Related papers: Fractal dimension versus process complexity
Analysis and modeling of networked objects are fundamental pieces of modern data mining. Most real-world networks, from biological to social ones, are known to have common structural properties. These properties allow us to model the growth…
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
The paper deals with the fundamental problem of a modeling of the physical, in particular, thermal hydraulic processes, in various media of fractal structure of the natural, technological and technical systems and devices. The examples of a…
A simple multifractal coarsening model is suggested that can explain the observed dynamical behavior of the fractal dimension in a wide range of coarsening fractal systems. It is assumed that the minority phase (an ensemble of droplets) at…
Accurate segmentation of long and thin tubular structures is required in a wide variety of areas such as biology, medicine, and remote sensing. The complex topology and geometry of such structures often pose significant technical…
In this paper, we define new fractal dimensions of a metric space in order to calculate the roughness of a set on a large scale. These fractal dimensions are called upper zeta dimension and lower zeta dimension. The upper zeta dimension is…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
Fractal geometry proved to be an effective mathematical tool for exploring real geographical space based on digital maps and remote sensing images. Whether the fractal theory tool can be applied to abstract geographical space has not been…
We describe new families of random fractals, referred to as "V-variable", which are intermediate between the notions of deterministic and of standard random fractals. The parameter V describes the degree of "variability" : at each…
The fractal dimension $D$ is used to map the large-scale galaxy distribution in the Universe by color types: blue, green and red. Using a $NUVrK$-complete COSMOS2020 subsample of 618,952 galaxies observed up to $z=4$, number densities were…
Restructuring compilers use dependence analysis to prove that the meaning of a program is not changed by a transformation. A well-known limitation of dependence analysis is that it examines only the memory locations read and written by a…
We show that the ``time'' t_s defined via spin clusters in the Ising model coupled to 2d gravity leads to a fractal dimension d_h(s) = 6 of space-time at the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized phase,…
While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is…
The study of human dynamics has attracted much interest from many fields recently. In this paper, the fractal characteristic of human behaviors is investigated from the perspective of time series constructed with the amount of library…
We shed new light on entanglement measures in multipartite quantum systems by taking a computational-complexity approach toward quantifying quantum entanglement with two familiar notions--approximability and distinguishability. Built upon…
The theory of complex dimensions of fractal strings developed by Lapidus and van Frankenhuijsen has proven to be a powerful tool for the study of Minkowski measurability of fractal subsets of the real line. In a very general setting, the…
Texture is an important visual attribute used to describe images. There are many methods available for texture analysis. However, they do not capture the details richness of the image surface. In this paper, we propose a new method to…
Parameterized complexity theory offers a framework for a refined analysis of hard algorithmic problems. Instead of expressing the running time of an algorithm as a function of the input size only, running times are expressed with respect to…
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…
Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of study area. This phenomenon has been puzzling many researchers. This…