Dynamical analysis of the global warming

Global warming is a major concern nowadays. Weather conditions are changing, and it seems that human activity is one of the main causes. In fact, since the beginning of the industrial revolution, the burning of fossil fuels has increased the nonnatural emissions of carbon dioxide to the atmosphere. Carbon dioxide is a greenhouse gas that absorbs the infrared radiation produced by the reflection of the sunlight on the Earth’s surface, trapping the heat in the atmosphere. Global warming and the associated climate changes are being the subject of intensive research due to their major impact on social, economic, and health aspects of human life. This paper studies the global warming trend in the perspective of dynamical systems and fractional calculus, which is a new standpoint in this context. Worldwide distributed meteorological stations and temperature records for the last 100 years are analysed. It is shown that the application of Fourier transforms and power law trend lines leads to an assertive representation of the global warming dynamics and a simpler analysis of its characteristics.

Power law analysis of financial index dynamics

Power law PL and fractional calculus are two faces of phenomena with long memory behavior. This paper applies PL description to analyze different periods of the business cycle. With such purpose the evolution of ten important stock market indices DAX, Dow Jones, NASDAQ, Nikkei, NYSE, S&P500, SSEC, HSI, TWII, and BSE over time is studied. An evolutionary algorithm is used for the fitting of the PL parameters. It is observed that the PL curve fitting constitutes a good tool for revealing the signal main characteristics leading to the emergence of the global financial dynamic evolution.

Bilirubin directly disrupts membrane lipid polarity and fluidity, protein order, and redox status in rat mitochondria

Background/Aims: Unconjugated bilirubin (UCB) impairs crucial aspects of cell function and induces apoptosis in primary cultured neurones. While mechanisms of cytotoxicity begin to unfold, mitochondria appear as potential primary targets. Methods: We used electron paramagnetic resonance spectroscopy analysis of isolated rat mitochondria to test the hypothesis that UCB physically interacts with mitochondria to induce structural membrane perturbation, leading to increased permeability, and subsequent release of apoptotic factors. Results: Our data demonstrate profound changes on mitochondrial membrane properties during incubation with UCB, including modified membrane lipid polarity and fluidity (P , 0:01), as well as disrupted protein mobility(P , 0:001). Consistent with increased permeability, cytochrome c was released from the intermembrane space(P , 0:01), perhaps uncoupling the respiratory chain and further increasing oxidative stress (P , 0:01). Both ursodeoxycholate, a mitochondrial-membrane stabilising agent, and cyclosporine A, an inhibitor of the permeability transition, almost completely abrogated UCB-induced perturbation. Conclusions: UCB directly interacts with mitochondria influencing membrane lipid and protein properties, redox status, and cytochrome c content. Thus, apoptosis induced by UCB may be mediated, at least in part, by physical perturbation of the mitochondrial membrane. These novel findings should ultimately prove useful to our evolving understanding of UCB cytotoxicity.

An introduction to the fractional continuous-time linear systems

A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.

A CMOS micro power switched-capacitor DC-DC step-up converter for indoor light energy harvesting applications

This paper presents a micro power light energy harvesting system for indoor environments. Light energy is collected by amorphous silicon photovoltaic (a-Si:H PV) cells, processed by a switched capacitor (SC) voltage doubler circuit with maximum power point tracking (MPPT), and finally stored in a large capacitor. The MPPT fractional open circuit voltage (V-OC) technique is implemented by an asynchronous state machine (ASM) that creates and dynamically adjusts the clock frequency of the step-up SC circuit, matching the input impedance of the SC circuit to the maximum power point condition of the PV cells. The ASM has a separate local power supply to make it robust against load variations. In order to reduce the area occupied by the SC circuit, while maintaining an acceptable efficiency value, the SC circuit uses MOSFET capacitors with a charge sharing scheme for the bottom plate parasitic capacitors. The circuit occupies an area of 0.31 mm(2) in a 130 nm CMOS technology. The system was designed in order to work under realistic indoor light intensities. Experimental results show that the proposed system, using PV cells with an area of 14 cm(2), is capable of starting-up from a 0 V condition, with an irradiance of only 0.32 W/m(2). After starting-up, the system requires an irradiance of only 0.18 W/m(2) (18 mu W/cm(2)) to remain operating. The ASM circuit can operate correctly using a local power supply voltage of 453 mV, dissipating only 0.085 mu W. These values are, to the best of the authors' knowledge, the lowest reported in the literature. The maximum efficiency of the SC converter is 70.3 % for an input power of 48 mu W, which is comparable with reported values from circuits operating at similar power levels.

Time-delay and fractional derivatives

This paper proposes the calculation of fractional algorithms based on time-delay systems. The study starts by analyzing the memory properties of fractional operators and their relation with time delay. Based on the Fourier analysis an approximation of fractional derivatives through timedelayed samples is developed. Furthermore, the parameters of the proposed approximation are estimated by means of genetic algorithms. The results demonstrate the feasibility of the new perspective.

Complex-order forced van der Pol oscillator

In this paper we consider a complex-order forced van der Pol oscillator. The complex derivative Dα1jβ, with α, β ∈ ℝ+, is a generalization of the concept of an integer derivative, where α = 1, β = 0. The Fourier transforms of the periodic solutions of the complex-order forced van der Pol oscillator are computed for various values of parameters such as frequency ω and amplitude b of the external forcing, the damping μ, and parameters α and β. Moreover, we consider two cases: (i) b = 1, μ = {1.0, 5.0, 10.0}, and ω = {0.5, 2.46, 5.0, 20.0}; (ii) ω = 20.0, μ = {1.0, 5.0, 10.0}, and b = {1.0, 5.0, 10.0}. We verified that most of the signal energy is concentrated in the fundamental harmonic ω0. We also observed that the fundamental frequency of the oscillations ω0 varies with α and μ. For the range of tested values, the numerical fitting led to logarithmic approximations for system (7) in the two cases (i) and (ii). In conclusion, we verify that by varying the parameter values α and β of the complex-order derivative in expression (7), we accomplished a very effective way of perturbing the dynamical behavior of the forced van der Pol oscillator, which is no longer limited to parameters b and ω.

Complex order van der Pol oscillator

In this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.

Identifying economic periods and crisis with the multidimensional scaling

This paper applied MDS and Fourier transform to analyze different periods of the business cycle. With such purpose, four important stock market indexes (Dow Jones, Nasdaq, NYSE, S&P500) were studied over time. The analysis under the lens of the Fourier transform showed that the indexes have characteristics similar to those of fractional noise. By the other side, the analysis under the MDS lens identified patterns in the stock markets specific to each economic expansion period. Although the identification of patterns characteristic to each expansion period is interesting to practitioners (even if only in a posteriori fashion), further research should explore the meaning of such regularities and target to find a method to estimate future crisis.

Application of fractional controllers for quad rotor

This paper studies the application of fractional algorithms in the control of a quad-rotor rotorcraft. The development of a flight simulator provide the evaluation of the controller algorithm. Several basic maneuvers are investigated, namely the elevation and the position control.

Fractional central pattern generators for bipedal locomotion

Locomotion has been a major research issue in the last few years. Many models for the locomotion rhythms of quadrupeds, hexapods, bipeds and other animals have been proposed. This study has also been extended to the control of rhythmic movements of adaptive legged robots. In this paper, we consider a fractional version of a central pattern generator (CPG) model for locomotion in bipeds. A fractional derivative D α f(x), with α non-integer, is a generalization of the concept of an integer derivative, where α=1. The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a network of four coupled identical oscillators which has dihedral symmetry. We study parameter regions where periodic solutions, identified with legs’ rhythms in bipeds, occur, for 0<α≤1. We find that the amplitude and the period of the periodic solutions, identified with biped rhythms, increase as α varies from near 0 to values close to unity.

Dynamics of the Dow Jones and the NASDAQ stock indexes

The goal of this study is the analysis of the dynamical properties of financial data series from worldwide stock market indices. We analyze the Dow Jones Industrial Average ( ∧ DJI) and the NASDAQ Composite ( ∧ IXIC) indexes at a daily time horizon. The methods and algorithms that have been explored for description of physical phenomena become an effective background, and even inspiration, for very productive methods used in the analysis of economical data. We start by applying the classical concepts of signal analysis, Fourier transform, and methods of fractional calculus. In a second phase we adopt a pseudo phase plane approach.

Application of fractional algorithms in the control of a robotic bird

In this paper, it is studied the dynamics of the robotic bird in terms of time response and robustness. It is analyzed the wing angle of attack and the velocity of the bird, the tail influence, the gliding flight and the flapping flight. The results are positive for the construction of flying robots. The development of computational simulation based on the dynamic of the robotic bird should allow testing strategies and different algorithms of control such as integer and fractional controllers.

An introduction to the fractional continuous- time linear systems: the 21st century systems

IEEE CIRCUITS AND SYSTEMS MAGAZINE, Third Quarter

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7