The Two-Dimensional Clifford-Fourier Transform

Recently several generalizations to higher dimension of the Fourier transform using Clifford algebra have been introduced, including the Clifford-Fourier transform by the authors, defined as an operator exponential with a Clifford algebra-valued kernel. In this paper an overview is given of all these generalizations and an in depth study of the two-dimensional Clifford-Fourier transform of the authors is presented. In this special two-dimensional case a closed form for the integral kernel may be obtained, leading to further properties, both in the L ₁ and in the L ₂ context. Furthermore, based on this Clifford-Fourier transform Clifford-Gabor filters are introduced. AMS subject classification numbers: 42B10, 30G35 Fred Brackx received a diploma degree in mathematics from Ghent University, Belgium, in 1970 and a Ph.D. degree in mathematics from the same university in 1973. Since 1984 he is professor for mathematical analysis at Ghent University and currently he is leading the Clifford Research Group. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets. Nele De Schepper received a diploma degree in mathematics from Ghent University, Belgium, in 2001. Since then she holds an assistantship at the Department of Mathematical Analysis of Ghent University and is a member of the Clifford Research Group. Her main interests are function theory and functional analysis for functions with values in Clifford algebras. The research covers generalized Fourier transforms, orthogonal polynomials and multi-dimensional wavelets. Frank Sommen received a diploma degree in mathematics from Ghent University, Belgium, in 1978, a Ph.D. degree in mathematics from the same university in 1980, and a habilitation degree in mathematical analysis in 1984. From 1978 until 1999 he was at the National Fund for Scientific Research (Flanders). Since 2000 he holds a Research professorship at Ghent University. His main interests are function theory and functional analysis for functions with values in quaternion and Clifford algebras. The research covers Clifford distributions, generalized Fourier, Radon and Hilbert transforms, orthogonal polynomials and multi-dimensional wavelets, algebraic analysis, hyperfunctions and radial algebra.     

Implementation of RNS-Based Distributed Arithmetic Discrete Wavelet Transform Architectures Using Field-Programmable Logic

Currently there are design barriers inhibiting the implementation of high-precision digital signal processing (DSP) objects with field programmable logic (FPL) devices. This paper explores overcoming these barriers by fusing together the popular distributed arithmetic (DA) method with the residue number system (RNS) for use in FPL-centric designs. The new design paradigm is studied in the context of a high-performance filter bank and a discrete wavelet transform (DWT). The proposed design paradigm is facilitated by a new RNS accumulator structure based on a carry save adder (CSA). The reported methodology also introduces a polyphase filter structure that results in a reduced look-up table (LUT) budget. The 2C-DA and RNS-DA are compared, in the context of a FPL implementation strategy, using a discrete wavelet transform (DWT) filter bank as a common design theme. The results show that the RNS-DA, compared to a traditional 2C-DA design, enjoys a performance advantage that increases with precision (wordlength).     

Resumption of mitosis during post-thaw culture: a key parameter in selecting the right embryos for transfer

A new oxidative pathway for the degradation of caffeine(1,3,7-Trimethylxanthine, I) by a mixed culture consisting of strains belonging to the genera Klebsiella and Rhodococcus is presented. The mixed culture does not initiate degradation by N-demethylation either complete or partial, but instead carries out oxidation at the C-8 position resulting in the formation of 1,3,7-trimethyluric acid (TMU, II) which further gets degraded to 3,6,8-trimethylallantoin (TMA, III). Both TMU and TMA are hitherto not shown to be formed in the microbial system. Further degradation of TMA (III) by caffeine grown cells yields dimethylurea (VII) as one of the metabolites. Oxygen uptake studies indicated that caffeine(I) grown cells oxidized TMU(II), TMA (III), glyoxalic acid (VI), dimethylurea(VII), and monomethylurea(V), but not monomethyl and dimethyluric acids. The mixed culture does not accept theophylline(1,3-dimethylxanthine), theobromine(3,7-dimethylxanthine), and paraxanthine(1,7-dimethylxanthine) as the carbon source.     

THERMODYNAMICS OF ASPHALTENE PRECIPITATION AND DISSOLUTION INVESTIGATION OF TEMPERATURE AND SOLVENT EFFECTS

Petroleum asphaltenes have been precipitated in solvent mixtures of n-heptane and toluene at various temperatures, likewise n-heptane asphaltenes have been dissolved in under similar conditions. This give added evidence to apparent hysteresis phenomenon between the two processes. The Asphaltenes have been characterized showing that although data is scattered convergence to certain structural parameters as incipient flocculation is approached. The asphaltenes are seen to consist of an associating and a non-associating part. The solubility of asphaltenes has been correlated/modelled using the Flory-Huggins equation using two different terms for the Flory parameter. A process for evaluation of best choice of solubility parameter and molar volume for the asphaltenes is proposed. Dissolution processes are seen to be best fitted by the equations. Based on these findings the asphaltenes are proposed to be formed by a colloidal and a true solution part.     

Tuning of MST neurons to spiral motions

Cells in the dorsal division of the medial superior temporal area (MSTd) have large receptive fields and respond to expansion/contraction, rotation, and translation motions. These same motions are generated as we move through the environment, leading investigators to suggest that area MSTd analyzes the optical flow. One influential idea suggests that navigation is achieved by decomposing the optical flow into the separate and discrete channels mentioned above, that is, expansion/contraction, rotation, and translation. We directly tested whether MSTd neurons perform such a decomposition by examining whether there are cells that are preferentially tuned to intermediate spiral motions, which combine both expansion/contraction and rotation components. The finding that many cells in MSTd are preferentially selective for spiral motions indicates that this simple three-channel decomposition hypothesis for MSTd does not appear to be correct. Instead, there is a continuum of patterns to which MSTd cells are selective. In addition, we find that MSTd cells maintain their selectivity when stimuli are moved to different locations in their large receptive fields. This position invariance indicates that MSTd cells selective for expansion cannot give precise information about the retinal location of the focus of expansion. Thus, individual MSTd neurons cannot code, in a precise fashion, the direction of heading by using the location of the focus of expansion. The only way this navigational information could be accurately derived from MSTd is through the use of a coarse, population encoding. Positional invariance and selectivity for a wide array of stimuli suggest that MSTd neurons encode patterns of motion per se, regardless of whether these motions are generated by moving objects or by motion induced by observer locomotion.     

A unified framework for off-line permutation routing in parallel networks

In this paper we present a general strategy for finding efficient permutation routes in parallel networks. Among the popular parallel networks to which the strategy applies are mesh networks, hypercube networks, hypercube-derivative networks, ring networks, and star networks. The routes produced are generally congestion-free and take a number of routing steps that is within a small constant factor of the diameter of the network. Our basic strategy is derived from an algorithm that finds (in polynomial time) efficient permutation routes for aproduct network, G×H, given efficient permutation routes forG andH. We investigate the use of this algorithm for routingmultiple permutations and extend its applicability to a wide class of graphs, including several families ofCayley graphs. Finally, we show that our approach can be used to find efficient permutation routes among the remaining live nodes infaulty networks.This research was supported in part by a grant from the NSF, Grant No. CCR-88-12567.     

Finite-element grid improvement by minimization of stiffness matrix trace

A new and simple method of finite-element grid improvement is presented. The objective is to improve the accuracy of the analysis. The procedure is based on a minimization of the trace of the stiffness matrix. For a broad class of problems this minimization is seen to be equivalent to minimizing the potential energy. The method is illustrated with the classical tapered bar problem examined earlier by Prager and Masur. Identical results are obtained.     

Sexual functioning among breast cancer, gynecologic cancer, and healthy women.

Determined the specific type of sexual functioning deficits and the relationship between global sexual satisfaction and adjustment in 2 related life areas (marital relationship and body image) for 2 groups of cancer patients at high risk for sexual difficulties. The 2 groups included 16 27–67 yr old females with Stage 2 breast cancer and 16 31–65 yr old females with gynecologic cancer. These Ss were compared to 16 healthy female outpatients (controls). Measures included the Sexual Activities scale from the Derogatis Sexual Functioning Inventory, a modified version of the Dyadic Assessment Scale (marital adjustment), a global sexual evaluation, and a body-image scale. Analyses revealed that the aspects of sexual functioning for breast-cancer and gynecologic-cancer Ss that differed from those of controls were the frequency of sexual behaviors and the level of sexual arousal. Whereas Ss' evaluations of their current sexual life had no relationship to their marital-adjustment ratings, analyses suggested that body-image disruption may be a prevalent problem for gynecologic cancer patients. Data suggest that cancer diagnosis and treatment are instrumental in producing reductions in sexual activity and arousability. (34 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Technology Scapegoats and Policy Saviors

IEEE Security & Privacy's associate editor in chief discusses technology's role in identity fraud and identity theft.