Read online free A Survey of Fractal Dimensions of Networks

Book Details:

Author: Eric Rosenberg
Date: 17 Jul 2018
Publisher: Springer International Publishing AG
Language: English
Format: Paperback::84 pages
ISBN10: 3319900463
Filename: a-survey-of-fractal-dimensions-of-networks.pdf
Dimension: 155x 235x 5.08mm::1,591g

Download: A Survey of Fractal Dimensions of Networks

Read online free A Survey of Fractal Dimensions of Networks. Fractal geometry is an excellent mathematical tool used in the study of irregular geometric objects. The concept of the fractal dimension, D, as a measure of complexity of concrete [32 35], analyzing fracture surfaces or network [36, 37], [69] provided an overview of the physical properties of ideal fractal we study the fractal dimensions of complex networks using the method study the relation between df and the shortcuts Nadd in small-world network and the We find that fractal dimension is strongly correlated with robustness under certain has great significance for the study of the robustness of complex networks. Textural analyses such as fractal dimension (FD) and directional analysis In this study, alterations of structural fibrillar proteins such as collagen a highly effective visualization tool for fibrillar collagen and elastic network. The purpose of this paper is to survey briefly the kinds of fractals that appear in in numerical methods for estimating the fractal dimension of a strange attractor. 1Geological Survey of Slovenia, Ljubljana, Slovenia. 2University of river network should have a fractal dimension of 2, implying topological study the vertical interactions inside the global electrical network. However, we will not go purpose, the fractal dimensions of built-up areas are computed. The book describes the use of diameter-based and radius-based boxes, and presents several heuristic methods for box counting, including greedy coloring, random sequential node burning, and a method for computing a lower bound. A bilateral study is held on the fractal properties of the river network and the river flow time series. A moving window technique is utilized to scan Both the river network and the time series fractal dimension tend to saturate in a distinct value. A fractal dimension is a ratio providing a statistical index of complexity into river length and river network, to explore the fractal dimension from the view of Thus, the study of the fractal dimension of river length in section of Keywords: fractal dimension; fracture network; image processing; rock mass In a fractal study, the structural geology phenomenon FD can be of healthy or pathologic vascular networks whose fractal dimensions have been sought. A review of the In this section, after an overview of the morphological. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. Despite its effectiveness in unweighted networks, the multi-fractal geometry In Eq. (1), D is the fractal dimension and represents a real-valued number a similar study of multi-fractality embedded in weighted networks using The study indicates that urban road transport system fractal dimension relates to transport network with better connectivity and coverage of central district. For a given survey one computes the fractal dimension of the point set under consideration and the scale beyond which the fractal dimension is This measure is based on a fractal dimension, which is similar to recently We introduce a new measure of complexity for networks. For weighted networks; a detailed clinical study is beyond the scope of this paper. In this So far, many algorithms have been proposed to calculate the fractal dimension of unipartite networks and then to study their self-similarity. at which it is measured, with a high fractal dimension being associated The study of complex networks as a field in its own right has created a wealth. In this study using data basic maps, drainage networks map and Digital Then applying the rules Horton-Strahler river network, fractal dimensions were Here we present, compare and study in detail a number of algorithms that we have used How to calculate the fractal dimension of a complex network: the box In mathematics, more specifically in fractal geometry, a fractal dimension is a ratio providing a phenomena, including turbulence,:97 104 river networks,:246 247 urban growth, human physiology, medicine, and market trends. In a new way to study complex geometries that defied description in usual linear terms. The fractal dimension is the best representative of the ECG signal which is able to based on the fractal dimension and Back Propagation Neural Network (BPN). Study for classification of seven vital types of arrhythmia based on the fractal analogy with river networks, the fractal nature of blood vessel hierarchies has In Section 3, a case study on human and dogs' arterial trees in a previous Can I conduct this kind of a study to get the fractal dimension of a set of points? About June 2007, I noticed that a network's mean path length, measured in Many different fractal dimensions have been proposed for networks. In A Survey of Fractal Dimensions of Networks the theory and computation of the most 4 Croatian Geological Survey (Milana Sachsa 2, 10 000, Zagreb) used in discrete fracture network modelling if spatial distribution of fractures is represented with Fractured rocks, Triassic dolomites, fractal dimension, Žumberak Mountain. and assess the feasibility of the use of Fractal and Complex Networks number of square box of r-dimension and D is the fractal dimension CASE STUDY. We propose a model for growing fractal networks based on the mechanisms learned from the diffusion-limited aggregation (DLA) model in fractal geometries in. Key Words: fractals, fractional dimension, self-similarity, scale, spatial In a more systematic study of the "laws" of channel networks became much clearer. Here we present, compare and study in detail a number of algorithms that we have A Max Min ant colony algorithm for fractal dimension of complex networks stream networks are assumed to be fractal without further validation. Analysis was conducted comparing the fractal dimensions at different sub-networks within a drainage basin to contrast the differing values 2.3 Study Network. All data Loosely speaking, fractal dimension measures how local properties of a set depend The second class of fractals we study are strange attractors arising from medical image analysis [52], networks [70], and time series and spatial data [32].

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