A coordinated survey for Cronobacter and related organisms in powdered infant formula, follow up formula and infant foods was undertaken by 8 laboratories in 7 countries in recognition of and in response to the data needs identified in an FAO/WHO call for data in order to develop global risk management guidance for these products. The products (domestic and imported) were purchased from the local market and were categorised according to their principle ingredients. A total of 290 products were analysed using a standardised procedure of pre-enrichment in 225 ml Buffered Peptone Water (BPW), followed by enrichment in Enterobacteriaceae Enrichment (EE) broth, plating on the chromogenic Cronobacter Druggan-Forsythe-Iversen (DFI) agar and presumptive identification with ID 32 E. Presumptive Cronobacter isolates were identified using 16S rRNA gene sequence analysis. Aerobic plate counts (APC) of the products were also determined on nutrient agar. Fourteen samples had APC>10(5) cfu/g, 3 of which contained probiotic cultures. C. sakazakii was isolated from 27 products; 3/91 (3%) follow up formulas (as defined by Codex Alimentarius Commission), and 24/199 (12%) infant foods and drinks. Hence C. sakazakii was less prevalent in follow up formula than other foods given to infants over the same age range. A range of other bacteria were also isolated from follow up formulas, including Acinetobacter baumannii, Enterobacter cloacae, Klebsiella pneumoniae, Citrobacter freundii, and Serratia ficaria. There was significant variation in the reconstitution instructions for follow up formulas. These included using water at temperatures which would enable bacterial growth. Additionally, the definition of follow up formula varied between countries.
We show that commutative group spherical codes in R n , as introduced by D. Slepian, are directly related to flat tori and quotients of lattices. As consequence of this view, we derive new results on the geometry of these codes and an upper bound for their cardinality in terms of minimum distance and the maximum center density of lattices and general spherical packings in the half dimension of the code. This bound is tight in the sense it can be arbitrarily approached in any dimension. Examples of this approach and a comparison of this bound with Union and Rankin bounds for general spherical codes is also presented.
A method for finding an optimum n-dimensional commutative group code of a given order M is presented. The approach explores the structure of lattices related to these codes and provides a significant reduction in the number of non-isometric cases to be analyzed. The classical factorization of matrices into Hermite and Smith normal forms and also basis reduction of lattices are used to characterize isometric commutative group codes. Several examples of optimum commutative group codes are also presented.
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