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929
The quantum structure of spacetime at the Planck scale and quantum fields
 COMMUN. MATH. PHYS. 172, 187–220 (1995)
, 1995
"... We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg’s principle and by Einstein’s theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation relations exactly implement our uncertainty relations. We outl ..."
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Cited by 332 (6 self)
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outline the definition of free fields and interactions over QST and take the first steps to adapting the usual perturbation theory. The quantum nature of the underlying spacetime replaces a local interaction by a specific nonlocal effective interaction in the ordinary Minkowski space. A detailed study
MODELLING USUAL AND UNUSUAL ANISOTROPIC SPHERES
, 2009
"... In this paper, we study anisotropic spheres builded from known static spherical solutions. In particular, we are interested in the physical consequences caused by a ”small ” departure from a physically sensible configuration. The obtained solutions smoothly depend on free parameters. By setting thes ..."
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In this paper, we study anisotropic spheres builded from known static spherical solutions. In particular, we are interested in the physical consequences caused by a ”small ” departure from a physically sensible configuration. The obtained solutions smoothly depend on free parameters. By setting
QUANTUM ISOMETRIES AND NONCOMMUTATIVE SPHERES
, 905
"... Abstract. We introduce and study two new examples of noncommutative spheres: the halfliberated sphere, and the free sphere. Together with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is “easy”, in the representation theory sense. We present as ..."
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Cited by 20 (10 self)
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Abstract. We introduce and study two new examples of noncommutative spheres: the halfliberated sphere, and the free sphere. Together with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is “easy”, in the representation theory sense. We present
Agnostic active learning
 In ICML
, 2006
"... We state and analyze the first active learning algorithm which works in the presence of arbitrary forms of noise. The algorithm, A2 (for Agnostic Active), relies only upon the assumption that the samples are drawn i.i.d. from a fixed distribution. We show that A2 achieves an exponential improvement ..."
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Cited by 190 (15 self)
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(i.e., requires only O � ln 1 ɛ samples to find an ɛoptimal classifier) over the usual sample complexity of supervised learning, for several settings considered before in the realizable case. These include learning threshold classifiers and learning homogeneous linear separators with respect
Quantization of the sphere . . .
, 2008
"... Current views link quantization with dynamics. The reason is that quantum mechanics or quantum field theories address to dynamical systems, i.e., particles or fields. Our point of view here breaks the link between quantization and dynamics: any (classical) physical system can be quantized. Only dyna ..."
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, or any kind of parameters. When X has a symplectic structure, it can be considered as a phase space, and our approach is then equivalent to the usual quantization, although with some peculiar characteristics. But the CS procedure is much more general and can be applied even in the absence of symplectic
Wavelets on the 2sphere: A grouptheoretical approach
 APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
, 1999
"... We present a purely grouptheoretical derivation of the continuous wavelet transform (CWT) on the 2sphere S 2, based on the construction of general coherent states associated to square integrable group representations. The parameter space X of our CWT is the product of SO(3) for motions and R + ∗ f ..."
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Cited by 70 (14 self)
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We present a purely grouptheoretical derivation of the continuous wavelet transform (CWT) on the 2sphere S 2, based on the construction of general coherent states associated to square integrable group representations. The parameter space X of our CWT is the product of SO(3) for motions and R
Classification of tilings of the 2dimensional sphere by congruent triangles
 Hiroshima Math. J
, 2002
"... We give a new classification of tilings of the 2dimensional sphere by congruent triangles accompanied with a complete proof. This accomplishes the old classification by Davies, who only gave an outline of the proof, regrettably with some redundant tilings. We clarify Davies ’ obscure points, give a ..."
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Cited by 16 (0 self)
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of constant positive curvature with boundary possessing a special 5valent vertex that never appear in the tiling of the usual sphere.
P.Saponov Quantum line bundles on noncommutative sphere
 J. Phys A: Math. Gen
"... Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Following [GS] and using the CayleyHamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a ..."
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Cited by 5 (4 self)
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Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Following [GS] and using the CayleyHamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a
Directional Wavelets on the Sphere
, 2001
"... In this paper we propose a construction of directional wavelets on the sphere. We make use of the Euclidean Limit defined in [1] for lifting up to usual directional wavelets in . We finally discuss implementation issues and potential applications. Keywords Wavelets on the sphere, signal analy ..."
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Cited by 9 (0 self)
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In this paper we propose a construction of directional wavelets on the sphere. We make use of the Euclidean Limit defined in [1] for lifting up to usual directional wavelets in . We finally discuss implementation issues and potential applications. Keywords Wavelets on the sphere, signal
1 Quantum line bundles on noncommutative sphere
, 2008
"... Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Following [GS] and using the CayleyHamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a ..."
Abstract
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Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Following [GS] and using the CayleyHamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a
Results 1  10
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929