Local Holder regularity-based modeling of RR intervals

International audienceWe analyze the local regularity of RR traces from ECG through the computation of the so-called Hölder exponents. These exponents are at the basis of multifractal analysis, which has been shown to be relevant in the study of RR data. While multifractal analysis yields a global picture of the (statistical) distribution of regularity, we focus here on its time evolution. We show that this evolution is strongly correlated with the signal itself, a feature that seems to have remained unnoticed so far. We use this fact to build realistic synthetic RR traces

Multi-Fractal Spectral Analysis of the 1987 Stock Market Crash

The multifractal model of asset returns captures the volatility persistence of many financial time series. Its multifractal spectrum computed from wavelet modulus maxima lines provides the spectrum of irregularities in the distribution of market returns over time and thereby of the kind of uncertainty or randomness in a particular market. Changes in this multifractal spectrum display distinctive patterns around substantial market crashes or drawdowns. In other words, the kinds of singularities and the kinds of irregularity change in a distinct fashion in the periods immediately preceding and following major market drawdowns. This paper focuses on these identifiable multifractal spectral patterns surrounding the stock market crash of 1987. Although we are not able to find a uniquely identifiable irregularity pattern within the same market preceding different crashes at different times, we do find the same uniquely identifiable pattern in various stock markets experiencing the same crash at the same time. Moreover, our results suggest that all such crashes are preceded by a gradual increase in the weighted average of the values of the Lipschitz regularity exponents, under low dispersion of the multifractal spectrum. At a crash, this weighted average irregularity value drops to a much lower value, while the dispersion of the spectrum of Lipschitz exponents jumps up to a much higher level after the crash. Our most striking result, therefore, is that the multifractal spectra of stock market returns are not stationary. Also, while the stock market returns show a global Hurst exponent of slight persistence 0.5Financial Markets, Persistence, Multi-Fractal Spectral Analysis, Wavelets

Girsanov theorem for multifractional Brownian processes

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Wavelet denoising based on local regularity information

International audienceWe present a denoising method that is well fitted to the processing of extremely irregular signals such as (multi)fractal ones. Such signals are often encountered in practice, e.g., in biomedical applications. The basic idea is to estimate the regularity of the original data from the observed noisy ones using the large scale information, and then to extrapolate this information to the small scales. We present theoretical results describing the precise properties of the method. Numerical experiments show that this denoising scheme indeed performs well on irregular signals

Fractal Physiology and the Fractional Calculus: A Perspective

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine, in particular, understanding and controlling physiological networks in order to ensure their proper operation. We emphasize the difference between homeostatic and allometric control mechanisms. Homeostatic control has a negative feedback character, which is both local and rapid. Allometric control, on the other hand, is a relatively new concept that takes into account long-time memory, correlations that are inverse power law in time, as well as long-range interactions in complex phenomena as manifest by inverse power-law distributions in the network variable. We hypothesize that allometric control maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can often be described using the fractional calculus to capture the dynamics of complex physiologic networks

Computer-aided detection and diagnosis of breast cancer in 2D and 3D medical imaging through multifractal analysis

This Thesis describes the research work performed in the scope of a doctoral research program and presents its conclusions and contributions. The research activities were carried on in the industry with Siemens S.A. Healthcare Sector, in integration with a research team. Siemens S.A. Healthcare Sector is one of the world biggest suppliers of products, services and complete solutions in the medical sector. The company offers a wide selection of diagnostic and therapeutic equipment and information systems. Siemens products for medical imaging and in vivo diagnostics include: ultrasound, computer tomography, mammography, digital breast tomosynthesis, magnetic resonance, equipment to angiography and coronary angiography, nuclear imaging, and many others. Siemens has a vast experience in Healthcare and at the beginning of this project it was strategically interested in solutions to improve the detection of Breast Cancer, to increase its competitiveness in the sector. The company owns several patents related with self-similarity analysis, which formed the background of this Thesis. Furthermore, Siemens intended to explore commercially the computer- aided automatic detection and diagnosis eld for portfolio integration. Therefore, with the high knowledge acquired by University of Beira Interior in this area together with this Thesis, will allow Siemens to apply the most recent scienti c progress in the detection of the breast cancer, and it is foreseeable that together we can develop a new technology with high potential. The project resulted in the submission of two invention disclosures for evaluation in Siemens A.G., two articles published in peer-reviewed journals indexed in ISI Science Citation Index, two other articles submitted in peer-reviewed journals, and several international conference papers. This work on computer-aided-diagnosis in breast led to innovative software and novel processes of research and development, for which the project received the Siemens Innovation Award in 2012. It was very rewarding to carry on such technological and innovative project in a socially sensitive area as Breast Cancer.No cancro da mama a deteção precoce e o diagnóstico correto são de extrema importância na prescrição terapêutica e caz e e ciente, que potencie o aumento da taxa de sobrevivência à doença. A teoria multifractal foi inicialmente introduzida no contexto da análise de sinal e a sua utilidade foi demonstrada na descrição de comportamentos siológicos de bio-sinais e até na deteção e predição de patologias. Nesta Tese, três métodos multifractais foram estendidos para imagens bi-dimensionais (2D) e comparados na deteção de microcalci cações em mamogramas. Um destes métodos foi também adaptado para a classi cação de massas da mama, em cortes transversais 2D obtidos por ressonância magnética (RM) de mama, em grupos de massas provavelmente benignas e com suspeição de malignidade. Um novo método de análise multifractal usando a lacunaridade tri-dimensional (3D) foi proposto para classi cação de massas da mama em imagens volumétricas 3D de RM de mama. A análise multifractal revelou diferenças na complexidade subjacente às localizações das microcalci cações em relação aos tecidos normais, permitindo uma boa exatidão da sua deteção em mamogramas. Adicionalmente, foram extraídas por análise multifractal características dos tecidos que permitiram identi car os casos tipicamente recomendados para biópsia em imagens 2D de RM de mama. A análise multifractal 3D foi e caz na classi cação de lesões mamárias benignas e malignas em imagens 3D de RM de mama. Este método foi mais exato para esta classi cação do que o método 2D ou o método padrão de análise de contraste cinético tumoral. Em conclusão, a análise multifractal fornece informação útil para deteção auxiliada por computador em mamogra a e diagnóstico auxiliado por computador em imagens 2D e 3D de RM de mama, tendo o potencial de complementar a interpretação dos radiologistas

A stream scheduling scheme based on local regularity of internet traffic

Orientador: Lee Luan LingDissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: Nas redes de comunicações, a atual integração de vários tipos de serviços, cada qual com características estatísticas e requisitos de qualidade de serviço distintos, traz consigo a necessidade de esquemas eficientes de gerenciamento e controle de congestionamento do tráfego presente. Em pequenas escalas de tempo, os esquemas atuais podem ter sua eficiência reduzida devido à alta irregularidade do tráfego. Desta forma, neste presente trabalho, tendo como base à disciplina de escalonamento Generalized Processor Sharing (GPS), propõe-se um esquema de escalonamento de fluxos de dados que utiliza o expoente de Hölder pontual para caracterização local de cada fluxo. Para isso, propõe-se conjuntamente um estimador dinâmico destes expoentes e um preditor. Os expoentes de Hölder pontuais são estimados dinamicamente por meio do decaimento dos coeficientes wavelets em janelas de tempo. O preditor proposto possui características adaptativas e baseia-se no filtro de Kalman e no filtro de Mínimos Médios Quadrados Normalizado (Normalized Least-Mean-Square - NLMS). As avaliações realizadas mostram que este esquema de escalonamento contribui para o controle dinâmico preventivo no sentido de se obter uma menor perda de dados e um melhor uso da taxa de transmissão do enlace, em comparação com o GPS convencionalAbstract: Today network traffic is composed of many services with different statistical characteristics and quality of service requirements. This integration needs efficient traffic congestion control and management schemes. Dynamic and preventive schemes usually anticipate traffic conditions by means of a prediction process. Nevertheless, at fine-grained time scales, traffic exhibits strong irregularities and more complex scaling law that make this prediction process a non-trivial task. In this work we model network traffic flows as multifractal processes and introduce the pointwise Hölder exponent as an indicator of the local regularity degree. Also we propose a new traffic flow scheduling scheme based on the Generalized Processor Sharing (GPS) discipline that incorporate the pointwise Hölder exponent to locally characterize each data flow. For this end we explicitly present both dynamic pointwise Hölder exponent estimation and prediction mechanisms. The pointwise Hölder estimation is carried out dynamically based on the decay of the wavelet coefficients in the selected time windows. The proposed predictor is adaptive and implemented with both Kalman and Normalized Least Mean Squares (NLMS) filters. Experimental evaluations have validated the proposed scheduling scheme, resulting in low data loss rate and a better sharing of the network resources in comparison with the usual GPS schemeMestradoTelecomunicações e TelemáticaMestre em Engenharia Elétric