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Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the dynamic variable. Nonlinearities in the scaling function of empirical moments…
Generalized linear models, such as logistic regression, are widely used to model the association between a treatment and a binary outcome as a function of baseline covariates. However, the coefficients of a logistic regression model…
Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important…
Multifractal processes are a relatively new tool of stock market analysis. Their power lies in the ability to take multiple orders of autocorrelations into account explicitly. In the first part of the paper we discuss the framework of the…
Random multifractals occur in particular at critical points of disordered systems. For Anderson localization transitions, Mirlin and Evers [PRB 62,7920 (2000)] have proposed the following scenario (a) the Inverse Participation Ratios…
Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)) on the case of diluted two-dimensional Potts model, the moments $\bar{\rho^q(r)}$ of…
This contribution aims at studying the behaviour of the classical sample moment estimator, $S(n,q)= \sum_{k=1}^n X_k^{q}/n $, as a function of the number of available samples $n$, in the case where the random variables $X$ are positive,…
Due to their analytical tractability, random matrix ensembles serve as robust platforms for exploring exotic phenomena in systems that are computationally demanding. Building on a companion letter [arXiv:2312.17481], this paper investigates…
The multifractal analysis of disorder induced localization-delocalization transitions is reviewed. Scaling properties of this transition are generic for multi parameter coherent systems which show broadly distributed observables at…
Critical fluctuations of wave functions and energy levels at the Anderson transition are studied for the family of the critical power-law random banded matrix ensembles. It is shown that the distribution functions of the inverse…
The creativity and emergence of biological and psychological behavior are nonlinear. However, that does not necessarily mean only that the measurements of the behaviors are curvilinear. Furthermore, the linear model might fail to reduce…
Through a combination of rigorous analytical derivations and extensive numerical simulations, this work reports an exotic multifractal behavior, dubbed "logarithmic multifractality", in effectively infinite-dimensional systems undergoing…
Among the statistical models employed to approximate nonlinear interactions in biological and psychological processes, one prominent framework is that of cascades. Despite decades of empirical work using multifractal formalisms, a…
Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…
We study multifractality in a broad class of disordered systems which includes, e.g., the diluted x-y model. Using renormalized field theory we analyze the scaling behavior of cumulant averaged dynamical variables (in case of the x-y model…
We investigate the scaling properties of products of the exponential of birth--death processes with certain given marginal discrete distributions and covariance structures. The conditions on the mean, variance and covariance functions of…
The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
Under the formalism of annealed averaging of the partition function, two types of random multifractal measures with their probability of multipliers satisfying power distribution and triangular distribution are investigated mathematically.…
In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using…