Application of Fractals in Complex Networks of Engineering and Medicine

A special issue of Fractal and Fractional (ISSN 2504-3110). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: 31 July 2024 | Viewed by 6605

Special Issue Editors


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Guest Editor
Faculty of Information Studies, 8000 Novo Mesto, Slovenia
Interests: fractals; theory of complexity; method of intelligent systems; hybrid machine learning; data mining; pattern recognition; nanomaterials; mechanical engineering; metallurgy; tribology; robotics; topography of materials after hardening; public transport

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Guest Editor
Institute for Economic Research (IER), University of Ljubljana, 1000 Ljubljana, Slovenia
Interests: mathematical statistics; probability; econometrics; stochastic processes; economic modelling; statistical learning

Special Issue Information

Dear Colleagues,

Fractals are models generated by mathematical equations, resulting in chaotic systems. The extension of the concepts of the fractal geometry toward the life sciences has brought significant progress in understanding the complexity and topological properties of networks that characterize DNA sequences, material microstructures, transport systems, and landscape roughness. Fractal analysis is useful in the study of complex networks, present in both natural and artificial systems (e.g., computer systems, transport systems, brain and social networks), allowing further development of the field in network science. A large body of research has been devoted to identifying the complexity of structures in networks. In the context of network theory, a complex network is a graph with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs, but often occur in graphs modelling real systems. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks, such as computer networks.

The focus of this Special Issue is to continue to advance research on topics relating to fractals and application to complex networks in engineering and medicine. We welcome you to contribute your interesting work.

Dr. Matej Babič
Dr. Andrej Srakar
Guest Editors

Manuscript Submission Information

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Keywords

  • fractals
  • complex networks
  • data mining
  • complex systems
  • chaos
  • engineering
  • medicine

Published Papers (4 papers)

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Research

13 pages, 3924 KiB  
Article
A New Approach to Determining the Network Fractality with Application to Robot-Laser-Hardened Surfaces of Materials
by Matej Babič and Dragan Marinković
Fractal Fract. 2023, 7(10), 710; https://doi.org/10.3390/fractalfract7100710 - 27 Sep 2023
Viewed by 671
Abstract
A new method to determine a fractal network in chaotic systems is presented together with its application to the microstructure recognition of robot-laser-hardened (RLH) steels under various angles of a laser beam. The method is based on fractal geometry. An experimental investigation was [...] Read more.
A new method to determine a fractal network in chaotic systems is presented together with its application to the microstructure recognition of robot-laser-hardened (RLH) steels under various angles of a laser beam. The method is based on fractal geometry. An experimental investigation was conducted by investigating the effect of several process parameters on the final microstructures of material that has been heat-treated. The influences of the surface temperature, laser speed, and different orientation angles of the laser beam on the microstructural geometry of the treated surfaces were considered. The fractal network of the microstructures of robot-laser-hardened specimens was used to describe how the geometry was changed during the heat treatment of materials. In order to predict the fractal network of robot-laser-hardened specimens, we used a method based on intelligent systems, namely genetic programming (GP) and a convolutional neural network (CNN). The proposed GP model achieved a prediction accuracy of 98.4%, while the proposed CNN model reached 96.5%. The performed analyses demonstrate that the angles of the robot laser cell have a noticeable effect on the final microstructures. The specimen laser-hardened under the conditions of 4 mm/s, 1000 °C, and an impact angle of the laser beam equal to 75° presented the maximum fractal network. The minimum fractal network was observed for the specimen before the robot-laser-hardening process. Full article
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17 pages, 1543 KiB  
Article
Probabilistic Machine Learning Methods for Fractional Brownian Motion Time Series Forecasting
by Lyudmyla Kirichenko and Roman Lavrynenko
Fractal Fract. 2023, 7(7), 517; https://doi.org/10.3390/fractalfract7070517 - 29 Jun 2023
Cited by 2 | Viewed by 1354
Abstract
This paper explores the capabilities of machine learning for the probabilistic forecasting of fractional Brownian motion (fBm). The focus is on predicting the probability of the value of an fBm time series exceeding a certain threshold after a specific number of time steps, [...] Read more.
This paper explores the capabilities of machine learning for the probabilistic forecasting of fractional Brownian motion (fBm). The focus is on predicting the probability of the value of an fBm time series exceeding a certain threshold after a specific number of time steps, given only the knowledge of its Hurst exponent. The study aims to determine if the self-similarity property is preserved in a forecasting time series and which machine learning algorithms are the most effective. Two types of forecasting methods are investigated: methods with a predefined distribution shape and those without. The results show that the self-similar properties of the fBm time series can be reliably reproduced in the continuations of the time series predicted by machine learning methods. The study also provides an experimental comparison of various probabilistic forecasting methods and their potential applications in the analysis and modeling of fractal time series. Full article
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35 pages, 4069 KiB  
Article
Self-Similar Growth and Synergistic Link Prediction in Technology-Convergence Networks: The Case of Intelligent Transportation Systems
by Yuxuan Xiu, Kexin Cao, Xinyue Ren, Bokui Chen and Wai Kin (Victor) Chan
Fractal Fract. 2023, 7(2), 109; https://doi.org/10.3390/fractalfract7020109 - 20 Jan 2023
Cited by 6 | Viewed by 1989
Abstract
Self-similar growth and fractality are important properties found in many real-world networks, which could guide the modeling of network evolution and the anticipation of new links. However, in technology-convergence networks, such characteristics have not yet received much attention. This study provides empirical evidence [...] Read more.
Self-similar growth and fractality are important properties found in many real-world networks, which could guide the modeling of network evolution and the anticipation of new links. However, in technology-convergence networks, such characteristics have not yet received much attention. This study provides empirical evidence for self-similar growth and fractality of the technology-convergence network in the field of intelligent transportation systems. This study further investigates the implications of such fractal properties for link prediction via partial information decomposition. It is discovered that two different scales of the network (i.e., the micro-scale structure measured by local similarity indices and the scaled-down structure measured by community-based indices) have significant synergistic effects on link prediction. Finally, we design a synergistic link prediction (SLP) approach which enhances local similarity indices by considering the probability of link existence conditional on the joint distribution of two scales. Experimental results show that SLP outperforms the benchmark local similarity indices in most cases, which could further validate the existence and usefulness of the synergistic effect between two scales on link prediction. Full article
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11 pages, 1825 KiB  
Article
A New Method of Quantifying the Complexity of Fractal Networks
by Matej Babič, Dragan Marinković, Miha Kovačič, Branko Šter and Michele Calì
Fractal Fract. 2022, 6(6), 282; https://doi.org/10.3390/fractalfract6060282 - 24 May 2022
Cited by 5 | Viewed by 1727
Abstract
There is a large body of research devoted to identifying the complexity of structures in networks. In the context of network theory, a complex network is a graph with nontrivial topological features—features that do not occur in simple networks, such as lattices or [...] Read more.
There is a large body of research devoted to identifying the complexity of structures in networks. In the context of network theory, a complex network is a graph with nontrivial topological features—features that do not occur in simple networks, such as lattices or random graphs, but often occur in graphs modeling real systems. The study of complex networks is a young and active area of scientific research inspired largely by the empirical study of real-world networks, such as computer networks and logistic transport networks. Transport is of great importance for the economic and cultural cooperation of any country with other countries, the strengthening and development of the economic management system, and in solving social and economic problems. Provision of the territory with a well-developed transport system is one of the factors for attracting population and production, serving as an important advantage for locating productive forces and providing an integration effect. In this paper, we introduce a new method for quantifying the complexity of a network based on presenting the nodes of the network in Cartesian coordinates, converting to polar coordinates, and calculating the fractal dimension using the ReScaled ranged (R/S) method. Our results suggest that this approach can be used to determine complexity for any type of network that has fixed nodes, and it presents an application of this method in the public transport system. Full article
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