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19,387
Euler characters and submanifolds of constant positive curvature
 Trans. Amer. Math. Soc
"... Abstract. This article develops methods for studying the topology of submanifolds of constant positive curvature in Euclidean space. It proves that if M n is an ndimensional compact connected Riemannian submanifold of constant positive curvature in E 2n−1,thenM n must be simply connected. It also g ..."
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Cited by 3 (1 self)
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Abstract. This article develops methods for studying the topology of submanifolds of constant positive curvature in Euclidean space. It proves that if M n is an ndimensional compact connected Riemannian submanifold of constant positive curvature in E 2n−1,thenM n must be simply connected. It also
Finsler metrics of constant positive curvature on the Lie group
 S 3 , J. Lond. Math. Soc
"... Abstract. Guided by the Hopf fibration, we single out a family (indexed by a positive constant K) of right invariant Riemannian metrics on the Lie group S 3. Using the Yasuda–Shimada theorem as an inspiration, we determine for each K> 1 a privileged right invariant Killing field of constant lengt ..."
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Cited by 17 (3 self)
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length. Each such Riemannian metric pairs with the corresponding Killing field to produce a yglobal and explicit Randers metric on S 3. Using the machinery of spray curvature and Berwald’s formula for it, we prove directly that the said Randers metric has constant positive flag curvature K, as predicted
A twocomponent geodesic equation on a space of constant positive curvature
 J. Geom. Phys
"... Abstract. We propose a new twocomponent geodesic equation with the unusual property that the underlying space has constant positive curvature. In the special case of one space dimension, the equation reduces to the twocomponent HunterSaxton equation. ..."
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Cited by 1 (0 self)
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Abstract. We propose a new twocomponent geodesic equation with the unusual property that the underlying space has constant positive curvature. In the special case of one space dimension, the equation reduces to the twocomponent HunterSaxton equation.
Implicit Fairing of Irregular Meshes using Diffusion and Curvature Flow
, 1999
"... In this paper, we develop methods to rapidly remove rough features from irregularly triangulated data intended to portray a smooth surface. The main task is to remove undesirable noise and uneven edges while retaining desirable geometric features. The problem arises mainly when creating highfidelit ..."
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Cited by 542 (23 self)
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curvature flow operator that achieves a smoothing of the shape itself, distinct from any parameterization. Additional features of the algorithm include automatic exact volume preservation, and hard and soft constraints on the positions of the points in the mesh. We compare our method to previous operators
Conformal deformation of a Riemannian metric to constant curvature
 J. Diff. Geome
, 1984
"... A wellknown open question in differential geometry is the question of whether a given compact Riemannian manifold is necessarily conformally equivalent to one of constant scalar curvature. This problem is known as the Yamabe problem because it was formulated by Yamabe [8] in 1960, While Yamabe&apos ..."
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Cited by 308 (0 self)
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of Yamabe's problem gives a conformally flat metric of constant scalar curvature, a metric of some geometric interest. Note that the class of conformally flat manifolds of positive scalar curvature is closed under the operation of connected sum, and hence contains connected sums of spherical space
A Fast Marching Level Set Method for Monotonically Advancing Fronts
 PROC. NAT. ACAD. SCI
, 1995
"... We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential eq ..."
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Cited by 630 (24 self)
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We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential
Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features
, 1983
"... For a successful analysis of the relation between amino acid sequence and protein structure, an unambiguous and physically meaningful definition of secondary structure is essential. We have developed a set of simple and physically motivated criteria for secondary structure, programmed as a patternr ..."
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Cited by 2096 (5 self)
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. ” Geometric structure is defined in terms of the concepts torsion and curvature of differential geometry. Local chain “chirality ” is the torsional handedness of four consecutive Ca positions and is positive for righthanded helices and negative for ideal twisted @sheets. Curved pieces are defined as “bends
Shape modeling with front propagation: A level set approach
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and over ..."
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Cited by 808 (20 self)
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along its gradient field with constant speed or a speed that depends on the curvature. It is moved by solving a “HamiltonJacob? ’ type equation written for a function in which the interface is a particular level set. A speed term synthesizpd from the image is used to stop the interface in the vicinity
Attention and the detection of signals
 Journal of Experimental Psychology: General
, 1980
"... Detection of a visual signal requires information to reach a system capable of eliciting arbitrary responses required by the experimenter. Detection latencies are reduced when subjects receive a cue that indicates where in the visual field the signal will occur. This shift in efficiency appears to b ..."
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Cited by 565 (2 self)
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about the way in which expectancy improves performance. First, when subjects are cued on each trial, they show stronger expectancy effects than when a probable position is held constant for a block, indicating the active nature of the expectancy. Second, while information on spatial position improves
Results 1  10
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19,387