When Do Adobe Bricks Collapse under Compressive Forces: A Simulation Approach

The collapse of adobe bricks under compressive forces and exposure to water has a duration of several minutes, with only minor displacements before and after the collapse, whence a conceptual question arises: When does the collapse start and when does it end? The paper compares several mathematical models for the description of the fracture process from displacement data. It recommends the use of linear splines to identify the beginning and end of the collapse phase of adobe bricks.

Dynamics of the Austrian Food Market: Application of Lotka-Volterra Differential Equations

The organic food market has become an important part of food industry. We analyze sales data from Austria for 2014 to 2020 of 124 products from 25 product groups in six categories, each in conventional and organic form. We fitted their market shares by means of a modified Lotka-Volterra model with constant coefficients. When only organic and conventional products were compared, a significant increase in market shares was observed for 15 of 25 organic product groups, indicating a continuing growth of the organic food market. The typical Lotka-Volterra dynamics was a predator-prey dynamics with an organic product (group) predating on conventional products that were in symbiosis.

AIC-Based Selection of Growth Models: The Case of Piglets from Organic Farming

The selection and comparison of different growth models for describing weight gain of piglets raised in organic farming is investigated by using the Akaike’s Information Criterion (AIC). In total, 49,699 data points of 5188 piglets recorded between 2007 and 2013 were considered. From the day of birth, up to 40 days (i.e. until weaning) the model of von Bertalanffy was favored by the AIC. This model is with 60.32% more likely to truly reflect reality than any other of the analyzed models. Up to 105 days, the two-linear model was favored by the AIC (probability 99.75%). The intersection point of the two-linear model was calculated by 53.8 days, which fitted well to the actual change in the food situations.

A Model for the Mass-Growth of Wild-Caught Fish

The paper searched for raw data about wild-caught fish, where a sigmoidal growth function described the mass growth significantly better than non-sigmoidal functions. Specifically, von Bertalanffy’s sigmoidal growth function (metabolic exponent-pair a = 2/3, b = 1) was compared with unbounded linear growth and with bounded exponential growth using the Akaike information criterion. Thereby the maximum likelihood fits were compared, assuming a lognormal distribution of mass (i.e. a higher variance for heavier animals). Starting from 70+ size-at-age data, the paper focused on 15 data coming from large datasets. Of them, six data with 400 - 20,000 data-points were suitable for sigmoidal growth modeling. For these, a custom-made optimization tool identified the best fitting growth function from the general von Bertalanffy-Pütter class of models. This class generalizes the well-known models of Verhulst (logistic growth), Gompertz and von Bertalanffy. Whereas the best-fitting models varied widely, their exponent-pairs displayed a remarkable pattern, as their difference was close to 1/3 (example: von Bertalanffy exponent-pair). This defined a new class of models, for which the paper provided a biological motivation that relates growth to food consumption.

Bertalanffy-Pütter Models for the Growth of Tropical Trees and Stands

The Bertalanffy-Pütter (BP) five-parameter growth model provides a versatile framework for the modeling of growth. Using data from a growth experiment in literature about the average size-at-age of 24 species of tropical trees over ten years in the same area, we identified their best-fit BP-model parameters. While different species had different best-fit exponent-pairs, there was a model with a good fit to 21 (87.5%) of the data (“Good fit” means a normalized root-mean-squared-error NRMSE below 2.5%. This threshold was the 95% quantile of the lognormal distribution that was fitted to the NRMSE values for the best-fit models for the data). In view of the sigmoidal character of this model despite the early stand we discuss whether the setting of the growth experiment may have impeded growth.

Bertalanffy-Pütter models for the first wave of the COVID-19 outbreak

The COVID-19 pandemics challenges governments across the world.To develop adequate responses,they need accurate models for the spread of the disease.Using least squares,we fitted Bertalanffy-Pütter(BP)trend curves to data about the first wave of the COVID-19 pandemic of 2020 from 49 countries and provinces where the peak of the first wave had been passed.BP-models achieved excellent fits(R-squared above 99%)to all data.Using them to smoothen the data,in the median one could forecast that the final count(asymptotic limit)of infections and fatalities would be 2.48 times(95%confidence limits 2.42-2.6)and 2.67 times(2.39-2.765)the total count at the respective peak(inflection point).By comparison,using logistic growth would evaluate this ratio as 2.00 for all data.The case fatality rate,defined as the quotient of the asymptotic limits of fatalities and confirmed infections,was in the median 4.85%(confidence limits 4.4%e6.5%).Our result supports the strategies of governments that kept the epidemic peak low,as then in the median fewer infections and fewer fatalities could be expected.