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).     

Viral dynamics of primary viremia and antiretroviral therapy in simian immunodeficiency virus infection

Mathematical modeling of viral replication dynamics, based on sequential measurements of levels of virion-associated RNA in plasma during antiretroviral treatment, has led to fundamental new insights into human immunodeficiency virus type 1 pathogenesis. We took advantage of the simian immunodeficiency virus (SIV)-infected macaque model to perform detailed measurements and mathematical modeling during primary infection and during treatment of established infection with the antiretroviral drug (R)-9-(2-phosphonylmethoxypropyl)adenine (PMPA). The calculated clearance half-life for productively infected cells during resolution of the peak viremia of primary infection was on the order of 1 day, with slightly shorter clearance half-lives calculated during PMPA treatment. Viral reproduction rates upon discontinuation of PMPA treatment after 2 weeks were approximately twofold greater than those obtained just prior to initiation of treatment in the same animals, likely reflecting accumulation of susceptible target cells during treatment. The basic reproductive ratio (R0) for the spread of SIV infection in vivo, which represents the number of productively infected cells derived from each productively infected cell at the beginning of infection, was also estimated. This parameter quantifies the extent to which antiviral therapy or vaccination must limit the initial spread of virus to prevent establishment of chronic disseminated infection. The results thus provide an important guide for efforts to develop vaccines against SIV and, by extension, human immunodeficiency virus.     

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.     

Foetal alcohol syndrome in Saskatchewan: unchanged incidence in a 20-year period

Ethers and thioethers of monosaccharides have been synthesised which show potent toxicity to mouse (LD50 > or = 4 g.kg-1 O.W. and 0.2 to 1.5 g.kg-1 I.P.W.). A study of calcium antagonist activity for the full series of compounds indicated that the activity was similar for both O- and S- ethers and maximum activities were observed for monoacetoneglucose ethers possessing carbon chain close to 8 carbons.     

Regional lipid peroxidation and protein oxidation in rat brain after hyperbaric oxygen exposure

Reactive oxygen species may participate in development of neurological toxicity resulting from hyperbaric oxygen exposure. To explore the possibility that increased reactive O2 metabolite generation may result in oxidative modification of lipids and proteins, rats were exposed to five atmospheres (gauge pressure) of O2 until development of an electroencephalographic seizure. Lipid peroxidation (as thiobarbituric acid-reactive substances) and protein oxidation (as 2,4-dinitrophenyl-hydrazones) were measured in five brain regions. Oxidized and reduced glutathione were also determined because of their role in regulating lipid peroxidation. Lipid peroxidation was confined to the frontal cortex and hippocampus, while protein oxidation (in both cytoplasmic and membranous fractions) and increased oxidized glutathione was evident throughout the brain. These results support a role for formation of reactive O2 metabolites from hyperbaric O2 exposure and suggest that protein oxidation, especially in soluble proteins, may be one of the most sensitive measures.     

Differential divalent cation requirements uncouple the assembly and catalytic reactions of human immunodeficiency virus type 1 integrase

Previous in vitro analyses have shown that the human immunodeficiency virus type 1 (HIV-1) integrase uses either manganese or magnesium to assemble as a stable complex on the donor substrate and to catalyze strand transfer. We now demonstrate that subsequent to assembly, catalysis of both 3' end processing and strand transfer requires a divalent cation cofactor and that the divalent cation requirements for assembly and catalysis can be functionally distinguished based on the ability to utilize calcium and cobalt, respectively. The different divalent cation requirements manifest by these processes are exploited to uncouple assembly and catalysis, thus staging the reaction. Staged 3' end processing and strand transfer assays are then used in conjunction with exonuclease III protection analysis to investigate the effects of integrase inhibitors on each step in the reaction. Analysis of a series of related inhibitors demonstrates that these types of compounds affect assembly and not either catalytic process, therefore reconciling the apparent disparate results obtained for such inhibitors in assays using isolated preintegration complexes. These studies provide evidence for a distinct role of the divalent cation cofactor in assembly and catalysis and have implications for both the identification and characterization of integrase inhibitors.     

Reasons for personnel turnover in a private health facility

In this article 1 describe efforts to build a genetically informative, population-based sample of black twins to study physical frailty and aging in the United States. This project involves the use of governmental registries combined with sampling techniques developed to overcome limitations in the registry data. Two analytical approaches to measures of disability are included to illustrate the types of questions that can be addressed with this sample. These results suggest that physical disability in late life has both genetic and environmental determinants. Only with a genetically informative sample can evidence be collected indicating that frailty may be driven by fixed processes (i.e., disability resulting from activation of senescence genes), fluid processes (i.e., disability resulting from changes in the features of the environment), or a combination of both.     

Polymorphonuclear neutrophil granulocyte chemotactic hyperresponsiveness in a case of canine acromegaly

Growth hormone (GH) has recently been shown to affect polymorphonuclear neutrophil granulocyte (PMN) function and to be secreted by mononuclear cells, indicating that the hormone may be active in an immunophysiologic network, acting as an endo- or paracrine priming agent. The purpose of the present study was to evaluate the chemotactic responsiveness of canine peripheral PMN in a dog with acromegaly, caused by spontaneous, progesterone-induced hypersecretion of GH and, secondary to this, a seven-fold increase in insulin-like growth factor I (IGF-I). The chemotactic responsiveness towards zymosan-activated serum (ZAS) and leukotriene B4 (LTB4) was evaluated at a time when the dog suffered from acromegaly and again 57 days after corrective surgery (ovariohysterectomy). The experiments showed that PMN from the patient exhibited enhanced chemotactic migration that appeared to be associated with the hypersomatotropic condition as judged from the reversibility of the phenomenon. The glucose intolerance and elevated serum alkaline phosphatase that were observed in the acromegalic dog were also shown to be reversible following surgery.