Cells of Listeria monocytogenes or Salmonella enterica serovar Typhimurium taken from six characteristic stages of growth were subjected to an acidic stress (pH 3.3). As expected, the bacterial resistance increased from the end of the exponential phase to the late stationary phase. Moreover, the shapes of the survival curves gradually evolved as the physiological states of the cells changed. A new primary model, based on two mixed Weibull distributions of cell resistance, is proposed to describe the survival curves and the change in the pattern with the modifications of resistance of two assumed subpopulations. This model resulted from simplification of the first model proposed. These models were compared to the Whiting's model. The parameters of the proposed model were stable and showed consistent evolution according to the initial physiological state of the bacterial population. Compared to the Whiting's model, the proposed model allowed a better fit and more accurate estimation of the parameters. Finally, the parameters of the simplified model had biological significance, which facilitated their interpretation.When thermal or nonthermal inactivation of spores or vegetative microorganisms is considered, the log-linear shape of bacterial survival curves is a particular case among types of curves (12,17,43,49). In the case of nonthermal inactivation caused by unfavorable environmental conditions, the shape of curves indicates more pronounced heterogeneity according to the intensity of the stress. A bacterial strain can produce different shapes of survival curves. Frequently, concave curves may become convex or sigmoidal when the intensity of the stress varies (6,7,10,19,24,38,45,47,48). The patterns of survival curves may also vary with the physiological state of the cells and are dependent on the phase of growth (exponential or stationary phase) and also on the conditions of adaptation before the stress (18,25,36).In order to model nonthermal inactivation curves, a number of primary models have been proposed. Among these models are the vitalistic models proposed by Cole et al. (13,28,39), models describing both growth and inactivation (26,27,32,37,40,41), the modified Gompertz model (24, 32), the exponential model (31), and the log-linear model with latency time (6) and/or with a tail (5). These models cannot deal with all shapes of curves, and most of them are based on log-linear inactivation.Some models can describe non-log-linear decrease or sigmoidal inactivation curves. The Weibull model has largely been used in thermal and nonthermal treatment studies. It is based on the hypothesis that the resistance to stress of a population follows a Weibull distribution (14,19,34,44,45). This type of model can describe linear, concave, or convex curves. It was modified and extended to sigmoidal curves in heat treatment studies (2). The model of Baranyi and Roberts (3) and the model of Geeraerd et al. (17) can describe a linear shape with or without shoulder or tail and sigmoidal shapes (21,22). These models, which can...

The classical D-value of first order inactivation kinetic is not suitable for quantifying bacterial heat resistance for non-log linear survival curves. One simple model derived from the Weibull cumulative function describes non-log linear kinetics of micro-organisms. The influences of environmental factors on Weibull model parameters, shape parameter "p" and scale parameter "delta", were studied. This paper points out structural correlation between these two parameters. The environmental heating and recovery conditions do not present clear and regular influence on the shape the parameter "p" and could not be described by any model tried. Conversely, the scale parameter "delta" depends on heating temperature and heating and recovery medium pH. The models established to quantify these influences on the classical "D" values could be applied to this parameter "delta". The slight influence of the shape parameter p variation on the goodness of fit of these models can be neglected and the simplified Weibull model with a constant p-value for given microbial population can be applied for canning process calculations.

In this paper, we provide upper bounds on several Rubinsteintype distances on the configuration space equipped with the Poisson measure. Our inequalities involve the two well-known gradients, in the sense of Malliavin calculus, which can be defined on this space. Actually, we show that depending on the distance between configurations which is considered, it is one gradient or the other which is the most effective. Some applications to distance estimates between Poisson and other more sophisticated processes are also provided, and an application of our results to tail and isoperimetric estimates completes this work.

We construct the basis of a stochastic calculus for a new class of processes: filtered Poisson processes. These processes are defined by an fBm-like stochastic integral but a Poisson process is subsided to the Brownian motion. We use Malliavin calculus to first construct a gradient then a divergence operator, which will play the role of an anticipative stochastic integral. We study into details the sample-paths regularity of this integral and give an Itô formula for Itô-like processes.  2005 Elsevier SAS. All rights reserved. RésuméLes processus de Poisson filtrés sont définis par une intégrale stochastique d'un noyau déterministe relativement à un processus de Poisson. Ils sont au processus de Poisson ce que le mouvement brownien fractionnaire est au mouvement brownien ordinaire. Nous construisons pour ces processus les bases du calcul anticipatif. Ce travail similaire à celui d'Oksendal et ses collaborateurs sur les processus de sauts de Lévy, emprunte une autre approche que celle du calcul de Hida. Nous introduisons l'opérateur gradient sans utiliser la décomposition en chaos puis nous définissons son adjoint, ce qui nous permet de construire une notion d'intégrale anticipante. Les propriétés de régularité trajectorielle de cette intégrale sont précisées. Nous terminons notre travail par une formule d'Itô pour ces processus.