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     

Estimation of the interindividual variability in the one-compartment pharmacokinetic model for methylmercury: implications for the derivation of a reference dose

A critical step in the U.S. EPA's derivation of an Reference Dose (RfD) for methylmercury is conversion of the maternal hair Hg concentration of 11 ppm to average daily intake using the one-compartment pharmacokinetic model. A default uncertainty factor (UF) adjustment of 3 for interindividual variability was then applied to this conversion. A probabilistic (Monte Carlo) analysis is presented estimating the interindividual variability inherent in this dose conversion for women 18-40 years old based on data in the scientific literature. The dose of 1.1 micrograms/kg/day, calculated by the U.S. EPA to correspond to 11 ppm Hg in hair, is estimated in this analysis to be larger than 94-99% of corresponding doses. The application of a UF of 3 to this U.S. EPA value gives a dose which is estimated to be larger than 28-73% of corresponding doses. This analysis suggests that if the dose conversion in the RfD is intended to be inclusive of 95-99% of women 18-40, the daily intake should be set at 0.1-0.3 microgram/kg/day. The RfD of 0.03-0.1 microgram/kg/day, derived from this dose by the U.S. EPA's application of an additional UF of 3 for additional toxicologic concerns, is somewhat smaller than the current RfD of 0.1 microgram/kg/day.     

Partial cricotracheal resection with primary anastomosis in the pediatric age group

The traditional approach to severe subglottic stenosis (SGS) in the pediatric age group is laryngotracheal reconstruction (LTR). This approach may be complex and multistaged, with variable and unpredictable success rates in the individual patient. Excellent results have been reported in adults who had severe SGS and underwent partial resection of the cricoid and primary thyrotracheal anastomosis. This procedure has not been widely reported in infants and children. We report our experience with this procedure in 16 pediatric patients with grade III or IV SGS. Eleven patients had multiple previous LTR operations. The preoperative evaluation, surgical techniques, postoperative care, complications, and final results are described and discussed. Fourteen patients were decannulated after the procedure, 1 patient needed a second open procedure prior to decannulation, and 1 patient with concomitant bronchopulmonary dysplasia remains cannulated, for an overall 94% decannulation rate. Fourteen patients have no limitation of respiration, and 1 patient has moderate exercise intolerance. The results of this series suggest that partial cricotracheal resection with primary anastomosis is a relatively safe and effective procedure for pediatric patients with severe SGS.     

Activating mutations of the Gs alpha-gene in nonfunctioning pituitary tumors

The majority of pituitary tumors are of monoclonal origin; however, the molecular basis for their formation is poorly understood. Somatic mutations in the alpha-subunit of the GTP-binding protein, Gs alpha (gsp oncogene) have been found in about one third of GH-secreting tumors. Mutations in another alpha-subunit of a GTP-binding protein, Gi2 alpha (gip mutations) have been described in other endocrine tumors. In this study, we examined 21 nonfunctioning pituitary tumors and 4 macroprolactinomas for gsp mutations and 27 nonfunctioning tumors and 4 macroprolactinomas for gip mutations. Using the polymerase chain reaction and denaturing gradient gel electrophoresis, 2 nonfunctioning pituitary tumors displayed migration abnormalities when the Gs alpha-gene was analyzed. Sequence analysis of these abnormally migrating polymerase chain reaction products revealed two previously known gsp mutations: arginine at codon 201 altered to cysteine, and glutamine at codon 227 changed to leucine. No gip mutations could be demonstrated. These findings emphasize the monoclonal origin of nonfunctioning pituitary tumors and suggest that cAMP may play a role in tumorigenesis of nonfunctioning pituitary tumors.     

Category Norms as a Function of Culture and Age: Comparisons of Item Responses to 105 Categories by American and Chinese Adults.

Understanding how aging influences cognition across different cultures has been hindered by a lack of standardized, cross-referenced verbal stimuli. This study introduces a database of such item-level stimuli for both younger and older adults, in China and the United States, and makes 3 distinct contributions. First, the authors specify which item categories generalize across age and/or cultural groups, rigorously quantifying differences among them. Second, they introduce novel, powerful methods to measure between-group differences in freely generated ranked data, the rank-ordered logit model and Hellinger Affinity. Finally, a broad archive of tested, cross-linguistic stimuli is now freely available to researchers: data, similarity measures, and all stimulus materials for 105 categories and 4 culture-by-age groups, comprising over 10,000 fully translated unique item responses. (PsycINFO Database Record (c) 2010 APA, all rights reserved)