The quantification of the relative mineralogical composition of clay mixtures by powder X-ray diffraction or chemical mass balance methods has been severely hampered by a lack of representative standards. The recent development of elemental mass balance models that do not require standards for all minerals in the mixture may help circumvent this problem. These methods, which are based on the numerical optimization of systems of non-linear equations using the Marquardt algorithm, show promise for mineral quantification. The objective of this study is to make a preliminary assessment of the accuracy of these methods and to compare them to linear models that require standards for all mineral phases. Methods 1 and 2 are based on weighted average solutions to simultaneous linear equations solved for single samples with known standards. Solutions were achieved by a matrix decomposition algorithm and the Marquardt algorithm, respectively. Methods 3 and 4 are based on a set of simultaneous non-linear equations with reduced non-linearity solved by least squares optimization based on the Marquardt algorithm for multiple samples. Illite and halloysite compositions were fixed in Method 3, only the halloysite composition was fixed in Method 4. All models yielded relative weight fractions of the three mineral components; additionally, Methods 3 and 4 yielded compositions of smectite, and smectite and illite, respectively. Ten clay mixtures with varying proportions of the <0.2 μm size fraction of three different reference clays (Wyoming bentonite, Fithian illite, and New Bedford halloysite) were prepared gravi-metrically and analyzed by inductively coupled plasma-atomic emission spectroscopy. Accuracy of the four methods was evaluated by comparing the known mineralogical compositions of the mixtures with those predicted by the models. Relative errors of 5 and 10% (randomly +/-) were imposed on the elemental composition of the smectite standard to simulate errors due to lack of good standards. Not surprisingly, the accuracy of Methods 1 and 2 decreased rapidly with increasing error. Because Methods 3 and 4 optimized for the smectite composition and only used it for an initial guess, they were unaffected by the level of introduced error. They accurately quantified the mineralogical compositions of the mixtures and the elemental compositions of smectite, and smectite and illite, respectively.

Growth rate is a major component of feed efficiency when estimating residual feed intake (RFI). Quantile regression (QR) methodology can be used to identify animals with different growth trajectories. The objective of this study was to evaluate the use of QR to identify phenotypic and genetic differences in pigs selected for low RFI. Using performance data on 750 Yorkshire pigs selected for low RFI, individual average daily gain (ADG), average daily feed intake (ADFI), RFI and Gompertz growth curve parameters (asymptotic weight (a), inflection point (b) and decay parameter (c)) were estimated for each pig. Using QR methodology, three Gompertz growth curves were estimated for the whole population for three quantiles (0.1, 0.5 and 0.9) of the BW data. Each animal was classified into one of the quantile regression groups (QRG) based on their overall Euclidian distance between each observed and estimated BW from the quantile growth curves. These three curves were also estimated using only part of the data (generations −1 to 3, and −1 to 4) in order to evaluate the agreement classification rate of animals from later generations into QRGs. We evaluated the effect of QRG on growth parameters and performance traits. Genetic parameters were estimated for these traits, as well as for QRG. In addition, genetic trends for each QRG were estimated. Three distinct growth curves were observed for animals classified into either quantiles 0.1 (QRG0.1), 0.5 (QRG0.5) or 0.9 (QRG0.9). When only part of the data was used to estimate quantile growth curves, all animals from QRG0.1 were correctly classified in their group. Animals in QRG0.1 had significantly lower ADFI, ADG and RFI, and greater a, b and c than animals in the other groups. Quantile regression groups analysed as a trait was highly heritable (0.41) and had high (0.8) and moderate (0.46) genetic correlations with ADG and RFI, respectively. Selection for reduced RFI increased the number of animals classified as QRG0.1 in the population. Overall, downward genetic trends were observed for all traits as a function of selection for reduced RFI. However, QRG0.1 was the only group that had a positive genetic trend for ADG. Altogether, these results indicate that selection for reduced RFI changes the shape of growth curves in Yorkshire in pigs, and that QR methodology was able to identify animals having different genetic potential for feed efficiency, bringing a new opportunity to improve selection for reduced RFI.

This paper reviews the stochastic asset model described in Wilkie (1995) and previous work on refining this model. The paper then considers the application on non-linear modelling to investment series, considering both ARCH techniques and threshold modelling. The paper suggests a threshold autoregressive (TAR) system as a useful progression from the Wilkie (1995) model. The authors are making available (on compact disk) a collection of spreadsheets, which they have used to simulate the stochastic asset models which are considered in this paper.

The objectives of this study were to compare the goodness of fit of four non-linear growth models, i.e. Brody, Gompertz, Logistic and Von Bertalanffy, in West African Dwarf (WAD) sheep. A total of 5274 monthly weight records from birth up to 180 days of age from 889 lambs, collected during 2001 to 2004 in Betecoucou breeding farm in Benin were used. In the preliminary analysis, the General Linear Model Procedure of the Statistical Analysis Systems Institute was applied to the dataset to identify the significant effects of the sex of lamb (male and female), type of birth (single and twin), season of birth (rainy season and dry season), parity of dam (1, 2 and 3) and year of birth (2001, 2002, 2003 and 2004) on the observed birth weight and monthly weight up to 6 months of age. The models parameters (A, B and k), coefficient of determination (R2), mean square error (MSE) were calculated using language of technical computing package Matlab®, 2006. The mean values of A, B and k were substituted into each model to calculate the corresponding Akaike’s Information Criterion (AIC). Among the four growth functions, the Brody model has been selected for its accuracy of fit according to the higher R2, lower MSE and AIC. Finally, the parameters A, B and k were adjusted in Matlab®, 2006 for the sex of lamb, year of birth, season of birth, birth type and the parity of ewe, providing a specific slope of the Brody growth curve. The results of this study suggest that Brody model can be useful for WAD sheep breeding in Betecoucou farm conditions through growth monitoring.

This paper describes an extension of the SDM scheme introduced by Priestley (1980) to the problem of the identification of non-linear systems using only input/output records. It is shown that, under quite general assumptions on the structure of the system, it is possible to identify a non-linear relationship between the input and output processes via a modified version of the Kalman-type algorithm previously applied to the study of non-linear time series models. The paper includes a numerical study of data generated from various types of non-linear systems.