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Mathematics
Special Issues
Complex Networks with Their Applications
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Complex Networks with Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Network Science".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 5374

Special Issue Editors

Dr. Andrey V. Andreev

E-Mail Website
Guest Editor
1. Neuroscience and Cognitive Technology Laboratory, Innopolis University, 420500 Innopolis, Russia
2. Baltic Center for Neurotechnology and Artificial Intelligence, Immanuel Kant Baltic Federal University, 23601 Kaliningrad, Russia
Interests: nonlinear dynamics; complex networks; neural networks; mathematical modeling; machine learning
Prof. Dr. Victor B. Kazantsev

E-Mail Website
Guest Editor
1. Neuroscience and Cognitive Technology Laboratory, Innopolis University, 420500 Innopolis, Russia
2. Institute of Biology and Biomedicine, Lobachevsky State University of Nizhny Novgorod, 603950 Nizhny Novgorod, Russia
Interests: computational neuroscience; spiking neuron networks; neurointerfaces; neurocontrol; biomorphic robotics; nonlinear dynamics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Complex networks are one of the most important objects of investigation in the modern science today, starting with modeled systems including artificial models and neuronal networks and all the way to real networks such as brain functional networks, social graphs, etc. They have many applications, the most widespread of which is using artificial neural networks for classification, recognition, and prediction; restoring brain functional networks for BCI application; modeling spiking neural networks for understanding of different brain dynamics; etc. Even though a lot of research has been carried out in this area, this topic is still relevant for researchers from different fields of science. This Special Issue is devoted to answering the following specific questions:

  1. Mathematical modeling of complex networks and investigation of their dynamics;
  2. Restoration of brain functional networks from real data;
  3. Applications of artificial neural networks;
  4. Investigation of graph networks and applications of graph neural networks;
  5. Investigation of adaptation and synchronization in complex networks;
  6. Application of complex networks for controlling an external system;
  7. Neuromorphic systems and technologies;
  8. Biomorphic robotics.

Submissions on any other topics related to the general subject of this Special Issue are also welcome.

Dr. Andrey V. Andreev
Prof. Dr. Victor B. Kazantsev
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • complex networks
  • neural networks
  • functional networks
  • graph networks
  • nonlinear dynamics
  • mathematical modeling
  • neuromorphic systems

Published Papers (6 papers)

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Research

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14 pages, 2382 KiB  
Article
Method of Extracting the Instantaneous Phases and Frequencies of Respiration from the Signal of a Photoplethysmogram
by Ekaterina I. Borovkova, Vladimir I. Ponomarenko, Anatoly S. Karavaev, Elizaveta S. Dubinkina and Mikhail D. Prokhorov
Mathematics 2023, 11(24), 4903; https://doi.org/10.3390/math11244903 - 8 Dec 2023
Cited by 1 | Viewed by 780
Abstract
We propose for the first time a method for extracting the instantaneous phases of respiration from the signal of a photoplethysmogram (PPG). In addition to the instantaneous phases of respiration, this method allows for more accurately extracting the instantaneous frequencies of respiration from [...] Read more.
We propose for the first time a method for extracting the instantaneous phases of respiration from the signal of a photoplethysmogram (PPG). In addition to the instantaneous phases of respiration, this method allows for more accurately extracting the instantaneous frequencies of respiration from a PPG than other methods. The proposed method is based on a calculation of the element-wise product of the wavelet spectrum of a PPG and the sequence of intervals between the heartbeats extracted from a PPG, and a calculation of the skeleton of the resulting spectrum in the respiratory frequency range. It is shown that such an element-wise product makes it possible to extract the instantaneous phases and instantaneous frequencies of respiration more accurately than using the wavelet transform of a PPG signal or the sequence of the heartbeat intervals. The proposed method was verified by analyzing the signals from healthy subjects recorded during stress-inducing cognitive tasks. This method can be used in wearable devices for signal processing. Full article
(This article belongs to the Special Issue Complex Networks with Their Applications)
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20 pages, 12213 KiB  
Article
Random Walks-Based Node Centralities to Attack Complex Networks
by Massimiliano Turchetto, Michele Bellingeri, Roberto Alfieri, Ngoc-Kim-Khanh Nguyen, Quang Nguyen and Davide Cassi
Mathematics 2023, 11(23), 4827; https://doi.org/10.3390/math11234827 - 30 Nov 2023
Cited by 1 | Viewed by 871
Abstract
Investigating the network response to node removal and the efficacy of the node removal strategies is fundamental to network science. Different research studies have proposed many node centralities based on the network structure for ranking nodes to remove. The random walk (RW) on [...] Read more.
Investigating the network response to node removal and the efficacy of the node removal strategies is fundamental to network science. Different research studies have proposed many node centralities based on the network structure for ranking nodes to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks and is an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node centralities for network dismantling with effective node removal strategies from the literature, namely betweenness, closeness, degree, and k-shell node removal, for synthetic and real-world networks. We evaluate the dismantling of the network by using the size of the largest connected component (LCC). We find that the degree nodes attack is the best strategy overall, and the new node removal strategies based on RW show the highest efficacy in regard to peculiar network topology. Specifically, RW strategy based on covering time emerges as the most effective strategy for a synthetic lattice network and a real-world road network. Our results may help researchers select the best node attack strategies in a specific network class and build more robust network structures. Full article
(This article belongs to the Special Issue Complex Networks with Their Applications)
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14 pages, 1157 KiB  
Article
Control of Network Bursting in a Model Spiking Network Supplied with Memristor—Implemented Plasticity
by Sergey V. Stasenko, Alexey N. Mikhaylov and Victor B. Kazantsev
Mathematics 2023, 11(18), 3888; https://doi.org/10.3390/math11183888 - 12 Sep 2023
Cited by 3 | Viewed by 1125
Abstract
We consider an unstructured neuron network model composed of excitatory and inhibitory neurons. The synaptic connections are supplied with spike timing-dependent plasticity (STDP). We take the STDP model implemented using a memristor. In normal conditions, the network forms so-called bursting discharges typical of [...] Read more.
We consider an unstructured neuron network model composed of excitatory and inhibitory neurons. The synaptic connections are supplied with spike timing-dependent plasticity (STDP). We take the STDP model implemented using a memristor. In normal conditions, the network forms so-called bursting discharges typical of unstructured living networks in dissociated neuronal cultures. Incorporating a biologically inspired model, we demonstrate how memristive plasticity emulates spike timing-dependent plasticity, which is crucial for regulating synchronous brain activity. We have found that, when the memristor-based STDP for inhibitory connections is activated, the bursting dynamics are suppressed and the network turns to a random spiking mode. The dependence of bursting properties on the degree of the memristor-based STDP plasticity is analyzed. These findings hold implications for advancing invasive neurointerfaces and for the identification and management of epileptiform activity. Full article
(This article belongs to the Special Issue Complex Networks with Their Applications)
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12 pages, 1957 KiB  
Article
Effect of Weight Thresholding on the Robustness of Real-World Complex Networks to Central Node Attacks
by Jisha Mariyam John, Michele Bellingeri, Divya Sindhu Lekha, Davide Cassi and Roberto Alfieri
Mathematics 2023, 11(16), 3482; https://doi.org/10.3390/math11163482 - 11 Aug 2023
Viewed by 845
Abstract
In this study, we investigate the effect of weight thresholding (WT) on the robustness of real-world complex networks. Here, we assess the robustness of networks after WT against various node attack strategies. We perform WT by removing a fixed fraction of weak links. [...] Read more.
In this study, we investigate the effect of weight thresholding (WT) on the robustness of real-world complex networks. Here, we assess the robustness of networks after WT against various node attack strategies. We perform WT by removing a fixed fraction of weak links. The size of the largest connected component indicates the network’s robustness. We find that real-world networks subjected to WT hold a robust connectivity structure to node attack even for higher WT values. In addition, we analyze the change in the top 30% of central nodes with WT and find a positive correlation in the ranking of central nodes for weighted node centralities. Differently, binary node centralities show a lower correlation when networks are subjected to WT. This result indicates that weighted node centralities are more stable indicators of node importance in real-world networks subjected to link sparsification. Full article
(This article belongs to the Special Issue Complex Networks with Their Applications)
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15 pages, 1447 KiB  
Article
Synchronization of Markov Switching Inertial Neural Networks with Mixed Delays under Aperiodically On-Off Adaptive Control
by Beibei Guo and Yu Xiao
Mathematics 2023, 11(13), 2906; https://doi.org/10.3390/math11132906 - 28 Jun 2023
Cited by 1 | Viewed by 682
Abstract
In this paper, the issue of exponential synchronization in Markov switching inertial neural networks with mixed delays is investigated via aperiodically on–off adaptive control. The inertial term is considered, which extends the existing network modes with first-order differential term. Combined with the Lyapunov [...] Read more.
In this paper, the issue of exponential synchronization in Markov switching inertial neural networks with mixed delays is investigated via aperiodically on–off adaptive control. The inertial term is considered, which extends the existing network modes with first-order differential term. Combined with the Lyapunov method, graph theory, and the differential inequalities technique, two types of synchronization criteria are presented which take into account all of the time delay information and reduce the conservativeness. Finally, some numerical simulations are provided in order to show the validity of the theoretical results. Full article
(This article belongs to the Special Issue Complex Networks with Their Applications)
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Review

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11 pages, 1183 KiB  
Review
The Critical Role of Networks to Describe Disease Spreading Dynamics in Social Systems: A Perspective
by Michele Bellingeri, Daniele Bevacqua, Francesco Scotognella and Davide Cassi
Mathematics 2024, 12(6), 792; https://doi.org/10.3390/math12060792 - 8 Mar 2024
Viewed by 564
Abstract
This review underscores the critical significance of incorporating networks science in epidemiology. Classic mathematical compartmental models (CMs) employed to describe epidemic spreading may fail to capture the intricacies of real disease dynamics. Rooted in the mean-field assumption, CMs oversimplify by assuming that every [...] Read more.
This review underscores the critical significance of incorporating networks science in epidemiology. Classic mathematical compartmental models (CMs) employed to describe epidemic spreading may fail to capture the intricacies of real disease dynamics. Rooted in the mean-field assumption, CMs oversimplify by assuming that every individual has the potential to “infect” any other, neglecting the inherent complexity of underlying network structures. Since social interactions follow a networked pattern with specific links between individuals based on social behaviors, joining classic CMs and network science in epidemiology becomes essential for a more authentic portrayal of epidemic spreading. This review delves into noteworthy research studies that, from various perspectives, elucidate how the synergy between networks and CMs can enhance the accuracy of epidemic descriptions. In conclusion, we explore research prospects aimed at further elevating the integration of networks within the realm of epidemiology, recognizing its pivotal role in refining our understanding of disease dynamics. Full article
(This article belongs to the Special Issue Complex Networks with Their Applications)
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