was comparable to the interaction between space-time curvature and energy-momentum. A value of about 10 to the -20th is obtained for the spin-spin interaction constant in the case where the de Sitter stage occurs at quantum densities (10 to the 94th g/cu cm).
Effect of intrinsic curvature on semiflexible polymers
Ghosh, Surya K.; Singh, Kulveer; Sain, Anirban
2009-11-01
Recently many important biopolymers have been found to possess intrinsic curvature. Tubulin protofilaments in animal cells, FtsZ filaments in bacteria and double stranded DNA are examples. We examine how intrinsic curvature influences the conformational statistics of such polymers. We give exact results for the tangent-tangent spatial correlation function C(r)=⟨t̂(s).t̂(s+r)⟩ , both in two and three dimensions. Contrary to expectation, C(r) does not show any oscillatory behavior, rather decays exponentially and the effective persistence length has strong length dependence for short polymers. We also compute the distribution function P(R) of the end to end distance R and show how curved chains can be distinguished from wormlike chains using loop formation probability.
Measuring Intrinsic Curvature of Space with Electromagnetism
Mabin, Mason; Becker, Maria; Batelaan, Herman
2016-10-01
The concept of curved space is not readily observable in everyday life. The educational movie "Sphereland" attempts to illuminate the idea. The main character, a hexagon, has to go to great lengths to prove that her world is in fact curved. We present an experiment that demonstrates a new way to determine if a two-dimensional surface, the 2-sphere, is curved. The behavior of an electric field, placed on a spherical surface, is shown to be related to the intrinsic Gaussian curvature. This approach allows students to gain some understanding of Einstein's theory of general relativity, which relates the curvature of spacetime to the presence of mass and energy. Additionally, an opportunity is provided to investigate the dimensionality of Gauss's law.
Scaling up the curvature of mammalian metabolism
Directory of Open Access Journals (Sweden)
Juan eBueno
2014-10-01
Full Text Available A curvilinear relationship between mammalian metabolic rate and body size on a log-log scale has been adopted in lieu of thelongstanding concept of a 3/4 allometric relationship (Kolokotrones et al. 2010. The central tenet of Metabolic Ecology (ME states that metabolism at the individual level scales-up to drive the ecology of populations, communities and ecosystems. If this tenet is correct, the curvature of metabolism should be perceived in other ecological traits. By analyzing the size scaling allometry of eight different mammalian traits including basal and field metabolic rate, offspring biomass production, ingestion rate, costs of locomotion, life span, population growth rate and population density we show that the curvature affects most ecological rates and
Cosmological scalar field perturbations can grow
Alcubierre, Miguel; Diez-Tejedor, Alberto; Torres, José M
2015-01-01
It has been argued that the small perturbations in the energy density to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the misunderstanding. We revisit a simple model in which the linear perturbations grow like those in the standard cold dark matter scenario, but with the Jeans length at the scale of the Compton wavelength of the scalar particle.
The scalar magnetic potential in magnetoencephalography
Energy Technology Data Exchange (ETDEWEB)
Dassios, G [Department of Applied Mathematics and Theoretical Physics University of Cambridge, Cambridge (United Kingdom)], E-mail: G.Dassios@damtp.cam.ac.uk
2008-07-15
Two results on Magnetoencephalography (MEG) are reported in this presentation. First, we present an integral formula connecting the scalar magnetic potential with the values of the electric potential on the boundary of a conductive region. This formula provides the magnetic potential analogue of the well known Geselowitz formula. Second, we construct the scalar magnetic potential for the realistic ellipsoidal model of the brain, as an eigenfunction expansion in terms of surface ellipsoidal harmonics.
Inflation in anisotropic scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Pimentel, L.O.; Stein-Schabes, J.
1989-01-05
The existence of an inflationary phase in anisotropic scalar-tensor theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a non-trivial potential. We then use the explicit form of the potential and the no hair theorem to conclude that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.
Inflation in anisotropic scalar-tensor theories
Pimentel, Luis O.; Stein-Schabes, Jaime
1988-01-01
The existence of an inflationary phase in anisotropic Scalar-Tensor Theories is investigated by means of a conformal transformation that allows us to rewrite these theories as gravity minimally coupled to a scalar field with a nontrivial potential. The explicit form of the potential is then used and the No Hair Theorem concludes that there is an inflationary phase in all open or flat anisotropic spacetimes in these theories. Several examples are constructed where the effect becomes manifest.
On the curvature of the real amoeba
Passare, Mikael
2011-01-01
For a real smooth algebraic curve $A \\subset (\\mathhbb{C}^*)^2$, the amoeba $\\mathcal{A} \\subset \\mathbb{R}^2$ is the image of $A$ under the map Log : $(x,y) \\mapsto (\\log |x|, \\log | y |)$. We describe an universal bound for the total curvature of the real amoeba $\\mathcal{A}_{\\mathbb{R} A}$ and we prove that this bound is reached if and only if the curve $A$ is a simple Harnack curve in the sense of Mikhalkin.
Curvature Could Give Fish Fins Their Strength
National Research Council Canada - National Science Library
2017-01-01
... maneuverable is by having the ability to generate varying amounts of force on the water when flapping a fin,” said Shreyas Mandre, an assistant professor in Brown’s School of Engineering and a co-author of the research. “We think that fish modulate curvature at the base of the fin to make it stiffer or softer, which alters the force they gene...
Transformation optics, curvature and beyond (Conference Presentation)
McCall, Martin W.
2016-04-01
Although the transformation algorithm is very well established and implemented, some intriguing questions remain unanswered. 1) In what precise mathematical sense is the transformation optics algorithm `exact'? The invariance of Maxwell's equations is well understood, but in what sense does the same principle not apply to acoustics (say)? 2) Even if the fields are transformed in a way that apparently mimic vacuum perfectly, it is easy to construct very simple examples where the impedance of the transformed medium is no longer isotropic and homogeneous. This would seem to imply a fundamental shortcoming in any claim that electromagnetic cloaking has been reduced to technology. 3) Transformations are known to exist that introduce a discrepancy between the Poynting vector and the wave-vector. Does this distinction carry any physical significance? We have worked extensively on understanding a commonality between transformation theories that operates at the level of rays - being interpreted as geodesics of an appropriate manifold. At this level we now understand that the *key* problem underlying all attempts to unify the transformational approach to disparate areas of physics is how to relate the transformation of the base metric (be it Euclidean for spatial transformation optics, or Minkowskian for spacetime transformation optics) to the medium parameters of a given physical domain (e.g. constitutive parameters for electromagnetism, bulk modulus and mass density for acoustics, diffusion constant and number density for diffusion physics). Another misconception we will seek to address is the notion of the relationship between transformation optics and curvature. Many have indicated that transformation optics evinces similarities with Einstein's curvature of spacetime. Here we will show emphatically that transformation optics cannot induce curvature. Inducing curvature in an electromagnetic medium requires the equivalent of a gravitational source. We will propose a scheme
Menger curvature and rectifiability in metric spaces
2012-01-01
We show that for any metric space $X$ the condition \\[ \\int_X\\int_X\\int_X c(z_1,z_2,z_3)^2\\, d\\Hm z_1\\, d\\Hm z_2\\, d\\Hm z_3 < \\infty, \\] where $c(z_1,z_2,z_3)$ is the Menger curvature of the triple $(z_1,z_2,z_3)$, guarantees that $X$ is rectifiable.
Gravitational curvature an introduction to Einstein's theory
Frankel, Theodore
2011-01-01
This classic text and reference monograph applies modern differential geometry to general relativity. A brief mathematical introduction to gravitational curvature, it emphasizes the subject's geometric essence, replacing the often-tedious analytical computations with geometric arguments. Clearly presented and physically motivated derivations express the deflection of light, Schwarzchild's exterior and interior solutions, and the Oppenheimer-Volkoff equations. A perfect choice for advanced students of mathematics, this volume will also appeal to mathematicians interested in physics. It stresses
Curvature of spacetime: A simple student activity
Wood, Monika; Smith, Warren; Jackson, Matthew
2016-12-01
The following is a description of an inexpensive and simple student experiment for measuring the differences between the three types of spacetime topology—Euclidean (flat), Riemann (spherical), and Lobachevskian (saddle) curvatures. It makes use of commonly available tools and materials, and requires only a small amount of construction. The experiment applies to astronomical topics such as gravity, spacetime, general relativity, as well as geometry and mathematics.
Physics performances for Scalar Electrons, Scalar Muons and Scalar Neutrinos searches at CLIC
Battaglia, M; Marshall, J; Nardulli, J; Thomson, M A; Sailer, A; van der Kraaij, E
2011-01-01
The determination of scalar leptons and gauginos masses is an important part of the program of spectroscopic studies of Supersymmetry at a high energy linear collider. In this note we present results of a study of the processes: e+e− → e ̃+R e ̃−R → e+e− χ ̃10 χ ̃10, e+e− → μ ̃R+ μ ̃R− → e+e− χ ̃10 χ ̃10, e+e− → e ̃+L e ̃−L → e+ e− χ ̃20 χ ̃20 and e+e− → ν ̃e ν ̃e → e+ e− χ ̃1+ χ ̃1− in a Supersymmetric scenario at 3 TeV at CLIC. We report the expected accuracies on the production cross sections and on the e ̃R, μ ̃R, ν ̃e, χ ̃1± and χ ̃10 mass determination. We present the performances on the lepton energy resolution and boson mass resolution, and discuss the requirements on the luminosity spectrum, boson tagging, as well as on the detector time stamping capability and beam polarization. Results are obtained after full simulation and reconstruction with overlay of beam-beam induced background.
Ultrafast Drop Movements Arising from Curvature Gradient
Lv, Cunjing; Chuang, Yin-Chuan; Tseng, Fan-Gang; Yin, Yajun; Zheng, Quanshui
2011-01-01
We report experimental observation of a kind of fast spontaneous movements of water drops on surfaces of cones with diameters from 0.1 to 1.5 mm. The observed maximum speed (0.22 m/s) under ambient conditions were at least two orders of magnitude higher than that resulting from any known single spontaneous movement mechanism, for example, Marangoni effect due to gradient of surface tension. We trapped even higher spontaneous movement speeds (up to 125 m/s) in virtual experiments for drops on nanoscale cones by using molecular dynamics simulations. The underlying mechanism is found to be universally effective - drops on any surface either hydrophilic or hydrophobic with varying mean curvature are subject to driving forces toward the gradient direction of the mean curvature. The larger the mean curvature of the surface and the lower the contact angle of the liquid are, the stronger the driving force will be. This discovery can lead to more effective techniques for transporting droplets.
Intrinsically disordered proteins drive membrane curvature
Busch, David J.; Houser, Justin R.; Hayden, Carl C.; Sherman, Michael B.; Lafer, Eileen M.; Stachowiak, Jeanne C.
2015-07-01
Assembly of highly curved membrane structures is essential to cellular physiology. The prevailing view has been that proteins with curvature-promoting structural motifs, such as wedge-like amphipathic helices and crescent-shaped BAR domains, are required for bending membranes. Here we report that intrinsically disordered domains of the endocytic adaptor proteins, Epsin1 and AP180 are highly potent drivers of membrane curvature. This result is unexpected since intrinsically disordered domains lack a well-defined three-dimensional structure. However, in vitro measurements of membrane curvature and protein diffusivity demonstrate that the large hydrodynamic radii of these domains generate steric pressure that drives membrane bending. When disordered adaptor domains are expressed as transmembrane cargo in mammalian cells, they are excluded from clathrin-coated pits. We propose that a balance of steric pressure on the two surfaces of the membrane drives this exclusion. These results provide quantitative evidence for the influence of steric pressure on the content and assembly of curved cellular membrane structures.
Localization of gravity on a thick braneworld without scalar fields
Herrera-Aguilar, Alfredo; Mora-Luna, Refugio Rigel
2010-01-01
In this work we present a simple thick braneworld model that is generated by an intriguing interplay between a 5D cosmological constant with a de Sitter metric induced in the 3-brane without the inclusion of scalar fields. We show that 4D gravity is localized on this brane, provide analytic expressions for the massive Kaluza-Klein (KK) fluctuation modes and also show that the spectrum of metric excitations displays a mass gap. We finally present the corrections to Newton's law due to these massive modes. This model has no naked singularities along the fifth dimension despite the existence of a mass gap in the graviton spectrum as it happens in thick branes with 4D Poincare symmetry, providing a simple model with very good features: the curvature is completely smooth along the fifth dimension, it localizes 4D gravity and the spectrum of gravity fluctuations presents a mass gap, a fact that rules out the existence of phenomenologically dangerous ultralight KK excitations in the model.
Distributed mean curvature on a discrete manifold for Regge calculus
Conboye, Rory; Ray, Shannon
2015-01-01
The integrated mean curvature of a simplicial manifold is well understood in both Regge Calculus and Discrete Differential Geometry. However, a well motivated pointwise definition of curvature requires a careful choice of volume over which to uniformly distribute the local integrated curvature. We show that hybrid cells formed using both the simplicial lattice and its circumcentric dual emerge as a remarkably natural structure for the distribution of this local integrated curvature. These hybrid cells form a complete tessellation of the simplicial manifold, contain a geometric orthonormal basis, and are also shown to give a pointwise mean curvature with a natural interpretation as a fractional rate of change of the normal vector.
Free-streaming radiation in cosmological models with spatial curvature
Wilson, M. L.
1982-01-01
The effects of spatial curvature on radiation anisotropy are examined for the standard Friedmann-Robertson-Walker model universes. The effect of curvature is found to be very important when considering fluctuations with wavelengths comparable to the horizon. It is concluded that the behavior of radiation fluctuations in models with spatial curvature is quite different from that in spatially flat models, and that models with negative curvature are most strikingly different. It is therefore necessary to take the curvature into account in careful studies of the anisotropy of the microwave background.
A curvature theory for discrete surfaces based on mesh parallelity
Bobenko, Alexander Ivanovich
2009-12-18
We consider a general theory of curvatures of discrete surfaces equipped with edgewise parallel Gauss images, and where mean and Gaussian curvatures of faces are derived from the faces\\' areas and mixed areas. Remarkably these notions are capable of unifying notable previously defined classes of surfaces, such as discrete isothermic minimal surfaces and surfaces of constant mean curvature. We discuss various types of natural Gauss images, the existence of principal curvatures, constant curvature surfaces, Christoffel duality, Koenigs nets, contact element nets, s-isothermic nets, and interesting special cases such as discrete Delaunay surfaces derived from elliptic billiards. © 2009 Springer-Verlag.
Dengiz, Suat
2014-01-01
Weyl-invariant extensions of three-dimensional New Massive Gravity, generic n-dimensional Quadratic Curvature Gravity theories and three-dimensional Born-Infeld gravity theory are analyzed in details. As required by Weyl-invariance, the actions of these gauge theories do not contain any dimensionful parameter hence the local symmetry is spontaneously broken in (Anti) de Sitter vacua in complete analogy with the Standard Model Higgs mechanism. In flat vacuum, symmetry breaking mechanism is more complicated: The dimensionful parameters come from dimensional transmutation in the quantum field theory; therefore, the conformal symmetry is radiatively broken (at two loop level in 3-dimensions and at one-loop level in 4-dimensions) \\`{a} la Coleman-Weinberg mechanism. In the broken phases, save for New Massive Gravity, the theories generically propagate with a unitary (tachyon and ghost-free) massless tensor, massive (or massless) vector and massless scalar particles for the particular intervals of the dimensionless...
Castel-Branco, Nuno; March, Riccardo
2014-01-01
In this work, the effects of a nonminimally coupled model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. Based upon a Taylor expansion around $R = 0$ for both functions $f^1(R)$ and $f^2(R)$, we find that the metric around a spherical object is a perturbation of the weak-field Schwarzschild metric: the time perturbation is shown to be a Newtonian plus Yukawa term, which can be constrained using the available experimental results. We conclude that the Starobinsky model for inflation complemented with a generalized preheating mechanism is not experimentally constrained by observations. The geodetic precession effects of the model are also shown to be of no relevance for the constraints.
The Scale-invariant Power Spectrum of Primordial Curvature Perturbation in CSTB Cosmos
Li, Changhong
2014-01-01
We investigate the spectrum of cosmological perturbations in a bounce cosmos modeled by a scalar field coupled to the string tachyon field (CSTB cosmos). By explicit computation of its primordial spectral index we show the power spectrum of curvature perturbations, generated during the tachyon matter dominated contraction phase, to be nearly scale invariant. We propose a unified space of parameters for a systematic study of inflationary/bouncing cosmologies. We find that CSTB cosmos is dual--in Wands's sense--to the slow-roll inflation model as can be easily seen from this unified parameter space. Guaranteed by the dynamical attractor behavior of CSTB Cosmos, this scale invariance is free of the fine-tuning problem, in contrast to the slow-roll inflation model.