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Micha P.,University of Massachusetts Amherst | Corradini M.G.,Argentine Business University, Buenos Aires
Critical Reviews in Food Science and Nutrition | Year: 2011

Most of the models of microbial growth in food are Empirical algebraic, of which the Gompertz model is the most notable, Rate equations, mostly variants of the Verhulst's logistic model, or Population Dynamics models, which can be deterministic and continuous or stochastic and discrete. The models of the first two kinds only address net growth and hence cannot account for cell mortality that can occur at any phase of the growth. Almost invariably, several alternative models of all three types can describe the same set of experimental growth data. This lack of uniqueness is by itself a reason to question any mechanistic interpretation of growth parameters obtained by curve fitting alone. As argued, all the variants of the Verhulst's model, including the Baranyi-Roberts model, are empirical phenomenological models in a rate equation form. None provides any mechanistic insight or has inherent advantage over the others. In principle, models of all three kinds can predict non-isothermal growth patterns from isothermal data. Thus a modeler should choose the simplest and most convenient model for this purpose. There is no reason to assume that the dependence of the "maximum specific growth rate" on temperature, pH, water activity, or other factors follows the original or modified versions of the Arrhenius model, as the success of Ratkowsky's square root model testifies. Most sigmoid isothermal growth curves require three adjustable parameters for their mathematical description and growth curves showing a peak at least four. Although frequently observed, there is no theoretical reason that these growth parameters should always rise and fall in unison in response to changes in external conditions. Thus quantifying the effect of an environmental factor on microbial growth require that all the growth parameters are addressed, not just the "maximum specific growth rate." Different methods to determine the "lag time" often yield different values, demonstrating that it is a poorly defined growth parameter. The combined effect of several factors, such as temperature and pH or a w, need not be "multiplicative" and therefore ought to be revealed experimentally. This might not be always feasible, but keeping the notion in mind will eliminate theoretical assumptions that are hard to confirm. Modern mathematical software allows to model growing or dying microbial populations where cell division and mortality occur simultaneously and can be used to explain how different growth patterns emerge. But at least in the near future, practical problems, like translating a varying temperature into a corresponding microbial growth curve, will be solved with empirical rate models, which despite not being "mechanistic" are perfectly suitable for this purpose. © Taylor and Francis Group, LLC. Source

Wehbe R.,Argentine Business University, Buenos Aires
IEEE Latin America Transactions | Year: 2013

During the requirements elicitation phase a software engineer tries to determine what the customer really wants (and needs.) This task requires, on the one hand, strong communication skills and, on the other hand, a good engineering background to construct a coherent set of requirements. There is a thus a conflict informal and formal techniques. Scenarios are a powerful communication tool and may be given a formal semantics so that they may be amenable to formal verification. We present a method to verifying properties of scenarios based on fixed points of predicate transformers. This work is adapted from an approach that had been originally proposed by Sifakis for transition systems. Scenarios are modelled in a similar way to Diijkstras guarded commands. © 2003-2012 IEEE. Source

Bulus-Rossini L.A.,CONICET | Costanzo-Caso P.A.,CONICET | Duchowicz R.,CONICET | Sicre E.E.,Argentine Business University, Buenos Aires
Optics Communications | Year: 2010

The temporal Radon-Wigner transform (RWT), which is the squared modulus of the fractional Fourier transform (FRT) for a varying fractional order p, is here employed as a tool for pulse compression applications. To synthesize the compressed pulse, a selected FRT irradiance is optically produced employing a photonic device that combines phase modulation and dispersive transmission. For analysis purposes, the complete numerical generation of the RWT with 0 < p < 1 is proposed to select the value of p required for pulse compression. To this end, the amplitude and phase of the signal to be processed should be known. In order to obtain this information we use a method based on the recording of two different FRT irradiances of the pulse. The amplitude and phase errors of the recovered signal, which are inherent to the recording process, are discussed in connection with the RWT production. Numerical simulations were performed to illustrate the implementation of the proposed method. The technique is applied to compress signals commonly found in fiber optic transmission systems, such as chirped gaussian pulses, pulses distorted by second and third-order dispersion and nonlinear self-modulated pulses. © 2010 Elsevier B.V. All rights reserved. Source

Corradini M.G.,Argentine Business University, Buenos Aires | Normand M.D.,University of Massachusetts Amherst | Peleg M.,University of Massachusetts Amherst
Journal of Food Science | Year: 2010

Microbial inactivation is described by a model based on the changing survival probabilities of individual cells or spores. It is presented in a stochastic and discrete form for small groups, and as a continuous deterministic model for larger populations. If the underlying mortality probability function remains constant throughout the treatment, the model generates first-order (" log-linear" ) inactivation kinetics. Otherwise, it produces survival patterns that include Weibullian (" power-law" ) with upward or downward concavity, tailing with a residual survival level, complete elimination, flat " shoulder" with linear or curvilinear continuation, and sigmoid curves. In both forms, the same algorithm or model equation applies to isothermal and dynamic heat treatments alike. Constructing the model does not require assuming a kinetic order or knowledge of the inactivation mechanism. The general features of its underlying mortality probability function can be deduced from the experimental survival curve's shape. Once identified, the function's coefficients, the survival parameters, can be estimated directly from the experimental survival ratios by regression. The model is testable in principle but matching the estimated mortality or inactivation probabilities with those of the actual cells or spores can be a technical challenge. The model is not intended to replace current models to calculate sterility. Its main value, apart from connecting the various inactivation patterns to underlying probabilities at the cellular level, might be in simulating the irregular survival patterns of small groups of cells and spores. In principle, it can also be used for nonthermal methods of microbial inactivation and their combination with heat. © 2010 Institute of Food Technologists®. Source

Corradini M.G.,Argentine Business University, Buenos Aires | Normand M.D.,University of Massachusetts Amherst | Eisenberg M.,University of Massachusetts Amherst | Peleg M.,University of Massachusetts Amherst
Applied and Environmental Microbiology | Year: 2010

Heat activates the dormant spores of certain Bacillus spp., which is reflected in the "activation shoulder" in their survival curves. At the same time, heat also inactivates the already active and just activated spores, as well as those still dormant. A stochastic model based on progressively changing probabilities of activation and inactivation can describe this phenomenon. The model is presented in a fully probabilistic discrete form for individual and small groups of spores and as a semicontinuous deterministic model for large spore populations. The same underlying algorithm applies to both isothermal and dynamic heat treatments. Its construction does not require the assumption of the activation and inactivation kinetics or knowledge of their biophysical and biochemical mechanisms. A simplified version of the semicontinuous model was used to simulate survival curves with the activation shoulder that are reminiscent of experimental curves reported in the literature. The model is not intended to replace current models to predict dynamic inactivation but only to offer a conceptual alternative to their interpretation. Nevertheless, by linking the survival curve's shape to probabilities of events at the individual spore level, the model explains, and can be used to simulate, the irregular activation and survival patterns of individual and small groups of spores, which might be involved in food poisoning and spoilage. Copyright © 2010, American Society for Microbiology. All Rights Reserved. Source

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