We present a parallel 2D wavelet transform algorithm with modest communication requirements. Data are transmitted between nearest neighbors only and the amount is independent of the problem size as well as the number of processors. An analysis of the theoretical performance shows that the algorithm is scalable approaching perfect speedup as the problem size is increased. This performance is rea...

The discrete Hartley transform (DHT) has proved to be a valuable tool in digital signal/image processing and communications and has also attracted research interests in many multidimensional applications. Although many fast algorithms have been developed for the calculation of oneand two-dimensional (1-D and 2-D) DHT, the development of multidimensional algorithms in three and more dimensions i...

A general f ramework is presented for constructing transforms in the field of the input which have a convolutionlike property. The construction is carried out over finite fields, but is shown to be valid over the real and complex fields as well. It is shown that these basefield transforms can be v iewed as “projections” of the discrete Fourier transform @IT) and that they exist for all lengths ...

This paper presents folded architectures and scheduling algorithms for computing the 2-D DWT for analysis and synthesis lters. The folded architectures consist of two parallel computation units (one for computations along the rows and the other for computations along the columns) and two storage units to store the intermediate outputs that are generated by the two units. The scheduling algorith...

Sequences of points with a low discrepancy are the basic building blocks for quasi-Monte Carlo methods. Traditionally these points are generated in a unit cube. To develop point sets on a simplex we will transform the lowdiscrepancy points for the unit cube to a simplex. An advantage of this approach is that most of the known results on low discrepancy sequences can be re-used. After introducin...

Let D denote the open unit disk {z ∈ C | |z| < 1}, and C+ denote the right half-plane {s ∈ C | Re(s) ≥ 0}. (1) Let W (D) be the Wiener algebra of the disc, that is the set of all absolutely convergent Taylor series in the open unit disk D, with pointwise operations. (2) Let W (C+) be the set of all functions defined in the right halfplane C+ that differ from the Laplace transform of a function ...

We study wrappings of the unit sphere by a piece of paper (or, perhaps more accurately, a piece of foil). Such wrappings differ from standard origami because they require infinitely many infinitesimally small “folds” in order to transform the flat sheet into a positive-curvature sphere. Our goal is to find shapes that have small area even when expanded to shapes that tile the plane. We characte...

We develop a novel modeling framework for Boltzmann machines, augmenting each hidden unit with a latent transformation assignment variable which describes the selection of the transformed view of the canonical connection weights associated with the unit. This enables the inferences of the model to transform in response to transformed input data in a stable and predictable way, and avoids learni...

The title compound, C4H8O4Te, crystallized from a solution of Te(4+) in ethyl-ene glycol. The Te(IV) atom is in a distorted seesaw coordination defined by four O atoms from two different ethyl-eneglycate ligands. The C atoms of the ethyl-eneglycate ligands are disorderd over two positions, with population parameters of 50.3 (6) and 49.7 (6)% indicating a statistical distribution. Due to the pos...

This paper is motivated by the outsanding achievements of Emmanuel Candès and Terence Tao on what is now called “compressed sensing”. Let us begin with a theorem by Terence Tao. Let p be a prime number and Fp be the finite field with p elements. We denote by #E the cardinality of E ⊂ Fp. The Fourier transform of a complex valued function f defined on Fp is denoted by f̂ . Let Mq be the collectio...