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.

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.

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.

A cellulosic liquid crystal pool for cellulose nanocrystals: structure and molecular dynamics at high shear rates

Cellulose and its derivatives, such as hydroxypropylcellulose (HPC) have been studied for a long time but they are still not well understood particularly in liquid crystalline solutions. These systems can be at the origin of networks with properties similar to liquid crystalline (LC) elastomers. The films produced from LC solutions can be manipulated by the action of moisture allowing for instance the development of a soft motor (Geng et al., 2013) driven by humidity. Cellulose nanocrystals (CNC), which combine cellulose properties with the specific characteristics of nanoscale materials, have been mainly studied for their potential as a reinforcing agent. Suspensions of CNC can also self-order originating a liquid-crystalline chiral nematic phases. Considering the liquid crystalline features that both LC-HPC and CNC can acquire, we prepared LC-HPC/CNC solutions with different CNC contents (1,2 and 5 wt.%). The effect of the CNC into the LC-HPC matrix was determined by coupling rheology and NMR spectroscopy - Rheo-NMR a technique tailored to analyse orientational order in sheared systems. (C) 2015 Elsevier Ltd. All rights reserved.

Complete synchronization and delayed synchronization in couplings

We consider a general coupling of two identical chaotic dynamical systems, and we obtain the conditions for synchronization. We consider two types of synchronization: complete synchronization and delayed synchronization. Then, we consider four different couplings having different behaviors regarding their ability to synchronize either completely or with delay: Symmetric Linear Coupled System, Commanded Linear Coupled System, Commanded Coupled System with delay and symmetric coupled system with delay. The values of the coupling strength for which a coupling synchronizes define its Window of synchronization. We obtain analytically the Windows of complete synchronization, and we apply it for the considered couplings that admit complete synchronization. We also obtain analytically the Window of chaotic delayed synchronization for the only considered coupling that admits a chaotic delayed synchronization, the commanded coupled system with delay. At last, we use four different free chaotic dynamics (based in tent map, logistic map, three-piecewise linear map and cubic-like map) in order to observe numerically the analytically predicted windows.

Mediterranean spotted fever and identification of new agents of rickettsioses in Portugal : epidemiological determinants, host and microbial features in portuguese patients

Resumo: a febre botonosa, também conhecida por febre escaro-nodular (FEN) é uma doença endémica nos Países da bacia do Mediterrâneo, África, Médio Oriente, Índia e Paquistão. O agente etiológico responsável por esta patologia é a bactéria Rickettsia conorii. Contudo, em alguns países, como Portugal e Itália, esta patologia é causada por duas estirpes diferentes: R conorii Malish e R conorii Israeli spotted fever strain. O principal vector e reservatório é o ixodídeo Rhipicephalus sanguineus. Mesmo com uma elevada taxa de subnotificação detectada no nosso País, a taxa incidência da FEN é de 8.4/105 habitantes (1989-2005), uma das mais altas quando comparada coom a de outros países da bacia do Mediterrâneo. De todos os distritos portugueses, Bragança e Beja são aqueles que apresentam as taxas de incidência mais elevadas, 56,8/105 habitantes e 47,4 / 105 habitantes respectivamente. Em Portugal, as alterações climáticas verificadas na última década, nomeadamente a subida das temperaturas médias anuais, parecem ter influenciado o ciclo de vida do vector e a sua dinâmica sazonal, permitindo ao R. sanguineus completar mais de um ciclo de vida por ano. Este facto, e a possibilidade deste vector se manter activo noutros meses do ano, nomeadamente nos meses de inverno, tem influenciado consequentemente o padrão de distribuição anual dos casos de FEN. A febre escaro-nodular caracteriza-se clinicamente como uma doença exantemática, com um processo de vasculite generalizado. Apesar de na generalidade ser considerada uma doença benigna (quando tratada atempadamente e com terapêutica adequada e específica)e de estarem descritos casos graves em cerca de 5-6% dos doentes, em Portugal essa percentagem aumentou e consequentemente levou a um aumento de casos fatais. Este facto tornou-se mais evidente em 1997, no Hospital Distrital de Beja e no Hospital Garcia de Orta, onde a taxa de letalidade atingiu os 32% e 18% respectivamente.Para além dos factores de co-morbilidade encontrados nos doentes mais graves, como diabetes mellitus, ou o atraso na instituição da terapêutica específica, foi colocada de que a estirpe R. conorii Israel spotted fever strain pudesse ser mais virulenta ou então estivesse associada a diferentes manifestações clínicas que dificultassem o diagnóstico clínico e a instituição atempada da terapêutica. Houve ainda a necessidade de avaliar alguns parâmetros imunológicos dos doentes e tentar identificar que factores, nomeadamente que citoquinas, poderiam estar envolvidos na resposta a uma infecção por R.conorii.Face a estas questões foi avaliada e comparada a epidemiologia, manifestações clínicas e laboratoriais de 140 doentes (71 infectados com R. conorii Malish e 69 infectados com R. conorii Israel spotted fever strain). Concluiu-se que existe uma sobreposição de manifestações clinicas entre os dois grupos de doentes, mas que a percentagem da escara de inoculação é significativamente inferior em doentes infectados com R. conorii Israel spotted fever strain. Dos resultados mais importantes encontrados neste estudo concluiu-se que a estirpe R. conorii Malish e é demonstrado, pela primeira vez, estatisticamente que o alcoolismo é um factor de risco para a morte de doentes com FEN. Associadas a factores de um mau prognósitco da doença, estão as manifestações gastrointestinais, que poderão ser ou não reflexo de alterações do sistema nervoso central, e ainda a alteração de parâmetros laboratoriais como a presença de hiperbilirubinemia e aumento dos valores da ureia.A maior parte dos estudos realizados sobre os mecanismos da resposta imunitária à infecção por R. conorii e as interacções hospedeiro - agente etiológico têm sido elucidados com base em modelos animais. Poucos estudos têm sido efectuados em doentes e nenhum estudo prévio tinha sido realizado no sentido de avaliar localmente (escara/pele) quais os mediadores ou outras moléculas envolvidas na resposta imunitária às rickettsioses. Foi avaliado o nível de expressão génica de RNA mensageiro (RNAm)de diferentes citoquinas em amostras de pele de doentes com FEN pela técnica de PCR em tempo real.Os resultados deste estudo mostraram que, quando comparado com o grupo controlo, os 23 doentes analisados apresentavam níveis estatisticamente significativos, mais elevados de expressão génica de interferão (IFN-γ, Tumor necrosis factor (TFN-α, interleucina 10 (IL-10, RANTES (regulated by activation, normal T-cell-expressed and secreted chemokine)e indolamina 2-3 desoxigenase (IDO),uma enzima envolvida no controlo e limitação do crescimento intracelular das rickettsias, através da degradação do triptofano. Seis dos 23 doentes apresentaram ainda niveis de expressão elevados de óxido nítrico indutível (iNOS)que actua como microbicida. Encontrou-se uma correlação positiva entre a expressão de RNAm de TNF-α, γ, iNOS e IDO e os casos menos graves de FEN sugerindo um tipo de resposta imunitária tipo Th1, i.e. com papel protector na resposta à infecção.Verificou-se também que os valores de expressão genética do RNAm de IL-10, estavam inversamente correlacionados com a expressão do RNAm de TNF-α e IFN-γ. Os casos menos graves de FEN parecem assim envolver um balanço entre a resposta pró-inflamatória e anti-inflamatória. Já os níveis de expressão génica do RNAm de IL-10 estavam inversamente correlacionados com a expressão RNAm de TNF-α e IFN-γ. Os casos menos graves de FEN parecem assim envolver um balanço entre uma resposta pró-inflamatória e anti-inflamatória. Já os níveis de expressão RNAm da quimoquina RANTES foram estatisticamente mais elevados em doentes graves.Nesta dissertação é ainda descrita uma nova rickettsiose presente em Portugal, causada pela bactéria R. sibirica mongolitimonae, que foi identificada laboratorialmente por isolamento do agente, e por detecção do DNA em biopsia de pele. A presença deste agente foi ainda corroborada pela detecção em paralelo do mesmo agente no ixodídeos como R. africae like e em pulgas como R. felis e R.typhi alertam para a possibilidade de existência de outras rickettsioses que possam estar diagnosticadas em Portugal. Abstract: Mediterranean spotted fever (MSF), a tick-borne disease caused by Rickettsia conorii, is widley distributed in the Old World, being endemic in the southern Europe, Africa, Middle East, India and Pakistan. In Portugal two strains cause disease: R.conorii Malish and R.conorii Israeli spotted fever.Rhipicephalus sanguineus, the brown dog tick, is considered the main vector and reservoir. MSF is characterized by seasonality, and most of cases are encountered in late spring and summer, peaking in July and August. However, CEVDI/INSA laboratory has observed that the incidence of MSF cases has changed during winter season.The increasing annual averages of air temperatures and warmer and drier winters might have influenced the dynamics of the life cycle and activity of R. sanguineus, and indirectley the number MSF cases during the so called MSF off-season.In the period of 1989-2005, the incidence rate of MSF was 8.4/105 inhabitants, one of the highest rates compared with other endemic countries. In the Portugal during the same period, the highest incidence rates were reported in the districts of Bragança, with 56.8/105 inhabitants, and Beja, with 47.4/105 inhabitants. Severe cases of MSF are reported in 6% of the patients, but it seems that this pattern of disease in Portugal has been changing.This factor became more evident in 1997, with a reported case fatality rate of 32% and 18% in patients with MSF admited at Beja and Garcia Orta Hospitals, respectively. Although it was found that diabetes mellitus and delay in therapy have been implicated as a risk factor for death, the hypothesis was considered, that the new ISF strain isolated from Portugueses patients in the same year (1997)causes different or atypical clinical conorii Malish strain. The local (skin biopsies) immune response to R. conorii infection was also evaluated.A prospective study was performed to characterized epidemiological, clinical, laboratory features and determined risk factors for a fatal outcome. One hundred forty patients (51% patients were infected with Rickettsia conorii Malish stain and 49% with Israeli spotted fever strain)with diagnosis documented with identification of the causative rickettsial strain were admitted to 13 Portugueses Hospitals during 1994-2006.Comparison of the clinical manifestations of MSF caused by Malish and ISF strains revealed tremendous overlap that would not permit clinical recognition of the strain envolved, but an eschar was observed in a significantly higher percentage of patients with Malish than ISF strain.A fatal outcome was significantly more likely for patients with ISF strain infection meaning that ISF strain was more virulent than Malish strain, and also alcoholism was a host risk factor for a fatal outcome.The pathophysiology of a fatal outcome involved significantly greater incidence of petechial rash, gastrointestinal symptoms, confusion/obtundation, dehydration, tachypnea, hepatomegaly, leukocytosis, coagulopathy, azotemia, hyperbilirubinemia, and elevated hepatic enzymes and creatine kinase. Multivariate analysis revealed that acute renal failure and hyperbilirubinemia were most strong associated with a fatal oucome of infections with both strains.The immune response to R. conorii infection determined with both strains. The immune response to R. conorii infection determined by the expression levels of inflammatory and immune mediators in skin biopsies collected from untreated patients with Mediterranean spotted fever reveal that intralesional expression of mRNA of TNF-α, IFN-γ, IL-10, RANTES, and indoleamine-2, 3-dioxygenase (IDO)an enzyme involved in limiting rickettsial growth by tryptophan degradation, were elevated in skin of MSF patients compared to controls. Six patients had elevated levels of inducible nitric oxide synthase (NOS2, a source microbicidal nitric oxide.Positive correlations among TNF-α, IFN-γ, NOS2,IDO and mild-to-moderate disease suggested that type 1 polarization plays a protective role. Significantly high levels of intralesional IL-10 were inversely correlated with IFN-γ and TNF-α. The chemokine RANTES was significantly higher in patients with several MSF. It seems that MSF patients with mild-to-moderate disease have a strong and balanced intralesional pro-inflammatory and anti-inflammatory response, while severe disease is associated with higher chemokine expression.Whether these findings are simply a correlate of mild and severe disease or contribute to anti-rickettsial immunity and pathogenesis remains to be determined.In this dissertation is also described a new rickettsiois present in Portugal caused by R.sibirica mongolitimonae strain, identified based on agent isolation and DNA detection by PCR technique in a skin biopsy.The presence of this agent corroborated by its detection also in Rhipicephalus pusillus tick. Also, pathogenic tick and flea-borne rickettsial agents such as R. africae strain detected in Rhipicephalus bursa tick, and R.felis and R.typhi detected in different fleas species raise the alert for the possible existence of other rickettsioses in Portugal that might be underdiagnosed.

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.

Chromatin dynamics in Arbidopsis development: a live cell imaging approach

Dissertation presented to obtain the Ph.D degree in Biology

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.

Control and Dynamics of Fractional Order Systems

Fractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades due to the progress in the area of nonlinear dynamics. This article discusses several applications of fractional calculus in science and engineering, namely: the control of heat systems, the tuning of PID controllers based on fractional calculus concepts and the dynamics in hexapod locomotion.

Chaos Dynamics in the Trajectory Conjtrol of Redundant Manipulators

Nonlinear Dynamics, chaos, Control, and Their Applications to Engineering Sciences: Vol. 6 - Applications of nonlinear phenomena

Chaotic Phenomena and Performance Optimization in the Trajectory Control of Redundant Manipulators

Redundant manipulators have some advantages when compared with classical arms because they allow the trajectory optimization, both on the free space and on the presence of abstacles, and the resolution of singularities. For this type of manipulators, several kinetic algorithms adopt generalized inverse matrices. In this line of thought, the generalized inverse control scheme is tested through several experiments that reveal the difficulties that often arise. Motivated by theseproblems this paper presents a new method that ptimizes the manipulability through a least squre polynomialapproximation to determine the joints positions. Moreover, the article studies influence on the dynamics, when controlling redundant and hyper-redundant manipulators. The experiment confirm the superior performance of the proposed algorithm for redundant and hyper-redundant manipulators, revealing several fundamental properties of the chaotic phenomena, and gives a deeper insight towards the future development of superior trajectory control algorithms.

Fractional Dynamics in Forest Fires

Every year forest fires consume large areas, being a major concern in many countries like Australia, United States and Mediterranean Basin European Countries (e.g., Portugal, Spain, Italy and Greece). Understanding patterns of such events, in terms of size and spatiotemporal distributions, may help to take measures beforehand in view of possible hazards and decide strategies of fire prevention, detection and suppression. Traditional statistical tools have been used to study forest fires. Nevertheless, those tools might not be able to capture the main features of fires complex dynamics and to model fire behaviour [1]. Forest fires size-frequency distributions unveil long range correlations and long memory characteristics, which are typical of fractional order systems [2]. Those complex correlations are characterized by self-similarity and absence of characteristic length-scale, meaning that forest fires exhibit power-law (PL) behaviour. Forest fires have also been proved to exhibit time-clustering phenomena, with timescales of the order of few days [3]. In this paper, we study forest fires in the perspective of dynamical systems and fractional calculus (FC). Public domain forest fires catalogues, containing data of events occurred in Portugal, in the period 1980 up to 2011, are considered. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses. The frequency spectra of such signals are determined using Fourier transforms, and approximated through PL trendlines. The PL parameters are then used to unveil the fractional-order dynamics characteristics of the data. To complement the analysis, correlation indices are used to compare and find possible relationships among the data. It is shown that the used approach can be useful to expose hidden patterns not captured by traditional tools.

Strange Dynamics in a Fractional Derivative of Complex-Order Network of Chaotic Oscillators

We study the peculiar dynamical features of a fractional derivative of complex-order network. The network is composed of two unidirectional rings of cells, coupled through a "buffer" cell. The network has a Z3 × Z5 cyclic symmetry group. The complex derivative Dα±jβ, with α, β ∈ R+ is a generalization of the concept of integer order derivative, where α = 1, β = 0. Each cell is modeled by the Chen oscillator. Numerical simulations of the coupled cell system associated with the network expose patterns such as equilibria, periodic orbits, relaxation oscillations, quasiperiodic motion, and chaos, in one or in two rings of cells. In addition, fixing β = 0.8, we perceive differences in the qualitative behavior of the system, as the parameter c ∈ [13, 24] of the Chen oscillator and/or the real part of the fractional derivative, α ∈ {0.5, 0.6, 0.7, 0.8, 0.9, 1.0}, are varied. Some patterns produced by the coupled system are constrained by the network architecture, but other features are only understood in the light of the internal dynamics of each cell, in this case, the Chen oscillator. What is more important, architecture and/or internal dynamics?

Impact of dams and irrigation schemes in Anopheline (Diptera: Culicidae) bionomics and malaria epidemiology

Irrigation schemes and dams have posed a great concern on public health systems of several countries, mainly in the tropics. The focus of the present review is to elucidate the different ways how these human interventions may have an effect on population dynamics of anopheline mosquitoes and hence, how local malaria transmission patterns may be changed. We discuss different studies within the three main tropical and sub-tropical regions (namely Africa, Asia and the Pacific and the Americas). Factors such as pre-human impact malaria epidemiological patterns, control measures, demographic movements, human behaviour and local Anopheles bionomics would determine if the implementation of an irrigation scheme or a dam will have negative effects on human health. Some examples of successful implementation of control measures in such settings are presented. The use of Geographic Information System as a powerful tool to assist on the study and control of malaria in these scenarios is also highlighted.