Search results for "Multifractal"
showing 10 items of 36 documents
A discrimination technique for extensive air showers based on multiscale, lacunarity and neural network analysis
2011
We present a new method for the identification of extensive air showers initiated by different primaries. The method uses the multiscale concept and is based on the analysis of multifractal behaviour and lacunarity of secondary particle distributions together with a properly designed and trained artificial neural network. In the present work the method is discussed and applied to a set of fully simulated vertical showers, in the experimental framework of ARGO-YBJ, to obtain hadron to gamma primary separation. We show that the presented approach gives very good results, leading, in the 1–10 TeV energy range, to a clear improvement of the discrimination power with respect to the existing figu…
WAVELET ANALYSIS OF THE MULTIFRACTAL CHARACTER OF THE GALAXY DISTRIBUTION
1993
We have determined generalized dimensions of the observed distribution of galaxies. Their different values indicate that this distribution may be described as a multifractal. In order to analyse this distribution further, we have applied local wavelet transforms. Wavelets provide us with an interesting tool to analyse the large-scale structure which can be mathematically quantified and intuitively visualized. Comparing the results of these transforms at different dilation factors helps to visualize more clearly the nearly singular nature of the distribution. This method also allows us to determine the range of the local density power laws
Multifractal fits to the observed main belt asteroid distribution
2002
Dohnanyi's (1969) theory predicts that a collisional system such as the asteroidal population of the main belt should rapidly relax to a power-law stationary size distribution of the kind $N(m)\propto m^{-\alpha}$, with $\alpha$ very close to 11/6, provided all the collisional response parameters are independent on size. The actual asteroid belt distribution at observable sizes, instead, does not exhibit such a simple fractal size distribution. We investigate in this work the possibility that the corresponding cumulative distribution may be instead fairly fitted by multifractal distributions. This multifractal behavior, in contrast with the Dohnany fractal distribution, is related to the re…
Multifractal Properties of Eigenstates in Weakly Disordered Two-Dimensional Systems without Magnetic Field
1992
In order to investigate the electronic states in weakly disordered 2D samples very large (up to 180 000 * 180 000) secular matrices corresponding to the Anderson Hamiltonian are diagonalized. The analysis of the resulting wave functions shows multifractal fluctuations on all length scales in the considered systems. The set of generalized (fractal) dimensions and the singularity spectrum of the fractal measure are determined in order to completely characterize the eigenfunctions.
Local multifractal analysis in metric spaces
2013
We study the local dimensions and local multifractal properties of measures on doubling metric spaces. Our aim is twofold. On one hand, we show that there are plenty of multifractal type measures in all metric spaces which satisfy only mild regularity conditions. On the other hand, we consider a local spectrum that can be used to gain finer information on the local behaviour of measures than its global counterpart.
Improved moment scaling estimation for multifractal signals
2018
A fundamental problem in the analysis of multifractal processes is to estimate the scaling exponent K(q) of moments of different order q from data. Conventional estimators use the empirical moments μ^[subscript r][superscript q]=⟨ | ε[subscript r](τ)|[superscript q]⟩ of wavelet coefficients ε[subscript r](τ), where τ is location and r is resolution. For stationary measures one usually considers "wavelets of order 0" (averages), whereas for functions with multifractal increments one must use wavelets of order at least 1. One obtains K^(q) as the slope of log(μ^[subscript r][superscript q]) against log(r) over a range of r. Negative moments are sensitive to measurement noise and quantization.…
Is there any scaling in the cluster distribution?
1994
We apply fractal analysis methods to investigate the scaling properties in the Abell and ACO catalogs of rich galaxy clusters. We also discuss different technical aspects of the method when applied to data sets with small number of points as the cluster catalogs. Results are compared with simulations based on the Zel'dovich approximation. We limit our analysis to scales less than 100 $\hm$. The cluster distribution show a scale invariant multifractal behavior in a limited scale range. For the Abell catalog this range is 15--60$\hm$, while for the ACO sample it extends to smaller scales. Despite this difference in the extension of the scale--range where scale--invariant clustering takes plac…
Analyse de la distribution spatiale des implantations humaines : apports et limites d’indicateurs multi-échelles et trans-échelles
2020
As human beings, it is easy for us to judge visually whether a distribution is dispersed or concentrated. However, the quantitative formalization of our impressions is problematic. It depends on the scales of the chosen analysis. This dependence of indicators on scales has changed. It is initially considered as a barrier to knowledge, it now reflects the multi-scale organisation of the distributions studied. The central objective of this thesis is to investigate the limits and contribution of multi-scale and trans-scale indicators to the study of the spatial distributions of human settlements.Spatial analysis aims at comparing spatial distributions to a uniform distribution. The way in whic…
Reliability of fractal estimations on noisy patterns
2019
ECTQG 2019, European Colloquium of Theoretical and Quantitative Geography, Mondorf-les-Bains, LUXEMBOURG, 05-/09/2019 - 09/09/2019