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.

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.

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.

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.

Four adult hemoglobin types in one mulatto family

The studied family showed the presence of four different types of hemoglobin. The family member who gave rise to this study (=propositus) presented Hb C and the hybrid Hb CG-phila. The propositus has three children, all of which have Hb AC; none of the family members showed any clinical symptoms. The investigation of the hemoglobin arose from the finding of target red cells in a blood test done during the pre-operatory examination for lower limb varicose vein stripping. The hybrid Hb CG-phila is due to two gene pairs, each of which with individual expression, determining the synthesis and the particular type subunits. The hybrid Hb CG-phila is formed by the combination velocity of the subunits alpha2G-philabeta2; therefore the proportion of the hybrid Hb CG-phila is lower than Hb G-phila and Hb C. The identification and molecular characterization of Hb G-phila showed the position alpha268 Asn->Lys beta2 and Hb C showed alpha2beta26 Glu->Lys.

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.

Expectativas de responsabilidade filial e orientação da responsabilidade no cuidado aos idosos

RESUMO: Muitos desenvolvimentos demográficos e estruturais ocorreram nas relações intergeracionais, os quais provocaram um impacto nas ligações familiares, tais como o aumento da longevidade e as alterações da dinâmica estrutural e social da família, tendo sido colocado em causa a vitalidade das obrigações familiares e solidariedade familiar, nomeadamente entre pais e filhos adultos. Assim, com este estudo pretendeu-se verificar a presença de solidariedade entre pais e os seus filhos adultos, assim como as expectativas de responsabilidade filial dos pais e as suas opiniões e preferências no que se refere à orientação da responsabilidade para família/ serviços públicos no cuidado aos idosos. De forma a alcançar os objectivos, foi aplicado um questionário a 97 alunos, da Universidade Sénior da Póvoa de Santa Iria, com 55 ou mais anos e que tivessem pelo menos um filho adulto. Foi possível chegar à conclusão de que existe solidariedade entre pais e filhos adultos, assim como os pais consideram que existe uma responsabilidade mista (família/Estado) no cuidado aos idosos e que preferem os apoios formais em detrimento dos informais (familiares) – contrariando a orientação familística. Contudo, apesar disso continuam a apresentar expectativas elevadas em relação à responsabilidade que os filhos devem ter para com os pais, nomeadamente a nível da dimensão de apoio emocional, sendo a dimensão de apoio instrumental a excepção. Desta forma, é possível concluir que há uma tendência por parte da população inquirida em preferir a complementaridade de apoios formais e informais, com consequente especialização de tarefas: instrumental e emocional, respectivamente-----------ABSTRACT: Intergenerational relations have been affected by demographical and structural changes that had impact on family relationships. The increase in life expectancy and the changes in the families’ structural and social dynamics have put at risk the vitality of family obligations and solidarity, namely between parents and adult children. Therefore, this research aimed at studying the existence of solidarity between parents and adult children as well as the parents’ expectations towards their children’s responsibilities and their views and preferences on family and welfare state responsibility as far as elderly people are concerned. In order to achieve this, a questionnaire was devised and subsequently applied to 97 participants attending the Universidade Sénior in Póvoa de Santa Iria, aged 55 or older, with at least one adult child. The results indicate that there is solidarity between parents and adult children and that parents consider that both the family and the state should share the responsibility towards elderly people. Moreover, the study proves that formal support is preferred to the detriment of an informal one (family), which contradicts the familistic approach. However, parents evince high expectations as far as children responsibility towards them is concerned, specially in terms of emotional support. This does not apply, however, to the instrumental support domain. In conclusion, the study indicates that the participants tend to prefer the complementariness of formal and informal support with subsequent task specialisation: instrumental and emotional, respectively.

Functional and structural characterization of the RNase II-family of enzymes

Dissertation presented to obtain a Doctoral Degree in Biology by Instituto de Tecnologia Química e Biológica, Universidade Nova de Lisboa

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

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.