相关论文: Information fractal dimension of mass function
The possibility of facing critical phenomena in nuclear fragmentation is a topic of great interest. Different observables have been proposed to identify such a behavior, in particular, some related to the use of information entropy as a…
We study algorithmic problems on subsets of Euclidean space of low fractal dimension. These spaces are the subject of intensive study in various branches of mathematics, including geometry, topology, and measure theory. There are several…
The fractal dimension of large-scale galaxy clustering has been demonstrated to be roughly $D_F \sim 2$ from a wide range of redshift surveys. If correct, this statistic is of interest for two main reasons: fractal scaling is an implicit…
This paper surveys work on the relation between fractal dimensions and algorithmic information theory over the past thirty years. It covers the basic development of prefix-free Kolmogorov complexity from an information theoretic point of…
The conventional mathematical methods are based on characteristic length, while urban form has no characteristic length in many aspects. Urban area is a measure of scale dependence, which indicates the scale-free distribution of urban…
The distribution of the fractal dimension of the two-dimensional Ising model at the critical temperature measured by the Monte-Carlo simulation is discussed. At small spatio-temporal scales it exhibits a multifractal behavior and is well…
Most of the known methods for estimating the fractal dimension of fractal sets are based on the evaluation of a single geometric characteristic, e.g. the volume of its parallel sets. We propose a method involving the evaluation of several…
Two-dimensional random Lorentz gases with absorbing traps are considered in which a moving point particle undergoes elastic collisions on hard disks and annihilates when reaching a trap. In systems of finite spatial extension, the…
The authors have recently defined the R\'enyi information dimension rate $d(\{X_t\})$ of a stationary stochastic process $\{X_t,\,t\in\mathbb{Z}\}$ as the entropy rate of the uniformly-quantized process divided by minus the logarithm of the…
We introduce derangetropy, a novel functional measure designed to characterize the dynamics of information within probability distributions. Unlike scalar measures such as Shannon entropy, derangetropy offers a functional representation…
Following \cite{Visintin}, we exploit the fractional perimeter of a set to give a definition of fractal dimension for its measure theoretic boundary. We calculate the fractal dimension of sets which can be defined in a recursive way and we…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and…
We propose a novel method to measure the fractal dimension of a submonolayer metal adatom system grown under conditions of limited diffusivity on a surface. The method is based on measuring the specular peak attenuation of He atoms…
This chapter deals with error and uncertainty in data. Treats their measuring methods and meaning. It shows that uncertainty is a natural property of many data sets. Uncertainty is fundamental for the survival os living species, Uncertainty…
The present work shows a novel fractal dimension method for shape analysis. The proposed technique extracts descriptors from the shape by applying a multiscale approach to the calculus of the fractal dimension of that shape. The fractal…
While the numerical methods which utilizes partitions of equal-size, including the box-counting method, remain the most popular choice for computing the generalized dimension of multifractal sets, two mass- oriented methods are investigated…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
The role played by non extensive thermodynamics in physical systems has been under intense debate for the last decades. With many applications in several areas, the Tsallis statistics has been discussed in details in many works and…
In this paper, we study the effective dimension of points in infinite fractal trees generated recursively by a finite tree over some alphabet. Using unequal costs coding, we associate a length function with each such fractal tree and show…