A Fast Method for Detecting Interdependence between Time Series and Its Directionality

We propose a fast nonlinear method for assessing quantitatively both the existence and directionality of linear and nonlinear couplings between a pair of time series. We test this method, called Boolean Slope Coherence (BSC), on bivariate time series generated by various models, and compare our results with those obtained from different well-known methods. A similar approach is employed to test the BSC’s capability to determine the prevalent coupling directionality. Our results show that the BSC method is successful for both quantifying the coupling level between a pair of signals and determining their directionality. Moreover, the BSC method also works for noisy as well as chaotic signals and, as an example of its application to real data, we tested it by analyzing neurophysiological recordings from visual cortices.

THE INFLUENCE OF FORWARD SPEED AND NONLINEARITIES ON THE DYNAMIC BEHAVIOUR OF A CONTAINER SHIP IN REGULAR WAVES

The aim of this paper is to compare the heave and pitch motions for the S175 containership, travelling in head regular waves, obtained from frequency domain linear and time domain partly nonlinear potential flow analyses. The frequency domain methods comprise the pulsating and the translating, pulsating Green’s function methods, with the relevant source distribution over the mean wetted surface of the hull. The time domain method uses the radiation and diffraction potentials related to the mean wetted surface, implemented using Impulse Response Functions (IRF), whilst the incident wave and restoring actions are evaluated on the instantaneous wetted surface. The calculations are carried out for a range of Froude numbers, and in the case of the partly nonlinear method for different wave steepness values. Comparisons are made with available experimental measurements. The discussion focuses on the necessity for a nonlinear approach for predicting the radiation potential and the possible numerical methods for its formulation.

Laser Opto-Electronic Oscillator and the Modulation of a Laser Emission

The autonomous optoelectronic generator (OEO) is considered in the chapter as a source of low-noise oscillations. Differential equations are considered and methods with OEO modulation with direct and external modulation are analyzed. The complexity of both approaches is related to the non-standard way of description of the nonlinear method modulation for the internal (direct) structure and the utilization of the specific Mach-Zehnder modulator for the first stage on external modulation. The purpose of the presentation is to consider the main features of OEO as a low-noise generator. This includes consideration based on the study of differential equations, the study of transients in OEO, and the calculation of phase noise. It is shown that different types of fibers with low losses at small bending radii can be used as a FOLD in OEO. The important role of the choice of a coherent laser for OEO with a small spectral line width is shown. The prospects of using structured fibers with low losses at bends of less than 10 mm in OEO are described. The results of modeling dynamic processes in OEO with direct modulation are presented.

Linear and non-linear regression analysis for the biosorption kinetics of methylene blue

The nonviable biomass of Rhizopus sp. R-18, Penicillium candidum and Penicillium chrysogenum was studied for biosorption of methylene blue (MB). The sorption of MB was studied be performing batch kinetic experiments. Kinetic measurements showed that sorption of MB reached equilibrium in 4 hours. The batch sorption models, based on a pseudo-first, pseudo-second and pseudo-nth order were applied to predict the rate constant of sorption and the equilibrium capacity. The linear and nonlinear least-square methods were used to obtain the kinetic parameters. The best-fit model was identified using statistic analysis. The results showed that both linear and nonlinear form of pseudo- second order expression could be used to fit the experimental data but nonlinear method may be a better way to obtain the desired parameters. As well the pseudo n-th order kinetic model was successfully applied to the kinetic data. The order (n) of adsorption reaction was found for all employed biosorbents: for Rhizopus sp. R-18 it had value 3.1, P. candidum 3.0 and P. chrysogenum 3.8.

Application of nonlinear analysis for the assessment of gait in patients with Parkinson’s disease

BACKGROUND: Gait can be affected by diseases such as Parkinson’s disease (PD), which lead to alterations like shuffle gait or loss of balance. PD diagnosis is based on subjective measures to generate a score using the Unified Parkinson’s Disease Rating Scale (UPDRS). To improve clinical assessment accuracy, gait analysis can utilise linear and nonlinear methods. A nonlinear method called the Lyapunov exponent (LE) is being used to identify chaos in dynamic systems. This article presents an application of LE for diagnosing PD. OBJECTIVE: The objectives were to use the largest Lyapunov exponents (LaLyEx), sample entropy (SampEn) and root mean square (RMS) to assess the gait of subjects diagnosed with PD; to verify the applicability of these parameters to distinguish between people with PD and healthy controls (CO); and to differentiate subjects within the PD group according to the UPDRS assessment. METHODS: The subjects were divided into the CO group (n= 12) and the PD group (n= 14). The PD group was also divided according to the UPDRS score: UPDRS 0 (n= 7) and UPDRS 1 (n= 7). Kinematic data of lower limbs were measured using inertial measurement units (IMU) and nonlinear parameters (LaLyEx, SampEn and RMS) were calculated. RESULTS: There were significant differences between the CO and PD groups for RMS, SampEn and the LaLyEx. After dividing the PD group according to the UPDRS score, there were significant differences in LaLyEx and RMS. CONCLUSIONS: The selected parameters can be used to distinguish people with PD from CO subjects, and separate people with PD according to the UPDRS score.

Survey of Eight Modern Methods of Hamiltonian Mechanics

Here we describe eight new methods, arisen in the last 60 years, to study solutions of a Hamiltonian system with n degrees of freedom. The first six of them are intended for systems with small parameters or without them. The methods allow to find families of periodic solutions and families of invariant n-dimensional tori by means of analytic computation near a stationary solution, near a periodic solution and near an invariant torus, using the corresponding normal form of a Hamiltonian. Then we can continue the founded families by means of numerical computation. In a Hamiltonian system without parameters, only periodic solutions and invariant n-dimensional tori form one-parameter families. The last two methods are intended for systems with not small parameters, which do not depend on time. They allow computing sets of parameters, which guarantee the stability of some solutions for linear (method seven) and nonlinear (method eight) systems. We do not consider chaotic behaviors, but only regular ones.

Tracking ankle joint movements during gait cycle via control of functional electrical stimulation

Functional electrical stimulation (FES) is an effective method to induce muscle contraction and to improve movements in individuals with injured central nervous system. In order to develop the FES systems for an individual with gait impairment, an appropriate control strategy must be designed to accurate tracking performance. The goal of this study is to present a method for designing proportional-derivative (PD) and sliding mode controllers (SMC) for the FES applied to the musculoskeletal model of an ankle joint to track the desired movements obtained by experiments on two healthy individuals during the gait cycle. Simulation results of the developed controller on musculoskeletal model of the ankle joint illustrated that the SMC is able to track the desired movements more accurately than the PD controller and prevents oscillating patterns around the experimentally measured data. Therefore, the sliding mode as the nonlinear method is more robust in face to unmodeled dynamics and model errors and track the desired path smoothly. Also, the required control effort is smoother in SMC with respect to the PD controller because of the nonlinearity.

New Tuning Approach of Fuzzy Logic System Using Proportional Integral Observer for Tracking a Nonlinear System

Proportional integral observer (PIO) for tracking a nonlinear method has a lower sentiency to cipher the state and output variables. So a more nonlinear controller has to be else to control to activity. In this paper, a fuzzy logic (FLC) controller has been added to the PIO to meliorate the calculation transmute. A fuzzy proportional integral observer (FPIO) for following a nonlinear system has been premeditated to decimate the susceptibleness to cipher the tell and turnout variables with the existent posit and product variables. The FPIO controller has been tested for improving the estimation control using a nonlinear quarter vehicle active suspension system with a nonlinear hydraulic actuator. A comparison simulation of the proposed nonlinear system for estimating the state variables and tracking the output (suspension deflection) with a set point bump road disturbance using FPIO and PIO. The comparison simulation result shows that the estimated state variables and system output match the actual ones perfectly using a fuzzy PIO controller.

Determination of Parameters for an Entropy-Based Atrial Fibrillation Detector

Entropy algorithm is an important nonlinear method for cardiovascular disease detection due to its power in analyzing short-term time series. In previous a study, we proposed a new entropy-based atrial fibrillation (AF) detector, i.e., EntropyAF, which showed a high classification accuracy in identifying AF and non-AF rhythms. As a variation of entropy measures, EntropyAF has two parameters that need to be initialized before the calculation: (1) tolerance threshold r and (2) similarity weight n. In this study, a comprehensive analysis for the two parameters determination was presented, aiming to achieve a high detection accuracy for AF events. Data were from the MIT-BIH AF database. RR interval recordings were segmented using a 30-beat time window. The parameters r and n were initialized from a relatively small value, then gradually increased, and finally the best parameter combination was determined using grid searching. AUC (area under curve) values from the receiver operator characteristic curve (ROC) were compared under different parameter combinations of parameters r and n, and the results demonstrated that the selection of these two parameters plays an important role in AF/non-AF classification. Small values of parameters r and n can lead to a better detection accuracy than other selections. The best AUC value for AF detection was 98.15%, and the corresponding parameter combinations for EntropyAF were as follows: r = 0.01, n = 0.0625, 0.125, 0.25, or 0.5; r = 0.05 and n = 0.0625, 0.125, or 0.25; and r = 0.10 and n = 0.0625 or 0.125.

Detecting hydrological connectivity using causal inference from time-series: synthetic and real karstic study cases

We investigate the potential of causal inference methods (CIMs) to reveal hydrological connections from time-series. Four CIMs are selected from two criteria, linear or nonlinear, and bivariate or multivariate. A priori, multivariate and nonlinear CIMs are best suited for revealing hydrological connections because they suit nonlinear processes and deal with confounding factors such as rainfall, evapotranspiration, or seasonality. The four methods are applied to a synthetic case and a real karstic study case. The synthetic experiment indicates that, unlike the other methods, the multivariate nonlinear framework has a low false-positive rate and allows for ruling out a connection between two disconnected reservoirs forced with similar effective precipitation. However, the multivariate nonlinear method appears unstable when it comes to real cases, making the overall meaning of the causal links uncertain. Nevertheless, all CIMs bring valuable insights into the system’s dynamics, making them a cost-effective and recommendable tool for exploring data. Still, causal inference remains attached to subjective choices and operational constraints while building the dataset or constraining the analysis. As a result, the robustness of the conclusions that the CIMs can draw deserves to be questioned, especially with real and imperfect data. Therefore, alongside research perspectives, we encourage a flexible, informed, and limit-aware use of CIMs, without omitting any other approach that aims at the causal understanding of a system.