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classical phase space of the Lie group SU(n)
, 2002
"... The appearence of the resolved singular hypersurface x0x1 − x2 n = 0 in the ..."
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The appearence of the resolved singular hypersurface x0x1 − x2 n = 0 in the
GLOBAL QUANTIZATION OF PSEUDODIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS, SU(2) AND 3SPHERE
, 812
"... Abstract. Global quantization of pseudodifferential operators on compact Lie groups is introduced relying on the representation theory of the group rather than on expressions in local coordinates. Operators on the 3dimensional sphere S 3 and on group SU(2) are analysed in detail. A new class of gl ..."
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Cited by 20 (17 self)
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Abstract. Global quantization of pseudodifferential operators on compact Lie groups is introduced relying on the representation theory of the group rather than on expressions in local coordinates. Operators on the 3dimensional sphere S 3 and on group SU(2) are analysed in detail. A new class
LETTER Communicated by Toshihisa Tanaka A Study on Neural Learning on Manifold Foliations: The Case of the Lie Group SU(3)
"... Learning on differential manifolds may involve the optimization of a function of many parameters. In this letter, we deal with Riemanniangradientbased optimization on a Lie group, namely, the group of unitary unimodular matrices SU(3). In this special case, subalgebras of the associated Lie algeb ..."
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Learning on differential manifolds may involve the optimization of a function of many parameters. In this letter, we deal with Riemanniangradientbased optimization on a Lie group, namely, the group of unitary unimodular matrices SU(3). In this special case, subalgebras of the associated Lie
Simultaneous controllability and discrimination of collections of perturbed bilinear control systems on the Lie group SU(N)
, 2013
"... The controllability of bilinear systems is well understood for isolated systems where the control can be implemented exactly. However when perturbations are present some interesting theoretical questions are raised. We consider in this paper a control system whose control cannot be implemented exact ..."
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the perturbations are constant over a common, long enough, time frame. We apply the result to the controllability of quantum systems. Keywords: quantum control, Lie group controllability, bilinear system, perturbations
A direct link between the Lie group SU(3) and the singular hypersurface X³ + . . . = 0 via quantum mechanics
, 2002
"... ..."
Equivariant KTheory of SU(2) and SU(3)
, 1997
"... We conputed the equivariant Ktheory for Lie groups SU(2) and SU(3), which are the Grothendieck differential algebras of their representation rings over Z. 1 ..."
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We conputed the equivariant Ktheory for Lie groups SU(2) and SU(3), which are the Grothendieck differential algebras of their representation rings over Z. 1
Fundamental Groups of Commuting Elements in Lie Groups
, 2008
"... We compute the fundamental group of the spaces of ordered commuting ntuples of elements in the Lie groups SU(2), U(2) and SO(3). For SO(3) the mod2 cohomology of the components of these spaces is also obtained. 1 ..."
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Cited by 5 (0 self)
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We compute the fundamental group of the spaces of ordered commuting ntuples of elements in the Lie groups SU(2), U(2) and SO(3). For SO(3) the mod2 cohomology of the components of these spaces is also obtained. 1
Renormalization in quantum field theory and the RiemannHilbert problem. II. The βfunction, diffeomorphisms and the renormalization group
 Comm. Math. Phys
"... We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given by evalu ..."
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Cited by 332 (39 self)
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We show that renormalization in quantum field theory is a special instance of a general mathematical procedure of multiplicative extraction of finite values based on the Riemann–Hilbert problem. Given a loop γ(z), z  = 1 of elements of a complex Lie group G the general procedure is given
A Tight Bound on Approximating Arbitrary Metrics by Tree Metrics
 In Proceedings of the 35th Annual ACM Symposium on Theory of Computing
, 2003
"... In this paper, we show that any n point metric space can be embedded into a distribution over dominating tree metrics such that the expected stretch of any edge is O(log n). This improves upon the result of Bartal who gave a bound of O(log n log log n). Moreover, our result is existentially tight; t ..."
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Cited by 306 (8 self)
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; there exist metric spaces where any tree embedding must have distortion#sto n)distortion. This problem lies at the heart of numerous approximation and online algorithms including ones for group Steiner tree, metric labeling, buyatbulk network design and metrical task system. Our result improves
Interactive Digital Photomontage
 ACM TRANS. GRAPH
, 2004
"... We describe an interactive, computerassisted framework for combining parts of a set of photographs into a single composite picture, a process we call "digital photomontage." Our framework makes use of two techniques primarily: graphcut optimization, to choose good seams within the consti ..."
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Cited by 304 (17 self)
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location in the set of source images. Typically, a user applies a series of image objectives iteratively in order to create a finished composite. The power of this framework lies in its generality; we show how it can be used for a wide variety of applications, including "selective composites
Results 1  10
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