Multiplexing Networks Research Articles

Deep-reinforcement-learning-based RMSCA for space division multiplexing networks with multi-core fibers [Invited Tutorial

The escalating demands for network capacities catalyze the adoption of space division multiplexing (SDM) technologies. With continuous advances in multi-core fiber (MCF) fabrication, MCF-based SDM networks are positioned as a viable and promising solution to achieve higher transmission capacities in multi-dimensional optical networks. However, with the extensive network resources offered by MCF-based SDM networks comes the challenge of traditional routing, modulation, spectrum, and core allocation (RMSCA) methods to achieve appropriate performance. This paper proposes an RMSCA approach based on deep reinforcement learning (DRL) for MCF-based elastic optical networks (MCF-EONs). Within the solution, a novel state representation with essential network information and a fragmentation-aware reward function were designed to direct the agent in learning effective RMSCA policies. Additionally, we adopted a proximal policy optimization algorithm featuring an action mask to enhance the sampling efficiency of the DRL agent and speed up the training process. The performance of the proposed algorithm was evaluated with two different network topologies with varying traffic loads and fibers with different numbers of cores. The results confirmed that the proposed algorithm outperforms the heuristics and the state-of-the-art DRL-based RMSCA algorithm in reducing the service blocking probability by around 83% and 51%, respectively. Moreover, the proposed algorithm can be applied to networks with and without core switching capability and has an inference complexity compatible with real-world deployment requirements.

Temporal dynamics of coordinated online behavior: Stability, archetypes, and influence

Large-scale online campaigns, malicious or otherwise, require a significant degree of coordination among participants, which sparked interest in the study of coordinated online behavior. State-of-the-art methods for detecting coordinated behavior perform static analyses, disregarding the temporal dynamics of coordination. Here, we carry out a dynamic analysis of coordinated behavior. To reach our goal, we build a multiplex temporal network and we perform dynamic community detection to identify groups of users that exhibited coordinated behaviors in time. We find that i) coordinated communities (CCs) feature variable degrees of temporal instability; ii) dynamic analyses are needed to account for such instability, and results of static analyses can be unreliable and scarcely representative of unstable communities; iii) some users exhibit distinct archetypal behaviors that have important practical implications; iv) content and network characteristics contribute to explaining why users leave and join CCs. Our results demonstrate the advantages of dynamic analyses and open up new directions of research on the unfolding of online debates, on the strategies of CCs, and on the patterns of online influence.

Cross-connection of multiplexed cylindrical vector beams using off-axis spin-decoupled metasurfaces.

Cylindrical vector beam (CVB) multiplexing communication demands effective mode cross-connection techniques to establish communication networks. While methods like polarized grating and coordinate transformation have been developed for (de)multiplexing CVB modes, challenges persist in the cross-connection of these multiplexed mode channels, including multi-mode conversion and inhomogeneous polarization control. Herein, we present an independent off-axis spin-orbit interaction strategy utilizing spin-decoupled metasurfaces. Cross-connection is achieved by encoding conjugated Dammann optical vortex grating phases onto the two orthogonal circularly polarized components of CVBs. Experimental results demonstrate the successful interconversion of four CVB modes (CVB+1 and CVB-2, CVB+2 and CVB-4) using a Si-based metasurface with a polarization conversion efficiency exceeding 85%. This facilitates the cross-connection of 200 Gbit/s quadrature phase-shift keying signals with bit-error-rates below 10-6. Offering advantages such as ultra-compact device size, flexible control of CVB modes, and multi-mode parallel processing, this approach shows promise in advancing the networking capabilities of CVB mode multiplexing communication networks.

Synchronization effects in multiplex networks of chaotic maps with memristive interlayer coupling

Models of two-layer multiplex networks of one-dimensional maps with memristive interlayer coupling are studied. In the absence of coupling, the layers exhibit different types of chimera states. Two types of maps are considered as the elements of networks: modified Ricker maps and cubic maps. The effects of complete and partial synchronization of the spatiotemporal dynamics of layers are observed in the case of a homogeneous and inhomogeneous network, respectively. The dependence of the synchronization threshold for the coupling parameter on the initial states of the memristors has been established. This dependence is partially preserved in the case of non-ideal memristors. Diagrams of the synchronization error are constructed on the plane of the initial state variable of memristors and the interlayer coupling coefficient. The effect of noise in memristive coupling elements on synchronization is considered.

Impact of information adoption and the resulted self-protective actions on epidemic spreading in awareness-disease coupled multiplex networks

Impact of information adoption and the resulted self-protective actions on epidemic spreading in awareness-disease coupled multiplex networks

Multilayer analysis of energy networks

Modern interconnected and vulnerable energy infrastructures highlight the critical need for resilience and robustness to maintain the functioning of modern societies amidst growing environmental and operational challenges. This study introduces both multilayer and multiplex network analysis of Belgium’s electricity and gas systems, addressing the complex interdependence inherent in such infrastructure. The resilience is evaluated through random and targeted disruptions, while the robustness is assessed by employing the Molloy-Reed criteria for structural integrity and setting minimum operational thresholds for continuity. Multiplex layer similarities are assessed and subnetworks are identified. The coverage evolution metric quantifies the network’s adaptability under various disruption scenarios. Belgium’s energy infrastructure is used as a case study to uncover critical nodes from different centrality perspectives whose stability is essential for overall network resilience and identify vulnerabilities to disruptions, whether random or targeted. Our insights into the structural robustness, cluster cohesion, and Navigability of energy networks pave the way for more informed decisions in energy infrastructure planning and complex systems management, offering valuable lessons that can be applied globally.

Dynamic analysis of the rumor propagation model with consideration of the refutation mechanism and activity rate in multiplex networks

With the development of social networks, misinformation including rumors is spreading through multiple channels, which brings many negative effects to society. The government and several Nongovernmental Organizations (NGOs) use relevant rumor rebuttal tactics to control the spread of rumors to prevent these detrimental impacts. In this paper, we consider the responses of different individuals to rumors and classify individuals into three categories: active, normal and inactive, with different activity rates for the three categories. In order to study the interaction between rumor repudiation mechanisms and rumor propagation, we propose a rumor propagation model that considers global and local rumor repudiation mechanisms as well as activity rates in multiplex networks. The upper layer represents the rumor refutation information propagation and the lower layer expresses the rumor propagation. And mean-field equations describing the dynamics of this model in multiplex networks are derived. We found that the threshold of rumor propagation is significantly affected by individual activity rates. Another interesting finding is that the global rumor refutation mechanism suppresses rumor propagation more than the local disinformation mechanism.

Exploring the disruptions of the neurophysiological organization in Alzheimer’s disease: An integrative approach

Background and Objective:Alzheimer’s disease (AD) is a neurological disorder that impairs brain functions associated with cognition, memory, and behavior. Noninvasive neurophysiological techniques like magnetoencephalography (MEG) and electroencephalography (EEG) have shown promise in reflecting brain changes related to AD. These techniques are usually assessed at two levels: local activation (spectral, nonlinear, and dynamic properties) and global synchronization (functional connectivity, frequency-dependent network, and multiplex network organization characteristics). Nonetheless, the understanding of the organization formed by the existing relationships between these levels, henceforth named neurophysiological organization, remains unexplored. This work aims to assess the alterations AD causes in the resting-state neurophysiological organization. Methods:To that end, three datasets from healthy controls (HC) and patients with dementia due to AD were considered: MEG database (55 HC and 87 patients with AD), EEG1 database (51 HC and 100 patients with AD), and EEG2 database (45 HC and 82 patients with AD). To explore the alterations induced by AD in the relationships between several features extracted from M/EEG data, association networks (ANs) were computed. ANs are graphs, useful to quantify and visualize the intricate relationships between multiple features. Results:Our results suggested a disruption in the neurophysiological organization of patients with AD, exhibiting a greater inclination towards the local activation level; and a significant decrease in the complexity and diversity of the ANs (p-value ¡ 0.05, Mann–Whitney U-test, Bonferroni correction). This effect might be due to a shift of the neurophysiological organization towards more regular configurations, which may increase its vulnerability. Moreover, our findings support the crucial role played by the local activation level in maintaining the stability of the neurophysiological organization. Classification performance exhibited accuracy values of 83.91%, 73.68%, and 72.65% for MEG, EEG1, and EEG2 databases, respectively. Conclusion:This study introduces a novel, valuable methodology able to integrate parameters characterize different properties of the brain activity and to explore the intricate organization of the neurophysiological organization at different levels. It was noted that AD increases susceptibility to changes in functional neural organization, suggesting a greater ease in the development of severe impairments. Therefore, ANs could facilitate a deeper comprehension of the complex interactions in brain function from a global standpoint.

Motif-based community detection in heterogeneous multilayer networks

Multilayer networks composed of intralayer edges and interlayer edges are an important type of complex networks. Considering the heterogeneity of nodes and edges, it is necessary to design more reasonable and diverse community detection methods for multilayer networks. Existing research on community detection in multilayer networks mainly focuses on multiplexing networks (where the nodes are homogeneous and the edges are heterogeneous), but few studies have focused on heterogeneous multilayer networks where both nodes and edges represent different semantics. In this paper, we studied community detection on heterogeneous multilayer networks and proposed a motif-based detection algorithm. First, the communities and motifs of multilayer networks are defined, especially the interlayer motifs. Then, the modularity of multilayer networks based on these motifs is designed, and the community structure of the multilayer network is detected by maximizing the modularity of multilayer networks. Finally, we verify the effectiveness of the detection algorithm on synthetic networks. In the experiments on synthetic networks, comparing with the classical community detection algorithms (without considering interlayer heterogeneity), the motif-based modularity community detection algorithm can obtain better results under different evaluation indexes, and we found that there exists a certain relationship between motifs and communities. In addition, the proposed algorithm is applied in the empirical network, which shows its practicability in the real world. This study provides a solution for the investigation of heterogeneous information in multilayer networks.

Community Detection in Multiplex Networks Using Orthogonal Non-Negative Matrix Tri-Factorization Based on Graph Regularization and Diversity

In recent years, community detection has received increasing interest. In network analysis, community detection refers to the identification of tightly connected subsets of nodes, which are called “communities” or “groups”, in the network. Non-negative matrix factorization models are often used to solve the problem. Orthogonal non-negative matrix tri-factorization (ONMTF) exhibits significant potential as an approach for community detection within multiplex networks. This paper explores the application of ONMTF in multiplex networks, aiming to detect both shared and exclusive communities simultaneously. The model decomposes each layer within the multiplex network into two low-rank matrices. One matrix corresponds to shared communities across all layers, and the other to unique communities within each layer. Additionally, graph regularization and the diversity of private communities are taken into account in the algorithm. The Hilbert Schmidt Independence Criterion (HSIC) is used to constrain the independence of private communities. The results prove that ONMTF effectively addresses community detection in multiplex networks. It also offers strong interpretability and feature extraction capabilities. Therefore, it is an advanced method for community detection in multiplex networks.

Critical properties of Heider balance on multiplex networks

Critical properties of Heider balance on multiplex networks

Finite-time observability of probabilistic Boolean multiplex control networks

Finite-time observability of probabilistic Boolean multiplex control networks

A multiplex network approach to the self-organizing bonding and bridging social capital fostered among local residents: A case study of community currency in Korea under the Hanbat LETS

A variety of community currency systems have been adopted, implemented, and terminated among the local communities of Korea over the last two decades. Despite its volatility due to the economic, social, and political environmental changes occurring in Korean society, the Hanbat local exchange trading system (LETS) is regarded as an innovative practice in grassroots community currency schemes based on trust and cooperation among local residents and plays a critical role in promoting community rebuilding and the formation of a sharing economy in this area. This study is aimed at empirically investigating the microprocesses underlying the formation of multiple types of social capital—bonding, bridging, and linking social capital—that were observed in the transactions among the Hanbat LETS members through inferential network analysis. The findings show that bonding and bridging social capital coexist in both a singular (or uniplex) type and in distinct (or multiplex) types of transactional tie developments among the participants through this community currency system. By examining the ways in which these multiple types of social capital are fostered through a bottom-up approach focused on a community currency system, the results of this study suggest the potential roles played by peer-to-peer support exchanges and the sharing economy in a local community.

Rcoco: contrastive collective link prediction across multiplex network in Riemannian space

Rcoco: contrastive collective link prediction across multiplex network in Riemannian space

Pinning intra-layer synchronization in multiplex networks of nonidentical layers

In this paper, we investigate intra-layer synchronization in multiplex networks via pinning control strategies. All layers have different topologies and different intrinsic node dynamics. Novel sufficient criteria are derived for pinning intra-layer synchronization of multiplex networks, which indicates that the pinned node set can stabilize the multiplex network if, for each layer, the pinned node(s) can access all unpinned nodes. A distributed adaptive algorithm and finite-time pinning algorithm for intra-layer synchronization of multiplex networks are also proposed. Finally, we give some numerical examples to validate the effectiveness of these theoretical results.

Describing financial crisis propagation through epidemic modelling on multiplex networks

This paper proposes a novel framework for modelling the spread of financial crises in complex networks, combining financial data, Extreme Value Theory and an epidemiological transmission model. We accommodate two key aspects of contagion modelling: fundamentals-based contagion, where the transmission is due to direct financial linkages, and pure contagion, where a crisis might trigger additional crises due to global effects. We use stock price, geographical location and economic sector data for a set of 398 companies to construct multiplex networks of four layers, on which a susceptible-infected-recovered transmission model is defined, in order to model the spread of financial shocks between companies by accounting for their interconnected nature. By utilizing stock price data for the 2008 and 2020 financial crises, we investigate and assess the effectiveness of our model in forecasting the propagation of financial shocks through the network, where a shock is detected by measuring stock price volatility. The results suggest that the proposed framework is effective in predicting the spread of financial crises. Our findings demonstrate the significance of each layer of the multiplex network structure, which differentiates between various transmission pathways, for predicting the number of affected companies, as well as for company-, sector- or location-specific predictions.

Post global financial crisis multiplex financial network structure longevity: Does it predict re-globalization? Empirical investigation for 234 countries

Research background: International capital flows show decreasing trend after each financial crisis as countries become unwilling to invest in risky counterparties. Recent discussions over structural changes within the global financial network suggest that its structure may be still undergoing some changes. Uncovered weaknesses of over-connectedness with unstable un-ally countries during global financial crisis were further highlighted by recent Covid-19 pandemic. However, previous research suggest that important structural changes happened after global financial crisis. Thus, such situation raises a question whether post global financial crisis multiplex network structure is long-term and is it exhibiting re-globalization pattern as suggested by re-globalization megatrend. Purpose of the article: The main objective of the paper is to assess post global financial crisis multiplex financial network structure longevity and to identify whether it exhibits re-globalization pattern. Methods: Multiplex financial network mapping, network topological analysis and structure longevity methods were employed to evaluate network connectedness, topological structural properties of multiplex financial network and its’ structure longevity. 5-layer multiplex financial network was mapped for different types of capital flows for each layer: net direct and portfolio investments in debt, equity and net banking assets for each year in the post global financial crisis period 2009–2020. Each network layer employed bilateral data from up to 234 countries of the world. Next step of research employed a set of network-level measures defining topological features of each network in the period of 2009–2020 in order to capture the trend of structural changes and evidence of re-globalization. The final stage analyzes multiplex financial network structure by layer and country longevity. Findings & value added: Analysis reveals that stock (positions) multiplex financial network aggregate connectedness, i.e., density and value, increased during post- global financial crisis period until Covid-19 pandemic period, thus, suggesting that globalization in terms of stock is continuing. Topological structural properties of multiplex financial network changed as number of strongly and weakly connected countries decreased and more countries became included in network. Longevity analysis of layer and country structure within multiplex financial network reveal that banking and debt investments are increasing since 2018, while equity part is decreasing. Developed countries, i.e., the United Kingdom and Germany, decrease in multiplex financial network structure, while developing, especially from Asia region (i.e., Hong Kong SAR, China and Singapore) increase. Such empirical results support the re-globalization megatrend in terms of investment type and counterparty structure as highlighted by most recent scientific discussion showing that it started early after global financial crisis. Research also uncovers some regional trends of Asia region increasing in investment network structure, while Europe decreasing. As developing countries attract more and more investment and further develop, global cost saving and, thus, returns from global investment into these countries may be decreasing, resulting in lower gain from globalization. Our analysis may facilitate investment strategy decisions by suggesting that even though gains from globalization might be decreasing, instead of localization, countries could follow ally investment strategy to manage the risk of over-dependency from unstable counterparty while preserving globalization wealth.

Epidemic models in well-mixed multiplex networks with distributed time delay

In this paper, we consider an epidemic model in well-mixed multiplex networks with distributed time delay. Specifically, the model consists of two layers of well-mixed networks in the physical and virtual worlds, respectively, where two diffusive processes interact and influence each other within the same individual. We assume that there is a distributed time delay for an individual to become infected, but no delay for an individual to transition from unawareness to awareness. Our main results are as follows: Let R0P and R0V represent the basic reproduction numbers in the physical and virtual worlds, respectively. First, we demonstrate that the disease will die out for any delay time, provided that R0P≤1 or 1<R0P≤R0V. The latter condition emphasizes the significance of effective information spreading in eradicating the disease. Secondly, in the case of R0P>max⁡{1,R0V}, we establish that the model exhibits an endemic and information saturated equilibrium, denoted as E3. Additionally, we show that the model is uniformly persistent, indicating the sustained outbreak of the disease.

The universality of physical images at relative timescales on multiplex networks

The duration of the accumulation rate (physical image) is a key factor in analysis of counterintuitive phenomena involving relative timescales on multiplex networks. Typically, the relative timescales are represented by multiplying any layer by the same factor. However, researchers often overlook the changes in the relative timescales caused by local parameters, resulting in incomplete analysis of phenomena. This paper examines the survival time of stifler individuals in the information-epidemic model on multiplex networks. The relative timescales can be affected by the survival time (only one parameter), reversing the monotonically increasing phenomenon into a monotonically decreasing one, that is, a counterintuitive phenomenon under incomplete analysis. Additionally, the relative timescales can influence the epidemic threshold, which is different from the previous studies. Our work suggests that considering the physical image of relative timescales is crucial when analyzing multiplex networks, even when only one parameter is altered.

Mode-selective power splitters for mode-division multiplexing optical networks

We propose an all-fiber mode-selective power splitter (MSPS) for non-circular-symmetric LP lm (l = 1, 2, …) modes, which is suitable for multicasting and optical performance monitoring in mode-division multiplexing optical fiber networks. The MSPSs are asymmetric two-core few-mode directional couplers composed of a few-mode fiber and a two-mode fiber. We theoretically studied the three conditions required by the MSPSs. By carefully choosing the core-to-core distance and coupling length, the MSPS can achieve arbitrary splitting ratio regardless of the modal field orientation of the input non-circular-symmetric LP mode. By using an asymmetric structure, the MSPS can ensure the power splitting only happens on the target non-circular-symmetric LP mode when the phase matching condition is satisfied. In addition, we designed and numerically simulated LP31 MSPSs with four kinds of splitting ratios, among which the one with 90/10 splitting ratio was fabricated based on tapering and polishing method. The fabricated LP31 MSPS is characterized and the results show that its splitting ratio is much more stable than regular LP31 mode-selective coupler.