Avoiding healthy cells extinction in a cancer model

We consider a dynamical model of cancer growth including three interacting cell populations of tumor cells, healthy host cells and immune effector cells. For certain parameter choice, the dynamical system displays chaotic motion and by decreasing the response of the immune system to the tumor cells, a boundary crisis leading to transient chaotic dynamics is observed. This means that the system behaves chaotically for a finite amount of time until the unavoidable extinction of the healthy and immune cell populations occurs. Our main goal here is to apply a control method to avoid extinction. For that purpose, we apply the partial control method, which aims to control transient chaotic dynamics in the presence of external disturbances. As a result, we have succeeded to avoid the uncontrolled growth of tumor cells and the extinction of healthy tissue. The possibility of using this method compared to the frequently used therapies is discussed. (C) 2014 Elsevier Ltd. All rights reserved.

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.

Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Spatial dynamics of team sports exposed by Voronoi diagrams

Team sports represent complex systems: players interact continuously during a game, and exhibit intricate patterns of interaction, which can be identified and investigated at both individual and collective levels. We used Voronoi diagrams to identify and investigate the spatial dynamics of players' behavior in Futsal. Using this tool, we examined 19 plays of a sub-phase of a Futsal game played in a reduced area (20 m(2)) from which we extracted the trajectories of all players. Results obtained from a comparative analysis of player's Voronoi area (dominant region) and nearest teammate distance revealed different patterns of interaction between attackers and defenders, both at the level of individual players and teams. We found that, compared to defenders, larger dominant regions were associated with attackers. Furthermore, these regions were more variable in size among players from the same team but, at the player level, the attackers' dominant regions were more regular than those associated with each of the defenders. These findings support a formal description of the dynamic spatial interaction of the players, at least during the particular sub-phase of Futsal investigated. The adopted approach may be extended to other team behaviors where the actions taken at any instant in time by each of the involved agents are associated with the space they occupy at that particular time.

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.

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.

Complex dynamics in the trajectory control of redundant manipulators

Redundant manipulators allow the trajectory optimization, the obstacle avoidance, and the resolution of singularities. For this type of manipulators, the kinematic control algorithms adopt generalized inverse matrices that may lead to unpredictable responses. Motivated by these problems this paper studies the complexity revealed by the trajectory planning scheme when controlling redundant manipulators. The results reveal fundamental properties of the chaotic phenomena and give a deeper insight towards the development of superior trajectory control algorithms.

Dynamics of transmission of Trypanosoma cruzi in a rural area of Argentina: III. Persistence of T. cruzi parasitemia among canine reservoirs in a two-year follow-up

A new cross-sectional survey of household- associated mongrel dogs as well as follow-up of previously parasitemic individuals was carried out in 1984 toy means of xenodiagnosis and serologic techniques to get a deeper insight into the relationship of T. cruzi parasitemia and age among canine hosts in a rural area of Argentina. Persistence of detectable parasitemia was age-independent, or at most, loosely related to age, confirming the pattern observed in 1982. Similarly no significant age-decreasing effect was recorded among seropositive dogs in: a) the probability of detecting parasites in a 2-year follow-up; b) their intensity of infectiousness (=infective force) for T. infestans 3rd-4th instar nymphs, as measured by the percentage of infected bugs observed in each dog xenodiagnosis. Moreover, not only was the infective force of seropositive dogs for bugs approximately constant through lifetime, but it was significantly higher than the one recorded for children in the present survey, and for human people by other researchers. Therefore, and since T. infestans field populations show high feeding frequencies on dogs, the latter are expected to make the greatest contribution to the pool of infected vectors in the rural household of Argentina. This characteristic should be sufficient to involve canine reservoirs definitely as a risk factor for human people residing in the same house. The increased severity of parasitemia observed among dogs in this survey may be related to the acute undernutrition characteristic of canine populations of poor rural areas in our country, which is expected to affect the ability of the host to manage the infection.

Fractional dynamics in the trajectory control of redundant manipulators

Under the pseudoinverse control, robots with kinematical redundancy exhibit an undesirable chaotic joint motion which leads to an erratic behavior. This paper studies the complexity of fractional dynamics of the chaotic response. Fourier and wavelet analysis provides a deeper insight, helpful to know better the lack of repeatability problem of redundant manipulators. This perspective for the study of the chaotic phenomena will permit the development of superior trajectory control algorithms.

Simulation and dynamics of freeway traffic

This paper presents the new package entitled Simulator of Intelligent Transportation Systems (SITS) and a computational oriented analysis of traffic dynamics. The SITS adopts a microscopic simulation approach to reproduce real traffic conditions considering different types of vehicles, drivers and roads. A set of experiments with the SITS reveal the dynamic phenomena exhibited by this kind of system. For this purpose a modelling formalism is developed that embeds the statistics and the Laplace transform. The results make possible the adoption of classical system theory tools and point out that it is possible to study traffic systems taking advantage of the knowledge gathered with automatic control algorithms. A complementary perspective for the analysis of the traffic flow is also quantified through the entropy measure.

Complex-order dynamics in hexapod locomotion

This paper studies the dynamics of foot–ground interaction in hexapod locomotion systems. For that objective the robot motion is characterized in terms of several locomotion variables and the ground is modelled through a non-linear spring-dashpot system, with parameters based on the studies of soil mechanics. Moreover, it is adopted an algorithm with foot-force feedback to control the robot locomotion. A set of model-based experiments reveals the influence of the locomotion velocity on the foot–ground transfer function, which presents complex-order dynamics.

Kinetic measurements during transient film growth on zinc

Quimica Nova, Vol. 32, Nº2

Soil attributes dynamics evaluation after prescribed burning practice in northwestern Portugal forest

The Portuguese northern forests are often and severely affected by wildfires during the summer season. These occurrences affect significant and rudely all ecosystems, namely soil, fauna and flora. Preventive actions such as prescribed burnings and clear-cut logging are frequently used and have showed a significant reduction of the natural wildfires occurrences. In Portugal, and due to some technical and operational conditions, prescribed burnings in forests are the most common preventive action used to reduce the existing fuel hazard. The overall impacts of this preventive action on Portuguese ecosystems are complex and not fully understood. This work reports to the study of a prescribed burning impact in soil chemical properties, namely pH, humidity and organic matter, by monitoring the soil self-recovery capacity. The experiments were carried out in soil cover over a natural site of Andaluzitic schist, in Gramelas, Caminha, Portugal, who was able to maintain itself intact from prescribed burnings from four years. The composed soil samples were collected from five plots at three different layers (0-3cm, 3-6cm and 6-18cm) 1 day before prescribed fire and after the prescribed fire. The results have shown that the dynamic equilibrium in soil was affected significantly.

Transient Spaces: unsettling boundaries and norms at the cultural event Noc Noc, Guimarães, Portugal

Cities are increasingly expected to be creative, inventive and to exhibit intense expressivity. In the past decades many cities have experienced growing pressure to produce and stage cultural events of different sorts and to develop new strategies that optimize competitive advantages, in order to promote themselves and to boost and sell their image. Often these actions have relied on heavy public investment and major private corporation sponsoring, but it is not always clear or measured how successful and reproductive these investments have been. In the context of strained public finances and profound economic crisis of European peripheral countries, events that emerge from local communities and have low budgets, which manage to create significant fluxes of visitors and visibility, assume an increased interest. In order to reflect and sketch possible answers, we look to an emerging body of literature concerning creative cities, and we focus on the organisation of a particular cultural event and its impact and assimilation into a medium size Portuguese city. This paper looks at the two editions (2011 and 2012) of one of such events – Noc Noc – organized by a local association in the city of Guimarães, Portugal. Inspired by similar events, Noc Noc is based on creating transient spaces of culture which are explored by artists and audiences, by transforming numerous homes into ephemeral convivial and playful social ‘public’ environments. The event is based on a number of cultural venues/homes scattered around the old and newer city, which allows for an informal urban exploration and an autonomous rambling and getting lost along streets. This strategy not only disrupts the cleavages between public and private space permitting for various transgressions, but it also disorders normative urban experiences and unsettles the dominant role of the city council as the culture patron of the large majority of events. Guimarães, an UNESCO World Heritage City was the European Capital of Culture in 2012, with a public investment of roughly 73 million euro. By interviewing a sample of people who have hosted these transitory art performances and exhibitions, sometimes doubling as artists, the events’ organizers and by experience both editions of the event, this paper illustrates how urban citizens’ engagement and motivations in a low budget cultural event can strengthen community ties. Furthermore, it also questions the advantages of large scale high budget events, and how this event may be seen as unconscious counter movement against a commodification of cultural events and everyday urban experience at large, engaging with the concepts of staging and authenticity.

Mathematical model for HIV dynamics in HIV-specific helper cells

In this paper we study a delay mathematical model for the dynamics of HIV in HIV-specific CD4 + T helper cells. We modify the model presented by Roy and Wodarz in 2012, where the HIV dynamics is studied, considering a single CD4 + T cell population. Non-specific helper cells are included as alternative target cell population, to account for macrophages and dendritic cells. In this paper, we include two types of delay: (1) a latent period between the time target cells are contacted by the virus particles and the time the virions enter the cells and; (2) virus production period for new virions to be produced within and released from the infected cells. We compute the reproduction number of the model, R0, and the local stability of the disease free equilibrium and of the endemic equilibrium. We find that for values of R0<1, the model approaches asymptotically the disease free equilibrium. For values of R0>1, the model approximates asymptotically the endemic equilibrium. We observe numerically the phenomenon of backward bifurcation for values of R0⪅1. This statement will be proved in future work. We also vary the values of the latent period and the production period of infected cells and free virus. We conclude that increasing these values translates in a decrease of the reproduction number. Thus, a good strategy to control the HIV virus should focus on drugs to prolong the latent period and/or slow down the virus production. These results suggest that the model is mathematically and epidemiologically well-posed.