相关论文: Stochastic models which separate fractal dimension…

Statistical mechanical systems at and near their points of phase transition are expected to exhibit rich, fractal-like behaviour that is independent of the small-scale details of the system but depends strongly on the dimension in which the…

We study the morphology of watersheds in two and three dimensional systems subjected to different degrees of spatial correlations. The response of these objects to small, local perturbations is also investigated with extensive numerical…

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with…

The fractional stable motion is a prototypical stochastic process exhibiting both heavy tails and long-range dependence, parameterized via a stability index $\alpha$ and a Hurst exponent $H$. We consider a nonstationary extension where the…

In this article, we have employed fractal formalism to calculate the Fracture Functions of the Leading neutron produced in \textit{ep} collisions. The fractal concept describes the self-similar behavior of the proton structure at Leading…

Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?)…

We propose to use the rescaled range analysis to examine the records of rapidity-dependence of multiplicities in high-energy collision processes. We probe event by event the existence of global statistical dependence in the system of…

An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…

In this paper, we focus on the problem of statistical dependence estimation using characteristic functions. We propose a statistical dependence measure, based on the maximum-norm of the difference between joint and product-marginal…

While scale invariance is commonly observed in each component of real world multivariate signals, it is also often the case that the inter-component correlation structure is not fractally connected, i.e., its scaling behavior is not…

It is shown that due to memory effects the complex behaviour of components in a stochastic system can be transmitted to macroscopic evolution of the system as a whole. Within the Markov approximation widely using in ordinary statistical…

Stochastic models with fractional Brownian motion as source of randomness have become popular since the early 2000s. Fractional Brownian motion (fBm) is a Gaussian process, whose covariance depends on the so-called Hurst parameter $H\in…

This paper endeavors to show how a fractal-based approach can offer an alternative to differential equations for describing rates of interaction in complex systems. The specific example given is for combat analysis. This concerns a scenario…

A class of Gaussian processes generalizing the usual fractional Brownian motion for Hurst indices in (1/2,1) and multifractal Brownian motion introduced in Ralchenko and Shevchenko (Theory Probab Math Stat 80, 2010) and Boufoussi et al.…

Machine learning is rapidly making its path into natural sciences, including high-energy physics. We present the first study that infers, directly from experimental data, a functional form of fragmentation functions. The latter represent a…

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the…

We present the results of a simulation study into the properties of 12 different estimators of the Hurst parameter, $H$, or the fractional integration parameter, $d$, in long memory time series. We compare and contrast their performance on…

We establish properties of a new type of fractal which has partial self similarity at all scales. For any collection of iterated functions systems with an associated probability distribution and any positive integer V there is a…

The purpose of this paper is to study the fractal phenomena in large data sets and the associated questions of dimension reduction. We examine situations where the classical Principal Component Analysis is not effective in identifying the…

The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…