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On the Early History of the Singular Value Decomposition
, 1992
"... This paper surveys the contributions of five mathematicians  Eugenio Beltrami (18351899), Camille Jordan (18381921), James Joseph Sylvester (18141897), Erhard Schmidt (18761959), and Hermann Weyl (18851955)  who were responsible for establishing the existence of the singular value de ..."
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Cited by 122 (1 self)
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This paper surveys the contributions of five mathematicians  Eugenio Beltrami (18351899), Camille Jordan (18381921), James Joseph Sylvester (18141897), Erhard Schmidt (18761959), and Hermann Weyl (18851955)  who were responsible for establishing the existence of the singular value
Comprehending Monads
 Mathematical Structures in Computer Science
, 1992
"... Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised t ..."
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Cited by 522 (16 self)
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Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be generalised to an arbitrary monad, and how the resulting programming feature can concisely express in a pure functional language some programs that manipulate state, handle exceptions, parse text, or invoke continuations. A new solution to the old problem of destructive array update is also presented. No knowledge of category theory is assumed.
A geometrical framework for low level vision
 IEEE Trans. on Image Processing
, 1998
"... Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, an ..."
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Cited by 221 (35 self)
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Abstract—We introduce a new geometrical framework based on which natural flows for image scale space and enhancement are presented. We consider intensity images as surfaces in the space. The image is, thereby, a twodimensional (2D) surface in threedimensional (3D) space for graylevel images, and 2D surfaces in five dimensions for color images. The new formulation unifies many classical schemes and algorithms via a simple scaling of the intensity contrast, and results in new and efficient schemes. Extensions to multidimensional signals become natural and lead to powerful denoising and scale space algorithms. Index Terms — Color image processing, image enhancement, image smoothing, nonlinear image diffusion, scalespace. I.
Pseudospheres in geometry and physics: from Beltrami to De Sitter and beyond ∗
, 2005
"... We review the extraordinary fertility and proliferation in mathematics and physics of the concept of a surface with constant and negative Gaussian curvature. In his outstanding 1868 paper Beltrami discussed how nonEuclidean geometry is actually realized and displayed in a disk on the plane. This me ..."
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Cited by 2 (0 self)
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We review the extraordinary fertility and proliferation in mathematics and physics of the concept of a surface with constant and negative Gaussian curvature. In his outstanding 1868 paper Beltrami discussed how nonEuclidean geometry is actually realized and displayed in a disk on the plane
On convex Sobolev inequalities and the rate of convergence to equilibrium for FokkerPlanck type equations
, 2000
"... It is well known that the analysis of the largetime asymptotics of FokkerPlanck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view. In our unified presentation of the th ..."
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Cited by 168 (23 self)
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It is well known that the analysis of the largetime asymptotics of FokkerPlanck type equations by the entropy method is closely related to proving the validity of convex Sobolev inequalities. Here we highlight this connection from an applied PDE point of view. In our unified presentation of the theory we present new results to the following topics: an elementary derivation of BakryEmery type conditions, results concerning perturbations of invariant measures with general admissible entropies, sharpness of convex Sobolev inequalities, applications to nonsymmetric linear and certain nonlinear FokkerPlanck type equations (DesaiZwanzig model, driftdiffusionPoisson model).
A TRANSMISSION LINE MODEL FOR THE SPHERICAL BELTRAMI PROBLEM
"... We extend a previously introduced model for finding eigenvalues and eigenfunctions of PDEs with a certain natural symmetry set based on an analysis of an equivalent transmission line circuit. This was previously applied with success in the case of optical fibers [8], [9] as well as in the case of a ..."
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linear Schroedinger equation [10], [11] and recently in the case of spherical symmetry (Ball Lightning) [12]. We explore the interpretation of eigenvalues as resonances of the corresponding transmission line model. We use the generic Beltrami problem of nonconstant eigenvorticity in spherical
LaplaceBeltrami Eigenfunctions Towards an algorithm that “understands ” geometry
"... One of the challenges in geometry processing is to automatically reconstruct a higherlevel representation from raw geometric data. For instance, computing a parameterization of an object helps attaching information to it and converting between various representations. More generally, this family ..."
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ally, this family of problems may be thought of in terms of constructing structured function bases attached to surfaces. In this paper, we study a specific type of hierarchical function bases, defined by the eigenfunctions of the LaplaceBeltrami operator. When applied to a sphere, this function basis corresponds
Results 1  10
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1,482