Fractional Dynamics Representation in the Pseudo Phase Plane

Proceedings of the 10th Conference on Dynamical Systems Theory and Applications

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.

Fractional Dynamics and Control of Distributed Parameter 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 chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of some distributed parameter systems.

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

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.

Molecular screening of Plasmodium sp. asymptomatic carriers among transfusion centers from Brazilian Amazon region

The transmission of malaria in Brazil is heterogeneous throughout endemic areas and the presence of asymptomatic Plasmodium sp. carriers (APCs) in the Brazilian Amazon has already been demonstrated. Malaria screening in blood banks is based on the selection of donors in respect to possible risks associated with travel or residence, clinical evidence and/or inaccurate diagnostic methods thereby increasing the probability of transfusion-transmitted infection. We evaluated the frequency of APCs in four blood services in distinct areas of the Brazilian Amazon region. DNA was obtained from 400 human blood samples for testing using the phenol-chloroform method followed by a nested-PCR protocol with species-specific primers. The positivity rate varied from 1 to 3% of blood donors from the four areas with an average of 2.3%. All positive individuals had mixed infections for Plasmodium vivax and Plasmodium falciparum. No significant differences in the results were detected among these areas; the majority of cases originated from the transfusion centres of Porto Velho, Rondônia State and Macapá, Amapá State. Although it is still unclear whether APC individuals may act as reservoirs of the parasite, efficient screening of APCs and malaria patients in Brazilian blood services from endemic areas needs to be improved.

Replacement of HIV p24 Ag test by a multiplex RT-PCR method for primary screening of blood donors

Nucleic Acid Testing (NAT) as a tool for primary screening of blood donors became a reality in the end of the 1990 decade. We report here the development of an "in-house" RT-PCR method that allows the simultaneous (multiplex) detection of HCV and HIV-RNA in addition to an artificial RNA employed as an external control. This method detects all HIV group M subtypes, plus group N and O, with a detection threshold of 500 IU/mL. After validation, the method replaced p24 Ag testing, in use for blood donation screening since 1996 at our services. From July 2001 to February 2006, 102,469 donations were tested and 41 (0.04%) were found HIV-RNA reactive. One NAT-only reactive donation (antibody non-reactive) was observed, with subsequent seroconversion of the implied donor, giving a yield of 1:102,469. This rate is in contrast to the international experience that reports a detection of approximately 1:600,000 - 1:3,100,000 of isolated HIV-RNA donations.

Primary screening of blood donors by nat testing for HCV-RNA: development of an "in-house" method and results

An "in-house" RT-PCR method was developed that allows the simultaneous detection of the RNA of the Hepatitis C Virus (HCV) and an artificial RNA employed as an external control. Samples were analyzed in pools of 6-12 donations, each donation included in two pools, one horizontal and one vertical, permitting the immediate identification of a reactive donation, obviating the need for pool dismembering. The whole process took 6-8 hours per day and results were issued in parallel to serology. The method was shown to detect all six HCV genotypes and a sensitivity of 500 IU/mL was achieved (95% hit rate). Until July 2005, 139,678 donations were tested and 315 (0.23%) were found reactive for HCV-RNA. Except for five false-positives, all 310 presented the corresponding antibody as well, so the yield of NAT-only donations was zero, presenting a specificity of 99.83%. Detection of a window period donation, in the population studied, will probably demand testing of a larger number of donations. International experience is showing a rate of 1:200,000 - 1:500,000 of isolated HCV-RNA reactive donations.

Symmetry and order parameter dynamics of the human odometer

Bipedal gaits have been classified on the basis of the group symmetry of the minimal network of identical differential equations (alias cells) required to model them. Primary bipedal gaits (e.g., walk, run) are characterized by dihedral symmetry, whereas secondary bipedal gaits (e.g., gallop-walk, gallop- run) are characterized by a lower, cyclic symmetry. This fact has been used in tests of human odometry (e.g., Turvey et al. in P Roy Soc Lond B Biol 276:4309–4314, 2009, J Exp Psychol Hum Percept Perform 38:1014–1025, 2012). Results suggest that when distance is measured and reported by gaits from the same symmetry class, primary and secondary gaits are comparable. Switching symmetry classes at report compresses (primary to secondary) or inflates (secondary to primary) measured distance, with the compression and inflation equal in magnitude. The present research (a) extends these findings from overground locomotion to treadmill locomotion and (b) assesses a dynamics of sequentially coupled measure and report phases, with relative velocity as an order parameter, or equilibrium state, and difference in symmetry class as an imperfection parameter, or detuning, of those dynamics. The results suggest that the symmetries and dynamics of distance measurement by the human odometer are the same whether the odometer is in motion relative to a stationary ground or stationary relative to a moving ground.

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?

Specificity and Sensitivity of Screening for Anti-HLA Antibodies in Kidney Allograft Dysfunction

BACKGROUND: Prospective testing for posttransplant circulating anti-HLA antibodies seems to be a critical noninvasive tool, but confirmatory data are lacking. MATERIALS AND METHODS: Over the last 3 years, peritubular capillary (PTC) C4d deposition was prospectively sought by an immunofluorescence technique applied to frozen tissue in biopsies obtained for allograft dysfunction. Screening for circulating anti-HLA class I/II alloantibodies (AlloAb) by the flow cytometric test was performed simultaneously. RESULTS: We evaluated 132 sets of biopsies and simultaneous serum samples. PTC C4d deposition was demonstrated in 15.9% (21/132) of biopsies. Circulating anti-HLA I/II AlloAb were detected in 25% (33/132) of serum samples. Employing receiver-operator characteristic (ROC) curves for all C4d-positive biopsies, screening for AlloAb showed a global specificity of 82% and sensitivity of 61.9%. When this analysis was restricted to biopsies obtained in the first month posttransplantation, the sensitivity increased to 81.8%, but the specificity decreased to 76.9%. After the first month posttransplantation, we observed sensitivity of 40.0% and a specificity of 86.4%. In the first month posttransplantation, all patients with a diagnosis of acute antibody-mediated rejection displayed circulating anti-HLA class I/II, but not always at the same time as the C4d-positive biopsy. CONCLUSIONS: In the first month posttransplantation, prospective monitoring of anti-HLA antibodies may be useful. The high sensitivity allows the identification of patients at risk, affording an earlier diagnosis of antibody-mediated rejection. After the first month, the test can be used to evaluate allograft dysfunction episodes, since positivity is highly suggestive of an antibody-mediated process.

Simulation of masonry out-of-plane failure modes by multi-body dynamics

The seismic assessment of the local failure modes in existing masonry buildings is currently based on the identification of the so-called local mechanisms, often associated with the out-of-plane wall behavior, whose stability is evaluated by static force-based approaches and, more recently, by some displacement-based proposals. Local mechanisms consist of kinematic chains of masonry portions, often regarded as rigid bodies, with geometric nonlinearity and concentrated nonlinearity in predefined contact regions (unilateral no-tension behavior, possible sliding with friction). In this work, the dynamic behavior of local mechanisms is simulated through multi-body dynamics, to obtain the nonlinear response with efficient time history analyses that directly take into account the characteristics of the ground motion. The amplification/filtering effects of the structure are considered within the input motion. The proposed approach is validated with experimental results of two full-scale shaking-table tests on stone masonry buildings: a sacco-stone masonry façade tested at Laboratório Nacional de Engenharia Civil and a two-storey double-leaf masonry building tested at European Centre for Training and Research in Earthquake Engineering (EUCENTRE).

Peritubular Capillaries C4d Deposits in Renal Allograft Biopsies and Anti HLA I/II Alloantibodies Screening. Incidence and Clinical Importance

Aim: To characterise clinically the patients with C4d in peritubular capillaries deposits (C4dPTCD) and/or circulating anti-HLA class I/II alloantibodies. To determine the correlation between positive C4dPTCD and circulating anti-HLA class I/II alloantibodies during episodes of graft dysfunction. Subjects and Methods: C4d staining was performed in biopsies with available frozen tissue obtained between January 2004 and December 2006. The study was prospective from March 2005, when a serum sample was obtained at the time of biopsy to detect circulating anti-HLA class I/II alloantibodies. Results: We studied 109 biopsies in 86 cadaver renal transplant patients. Sixteen of these (14.7%) presented diffuse positive C4dPTCD. There was a 13.5% rate of +C4dPTCD incidence within the first six months of transplantation and 16% after six months (p>0.05). Half of the +C4dPTCD in the first six months was associated with acute humoral rejection. After six months, the majority of +C4dPTCD (n=7/8) was present in biopsies with evidence of interstitial fibrosis/tubular atrophy and/or transplant glomerulopathy. The C4dPTCD was more frequent in patients with positive anti-HCV antibodies(p<0.0001), a previous renal transplant (p=0.007), and with a panel reactivity antibody (PRA) ≥ 50%(p=0.0098). The anti-HCV+ patients had longer time on dialysis (p=0.0019) and higher PRA(p=0.005). Circulating anti-HLA I/II alloantibodies were screened in 46 serum samples. They were positive in 10.9% of samples, all obtained after six months post transplant. Circulating alloantibodies were absent in 92.5% of the C4d negative biopsies. Conclusion: We found an association between the presence of C4dPTCD and 2nd transplant recipients,higher PRA and the presence of anti-HCV antibodies. The presence of HCV antibodies is not a risk factor for C4dPTCD per se, but appears to reflect longer time on dialysis and presensitisation. In renal dysfunction a negative alloantibody screening is associated with a reduced risk of C4dPTCD (<10%).

Land cover dynamics in Savanna Ecosystem of Borena Ethiopia

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.

Urban land cover change detection analysis and modeling spatio-temporal Growth dynamics using Remote Sensing and GIS Techniques: A case study of Dhaka, Bangladesh

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.