Related papers: A box-covering algorithm for fractal scaling in sc…
We compare different partitioning schemes for the box-counting algorithm in the multifractal analysis by computing the singularity spectrum and the distribution of the box probabilities. As model system we use the Anderson model of…
Multiple resolution analysis of two dimensional structures composed of randomly adsorbed penetrable rods, for densities below the percolation threshold, has been carried out using box-counting functions. It is found that at relevant…
Estimating a fractal dimension from a finite stochastic trajectory is a finite-size scaling problem: the apparent box-counting exponent is shaped by an occupancy crossover between the resolved range of scales and the finite number of…
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…
In this paper, we pose a hypothesis that the structure of communities in complex networks may result from their latent fractal properties. This hypothesis is based not only on the general observation that many real networks have multilevel…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
We introduce appropriate definitions of dimensions in order to characterize the fractal properties of complex networks. We compute these dimensions in a hierarchically structured network of particular interest. In spite of the nontrivial…
The box-counting (BC) algorithm is applied to calculate fractal dimensions of four fractal sets. The sets are contaminated with an additive noise with amplitude $\gamma = 10^{-5} \div 10^{-1}$. The accuracy of calculated numerical values of…
Network embedding aims to learn the low-dimensional representations of vertexes in a network, while structure and inherent properties of the network is preserved. Existing network embedding works primarily focus on preserving the…
The fractal properties of models of randomly placed $n$-dimensional spheres ($n$=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using…
In this paper, we introduce a new concept: the transfinite fractal dimension of graph sequences motivated by the notion of fractality of complex networks proposed by Song et al. We show that the definition of fractality cannot be applied to…
Complex networks have been studied in recent years due to their relevance in biological, social and technical real systems, such as the world wide web, social networks and biochemical interactions. One of the most current features of…
Fractal image compression has some desirable properties like high quality at high compression ratio, fast decoding, and resolution independence. Therefore it can be used for many applications such as texture mapping and pattern recognition…
Least box number coverage problem for calculating dimension of fractal networks is a NP-hard problem. Meanwhile, the time complexity of random ball coverage for calculating dimension is very low. In this paper we strictly present the upper…
We propose a novel finite size scaling analysis for percolation transition observed in complex networks. While it is known that cooperative systems in growing networks often undergo an infinite order transition with inverted…
We propose and analyze a stochastic model which explains, analytically, the cutoff behavior of real scale-free networks previously modeled computationally by Amaral et al. [Proc. Natl. Acad. Sci. U.S.A. 97, 11149 (2000)] and others. We…
We study the kinetics of random sequential adsorption of a mixture of particles with continuous distribution of sizes for different deposition rules. It appears in the long time limit the resulting system can be described using the fractal…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
Cohesive particles form agglomerates that are usually very porous. Their geometry, particularly their fractal dimension, depends on the agglomeration process (diffusion-limited or ballistic growth by adding single particles or…