Related papers: What is the dimension of your binary data?
This paper investigates fractal dimension of linear combination of fractal continuous functions with the same or different fractal dimensions. It has been proved that: (1) $BV_{I}$ all fractal continuous functions with bounded variation is…
Recently, we pointed out that on a class on non exactly decimable fractals two different parameters are required to describe diffusive and vibrational dynamics. This phenomenon we call dynamical dimension splitting is related to the lack of…
Dimension reduction of data sets is a standard problem in the realm of machine learning and knowledge reasoning. They affect patterns in and dependencies on data dimensions and ultimately influence any decision-making processes. Therefore,…
We examine Frostman-type characterisations and other extremal measure criteria for a range of fractal dimensions of sets. In particular we derive properties of the less familiar modified lower box dimension and upper correlation dimension.…
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is false, is mainly attributed to the strict definition of fractal…
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…
In this paper, we study the fractal dimension of the graph of a fractal transformation and also determine the quantization dimension of a probability measure supported on the graph of the fractal transformation. Moreover, we estimate the…
Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a…
It is demonstrated that the dynamic structure is very important for the rate of drainage of a thin liquid film and it can be effectively taken into account by a dynamic fractal dimension. It is shown that the latter is a powerful tool for…
We study domain formation in the two-dimensional O(3) model near criticality. The fractal dimension of these domains is determined with good statistical accuracy.
A fractal bears a complex structure that is reflected in a scaling hierarchy, indicating that there are far more small things than large ones. This scaling hierarchy can be effectively derived using head/tail breaks - a clustering and…
It is wellknown that the ordinary calculus is inadequate to handle fractal structures and processes and another suitable calculus needs to be developed for this purpose. Recently it was realized that fractional calculus with suitable…
Fractal plays an important role in nonlinear science. The most important parameter to model fractal is fractal dimension. Existing information dimension can calculate the dimension of probability distribution. However, given a mass function…
We present a generalized stochastic Cantor set by means of a simple {\it cut and delete process} and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, $m$…
We propose a procedure to determine the dimension of the common factor space in a large, possibly non-stationary, dataset. Our procedure is designed to determine whether there are (and how many) common factors (i) with linear trends, (ii)…
The fractal dimension curves of urban form and growth fall into two categories: One can be described by common logistic function, and the other can be described with quadratic logistic function. The approach to estimating the parameter of…
A statistical measure of dimension is used to compute the effective average space dimension for the Internet and other graphs, based on typed edges (links) from an ensemble of starting points. The method is applied to CAIDA's ITDK data for…
A theoretical model for fractal growth of DLA-clusters in two- and three-dimensional Euclidean space is proposed. This model allows to study some statistical properties of growing clusters in two different situations: in the static case…
There are three important types of structural properties that remain unchanged under the structural transformation of condensed matter physics and chemistry. They are the properties that remain unchanged under the structural periodic…
We consider the notion of dimension in four categories: the category of (unbounded) separable metric spaces and (metrically proper) Lipschitz maps, and the category of (unbounded) separable metric spaces and (metrically proper) uniform…