Estimating Attractor Dimension on the Nonlinear Pendulum Time Series

Chaotic dynamical systems exhibit trajectories in their phase space that converges to a strange attractor. The strangeness of the chaotic attractor is associated with its dimension in which instance it is described by a noninteger dimension. This contribution presents an overview of the main definitions of dimension discussing their evaluation from time series employing the correlation and the generalized dimension. The investigation is applied to the nonlinear pendulum where signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the time series. State space reconstruction and the determination of attractor dimensions are carried out regarding periodic and chaotic signals. Results obtained from time series analyses are compared with a reference value obtained from the analysis of mathematical model, estimating noise sensitivity. This procedure allows one to identify the best techniques to be applied in the analysis of experimental data.

Non-Linear Unsteady Aerodynamic Response Approximation Using Multi-Layer Functionals

Non-linear functional representation of the aerodynamic response provides a convenient mathematical model for motion-induced unsteady transonic aerodynamic loads response, that accounts for both complex non-linearities and time-history effects. A recent development, based on functional approximation theory, has established a novel functional form; namely, the multi-layer functional. For a large class of non-linear dynamic systems, such multi-layer functional representations can be realised via finite impulse response (FIR) neural networks. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process in which a limited sample of system input-output data sets is presented to the temporal neural network. The present work describes a procedure for the systematic identification of parameterised neural network models of motion-induced unsteady transonic aerodynamic loads response. The training process is based on a conventional genetic algorithm to optimise the network architecture, combined with a simplified random search algorithm to update weight and bias values. Application of the scheme to representative transonic aerodynamic loads response data for a bidimensional airfoil executing finite-amplitude motion in transonic flow is used to demonstrate the feasibility of the approach. The approach is shown to furnish a satisfactory generalisation property to different motion histories over a range of Mach numbers in the transonic regime.

Floristic and vegetation structure of a granitic grassland in Southern Brazil

A floristic and structural survey of a natural grassland community was conducted on Morro do Osso, a granitic hill in Porto Alegre, RS, Brazil. Structural data were surveyed in 39 one square meter plots placed over two major grassland areas. An accidental fire has occurred in one of the areas approximately one year prior to our survey, leading to further analysis of parameters differences between sites. The floristic list contains 282 species, whereas the structural survey has found 161 species. Families with highest accumulated importance values were Poaceae, Asteraceae and Fabaceae. The diversity and evenness indexes were 4.51 nats ind-1 and 0.86, respectively. Cluster analysis denoted two groups coinciding with the areas distinguished by the fire disturbance. A similarity analysis between our data and two other data sets from nearby granitic hills resulted in 28% to 35% similarity, with equivalent species-family distribution and many common dominant species, corroborating the concept of a continuous flora along the South Brazilian granitic hills.

Limited-sampling strategy models for estimating the pharmacokinetic parameters of 4-methylaminoantipyrine, an active metabolite of dipyrone

Bioanalytical data from a bioequivalence study were used to develop limited-sampling strategy (LSS) models for estimating the area under the plasma concentration versus time curve (AUC) and the peak plasma concentration (Cmax) of 4-methylaminoantipyrine (MAA), an active metabolite of dipyrone. Twelve healthy adult male volunteers received single 600 mg oral doses of dipyrone in two formulations at a 7-day interval in a randomized, crossover protocol. Plasma concentrations of MAA (N = 336), measured by HPLC, were used to develop LSS models. Linear regression analysis and a "jack-knife" validation procedure revealed that the AUC0-¥ and the Cmax of MAA can be accurately predicted (R²>0.95, bias <1.5%, precision between 3.1 and 8.3%) by LSS models based on two sampling times. Validation tests indicate that the most informative 2-point LSS models developed for one formulation provide good estimates (R²>0.85) of the AUC0-¥ or Cmax for the other formulation. LSS models based on three sampling points (1.5, 4 and 24 h), but using different coefficients for AUC0-¥ and Cmax, predicted the individual values of both parameters for the enrolled volunteers (R²>0.88, bias = -0.65 and -0.37%, precision = 4.3 and 7.4%) as well as for plasma concentration data sets generated by simulation (R²>0.88, bias = -1.9 and 8.5%, precision = 5.2 and 8.7%). Bioequivalence assessment of the dipyrone formulations based on the 90% confidence interval of log-transformed AUC0-¥ and Cmax provided similar results when either the best-estimated or the LSS-derived metrics were used.

Modeling the pressure inactivation dynamics of Escherichia coli

Escherichia coli, as a model microorganism, was treated in phosphate-buffered saline under high hydrostatic pressure between 100 and 300 MPa, and the inactivation dynamics was investigated from the viewpoint of predictive microbiology. Inactivation data were curve fitted by typical predictive models: logistic, Gompertz and Weibull functions. Weibull function described the inactivation curve the best. Two parameters of Weibull function were calculated for each holding pressure and their dependence on holding pressure was obtained by interpolation. With the interpolated parameters, inactivation curves were simulated and compared with the experimental data sets.