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The Weyl Integration Model for KAK decomposition of Reductive Lie Group
, 2005
"... The Weyl integration model presented by An and Wang can be effectively used to reduce the integration over Gspace. In this paper, we construct an especial Weyl integration model for KAK decomposition of Reductive Lie Group and obtain an integration formula which implies that the integration of L 1 ..."
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The Weyl integration model presented by An and Wang can be effectively used to reduce the integration over Gspace. In this paper, we construct an especial Weyl integration model for KAK decomposition of Reductive Lie Group and obtain an integration formula which implies that the integration of L 1
NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation
, 2005
"... using KAK decompositions ..."
Note on the Khaneja Glaser decomposition
, 2004
"... Recently, Vatan and Williams utilize a matrix decomposition of SU(2n) introduced by Khaneja and Glaser to produce CNOTefficient circuits for arbitrary threequbit unitary evolutions. In this note, we place the Khaneja Glaser Decomposition (KGD) in context as a SU(2n) = KAK decomposition by proving ..."
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Cited by 8 (2 self)
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Recently, Vatan and Williams utilize a matrix decomposition of SU(2n) introduced by Khaneja and Glaser to produce CNOTefficient circuits for arbitrary threequbit unitary evolutions. In this note, we place the Khaneja Glaser Decomposition (KGD) in context as a SU(2n) = KAK decomposition
Orthogonal Rank Decompositions for Tensors
 In preparation
, 1999
"... rder and all subdimensions are equal) then the inner product of A and B is defined as A \Delta B j m 1 X i 1 =1 m 2 X i 2 =1 \Delta \Delta \Delta mn X i n=1 A i 1 i 2 \Delta\Delta\Deltai n B i 1 i 2 \Delta\Delta\Deltai n : Correspondingly, the norm of A, kAk, is defined as kAk 2 j A \D ..."
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Cited by 3 (3 self)
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rder and all subdimensions are equal) then the inner product of A and B is defined as A \Delta B j m 1 X i 1 =1 m 2 X i 2 =1 \Delta \Delta \Delta mn X i n=1 A i 1 i 2 \Delta\Delta\Deltai n B i 1 i 2 \Delta\Delta\Deltai n : Correspondingly, the norm of A, kAk, is defined as kAk 2 j A
Regularized Gaussian Discriminant Analysis Through Eigenvalue Decomposition
 Journal of the American Statistical Association
, 1996
"... Friedman (1989) has proposed a regularization technique (RDA) of discriminant analysis in the Gaussian framework. RDA makes use of two regularization parameters to design an intermediate classi cation rule between linear and quadratic discriminant analysis. In this paper, we propose an alternative a ..."
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Cited by 54 (7 self)
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approach to design classi cation rules which have also a median position between linear and quadratic discriminant analysis. Our approach is based on the reparametrization of the covariance matrix k of a group Gk in terms of its eigenvalue decomposition, k = kDkAkD 0 k where k speci es the volume of Gk, Ak
Decompositions for the Kakwani poverty index
"... Since Sen’s seminal article in 1976, it is very known that every poverty measure should be sensitive to the three components of poverty: incidence, intensity and inequality. The paper concentrates on the poverty measure proposed by Kakwani. If the Kakwani index is normalized, an ordered weighted a ..."
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Since Sen’s seminal article in 1976, it is very known that every poverty measure should be sensitive to the three components of poverty: incidence, intensity and inequality. The paper concentrates on the poverty measure proposed by Kakwani. If the Kakwani index is normalized, an ordered weighted
K 2004 Canonical decompositions of nqubit quantum computations and concurrence
"... The twoqubit canonical decomposition SU(4) = [SU(2) ⊗ SU(2)]∆[SU(2) ⊗ SU(2)] writes any twoqubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an nqubit decomposition, the concurre ..."
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Cited by 4 (1 self)
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, the concurrence canonical decomposition (C.C.D.) SU(2 n) = KAK. The group K fixes a bilinear form related to the concurrence, and in particular any computation in K preserves the tangle 〈φ ∗ (−iσ y 1)···(−iσy n)φ〉  2 for n even. Thus, the C.C.D. shows that any nqubit quantum computation is a composition
Spherical Functions on SO0(p, q) / SO(p) × SO(q)
"... Abstract. An integral formula is derived for the spherical functions on the symmetric space G/K = SO0(p, q) / SO(p) × SO(q). This formula allows us to state some results about the analytic continuation of the spherical functions to a tubular neighbourhood of the subalgebra a of the abelian part in ..."
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in the decomposition G = KAK. The corresponding result is then obtained for the heat kernel of the symmetric space SO0(p, q) / SO(p) × SO(q) using the Plancherel formula. In the Conclusion, we discuss how this analytic continuation can be a helpful tool to study the growth of the heat kernel. 1
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