A utilização de transformadas de wavelet e de detrended fluctuation analysis no estudo da microcirculação da pele humana

A Fluxometria por Laser Doppler (LDF) é uma técnica não invasiva usada para medir o fluxo microvascular da pele humana. No fluxo é possível isolar componentes oscilatórias em gamas de frequências características que se encontram relacionadas com as actividades cardíaca, respiratória, miogénica, simpática e metabólica. A LDF permite assim estudar a fisiologia do fluxo sanguíneo. Neste trabalho foram realizadas medições de LDF nos tornozelos de 9 mulheres saudáveis numa situação de restrição à perfusão, usando uma braçadeira nos tornozelos. Os dados foram analisados com Transformada de Wavelet e Detrended Fluctuation Analysis (DFA) de modo a estudar os rácios das amplitudes das componentes de Wavelet e os respectivos expoentes . Estes parâmetros foram comparados nas situações de repouso, de restrição à perfusão e de recuperação após remoção da braçadeira. Observou-se que durante a restrição à perfusão houve um aumento significativo dos rácios de amplitude e dos expoentes a para as componentes cardíaca, respiratória e miogénica, o que pode reflectir vasoconstrição. Os parâmetros da componente metabólica apresentaram uma diminuição que se pode relacionar com variações na libertação de NO por parte do endotélio. Após a libertação da braçadeira, os parâmetros das componentes respiratória, miogénica e metabólica retornaram aos valores iniciais. Aanálise combinada de Wavelet com DFAoferece uma nova visão sobre a regulação do fluxo microvascular.

Correlações nos dfa de diversos perfis geológicos. estudo de caso: Bacia de Campos - RJ

This work aims to study the fluctuation structure of physical properties of oil well profiles. It was used as technique the analysis of fluctuations without trend (Detrended Fluctuation Analysis - DFA). It has been made part of the study 54 oil wells in the Campo de Namorado located in the Campos Basin in Rio de Janeiro. We studied five sections, namely: sonic, density, porosity, resistivity and gamma rays. For most of the profiles , DFA analysis was available in the literature, though the sonic perfile was estimated with the aid of a standard algorithm. The comparison between the exponents of DFA of the five profiles was performed using linear correlation of variables, so we had 10 comparisons of profiles. Our null hypothesis is that the values of DFA for the various physical properties are independent. The main result indicates that no refutation of the null hypothesis. That is, the fluctuations observed by DFA in the profiles do not have a universal character, that is, in general the quantities display a floating structure of their own. From the ten correlations studied only the profiles of density and sonic one showed a significant correlation (p> 0.05). Finally these results indicate that one should use the data from DFA with caution, because, in general, based on geological analysis DFA different profiles can lead to disparate conclusions

Correlações nos dfa de diversos perfis geológicos. estudo de caso: Bacia de Campos - RJ

This work aims to study the fluctuation structure of physical properties of oil well profiles. It was used as technique the analysis of fluctuations without trend (Detrended Fluctuation Analysis - DFA). It has been made part of the study 54 oil wells in the Campo de Namorado located in the Campos Basin in Rio de Janeiro. We studied five sections, namely: sonic, density, porosity, resistivity and gamma rays. For most of the profiles , DFA analysis was available in the literature, though the sonic perfile was estimated with the aid of a standard algorithm. The comparison between the exponents of DFA of the five profiles was performed using linear correlation of variables, so we had 10 comparisons of profiles. Our null hypothesis is that the values of DFA for the various physical properties are independent. The main result indicates that no refutation of the null hypothesis. That is, the fluctuations observed by DFA in the profiles do not have a universal character, that is, in general the quantities display a floating structure of their own. From the ten correlations studied only the profiles of density and sonic one showed a significant correlation (p> 0.05). Finally these results indicate that one should use the data from DFA with caution, because, in general, based on geological analysis DFA different profiles can lead to disparate conclusions

Complexity of human postural control in young and older adults during prolonged standing

Aging is known to have a degrading influence on many structures and functions of the human sensorimotor system. The present work assessed aging-related changes in postural sway using fractal and complexity measures of the center of pressure (COP) dynamics with the hypothesis that complexity and fractality decreases in the older individuals. Older subjects (68 +/- 4 years) and young adult subjects (28 +/- 7 years) performed a quiet stance task (60 s) and a prolonged standing task (30 min) where subjects were allowed to move freely. Long-range correlations (fractality) of the data were estimated by the detrended fluctuation analysis (DFA); changes in entropy were estimated by the multi-scale entropy (MSE) measure. The DFA results showed that the fractal dimension was lower for the older subjects in comparison to the young adults but the fractal dimensions of both groups were not different from a 1/f noise, for time intervals between 10 and 600 s. The MSE analysis performed with the typically applied adjustment to the criterion distance showed a higher degree of complexity in the older subjects, which is inconsistent with the hypothesis that complexity in the human physiological system decreases with aging. The same MSE analysis performed without adjustment showed no differences between the groups. Taken all results together, the decrease in total postural sway and long-range correlations in older individuals are signs of an adaptation process reflecting the diminishing ability to generate adequate responses on a longer time scale.

Ultrasound, eddy current and magnetic Barkhausen noise as tools for sigma phase detection on a UNS S31803 duplex stainless steel

Sigma phase is a deleterious one which can be formed in duplex stainless steels during heat treatment or welding. Aiming to accompany this transformation, ferrite and sigma percentage and hardness were measured on samples of a UNS S31803 duplex stainless steel submitted to heat treatment. These results were compared to measurements obtained from ultrasound and eddy current techniques, i.e., velocity and impedance, respectively. Additionally, backscattered signals produced by wave propagation were acquired during ultrasonic inspection as well as magnetic Barkhausen noise during magnetic inspection. Both signal types were processed via a combination of detrended-fluctuation analysis (DFA) and principal component analysis (PCA). The techniques used were proven to be sensitive to changes in samples related to sigma phase formation due to heat treatment. Furthermore, there is an advantage using these methods since they are nondestructive. (C) 2010 Elsevier B.V. All rights reserved.

Memória de longo prazo nos retornos acionistas dos índices de referência da euronext, implicações para a hipótese de mercados eficientes e contributo fractal para aperfeiçoamento do capital asset pricing model

Não existe uma definição única de processo de memória de longo prazo. Esse processo é geralmente definido como uma série que possui um correlograma decaindo lentamente ou um espectro infinito de frequência zero. Também se refere que uma série com tal propriedade é caracterizada pela dependência a longo prazo e por não periódicos ciclos longos, ou que essa característica descreve a estrutura de correlação de uma série de longos desfasamentos ou que é convencionalmente expressa em termos do declínio da lei-potência da função auto-covariância. O interesse crescente da investigação internacional no aprofundamento do tema é justificado pela procura de um melhor entendimento da natureza dinâmica das séries temporais dos preços dos ativos financeiros. Em primeiro lugar, a falta de consistência entre os resultados reclama novos estudos e a utilização de várias metodologias complementares. Em segundo lugar, a confirmação de processos de memória longa tem implicações relevantes ao nível da (1) modelação teórica e econométrica (i.e., dos modelos martingale de preços e das regras técnicas de negociação), (2) dos testes estatísticos aos modelos de equilíbrio e avaliação, (3) das decisões ótimas de consumo / poupança e de portefólio e (4) da medição de eficiência e racionalidade. Em terceiro lugar, ainda permanecem questões científicas empíricas sobre a identificação do modelo geral teórico de mercado mais adequado para modelar a difusão das séries. Em quarto lugar, aos reguladores e gestores de risco importa saber se existem mercados persistentes e, por isso, ineficientes, que, portanto, possam produzir retornos anormais. O objetivo do trabalho de investigação da dissertação é duplo. Por um lado, pretende proporcionar conhecimento adicional para o debate da memória de longo prazo, debruçando-se sobre o comportamento das séries diárias de retornos dos principais índices acionistas da EURONEXT. Por outro lado, pretende contribuir para o aperfeiçoamento do capital asset pricing model CAPM, considerando uma medida de risco alternativa capaz de ultrapassar os constrangimentos da hipótese de mercado eficiente EMH na presença de séries financeiras com processos sem incrementos independentes e identicamente distribuídos (i.i.d.). O estudo empírico indica a possibilidade de utilização alternativa das obrigações do tesouro (OT’s) com maturidade de longo prazo no cálculo dos retornos do mercado, dado que o seu comportamento nos mercados de dívida soberana reflete a confiança dos investidores nas condições financeiras dos Estados e mede a forma como avaliam as respetiva economias com base no desempenho da generalidade dos seus ativos. Embora o modelo de difusão de preços definido pelo movimento Browniano geométrico gBm alegue proporcionar um bom ajustamento das séries temporais financeiras, os seus pressupostos de normalidade, estacionariedade e independência das inovações residuais são adulterados pelos dados empíricos analisados. Por isso, na procura de evidências sobre a propriedade de memória longa nos mercados recorre-se à rescaled-range analysis R/S e à detrended fluctuation analysis DFA, sob abordagem do movimento Browniano fracionário fBm, para estimar o expoente Hurst H em relação às séries de dados completas e para calcular o expoente Hurst “local” H t em janelas móveis. Complementarmente, são realizados testes estatísticos de hipóteses através do rescaled-range tests R/S , do modified rescaled-range test M - R/S e do fractional differencing test GPH. Em termos de uma conclusão única a partir de todos os métodos sobre a natureza da dependência para o mercado acionista em geral, os resultados empíricos são inconclusivos. Isso quer dizer que o grau de memória de longo prazo e, assim, qualquer classificação, depende de cada mercado particular. No entanto, os resultados gerais maioritariamente positivos suportam a presença de memória longa, sob a forma de persistência, nos retornos acionistas da Bélgica, Holanda e Portugal. Isto sugere que estes mercados estão mais sujeitos a maior previsibilidade (“efeito José”), mas também a tendências que podem ser inesperadamente interrompidas por descontinuidades (“efeito Noé”), e, por isso, tendem a ser mais arriscados para negociar. Apesar da evidência de dinâmica fractal ter suporte estatístico fraco, em sintonia com a maior parte dos estudos internacionais, refuta a hipótese de passeio aleatório com incrementos i.i.d., que é a base da EMH na sua forma fraca. Atendendo a isso, propõem-se contributos para aperfeiçoamento do CAPM, através da proposta de uma nova fractal capital market line FCML e de uma nova fractal security market line FSML. A nova proposta sugere que o elemento de risco (para o mercado e para um ativo) seja dado pelo expoente H de Hurst para desfasamentos de longo prazo dos retornos acionistas. O expoente H mede o grau de memória de longo prazo nos índices acionistas, quer quando as séries de retornos seguem um processo i.i.d. não correlacionado, descrito pelo gBm(em que H = 0,5 , confirmando- se a EMH e adequando-se o CAPM), quer quando seguem um processo com dependência estatística, descrito pelo fBm(em que H é diferente de 0,5, rejeitando-se a EMH e desadequando-se o CAPM). A vantagem da FCML e da FSML é que a medida de memória de longo prazo, definida por H, é a referência adequada para traduzir o risco em modelos que possam ser aplicados a séries de dados que sigam processos i.i.d. e processos com dependência não linear. Então, estas formulações contemplam a EMH como um caso particular possível.

Persistence characteristics in financial prices: evidence from the portuguese stock market returns

The objective of this article is to provide additional knowledge to the discussion of long-term memory, leaning over the behavior of the main Portuguese stock index. The first four moments are calculated using time windows of increasing size and sliding time windows of fixed size equal to 50 days and suggest that daily returns are non-ergodic and non-stationary. Seeming that the series is best described by a fractional Brownian motion approach, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA). The findings indicate evidence of long term memory in the form of persistence. This evidence of fractal structure suggests that the market is subject to greater predictability and contradicts the efficient market hypothesis in its weak form. This raises issues regarding theoretical modeling of asset pricing. In addition, we carried out a more localized (in time) study to identify the evolution of the degree of long-term dependency over time using windows 200-days and 400-days. The results show a switching feature in the index, from persistent to anti-persistent, quite evident from 2010.

Long-term dependence in financial prices: evidence from the Belgian stock market returns

This article aims to contribute to the discussion of long-term dependence, focusing on the behavior of the main Belgian stock index. Non-parametric analyzes of the general characteristics of temporal frequency show that daily returns are non-ergodic and non-stationary. Therefore, we use the rescaled-range analysis (R/S) and the detrended fluctuation analysis (DFA), under the fractional Brownian motion approach, and we found slight evidence of long-term dependence. These results refute the random walk hypothesis with i.i.d. increments, which is the basis of the EMH in its weak form, and call into question some theoretical modeling of asset pricing. Other more localized complementary study, to identify the evolution of the degree of dependence over time windows, showed that the index has become less persistent from 2010. This may mean a maturing market by the extension of the effects of current financial crisis.

Long-term memory in financial prices: evidence from the Dutch stock market returns

Prepared for presentation at the Portuguese Finance Network International Conference 2014, Vilamoura, Portugal, June 18-20

Study of the electromyographic signal dynamic behavior in Amyotrophic Lateral Sclerosis (ALS)

Amyotrophic Lateral Sclerosis (ALS) is a neurodegenerative disease characterized by motor neurons degeneration, which reduces muscular force, being very difficult to diagnose. Mathematical methods are used in order to analyze the surface electromiographic signal’s dynamic behavior (Fractal Dimension (FD) and Multiscale Entropy (MSE)), evaluate different muscle group’s synchronization (Coherence and Phase Locking Factor (PLF)) and to evaluate the signal’s complexity (Lempel-Ziv (LZ) techniques and Detrended Fluctuation Analysis (DFA)). Surface electromiographic signal acquisitions were performed in upper limb muscles, being the analysis executed for instants of contraction for ipsilateral acquisitions for patients and control groups. Results from LZ, DFA and MSE analysis present capability to distinguish between the patient group and the control group, whereas coherence, PLF and FD algorithms present results very similar for both groups. LZ, DFA and MSE algorithms appear then to be a good measure of corticospinal pathways integrity. A classification algorithm was applied to the results in combination with extracted features from the surface electromiographic signal, with an accuracy percentage higher than 70% for 118 combinations for at least one classifier. The classification results demonstrate capability to distinguish members between patients and control groups. These results can demonstrate a major importance in the disease diagnose, once surface electromyography (sEMG) may be used as an auxiliary diagnose method.

Long-term correlation of the electrocorticogram as a bioindicator of brain exposure to ionizing radiation

Understanding the effects of radiation and its possible influence on the nervous system are of great clinical interest. However, there have been few electrophysiological studies on brain activity after exposure to ionizing radiation (IR). A new methodological approach regarding the assessment of the possible effects of IR on brain activity is the use of linear and nonlinear mathematical methods in the analysis of complex time series, such as brain oscillations measured using the electrocorticogram (ECoG). The objective of this study was to use linear and nonlinear mathematical methods as biomarkers of gamma radiation regarding cortical electrical activity. Adult Wistar rats were divided into 3 groups: 1 control and 2 irradiated groups, evaluated at 24 h (IR24) and 90 days (IR90) after exposure to 18 Gy of gamma radiation from a cobalt-60 radiotherapy source. The ECoG was analyzed using power spectrum methods for the calculation of the power of delta, theta, alpha and beta rhythms and by means of the α-exponent of the detrended fluctuation analysis (DFA). Using both mathematical methods it was possible to identify changes in the ECoG, and to identify significant changes in the pattern of the recording at 24 h after irradiation. Some of these changes were persistent at 90 days after exposure to IR. In particular, the theta wave using the two methods showed higher sensitivity than other waves, suggesting that it is a possible biomarker of exposure to IR.

Fractal correlation of heart rate variability in obese children

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Fractal scaling exponents of heart rate variability association with linear indices and Poincaré Plot

The literature indicated that the fractal analysis of heart rate variability (HRV) is related to the chaos theory. However, it is not clear if the both short and long-term fractal scaling exponents of HRV are reliable for short period analysis in women. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV. We evaluated 65 healthy women between 18 and 30 years old. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains, the geometric index were also analyzed (triangular indexRRtri, triangular interpolation of RR intervals-TINN and Poincaré plot-SD1, SD2 and SD1/SD2) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). No significant correlation was observed for alpha-2 exponent with all indices. There was significant correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu and ms2 ), LF/HF ratio, SD1 and SD1/SD2 ratio. Our data does not indicate the alpha-2 exponent to be used for 256 RR intervals and we support the alpha-1 exponent to be used for HRV analysis in this condition.

Fractal dynamics of heart rate variability for short term

The fractal analysis of heart rate variability (HRV) has been associated to the chaos theory. We evaluated the association of the fractal exponents of HRV with the time and frequency domain and geometric indices of HRV for short period. HRV was analyzed with a minimal number of 256 RR intervals in the time (SDNN-standard deviation of normal-to-normal R-R intervals, pNN50-percentage of adjacent RR intervals with a difference of duration greater than 50ms and RMSSD-root-mean square of differences between adjacent normal RR intervals in a time interval) and frequency (LF-low frequency, HF-high frequency and LF/HF ratio) domains. The geometric indexes were also analyzed (RRtri-triangular index, TINN-triangular interpolation of RR intervals and Poincaré plot) as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). We observed strong correlation of the alpha-1 exponent with RMSSD, pNN50, SDNN/RMSSD, LF (nu), HF (nu), LF/HF ratio, SD1 and SD1/Sd2 ratio. In conclusion, we suggest that the alpha-1 exponent could be applied for HRV analysis with a minimal number of 256 RR intervals.

Fractal correlation property of heart rate variability in response to the postural change maneuver in healthy women

Background: We evaluated the effects of the PCM on the fractal analysis of the HRV in healthy women Method: We evaluated healthy women between 18 and 30 years old. HRV was analyzed in the time (SDNN, RMSSD, NN50 and pNN50) and frequency (LF, HF and LF/HF ratio) domains as well as short and long-term fractal exponents (alpha-1 and alpha-2) of the detrended fluctuation analysis (DFA). HRV was recorded at rest for ten minutes at seated rest and then the women quickly stood up from a seated position in up to three seconds and remained standing for 15 minutes. HRV was recorded at the following time: rest, 0–5 min, 5–10 min and 10–15 min during standing. Results: We observed decrease (p < 0.05) in the time-domain indices of HRV between seated and 10–15 minutes after the volunteer stood up. The LF (ms2) and HF (ms2) indices were also reduced (p < 0.05) at 10–15 minutes after the volunteer stood up compared to seated while the LF (nu) was increased at 5–10 min and 10–15 min (p < 0.05). The short-term alpha-1 exponent was increased (p < 0.05) at all moments investigated compared to seated. Increase in the properties of short-term fractal correlations of heart rate dynamics accompanied by a decrease in the parasympathetic modulation and global HRV was observed in response to the postural change maneuver. Conclusion: We suggest that fractal analysis of HRV is more sensitive than frequency and time-domain analysis of HRV during the postural change maneuver.