Algebraic structure for interaction on mixed models

Binary operations on commutative Jordan algebras, CJA, can be used to study interactions between sets of factors belonging to a pair of models in which one nests the other. It should be noted that from two CJA we can, through these binary operations, build CJA. So when we nest the treatments from one model in each treatment of another model, we can study the interactions between sets of factors of the first and the second models.

Layerwise mixed models for analysis of multilayered piezoelectric composite plates using least-squares formulation

This work provides an assessment of layerwise mixed models using least-squares formulation for the coupled electromechanical static analysis of multilayered plates. In agreement with three-dimensional (3D) exact solutions, due to compatibility and equilibrium conditions at the layers interfaces, certain mechanical and electrical variables must fulfill interlaminar C-0 continuity, namely: displacements, in-plane strains, transverse stresses, electric potential, in-plane electric field components and transverse electric displacement (if no potential is imposed between layers). Hence, two layerwise mixed least-squares models are here investigated, with two different sets of chosen independent variables: Model A, developed earlier, fulfills a priori the interiaminar C-0 continuity of all those aforementioned variables, taken as independent variables; Model B, here newly developed, rather reduces the number of independent variables, but also fulfills a priori the interlaminar C-0 continuity of displacements, transverse stresses, electric potential and transverse electric displacement, taken as independent variables. The predictive capabilities of both models are assessed by comparison with 3D exact solutions, considering multilayered piezoelectric composite plates of different aspect ratios, under an applied transverse load or surface potential. It is shown that both models are able to predict an accurate quasi-3D description of the static electromechanical analysis of multilayered plates for all aspect ratios.

Generalized models from Beta(p,2) densities with strong allee effect: dynamical approach

A dynamical approach to study the behaviour of generalized populational growth models from Bets(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.

Modeling Allee Effect from Beta(p, 2) Densities

In this work we develop and investigate generalized populational growth models, adjusted from Beta(p, 2) densities, with Allee effect. The use of a positive parameter leads the presented generalization, which yields some more flexible models with variable extinction rates. An Allee limit is incorporated so that the models under study have strong Allee effect.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

The effect of long-chain polyunsaturated fatty acids intake during pregnancy on adiposity of healthy full-term offspring at birth

Objective - The adjusted effect of long-chain polyunsaturated fatty acid (LCPUFA) intake during pregnancy on adiposity at birth of healthy full-term appropriate-for-gestational age neonates was evaluated. Study Design - In a cross-sectional convenience sample of 100 mother and infant dyads, LCPUFA intake during pregnancy was assessed by food frequency questionnaire with nutrient intake calculated using Food Processor Plus. Linear regression models for neonatal body composition measurements, assessed by air displacement plethysmography and anthropometry, were adjusted for maternal LCPUFA intakes, energy and macronutrient intakes, prepregnancy body mass index and gestational weight gain. Result - Positive associations between maternal docosahexaenoic acid intake and ponderal index in male offspring (β=0.165; 95% confidence interval (CI): 0.031–0.299; P=0.017), and between n-6:n-3 LCPUFA ratio intake and fat mass (β=0.021; 95% CI: 0.002–0.041; P=0.034) and percentage of fat mass (β=0.636; 95% CI: 0.125–1.147; P=0.016) in female offspring were found. Conclusion - Using a reliable validated method to assess body composition, adjusted positive associations between maternal docosahexaenoic acid intake and birth size in male offspring and between n-6:n-3 LCPUFA ratio intake and adiposity in female offspring were found, suggesting that maternal LCPUFA intake strongly influences fetal body composition.