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SemiSupervised Learning Using Gaussian Fields and Harmonic Functions
 IN ICML
, 2003
"... An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning ..."
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Cited by 741 (15 self)
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An approach to semisupervised learning is proposed that is based on a Gaussian random field model. Labeled and unlabeled data are represented as vertices in a weighted graph, with edge weights encoding the similarity between instances. The learning
On the applications of harmonic functions to robotics
 Journal of Robotic Systems
, 1993
"... Harmonic functions are solutions to Laplace's Equation. As noted in a previous paper, they can be used to advantage for potential eld path planning, since they do not exhibit spurious local minima. In this paper, harmonic functions are shown to have a number of other properties (including comp ..."
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Cited by 168 (40 self)
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Harmonic functions are solutions to Laplace's Equation. As noted in a previous paper, they can be used to advantage for potential eld path planning, since they do not exhibit spurious local minima. In this paper, harmonic functions are shown to have a number of other properties (including
INTERPOLATION BY POSITIVE HARMONIC FUNCTIONS
, 2006
"... Abstract. A natural interpolation problem in the cone of positive harmonic functions is considered and the corresponding interpolating sequences are geometrically described. 1. ..."
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Abstract. A natural interpolation problem in the cone of positive harmonic functions is considered and the corresponding interpolating sequences are geometrically described. 1.
Spaces of harmonic functions
 J. London Math. Soc
"... It is important and interesting to study harmonic functions on a Riemannian manifold. In an earlier work of Li and Tam [21] it was demonstrated that the dimensions of various spaces of bounded and positive harmonic functions are closely related to the number of ends of a manifold. For the linear spa ..."
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Cited by 16 (4 self)
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It is important and interesting to study harmonic functions on a Riemannian manifold. In an earlier work of Li and Tam [21] it was demonstrated that the dimensions of various spaces of bounded and positive harmonic functions are closely related to the number of ends of a manifold. For the linear
Singular sets of harmonic functions
 in R2 and their complexifications in C2, Indiana Univ. Math J
"... In the present lecture notes, we shall discuss the relation between the growth of harmonic functions and the growth of nodal sets of those functions. The growth of harmonic functions is measured by their frequency. For any harmonic function u in the unit ball B1 ⊂ Rn, the frequency is defined as ..."
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Cited by 8 (0 self)
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In the present lecture notes, we shall discuss the relation between the growth of harmonic functions and the growth of nodal sets of those functions. The growth of harmonic functions is measured by their frequency. For any harmonic function u in the unit ball B1 ⊂ Rn, the frequency is defined as
Applications of Harmonic Functions to Robotics
 Journal of Robotic Systems
, 1992
"... Harmonic functions are solutions to Laplace's Equation. As noted in a previous paper, they can be used to advantage for potentialfield path planning, since they do not exhibit spurious local minima. In this paper, harmonic functions are shown to have a number of other properties (including ..."
Abstract
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Harmonic functions are solutions to Laplace's Equation. As noted in a previous paper, they can be used to advantage for potentialfield path planning, since they do not exhibit spurious local minima. In this paper, harmonic functions are shown to have a number of other properties (including
SURFACE INTEGRALS AND HARMONIC FUNCTIONS
, 2003
"... Using the notion of inferior mean due to M. Heins, we establish two inequalities for such a mean relative to a positive harmonic function defined on the open unit ball or halfspace in Rn+1. 1. ..."
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Using the notion of inferior mean due to M. Heins, we establish two inequalities for such a mean relative to a positive harmonic function defined on the open unit ball or halfspace in Rn+1. 1.
Harmonic functions and collision probabilities
 in Proceedings of the IEEE International Conference on Robotics and Automation
, 1994
"... There is a close relationship between harmonic functions— which have recently been proposed for path planning—and hitting probabilities for random processes. The hitting probabilities for random walks can be cast as a Dirichlet problem for harmonic functions, in much the same wa ..."
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Cited by 21 (2 self)
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There is a close relationship between harmonic functions— which have recently been proposed for path planning—and hitting probabilities for random processes. The hitting probabilities for random walks can be cast as a Dirichlet problem for harmonic functions, in much the same
AN APPLICATION OF SUBORDINATION ON HARMONIC FUNCTION
, 2007
"... ABSTRACT. The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belonging to the classes S ∗ H [A, B], KH[A, B] defined by subordination, and we give some convolution conditions. Finally, we examine the closure properties of the operator D n on these classes under ..."
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ABSTRACT. The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belonging to the classes S ∗ H [A, B], KH[A, B] defined by subordination, and we give some convolution conditions. Finally, we examine the closure properties of the operator D n on these classes under
TYPICALLY REAL HARMONIC FUNCTIONS
, 903
"... Abstract. We consider a class T O H of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class. 1. ..."
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Abstract. We consider a class T O H of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class. 1.
Results 1  10
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354,089