Ozone Levels in Central Israel

Measurements performed during the early summer months of 1988–1991 at a rural site in central Israel, some 50 km east of the highly urbanized coastal region, have shown that during the afternoon hours the area was often under the influence of ozone mixing ratios above the Israel ambient standard (117 ppbv) and occasionally even above 150 ppbv. Analysis of air mass back trajectories has shown that only those air masses passing over the Tel Aviv metropolitan area cause elevated ozone mixing ratios at the rural site. This highly urbanized region emits large amounts of precursors which are entrapped in the air parcels entering Israel under the predominantly westerly wind flows. As these air masses travel inland, sufficient time is available (3–5 h) to allow the photochemical reactions to generate ozone before reaching the rural site. The above hypothesis is further supported by the fact that parallel to the increase of ozone at the rural site, elevated carbon monoxide (up to 0.8 ppmv) and other trace gases were also observed. A significant correlation (R² > 0.8) was found to exist between the ozone mixing ratio and the NO_x concentrations in photochemically aged air masses. In several cases an excess of up to 12 ozone molecules was formed for each NO_x molecule present.     

A model of non‐isothermal degradation of nutrients,pigments and enzymes

Published isothermal degradation curves for chlorophyll A and thiamine in the range 100–150 °C and the inactivation curves of polyphenol oxidase (PPO) in the range 50–80 °C could be described by the model C(t)/C₀ = exp[?b(T)tⁿ] where C(t) and C₀ are the momentary and initial concentrations, respectively, b(T) a temperature dependent ‘rate parameter’ and n, a constant. This suggested that the temporal degradation/inactivation events of all three had a Weibull distribution with a practically constant shape factor. The temperature dependence of the ‘rate parameter’ could be described by the log logistic model, b(T) = log_e[1 + exp[k(T ? T_c)], where T_c is a marker of the temperature level where the degradation/inactivation occurs at a significant rate and k the steepness of the b(T) increase once this temperature range has been exceeded. These two models were combined to produce a non‐isothermal degradation/inactivation model, similar to one recently developed for microbial inactivation. It is based on the assumption that the local slope of the non‐isothermal decay curve, ie the momentary decay rate, is the slope of the isothermal curve at the momentary temperature at a time that corresponds to the momentary concentration of the still intact or active molecules. This model, in the form of a differential equation, was solved numerically to produce degradation/inactivation curves under temperature profiles that included heating and cooling and oscillating temperatures. Such simulations can be used to assess the impact of planned commercial heat processes on the stability of compounds of nutritional and quality concerns and the efficacy of methods to inactivate enzymes. Simulated decay curves on which a random noise was superimposed were used to demonstrate that the degradation/inactivation parameters, k and T_c, can be calculated directly from non‐isothermal decay curves, provided that the validity of the Weibullian and log logistic models and the constancy of the shape factor n could be assumed. Copyright © 2004 Society of Chemical Industry     

Expressing the equivalence of non‐isothermal and isothermal heat sterilization processes

Currently, the sterility of heat‐processed food and pharmaceuticals is assessed in terms of an F₀ value, based on the equivalence of the heat treatment to an isothermal process at a reference temperature. This F₀ value, however, has a meaning if, and only if, the inactivation kinetics of the targeted spores (or cells) follow a first‐order relationship and the temperature dependence of the D value, the reciprocal of the rate constant, is log‐linear. There is growing evidence that these conditions are not satisfied by many spores, including those of Clostridium botulinum and vegetative cells. Consequently, a replacement for the F₀ value is proposed in the form of a momentary equivalent time at the reference temperature based on the actual survival pattern of the spores, which need not be log‐linear. This equivalent time can be calculated together with the theoretical survival ratio in real time, thus enabling an operator to monitor the lethality of ongoing industrial heat processes. The concept is demonstrated with published survival data of C. botulinum, for which the Weibullian and log‐logistic models served as primary and secondary models, respectively. The safety factor according to the proposed method is in the number of added minutes of processing, beyond the theoretical time needed to reduce the survival ratio of the targeted spores or cells to a level that would produce practical (or commercial) sterility. Copyright © 2006 Society of Chemical Industry     

The Arrhenius equation revisited

The Arrhenius equation has been widely used as a model of the temperature effect on the rate of chemical reactions and biological processes in foods. Since the model requires that the rate increase monotonically with temperature, its applicability to enzymatic reactions and microbial growth, which have optimal temperature, is obviously limited. This is also true for microbial inactivation and chemical reactions that only start at an elevated temperature, and for complex processes and reactions that do not follow fixed order kinetics, that is, where the isothermal rate constant, however defined, is a function of both temperature and time. The linearity of the Arrhenius plot, that is, Ln[k(T)] vs. 1/T where T is in °K has been traditionally considered evidence of the model's validity. Consequently, the slope of the plot has been used to calculate the reaction or processes' "energy of activation," usually without independent verification. Many experimental and simulated rate constant vs. temperature relationships that yield linear Arrhenius plots can also be described by the simpler exponential model Ln[k(T)/k(T(reference))] = c(T-T(reference)). The use of the exponential model or similar empirical alternative would eliminate the confusing temperature axis inversion, the unnecessary compression of the temperature scale, and the need for kinetic assumptions that are hard to affirm in food systems. It would also eliminate the reference to the Universal gas constant in systems where a "mole" cannot be clearly identified. Unless proven otherwise by independent experiments, one cannot dismiss the notion that the apparent linearity of the Arrhenius plot in many food systems is due to a mathematical property of the model's equation rather than to the existence of a temperature independent "energy of activation." If T+273.16°C in the Arrhenius model's equation is replaced by T+b, where the numerical value of the arbitrary constant b is substantially larger than T and T(reference), the plot of Ln k(T) vs. 1/(T+b) will always appear almost perfectly linear. Both the modified Arrhenius model version having the arbitrary constant b, Ln[k(T)/k(T(reference)) = a[1/ (T(reference)+b)-1/ (T+b)], and the exponential model can faithfully describe temperature dependencies traditionally described by the Arrhenius equation without the assumption of a temperature independent "energy of activation." This is demonstrated mathematically and with computer simulations, and with reprocessed classical kinetic data and published food results.     

On quantifying nonthermal effects on the lethality of pressure-assisted heat preservation processes

Direct experimental identification and quantification of the pressure contribution to a pressure-assisted sterilization process efficacy is difficult. However, dynamic kinetic models of thermal inactivation can be used to assess the lethality of a purely thermal process having the same temperature profile. Thus, a pressure-assisted process' temperature record can be used to generate a corresponding purely thermal survival curve with parameters determined in conventional heating experiments. Comparison of the actual final survival ratio with that calculated for the purely thermal process would reveal whether the hydrostatic pressure had synergistic or antagonistic effect on bacterial spores survival. The effect would be manifested in the number of log cycles subtracted or added to the survival ratio, and in the length of time at the holding temperature needed to produce the final survival ratio of the combined process. A set of combined treatments would reveal how the temperature and pressure profiles affect the pressure's influence on the process' lethality to either vegetative cells or spores. The need to withdraw samples during the thermal and combined processes would be avoided if the thermal survival parameters could be calculated by the "three endpoints method," which does not require the entire survival curve determination. Currently however, this method is limited to thermal inactivation patterns characterized by up to 3 survival parameters, the Weibull-Log logistic (WeLL) model, for example.     

Noisy image restoration by cost function minimization

Implementation of a new approach to the nonlinear noisy image restoration problem, which is feasible for large images, is described. The approach is based on a vector space representation of images and on using the conjugate gradient algorithm to solve a least squares minimization problem. Computer simulations yield good results with relatively little computational cost.     

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.     

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