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Factoring wavelet transforms into lifting steps
 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 ..."
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Cited by 584 (8 self)
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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
Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a cost in computation time of at most a polynomial factol: It is not clear whether this is still true when quantum mechanics is taken into consider ..."
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Cited by 1111 (5 self)
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into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their computational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number
PolynomialTime Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
 SIAM J. on Computing
, 1997
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 1277 (4 self)
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. This paper considers factoring integers and finding discrete logarithms, two problems which are generally thought to be hard on a classical computer and which have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical
Numerical Solutions of the Euler Equations by Finite Volume Methods Using RungeKutta TimeStepping Schemes
, 1981
"... A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used to deter ..."
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Cited by 517 (78 self)
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A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective method for solving the Euler equations in arbitrary geometric domains. The method has been used
Singletrial Spike Trains in Parietal Cortex Reveal Discrete Steps During
"... Singletrial spike trains in parietal cortex reveal discrete steps during decisionmaking ..."
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Cited by 1 (0 self)
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Singletrial spike trains in parietal cortex reveal discrete steps during decisionmaking
Quantum complexity theory
 in Proc. 25th Annual ACM Symposium on Theory of Computing, ACM
, 1993
"... Abstract. In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s model of a quantum Turing machine (QTM) [Proc. Roy. Soc. London Ser. A, 400 (1985), pp. 97–117]. This constructi ..."
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Cited by 574 (5 self)
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to be specified. We prove that O(log T) bits of precision suffice to support a T step computation. This justifies the claim that the quantum Turing machine model should be regarded as a discrete model of computation and not an analog one. We give the first formal evidence that quantum Turing machines violate
Sum Over Histories: Discrete Step Interpretation
"... We study the transition of a particle between two points such that the particle takes discrete spatial steps in this transition. We analyze how the sum over histories interpretation of quantum mechanics can be implemented in this scenario. We show that the Euclidean propagator of a free particle is ..."
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We study the transition of a particle between two points such that the particle takes discrete spatial steps in this transition. We analyze how the sum over histories interpretation of quantum mechanics can be implemented in this scenario. We show that the Euclidean propagator of a free particle
The Large Discretization Step Method for TimeDependent Partial Differential Equations
"... A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS, in short) approximation, de ned in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete approx ..."
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Cited by 1 (0 self)
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A new method for the acceleration of linear and nonlinear time dependent calculations is presented. It is based on the Large Discretization Step (LDS, in short) approximation, de ned in this work, which employs an extended system of low accuracy schemes to approximate a high accuracy discrete
B cell development in the spleen takes place in discrete steps and is determined by the quality of B cell receptorderived signals
, 1999
"... Only mature B lymphocytes can enter the lymphoid follicles of spleen and lymph nodes and thus efficiently participate in the immune response. Mature, longlived B lymphocytes derive from shortlived precursors generated in the bone marrow. We show that selection into the mature pool is an active pro ..."
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Cited by 90 (2 self)
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Only mature B lymphocytes can enter the lymphoid follicles of spleen and lymph nodes and thus efficiently participate in the immune response. Mature, longlived B lymphocytes derive from shortlived precursors generated in the bone marrow. We show that selection into the mature pool is an active process and takes place in the spleen. Two populations of splenic B cells were identified as precursors for mature B cells. Transitional B cells of type 1 (T1) are recent immigrants from the bone marrow. They develop into the transitional B cells of type 2 (T2), which are cycling and found exclusively in the primary follicles of the spleen. Mature B cells can be generated from T1 or T2 B cells. Mice with genetic deletions of elements participating in the B cell receptor signaling cascade display developmental arrest at the T1 or T2 stage. The analysis of these defects showed that the development of T2 and mature B cells from T1 precursors requires defined qualitative and quantitative signals derived from the B cell receptor and that the induction of longevity and maturation requires different signals. Key words: In the adult mouse, B cells are generated in the bone marrow.
An EM Algorithm for WaveletBased Image Restoration
, 2002
"... This paper introduces an expectationmaximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain. Regularization is achieved by promoting a reconstruction with lowcomplexity, expressed in terms of the wavelet coecients, taking a ..."
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Cited by 352 (22 self)
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the efficient image representation oered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator obtained in the Fourier domain. The algorithm alternates between an Estep based on the fast Fourier transform (FFT) and a DWTbased Mstep, resulting in an ecient iterative
Results 1  10
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