Calculation of the total lethality of conductive heat in cylindrical cans sterilization using linear and non linear survival kinetic models

There is growing evidence suggesting that inactivation of bacterial spores may follow the Weibullian model, of which the log linear relationship between survival ratio and time is just a special case. Where true, the time and not only the temperature dependence of the rate must be taken into account. Also, it is of interest to estimate spores survival not only at the coldest point but also throughout the whole container's volume.Numerical calculation on changing survival ratios was performed by combining the conductive heat transfer model with that of the nonlinear inactivation kinetics. Results are based on published linear and non linear inactivation parameters of Clostridium botulinum spores, typical thermal properties of solid foods and realistic thermal processing conditions. Results could be used to quantify the efficacy of thermal processes of solid products in terms of spores' residual survival ratio at the coldest point and in the container as a whole.     

An expanded Fermi solution for microbial risk assessment

'Fermi solution' refers to an estimate of a quantity of interest derived from a sequence of guesses about factors of which detailed knowledge is unavailable. When one makes such guesses, it is unlikely that the large majority of them will be either too high or too low. Most probably, some of the overestimates will be offset by some of the underestimates, and the final result will be often close to the correct value. The method has been popularized as recreational physics but it has also been applied in risk assessment, where the factors involved, but not their exact magnitudes, are known. The concept has potential application in certain types of food poisoning risk assessments, and in estimating the number victims of a bioterrorist attack on the food or water supply, where some guessing is inevitable because of the absence of accurate relevant data. We consider a version of the method in which ranges instead of single values are entered as the factors' estimates. For simplicity, the risk to be assessed is taken to be the product of the factors, and their true values are regarded as being uniformly distributed over their respective ranges. The risk itself is therefore construed as a random variable with a probability distribution whose parameters are explicitly determined by the individual factors' ranges and which can often be approximated by a lognormal distribution. The mode of this lognormal distribution is taken to be the "best guess" of the risk, and a credible interval is constructed with a specified level of "confidence". The best guess and credible interval are shown to be robust against small perturbations of the ranges. Thus, even if the ranges are misspecified to some degree, assessments based on the best guess or credible interval will not be substantially altered. This can help to achieve consensus among assessors in situations where very little hard knowledge exists. The calculation procedure has been automated in software that has been made freely available over the Internet. The concept is demonstrated with two hypothetical problems: predicting the number of persons who would come down with acute food poisoning after consuming a contaminated dish, and estimating the number of daily salmonellosis cases in a large metropolitan area.     

Demonstration of the applicability of the Weibull-log-logistic survival model to the isothermal and nonisothermal inactivation of Escherichia coli K-12 MG1655

Published isothermal semilogarithmic survival curves of Escherichia coli K-12 MG1655, in the range of 49.8 to 60.6 degrees C, all had noticeable downward concavity. They could be described by the model log S(t) = -b(T)t n, where S(t) = N(t)/N0, N(t) and N0 being the momentary and initial number of organisms, respectively; b(T) is a temperature-dependent rate parameter; and n is a constant found to be about 1.5. The temperature dependence of b(T) could be described by the log-logistic model, b(T) = ln[1 + exp[k(T - Tc)]], which had an almost perfect fit, with k = 0.88 degrees C(-1) and Tc = 60.5 degrees C. The constants, n, k, and Tc were considered the organism's survival parameters in the particular medium. They were incorporated into a rate equation on the assumption that in nonisothermal heating, the momentary inactivation rate is the isothermal rate at the momentary temperature at a time that corresponds to the momentary survival ratio. This model's estimates matched the actual survival curves obtained in the same work under two different nonisothermal heating profiles, lending support to the notion that the Weibull-log-logistic model combination can be used not only to describe isothermal inactivation mathematically, but also to predict survival patterns under nonisothermal conditions.     

The achievable accuracy in estimating the instantaneous phase andfrequency of a constant amplitude signal

The approach is based on modeling the signal phase by a polynomial function of time on a finite interval. The phase polynomial is expressed as a linear combination of the Legendre basis polynomials. First, the Cramer-Rao bound (CRB) of the instantaneous phase and frequency of constant-amplitude polynomial-phase signals is derived. Then some properties of the CRBs are used to estimate the order of magnitude of the bounds. The analysis is extended to signals whose phase and frequency are continuous but not polynomial. The CRB can be achieved asymptotically if the estimation of the phase coefficients is done by maximum likelihood. The maximum-likelihood estimates are used to show that the achievable accuracy in phase and frequency estimation is determined by the CRB of the polynomial coefficients and the deviation of true phase and frequency from the polynomial approximations     

Iterative decoding of space-time differentially coded unitary matrix modulation

Noncoherent communication over the Rayleigh flat fading channel with multiple transmit and receive antennas is investigated. Codes achieving bit error rate (BER) lower than 10/sup -4/ at bit energy over the noise spectral density ratio (E/sub b//N/sub 0/) of 0.8 to 2.8 dB from the capacity limit were found with coding rates of 0.5 to 2.25 bits per channel use. The codes are serial concatenation of a turbo code and a unitary matrix differential modulation code. The receiver is based on a high-performance joint iterative decoding of the turbo code and the modulation code. Information-theoretic arguments are harnessed to form guidelines for code design and to evaluate performance of the iterative decoder.     

Crumbling walls: a class of practical and efficient quorum systems

Summary.  A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication and dissemination of information. In this paper we introduce a general class of quorum systems called Crumbling Walls and study its properties. The elements (processors) of a wall are logically arranged in rows of varying widths. A quorum in a wall is the union of one full row and a representative from every row below the full row. This class considerably generalizes a number of known quorum system constructions. The best crumbling wall is the CWlog quorum system. It has small quorums, of size O(lg n), and structural simplicity. The CWlog has optimal availability and optimal load among systems with such small quorum size. It manifests its high quality for all universe sizes, so it is a good choice not only for systems with thousands or millions of processors but also for systems with as few as 3 or 5 processors. Moreover, our analysis shows that the availability will increase and the load will decrease at the optimal rates as the system increases in size. Received: August 1995 / Accepted: August 1996     

Recovery of ego-motion using region alignment

A method for computing the 3D camera motion (the ego-motion) in a static scene is described, where initially a detected 2D motion between two frames is used to align corresponding image regions. We prove that such a 2D registration removes all effects of camera rotation, even for those image regions that remain misaligned. The resulting residual parallax displacement field between the two region-aligned images is an epipolar field centered at the FOE (Focus-of-Expansion). The 3D camera translation is recovered from the epipolar field. The 3D camera rotation is recovered from the computed 3D translation and the detected 2D motion. The decomposition of image motion into a 2D parametric motion and residual epipolar parallax displacements avoids many of the inherent ambiguities and instabilities associated with decomposing the image motion into its rotational and translational components, and hence makes the computation of ego-motion or 3D structure estimation more robust     

Modeling microbial populations with the original and modified versions of the continuous and discrete logistic equations

The life histories of microbial populations, under favorable and adverse conditions, exhibit a variety of growth, decay, and fluctuation patterns. They have been described by numerous mathematical models that varies considerably in structure and number of constants. The continuous logistic equation alone and combined with itself or with its mirror image, the Fermi function, can produce many of the observed growth patterns. They include those that are traditionally described by the Gompertz equation and peaked curves, with the peak being symmetric or asymmetric narrow or wide. The shape of survival and dose response curves appears to be determined by the distribution of the resistance's to the lethal agent among the individual organisms. Thus, exponential decay and Fermian or Gompertz-type curves can be considered manifestations of skewed to the right, symmetric, and skewed to the left distributions, respectively. Because of the mathematical constraints and determinism, the original discrete logistic equation can rarely be an adequate model of real microbial populations. However, by making its proportionality constant a normal-random variate it can simulate realistic histories of fluctuating microbial populations, including scenarios of aperiodic population explosions of varying intensities of the kind found in food-poisoning episodes.     

Comparison of the Acoustic and Mechanical Signatures of Two Cellular Crunchy Cereal Foods at Various Water Activity Levels

Cheese balls and croutons at various water activity levels (0·11–0·75) were compressed between parallel metal plates using a Universal testing machine and their acoustic emissions were recorded at compact disc quality (sampling rate of 44·1 kHz). The sound wave record (up to about 2 MB) had high intensity bursts at irregular intervals. These records were compressed after the background noise had been filtered out to produce files of less than 48 kB. The compressed signatures were characterised by their mean and peak amplitude, two measures of the sound emission intensity, and by the amplitude's standard deviation and the mean magnitude of the power spectrum, two measures of the acoustic signature complexity. All four parameters could be used to monitor the plasticisation effect of water. Although their magnitudes were correlated, they did not always change in unison upon moisture sorption. The standard deviation and mean magnitude of the power spectrum of the compressed acoustic signatures were only broadly correlated with their correspondents in the normalised mechanical signatures primarily because they were not determined from the same particles and because the latter, for technical reasons, were sampled at the low rate of 6 Hz.