The Experts below are selected from a list of 1914 Experts worldwide ranked by ideXlab platform
Ioulia Tchiguirinskaia - One of the best experts on this subject based on the ideXlab platform.
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multifractal vector fields and stochastic clifford algebra
Chaos, 2015Co-Authors: D. Schertzer, Ioulia TchiguirinskaiaAbstract:In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Levy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Levy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Levy stability grants a given statistical universality.
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2DVD Data Revisited: Multifractal Insights into Cuts of the Spatiotemporal Rainfall Process
Journal of Hydrometeorology, 2015Co-Authors: Auguste Gires, D. Schertzer, Ioulia Tchiguirinskaia, A. BerneAbstract:Data collected during four heavy rainfall events that occurred in Ardeche (France) with the help of a 2D video disdrometer (2DVD) are used to investigate the structure of the raindrop distribution in both space and time. A first type of analysis is based on the reconstruction of 36-m-height vertical rainfall columns above the measuring device. This reconstruction is obtained with the help of a ballistic hypothesis applied to 1-ms time step series. The corresponding snapshots are analyzed with the help of universal Multifractals. For comparison, a similar analysis is performed on the time series with 1-ms time steps, as well as on time series of accumulation maps of N consecutive recorded drops (therefore with variable time steps). It turns out that the drop distribution exhibits a good scaling behavior in the range 0.5-36 m during the heaviest portion of the events, confirming the lack of empirical evidence of the widely used homogenous assumption for drop distribution. For smaller scales, drop positions seem to be homogeneously distributed. The notion of multifractal singularity is well illustrated by the very high-resolution time series.
D. Schertzer - One of the best experts on this subject based on the ideXlab platform.
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multifractal vector fields and stochastic clifford algebra
Chaos, 2015Co-Authors: D. Schertzer, Ioulia TchiguirinskaiaAbstract:In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Levy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Levy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Levy stability grants a given statistical universality.
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2DVD Data Revisited: Multifractal Insights into Cuts of the Spatiotemporal Rainfall Process
Journal of Hydrometeorology, 2015Co-Authors: Auguste Gires, D. Schertzer, Ioulia Tchiguirinskaia, A. BerneAbstract:Data collected during four heavy rainfall events that occurred in Ardeche (France) with the help of a 2D video disdrometer (2DVD) are used to investigate the structure of the raindrop distribution in both space and time. A first type of analysis is based on the reconstruction of 36-m-height vertical rainfall columns above the measuring device. This reconstruction is obtained with the help of a ballistic hypothesis applied to 1-ms time step series. The corresponding snapshots are analyzed with the help of universal Multifractals. For comparison, a similar analysis is performed on the time series with 1-ms time steps, as well as on time series of accumulation maps of N consecutive recorded drops (therefore with variable time steps). It turns out that the drop distribution exhibits a good scaling behavior in the range 0.5-36 m during the heaviest portion of the events, confirming the lack of empirical evidence of the widely used homogenous assumption for drop distribution. For smaller scales, drop positions seem to be homogeneously distributed. The notion of multifractal singularity is well illustrated by the very high-resolution time series.
Branimir Reljin - One of the best experts on this subject based on the ideXlab platform.
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Research Article Classification of Prolapsed Mitral Valve versus Healthy Heart from Phonocardiograms by Multifractal Analysis
2016Co-Authors: Ana Gavrovska, Goran Zajit, Irini Reljin, Branimir ReljinAbstract:Copyright © 2013 Ana Gavrovska et al.This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Phonocardiography has shown a great potential for developing low-cost computer-aided diagnosis systems for cardiovascular monitoring. So far, most of the work reported regarding cardiosignal analysis using Multifractals is oriented towards heartbeat dynamics. This paper represents a step towards automatic detection of one of the most common pathological syndromes, so-called mitral valve prolapse (MVP), using phonocardiograms and multifractal analysis. Subtle features characteristic for MVP in phonocardiograms may be difficult to detect. The approach for revealing such features should be locally based rather than globally based. Nevertheless, if their appearances are specific and frequent, they can affect a multifractal spectrum. This has been the case in our experiment with the click syndrome. Totally, 117 pediatric phonocardiographic recordings (PCGs), 8 seconds long each, obtained from 117 patients were used for PMV automatic detection. We propose a two-step algorithm to distinguish PCGs that belong to children with healthy hearts and children with prolapsed mitral valves (PMVs). Obtained results show high accuracy o
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Classification of Prolapsed Mitral Valve versus Healthy Heart from Phonocardiograms by Multifractal Analysis
Hindawi Limited, 2013Co-Authors: Ana Gavrovska, Irini Reljin, Goran Zajić, Branimir ReljinAbstract:Phonocardiography has shown a great potential for developing low-cost computer-aided diagnosis systems for cardiovascular monitoring. So far, most of the work reported regarding cardiosignal analysis using Multifractals is oriented towards heartbeat dynamics. This paper represents a step towards automatic detection of one of the most common pathological syndromes, so-called mitral valve prolapse (MVP), using phonocardiograms and multifractal analysis. Subtle features characteristic for MVP in phonocardiograms may be difficult to detect. The approach for revealing such features should be locally based rather than globally based. Nevertheless, if their appearances are specific and frequent, they can affect a multifractal spectrum. This has been the case in our experiment with the click syndrome. Totally, 117 pediatric phonocardiographic recordings (PCGs), 8 seconds long each, obtained from 117 patients were used for PMV automatic detection. We propose a two-step algorithm to distinguish PCGs that belong to children with healthy hearts and children with prolapsed mitral valves (PMVs). Obtained results show high accuracy of the method. We achieved 96.91% accuracy on the dataset (97 recordings). Additionally, 90% accuracy is achieved for the evaluation dataset (20 recordings). Content of the datasets is confirmed by the echocardiographic screening
Borko Stosic - One of the best experts on this subject based on the ideXlab platform.
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multifractal analysis of human retinal vessels
IEEE Transactions on Medical Imaging, 2006Co-Authors: Tatijana Stosic, Borko StosicAbstract:In this paper, it is shown that vascular structures of the human retina represent geometrical Multifractals, characterized by a hierarchy of exponents rather then a single fractal dimension. A number of retinal images from the STARE database are analyzed, corresponding to both normal and pathological states of the retina. In all studied cases, a clearly multifractal behavior is observed, where capacity dimension is always found to be larger then the information dimension, which is in turn always larger then the correlation dimension, all the three being significantly lower then the diffusion limited aggregation (DLA) fractal dimension. We also observe a tendency of images corresponding to the pathological states of the retina to have lower generalized dimensions and a shifted spectrum range, in comparison with the normal cases
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multifractal analysis of human retinal vessels
arXiv: Biological Physics, 2004Co-Authors: Tatijana Stosic, Borko StosicAbstract:In this work it is shown that vascular structures of the human retina represent geometrical Multifractals, characterized by a hierarchy of exponents rather then a single fractal dimension. A number of retinal images from the STARE database (www.parl.clemson.edu/stare) are analyzed, corresponding to both normal and pathological states of the retina. In all studied cases a clearly multifractal behavior is observed, where capacity dimension is always found to be smaller then the information dimension, which is in turn always smaller then the correlation dimension, all the three being significantly lower then the DLA (Diffusion Limited Aggregation) fractal dimension. We also observe a tendency of images corresponding to the pathological states of the retina to have lower generalized dimensions and a shifted spectrum range, in comparison with the normal cases.
Soares, Roosewelt Fonseca - One of the best experts on this subject based on the ideXlab platform.
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Fractais e Percolação na Recuperação de Petróleo
Universidade Federal do Rio Grande do Norte, 2014Co-Authors: Soares, Roosewelt FonsecaAbstract:O comportamento complexo de uma ampla variedade de fenômenos que são de interesse de matemáticos, físicos, químicos e engenheiros é caracterizado quantitativamente por meio de idéias de distribuições de fractais e multifractais, que correspondem de modo único à forma geométrica e a propriedades dinâmicas dos sistemas em estudo. Nesta tese apresentamos o Espaço dos Fractais e os métodos de Hausdorff-Besicovitch, de Contagem de Caixas e de Escala, para calcular a Dimensão Fractal de um Conjunto. Estudamos também fenômenos de percolação em objetos multifractais construídos de maneira simples. O objeto central de nossas análises é um objeto multifractal que chamamos de Qmf . Nestes objetos a multifractalidade surge diretamente da sua forma geométrica. Identificamos algumas diferenças entre percolação nos multifractais que propusemos e percolação em uma rede quadrada. Existem basicamente duas fontes destas diferenças. A primeira está relacionada com o número de coordenação, c, que muda ao longo do multifractal. A segunda vem da maneira como o peso de cada célula no multifractal afeta o aglomerado percolante. Usamos muitas amostras de redes de tamanho finito e fizemos o histograma de redes percolantes versus a probabilidade de ocupação p. Dependendo de um parâmetro, ρ, que caracteriza o multifractal e o tamanho da rede, L, o histograma pode ter dois picos. Observamos que a probabilidade de ocupação no limiar de percolação, pc, para o multifractal, em suporte d = 2, é menor do que para a rede quadrada. Calculamos a dimensão fractal do aglomerado percolante e o expoente crítico β. A despeito das diferenças topológicas, encontramos que a percolação em um suporte multifractal está na mesma classe de universalidade da percolação padrão. A área e o número de vizinhos dos blocos de Qmf apresentam um comportamento não-trivial. Uma visão geral do objeto Qmf mostra uma anisotropia. O valor de pc é uma função de ρ que está relacionada com esta anisotropia. Analisamos a relação entre pc e o número médio de vizinhos dos blocos, assim como, a anisotropia de Qmf. Nesta tese estudamos também a distribuição de caminhos mínimos em sistemas percolativos no limiar de percolação em duas dimensões (2D). Estudamos caminhos que começam em um determinado ponto e terminam em vários outros pontos. Na terminologia da indústria do petróleo, ao ponto inicial dado associamos um poço de injeção (injetor) e aos outros pontos associamos poços de produção (produtores). No caso padrão apresentado anteriormente de um poço de injeção e um poço de produção, separados por uma distância euclidiana r, a distribuição de caminhos mínimos l, P(l|r), apresenta um comportamento de lei-de-potência com expoente gl = 2, 14 em 2D. Analisamos a situação de um injetor e uma matriz A de produtores. Configurações simétricas de produtores levam a uma distribuição, P(l|A), com um único pico, que é a probabilidade que o caminho mínimo entre o injetor e a matriz de produtores seja l, enquanto que as configurações assimétricas levam a vários picos na distribuição P(l|A). Analisamos situações em que o injetor está fora e situações em que o injetor está no interior do conjunto de poços produtores. O pico em P(l|A) nas configurações assimétricas decai mais rápido do que no caso padrão. Para os caminhos muito longos todas as configurações estudadas exibiram um comportamento de lei-de-potência com o expoente g ≃ gl.The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed Multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other point
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Fractais e percolação na recuperação de Petróleo
Universidade Federal do Rio Grande do Norte, 2014Co-Authors: Soares, Roosewelt FonsecaAbstract:O comportamento complexo de uma ampla variedade de fenômenos que são de interesse de matemáticos, físicos, químicos e engenheiros é caracterizado quantitativamente por meio de idéias de distribuições de fractais e multifractais, que correspondem de modo único á forma geométrica e a propriedades dinâmicas dos sistemas em estudo. Nesta tese apresentamos o Espaço dos Fractais e os métodos de Hausdorff-Besicovitch, de Contagem de Caixas e de Escala, para calcular a Dimensão Fractal de um Conjunto. Estudamos também fenômenos de percolação em objetos multifractais construídos de maneira simples. O objeto central de nossas análises é um objeto multifractal que chamamos de Qmf . Nestes objetos a multifractalidade surge diretamente da sua forma geométrica. Identificamos algumas diferenças entre percolação nos multifractais que propusemos e percolação em uma rede quadrada. Existem basicamente duas fontes destas diferenças. A primeira está relacionada com o número de coordenação, c, que muda ao longo do multifractal. A segunda vem da maneira como o peso de cada célula no multifractal afeta o aglomerado percolante. Usamos muitas amostras de redes de tamanho finito e fizemos o histograma de redes percolantes versus a probabilidade de ocupação p. Dependendo de um parâmetro, ρ, que caracteriza o multifractal e o tamanho da rede, L, o histograma pode ter dois picos. Observamos que a probabilidade de ocupação no limiar de percolação, pc, para o multifractal, em suporte d = 2, é menor do que para a rede quadrada. Calculamos a dimensão fractal do aglomerado percolante e o expoente crítico β. A despeito das diferenças topológicas, encontramos que a percolação em um suporte multifractal está na mesma classe de universalidade da percolação padrão. A área e o número de vizinhos dos blocos de Qmf apresentam um comportamento não-trivial. Uma visão geral do objeto Qmf mostra uma anisotropia. O valor de pc é uma função de ρ que está relacionada com esta anisotropia. Analisamos a relação entre pc e o número médio de vizinhos dos blocos, assim como, a anisotropia de Qmf . Nesta tese estudamos também a distribuição de caminhos mínimos em sistemas percolativos no limiar de percolação em duas dimensões (2D). Estudamos caminhos que começam em um determinado ponto e terminam em vários outros pontos. Na terminologia da indústria do petróleo, ao ponto inicial dado associamos um poço de injeção (injetor) e aos outros pontos associamos poços de produção (produtores). No caso padrão apresentado anteriormente de um poço de injeção e um poço de produção, separados por uma distância euclidiana r, a distribuição de caminhos mínimos l, P(l|r), apresenta um comportamento de lei-de-potência com expoente gl = 2, 14 em 2D. Analisamos a situação de um injetor e uma matriz A de produtores. Configurações simétricas de produtores levam a uma distribuição, P(l|A), com um único pico, que é a probabilidade que o caminho mínimo entre o injetor e a matriz de produtores seja l, enquanto que as configurações assimétricas levam a vários picos na distribuição P(l|A). Analisamos situações em que o injetor está fora e situações em que o injetor está no interior do conjunto de poços produtores. O pico em P(l|A) nas configurações assimétricas decai mais rápido do que no caso padrão. Para os caminhos muito longos todas as configurações estudadas exibiram um comportamento de lei-de-potência com o expoente g ≃ glThe complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed Multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl