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).     

New results for aggregating integer-valued equations

A variety of results have been given for aggregating integer-valued (diophantine) equations whose variables are restricted to nonnegative integers. In each, integer weights are identified for the equations so that their linear combination yields a single equation with the same solution set of the original system of equations. Because the coefficients of the aggregated equation tend to achieve unwieldy sizes as the number of original equations increases, the goal is to identify weights so these coefficients will lie in a range as limited as possible. We give theorems which separately and in combination provide new methods for aggregating general integer-valued equations. Our results include formulations that do not require linearity of the original system, or nonnegativity of component variables. We also demonstrate that our theorems yield as special cases earlier results (analytical formulae) conjectured to yield the smallest possible weights for less general domains. As another application, the presented results were used to develop a highly efficient approach for the integer knapsack problem. Empirical outcomes show that the developed solution procedure is significantly superior to advanced branch and bound methods (previously established to be the most efficient knapsack solution procedures).     

The potential of pyrolysis/gas chromatography/mass spectrometry for determining the progress of lignification: An investigation of maturing asparagus sclerenchyma tissue

Sclerenchyma tissues from semi-mature and mature asparagus spears were analysed by pyrolysis/gas chromatography/mass spectrometry and by conventional chemical methods in order to determine the degree of lignification and compare analytical techniques. The pyrolysis data are similar to those obtained by a chemical method involving alkaline extraction at 70°C followed by spectrophotometric determination of phenolic content. The pyrolysis method was more rapid, sensitive and informative than the chemical technique and shows considerable potential for studying the chemical basis of the textural development of plant foods.     

One-Dimensional Poisson Growth Models With Random and Asymmetric Growth

Suppose there is a Poisson process of points X _i on the line. Starting at time zero, a grain begins to grow from each point X _i , growing at rate A _i to the left and rate B _i to the right, with the pairs (A _i , B _i ) being i.i.d. A grain stops growing as soon as it touches another grain. When all growth stops, the line consists of covered intervals (made up of contiguous grains) separated by gaps. We show (i) a fraction 1/e of the line remains uncovered, (ii) the fraction of covered intervals which contain exactly k grains is (k–1)/k!, (iii) the length of a covered interval containing k grains has a gamma(k–1) distribution, (iv) the distribution of the grain sizes depends only on the distribution of the total growth rate A _i +B _i , and other results. Similar theorems are obtained for growth processes on a circle; in this case we need only assume the pairs (A _i , B _i ) are exchangeable. These results extend those of Daley, et al. (2000) who studied the case where A _i =B _i =1. Simulation results are given to illustrate the various theorems.     

Protonated ethanol and its neutral counterparts

Collisionally activated dissociation and neutralization-reionization experiments reveal that protonation of ethanol leads to two distinct isomers, the classical ion CH₃CH₂OH⁺₂ and the proton-bound complex C₂H₄…H⁺…OH₂. The neutral counterpart of the latter is unstable, whereas that of the former can be produced in a bound state if the CH₃CH₂OH⁺₂ precursor ion is formed under low ion source pressure conditions and, thus, with higher internal energies. This suggests that there are substantial differences in the geometries of CH₃CH₂OH⁺₂ and the hypervalent CH₃CH₂OH₂ ·. This provides only a partial explanation for unusual isotope effects; C₂H₅OD₂ ·, CH₃CD₂OD₂ ·, and CD₃CH₂OD₂ · are substantially more stable than C₂D₅OD₂ · and C₂H₅OH₂ ·.     

Backward bifurcations in simple vaccination models

We describe and analyze by elementary means some simple models for disease transmission with vaccination. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. We extend the results to include models in which the parameters may depend on the level of infection.