EFFECTS OF APODIZATION FUNCTION,ZERO FILLING,BACKGROUND SPECTRA,AND ABSORBANCE TRANSFORMATION ON MID-INFRARED CALIBRATIONS FOR FEED COMPOSITION

ABSTRACT

Research has demonstrated that diffuse reflectance mid-infrared spectroscopy can, like near-infrared diffuse reflectance, be used to quantitatively determine the composition of ground samples of forages and soils without the need for KBr dilution. While it has been demonstrated that the accuracy of calibrations developed using mid-infrared spectra can be equal to or better than that achieved using near-infrared spectra, the influence of factors such as apodization function has not been determined. Results based on the spectra of 173 treated forage samples obtained using a DigiLab FTS-60 spectrometer have demonstrated that many parameters associated with mid-infrared spectra have little or no effect on partial least squares calibrations. Additional zero filling of spectra had little effect other than to increase the derivative gaps found to produce optimal calibrations, but calibrations developed using Kubelka-Munk transformed data, as opposed to absorbance data, were not as accurate. Choice of apodization function also had little effect, although slightly better results were found using triangular or weak Norton-Beer. Likewise, the frequency of taking a background spectrum did not seem to have any great effect on calibrations, although results were slightly better with hourly or daily acquisitions as opposed to one for each sample as is done in the near-infrared.     

An information‐theoretic‐based (MaxEnt) approach to social dynamical systems

Jeffreys‐Jaynes’ Predictive Statistics appears to provide a promising approach for the study of general dynamical systems. We describe an application of such theory to the analysis of the dynamics of interacting social groups. For that purpose the said statistical theory is redirected towards the construction of an equivalent stochastic theory. The working of the formalism is illustrated by applying it to a simplified case of opinion forming in a two‐candidates election.     

Investigation of oxidation and tautomerization of a recently synthesized Schiff base in micellar media using multivariate curve resolution alternative least squares and rank annihilation factor analysis methods

The oxidation of the recently synthesized Schiff base 3,6-bis((2-aminoethyl-5-Br-salicyliden)thio)pyridazine (PABST) with hydrogen peroxide was investigated using spectrophotometric studies. The reaction rate order and observed rate constant of the oxidation reaction was obtained in the mixture of N,N-dimethylformamide (DMF):water (30:70, v/v) at pH 10 using multivariate cure resolution alternative least squares (MCR-ALS) method and rank annihilation factor analysis (RAFA). The effective parameters on the oxidation rate constant such as percents of DMF, the effect of transition metals like Cu²⁺, Zn²⁺, Mn²⁺ and Hg²⁺ and the presence of surfactants were investigated. The keto-enol equilibria in DMF:water (30:70, v/v) solution at pH 7.6 was also investigated in the presence of surfactants. At concentrations above critical micelle concentration (cmc) of cationic surfactant cetyltrimethylammonium bromide (CTAB), the keto form was the predominant species, while at concentrations above cmc of anionic surfactant sodium dodecyl sulfate (SDS), the enol form was the predominant species. The kinetic reaction order and the rate constant of tautomerization in micellar medium were obtained using MCR-ALS and RAFA. The results obtained by both the methods were in a good agreement with each other. Also the effect of different volume percents of DMF on the rate constant of tautomerization was investigated. The neutral surfactant (Triton X-100) had no effect on tautomerization equilibrium.     

ToF-SIMS PC-DFA analysis of prostate cancer cell lines

Three closely related cancer cell lines have been analysed with ToF-SIMS using a C₆₀⁺ primary ion beam. Principal component-discriminant function analysis (PC-DFA) has been applied for spectral classification. Various spectral pre-processing methods are discussed and assessed for optimum discrimination of this data set. The sum-normalised PC-DFA spectral model produced sensitivities as high as 83.3% and specificities as high as 100% at the 99% confidence limit. At this confidence limit only one errant spectrum was misclassified. The resulting loadings plots suggest that a range of lipid and amino-acid related signals are responsible for the cell line discrimination.     

Estimating L ∞ Norms by L 2k Norms for Functions on Orbits

Abstract. Let G be a compact group acting in a real vector space V . We obtain a number of inequalities relating the L ^∞ norm of a matrix element of the representation of G with its L ^2k norm for a positive integer k . As an application, we obtain approximation algorithms to find the maximum absolute value of a given multivariate polynomial over the unit sphere (in which case G is the orthogonal group) and for the assignment problem of degree d , a hard problem of combinatorial optimization generalizing the quadratic assignment problem (in which case G is the symmetric group).     

Visualizing hypothesis tests in multivariate linear models: the heplots package for R

Hypothesis-error (or “HE”) plots, introduced by Friendly (J Stat Softw 17(6):1–42, 2006a; J Comput Graph Stat 16:421–444, 2006b), permit the visualization of hypothesis tests in multivariate linear models by representing hypothesis and error matrices of sums of squares and cross-products as ellipses. This paper describes the implementation of these methods in the heplots package for R, as well as their extension, for example from two to three dimensions and by scaling hypothesis ellipses and ellipsoids in a natural manner relative to error. This is a paper for the proceedings of the Directions in Statistical Computing conference.     

Socio-economic determinants of HIV/AIDS pandemic and nations efficiencies

This paper examines the influence and direction of social and economic determinants of the HIV/AIDS global epidemic across nations and assesses each country’s efficiency in battling the pandemic. The initial dataset consisted of 151 countries with five dependent variables and 90 explanatory variables (reduced to 50 after extensive exploratory data analysis of missing value patterns, undesirable multi-colinearities and multivariate outliers).     

误差服从多元t分布的一类线性模型下参数估计的若干注记

研究一类线性模型下参数估计的若干问题．这类模型包含了多个因变量线性模型、增长曲线模型、扩充的增长曲线模型、似乎不相关回归方程组、方差分量模型等常用模型．在这类线性模型下,证明了当误差服从多元t分布时与误差服从多元正态分布时,具有相同的完全统计量和无偏估计,且在后一种情况下的充分统计量必为前一种情况下的充分统计量．对于带有多种协方差结构的前述几种模型,把在误差服从多元正态分布下,相应的协方差阵及有关参数的一致最小风险无偏(UMRU)估计存在性的结论推广到了相应的误差服从多元t分布情形．此外,对于误差服从多元t分布的这类统一的线性模型,给出了回归系数的线性可估函数的无偏估计的协方差阵的C-R下界．     

Evaluating Nearly Singular Multinormal Expectations with Application to Wave Distributions

The numerical computation of expectations for (nearly) singular multivariate normal distribution is a difficult problem, which frequently occurs in widely varying statistical contexts. In this article we discuss several strategies to improve the algorithm proposed by Genz and Kwong (2000) when either a moderate accuracy is requested, the correlation structure is strong, and, most importantly, the dimension of the integral is large. Test results for typical problems show an average speedup of 10 using the modified algorithm, but even more is gained as the dimension of the problem increases. We apply the modified algorithm to compute long-run distributions of Gaussian wave characteristics, a difficult problem where previous algorithms fail to compute accurate values in reasonable time. AMS 2000 Subject Classification 65C60, 65D15, 68W25     

Simultaneous spectrophotometric determination of four preservatives in foodstuffs by multivariate calibration and artificial neural networks

Benzoic acid(BA),methylparaben(MP),propylparaben(PP)and sorbic acid(SA)are food preservatives,and they have well defined UV spectra.However,their spectra overlap seriously,and it is difficult to determine them individually from their mixtures without preseparation.In this paper,seven different chemometric approaches were applied to resolve the overlapping spectra and to determine these compounds simultaneously.With respect to the criteria of%relative prediction error(RPE)and%recovery, principal component...