Dynamical analysis in growth models: Blumberg’s equation

We present a new dynamical approach to the Blumberg's equation, a family of unimodal maps. These maps are proportional to Beta(p, q) probability densities functions. Using the symmetry of the Beta(p, q) distribution and symbolic dynamics techniques, a new concept of mirror symmetry is defined for this family of maps. The kneading theory is used to analyze the effect of such symmetry in the presented models. The main result proves that two mirror symmetric unimodal maps have the same topological entropy. Different population dynamics regimes are identified, when the intrinsic growth rate is modified: extinctions, stabilities, bifurcations, chaos and Allee effect. To illustrate our results, we present a numerical analysis, where are demonstrated: monotonicity of the topological entropy with the variation of the intrinsic growth rate, existence of isentropic sets in the parameters space and mirror symmetry.

Lack of association between iron status at birth and growth of preterm infants

OBJECTIVE: To assess the association between iron status at birth and growth of preterm infants. METHODS: Ninety-five premature babies (26 to 36 weeks of gestational age) born from July 2000 to May 2001 in a public hospital in Rio de Janeiro, Southeastern Brazil, were followed up for six months, corrected by gestational age. Iron measurements at birth were available for 82 mothers and 78 children: hemoglobin, hematocrit, mean corpuscular volume and plasma iron. All children received free doses of iron supplement (2 mg/kg/day) during the follow-up period and up to two years of age. Multivariate linear regression analyses with repeated measurements were performed to assess factors associated to linear growth. RESULTS: Growth was more pronounced up to 40 weeks of gestational age, increasing about 1.0 cm/week and then slowing down to 0.75 cm/week. The multivariate analysis showed growth was positively associated with birth weight (0.4 cm/100 g; p<0.001) and negatively associated with gestational age at birth (-0.5 cm/week; p<0.001). There was no association between cord iron and mother iron measurements and growth (p>0.60 for all measures). Only two children had anemia at birth, whereas 43.9% of mothers were anemic (hemoglobin <11 g/dl). Also, there was no correlation between anemia indicators of mothers and children at birth (r<0.15; p>0.20). CONCLUSIONS: Maternal anemia was not associated with anemia in preterm infants and iron status of mothers and children at birth was not associated with short-term growth of preterm infants.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Topological Complexity and Predictability in the Dynamics of a Tumor Growth Model with Shilnikov's Chaos

Dynamical systems modeling tumor growth have been investigated to determine the dynamics between tumor and healthy cells. Recent theoretical investigations indicate that these interactions may lead to different dynamical outcomes, in particular to homoclinic chaos. In the present study, we analyze both topological and dynamical properties of a recently characterized chaotic attractor governing the dynamics of tumor cells interacting with healthy tissue cells and effector cells of the immune system. By using the theory of symbolic dynamics, we first characterize the topological entropy and the parameter space ordering of kneading sequences from one-dimensional iterated maps identified in the dynamics, focusing on the effects of inactivation interactions between both effector and tumor cells. The previous analyses are complemented with the computation of the spectrum of Lyapunov exponents, the fractal dimension and the predictability of the chaotic attractors. Our results show that the inactivation rate of effector cells by the tumor cells has an important effect on the dynamics of the system. The increase of effector cells inactivation involves an inverse Feigenbaum (i.e. period-halving bifurcation) scenario, which results in the stabilization of the dynamics and in an increase of dynamics predictability. Our analyses also reveal that, at low inactivation rates of effector cells, tumor cells undergo strong, chaotic fluctuations, with the dynamics being highly unpredictable. Our findings are discussed in the context of tumor cells potential viability.

Phase growth control in low temperature PLD Co: TiO2 films by pressure

This paper reports on the structural and optical properties of Co-doped TiO2 thin films grown onto (0001)Al2O3 substrates by non-reactive pulsed laser deposition (PLD) using argon as buffer gas. It is shown that by keeping constant the substrate temperature at as low as 310 degrees C and varying only the background gas pressure between 7 Pa and 70 Pa, it is possible to grow either epitaxial rutile or pure anatase thin films, as well as films with a mixture of both polymorphs. The optical band gaps of the films are red shifted in comparison with the values usually reported for undoped TiO2, which is consistent with n-type doping of the TiO2 matrix. Such band gap red shift brings the absorption edge of the Co-doped TiO2 films into the visible region, which might favour their photocatalytic activity. Furthermore, the band gap red shift depends on the films' phase composition, increasing with the increase of the Urbach energy for increasing rutile content. (C) 2012 Elsevier B.V. All rights reserved.

Modulation of translation factor's gene expression by histone deacetylase inhibitors in breast cancer cells

The histone deacetylase inhibitors sodium butyrate (NaBu) and trichostatin A (TSA) exhibit anti-proliferative activity by causing cell cycle arrest and apoptosis. The mechanisms by which NaBu and TSA cause apoptosis and cell cycle arrest are not yet completely clarified, although these agents are known to modulate the expression of several genes including cell-cycle- and apoptosis-related genes. The enzymes involved in the process of translation have important roles in controlling cell growth and apoptosis, and several of these translation factors have been described as having a causal role in the development of cancer. The expression patterns of the translation mechanism, namely of the elongation factors eEF1A1 and eEF1A2, and of the termination factors eRF1 and eRF3, were studied in the breast cancer cell line MCF-7 by real-time quantitative reverse transcription-polymerase chain reaction after a 24-h treatment with NaBu and TSA. NaBu induced inhibition of translation factors' transcription, whereas TSA caused an increase in mRNA levels. Thus, these two agents may modulate the expression of translation factors through different pathways. We propose that the inhibition caused by NaBu may, in part, be responsible for the cell cycle arrest and apoptosis induced by this agent in MCF-7 cells.