One- and Two-Step Kinetic Data Analysis Applied for Single and Co-Culture Growth of Staphylococcus aureus, Escherichia coli, and Lactic Acid Bacteria in Milk

The objective of this study was to compare one- and two-step kinetic data analysis approaches to describe the growth of Staphylococcus aureus, Escherichia coli, and lactic acid bacteria Fresco 1010 starter culture in milk under isothermal conditions between 10 and 37 °C. The primary Huang model (HM) and secondary square root model were applied to lag times and growth rates of each of the population. The one-step approach for single cultures data enabled the direct construction of a tertiary model combining primary and secondary models to determine parameters from all growth data, thus minimizing the transfer of errors from one model to another. The statistical indices showed a significant improvement in the prediction capability provided by this approach. Then, a one-step approach combining the primary Huang, Giménez, and Dalgaard model (H-GD) with the secondary square root model was used to simultaneously model the growth of the populations mentioned above in co-culture under the same conditions. Independent isothermal data sets were chosen for validation of the growth description of single cultures (HM) and co-culture (H-GD) using validation factors, including the bias (Bf) and accuracy (Af). For example, the values of Af for the one-step approach range from 1.17 to 1.20 and 1.04 to 1.08 for single cultures and co-culture, respectively, demonstrating high accuracy. Thus, this approach may be used for co-culture growth description in general or specifically, e.g., in various types of lactic acid fermentation, including artisanal cheese-making technology.

Modelling the Effect of Temperature on the Initial Decline during the Lag Phase of Geotrichum candidum

The study of lag phase provides essential knowledge for food quality control. With respect to significance of Geotrichum candidum in the food context, the aim of this study was to quantitatively characterize the relationship between temperature (6–25 °C) and initial decline period during G. candidum lag phase. The decrease in G. candidum cells in the lag phase was primary modelled by Weibull’s model to define the first-decimal reduction time (δ). Subsequently, the lag death rate (LDR) values were recalculated from δ and further modelled by using Arrhenius equations, as well as a square root model, and the models’ suitability was proven by selected statistical indices. The square root model with the estimated parameters b = 0.016 °C−1 h−0.5 and Tmin = −0.72 °C showed better indices relating to goodness of fit based on a low root mean sum of square error (RMSE = 0.028 log CFU mL−1), a higher coefficient of determination (R2 = 0.978), and the lowest value of AIC (AIC = −38.65). The present study provides a solution to the possible application of secondary predictive models to the death rate dependence on temperature during the microbial lag phase. Despite limited practical importance, under specific conditions, it is possible to consider its use, for example, in exposure assessment.

Isolation and Molecular Identification of the Native Microflora on Flammulina velutipes Fruiting Bodies and Modeling the Growth of Dominant Microbiota (Lactococcus lactis)

The objectives of this study were to isolate and identify the dominant microorganism in Flammulina velutipes fruiting bodies (FVFB) and to develop kinetic models for describing its growth. The native microflora community on FVFB was isolated and identified using morphological examination and high-throughput sequencing analysis. FVFB presented complex microbial communities with dominant microorganisms being Lactococcus lactis. Irradiated FVFB were inoculated with the isolated strain of L. lactis and cultivated at various temperatures (4, 10, 16, 20, 25, 32, and 37°C). Three primary models, namely the Huang, Baranyi and Roberts, and reparameterized Gompertz models, and three secondary models, namely the Huang square-root, Ratkowsky square-root, and Arrhenius-type models, were developed and evaluated. With the lowest values of mean square error (MSE, 0.023–0.161) and root mean square error (RMSE, 0.152–0.401) values, the reparameterized Gompertz model was more suitable to describe the growth of L. lactis on FVFB than both Huang and Baranyi and Roberts models. The Ratkowsky square-root model provided more accurate estimation for the effect of temperature on the specific growth rate of L. lactis. The minimum growth temperature predicted by the Ratkowsky square-root model was −7.1°C. The kinetic models developed in this study could be used to evaluate the growth behavior of L. lactis on FVFB and estimate the shelf-life of FVFB.

Performance evaluation and design criterion of a bistable nonlinear energy sink

In the evaluation of the vibration mitigation effect of a nonlinear energy sink (NES), the selection of performance measures is important. Based on a square root model, this paper aims to propose new reasonable performance measures and new design criteria of the NES in harmonic excitation. To broaden the application range of the slow invariant manifold, coordinate correction is carried out for the square root model of the bistable NES. Two original performance measures (the displacement amplitude of the main system and the energy dissipation rate of the NES) and two new performance measures (the mechanical energy and the input energy of the main system) are compared. The optimal geometric configuration and response form of the NES are found in different excitation conditions. The results show that the energy dissipation rate of the NES is not competent to evaluate the performance of the NES in harmonic excitation, while the two new performance measures show competence. By adjusting the geometry parameter, the nonlinear vibration absorber with positive linear stiffness and the bistable NES show optimal vibration mitigation effect in small and large excitation amplitudes, respectively. The optimal response form is the periodic response rather than the strongly modulated response.

The Cox–Ingersoll–Ross Interest Rate Model

In this chapter we study a special case of the factor model presented in Chapter 36. Assuming log utility and a square root model for the production process we derive the Cox–Ingersoll–Ross short rate model.

Effects of meal and body sizes on gastric evacuation rate in brooktrout Salvelinus fontinalis (Mitchill, 1814) fed commercial pellets in group feeding

The effects of meal and body sizes on gastric evacuation (GE) of brook trout Salvelinus fontinalis (Mitchill, 1814) were determined following group feeding instead of feeding individually maintained fish. The GE experiments included small (ranging from 64.75 to 69.72 g) and large fish (ranging from 161.59 to 170.95 g). Fish in each size group was fed with three different meal sizes under similar conditions. The stomach contents were then recovered at predetermined postprandial times by serial slaughtering. The square root model adequately described the course of GE in S. fontinalis independent of meal size. The estimates of mass and length exponent obtained from S. fontinalis fed individually are in line with the present estimates. The result of this study would facilitate the planning and management of feeding regimes for S. fontinalis to minimise food waste and optimise growth.