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).     

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.     

Optical networks for local loop applications

Some of the options for optical technology within the local loop environment are examined. In particular, passive shared access networks have been considered in some detail. These networks show great promise for delivering existing telephone services to small to medium business customers (4-30 lines) economically by the early 1990s. Extending fiber to the home will also be possible by virtue of a similar passive network infrastructure for customers requiring new broadband services beyond the single telephone line. For one-line plain old telephone service (POTS) customers, an intermediate approach of terminating the fiber network at the final network distribution point, with copper retained for the final leg, may be used prior to the provision of broadband services. A key feature of the passive optical network architecture is the use of wavelength-division multiplexing (WDM) as an upgrade strategy, allowing graceful upgrading from telephone services to multichannel high-definition television (HDTV) on gigabit/second bearers and full two-way switched broadband services employing wavelength routing across the network     

Technology Scapegoats and Policy Saviors

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

Impact of Elaboration on Socially Desirable Responding and the Validity of Biodata Measures.

The current study investigated the impact of requiring respondents to elaborate on their answers to a biodata measure on mean scores, the validity of the biodata item composites, subgroup mean differences, and correlations with social desirability. Results of this study indicate that elaborated responses result in scores that are much lower than nonelaborated responses to the same items by an independent sample. Despite the lower mean score on elaborated items, it does not appear that elaboration affects the size of the correlation between social desirability and responses to biodata items or that it affects criterion-related validity or subgroup mean differences in a practically significant way. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The validity of new memory complaints in the elderly

OBJECTIVE: To determine the validity of new subjective memory complaints (MCs) from individuals who previously, when without dementia, denied having MCs. DESIGN: Prospective cohort. SETTING: Longitudinal, community-based study of aging and dementia. PATIENTS: One hundred thirty-three community-dwelling elderly individuals who were part of a registry for the study of conditions related to aging in North Manhattan, NY. Patients were selected if they were initially without dementia and had completed at least 2 successive annual clinical and neuropsychological evaluations and provided their own medical history. MAIN OUTCOME MEASURES: Performance on memory tests--the Buschke Selective Reminding Test and a visual memory task--and global performance on a neuropsychological test battery and clinical evaluation, by which questionable dementia or dementia was diagnosed according to a well-defined paradigm. RESULTS: Fifty-three subjects with MCs at the initial evaluation performed no worse on the memory test than the 80 subjects who denied MCs initially. There was a weak association between MCs and the diagnosis of questionable dementia at baseline (P = .04), but this was nonsignificant after adjusting for age and education. At 1-year follow-up, 21 of the 80 without baseline MCs now reported MCs. At the follow-up evaluation, these 21 subjects performed significantly worse on the memory tests, were 5 times more likely to have significant cognitive impairment, and had shown significantly greater decline over the preceding year on several of the cognitive measures than the 59 who continued to deny MCs. CONCLUSION: New MCs from individuals, who when without dementia recently denied MCs, may suggest the presence of significant impairment of memory or cognition.     

Managing network security — Part 6: Computer games and network security management

Over the last few years, computing has changed to an almost purely networked environment, but the technical aspects of information protection have not kept up. As a result, the success of information security programmes has increasingly become a function of our ability to make prudent management decisions about organizational activities. This series of articles takes a management view of protection and seeks to reconcile the need for security with the limitations of technology.