Nonlinear analysis of cardiac rhythm fluctuations using DFA method

An approach by which the detrented fluctuation analysis (DFA) method can be used to help diagnose heart failure was demonstrated. DFA was applied to patients suffering from congestive heart failure (CHF) to check correlations between DFA indices and CHF, and determine a correlation between DFA indices and mortality, with a particular attention to the residue parameter, which is a measure of the departure of the DFA from its power law approximation. DFA parameters proved to be useful as a complement to the physiological parameters weber and FE to sort out the patients into three prognostic group.

Análise de agrupamentos dos dados de DFA oriundos de perfis elétricos de indução de poços de petróleo

The main objective of this study is to apply recently developed methods of physical-statistic to time series analysis, particularly in electrical induction s profiles of oil wells data, to study the petrophysical similarity of those wells in a spatial distribution. For this, we used the DFA method in order to know if we can or not use this technique to characterize spatially the fields. After obtain the DFA values for all wells, we applied clustering analysis. To do these tests we used the non-hierarchical method called K-means. Usually based on the Euclidean distance, the K-means consists in dividing the elements of a data matrix N in k groups, so that the similarities among elements belonging to different groups are the smallest possible. In order to test if a dataset generated by the K-means method or randomly generated datasets form spatial patterns, we created the parameter Ω (index of neighborhood). High values of Ω reveals more aggregated data and low values of Ω show scattered data or data without spatial correlation. Thus we concluded that data from the DFA of 54 wells are grouped and can be used to characterize spatial fields. Applying contour level technique we confirm the results obtained by the K-means, confirming that DFA is effective to perform spatial analysis

Análise de DFA e de agrupamento do perfil de densidade de poços de petróleo

In recent years, the DFA introduced by Peng, was established as an important tool capable of detecting long-range autocorrelation in time series with non-stationary. This technique has been successfully applied to various areas such as: Econophysics, Biophysics, Medicine, Physics and Climatology. In this study, we used the DFA technique to obtain the Hurst exponent (H) of the profile of electric density profile (RHOB) of 53 wells resulting from the Field School of Namorados. In this work we want to know if we can or not use H to spatially characterize the spatial data field. Two cases arise: In the first a set of H reflects the local geology, with wells that are geographically closer showing similar H, and then one can use H in geostatistical procedures. In the second case each well has its proper H and the information of the well are uncorrelated, the profiles show only random fluctuations in H that do not show any spatial structure. Cluster analysis is a method widely used in carrying out statistical analysis. In this work we use the non-hierarchy method of k-means. In order to verify whether a set of data generated by the k-means method shows spatial patterns, we create the parameter Ω (index of neighborhood). High Ω shows more aggregated data, low Ω indicates dispersed or data without spatial correlation. With help of this index and the method of Monte Carlo. Using Ω index we verify that random cluster data shows a distribution of Ω that is lower than actual cluster Ω. Thus we conclude that the data of H obtained in 53 wells are grouped and can be used to characterize space patterns. The analysis of curves level confirmed the results of the k-means

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

Comparação da análise de diferentes perfis de poços pelo método DFA

The study of complex systems has become a prestigious area of science, although relatively young . Its importance was demonstrated by the diversity of applications that several studies have already provided to various fields such as biology , economics and Climatology . In physics , the approach of complex systems is creating paradigms that influence markedly the new methods , bringing to Statistical Physics problems macroscopic level no longer restricted to classical studies such as those of thermodynamics . The present work aims to make a comparison and verification of statistical data on clusters of profiles Sonic ( DT ) , Gamma Ray ( GR ) , induction ( ILD ) , neutron ( NPHI ) and density ( RHOB ) to be physical measured quantities during exploratory drilling of fundamental importance to locate , identify and characterize oil reservoirs . Software were used : Statistica , Matlab R2006a , Origin 6.1 and Fortran for comparison and verification of the data profiles of oil wells ceded the field Namorado School by ANP ( National Petroleum Agency ) . It was possible to demonstrate the importance of the DFA method and that it proved quite satisfactory in that work, coming to the conclusion that the data H ( Hurst exponent ) produce spatial data with greater congestion . Therefore , we find that it is possible to find spatial pattern using the Hurst coefficient . The profiles of 56 wells have confirmed the existence of spatial patterns of Hurst exponents , ie parameter B. The profile does not directly assessed catalogs verification of geological lithology , but reveals a non-random spatial distribution

DFA e análise de agrupamento aplicadas a perfis de porosidade neutrônico em poços de petróleo

Peng was the first to work with the Technical DFA (Detrended Fluctuation Analysis), a tool capable of detecting auto-long-range correlation in time series with non-stationary. In this study, the technique of DFA is used to obtain the Hurst exponent (H) profile of the electric neutron porosity of the 52 oil wells in Namorado Field, located in the Campos Basin -Brazil. The purpose is to know if the Hurst exponent can be used to characterize spatial distribution of wells. Thus, we verify that the wells that have close values of H are spatially close together. In this work we used the method of hierarchical clustering and non-hierarchical clustering method (the k-mean method). Then compare the two methods to see which of the two provides the best result. From this, was the parameter � (index neighborhood) which checks whether a data set generated by the k- average method, or at random, so in fact spatial patterns. High values of � indicate that the data are aggregated, while low values of � indicate that the data are scattered (no spatial correlation). Using the Monte Carlo method showed that combined data show a random distribution of � below the empirical value. So the empirical evidence of H obtained from 52 wells are grouped geographically. By passing the data of standard curves with the results obtained by the k-mean, confirming that it is effective to correlate well in spatial distribution

Análise espacial de reservatórios usando DFA de dados geofísicos

This research aims to set whether is possible to build spatial patterns over oil fields using DFA (Detrended Fluctuation Analysis) of the following well logs: sonic, density, porosity, resistivity and gamma ray. It was employed in the analysis a set of 54 well logs from the oil field of Campos dos Namorados, RJ, Brazil. To check for spatial correlation, it was employed the Mantel test between the matrix of geographic distance and the matrix of the difference of DFA exponents of the well logs. The null hypothesis assumes the absence of spatial structures that means no correlation between the matrix of Euclidean distance and the matrix of DFA differences. Our analysis indicate that the sonic (p=0.18) and the density (p=0.26) were the profiles that show tendency to correlation, or weak correlation. A complementary analysis using contour plot also has suggested that the sonic and the density are the most suitable with geophysical quantities for the construction of spatial structures corroborating the results of Mantel test

Improving DPA and DFA resistance of circuits using asynchronous logic

International audience

Análise de agrupamentos dos dados de DFA oriundos de perfis elétricos de indução de poços de petróleo

The main objective of this study is to apply recently developed methods of physical-statistic to time series analysis, particularly in electrical induction s profiles of oil wells data, to study the petrophysical similarity of those wells in a spatial distribution. For this, we used the DFA method in order to know if we can or not use this technique to characterize spatially the fields. After obtain the DFA values for all wells, we applied clustering analysis. To do these tests we used the non-hierarchical method called K-means. Usually based on the Euclidean distance, the K-means consists in dividing the elements of a data matrix N in k groups, so that the similarities among elements belonging to different groups are the smallest possible. In order to test if a dataset generated by the K-means method or randomly generated datasets form spatial patterns, we created the parameter Ω (index of neighborhood). High values of Ω reveals more aggregated data and low values of Ω show scattered data or data without spatial correlation. Thus we concluded that data from the DFA of 54 wells are grouped and can be used to characterize spatial fields. Applying contour level technique we confirm the results obtained by the K-means, confirming that DFA is effective to perform spatial analysis

Análise de DFA e de agrupamento do perfil de densidade de poços de petróleo

In recent years, the DFA introduced by Peng, was established as an important tool capable of detecting long-range autocorrelation in time series with non-stationary. This technique has been successfully applied to various areas such as: Econophysics, Biophysics, Medicine, Physics and Climatology. In this study, we used the DFA technique to obtain the Hurst exponent (H) of the profile of electric density profile (RHOB) of 53 wells resulting from the Field School of Namorados. In this work we want to know if we can or not use H to spatially characterize the spatial data field. Two cases arise: In the first a set of H reflects the local geology, with wells that are geographically closer showing similar H, and then one can use H in geostatistical procedures. In the second case each well has its proper H and the information of the well are uncorrelated, the profiles show only random fluctuations in H that do not show any spatial structure. Cluster analysis is a method widely used in carrying out statistical analysis. In this work we use the non-hierarchy method of k-means. In order to verify whether a set of data generated by the k-means method shows spatial patterns, we create the parameter Ω (index of neighborhood). High Ω shows more aggregated data, low Ω indicates dispersed or data without spatial correlation. With help of this index and the method of Monte Carlo. Using Ω index we verify that random cluster data shows a distribution of Ω that is lower than actual cluster Ω. Thus we conclude that the data of H obtained in 53 wells are grouped and can be used to characterize space patterns. The analysis of curves level confirmed the results of the k-means

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

Comparação da análise de diferentes perfis de poços pelo método DFA

The study of complex systems has become a prestigious area of science, although relatively young . Its importance was demonstrated by the diversity of applications that several studies have already provided to various fields such as biology , economics and Climatology . In physics , the approach of complex systems is creating paradigms that influence markedly the new methods , bringing to Statistical Physics problems macroscopic level no longer restricted to classical studies such as those of thermodynamics . The present work aims to make a comparison and verification of statistical data on clusters of profiles Sonic ( DT ) , Gamma Ray ( GR ) , induction ( ILD ) , neutron ( NPHI ) and density ( RHOB ) to be physical measured quantities during exploratory drilling of fundamental importance to locate , identify and characterize oil reservoirs . Software were used : Statistica , Matlab R2006a , Origin 6.1 and Fortran for comparison and verification of the data profiles of oil wells ceded the field Namorado School by ANP ( National Petroleum Agency ) . It was possible to demonstrate the importance of the DFA method and that it proved quite satisfactory in that work, coming to the conclusion that the data H ( Hurst exponent ) produce spatial data with greater congestion . Therefore , we find that it is possible to find spatial pattern using the Hurst coefficient . The profiles of 56 wells have confirmed the existence of spatial patterns of Hurst exponents , ie parameter B. The profile does not directly assessed catalogs verification of geological lithology , but reveals a non-random spatial distribution

Discriminating between primary school students with high and low self-esteem.

From an initial sample of 747 primary school students, the top 16 percent (n =116) with high self-esteem (HSE) and the bottom 15 percent (n = I1 I) with low selfesteem (LSE) were se/eeted. These two groups were then compared on personal and classroom variables. Significant differences were found for all personal (self-talk, selfconcepts) and classroom (teacher feedback, praise, teacher-student relationship, and classroom environment) variables. Students with HSE scored more highly on all variables. Discriminant Function Analysis (DFA) was then used to determine which variables discriminated between these two groups of students. Learner self-concept, positive and negative self-talk, classroom environment, and effort feedback were the best discriminators of students with high and low self-esteem. Implications for educational psychologists and teachers are discussed.

Stochastic modelling of financial time series with memory and multifractal scaling

Financial processes may possess long memory and their probability densities may display heavy tails. Many models have been developed to deal with this tail behaviour, which reflects the jumps in the sample paths. On the other hand, the presence of long memory, which contradicts the efficient market hypothesis, is still an issue for further debates. These difficulties present challenges with the problems of memory detection and modelling the co-presence of long memory and heavy tails. This PhD project aims to respond to these challenges. The first part aims to detect memory in a large number of financial time series on stock prices and exchange rates using their scaling properties. Since financial time series often exhibit stochastic trends, a common form of nonstationarity, strong trends in the data can lead to false detection of memory. We will take advantage of a technique known as multifractal detrended fluctuation analysis (MF-DFA) that can systematically eliminate trends of different orders. This method is based on the identification of scaling of the q-th-order moments and is a generalisation of the standard detrended fluctuation analysis (DFA) which uses only the second moment; that is, q = 2. We also consider the rescaled range R/S analysis and the periodogram method to detect memory in financial time series and compare their results with the MF-DFA. An interesting finding is that short memory is detected for stock prices of the American Stock Exchange (AMEX) and long memory is found present in the time series of two exchange rates, namely the French franc and the Deutsche mark. Electricity price series of the five states of Australia are also found to possess long memory. For these electricity price series, heavy tails are also pronounced in their probability densities. The second part of the thesis develops models to represent short-memory and longmemory financial processes as detected in Part I. These models take the form of continuous-time AR(∞) -type equations whose kernel is the Laplace transform of a finite Borel measure. By imposing appropriate conditions on this measure, short memory or long memory in the dynamics of the solution will result. A specific form of the models, which has a good MA(∞) -type representation, is presented for the short memory case. Parameter estimation of this type of models is performed via least squares, and the models are applied to the stock prices in the AMEX, which have been established in Part I to possess short memory. By selecting the kernel in the continuous-time AR(∞) -type equations to have the form of Riemann-Liouville fractional derivative, we obtain a fractional stochastic differential equation driven by Brownian motion. This type of equations is used to represent financial processes with long memory, whose dynamics is described by the fractional derivative in the equation. These models are estimated via quasi-likelihood, namely via a continuoustime version of the Gauss-Whittle method. The models are applied to the exchange rates and the electricity prices of Part I with the aim of confirming their possible long-range dependence established by MF-DFA. The third part of the thesis provides an application of the results established in Parts I and II to characterise and classify financial markets. We will pay attention to the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX), the NASDAQ Stock Exchange (NASDAQ) and the Toronto Stock Exchange (TSX). The parameters from MF-DFA and those of the short-memory AR(∞) -type models will be employed in this classification. We propose the Fisher discriminant algorithm to find a classifier in the two and three-dimensional spaces of data sets and then provide cross-validation to verify discriminant accuracies. This classification is useful for understanding and predicting the behaviour of different processes within the same market. The fourth part of the thesis investigates the heavy-tailed behaviour of financial processes which may also possess long memory. We consider fractional stochastic differential equations driven by stable noise to model financial processes such as electricity prices. The long memory of electricity prices is represented by a fractional derivative, while the stable noise input models their non-Gaussianity via the tails of their probability density. A method using the empirical densities and MF-DFA will be provided to estimate all the parameters of the model and simulate sample paths of the equation. The method is then applied to analyse daily spot prices for five states of Australia. Comparison with the results obtained from the R/S analysis, periodogram method and MF-DFA are provided. The results from fractional SDEs agree with those from MF-DFA, which are based on multifractal scaling, while those from the periodograms, which are based on the second order, seem to underestimate the long memory dynamics of the process. This highlights the need and usefulness of fractal methods in modelling non-Gaussian financial processes with long memory.