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Smooth Localized Orthonormal Bases

by Mladen Victor Wickerhauser , 1992
"... . We describe an orthogonal decomposition of L 2 (R) which maps smooth functions to smooth periodic functions. It generalizes previous constructions by Malvar, Coifman and Meyer. The adjoint of the decomposition can be used to construct smooth orthonormal windowed exponential, wavelet and wavelet ..."
Abstract - Cited by 9 (0 self) - Add to MetaCart
. In this short note we sketch a construction of smoothness-preserving unitary maps onto periodic function...

Factoring wavelet transforms into lifting steps

by Ingrid Daubechies, Wim Sweldens - J. FOURIER ANAL. APPL , 1998
"... This paper is essentially tutorial in nature. We show how any discrete wavelet transform or two band subband filtering with finite filters can be decomposed into a finite sequence of simple filtering steps, which we call lifting steps but that are also known as ladder structures. This decompositio ..."
Abstract - Cited by 584 (8 self) - Add to MetaCart
in the biorthogonal, i.e, non-unitary case. Like the lattice factorization, the decomposition presented here asymptotically reduces the computational complexity of the transform by a factor two. It has other applications, such as the possibility of defining a wavelet-like transform that maps integers to integers.

Good quantum error correcting codes exist

by A. R. Calderbank, Peter W. Shor - REV. A , 1996
"... A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can be used ..."
Abstract - Cited by 349 (9 self) - Add to MetaCart
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not necessarily independently, the resulting n qubits can

Elementary Gates for Quantum Computation

by Adriano Barenco , Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John Smolin, Harald Weinfurter , 1995
"... We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x, y)to(x, x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We in ..."
Abstract - Cited by 280 (11 self) - Add to MetaCart
We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values (x, y)to(x, x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We

A point-charge force field for molecular mechanics simulations of proteins based on condensed-phase QM calculations

by Yong Duan, Chun Wu, Shibasish Chowdhury, Mathew C. Lee, Guoming Xiong - J. Comput. Chem , 2003
"... Abstract: Molecular mechanics models have been applied extensively to study the dynamics of proteins and nucleic acids. Here we report the development of a third-generation point-charge all-atom force field for proteins. Following the earlier approach of Cornell et al., the charge set was obtained b ..."
Abstract - Cited by 229 (6 self) - Add to MetaCart
that this force field parameter set will address certain critical short comings of previous force fields in condensed-phase simulations of proteins. Initial tests on peptides demonstrated a high-degree of similarity between the calculated and the statistically measured Ramanchandran maps for both Ace

The dS/CFT correspondence

by Andrew Strominger - JHEP , 2001
"... A holographic duality is proposed relating quantum gravity on dSD (D-dimensional de Sitter space) to conformal field theory on a single SD−1 ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future bou ..."
Abstract - Cited by 196 (7 self) - Add to MetaCart
boundary of dSD) are mapped to the antipodal points on SD−1 relative to those on I −. For the case of dS3, which is analyzed in some detail, the central charge of the CFT2 is computed in an analysis of the asymptotic symmetry group at I ±. This dS/CFT proposal is supported by the computation of correlation

Coil sensitivity encoding for fast MRI. In:

by Klaas P Pruessmann , Markus Weiger , Markus B Scheidegger , Peter Boesiger - Proceedings of the ISMRM 6th Annual Meeting, , 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
Abstract - Cited by 193 (3 self) - Add to MetaCart
phase is sufficiently smooth so as to endure map refinement largely unaltered. On the other hand, it offers the advantage of being more reliable in clearing modulus object contrast from raw maps. This is because a body coil reference cannot be acquired quite simultaneously with the array reference

THE MOMENT MAPPING FOR UNITARY REPRESENTATIONS

by Peter W. Michor - ANNALS OF GLOBAL ANALYSIS AND GEOMETRY VOL. 8, NO. 3 (1990), 299–313 , 1990
"... For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of analytic vectors the same construction is possible and leads ..."
Abstract - Cited by 7 (5 self) - Add to MetaCart
For any unitary representation of an arbitrary Lie group I construct a moment mapping from the space of smooth vectors of the representation into the dual of the Lie algebra. This moment mapping is equivariant and smooth. For the space of analytic vectors the same construction is possible

THE EXPONENTIAL MAP FOR THE UNITARY GROUP

by A. O. Barut, J. R. Zeni, A. Laufer , 1994
"... Abstract: In this article we extend our previous results for the orthogonal group, SO(2, 4), to its homomorphic group SU(2, 2). Here we present a closed, finite formula for the exponential of a 4 × 4 traceless matrix, which can be viewed as the generator (Lie algebra elements) of the SL(4, C) group. ..."
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. We apply this result to the SU(2, 2) group, which Lie algebra can be represented by the Dirac matrices, and discuss how the exponential map for SU(2, 2) can be written by means of the Dirac matrices.

Cayley differential unitary space–time codes

by Bertrand M. Hochwald - IEEE Trans. Inform. Theory , 2002
"... One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential ..."
Abstract - Cited by 80 (8 self) - Add to MetaCart
and decoding at any rate. The codes are named for their use of the Cayley transform, which maps the highly nonlinear Stiefel manifold of unitary matrices to the linear space of skew-Hermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain
Results 1 - 10 of 1,138