Journal of Fourier Analysis and Applications, 1998
This article is essentially tutorial in nature. We show how any discrete wavelet transform or two... more This article 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 decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed by the formulaSL(n;R[z, z−1])=E(n;R[z, z−1])); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used 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.
Consider n variables attaching to each individual of a population. These statistical variables xu... more Consider n variables attaching to each individual of a population. These statistical variables xu x2, . . . , xn might for example be scores made by school children in tests of speed and skill in solving arithmetical problems or in reading; or they might be various physical ...
Transformed petunia, tobacco, and tomato plants have been produced by means of a novel leaf disk ... more Transformed petunia, tobacco, and tomato plants have been produced by means of a novel leaf disk transformation-regeneration method. Surface-sterilized leaf disks were inoculated with an Agrobacterium tumefaciens strain containing a modified tumor-inducing plasmid (in which the phytohormone biosynthetic genes from transferred DNA had been deleted and replaced with a chimeric gene for kanamycin resistance) and cultured for 2 days. The leaf disks were then transferred to selective medium containing kanamycin. Shoot regeneration occurred within 2 to 4 weeks, and transformants were confirmed by their ability to form roots in medium containing kanamycin. This method for producing transformed plants combines gene transfer, plant regeneration, and effective selection for transformants into a single process and should be applicable to plant species that can be infected by Agrobacterium and regenerated from leaf explants.
A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in whi... more A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock ...
... Problems will make them-selves apparent in the new world state and choosing an appropriate ne... more ... Problems will make them-selves apparent in the new world state and choosing an appropriate next step will automatically take them into account. This paper describes an investigation into reactive planning that takes the extreme position of using no pre-diction of future states ...
RNA and DNA expression vectors containing genes for chloramphenicol acetyltransferase, luciferase... more RNA and DNA expression vectors containing genes for chloramphenicol acetyltransferase, luciferase, and beta-galactosidase were separately injected into mouse skeletal muscle in vivo. Protein expression was readily detected in all cases, and no special delivery system was required for these effects. The extent of expression from both the RNA and DNA constructs was comparable to that obtained from fibroblasts transfected in vitro under optimal conditions. In situ cytochemical staining for beta-galactosidase activity was localized to muscle cells following injection of the beta-galactosidase DNA vector. After injection of the DNA luciferase expression vector, luciferase activity was present in the muscle for at least 2 months.
Journal of Fourier Analysis and Applications, 1998
This article is essentially tutorial in nature. We show how any discrete wavelet transform or two... more This article 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 decomposition corresponds to a factorization of the polyphase matrix of the wavelet or subband filters into elementary matrices. That such a factorization is possible is well-known to algebraists (and expressed by the formulaSL(n;R[z, z−1])=E(n;R[z, z−1])); it is also used in linear systems theory in the electrical engineering community. We present here a self-contained derivation, building the decomposition from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering. This factorization provides an alternative for the lattice factorization, with the advantage that it can also be used 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.
Consider n variables attaching to each individual of a population. These statistical variables xu... more Consider n variables attaching to each individual of a population. These statistical variables xu x2, . . . , xn might for example be scores made by school children in tests of speed and skill in solving arithmetical problems or in reading; or they might be various physical ...
Transformed petunia, tobacco, and tomato plants have been produced by means of a novel leaf disk ... more Transformed petunia, tobacco, and tomato plants have been produced by means of a novel leaf disk transformation-regeneration method. Surface-sterilized leaf disks were inoculated with an Agrobacterium tumefaciens strain containing a modified tumor-inducing plasmid (in which the phytohormone biosynthetic genes from transferred DNA had been deleted and replaced with a chimeric gene for kanamycin resistance) and cultured for 2 days. The leaf disks were then transferred to selective medium containing kanamycin. Shoot regeneration occurred within 2 to 4 weeks, and transformants were confirmed by their ability to form roots in medium containing kanamycin. This method for producing transformed plants combines gene transfer, plant regeneration, and effective selection for transformants into a single process and should be applicable to plant species that can be infected by Agrobacterium and regenerated from leaf explants.
A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in whi... more A correlation-energy formula due to Colle and Salvetti [Theor. Chim. Acta 37, 329 (1975)], in which the correlation energy density is expressed in terms of the electron density and a Laplacian of the second-order Hartree-Fock ...
... Problems will make them-selves apparent in the new world state and choosing an appropriate ne... more ... Problems will make them-selves apparent in the new world state and choosing an appropriate next step will automatically take them into account. This paper describes an investigation into reactive planning that takes the extreme position of using no pre-diction of future states ...
RNA and DNA expression vectors containing genes for chloramphenicol acetyltransferase, luciferase... more RNA and DNA expression vectors containing genes for chloramphenicol acetyltransferase, luciferase, and beta-galactosidase were separately injected into mouse skeletal muscle in vivo. Protein expression was readily detected in all cases, and no special delivery system was required for these effects. The extent of expression from both the RNA and DNA constructs was comparable to that obtained from fibroblasts transfected in vitro under optimal conditions. In situ cytochemical staining for beta-galactosidase activity was localized to muscle cells following injection of the beta-galactosidase DNA vector. After injection of the DNA luciferase expression vector, luciferase activity was present in the muscle for at least 2 months.
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