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.

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.

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.

A hybrid approach to multi-agent decision-making

In the aftermath of a large-scale disaster, agents' decisions derive from self-interested (e.g. survival), common-good (e.g. victims' rescue) and teamwork (e.g. fire extinction) motivations. However, current decision-theoretic models are either purely individual or purely collective and find it difficult to deal with motivational attitudes; on the other hand, mental-state based models find it difficult to deal with uncertainty. We propose a hybrid, CvI-JI, approach that combines: i) collective 'versus' individual (CvI) decisions, founded on the Markov decision process (MDP) quantitative evaluation of joint-actions, and ii)joint-intentions (JI) formulation of teamwork, founded on the belief-desire-intention (BDI) architecture of general mental-state based reasoning. The CvI-JI evaluation explores the performance's improvement

Chaos and crises in a model for cooperative hunting: A symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K, C-0) and (K, sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K-c decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

A new sedimentary benchmark for the Deccan Traps volcanism?

The origin of the Cretaceous-Paleogene boundary (KPB) mass extinction is still the center of acrimonious debates by opposing partisans of the bolide impact theory to those who favored a terrestrial origin linked to the Deccan Traps volcanism. Here we apply an original and high-resolution environmental magnetic study of the reference Bidart section, France. Our results show that the KPB is identified by an abrupt positive shift of the magnetic susceptibility (MS), also observed by others at the KPB elsewhere. In addition, an anomalous interval of very low MS, carried by an unknown Cl-bearing iron oxide similar to specular hematite, is depicted just below the KPB. Grain-size and morphology of the Cl-iron oxide are typically in the range of hematitic dust currently transported by winds from Sahara to Europe. This discovery is confirmed in the referenced Gubbio section (Italy) suggesting a global scale phenomenon. As a conjecture we suggest an origin by heterogeneous reaction between HCl-rich volcanic gas and liquid-solid aerosols within buoyant atmospheric plumes formed above the newly emitted Deccan flood basalts. Based on this hypothesis, our discovery provides a new benchmark for the Deccan volcanism and witnesses the nature and importance of the related atmospheric change.

Modeling Allee Effect from Beta(p, 2) Densities

In this work we develop and investigate generalized populational growth models, adjusted from Beta(p, 2) densities, with Allee effect. The use of a positive parameter leads the presented generalization, which yields some more flexible models with variable extinction rates. An Allee limit is incorporated so that the models under study have strong Allee effect.

Strong and weak Allee effects and chaotic dynamics in Richards' growths

In this paper we define and investigate generalized Richards' growth models with strong and weak Allee effects and no Allee effect. We prove the transition from strong Allee effect to no Allee effect, passing through the weak Allee effect, depending on the implicit conditions, which involve the several parameters considered in the models. New classes of functions describing the existence or not of Allee effect are introduced, a new dynamical approach to Richards' populational growth equation is established. These families of generalized Richards' functions are proportional to the right hand side of the generalized Richards' growth models proposed. Subclasses of strong and weak Allee functions and functions with no Allee effect are characterized. The study of their bifurcation structure is presented in detail, this analysis is done based on the configurations of bifurcation curves and symbolic dynamics techniques. Generically, the dynamics of these functions are classified in the following types: extinction, semi-stability, stability, period doubling, chaos, chaotic semistability and essential extinction. We obtain conditions on the parameter plane for the existence of a weak Allee effect region related to the appearance of cusp points. To support our results, we present fold and flip bifurcations curves and numerical simulations of several bifurcation diagrams.

Mutation accumulation in Tetrahymena

Background - The rate and fitness effects of mutations are key in understanding the evolution of every species. Traditionally, these parameters are estimated in mutation accumulation experiments where replicate lines are propagated in conditions that allow mutations to randomly accumulate without the purging effect of natural selection. These experiments have been performed with many model organisms but we still lack empirical estimates of the rate and effects of mutation in the protists. Results - We performed a mutation accumulation (MA) experiment in Tetrahymena thermophila, a species that can reproduce sexually and asexually in nature, and measured both the mean decline and variance increase in fitness of 20 lines. The results obtained with T. thermophila were compared with T. pyriformis that is an obligate asexual species. We show that MA lines of T. thermophila go to extinction at a rate of 1.25 clonal extinctions per bottleneck. In contrast, populations of T. pyriformis show a much higher resistance to extinction. Variation in gene copy number is likely to be a key factor in explaining these results, and indeed we show that T. pyriformis has a higher mean copy number per cell than T. thermophila. From fitness measurements during the MA experiment, we infer a rate of mutation to copy number variation of 0.0333 per haploid MAC genome of T. thermophila and a mean effect against copy number variation of 0.16. A strong effect of population size in the rate of fitness decline was also found, consistent with the increased power of natural selection. Conclusions - The rate of clonal extinction measured for T. thermophila is characteristic of a mutational degradation and suggests that this species must undergo sexual reproduction to avoid the deleterious effects detected in the laboratory experiments. We also suggest that an increase in chromosomal copy number associated with the phenotypic assortment of amitotic divisions can provide an alternative mechanism to escape the deleterious effect of random chromosomal copy number variation in species like T. pyriformis that lack the resetting mechanism of sexual reproduction. Our results are relevant to the understanding of cell line longevity and senescence in ciliates.

Sistemas de automação e manutenção de edifícios: concepção dos sistemas de detecção e protecção contra incêndios de uma unidade industrial

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Halting the fuse discharge propagation using optical fiber microwires

We report and analyze the halting of the fuse effect propagation in optical fiber microwires. The increase of the mode field diameter in the tapered region decreases the optical intensity resulting in the extinction of the fuse effect. This fiber element presents a low insertion loss and can be introduced in the optical network in order to protect the active equipment from the damage caused by the fuse effect.

Controling delayed transitions with applications to prevent single species extinctions

A new method is proposed to control delayed transitions towards extinction in single population theoretical models with discrete time undergoing saddle-node bifurcations. The control method takes advantage of the delaying properties of the saddle remnant arising after the bifurcation, and allows to sustain populations indefinitely. Our method, which is shown to work for deterministic and stochastic systems, could generally be applied to avoid transitions tied to one-dimensional maps after saddle-node bifurcations.

Generalized models from Beta(p,2) densities with strong allee effect: dynamical approach

A dynamical approach to study the behaviour of generalized populational growth models from Bets(p, 2) densities, with strong Allee effect, is presented. The dynamical analysis of the respective unimodal maps is performed using symbolic dynamics techniques. The complexity of the correspondent discrete dynamical systems is measured in terms of topological entropy. Different populational dynamics regimes are obtained when the intrinsic growth rates are modified: extinction, bistability, chaotic semistability and essential extinction.

On chaos, transient chaos and ghosts in single populations models with allee effects

Density-dependent effects, both positive or negative, can have an important impact on the population dynamics of species by modifying their population per-capita growth rates. An important type of such density-dependent factors is given by the so-called Allee effects, widely studied in theoretical and field population biology. In this study, we analyze two discrete single population models with overcompensating density-dependence and Allee effects due to predator saturation and mating limitation using symbolic dynamics theory. We focus on the scenarios of persistence and bistability, in which the species dynamics can be chaotic. For the chaotic regimes, we compute the topological entropy as well as the Lyapunov exponent under ecological key parameters and different initial conditions. We also provide co-dimension two bifurcation diagrams for both systems computing the periods of the orbits, also characterizing the period-ordering routes toward the boundary crisis responsible for species extinction via transient chaos. Our results show that the topological entropy increases as we approach to the parametric regions involving transient chaos, being maximum when the full shift R(L)(infinity) occurs, and the system enters into the essential extinction regime. Finally, we characterize analytically, using a complex variable approach, and numerically the inverse square-root scaling law arising in the vicinity of a saddle-node bifurcation responsible for the extinction scenario in the two studied models. The results are discussed in the context of species fragility under differential Allee effects. (C) 2011 Elsevier Ltd. All rights reserved.

Halting the fuse discharge propagation Using optical fiber microwires

We report and analyze the halting of the fuse effect propagation in optical fiber microwires. The increase of the mode field diameter in the tapered region decreases the optical intensity resulting in the extinction of the fuse effect. This fiber element presents a low insertion loss and can be introduced in the optical network in order to protect the active equipment from the damage caused by the fuse effect. (C) 2012 Optical Society of America