Fractional dynamics in financial indexes

The goal of this study is the analysis of the dynamical properties of financial data series from 32 worldwide stock market indices during the period 2000–2009 at a daily time horizon. Stock market indices are examples of complex interacting systems for which a huge amount of data exists. The methods and algorithms that have been explored for the description of physical phenomena become an effective background in the analysis of economical data. In this perspective are applied the classical concepts of signal analysis, Fourier transform and methods of fractional calculus. The results reveal classification patterns typical of fractional dynamical systems.

And I say to myself: “What a fractional world!”

This paper discusses several complex systems in the perspective of fractional dynamics. For prototype systems are considered the cases of deoxyribonucleic acid decoding, financial evolution, earthquakes events, global warming trend, and musical rhythms. The application of the Fourier transform and of the power law trendlines leads to an assertive representation of the dynamics and to a simple comparison of their characteristics. Moreover, the gallery of different systems, both natural and man made, demonstrates the richness of phenomena that can be described and studied with the tools of fractional calculus.

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.

Fractional-order impulse response of the respiratory system

This paper presents the measurement, frequency-response modeling and identification, and the corresponding impulse time response of the human respiratory impedance and admittance. The investigated adult patient groups were healthy, diagnosed with chronic obstructive pulmonary disease and kyphoscoliosis, respectively. The investigated children patient groups were healthy, diagnosed with asthma and cystic fibrosis, respectively. Fractional order (FO) models are identified on the measured impedance to quantify the respiratory mechanical properties. Two methods are presented for obtaining and simulating the time-domain impulse response from FO models of the respiratory admittance: (i) the classical pole-zero interpolation proposed by Oustaloup in the early 90s, and (ii) the inverse discrete Fourier Transform (DFT). The results of the identified FO models for the respiratory admittance are presented by means of their average values for each group of patients. Consequently, the impulse time response calculated from the frequency response of the averaged FO models is given by means of the two methods mentioned above. Our results indicate that both methods provide similar impulse response data. However, we suggest that the inverse DFT is a more suitable alternative to the high order transfer functions obtained using the classical Oustaloup filter. Additionally, a power law model is fitted on the impulse response data, emphasizing the intrinsic fractal dynamics of the respiratory system.

Sistema automático de identificação e caracterização de zonas de actividade em imagens solares

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para obtenção do grau de Mestre em Engenharia Electrotécnica e Computadores

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.

Uma infra-estrutura computacional para aumentar objectos reais com informação adicional

Dissertação apresentada na Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa para a obtenção do grau de Mestre em Engenharia Informática

Particle swarm optimization: dynamical analysis through fractional calculus

This chapter considers the particle swarm optimization algorithm as a system, whose dynamics is studied from the point of view of fractional calculus. In this study some initial swarm particles are randomly changed, for the system stimulation, and its response is compared with a non-perturbed reference response. The perturbation effect in the PSO evolution is observed in the perspective of the fitness time behaviour of the best particle. The dynamics is represented through the median of a sample of experiments, while adopting the Fourier analysis for describing the phenomena. The influence upon the global dynamics is also analyzed. Two main issues are reported: the PSO dynamics when the system is subjected to random perturbations, and its modelling with fractional order transfer functions.

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.

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

Production, purification and characterisation of polysaccharides from pleurotus ostreatus with antitumor activity

Background: Mushroom polysaccharides play an important role in functional foods because they exhibit biological modulator properties such as antitumour, antiviral and antibacterial activities. The present study involved the production, purification and characterisation of intracellular and extracellular free and protein-bound polysaccharides from Pleurotus ostreatus and the investigation of their growth-inhibitory effect on human carcinoma cell lines. Results: Several fermentation parameters were obtained: batch polysaccharide productivities of 0.013 +/- 8.12 x 10-5 and 0.037 +/- 0.0005 g L-1 day-1 for intracellular and extracellular polysaccharides respectively, a maximum biomass concentration of 9.35 +/- 0.18 g L-1, Pmax = 0.935 +/- 0.018 g L-1 day-1, µmax = 0.218 +/- 0.02 day-1, YEP/X = 0.040 +/- 0.0015 g g-1 and YIP/X = 0.014 +/- 0.0003 g g-1. Some polysaccharides exhibited superoxide dismutase (SOD)-like activity of 50-200 units. Fourier transform infrared analysis of the polysaccharides revealed absorption bands characteristic of such biological macromolecules. Cytotoxicity assays showed that both intracellular and extracellular polysaccharides exhibited antitumour activity towards several tested human carcinoma cell lines in a dose-dependent manner. Conclusion - The polysaccharides of P. ostreatus exhibited high SOD-like activity, which strongly supports their biological effect on tumour cell lines. The extracellular polysaccharides presented the highest antitumour activity towards the RL95 carcinoma cell line and should be further investigated as an antitumour agent.

Complex dynamics in the trajectory control of redundant manipulators

Redundant manipulators allow the trajectory optimization, the obstacle avoidance, and the resolution of singularities. For this type of manipulators, the kinematic control algorithms adopt generalized inverse matrices that may lead to unpredictable responses. Motivated by these problems this paper studies the complexity revealed by the trajectory planning scheme when controlling redundant manipulators. The results reveal fundamental properties of the chaotic phenomena and give a deeper insight towards the development of superior trajectory control algorithms.

Paracoccidioidomicose pulmonar agressiva, endotraqueíte estenosante e cor-pulmonale subagudo: descrição de um caso

A paracoccidioidomicose (Pbmicose) atinge os pulmões pela via inalatória, onde se estabelece o complexo primário semelhante ao da tuberculose. A traquéia comprometida pela via tubohemolinfática desenvolveria reação inflamatória em processo granulomatoso levando à obstrução estenosante com asíixia. Acompanhou-se um doente, masculino, 32 anos, branco, natural de Sarutaiá (SP), lavrador, que há 8 meses desenvolveu tosse expectorativa branco-amarelada, diária, sem fatores de melhora ou piora e dispnéia inicial discreta. Há 4 meses, anorexia, fraqueza e astenia. Há 1 mês a dispneia se agravou. Perdeu 15 kg. Tabagista e etilista há 16 anos. Exame físico revelou: PA — 10/7 mmHg, FR = 28 bpm, peso 31 kg, hipocratismo digital e hipotrofia muscular Tórax enfisematoso e síndrome obstrutivo aos testes de função pulmonar. Coração: P2 desdobrada e hiperfonética. Hepatesplenomegalia. Desenvolveu cor-pulmonale e insuficiência adrenal à internação, evoluindo após 45 dias para óbito em insuficiência respiratória aguda asfixiante, apesar da terapia antifúngica ter sido completa. A literatura médica revista não mostrou registro de caso semelhante de cor-pulmonale e insuficiência adrenal de evolução subaguda.

Fractional dynamics in the trajectory control of redundant manipulators

Under the pseudoinverse control, robots with kinematical redundancy exhibit an undesirable chaotic joint motion which leads to an erratic behavior. This paper studies the complexity of fractional dynamics of the chaotic response. Fourier and wavelet analysis provides a deeper insight, helpful to know better the lack of repeatability problem of redundant manipulators. This perspective for the study of the chaotic phenomena will permit the development of superior trajectory control algorithms.