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

Phase transition for the frog model

We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1-p. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for Z^d and regular trees

Light trapping and guidance in plasmonic nanocrystals

We illustrate the possibility of light trapping and funneling in periodic arrays of metallic nanoparticles. A controllable minimum in the transmission spectra of such constructs arises from a collective plasmon resonance phenomenon, where an incident plane wave sharply localizes in the vertical direction, remaining delocalized in the direction parallel to the crystal plane. Using hybrid arrays of different structures or different materials, we apply the trapping effect to structure the eigen-mode spectrum, introduce overlapping resonances, and hence direct the light in space in a wavelength-sensitive fashion

Quantiles for Fractions and Other Mixed Data

This paper studies the estimation of quantile regression for fractional data, focusing on the case where there are mass-points at zero or/and one. More generally, we propose a simple strategy for the estimation of the conditional quantiles of data from mixed distributions, which combines standard results on the estimation of censored and Box-Cox quantile regressions. The implementation of the proposed method is illustrated using a well-known dataset.

Coulomb corrections to inclusive cross sections at the future Electron - Ion Collider

The experimental results of the future electron -- ion ($e A$) collider are expected to constrain the dynamics of the strong interactions at small values of the Bjorken -- $x$ variable and large nuclei. Recently it has been suggested that Coulomb corrections can be important in inclusive and diffractive $eA$ interactions. In this paper we present a detailed investigation of the impact of the Coulomb corrections to some of the observables that will be measured in the future $eA$ collider. In particular, we estimate the magnitude of these corrections for the charm and longitudinal cross sections in inclusive and diffractive interactions. Our results demonstrate that the Coulomb corrections for these observables are negligible, which implies that they can be used to probe the QCD dynamics.Comment: 9 pages, 6 figures. Improved version to be published in Physical Review

The type N Karlhede bound is sharp

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spacetimes are properly $CH_2$, i.e., curvature homogeneous of order 2 but non-homogeneous. This means that tetrad components of $R, \nabla R, \nabla^{(2)}R$ are constant, and that essential coordinates first appear as components of $\nabla^{(3)}R$. Covariant derivatives of orders 4,5,6 yield one additional invariant each, and $\nabla^{(7)}R$ is needed for invariant classification. Thus, our class proves that the bound of 7 on the order of the covariant derivative, first established by Karlhede, is sharp. Our finding corrects an outstanding assertion that invariant classification of four-dimensional Lorentzian manifolds requires at most $\nabla^{(6)}R$.Comment: 7 pages, typos corrected, added citation and acknowledgemen