Multidimensional quasi-eigenfunction approximations andmulticomponent AM-FM models

We develop multicomponent AM-FM models for multidimensional signals. The analysis is cast in a general n-dimensional framework where the component modulating functions are assumed to lie in certain Sobolev spaces. For both continuous and discrete linear shift invariant (LSI) systems with AM-FM inputs, powerful new approximations are introduced that provide closed form expressions for the responses in terms of the input modulations. The approximation errors are bounded by generalized energy variances quantifying the localization of the filter impulse response and by Sobolev norms quantifying the smoothness of the modulations. The approximations are then used to develop novel spatially localized demodulation algorithms that estimate the AM and FM functions for multiple signal components simultaneously from the channel responses of a multiband linear filterbank used to isolate components. Two discrete computational paradigms are presented. Dominant component analysis estimates the locally dominant modulations in a signal, which are useful in a variety of machine vision applications, while channelized components analysis delivers a true multidimensional multicomponent signal representation. We demonstrate the techniques on several images of general interest in practical applications, and obtain reconstructions that establish the validity of characterizing images of this type as sums of locally narrowband modulated components.     

A Genetic Programming Approach to System Identification of Rainfall-Runoff Models

Advancements in data acquisition, storage and retrieval are progressing at an extraordinary rate, whereas the same in the field of knowledge extraction from data is yet to be accomplished. The challenges associated with hydrological datasets, including complexity, non-linearity and multicollinearity, motivate the use of machine learning to build hydrological models. Increasing global climate change and urbanization call for better understanding of altered rainfall-runoff processes. There is a requirement that models are intelligible estimates of underlying physics, coupling explanatory and predictive components, maintaining parsimony and accuracy. Genetic Programming, an evolutionary computation technique has been used for short-term prediction and forecast in the field of hydrology. Advancing data science in hydrology can be achieved by tapping the full potential of GP in defining an evolutionary flexible modelling framework that balances prior information, simulation accuracy and strategy for future uncertainty. As a preliminary step, GP is used in conjunction with a conceptual rainfall-runoff model to solve model configuration problem. Two datasets belonging to a tropical catchment of Singapore and a temperate catchment of South Island, New Zealand with contrasting characteristics are analyzed in this study. The results indicate that proposed approach successfully combines the merits of evolutionary algorithm and conceptual knowledge in the generation of optimal model structure and associated parameters to capture runoff dynamics of catchments.     

PARTITION CHROMATOGRAPHY OF SUGARS IN WORT AND BEER ON ANION EXCHANGE RESINS

Partition chromatography on anion exchange resins in the sulphate form in 85% ethanol at 75°C was used for the separation of monosaccharides in beer and wort. The eluate was analysed automatically by the orcinol method. Simultaneous analysis by a periodate-formaldehyde method permitted determination of glycerol. Oligomers, except for those precipitated by 65% ethanol, were separated and characterized by chromatography in this medium. Sharp separations of disaccharides were made at an intermediate concentration. Species which were not separated on this resin were resolved on a cation exchanger in its lithium form. The identification of oligomers was facilitated by the fact that for oligomers having the same type of glycosidic bonds there exists a straight line relationship between the logarithm of the distribution coefficient and the number of monosaccharide residues.     

Properties of the magnitude terms of orthogonal scaling functions

The spectrum of the convolution of two continuous functions can be determined as the continuous Fourier transform of the cross-correlation function. The same can be said about the spectrum of the convolution of two infinite discrete sequences, which can be determined as the discrete time Fourier transform of the cross-correlation function of the two sequences. In current digital signal processing, the spectrum of the continuous Fourier transform and the discrete time Fourier transform are approximately determined by numerical integration or by densely taking the discrete Fourier transform. It has been shown that all three transforms share many analogous properties. In this paper we will show another useful property of determining the spectrum terms of the convolution of two finite length sequences by determining the discrete Fourier transform of the modified cross-correlation function. In addition, two properties of the magnitude terms of orthogonal wavelet scaling functions are developed. These properties are used as constraints for an exhaustive search to determine a robust lower bound on conjoint localization of orthogonal scaling functions.     

Limits on discrete modulated signals

We develop theorems of a general nature that apply to the analysis of AM-FM signals of the form a(m)exp [jφ(m)] or a(m) cos [φ(m)] and to their behavior both in linear systems and in simple nonlinear systems comprised of products of linear elements. Such product-systems include interesting nonlinear demodulation operators, such as the Teager-Kaiser (1990) operator. Expressions for the approximate system responses to AM-FM signals are derived by making an analogy to the eigenfunction interpretation of sinusoids in linear systems; for the case of sinusoidal signals, the approximations are exact. These expressions are collectively called quasieigenfunction approximations (QEAs). For nonsinusoidal AM-FM signals, the approximations have errors that are tightly bounded by functionals that express the smoothness of the AM and FM information signals and the durations of the involved system impulse responses. The bounds are independent of the bandwidths of the AM and FM functions. Two general applications are considered. First, the approximations are found to be useful for analyzing discrete-time nonlinear energy operators, including the Teager-Kaiser operator. Next, the approximation theorems lead to the selection of an optimal class of bandpass filters for use in a discrete multiband AM-FM demodulation system. The filter class selected is optimal in the sense of achieving the lower bound of a novel discrete uncertainty principle     

Multicomponent Multidimensional Signals

In this brief paper, we extend the notion of multicomponent signal into multiple dimensions. A definition for multidimensional instantaneous bandwidth is presented and used to develop criteria for determining the multicomponent nature of a signal. We demonstrate application of the criteria by testing the validity of a multicomponent interpretation for a complicated nonstationary texture image.     

COPERM: transform-domain energy compaction by optimal permutation

Compaction by optimal permutation (COPERM) is a tool for transform domain energy compaction of broadband signals, whose foundation is a simple but powerful idea: any signal can be transformed to resemble a more desirable (e.g., from a transform-domain compaction viewpoint) signal from a class of “target” signals (e.g., DCT basis functions) by means of a suitable permutation of its samples. One application of transform-domain energy compaction is in lossy compression. We pursue one possible thread in detail and demonstrate some interesting broadband image compression results     

Influence of lactation on metabolic characteristics and embryo development in postpartum Holstein dairy cows

The aim of this study was to examine the direct effect of lactation on the ability of the reproductive tract of postpartum dairy cows to support early embryo development. Twenty-one primiparous Holstein heifers were used. Immediately after calving, half of the cows were dried off (i.e., never milked), and the other half entered the milking herd and were milked twice daily. Jugular blood samples were taken twice per week from 15 d before calving to approximately 100 d postpartum to measure nonesterified fatty acids, β-hydroxybutyrate, glucose, insulin, and insulin-like growth factor-I. At the same time, body weight and body condition score were recorded for each cow. At approximately 60 d postpartum (experiment 1), approximately 65 two- to four-cell embryos, produced by in vitro maturation and fertilization, were endoscopically transferred to the oviduct ipsilateral to the corpus luteum of all cows on d 2 of the estrous cycle. Five days later (d 7), the oviduct and uterus were flushed nonsurgically and the number of embryos developing to the blastocyst stage was recorded. At approximately 90 d postpartum (experiment 2), the estrous cycles of the same cows were resynchronized and 15 to 20 in vitro-produced blastocysts were transferred to the uterus of each recipient on d 7. All cows were slaughtered on d 14 to assess embryo survival and dimensions. Body weight and body condition score were significantly different between groups for the entire postpartum period of the study. Concentrations of nonesterified fatty acids and β-hydroxybutyrate were higher and concentrations of glucose, insulin, and insulin-like growth factor-I were lower in lactating compared with nonlactating cows. Embryo recovery rates from lactating and dry cows were similar. In experiment 1, fewer embryos developed to the blastocyst stage in the lactating cows compared with the nonlactating cows. In experiment 2, embryo survival and conceptus dimensions were not different between lactating and nonlactating cows. In conclusion, the data indicate that the reproductive tract of the lactating dairy cow is compromised in its ability to support early embryo development compared with that of matched dry cows and this may contribute to early embryo mortality observed in such animals.