Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

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.

Fractional State Space Analysis of Economy Systems

This paper examines modern economic growth according to the multidimensional scaling (MDS) method and state space portrait (SSP) analysis. Electing GDP per capita as the main indicator for economic growth and prosperity, the long-run perspective from 1870 to 2010 identifies the main similarities among 34 world partners’ modern economic growth and exemplifies the historical waving mechanics of the largest world economy, the USA. MDS reveals two main clusters among the European countries and their old offshore territories, and SSP identifies the Great Depression as a mild challenge to the American global performance, when compared to the Second World War and the 2008 crisis.

Utilidade do Doppler Tecidular na Predição de Eventos Arrítmicos em Adultos com Tetralogia de Fallot Corrigida

INTRODUCTION: Adults with repaired tetralogy of Fallot (TOF) may be at risk for progressive right ventricular (RV) dilatation and dysfunction, which is commonly associated with arrhythmic events. In frequently volume-overloaded patients with congenital heart disease, tissue Doppler imaging (TDI) is particularly useful for assessing RV function. However, it is not known whether RV TDI can predict outcome in this population. OBJECTIVE: To evaluate whether RV TDI parameters are associated with supraventricular arrhythmic events in adults with repaired TOF. METHODS: We studied 40 consecutive patients with repaired TOF (mean age 35 +/- 11 years, 62% male) referred for routine echocardiographic exam between 2007 and 2008. The following echocardiographic measurements were obtained: left ventricular (LV) ejection fraction, LV end-systolic volume, LV end-diastolic volume, RV fractional area change, RV end-systolic area, RV end-diastolic area, left and right atrial volumes, mitral E and A velocities, RV myocardial performance index (Tei index), tricuspid annular plane systolic excursion (TAPSE), myocardial isovolumic acceleration (IVA), pulmonary regurgitation color flow area, TDI basal lateral, septal and RV lateral peak diastolic and systolic annular velocities (E' 1, A' 1, S' 1, E' s, A' s, S' s, E' rv, A' rv, S' rv), strain, strain rate and tissue tracking of the same segments. QRS duration on resting ECG, total duration of Bruce treadmill exercise stress test and presence of exercise-induced arrhythmias were also analyzed. The patients were subsequently divided into two groups: Group 1--12 patients with previous documented supraventricular arrhythmias (atrial tachycardia, fibrillation or flutter) and Group 2 (control group)--28 patients with no previous arrhythmic events. Univariate and multivariate analysis was used to assess the statistical association between the studied parameters and arrhythmic events. RESULTS: Patients with previous events were older (41 +/- 14 vs. 31 +/- 6 years, p = 0.005), had wider QRS (173 +/- 20 vs. 140 +/- 32 ms, p = 0.01) and lower maximum heart rate on treadmill stress testing (69 +/- 35 vs. 92 +/- 9%, p = 0.03). All patients were in NYHA class I or II. Clinical characteristics including age at corrective surgery, previous palliative surgery and residual defects did not differ significantly between the two groups. Left and right cardiac chamber dimensions and ventricular and valvular function as evaluated by conventional Doppler parameters were also not significantly different. Right ventricular strain and strain rate were similar between the groups. However, right ventricular myocardial TDI systolic (Sa: 5.4+2 vs. 8.5 +/- 3, p = 0.004) and diastolic indices and velocities (Ea, Aa, septal E/Ea, and RV free wall tissue tracking) were significantly reduced in patients with arrhythmias compared to the control group. Multivariate linear regression analysis identified RV early diastolic velocity as the sole variable independently associated with arrhythmic history (RV Ea: 4.5 +/- 1 vs. 6.7 +/- 2 cm/s, p = 0.01). A cut-off for RV Ea of < 6.1 cm/s identified patients in the arrhythmic group with 86% sensitivity and 59% specificity (AUC = 0.8). CONCLUSIONS: Our results suggest that TDI may detect RV dysfunction in patients with apparently normal function as assessed by conventional echocardiographic parameters. Reduction in RV early diastolic velocity appears to be an early abnormality and is associated with occurrence of arrhythmic events. TDI may be useful in risk stratification of patients with repaired tetralogy of Fallot.

Fractional Analysis of the DNA Information

Proceedings of the 12th Conference on 'Dynamical Systems -Theory and Applications'

Fractional Calculus: Application in modeling and control

This contribution introduces the fractional calculus (FC) fundamental mathematical aspects and discuses some of their consequences. Based on the FC concepts, the chapter reviews the main approaches for implementing fractional operators and discusses the adoption of FC in control systems. Finally are presented some applications in the areas of modeling and control, namely fractional PID, heat diffusion systems, electromagnetism, fractional electrical impedances, evolutionary algorithms, robotics, and nonlinear system control.

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.

Electrical Skin Phenomena: A Fractional Calculus Analysis

The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

A Fractional Calculus Perspective in the Evolutionary Design of Combinational Circuits

This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical evaluation.

Design of Digital Fractional-Order Integrators and Differentiators by Least Squares

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

Short-Circuit Impedance of Power Transformers: the Fractional Order Calculus Approach

First IFAC Workshop on Fractional Differentiation and Its Application - 19-21 July 2004, Enseirb, Bordeaux, France - FDA'04

On the Estimation of the Short-Circuit Impedance of Power Transformers Using Fractional Order Calculus

This paper reports investigation on the estimation of the short circuit impedance of power transformers, using fractional order calculus to analytically study the influence of the diffusion phenomena in the windings. The aim is to better characterize the medium frequency range behavior of leakage inductances of power transformer models, which include terms to represent the magnetic field diffusion process in the windings. Comparisons between calculated and measured values are shown and discussed.

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.

Improved Numerical Simulation for a Novel Adaptive Control Using Fractional Order Derivatives

A novel control technique is investigated in the adaptive control of a typical paradigm, an approximately and partially modeled cart plus double pendulum system. In contrast to the traditional approaches that try to build up ”complete” and ”permanent” system models it develops ”temporal” and ”partial” ones that are valid only in the actual dynamic environment of the system, that is only within some ”spatio-temporal vicinity” of the actual observations. This technique was investigated for various physical systems via ”preliminary” simulations integrating by the simplest 1st order finite element approach for the time domain. In 2004 INRIA issued its SCILAB 3.0 and its improved numerical simulation tool ”Scicos” making it possible to generate ”professional”, ”convenient”, and accurate simulations. The basic principles of the adaptive control, the typical tools available in Scicos, and others developed by the authors, as well as the improved simulation results and conclusions are presented in the contribution.