Symbolic dynamics and big bang bifurcation in Weibull-Gompertz-Fréchet's growth models

In this paper, motivated by the interest and relevance of the study of tumor growth models, a central point of our investigation is the study of the chaotic dynamics and the bifurcation structure of Weibull-Gompertz-Fréchet's functions: a class of continuousdefined one-dimensional maps. Using symbolic dynamics techniques and iteration theory, we established that depending on the properties of this class of functions in a neighborhood of a bifurcation point PBB, in a two-dimensional parameter space, there exists an order regarding how the infinite number of periodic orbits are born: the Sharkovsky ordering. Consequently, the corresponding symbolic sequences follow the usual unimodal kneading sequences in the topological ordered tree. We verified that under some sufficient conditions, Weibull-Gompertz-Fréchet's functions have a particular bifurcation structure: a big bang bifurcation point PBB. This fractal bifurcations structure is of the so-called "box-within-a-box" type, associated to a boxe ω1, where an infinite number of bifurcation curves issues from. This analysis is done making use of fold and flip bifurcation curves and symbolic dynamics techniques. The present paper is an original contribution in the framework of the big bang bifurcation analysis for continuous maps.

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.

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.

Big Bang bifurcations and allee effect in Blumberg’s dynamics

This paper concerns dynamics and bifurcations properties of a class of continuous-defined one-dimensional maps, in a three-dimensional parameter space: Blumberg's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon, associated with the stability of a fixed point. A central point of our investigation is the study of bifurcations structure for this class of functions. We verified that under some sufficient conditions, Blumberg's functions have a particular bifurcations structure: the big bang bifurcations of the so-called "box-within-a-box" type, but for different kinds of boxes. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct attractors. This work contributes to clarify the big bang bifurcation analysis for continuous maps. To support our results, we present fold and flip bifurcations curves and surfaces, and numerical simulations of several bifurcation diagrams.

Explosion birth and extinction: Double big bang bifurcations and Allee effect in Tsoularis-Wallace's growth models

This work concerns dynamics and bifurcations properties of a new class of continuous-defined one-dimensional maps: Tsoularis-Wallace's functions. This family of functions naturally incorporates a major focus of ecological research: the Allee effect. We provide a necessary condition for the occurrence of this phenomenon of extinction. To establish this result we introduce the notions of Allee's functions, Allee's effect region and Allee's bifurcation curve. Another central point of our investigation is the study of bifurcation structures for this class of functions, in a three-dimensional parameter space. We verified that under some sufficient conditions, Tsoularis-Wallace's functions have particular bifurcation structures: the big bang and the double big bang bifurcations of the so-called "box-within-a-box" type. The double big bang bifurcations are related to the existence of flip codimension-2 points. Moreover, it is verified that these bifurcation cascades converge to different big bang bifurcation curves, where for the corresponding parameter values are associated distinct kinds of boxes. This work contributes to clarify the big bang bifurcation analysis for continuous maps and understand their relationship with explosion birth and extinction phenomena.

An 40Ar/39Ar, Rb/Sr, and stable isotope study of micas in low-grade fold-and-thrust belt: An example from the Swiss Helvetic Alps

White micas in carbonate-rich tectonites and a few other rock types of large thrusts in the Swiss Helvetic fold-and-thrust belt have been analyzed by Ar-40/Ar-39 and Rb/Sr techniques to better constrain the timing of Alpine deformation for this region. Incremental Ar-40/Ar-39 heating experiments of 25 weakly metamorphosed (anchizone to low greenschist) samples yield plateau and staircase spectra. We interpret most of the staircase release spectra result from variable mixtures of syntectonic (neoformed) and detrital micas. The range in dates obtained within individual spectra depends primarily on the duration of mica nucleation and growth, and relative proportions of neoformed and detrital mica. Rb/Sr analyses of 12 samples yield dates of ca. 10-39 Ma (excluding one anomalously young sample). These dates are slightly younger than the Ar-40/Ar-39 total gas dates obtained for the same samples. The Rb/ Sr dates were calculated using initial Sr-87/Sr-86 ratios obtained from the carbonate-dominated host rocks, which are higher than normal Mesozoic carbonate values due to exchange with fluids of higher Sr-87/Sr-86 ratios (and lower O-18/O-16 ratios). Model dates calculated using Sr-87/Sr-86 values typical of Mesozoic marine carbonates more closely approximate the Ar-40/Ar-39 total gas dates for most of the samples. The similarities of Rb/Sr and Ar-40/Ar-39 total gas dates are consistent with limited amounts of detrital mica in the samples. The delta(18)O values range from 24-15%. (VSMOW) for 2-6 mum micas and 27-16parts per thousand for the carbonate host rocks. The carbonate values are significantly lower than their protolith values due to localized fluid-rock interaction and fluid flow along most thrust surfaces. Although most calcite-mica pairs are not in oxygen isotope equilibrium at temperatures of ca. 200-400 degreesC, their isotopic fractionations are indicative of either 1) partial exchange between the minerals and a common external fluid, or 2) growth or isotopic exchange of the mica with the carbonate after the carbonate had isotopically exchanged with an external fluid. The geological significance of these results is not easily or uniquely determined, and exemplifies the difficulties inherent in dating very fine-grained micas of highly deformed tectonites in low-grade metamorphic terranes. Two generalizations can be made regarding the dates obtained from the Helvetic thrusts: 1) samples from the two highest thrusts (Mt. Gond and Sublage) have all of their Ar-40/Ar-39 steps above 20 Ma, and 2) most samples from the deepest Helvetic thrusts have steps (often accounting for more than 80% of Ar-39 release) between 15 and 25 Ma. These dates are consistent with the order of thrusting in the foreland-imbricating system and increase proportions of neoformed to detrital mica in the more metamorphosed hinterland and deeply buried portions of the nappe pile. Individual thrusts accommodated the majority of their displacement during their initial incorporation into the foreland-imbricating system, and some thrusts remained active or were reactivated down to 15 Ma.

Steady periodic water waves with constant vorticity: regularity and local bifurcation

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.

Humanitarian law, human rights law and the bifurcation of armed conflict

This article offers a fresh examination of the distinction drawn in international humanitarian law (IHL) between international and non-international armed conflicts. In particular, it considers this issue from the under-explored perspective of the influence of international human rights law (IHRL). It is demonstrated how, over time, the effect of IHRL on this distinction in IHL has changed dramatically. Whereas traditionally IHRL encouraged the partial elimination of the distinction between types of armed conflict, more recently it has been invoked in debates in a manner that would preserve what remains of the distinction. By exploring this important issue, it is hoped that the present article will contribute to the ongoing debates regarding the future development of the law of non-international armed conflict.

The transaction cost economics theory of the family firm: family-based human asset specificity and the bifurcation bias

We develop a transaction cost economics theory of the family firm, building upon the concepts of family-based asset specificity, bounded rationality, and bounded reliability. We argue that the prosperity and survival of family firms depend on the absence of a dysfunctional bifurcation bias. The bifurcation bias is an expression of bounded reliability, reflected in the de facto asymmetric treatment of family vs. nonfamily assets (especially human assets). We propose that absence of bifurcation bias is critical to fostering reliability in family business functioning. Our study ends the unproductive divide between the agency and stewardship perspectives of the family firm, which offer conflicting accounts of this firm type's functioning. We show that the predictions of the agency and stewardship perspectives can be usefully reconciled when focusing on how family firms address the bifurcation bias or fail to do so.

Stability and Hopf bifurcation in an hexagonal governor system

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

NONDEGENERATE UMBILICS, THE PATH FORMULATION and GRADIENT BIFURCATION PROBLEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comparison of predicted and experimental DSC curves for vegetable oils

We compare experimental and predicted differential scanning calorimetry (DSC) curves for palm oil (PO), peanut oil (PeO) and grapeseed oil (GO). The predicted curves are computed from the solid-liquid equilibrium modelling and direct minimization of the Gibbs free energy. For PO, the lower the scan rate, the better the agreement. The temperature transitions of PeO and GO were predicted with an average deviation of -0.72 degrees C and -1.29 degrees C respectively, in relation to experimental data from literature. However, the predicted curves showed other peaks not reported experimentally, as computed DSC curves correspond to equilibrium hypothesis which is reached experimentally for an infinitely small scan rate. The results revealed that predicted transitions temperatures using equilibrium hypotheses can be useful in pre-experimental evaluation of vegetable oils formulations seeking for desired melting profiles. (C) 2012 Elsevier B.V. All rights reserved.

On the three-finger protein domain fold and CD59-like proteins in Schistosoma mansoni

Background: It is believed that schistosomes evade complement-mediated killing by expressing regulatory proteins on their surface. Recently, six homologues of human CD59, an important inhibitor of the complement system membrane attack complex, were identified in the schistosome genome. Therefore, it is important to investigate whether these molecules could act as CD59-like complement inhibitors in schistosomes as part of an immune evasion strategy. Methodology/Principal Findings: Herein, we describe the molecular characterization of seven putative SmCD59-like genes and attempt to address the putative biological function of two isoforms. Superimposition analysis of the 3D structure of hCD59 and schistosome sequences revealed that they contain the three-fingered protein domain (TFPD). However, the conserved amino acid residues involved in complement recognition in mammals could not be identified. Real-time RT-PCR and Western blot analysis determined that most of these genes are up-regulated in the transition from free-living cercaria to adult worm stage. Immunolocalization experiments and tegument preparations confirm that at least some of the SmCD59-like proteins are surface-localized; however, significant expression was also detected in internal tissues of adult worms. Finally, the involvement of two SmCD59 proteins in complement inhibition was evaluated by three different approaches: (i) a hemolytic assay using recombinant soluble forms expressed in Pichia pastoris and E. coli; (ii) complement-resistance of CHO cells expressing the respective membrane-anchored proteins; and (iii) the complement killing of schistosomula after gene suppression by RNAi. Our data indicated that these proteins are not involved in the regulation of complement activation. Conclusions: Our results suggest that this group of proteins belongs to the TFPD superfamily. Their expression is associated to intra-host stages, present in the tegument surface, and also in intra-parasite tissues. Three distinct approaches using SmCD59 proteins to inhibit complement strongly suggested that these proteins are not complement inhibitors and their function in schistosomes remains to be determined.