Designing Limit-Cycle Suppressor Using Dithering and Dual-Input Describing Function Methods

This paper described a method to design a limit-cycle suppressor. The dithering technique was used to eliminate self-sustained oscillations or limit cycles. Otherwise, the Dual Input Describing Function (DIDF) method was applied to design dither parameters and analyze the existence of limit cycles. This method was done in a nonlinear system with relay nonlinearity using three standard dither signals, namely sine, triangle, and square waves. The aim of choosing varying dithers was to investigate the effect of dither shapes and the minimum amplitude required for the quenching strategy. First, the possibility and amplitude of limit cycles were determined graphically on the DIDF curve. Then, the minimum amplitude of dither was calculated based on the DIDF analysis. Finally, a simulation was built to verify the analytical work using a digital computer. The simulation results were related to the analysis results. It was evident that the dithering technique is a simple way to suppress limit cycles in a nonlinear system. This paper also presented that dither is an amplitude function, and square-wave dither has the minimum amplitude to quench limit cycles.

Detection of crossover points in detrended fluctuation analysis: An application to EEG signals of patients with epilepsy

Motivation The quantification of long-range correlation of electroencephalogram (EEG) signals is an important research direction for its relevance in helping understanding the brain activity. Epileptic seizures have been studied in the past years where different non-linear statistical approaches have been employed to understand the relationship between the EEG signal and the epilepitc discharge. One of the most widely used method for to analyse long memory processes is the detrended fuctuation analysis (DFA). However, no objective and pragmatic methods have been developed to detect crossover points and reference channels in DFA. Results In this paper, we propose: (i) two automatic approaches that successfully detect crossover points in DFA related methods on the log-log plot; and (ii) a criteria to choose the reference channel for the log-amplitude function. Moreover, the DFA is applied to EEG signals of 10 epileptic patients collected from the CHB-MIT database, being the log-amplitude function used to compare the different brain hemispheres by making use of the methodology proposed in the paper. The existence of long-range power-law correlations is demonstrated and indicates that the EEG signals of epileptic patients present three well defined regions with the first region showing a 1/f 1/f noise (pink noise) for seven subjects and a random walk behaviour for three subjects. The second and third regions show anti-persistence behaviour. Moreover, the results of the log-amplitude function were divided in two groups: (i) the first, including seven subjects, where the increase in the scales results in an increase in the fluctuation in the the frontal channels; and (ii) the second, included three subjects, where the fluctuation for large scales are greater for the parietal channels. Availability The functions used in this paper are available in the R package DFA (Mesquita et al., 2020). Supplementary information Supplementary information are available at Bioinformatics online.

MODELING FOR THE APPLICATION OF ANALYTIC SIGNALS OF MAGNETIC GRADIENT TENSOR TO DETERMINE BOUNDARIES OF SOURCE

The analytic signals of the magnetic tensor gradient within two-and three-dimensional space can be applied as a useful tool to estimate the depth and position sources because its value characteristics only depend on location but magnetization direction of the sources of the magnetic anomaly [7]. In this paper, we present results of the study for application of the combination of derivatives of directional analytic signals of the magnetic tensor gradient to determine the edges of the sources through the new function Edge-detector (|ED|). Algorithms and programs written in the Matlab language have been used for test calculation on 3D models in correlative comparison with the method using the amplitude function of analytic signals ([2]). The calculation results showed the advantages of the new function |ED| and its applicability in determing the boundaries of sources of magnetic anomaly.

On Einstein’s Program and Quantum Mechanics

<p class="1Body">The Einstein’s program forms a consistent system for universe description, beside the standard model of particles. It is founded upon a scalar field propagating at speed of light c, which constitutes a common relativist framework for classical and quantum properties of matter and interactions. Matter corresponds to standing waves. Classical domain corresponds to geometrical optics approximation, when frequencies are infinitely high, and then hidden. Quantum domain corresponds to wave optics approximation. Adiabatic variations of frequencies yield electromagnetic interaction. They lead also to Classical and Quantum Mechanics equations, with unification of first and second quantifications for interactions and matter, and to the wave-particle duality, by space reduction of the introduced space-like amplitude function u(r,t), which completes the usual time-like function ψ(r,t).</p>