The Experts below are selected from a list of 16779 Experts worldwide ranked by ideXlab platform
Jonas Mureika - One of the best experts on this subject based on the ideXlab platform.
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Fractal Dimensions in perceptual color space a comparison study using jackson pollock s art
Chaos, 2005Co-Authors: Jonas MureikaAbstract:The Fractal Dimensions of color-specific paint patterns in various Jackson Pollock paintings are calculated using a filtering process that models perceptual response to color differences (L*a*b* color space). The advantage of the L*a*b* space filtering method over traditional red-green-blue (RGB) spaces is that the former is a perceptually uniform (metric) space, leading to a more consistent definition of “perceptually different” colors. It is determined that the RGB filtering method underestimates the perceived Fractal dimension of lighter-colored patterns but not of darker ones, if the same selection criteria is applied to each. Implications of the findings to Fechner’s “principle of the aesthetic middle” and Berlyne’s work on perception of complexity are discussed.
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Fractal Dimensions in perceptual color space a comparison study using jackson pollock s art
arXiv: Physics and Society, 2005Co-Authors: Jonas MureikaAbstract:The Fractal Dimensions of color-specific paint patterns in various Jackson Pollock paintings are calculated using a filtering process which models perceptual response to color differences ($\Lab$ color space). The advantage of the $\Lab$ space filtering method over traditional RGB spaces is that the former is a perceptually-uniform (metric) space, leading to a more consistent definition of ``perceptually different'' colors. It is determined that the RGB filtering method underestimates the perceived Fractal dimension of lighter colored patterns but not of darker ones, if the same selection criteria is applied to each. Implications of the findings to Fechner's 'Principle of the Aesthetic Middle' and Berlyne's work on perception of complexity are discussed.
Xueru Zhao - One of the best experts on this subject based on the ideXlab platform.
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comparative study of artificial neural networks and wavelet artificial neural networks for groundwater depth data forecasting with various curve Fractal Dimensions
Water Resources Management, 2014Co-Authors: Yaonan Zhang, Qingchun Guo, Xueru ZhaoAbstract:The objective of this study was comparative study of artificial neural networks (ANN) and wavelet artificial neural networks (WANN) for time-series groundwater depth data (GWD) forecasting with various curve Fractal Dimensions. The paper offered a better method of revealing the change characteristics of GWD. Time series prediction based on ANN algorithms is fundamentally difficult to capture the data change details, when the time-series GWD data changes are more complex. For this purpose, Wavelet analysis and Fractal theory methods are proposed to link to ANN models in predicting GWD and analysis the change characteristics. The trend and random components were separated from the original time-series GWD using wavelet methods. The Fractal dimension is convenient for quantitatively describing the irregularity or randomness of time series data. Three types of training algorithms for ANN and WANN models using a Mallat decomposition algorithm were investigated as case study at three sites in the Ganzhou region of northwest China to find an optimal model that is suitable for certain characteristics of time-series GWD data. The simulation results indicate that both WANN and ANN models with the Bayesian regularization algorithm are accurate in reproducing GWD at sites with smaller Fractal Dimensions. However, WANN models alone are suitable for sites at which the Fractal dimension of the wavelet decomposition detail components is larger. Prediction error is also greater when the Fractal dimension is larger.
R. Uthayakumar - One of the best experts on this subject based on the ideXlab platform.
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improved generalized Fractal Dimensions in the discrimination between healthy and epileptic eeg signals
Journal of Computational Science, 2011Co-Authors: D. Easwaramoorthy, R. UthayakumarAbstract:Abstract Recently, Fractal Analysis is the well developed theory in the Data Analysis of non-linear time series. Especially MultiFractal Analysis, based on Generalized Fractal Dimensions (GFD), is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). GFD is the measure to compute the complexity, irregularity and the chaotic nature of the EEG Signals. This paper proposes an improved method of GFD in order to discriminate the Healthy and the Epileptic EEGs. Finally we conclude that there are significant differences between the Healthy and Epileptic Signals in the designed method than the GFD through graphical and statistical tools. The improved multiFractal measure is very efficient technique to analyze the EEG Signals and to compute the state of illness of the Epileptic patients.
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analysis of eeg signals using advanced generalized Fractal Dimensions
International Conference on Computing Communication and Networking Technologies, 2010Co-Authors: D. Easwaramoorthy, R. UthayakumarAbstract:The Human Brain is a highly complex and a nonlinear system. The disorder in the Human Brain creates a lot of physiopathological diseases, especially the Epileptic Seizure. Electroencephalogram (EEG) was used by the physicians to diagnosis the patients who is suffering from Seizure. The Generalized Fractal Dimensions (GFD) is the measure of complexity and the chaotic behaviour (irregularity) of the Fractal Time Series (EEG Signals). We design the Advanced form of Generalized Fractal Dimensions to discriminate the Normal and Ictal EEGs and the comparison was done at last between the two methods namely Advanced GFD & GFD through graphical methods. Finally we conclude that there is significant differences between the Normal and Ictal EEGs in the Advanced GFD Method than the GFD Method by using the statistical tool called ANOVA Test. This multiFractal technique is a very efficient tool in the Non-linear Analysis to analyze the EEG Signals and to detect or predict the state of illness of the Epileptic Patients.
Franz Konstantin Fuss - One of the best experts on this subject based on the ideXlab platform.
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Research Article A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications
2016Co-Authors: Franz Konstantin FussAbstract:License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Standard methods for computing the Fractal Dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals.Therefore they can produce opposite results in extreme signals.These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare Fractal Dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the Fractal dimension of a normalised (dimensionless) andmodified time series signal with a robust algorithm and a running averagemethod, and that maximises the difference between two Fractal Dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by amultiplier, which has a non-linear effect on the signal’s time derivative.Theoptimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on Fractal Dimensions. The optimisationmethod provides an additional filter effect andmakes the Fractal Dimensions less noisy.Themethod is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals
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A robust algorithm for optimisation and customisation of Fractal Dimensions of time series modified by nonlinearly scaling their time derivatives: Mathematical theory and practical applications
Computational and Mathematical Methods in Medicine, 2013Co-Authors: Franz Konstantin FussAbstract:Standard methods for computing the Fractal Dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare Fractal Dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the Fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two Fractal Dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on Fractal Dimensions. The optimisation method provides an additional filter effect and makes the Fractal Dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
J L Carrilloestrada - One of the best experts on this subject based on the ideXlab platform.
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a universal dimensionality function for the Fractal Dimensions of laplacian growth
Scientific Reports, 2019Co-Authors: J R Nicolascarlock, J L CarrilloestradaAbstract:Laplacian growth, associated to the diffusion-limited aggregation (DLA) model or the more general dielectric-breakdown model (DBM), is a fundamental out-of-equilibrium process that generates structures with characteristic Fractal/non-Fractal morphologies. However, despite diverse numerical and theoretical attempts, a data-consistent description of the Fractal Dimensions of the mass-distributions of these structures has been missing. Here, an analytical model of the Fractal Dimensions of the DBM and DLA is provided by means of a recently introduced dimensionality equation for the scaling of clusters undergoing a continuous morphological transition. Particularly, this equation relies on an effective information-function dependent on the Euclidean dimension of the embedding-space and the control parameter of the system. Numerical and theoretical approaches are used in order to determine this information-function for both DLA and DBM. In the latter, a connection to the Renyi entropies and generalized Dimensions of the cluster is made, showing that DLA could be considered as the point of maximum information-entropy production along the DBM transition. The results are in good agreement with previous theoretical and numerical estimates for two- and three-dimensional DBM, and high-dimensional DLA. Notably, the DBM Dimensions conform to a universal description independently of the initial cluster-configuration and the embedding-space.
