On classical and other methods of discriminant analysis and estimation of log-odds

For two multinormal populations with equal covariance matrices the likelihood ratio discriminant function, an alternative allocation rule to the sample linear discriminant function when n1 ≠ n2 ,is studied analytically. With the assumption of a known covariance matrix its distribution is derived and the expectation of its actual and apparent error rates evaluated and compared with those of the sample linear discriminant function. This comparison indicates that the likelihood ratio allocation rule is robust to unequal sample sizes. The quadratic discriminant function is studied, its distribution reviewed and evaluation of its probabilities of misclassification discussed. For known covariance matrices the distribution of the sample quadratic discriminant function is derived. When the known covariance matrices are proportional exact expressions for the expectation of its actual and apparent error rates are obtained and evaluated. The effectiveness of the sample linear discriminant function for this case is also considered. Estimation of true log-odds for two multinormal populations with equal or unequal covariance matrices is studied. The estimative, Bayesian predictive and a kernel method are compared by evaluating their biases and mean square errors. Some algebraic expressions for these quantities are derived. With equal covariance matrices the predictive method is preferable. Where it derives this superiority is investigated by considering its performance for various levels of fixed true log-odds. It is also shown that the predictive method is sensitive to n1 ≠ n2. For unequal but proportional covariance matrices the unbiased estimative method is preferred. Product Normal kernel density estimates are used to give a kernel estimator of true log-odds. The effect of correlation in the variables with product kernels is considered. With equal covariance matrices the kernel and parametric estimators are compared by simulation. For moderately correlated variables and large dimension sizes the product kernel method is a good estimator of true log-odds.

Evaluation of microbial adjuncts and their effect on the ripening of cheddar cheese

A bacteriocin-producing strain of Lactobacillus paracasei DPC 4715 was used as an adjunct culture in Cheddar cheese in order to control the growth of “wild” nonstarter lactic acid bacteria. No suppression of growth of the indicator strain was observed in the experimental cheese. The bacteriocin produced by Lactobacillus paracasei DPC 4715 was sensitive to chymosin and cathepsin D and it may have been cleaved by the rennet used for the cheese manufactured or by indigenous milk proteases. A series of studies were performed using various microbial adjuncts to influence cheese ripening. Microbacterium casei DPC 5281, Corynebacterium casei DPC 5293 and Corynebacterium variabile DPC 5305 were added to the cheesemilk at level of 109 cfu/ml resulting in a final concentration of 108 cfu/g in Cheddar cheese. The strains significantly increased the level of pH 4.6-soluble nitrogen, total free amino acids after 60 and 180 d of ripening and some individual free amino acids after 180 d. Yarrowia lipolytica DPC 6266, Yarrowia lipolytica DPC 6268 and Candida intermedia DPC 6271 were used to accelerate the ripening of Cheddar cheese. Strains were grown in YG broth to a final concentration of 107 cfu/ml, microfluidized, freeze-dried and added to the curd during salting at level of 2% w/w. The yeasts positively affected the primary, secondary proteolysis and lipolysis of cheeses and had aminopeptidase, dipeptidase, esterase and 5’ phosphodiestere activities that contributed to accelerate the ripening and improve the flavor of cheese. Hafia alvei was added to Cheddar cheesemilk at levels of 107 cfu/ml and 108 cfu/ml and its contribution during ripening was evaluated. The strain significantly increased the level of pH 4.6-soluble nitrogen, total free amino-acids, and some individual free amino-acids of Cheddar cheese, whereas no differences in the urea-polyacrylamide gel electrophoresis (urea-PAGE) electrophoretograms of the cheeses were detected. Hafia alvei also significantly increased the level of some biogenic amines. A low-fat Cheddar cheese was made with Bifidobacterium animalis subsp. lactis, strain BB-12® at level of 108 cfu/ml, as a probiotic adjunct culture and Hi-Maize® 260 (resistant high amylose maize starch) at level of 2% and 4% w/v, as a prebiotic fiber which also played the role of fat replacer. Bifidobacterium BB-12 decreased by 1 log cycle after 60 d of ripening and remained steady at level of ~107 cfu/g during ripening. The Young’s modulus also increased proportionally with increasing levels of Hi-maize. Hencky strain at fracture decreased over ripening and increased with increasing in fat replacer. A cheese based medium (CBM) was developed with the purpose of mimicking the cheese environment at an early ripening stage. The strains grown in CBM showed aminopeptidase activity against Gly-, Arg-, Pro- and Phe-p-nitroanalide, whereas, when grown in MRS they were active against all the substrates tested. Both Lb. danicus strains grown in MRS and in CBM had aminotransferase activity towards aromatic amino acids (Phe and Trp) and also branched-chain amino acids (Leu and Val). Esterase activity was expressed against p-nitrophenyl-acetate (C2), pnitrophenyl- butyrate (C4) and p-nitrophenyl-palmitate (C16) and was significantly higher in CBM than in MRS.

Use of oxygen sensors for the non destructive measurement of oxygen in packaged food and beverage products and its impact on product quality and shelf life

The principal objective of this thesis was to investigate the ability of reversible optical O2 sensors to be incorporated into food/beverage packaging systems to continuously monitor O2 levels in a non-destructive manner immediately postpackaging and over time. Residual levels of O2 present in packs can negatively affect product quality and subsequently, product shelf-life, especially for O2-sensitive foods/beverages. Therefore, the ability of O2 sensors to continuously monitor O2 levels present within food/beverage packages was considered commercially relevant in terms of identifying the consequences of residual O2 on product safety and quality over time. Research commenced with the development of a novel range of O2 sensors based on phosphorescent platinum and palladium octaethylporphyrin-ketones (OEPk) in nano-porous high density polyethylene (HDPE), polypropylene (PP) polytetrafluoroethylene (PTFE) polymer supports. Sensors were calibrated over a temperature range of -10°C to +40°C and deemed suitable for food and beverage packaging applications. This sensor technology was used and demonstrated itself effective in determining failures in packaging containment. This was clearly demonstrated in the packaging of cheese string products. The sensor technology was also assessed across a wide range of packaged products; beer, ready-to-eat salad products, bread and convenience-style, muscle-based processed food products. The O2 sensor technology performed extremely well within all packaging systems. The sensor technology adequately detected O2 levels in; beer bottles prior to and following pasteurisation, modified atmosphere (MA) packs of ready-to-eat salad packs as respiration progressed during product storage and MA packs of bread and convenience-style muscle-based products as mycological growth occurred in food packs over time in the presence and absence of ethanol emitters. The use of the technology, in conjunction with standard food quality assessment techniques, showed remarkable usefulness in determining the impact of actual levels of O2 on specific quality attributes. The O2 sensing probe was modified, miniaturised and automated to screen for the determination of total aerobic viable counts (TVC) in several fish species samples. The test showed good correlation with conventional TVC test (ISO:4833:2003), analytical performance and ruggedness with respect to variation of key assay parameters (probe concentration and pipetting volume). Overall, the respirometric fish TVC test was simple to use, possessed a dynamic microbial range (104-107 cfu/g sample), had an accuracy of +/- one log(cfu/g sample) and was rapid. Its ability to assess highly perishable products such as fish for total microbial growth in <12 hr demonstrates commercial potential.