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27
Geometric Holography, the Renormalization Group and the cTheorem, hepth/9807226,Nucl.Phys. B541
, 1999
"... In this paper the whole geometrical setup giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a holographic version of Zamolodchikov’s ctheorem is proven. 1 ..."
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Cited by 43 (8 self)
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In this paper the whole geometrical setup giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a holographic version of Zamolodchikov’s ctheorem is proven. 1
Constrained Motion Control Using Vector Potential Fields
, 2000
"... This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and wellbehaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal ..."
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Cited by 24 (9 self)
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This paper discusses the generation of a control signal that would instruct the actuators of a robotics manipulator to drive motion along a safe and wellbehaved path to a desired target. The proposed concept of navigation control along with the tools necessary for its construction achieve this goal. The most significant tool is the artificial vector potential field which shows a better ability to steer motion than does a scalar potential field. The synthesis procedure emphasizes flexibility so that the effort needed to modify the control is commensurate with the change in the geometry of the workspace. Theoretical development along with simulation results are provided.
Brain surface conformal parameterization using riemann surface structure
 IEEE Trans. Med. Imaging
, 2007
"... Abstract—In medical imaging, parameterized 3D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surfacebased registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a s ..."
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Cited by 20 (15 self)
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Abstract—In medical imaging, parameterized 3D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surfacebased registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3D brain surface manifolds to modified PDEs on a twodimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified
Modelling and calibration of logarithmic CMOS image sensors
 in 1982 and the Ph.D. degree from the University of
, 2002
"... Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be ..."
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Cited by 5 (2 self)
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Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the author. Logarithmic CMOS image sensors capture high dynamic range scenes without saturation or loss of perceptible detail but problems exist with image quality. This thesis develops and applies methods of modelling and calibration to understand and improve the fixed pattern noise (FPN) and colour rendition of logarithmic imagers. Chapter 1 compares CCD and CMOS image sensors and, within the latter category, compares linear and logarithmic pixel designs. Chapter 2 reviews the literature on multilinear algebra, unifying and extending approaches for analytic and numeric manipulation of multiindex arrays, which are the generalisation of scalars, vectors and matrices. Chapter 3 defines and solves the problem of multilinear regression with linear constraints for the calibration of a sensor array, permitting models with linear relationships of parameters
String representation of Wilson loops
"... We explore the consequences of imposing Polyakov’s zig/zaginvariance in the search for a confining string. We first find that the requirement of zig/zaginvariance seems to be incompatible with spacetime supersymmetry. We then try to find zig/zaginvariant string backgrounds on which to implement th ..."
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Cited by 5 (1 self)
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We explore the consequences of imposing Polyakov’s zig/zaginvariance in the search for a confining string. We first find that the requirement of zig/zaginvariance seems to be incompatible with spacetime supersymmetry. We then try to find zig/zaginvariant string backgrounds on which to implement the minimalarea prescription for the calculation of Wilson loops considering different possibilities. 1
Deviation of geodesics in FLRW spacetime geometries
, 1997
"... The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the FriedmannLemaitreRobertsonWalker (`FLRW') models, where we assume the sources to be g ..."
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Cited by 4 (2 self)
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The geodesic deviation equation (`GDE') provides an elegant tool to investigate the timelike, null and spacelike structure of spacetime geometries. Here we employ the GDE to review these structures within the FriedmannLemaitreRobertsonWalker (`FLRW') models, where we assume the sources to be given by a noninteracting mixture of incoherent matter and radiation, and we also take a nonzero cosmological constant into account. For each causal case we present examples of solutions to the GDE and we discuss the interpretation of the related first integrals. The de Sitter spacetime geometry is treated separately. This paper is dedicated to Engelbert Schucking email: ellis@maths.uct.ac.za y email: henk@gmunu.mth.uct.ac.za 1 INTRODUCTION 2 1 Introduction It has been known for a long while that the geodesic deviation equation (`GDE'), first obtained by J L Synge [23, 24], provides a very elegant way of understanding features of curved spaces, and, as pointed out by Pirani [14, 1...
Remarks on the Calculation of Transonic Potential Flow by a Finite Volume Method
 Proc. IMA Conference on Numerical Methods in Fluid Dynamics
, 1978
"... The purpose of this paper is to review the development of a finite volume method for the numerical calculation of transonic flow, under the assumption that the flow is irrotational, so that the velocity can be represented as the gradient of the potential. Essentially this limits the application of t ..."
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Cited by 4 (4 self)
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The purpose of this paper is to review the development of a finite volume method for the numerical calculation of transonic flow, under the assumption that the flow is irrotational, so that the velocity can be represented as the gradient of the potential. Essentially this limits the application of the method to flows containing fairly week
Null geodesics in fivedimensional manifolds
 Gen. Rel. Grav
, 2001
"... We analyze a class of 5D noncompact warpedproduct spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the socalled canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricciflat, th ..."
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Cited by 3 (1 self)
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We analyze a class of 5D noncompact warpedproduct spaces characterized by metrics that depend on the extra coordinate via a conformal factor. Our model is closely related to the socalled canonical coordinate gauge of Mashhoon et al. We confirm that if the 5D manifold in our model is Ricciflat, then there is an induced cosmological constant in the 4D submanifold. We derive the general form of the 5D Killing vectors and relate them to the 4D Killing vectors of the embedded spacetime. We then study the 5D null geodesic paths and show that the 4D part of the motion can be timelike — that is, massless particles in 5D can be massive in 4D. We find that if the null trajectories are affinely parameterized in 5D, then the particle is subject to an anomalous acceleration or fifth force. However, this force may be removed by reparameterization, which brings the correct definition of the proper time into question. Physical properties of the geodesics — such as rest mass variations induced by a variable cosmological “constant”, constants of the motion and 5D timedilation effects — are discussed and are shown to be open to experimental or observational investigation.
Solving pdes on manifolds with global conformal parameterization
 In VLSM
, 2005
"... Abstract. In this paper, we propose a method to solve PDEs on surfaces with arbitrary topologies by using the global conformal parametrization. The main idea of this method is to map the surface conformally to 2D rectangular areas and then transform the PDE on the 3D surface into a modified PDE on t ..."
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Cited by 2 (1 self)
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Abstract. In this paper, we propose a method to solve PDEs on surfaces with arbitrary topologies by using the global conformal parametrization. The main idea of this method is to map the surface conformally to 2D rectangular areas and then transform the PDE on the 3D surface into a modified PDE on the 2D parameter domain. Consequently, we can solve the PDE on the parameter domain by using some wellknown numerical schemes on R 2. To do this, we have to define a new set of differential operators on the manifold such that they are coordinates invariant. Since the Jacobian of the conformal mapping is simply a multiplication of the conformal factor, the modified PDE on the parameter domain will be very simple and easy to solve. In our experiments, we demonstrated our idea by solving the NavierStoke’s equation on the surface. We also applied our method to some image processing problems such as segmentation, image denoising and image inpainting on the surfaces. 1
Fast instability indicator in few dimensional dynamical systems
 The Ninth Marcel Grossmann Meeting Proceedings of the MGIXMM Meeting held at The University of Rome ‘‘La Sapienza’’. Singapore: World Scientific Publishing
, 2002
"... Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e., quickly) than the usual tools, like Lyapunov Characteristic Numbers (LCN’s) or Poincaré Surface of Section. Moreover, at variance wi ..."
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Cited by 2 (0 self)
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Using the tools of Differential Geometry, we define a new fast chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e., quickly) than the usual tools, like Lyapunov Characteristic Numbers (LCN’s) or Poincaré Surface of Section. Moreover, at variance with other fast indicators proposed in the Literature, it gives informations about the asymptotic behaviour of trajectories, though being local in phasespace. Furthermore, it detects the chaotic or regular nature of geodesics without any reference to a given perturbation and it allows also to discriminate between different regimes (and possibly sources) of chaos in distinct regions of phasespace. Chaotic dynamics is believed to be the rule rather than the exception in any generic nonlinear dynamical system; however, there is no general fast method able to determine what’s the fraction of the allowed phase space occupied by chaotic orbits. This problem exists in the case of few degrees of freedom (dof) systems and for many dimensional ones as well, though it originates from different causes in the two situations. Recently the authors derived 4 a geometric indicator of Chaos, able