Modelling the kinetics of thermal inactivation of apple polyphenoloxidase

The enzymatic browning of fruits and vegetables caused by mechanical injury during postharvest storage or processing is initiated by the catalytic action of polyphenoloxidase (PPO). A bleaching treatment prior to processing is still considered mostly effective in inhibiting the catalytic activity of PPO, and thus controlling undesirable enzymatic browning. In this work, different mathematical routines were assessed in terms of their adequacy to describe the thermal inactivation of PPO from Golden apples over a range of temperatures from 62.5 to 72.5 ºC. The classical approach to kinetic modelling of the decay activity of apple PPO, commonly reported to follow a first-order model, employs a two-step procedure, in which the model parameters are individually obtained, by each temperature studied, using non-linear or linear regressions. Thereafter, the estimated parameters are further used to calculate their temperature dependence. Alternatively, a one-step method provides a regression fit to all experimental data sets, with the temperature dependence equation being directly built in the kinetic model. This fitting technique thus, (a) avoids the estimation of intermediate parameters and, (b) substantially increases the degrees of freedom and hence the precision of parameters’ estimates. Within this issue was further explored the logarithmic transformation of the mathematical equations used on the adequacy of the model to describe experimental data. In all cases non-weighted least-squares regression procedures were used. Both the examination and criticism of the current modelling strategies were done by assessing statistical data obtained, such as the confidence intervals of the estimates, correlation coefficients, sum of squares, and residuals normality

Shape instabilities in vesicles: a phase-field model

A phase field model for dealing with shape instabilities in fluid membrane vesicles is presented. This model takes into account the Canham-Helfrich bending energy with spontaneous curvature. A dynamic equation for the phase-field is also derived. With this model it is possible to see the vesicle shape deformation dynamically, when some external agent instabilizes the membrane, for instance, inducing an inhomogeneous spontaneous curvature. The numerical scheme used is detailed and some stationary shapes are shown together with a shape diagram for vesicles of spherical topology and no spontaneous curvature, in agreement with known results

Algorithms for network piecewise-linear programs

In this paper a subarea of Piecewise-Linear Programming named network Piecewise-Linear Programming (NPLP) is discussed. Initially the problem formulation, main efinitins and related Concepts are presented. In the sequence of the paper, four specialized algorithms for NPLP, as well as the results of a preliminary computational study, are presented