Partial spoilage data are generated by simulating experimental methods frequently used in food science. The basic experimental model that is simulated is as follows: N tubes (or cans) of substrate (food) are inoculated with a microbiological contaminant (e.g. PA 3679 or C BotuZinum). These replicates are then subjected to a lethal environment (heat or radiation, etc.) and after incubation the replicates are tested to determine the number of replicates with viable contaminants remaining. Exact counts are not possible. The algorithm developed has many useful options, so that the simulation can be used within many areas of food science. The basis of the methodology is probabilistic, and food scientists may use it to generate replicate data necessary for statistical analyses. The technique can be useful for understanding the underlying microbiological phenomena. Repetitive runs may be used for comparative analysis with actual experimental results, in an inexpensive way. The methodology also provides a possible explanation of 'skips' and 'tailing' as has been observed in partial spoilage data.
Real and simulated experimental data and theoretical data from quantal response experiments were used to make a comparison between the analysis of data from a quantal response experiment and data from a direct enumeration experiment. The method of analysis for each is differentiated, thereby enhancing the utility of the quantal response experiment in sterilization studies. From this comparison it appears that the Stumbo estimate of the D value is biased. Furthermore, the Stumbo estimate depends upon the spore load per replicate in quantal response type experiments, which makes experimental comparisons difficult. Another estimate of D is demonstrated which overcomes some of these shortcomings.
Let Bn be the unit ball in Rn, Euclidean n-space, i.e. Bn = {x: xERn, d(x, 0) ^ 1). If/ and g are any two functions of B" to itself define, as usual, ||/-g\\ =sup{d(f(x), g(x)): xEBn}. J. Ax [l] has conjectured that if/ is a continuous function of Bn onto itself such that/ restricted to the boundary is the identity, then ||/(m+1)-/|| ||/(m)-1\\ for w = l, 2, • • • , where / is the identity and f(m) is the mth iterate of/, e.g. f(f(x)) =/<2)(x).
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