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

into consideration. Several researchers, starting with David Deutsch, have developed models for quantum mechanical computers and have investigated their compu-tational properties. This paper gives Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number

. 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

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

Single-trial spike trains in parietal cortex reveal discrete steps during decision-making

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

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

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

Only mature B lymphocytes can enter the lymphoid follicles of spleen and lymph nodes and thus efficiently participate in the immune response. Mature, long-lived B lymphocytes derive from short-lived 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.

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 E-step based on the fast Fourier transform (FFT) and a DWT-based M-step, resulting in an ecient iterative