Scaling law in Saddle-node bifurcations for one-dimensional maps: A complex variable approach

The study of transient dynamical phenomena near bifurcation thresholds has attracted the interest of many researchers due to the relevance of bifurcations in different physical or biological systems. In the context of saddle-node bifurcations, where two or more fixed points collide annihilating each other, it is known that the dynamics can suffer the so-called delayed transition. This phenomenon emerges when the system spends a lot of time before reaching the remaining stable equilibrium, found after the bifurcation, because of the presence of a saddle-remnant in phase space. Some works have analytically tackled this phenomenon, especially in time-continuous dynamical systems, showing that the time delay, tau, scales according to an inverse square-root power law, tau similar to (mu-mu (c) )(-1/2), as the bifurcation parameter mu, is driven further away from its critical value, mu (c) . In this work, we first characterize analytically this scaling law using complex variable techniques for a family of one-dimensional maps, called the normal form for the saddle-node bifurcation. We then apply our general analytic results to a single-species ecological model with harvesting given by a unimodal map, characterizing the delayed transition and the scaling law arising due to the constant of harvesting. For both analyzed systems, we show that the numerical results are in perfect agreement with the analytical solutions we are providing. The procedure presented in this work can be used to characterize the scaling laws of one-dimensional discrete dynamical systems with saddle-node bifurcations.

Topological entropy of catalytic sets: Hypercycles revisited

The dynamics of catalytic networks have been widely studied over the last decades because of their implications in several fields like prebiotic evolution, virology, neural networks, immunology or ecology. One of the most studied mathematical bodies for catalytic networks was initially formulated in the context of prebiotic evolution, by means of the hypercycle theory. The hypercycle is a set of self-replicating species able to catalyze other replicator species within a cyclic architecture. Hypercyclic organization might arise from a quasispecies as a way to increase the informational containt surpassing the so-called error threshold. The catalytic coupling between replicators makes all the species to behave like a single and coherent evolutionary multimolecular unit. The inherent nonlinearities of catalytic interactions are responsible for the emergence of several types of dynamics, among them, chaos. In this article we begin with a brief review of the hypercycle theory focusing on its evolutionary implications as well as on different dynamics associated to different types of small catalytic networks. Then we study the properties of chaotic hypercycles with error-prone replication with symbolic dynamics theory, characterizing, by means of the theory of topological Markov chains, the topological entropy and the periods of the orbits of unimodal-like iterated maps obtained from the strange attractor. We will focus our study on some key parameters responsible for the structure of the catalytic network: mutation rates, autocatalytic and cross-catalytic interactions.

Complex Dynamics of defective interfering baculoviruses during serial passage in insect cells

Defective interfering (DI) viruses are thought to cause oscillations in virus levels, known as the ‘Von Magnus effect’. Interference by DI viruses has been proposed to underlie these dynamics, although experimental tests of this idea have not been forthcoming. For the baculoviruses, insect viruses commonly used for the expression of heterologous proteins in insect cells, the molecular mechanisms underlying DI generation have been investigated. However, the dynamics of baculovirus populations harboring DIs have not been studied in detail. In order to address this issue, we used quantitative real-time PCR to determine the levels of helper and DI viruses during 50 serial passages of Autographa californica multiple nucleopolyhedrovirus (AcMNPV) in Sf21 cells. Unexpectedly, the helper and DI viruses changed levels largely in phase, and oscillations were highly irregular, suggesting the presence of chaos. We therefore developed a simple mathematical model of baculovirus-DI dynamics. This theoretical model reproduced patterns qualitatively similar to the experimental data. Although we cannot exclude that experimental variation (noise) plays an important role in generating the observed patterns, the presence of chaos in the model dynamics was confirmed with the computation of the maximal Lyapunov exponent, and a Ruelle-Takens-Newhouse route to chaos was identified at decreasing production of DI viruses, using mutation as a control parameter. Our results contribute to a better understanding of the dynamics of DI baculoviruses, and suggest that changes in virus levels over passages may exhibit chaos.

Utilidad de las muestras de sangre total desecada en papel de filtro en la detección de anticuerpos antitoxoplasma

Se compara la técnica de Aglutinación Directa (AD) utilizando muestras de sangre total desecada en papel de filtro, con la técnica de ELISA y la misma AD utilizando muestras de suero de los mismos pacientes, para la detección de anticuerpos antitoxoplasma. Los resultados muestran la validez del método de la sangre desecada en papel de filtro para la detección de anticuerpos antitoxoplasma con la técnica de AD, y se considera su utilidad en los estudios epidemiológicos de campo.

Sero-epidemiologia de la toxoplasmosis en dos comunidades de Rwanda (Africa Central)

Se ha estudiado la prevalência de anticuerpos antitoxoplasma en dos comunidades rurales rwandesas, utilizando sangre total desecada en papel de filtro que se procesó por la técnica de Aglutinación Directa. En ambas comunidades están afectados el 50% de los adultos. La adquisición de los anticuerpos se hace tardiamente en NGD (a los 14 años sólo un 12% de la problación muestra anticuerpos antitoxoplasma) y más pronto en NVU (31% de la población estudiada tiene anticuerpos antitoxoplasma a los 14 años). Se destaca el posible papel que juega esta enfermedad en la patología materno-fetal, y la necesidad de nuevos studios que aumenten el conocimiento de la epidemiología de la toxoplasmosis y sus mecanismos de transmisión en Rwanda.

Migracion, prácticas artísticas y artivismos

Una de las potencialidades del arte es devenir una herramienta para enfocar determinados conflictos desde nuevos ángulos y articular preguntas que impacten en la comunidad. Aquí el arte se funde con la filosofía, la sociología, la antropología, con el activismo, y con la propia vida. A partir de tales parámetros, se esbozarán diversas propuestas artísticas que ilustran cómo distintos creadores abordan –desde distintos ángulos– el fenómeno de la migración Dentro de la amplia miríada de perspectivas desde las que se puede tratar la migración es interesante resaltar el trabajo de varios artistas que se transforman en altavoces de las experiencias de otras personas, tal y como ejemplifican los proyectos de Pep Dardanyà, Marisa González, He Chengyue y Josep María Martín. Desde un ángulo radicalmente distinto, Santiago Sierra y el colectivo Yes lab reproducen y llevan al límite las mismas dinámicas de explotación que critican, y para finalizar, bajo el prisma de la experiencia vivida, la artista Fiona Tan explora su propio proceso migratorio e investiga la construcción de la identidad.

Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach

In this article we provide homotopy solutions of a cancer nonlinear model describing the dynamics of tumor cells in interaction with healthy and effector immune cells. We apply a semi-analytic technique for solving strongly nonlinear systems – the Step Homotopy Analysis Method (SHAM). This algorithm, based on a modification of the standard homotopy analysis method (HAM), allows to obtain a one-parameter family of explicit series solutions. By using the homotopy solutions, we first investigate the dynamical effect of the activation of the effector immune cells in the deterministic dynamics, showing that an increased activation makes the system to enter into chaotic dynamics via a period-doubling bifurcation scenario. Then, by adding demographic stochasticity into the homotopy solutions, we show, as a difference from the deterministic dynamics, that an increased activation of the immune cells facilitates cancer clearance involving tumor cells extinction and healthy cells persistence. Our results highlight the importance of therapies activating the effector immune cells at early stages of cancer progression.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Analysis of the clonal relationship among clinical isolates of Salmonella enterica serovar Infantis by different typing methods

Salmonella Infantis has been the second most common serovar in Argentina in the last two years, being isolated mostly from paediatric hospitalised patients. In order to determine the clonal relationship among Salmonella Infantis strains, we examined 15 isolates from paediatric patient faeces in Argentina (12 geographically related and 3 geographically non-related) by using antimicrobial susceptibility, plasmid profiling, repetitive extragenic palindromic (REP) PCR, enterobacterial repetitive intergenic consensus (ERIC) PCR, and low-frequency restriction analysis of chromosomal DNA by pulsed field gel electrophoresis (PFGE). Four Spanish strains were included as controls of clonal diversity in molecular techniques. Antibiotype and plasmid profile was not useful as epidemiological tools. PFGE and REP-PCR were able to discriminate between Argentinean and Spanish isolates of Salmonella Infantis allowing to detect genetically related strains in three different cities. This finding indicates that a possible spread of a clone of this serovar in the North-eastern Region of Argentina has taken place in 1998.

À la búsqueda de la ciência política tomasiana. En torno al libro IV del "de regimine principum"

pp. 73-85

Unusual morphologies of Cryptococcus spp. in tissue specimens: report of 10 cases

Ten cases of cryptococcosis due to unusual microscopic forms of Cryptococcus sp. observed over a twenty-eight year period (1981-2009) are presented. The most important clinicopathological and laboratory data are tabulated. The uncommon forms of cryptococcal cells given are: structures resembling germ tube (one case), chains of budding yeasts (one case), pseudohyphae (two cases) and nonencapsulated yeast-like organisms (eight cases). The diagnosis was based on the histopathological findings. The causative organism was isolated and identified in seven cases; five were due to C. neoformans, and two to C. gattii. In addition, the importance of using staining histochemical techniques - Grocott's silver stain (GMS), Mayer's mucicarmine stain (MM) and Fontana-Masson stain (FM) - in the diagnosis of cryptococcosis is argued.

Population and railways in Portugal, 1801-1930

Portuguese historiography has mostly adopted a pessimistic view regarding the contribution of the railways to the development of country. Yet, railway access helped to increase population concentration and economic development, favoring migration into towns, the growth of pre-existing urban centers, and the emergence of new centers. But railways tended to be more beneficial to regions that were already prosperous and to aggravate the conditions unfavorable to development in areas with greater structural weaknesses.

Caminhos de ferro, população e desigualdades territoriais em Portugal, 1801-1930

A historiografia sobre os caminhos de ferro em Portugal tem analisado o seu impacto no país como um todo, dando pouca atenção à sua influência na dinâmica populacional. Este artigo defende que os caminhos de ferro estimularam o crescimento da população nas áreas servidas por esta infraestrutura, contribuíram para o desenvolvimento urbano e incentivaram as migrações internas. Porém, os seus efeitos foram desiguais, pois a ferrovia beneficiou as zonas já prósperas (Norte Atlântico), tendo uma influência negativa em regiões com maiores debilidades estruturais (Norte Interior). Além disso, não foi capaz de atrair uma significativa população migrante.