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.

Population dynamics and biting rhythm of the anthropophilic sandfly Lutzomyia cruciata (Diptera: Psychdidae) in Southeast, Mexico

Sandflies attracted by human bait were caught in an endemic focus of localized cutaneous leishmaniasis in the state of Campeche, Mexico. Catches were carried out monthly from February 1994 to January 1995 between 18:00 and 22:00 h. Lutzomyia cruciata was the only species caught. The highest population peak of Lu. cruciata was found in March with lesser peaks in February, December 1994, and January 1995. Maximum biting rate of Lu. cruciata was found between 18:00 and 19:00 h. The host-seeking females of Lu. cruciata were directly related to levels of humidity between 88 and 100%. Low and high temperature had a negative effect upon Lu. cruciata activity. The possible role of Lu. cruciata as vector of leishmaniasis in the state of Campeche, Mexico is discussed.

DETECTION OF IgM ANTIBODIES TO Schistosoma mansoni GUT-ASSOCIATED ANTIGENS FOR THE STUDY OF THE DYNAMICS OF SCHISTOSOMIASIS TRANSMISSION IN AN ENDEMIC AREA WITH LOW WORM BURDEN

For a period of 2 years, five follow-up measures of prevalence and incidence rates were estimated in a prospective study of S. mansoni infection in a group of schoolchildren who were living in a rural area of the Municipality of Itariri (São Paulo, Brazil), where schistosomiasis is transmitted by Biomphalaria tenagophila. Infection was determined by the examination of three Kato-Katz stool slides, and the parasitological findings were analyzed in comparison to serological data. In the five surveys, carried out at 6-month intervals (March-April and September-October), the prevalences were, respectively, 8.6, 6.8, 9.9, 5.8 and 17.2% by the Kato-Katz, and 56.5, 52.6, 60.8, 53.5 and 70.1% by the immunofluorescence test (IFT). Geometric mean egg counts were low: 57.8, 33.0, 35.6, 47.3 and 40.9 eggs per gram of feces, respectively. Of the total of 299 schoolchildren, who submitted five blood samples at 6-month intervals, one for each survey, 40% were IFT-positive throughout the study, and 22% were IFT-negative in all five surveys. Seroconversion from IFT negative to positive, indicating newly acquired S. mansoni infection, was observed more frequently in surveys carried out during March-April (after Summer holidays), than during September-October. Seasonal trends were not statistically significant for detection of S. mansoni eggs in stool. The results indicate that the use of IgM-IFT is superior to parasitological methods for detection of incidence of S. mansoni infection in areas with low worm burden.

Critical Velocity obtained using Simplified Models of the Railway Track: Viability and Applicability

Increased demands on the capacity of the railway network gave rise to new issues related to the dynamic response of railway tracks subjected to moving vehicles. Thus, it becomes important to evaluate the applicability of traditionally used simplified models which have a closed form solution. Regarding simplified models, transversal vibrations of a beam on a visco-elastic foundation subjected to a moving load are considered. Governing equations are obtained by Hamilton’s principle. Shear distortion, rotary inertia and effect of axial force are accounted for. The load is introduced as a time varying force moving at a constant velocity. Transversal vibrations induced by the load are solved by the normal-mode analysis. Reflected waves at the extremities of the full beam are avoided by introduction of semi-infinite elements. Firstly, the critical velocity obtained from this model is compared with results of an undamped Euler- Bernoulli formulation with zero axial force. Secondly, a finite element model in ABAQUS is examined. The new contribution lies in the introduction of semi- infinite elements and in the first step to a systematic comparison, which have not been published so fa

Explosion of smoothness from a point to everywhere for conjugacies between Markov families

For uniformly asymptotically affine (uaa) Markov maps on train tracks, we prove the following type of rigidity result: if a topological conjugacy between them is (uaa) at a point in the train track then the conjugacy is (uaa) everywhere. In particular, our methods apply to the case in which the domains of the Markov maps are Canter sets. We also present similar statements for (uaa:) and C-r Markov families. These results generalize the similar ones of Sullivan and de Faria for C-r expanding circle maps with r > 1 and have useful applications to hyperbolic dynamics on surfaces and laminations.

Hausdorff dimension bounds for smoothness of holonomies for codimension 1 hyperbolic dynamics

We prove that the stable holonomies of a proper codimension 1 attractor Λ, for a Cr diffeomorphism f of a surface, are not C1+θ for θ greater than the Hausdorff dimension of the stable leaves of f intersected with Λ. To prove this result we show that there are no diffeomorphisms of surfaces, with a proper codimension 1 attractor, that are affine on a neighbourhood of the attractor and have affine stable holonomies on the attractor.

Dissecting neuronal development deficits by inflammation: from morphology to cytoskeleton dynamics

Dissertação para obtenção do Grau de Mestre em Genética Molecular e Biomedicina

Nonlinear dynamics of the patient’s response to drug effect during general anesthesia

In today’s healthcare paradigm, optimal sedation during anesthesia plays an important role both in patient welfare and in the socio-economic context. For the closed-loop control of general anesthesia, two drugs have proven to have stable, rapid onset times: propofol and remifentanil. These drugs are related to their effect in the bispectral index, a measure of EEG signal. In this paper wavelet time–frequency analysis is used to extract useful information from the clinical signals, since they are time-varying and mark important changes in patient’s response to drug dose. Model based predictive control algorithms are employed to regulate the depth of sedation by manipulating these two drugs. The results of identification from real data and the simulation of the closed loop control performance suggest that the proposed approach can bring an improvement of 9% in overall robustness and may be suitable for clinical practice.

Chromatin dynamics in Arbidopsis development: a live cell imaging approach

Dissertation presented to obtain the Ph.D degree in Biology

Fractional Dynamics of Computer Virus Propagation

We propose a fractional model for computer virus propagation. The model includes the interaction between computers and removable devices. We simulate numerically the model for distinct values of the order of the fractional derivative and for two sets of initial conditions adopted in the literature. We conclude that fractional order systems reveal richer dynamics than the classical integer order counterpart. Therefore, fractional dynamics leads to time responses with super-fast transients and super-slow evolutions towards the steady-state, effects not easily captured by the integer order models.

Dynamics of cork mycobiota throughout stopper manufacturing process: from diversity to metabolite

Dissertation presented to obtain the Ph.D degree in Biology

A novel antibody-like material for breast cancer antigen CA15-3, used to track breast cancer by potentiometric transduction

This work presents the development of a low cost sensor device for the diagnosis of breast cancer in point-of-care, made with new synthetic biomimetic materials inside plasticized poly(vinyl chloride), PVC, membranes, for subsequent potentiometric detection. This concept was applied to target a conventional biomarker in breast cancer: Breast Cancer Antigen (CA15-3). The new biomimetic material was obtained by molecularly-imprinted technology. In this, a plastic antibody was obtained by polymerizing around the biomarker that acted as an obstacle to the growth of the polymeric matrix. The imprinted polymer was specifically synthetized by electropolymerization on an FTO conductive glass, by using cyclic voltammetry, including 40 cycles within -0.2 and 1.0 V. The reaction used for the polymerization included monomer (pyrrol, 5.0×10-3 mol/L) and protein (CA15-3, 100U/mL), all prepared in phosphate buffer saline (PBS), with a pH of 7.2 and 1% of ethylene glycol. The biomarker was removed from the imprinted sites by proteolytic action of proteinase K. The biomimetic material was employed in the construction of potentiometric sensors and tested with regard to its affinity and selectivity for binding CA15-3, by checking the analytical performance of the obtained electrodes. For this purpose, the biomimetic material was dispersed in plasticized PVC membranes, including or not a lipophilic ionic additive, and applied on a solid conductive support of graphite. The analytical behaviour was evaluated in buffer and in synthetic serum, with regard to linear range, limit of detection, repeatability, and reproducibility. This antibody-like material was tested in synthetic serum, and good results were obtained. The best devices were able to detect 5 times less CA15-3 than that required in clinical use. Selectivity assays were also performed, showing that the various serum components did not interfere with this biomarker. Overall, the potentiometric-based methods showed several advantages compared to other methods reported in the literature. The analytical process was simple, providing fast responses for a reduced amount of analyte, with low cost and feasible miniaturization. It also allowed the detection of a wide range of concentrations, diminishing the required efforts in previous sample pre-treating stages.

Nonlinear Dynamics for Local Fractional Burgers Equation Arising in Fractal Flow

The local fractional Burgers’ equation (LFBE) is investigated from the point of view of local fractional conservation laws envisaging a nonlinear local fractional transport equation with a linear non-differentiable diffusion term. The local fractional derivative transformations and the LFBE conversion to a linear local fractional diffusion equation are analyzed.

Fractional Dynamics in the Rayleigh's Piston

This paper studies the dynamics of the Rayleigh piston using the modeling tools of Fractional Calculus. Several numerical experiments examine the effect of distinct values of the parameters. The time responses are transformed into the Fourier domain and approximated by means of power law approximations. The description reveals characteristics usual in Fractional Brownian phenomena.

Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications