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.

Comparison of different breast planning techniques and algorithms for radiation therapy treatment

This work aims at investigating the impact of treating breast cancer using different radiation therapy (RT) techniques – forwardly-planned intensity-modulated, f-IMRT, inversely-planned IMRT and dynamic conformal arc (DCART) RT – and their effects on the whole-breast irradiation and in the undesirable irradiation of the surrounding healthy tissues. Two algorithms of iPlan BrainLAB treatment planning system were compared: Pencil Beam Convolution (PBC) and commercial Monte Carlo (iMC). Seven left-sided breast patients submitted to breast-conserving surgery were enrolled in the study. For each patient, four RT techniques – f-IMRT, IMRT using 2-fields and 5-fields (IMRT2 and IMRT5, respectively) and DCART – were applied. The dose distributions in the planned target volume (PTV) and the dose to the organs at risk (OAR) were compared analyzing dose–volume histograms; further statistical analysis was performed using IBM SPSS v20 software. For PBC, all techniques provided adequate coverage of the PTV. However, statistically significant dose differences were observed between the techniques, in the PTV, OAR and also in the pattern of dose distribution spreading into normal tissues. IMRT5 and DCART spread low doses into greater volumes of normal tissue, right breast, right lung and heart than tangential techniques. However, IMRT5 plans improved distributions for the PTV, exhibiting better conformity and homogeneity in target and reduced high dose percentages in ipsilateral OAR. DCART did not present advantages over any of the techniques investigated. Differences were also found comparing the calculation algorithms: PBC estimated higher doses for the PTV, ipsilateral lung and heart than the iMC algorithm predicted.

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Texture zeros and weak basis transformations

We investigate the physical meaning of some of the "texture zeros" which appear in most of the Ansatze on quark masses and mixings. It is shown that starting from arbitrary quark mass matrices and making a suitable weak basis transformation one can obtain some of these sets of zeros which therefore have no physical content. We then analyse the physical implications of a four-texture zero Ansatz which is in agreement with all present experimental data. (C) 2000 Elsevier Science B.V. AU rights reserved.

Optimal location of supports in beam structures using genetic algorithms

Real structures can be thought as an assembly of components, as for instances plates, shells and beams. This later type of component is very commonly found in structures like frames which can involve a significant degree of complexity or as a reinforcement element of plates or shells. To obtain the desired mechanical behavior of these components or to improve their operating conditions when rehabilitating structures, one of the eventual parameters to consider for that purpose, when possible, is the location of the supports. In the present work, a beam-type structure is considered, and for a set of cases concerning different number and types of supports, as well as different load cases, the authors optimize the location of the supports in order to obtain minimum values of the maximum transverse deflection. The optimization processes are carried out using genetic algorithms. The results obtained, clearly show a good performance of the approach proposed. © 2014 IEEE.

Spectral and weak polynomial completeness for the porduct of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F , satisfying the following property: for every monic polynomial f(x) = xn + an-1xn-1 + … +a1x + aο over F, with a root in F and aο = (-1)n det(AB), there are nonsingular matrices X, Y ϵ Fnxn such that X A X-1 Y BY-1 has characteristic polynomial f (x). © 2014 © 2014 Taylor & Francis.

Spectral and weak polynomial completeness for the product of nonsingular matrices

Let F be a field with at least four elements. In this paper, we identify all the pairs (A, B) of n x n nonsingular matrices over F, satisfying the following property: for every monic polynomial f (x) = x(n) + a(n-1)x(n-1) +... + a(1)x + a(0) over F, with a root in F and a(0) = (-1)(n) det(AB), there are nonsingular matrices X, Y is an element of F-nxn such that XAX(-1)Y BY-1 has characteristic polynomial f (x).

From weak Allee effect to no Allee effect in Richards’ growth models

Population dynamics have been attracting interest since many years. Among the considered models, the Richards’ equations remain one of the most popular to describe biological growth processes. On the other hand, Allee effect is currently a major focus of ecological research, which occurs when positive density dependence dominates at low densities. In this chapter, we propose the dynamical study of classes of functions based on Richards’ models describing the existence or not of Allee effect. We investigate bifurcation structures in generalized Richards’ functions and we look for the conditions in the (β, r) parameter plane for the existence of a weak Allee effect region. We show that the existence of this region is related with the existence of a dovetail structure. When the Allee limit varies, the weak Allee effect region disappears when the dovetail structure also disappears. Consequently, we deduce the transition from the weak Allee effect to no Allee effect to this family of functions. To support our analysis, we present fold and flip bifurcation curves and numerical simulations of several bifurcation diagrams.