Complex networks: Small-world, scale-free and beyond

LLMs and generative agent-based models for complex systems research

The advent of Large Language Models (LLMs) offers to transform research across natural and social sciences, offering new paradigms for understanding complex systems. In particular, Generative Agent-Based Models (GABMs), which integrate LLMs to simulate human behavior, have attracted increasing public attention due to their potential to model complex interactions in a wide range of artificial environments. This paper briefly reviews the disruptive role LLMs are playing in fields such as network science, evolutionary game theory, social dynamics, and epidemic modeling. We assess recent advancements, including the use of LLMs for predicting social behavior, enhancing cooperation in game theory, and modeling disease propagation. The findings demonstrate that LLMs can reproduce human-like behaviors, such as fairness, cooperation, and social norm adherence, while also introducing unique advantages such as cost efficiency, scalability, and ethical simplification. However, the results reveal inconsistencies in their behavior tied to prompt sensitivity, hallucinations and even the model characteristics, pointing to challenges in controlling these AI-driven agents. Despite their potential, the effective integration of LLMs into decision-making processes -whether in government, societal, or individual contexts- requires addressing biases, prompt design challenges, and understanding the dynamics of human-machine interactions. Future research must refine these models, standardize methodologies, and explore the emergence of new cooperative behaviors as LLMs increasingly interact with humans and each other, potentially transforming how decisions are made across various systems.

Combined influence of the nanoplastics and polycyclic aromatic hydrocarbons exposure on microbial community in seawater environment

Nanoplastics (NPs) and polycyclic aromatic hydrocarbons (PAHs) are recognized as persistent organic pollutant (POPs) with demonstrated physiological toxicity. When present in aquatic environments, the two pollutants could combine with each other, resulting in cumulative toxicity to organisms. However, the combined impact of NPs and PAHs on microorganisms in seawater is not well understood. In this study, we conducted an exposure experiment to investigate the individual and synergistic effects of NPs and PAHs on the composition, biodiversity, co-occurrence networks of microbial communities in seawater. Exposure of individuals to PAHs led to a reduction in microbial community richness, but an increase in the relative abundance of species linked to PAHs degradation. These PAHs-degradation bacteria acting as keystone species, maintained a microbial network complexity similar to that of the control treatment. Exposure to individual NPs resulted in a reduction in the complexity of microbial networks. Furthermore, when PAHs and NPs were simultaneously present, the toxic effect of NPs hindered the presence of keystone species involved in PAHs degradation, subsequently limiting the degradation of PAHs by marine microorganisms, resulting in a decrease in community diversity and symbiotic network complexity. This situation potentially poses a heightened threat to the ecological stability of marine ecosystems. Our work strengthened the understanding of the combined impact of NPs and PAHs on microorganisms in seawater.

Study on the Stability of Complex Networks in the Stock Markets of Key Industries in China

Investigating the significant "roles" within financial complex networks and their stability is of great importance for preventing financial risks. On one hand, this paper initially constructs a complex network model of the stock market based on mutual information theory and threshold methods, combined with the closing price returns of stocks. It then analyzes the basic topological characteristics of this network and examines its stability under random and targeted attacks by varying the threshold values. On the other hand, using systemic risk entropy as a metric to quantify the stability of the stock market, this paper validates the impact of the COVID-19 pandemic as a widespread, unexpected event on network stability. The research results indicate that this complex network exhibits small-world characteristics but cannot be strictly classified as a scale-free network. In this network, key roles are played by the industrial sector, media and information services, pharmaceuticals and healthcare, transportation, and utilities. Upon reducing the threshold, the network's resilience to random attacks is correspondingly strengthened. Dynamically, from 2000 to 2022, systemic risk in significant industrial share markets significantly increased. From a static perspective, the period around 2019, affected by the COVID-19 pandemic, experienced the most drastic fluctuations. Compared to the year 2000, systemic risk entropy in 2022 increased nearly sixtyfold, further indicating an increasing instability within this complex network.

African swine fever in wild boar: investigating model assumptions and structure

African swine fever (ASF) is a highly virulent viral disease that affects domestic pigs and wild boar. Current ASF transmission in Europe is in part driven by wild boar populations, which act as a disease reservoir. Wild boar are abundant throughout Europe and are highly social animals with complex social organization. Despite the known importance of wild boar in ASF spread and persistence, knowledge gaps remain surrounding wild boar transmission. We developed a wild boar modelling framework to investigate the influence of contact-density functions and wild boar social structure on disease dynamics. The framework included an ordinary differential equation model, a homogeneous stochastic model and various network-based stochastic models that explicitly included wild boar social grouping. We found that power-law functions (transmission∝ density0.5) and frequency-based contact-density functions were best able to reproduce recent Baltic outbreaks; however, power-law function models predicted considerable carcass transmission, while frequency-based models had negligible carcass transmission. Furthermore, increased model heterogeneity caused a decrease in the relative importance of carcass-based transmission. The transmission pathways predicted by each model type affected the efficacy of idealized interventions, which highlights the importance of evaluating model type and structure when modelling systems with significant uncertainties.

Entropy-Based Node Importance Identification Method for Public Transportation Infrastructure Coupled Networks: A Case Study of Chengdu

Public transportation infrastructure is a typical, complex, coupled network that is usually composed of connected bus lines and subway networks. This study proposes an entropy-based node importance identification method for this type of coupled network that is helpful for the integrated planning of urban public transport and traffic flows, as well as enhancing network information dissemination and maintaining network resilience. The proposed method develops a systematic entropy-based metric based on five centrality metrics, namely the degree centrality (DC), betweenness centrality (BC), closeness centrality (CC), eigenvector centrality (EC), and clustering coefficient (CCO). It then identifies the most important nodes in the coupled networks by considering the information entropy of the nodes and their neighboring ones. To evaluate the performance of the proposed method, a bus-subway coupled network in Chengdu, containing 10,652 nodes and 15,476 edges, is employed as a case study. Four network resilience assessment metrics, namely the maximum connectivity coefficient (MCC), network efficiency (NE), susceptibility (S), and natural connectivity (NC), were used to conduct group experiments. The experimental results demonstrate the following: (1) the multi-functional fitting analysis improves the analytical accuracy by 30% as compared to fitting with power law functions only; (2) for both CC and CCO, the improved metric's performance in important node identification is greatly improved, and it demonstrates good network resilience.

Synchronization enhancement subjected to adaptive blinking coupling

Synchronization holds a significant role, notably within chaotic systems, in various contexts where the coordinated behavior of systems plays a pivotal and indispensable role. Hence, many studies have been dedicated to investigating the underlying mechanism of synchronization of chaotic systems. Networks with time-varying coupling, particularly those with blinking coupling, have been proven essential. The reason is that such coupling schemes introduce dynamic variations that enhance adaptability and robustness, making them applicable in various real-world scenarios. This paper introduces a novel adaptive blinking coupling, wherein the coupling adapts dynamically based on the most influential variable exhibiting the most significant average disparity. To ensure an equitable selection of the most effective coupling at each time instance, the average difference of each variable is normalized to the synchronous solution's range. Due to this adaptive coupling selection, synchronization enhancement is expected to be observed. This hypothesis is assessed within networks of identical systems, encompassing Lorenz, Rössler, Chen, Hindmarsh-Rose, forced Duffing, and forced van der Pol systems. The results demonstrated a substantial improvement in synchronization when employing adaptive blinking coupling, particularly when applying the normalization process.

How online healthcare team evolve into organization: A social network analysis

Objective

The rapid development of online healthcare has greatly promoted the transformation of healthcare service. The effectiveness of online healthcare is enhanced by the team that supports the doctor-patient connection. However, extant researches lack the comprehensive analysis of social networks within online healthcare team. In this study, we aim to clarify the characteristics and models of online healthcare team.

Method

This study focuses on the online healthcare context and collects data from online healthcare team. Using social network analysis, the social networks of online healthcare members are also developed as part of the research.

Result

This study uncovers the different modes of online healthcare teams from individual, team and organizational levels. These results shed light on the characteristics of an online healthcare team and show that such teams are capable of restructuring social networks. In addition, collaboration between teams allows for the development of multilevel relationships and the potential for the online healthcare team to evolve into a large-scale online healthcare organization.

Conclusion

Through social network analysis, this study offers a fresh viewpoint on online healthcare and its implications for management, team construction, and organizational restruction. By examining the characteristics and models of online healthcare team, this research offers valuable insights for improving the overall effectiveness of online healthcare.

Desynchrony induced by higher-order interactions in triplex metapopulations

In a predator-prey metapopulation, two traits are adversely related: synchronization and persistence. A decrease in synchrony apparently leads to an increase in persistence and, therefore, necessitates the study of desynchrony in a metapopulation. In this article, we study predator-prey patches that communicate with one another while being interconnected through distinct dispersal structures in the layers of a three-layer multiplex network. We investigate the synchronization phenomenon among the patches of the outer layers by introducing higher-order interactions (specifically three-body interactions) in the middle layer. We observe a decrease in the synchronous behavior or, alternatively, an increase in desynchrony due to the inclusion of group interactions among the patches of the middle layer. The advancement of desynchrony becomes more prominent with increasing strength and numbers of three-way interactions in the middle layer. We analytically validate our numerical results by performing a stability analysis of the referred synchronous solution using the master stability function approach. Additionally, we verify our findings by taking into account two distinct predator-prey models and dispersal topologies, which ultimately supports that the findings are generalizable across various models and dispersal structures.

Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure

A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use mathematical frameworks like fractional calculus, which is capable of doing so. Here, we first present a fractional-order memristor synapse-coupling Hopfield neural network on two neurons and then extend the model to a neural network with a ring structure that consists of n sub-network neurons, increasing the synchronization in the network. Necessary and sufficient conditions for the stability of equilibrium points are investigated, highlighting the dependency of the stability on the fractional-order value and the number of neurons. Numerical simulations and bifurcation analysis, along with Lyapunov exponents, are given in the two-neuron case that substantiates the theoretical findings, suggesting possible routes towards chaos when the fractional order of the system increases. In the n-neuron case also, it is revealed that the stability depends on the structure and number of sub-networks.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

Power-grid vulnerability and its relation with network structure

Interconnected systems with critical infrastructures can be affected by small failures that may trigger a large-scale cascade of failures, such as blackouts in power grids. Vulnerability indices provide quantitative measures of a network resilience to component failures, assessing the break of information or energy flow in a system. Here, we focus on a network vulnerability analysis, that is, indices based solely on the network structure and its static characteristics, which are reliably available for most complex networks. This work studies the structural connectivity of power grids, assessing the main centrality measures in network science to identify vulnerable components (transmission lines or edges) to attacks and failures. Specifically, we consider centrality measures that implicitly model the power flow distribution in power systems. This framework allow us to show that the efficiency of the power flow in a grid can be highly sensitive to attacks on specific (central) edges. Numerical results are presented for randomly generated power-grid models and established power-grid benchmarks, where we demonstrate that the system's energy efficiency is more vulnerable to attacks on edges that are central to the power flow distribution. We expect that the vulnerability indices investigated in our work can be used to guide the design of structurally resilient power grids.

Gene prioritization based on random walks with restarts and absorbing states, to define gene sets regulating drug pharmacodynamics from single-cell analyses

Prioritizing genes for their role in drug sensitivity, is an important step in understanding drugs mechanisms of action and discovering new molecular targets for co-treatment. To formalize this problem, we consider two sets of genes X and P respectively composing the gene signature of cell sensitivity at the drug IC50 and the genes involved in its mechanism of action, as well as a protein interaction network (PPIN) containing the products of X and P as nodes. We introduce Genetrank, a method to prioritize the genes in X for their likelihood to regulate the genes in P. Genetrank uses asymmetric random walks with restarts, absorbing states, and a suitable renormalization scheme. Using novel so-called saturation indices, we show that the conjunction of absorbing states and renormalization yields an exploration of the PPIN which is much more progressive than that afforded by random walks with restarts only. Using MINT as underlying network, we apply Genetrank to a predictive gene signature of cancer cells sensitivity to tumor-necrosis-factor-related apoptosis-inducing ligand (TRAIL), performed in single-cells. Our ranking provides biological insights on drug sensitivity and a gene set considerably enriched in genes regulating TRAIL pharmacodynamics when compared to the most significant differentially expressed genes obtained from a statistical analysis framework alone. We also introduce gene expression radars, a visualization tool embedded in MA plots to assess all pairwise interactions at a glance on graphical representations of transcriptomics data. Genetrank is made available in the Structural Bioinformatics Library (https://sbl.inria.fr/doc/Genetrank-user-manual.html). It should prove useful for mining gene sets in conjunction with a signaling pathway, whenever other approaches yield relatively large sets of genes.

A Dynamic Event-Triggered Approach to Recursive Nonfragile Filtering for Complex Networks With Sensor Saturations and Switching Topologies

In this article, the nonfragile filtering issue is addressed for complex networks (CNs) with switching topologies, sensor saturations, and dynamic event-triggered communication protocol (DECP). Random variables obeying the Bernoulli distribution are utilized in characterizing the phenomena of switching topologies and stochastic gain variations. By introducing an auxiliary offset variable in the event-triggered condition, the DECP is adopted to reduce transmission frequency. The goal of this article is to develop a nonfragile filter framework for the considered CNs such that the upper bounds on the filtering error covariances are ensured. By the virtue of mathematical induction, gain parameters are explicitly derived via minimizing such upper bounds. Moreover, a new method of analyzing the boundedness of a given positive-definite matrix is presented to overcome the challenges resulting from the coupled interconnected nodes, and sufficient conditions are established to guarantee the mean-square boundedness of filtering errors. Finally, simulations are given to prove the usefulness of our developed filtering algorithm.

Neuroscience and Network Dynamics Toward Brain-Inspired Intelligence

This article surveys the interdisciplinary research of neuroscience, network science, and dynamic systems, with emphasis on the emergence of brain-inspired intelligence. To replicate brain intelligence, a practical way is to reconstruct cortical networks with dynamic activities that nourish the brain functions, instead of using only artificial computing networks. The survey provides a complex network and spatiotemporal dynamics (abbr. network dynamics) perspective for understanding the brain and cortical networks and, furthermore, develops integrated approaches of neuroscience and network dynamics toward building brain-inspired intelligence with learning and resilience functions. Presented are fundamental concepts and principles of complex networks, neuroscience, and hybrid dynamic systems, as well as relevant studies about the brain and intelligence. Other promising research directions, such as brain science, data science, quantum information science, and machine behavior are also briefly discussed toward future applications.

Pinning Impulsive Synchronization of Stochastic Delayed Neural Networks via Uniformly Stable Function

This article investigates the synchronization of stochastic delayed neural networks under pinning impulsive control, where a small fraction of nodes are selected as the pinned nodes at each impulsive moment. By proposing a uniformly stable function as a new tool, some novel mean square decay results are presented to analyze the error system obtained from the leader and the considered neural networks. For the divergent error system without impulsive effects, the impulsive gains of pinning impulsive controller can admit destabilizing impulse and the number of destabilizing impulse may be infinite. However, if the error system without impulsive effects is convergent, to achieve the synchronization of the stochastic neural networks, the growth exponent of the product of impulsive gains can not exceed some positive constant. It is shown that the obtained results increase the flexibility of the impulsive gains compared with the existing results. Finally, a numerical example is given to illustrate the practicality of synchronization criteria.

Benchmarking Cost-Effective Opinion Injection Strategies in Complex Networks

Inferring the diffusion mechanisms in complex networks is of outstanding interest since it enables better prediction and control over information dissemination, rumors, innovation, and even infectious outbreaks. Designing strategies for influence maximization in real-world networks is an ongoing scientific challenge. Current approaches commonly imply an optimal selection of spreaders used to diffuse and indoctrinate neighboring peers, often overlooking realistic limitations of time, space, and budget. Thus, finding trade-offs between a minimal number of influential nodes and maximizing opinion coverage is a relevant scientific problem. Therefore, we study the relationship between specific parameters that influence the effectiveness of opinion diffusion, such as the underlying topology, the number of active spreaders, the periodicity of spreader activity, and the injection strategy. We introduce an original benchmarking methodology by integrating time and cost into an augmented linear threshold model and measure indoctrination expense as a trade-off between the cost of maintaining spreaders’ active and real-time opinion coverage. Simulations show that indoctrination expense increases polynomially with the number of spreaders and linearly with the activity periodicity. In addition, keeping spreaders continuously active instead of periodically activating them can increase expenses by 69–84% in our simulation scenarios. Lastly, we outline a set of general rules for cost-effective opinion injection strategies.

Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes

The global synchronization of complex networks with fractional-order chaotic nodes is investigated via a simple Lyapunov function and the feedback controller in this paper. Firstly, the GMMP method is proposed to obtain the numerical solution of the fractional-order nonlinear equation based on the relation of the fractional derivatives. Then, the new feedback controllers are proposed to achieve synchronization between the complex networks with the fractional-order chaotic nodes based on feedback control. We propose some new sufficient synchronous criteria based on the Lyapunov stability and a simple Lyapunov function. By the numerical simulations of the complex networks, we find that these synchronous criteria can apply to the arbitrary complex dynamical networks with arbitrary fractional-order chaotic nodes. Numerical simulations of synchronization between two complex dynamical networks with the fractional-order chaotic nodes are given by the GMMP method and the Newton method, and the results of numerical simulation demonstrate that the proposed method is universal and effective.

Finite-Time Synchronization for Delayed Complex Dynamical Networks With Synchronizing or Desynchronizing Impulses

In this article, the finite-time synchronization problem of delayed complex dynamical networks (CDNs) with impulses is studied, where two types of impulses, namely, synchronizing impulses and desynchronizing impulses, are fully considered, respectively. Since the existence of impulses makes the discontinuity of the states, which means that the classical result for finite-time stability is inapplicable in such a case, the key challenge is how to guarantee the finite-time stability and estimate the settling time in impulse sense. We apply impulsive control theory and finite-time stability theory to CDNs and establish some sufficient conditions for finite-time synchronization, where two kinds of memory controllers are designed for synchronizing impulses and desynchronizing impulses, respectively. Moreover, the upper bounds for settling time of synchronization, which depends on the impulse sequences, are effectively estimated. It shows that the synchronizing impulses can shorten the settling time of synchronization; conversely, the desynchronizing impulses can delay it. Finally, the theoretical analysis is verified by two simulation examples.

Disrupting networks of hate: characterising hateful networks and removing critical nodes

Hateful individuals and groups have increasingly been using the Internet to express their ideas, spread their beliefs and recruit new members. Understanding the network characteristics of these hateful groups could help understand individuals’ exposure to hate and derive intervention strategies to mitigate the dangers of such networks by disrupting communications. This article analyses two hateful followers’ networks and three hateful retweet networks of Twitter users who post content subsequently classified by human annotators as containing hateful content. Our analysis shows similar connectivity characteristics between the hateful followers networks and likewise between the hateful retweet networks. The study shows that the hateful networks exhibit higher connectivity characteristics when compared to other “risky” networks, which can be seen as a risk in terms of the likelihood of exposure to, and propagation of, online hate. Three network performance metrics are used to quantify the hateful content exposure and contagion: giant component (GC) size, density and average shortest path. In order to efficiently identify nodes whose removal reduced the flow of hate in a network, we propose a range of structured node-removal strategies and test their effectiveness. Results show that removing users with a high degree is most effective in reducing the hateful followers network connectivity (GC, size and density), and therefore reducing the risk of exposure to cyberhate and stemming its propagation.

Synonymy Expansion Using Link Prediction Methods: A Case Study of Assamese WordNet

WordNets built for low-resource languages, such as Assamese, often use the expansion methodology. This may result in missing lexical entries and missing synonymy relations. As the Assamese WordNet is also built using the expansion method, using the Hindi WordNet, it also has missing synonymy relations. As WordNets can be visualized as a network of unique words connected by synonymy relations, link prediction in complex network analysis is an effective way of predicting missing relations in a network. Hence, to predict the missing synonyms in the Assamese WordNet, link prediction methods were used in the current work that proved effective. It is also observed that for discovering missing relations in the Assamese WordNet, simple local proximity-based methods might be more effective as compared to global and complex supervised models using network embedding. Further, it is noticed that though a set of retrieved words are not synonyms per se, they are semantically related to the target word and may be categorized as semantic cohorts.

Policy and behavioral response to shock events: An agent-based model of the effectiveness and equity of policy design features

In the aftermath of shock events, policy responses tend to be crafted under significant time constraints and high levels of uncertainty. The extent to which individuals comply with different policy designs can further influence how effective the policy responses are and how equitably their impacts are distributed in the population. Tools which allow policymakers to model different crisis trajectories, policy responses, and behavioral scenarios ex ante can provide crucial timely support in the decision-making process. Set in the context of COVID-19 shelter in place policies, in this paper we present the COVID-19 Policy Evaluation (CoPE) tool, which is an agent-based modeling framework that enables researchers and policymakers to anticipate the relative impacts of policy decisions. Specifically, this framework illuminates the extent to which policy design features and behavioral responsiveness influence the efficacy and equity of policy responses to shock events. We show that while an early policy response can be highly effective, the impact of the timing is moderated by other aspects of policy design such as duration and targeting of the policy, as well as societal aspects such as trust and compliance among the population. More importantly, we show that even policies that are more effective overall can have disproportionate impacts on vulnerable populations. By disaggregating the impact of different policy design elements on different population groups, we provide an additional tool for policymakers to use in the design of targeted strategies for disproportionately affected populations.

Graph coloring using the reduced quantum genetic algorithm

Genetic algorithms (GA) are computational methods for solving optimization problems inspired by natural selection. Because we can simulate the quantum circuits that implement GA in different highly configurable noise models and even run GA on actual quantum computers, we can analyze this class of heuristic methods in the quantum context for NP-hard problems. This paper proposes an instantiation of the Reduced Quantum Genetic Algorithm (RQGA) that solves the NP-hard graph coloring problem in O(N^1/2). The proposed implementation solves both vertex and edge coloring and can also determine the chromatic number (i.e., the minimum number of colors required to color the graph). We examine the results, analyze the algorithm convergence, and measure the algorithm's performance using the Qiskit simulation environment. Our Reduced Quantum Genetic Algorithm (RQGA) circuit implementation and the graph coloring results show that quantum heuristics can tackle complex computational problems more efficiently than their conventional counterparts.

Modelling digital and manual contact tracing for COVID-19. Are low uptakes and missed contacts deal-breakers?

Comprehensive testing schemes, followed by adequate contact tracing and isolation, represent the best public health interventions we can employ to reduce the impact of an ongoing epidemic when no or limited vaccine supplies are available and the implications of a full lockdown are to be avoided. However, the process of tracing can prove feckless for highly-contagious viruses such as SARS-CoV-2. The interview-based approaches often miss contacts and involve significant delays, while digital solutions can suffer from insufficient adoption rates or inadequate usage patterns. Here we present a novel way of modelling different contact tracing strategies, using a generalized multi-site mean-field model, which can naturally assess the impact of manual and digital approaches alike. Our methodology can readily be applied to any compartmental formulation, thus enabling the study of more complex pathogen dynamics. We use this technique to simulate a newly-defined epidemiological model, SEIR-T, and show that, given the right conditions, tracing in a COVID-19 epidemic can be effective even when digital uptakes are sub-optimal or interviewers miss a fair proportion of the contacts.

Lagrangian betweenness as a measure of bottlenecks in dynamical systems with oceanographic examples

The study of connectivity patterns in networks has brought novel insights across diverse fields ranging from neurosciences to epidemic spreading or climate. In this context, betweenness centrality has demonstrated to be a very effective measure to identify nodes that act as focus of congestion, or bottlenecks, in the network. However, there is not a way to define betweenness outside the network framework. By analytically linking dynamical systems and network theory, we provide a trajectory-based formulation of betweenness, called Lagrangian betweenness, as a function of Lyapunov exponents. This extends the concept of betweenness beyond the context of network theory relating hyperbolic points and heteroclinic connections in any dynamical system to the structural bottlenecks of the network associated with it. Using modeled and observational velocity fields, we show that such bottlenecks are present and surprisingly persistent in the oceanic circulation across different spatio-temporal scales and we illustrate the role of these areas in driving fluid transport over vast oceanic regions. Analyzing plankton abundance data from the Kuroshio region of the Pacific Ocean, we find significant spatial correlations between measures of diversity and betweenness, suggesting promise for ecological applications.

Suppression of chaotic bursting synchronization in clustered scale-free networks by an external feedback signal

Oscillatory activities in the brain, detected by electroencephalograms, have identified synchronization patterns. These synchronized activities in neurons are related to cognitive processes. Additionally, experimental research studies on neuronal rhythms have shown synchronous oscillations in brain disorders. Mathematical modeling of networks has been used to mimic these neuronal synchronizations. Actually, networks with scale-free properties were identified in some regions of the cortex. In this work, to investigate these brain synchronizations, we focus on neuronal synchronization in a network with coupled scale-free networks. The networks are connected according to a topological organization in the structural cortical regions of the human brain. The neuronal dynamic is given by the Rulkov model, which is a two-dimensional iterated map. The Rulkov neuron can generate quiescence, tonic spiking, and bursting. Depending on the parameters, we identify synchronous behavior among the neurons in the clustered networks. In this work, we aim to suppress the neuronal burst synchronization by the application of an external perturbation as a function of the mean-field of membrane potential. We found that the method we used to suppress synchronization presents better results when compared to the time-delayed feedback method when applied to the same model of the neuronal network.

An information theoretic approach to link prediction in multiplex networks

The entities of real-world networks are connected via different types of connections (i.e., layers). The task of link prediction in multiplex networks is about finding missing connections based on both intra-layer and inter-layer correlations. Our observations confirm that in a wide range of real-world multiplex networks, from social to biological and technological, a positive correlation exists between connection probability in one layer and similarity in other layers. Accordingly, a similarity-based automatic general-purpose multiplex link prediction method-SimBins-is devised that quantifies the amount of connection uncertainty based on observed inter-layer correlations in a multiplex network. Moreover, SimBins enhances the prediction quality in the target layer by incorporating the effect of link overlap across layers. Applying SimBins to various datasets from diverse domains, our findings indicate that SimBins outperforms the compared methods (both baseline and state-of-the-art methods) in most instances when predicting links. Furthermore, it is discussed that SimBins imposes minor computational overhead to the base similarity measures making it a potentially fast method, suitable for large-scale multiplex networks.

Interindividual Variation Refuses to Go Away: A Bayesian Computer Model of Language Change in Communicative Networks

Treating the speech communities as homogeneous entities is not an accurate representation of reality, as it misses some of the complexities of linguistic interactions. Inter-individual variation and multiple types of biases are ubiquitous in speech communities, regardless of their size. This variation is often neglected due to the assumption that “majority rules,” and that the emerging language of the community will override any such biases by forcing the individuals to overcome their own biases, or risk having their use of language being treated as “idiosyncratic” or outright “pathological.” In this paper, we use computer simulations of Bayesian linguistic agents embedded in communicative networks to investigate how biased individuals, representing a minority of the population, interact with the unbiased majority, how a shared language emerges, and the dynamics of these biases across time. We tested different network sizes (from very small to very large) and types (random, scale-free, and small-world), along with different strengths and types of bias (modeled through the Bayesian prior distribution of the agents and the mechanism used for generating utterances: either sampling from the posterior distribution [“sampler”] or picking the value with the maximum probability [“MAP”]). The results show that, while the biased agents, even when being in the minority, do adapt their language by going against their a priori preferences, they are far from being swamped by the majority, and instead the emergent shared language of the whole community is influenced by their bias.

Protein functional module identification method combining topological features and gene expression data

BACKGROUND

The study of protein complexes and protein functional modules has become an important method to further understand the mechanism and organization of life activities. The clustering algorithms used to analyze the information contained in protein-protein interaction network are effective ways to explore the characteristics of protein functional modules.

RESULTS

This paper conducts an intensive study on the problems of low recognition efficiency and noise in the overlapping structure of protein functional modules, based on topological characteristics of PPI network. Developing a protein function module recognition method ECTG based on Topological Features and Gene expression data for Protein Complex Identification.

CONCLUSIONS

The algorithm can effectively remove the noise data reflected by calculating the topological structure characteristic values in the PPI network through the similarity of gene expression patterns, and also properly use the information hidden in the gene expression data. The experimental results show that the ECTG algorithm can detect protein functional modules better.

Complex networks and deep learning for EEG signal analysis

Electroencephalogram (EEG) signals acquired from brain can provide an effective representation of the human's physiological and pathological states. Up to now, much work has been conducted to study and analyze the EEG signals, aiming at spying the current states or the evolution characteristics of the complex brain system. Considering the complex interactions between different structural and functional brain regions, brain network has received a lot of attention and has made great progress in brain mechanism research. In addition, characterized by autonomous, multi-layer and diversified feature extraction, deep learning has provided an effective and feasible solution for solving complex classification problems in many fields, including brain state research. Both of them show strong ability in EEG signal analysis, but the combination of these two theories to solve the difficult classification problems based on EEG signals is still in its infancy. We here review the application of these two theories in EEG signal research, mainly involving brain-computer interface, neurological disorders and cognitive analysis. Furthermore, we also develop a framework combining recurrence plots and convolutional neural network to achieve fatigue driving recognition. The results demonstrate that complex networks and deep learning can effectively implement functional complementarity for better feature extraction and classification, especially in EEG signal analysis.

Multistability in a star network of Kuramoto-type oscillators with synaptic plasticity

We analyze multistability in a star-type network of phase oscillators with coupling weights governed by phase-difference-dependent plasticity. It is shown that a network with N leaves can evolve into \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^N$$\end{document}2N various asymptotic states, characterized by different values of the coupling strength between the hub and the leaves. Starting from the simple case of two coupled oscillators, we develop an analytical approach based on two small parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}ε and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}ε is the ratio of the time scales of the phase variables and synaptic weights, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu$$\end{document}μ defines the sharpness of the plasticity boundary function. The limit \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu \rightarrow 0$$\end{document}μ→0 corresponds to a hard boundary. The analytical results obtained on the model of two oscillators are generalized for multi-leaf star networks. Multistability with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^N$$\end{document}2N various asymptotic states is numerically demonstrated for one-, two-, three- and nine-leaf star-type networks.

Network analysis in aged C. elegans reveals candidate regulatory genes of ageing

Ageing is a biological process guided by genetic and environmental factors that ultimately lead to adverse outcomes for organismal lifespan and healthspan. Determination of molecular pathways that are affected with age and increase disease susceptibility is crucial. The gene expression profile of the ideal ageing model, namely the nematode Caenorhabditis elegans mapped with the microarray technology initially led to the identification of age-dependent gene expression alterations that characterize the nematode's ageing process. The list of differentially expressed genes was then utilized to construct a network of molecular interactions with their first neighbors/interactors using the interactions listed in the WormBase database. The subsequent network analysis resulted in the unbiased selection of 110 candidate genes, among which well-known ageing regulators appeared. More importantly, our approach revealed candidates that have never been linked to ageing before, thus suggesting promising potential targets/ageing regulators.

Epidemic Propagation With Positive and Negative Preventive Information in Multiplex Networks

We propose a novel epidemic model based on two-layered multiplex networks to explore the influence of positive and negative preventive information on epidemic propagation. In the model, one layer represents a social network with positive and negative preventive information spreading competitively, while the other one denotes the physical contact network with epidemic propagation. The individuals who are aware of positive prevention will take more effective measures to avoid being infected than those who are aware of negative prevention. Taking the microscopic Markov chain (MMC) approach, we analytically derive the expression of the epidemic threshold for the proposed epidemic model, which indicates that the diffusion of positive and negative prevention information, as well as the topology of the physical contact network have a significant impact on the epidemic threshold. By comparing the results obtained with MMC and those with the Monte Carlo (MC) simulations, it is found that they are in good agreement, but MMC can well describe the dynamics of the proposed model. Meanwhile, through extensive simulations, we demonstrate the impact of positive and negative preventive information on the epidemic threshold, as well as the prevalence of infectious diseases. We also find that the epidemic prevalence and the epidemic outbreaks can be suppressed by the diffusion of positive preventive information and be promoted by the diffusion of negative preventive information.

Analyzing Neck Circumference as an Indicator of CPAP Treatment Response in Obstructive Sleep Apnea with Network Medicine

We explored the relationship between obstructive sleep apnea (OSA) patients' anthropometric measures and the CPAP treatment response. To that end, we processed three non-overlapping cohorts (D1, D2, D3) with 1046 patients from four sleep laboratories in Western Romania, including 145 subjects (D1) with one-night CPAP therapy. Using D1 data, we created a CPAP-response network of patients, and found neck circumference (NC) as the most significant qualitative indicator for apnea-hypopnea index (AHI) improvement. We also investigated a quantitative NC cutoff value for OSA screening on cohorts D2 (OSA-diagnosed) and D3 (control), using the area under the curve. As such, we confirmed the correlation between NC and AHI (ρ=0.35, p<0.001) and showed that 71% of diagnosed male subjects had bigger NC values than subjects with no OSA (area under the curve is 0.71, with 95% CI 0.63-0.79, p<0.001); the optimal NC cutoff is 41 cm, with a sensitivity of 0.8099, a specificity of 0.5185, positive predicted value (PPV) = 0.9588, negative predicted value (NPV) = 0.1647, and positive likelihood ratio (LR+) = 1.68. Our NC =41 cm threshold classified the D1 patients' CPAP responses-measured as the difference in AHI prior to and after the one-night use of CPAP-with a sensitivity of 0.913 and a specificity of 0.859.

A New Geo-Propagation Model of Event Evolution Chain Based on Public Opinion and Epidemic Coupling

The online public opinion is the sum of public views, attitudes and emotions spread on major public health emergencies through the Internet, which maps out the scope of influence and the disaster situation of public health events in real space. Based on the multi-source data of COVID-19 in the context of a global pandemic, this paper analyzes the propagation rules of disasters in the coupling of the spatial dimension of geographic reality and the dimension of network public opinion, and constructs a new gravity model-complex network-based geographic propagation model of the evolution chain of typical public health events. The strength of the model is that it quantifies the extent of the impact of the epidemic area on the surrounding area and the spread of the epidemic, constructing an interaction between the geographical reality dimension and online public opinion dimension. The results show that: The heterogeneity in the direction of social media discussions before and after the “closure” of Wuhan is evident, with the center of gravity clearly shifting across the Yangtze River and the cyclical changing in public sentiment; the network model based on the evolutionary chain has a significant community structure in geographic space, divided into seven regions with a modularity of 0.793; there are multiple key infection trigger nodes in the network, with a spatially polycentric infection distribution.

Spreading Control in Two-Layer Multiplex Networks

The problem of controlling a spreading process in a two-layer multiplex networks in such a way that the extinction state becomes a global attractor is addressed. The problem is formulated in terms of a Markov-chain based susceptible-infected-susceptible (SIS) dynamics in a complex multilayer network. The stabilization of the extinction state for the nonlinear discrete-time model by means of appropriate adaptation of system parameters like transition rates within layers and between layers is analyzed using a dominant linear dynamics yielding global stability results. An answer is provided for the central question about the essential changes in the step from a single to a multilayer network with respect to stability criteria and the number of nodes that need to be controlled. The results derived rigorously using mathematical analysis are verified using statical evaluations about the number of nodes to be controlled and by simulation studies that illustrate the stability property of the multilayer network induced by appropriate control action.

Visualizing the Process of Disaster Mental Health Services in the Joso Flood by Network Analyses of Emails

Joso City, Ibaraki Prefecture, Japan was severely affected by flooding of the River Kinugawa in September 2015. Local psychiatric organizations immediately began providing disaster mental health services (DMHS). In post-disaster settings, DMHS involving organizational interventions by multiple regional institutions are required to support disaster victims. However, little is known about the process of coordinating multiple institutions or determining whether appropriate support has been provided. To elucidate the characteristics of communications that enable effective disaster medical team formation, we conducted network analyses of sender-recipient pairs of emails during the period of DMHS activity. The network analysis is a research method that represents various objects as a network of nodes and edges and explores their structural characteristics. We obtained 2,450 time-series emails from five core members of DMHS, including 32,865 pairs of senders and recipients. The network generated by the emails was scale-free, and its structure changed according to the phases of disaster recovery. In the ultra-acute phase, which lasted about 1 week, spreading information and recruiting people to provide disaster support was given the highest priority. In the acute phase, which lasted about 1 month, support and swift decision-making were essential for directing large numbers of staff. In the mid- to long-term phase, support for staff to share information and experience in small groups was observed. Network analyses have revealed that disaster medical teams must change their communication styles during the mission to adapt to different health needs corresponding to each post-disaster phase.

Brain network similarity: methods and applications

Graph theoretical approach has proved an effective tool to understand, characterize, and quantify the complex brain network. However, much less attention has been paid to methods that quantitatively compare two graphs, a crucial issue in the context of brain networks. Comparing brain networks is indeed mandatory in several network neuroscience applications. Here, we discuss the current state of the art, challenges, and a collection of analysis tools that have been developed in recent years to compare brain networks. We first introduce the graph similarity problem in brain network application. We then describe the methodological background of the available metrics and algorithms of comparing graphs, their strengths, and limitations. We also report results obtained in concrete applications from normal brain networks. More precisely, we show the potential use of brain network similarity to build a "network of networks" that may give new insights into the object categorization in the human brain. Additionally, we discuss future directions in terms of network similarity methods and applications.

Spectral Analysis of Epidemic Thresholds of Temporal Networks

Many complex systems can be modeled as temporal networks with time-evolving connections. The influence of their characteristics on epidemic spreading is analyzed in a susceptible-infected-susceptible epidemic model illustrated by the discrete-time Markov chain approach. We develop the analytical epidemic thresholds in terms of the spectral radius of weighted adjacency matrix by averaging temporal networks, e.g., periodic, nonperiodic Markovian networks, and a special nonperiodic non-Markovian network (the link activation network) in time. We discuss the impacts of statistical characteristics, e.g., bursts and duration heterogeneity, as well as time-reversed characteristic on epidemic thresholds. We confirm the tightness of the proposed epidemic thresholds with numerical simulations on seven artificial and empirical temporal networks and show that the epidemic threshold of our theory is more precise than those of previous studies.

The Fractional Preferential Attachment Scale-Free Network Model

Many networks generated by nature have two generic properties: they are formed in the process of preferential attachment and they are scale-free. Considering these features, by interfering with mechanism of the preferential attachment, we propose a generalisation of the Barabási-Albert model-the 'Fractional Preferential Attachment' (FPA) scale-free network model-that generates networks with time-independent degree distributions p ( k ) ∼ k - γ with degree exponent 2 < γ ≤ 3 (where γ = 3 corresponds to the typical value of the BA model). In the FPA model, the element controlling the network properties is the f parameter, where f ∈ ( 0 , 1 〉 . Depending on the different values of f parameter, we study the statistical properties of the numerically generated networks. We investigate the topological properties of FPA networks such as degree distribution, degree correlation (network assortativity), clustering coefficient, average node degree, network diameter, average shortest path length and features of fractality. We compare the obtained values with the results for various synthetic and real-world networks. It is found that, depending on f, the FPA model generates networks with parameters similar to the real-world networks. Furthermore, it is shown that f parameter has a significant impact on, among others, degree distribution and degree correlation of generated networks. Therefore, the FPA scale-free network model can be an interesting alternative to existing network models. In addition, it turns out that, regardless of the value of f, FPA networks are not fractal.

Designating Regional Elements System in a Critical Infrastructure System in the Context of the Czech Republic

Critical infrastructure is a complex system whose disruption or failure results in significant impacts on state interests, i.e., territorial security, economy, and the basic needs of the population. The current European Critical Infrastructure Protection Model does not allow the direct identification of critical elements at the regional level. Based on this, the paper brings a proposal for a unified system of critical infrastructure design based on a bottom-up approach. It is a progressive approach, utilizing contemporary trends in the application of science-based knowledge to critical infrastructure. A holistic view of this issue allows us to take into account the needs and preferences of the population, the preferences of the stakeholders and the local conditions of the region under consideration. The novelty of this approach is seen, in particular, in the identification of regional critical infrastructure elements through an integral assessment of these elements’ failure impact, not only on the dependent subsectors, but also on the population (population equivalent) in the assessed region. The final part of the paper presents a case study demonstrating the practical application of the proposed system to the road infrastructure in the Pardubice Region of the Czech Republic.

Molecular Ecological Network Complexity Drives Stand Resilience of Soil Bacteria to Mining Disturbances among Typical Damaged Ecosystems in China

Understanding the interactions of soil microbial species and how they responded to disturbances are essential to ecological restoration and resilience in the semihumid and semiarid damaged mining areas. Information on this, however, remains unobvious and deficiently comprehended. In this study, based on the high throughput sequence and molecular ecology network analysis, we have investigated the bacterial distribution in disturbed mining areas across three provinces in China, and constructed molecular ecological networks to reveal the interactions of soil bacterial communities in diverse locations. Bacterial community diversity and composition were classified measurably between semihumid and semiarid damaged mining sites. Additionally, we distinguished key microbial populations across these mining areas, which belonged to Proteobacteria, Acidobacteria, Actinobacteria, and Chloroflexi. Moreover, the network modules were significantly associated with some environmental factors (e.g., annual average temperature, electrical conductivity value, and available phosphorus value). The study showed that network interactions were completely different across the different mining areas. The keystone species in different mining areas suggested that selected microbial communities, through natural successional processes, were able to resist the corresponding environment. Moreover, the results of trait-based module significances showed that several environmental factors were significantly correlated with some keystone species, such as OTU_8126 (Acidobacteria), OTU_8175 (Burkholderiales), and OTU_129 (Chloroflexi). Our study also implied that the complex network of microbial interaction might drive the stand resilience of soil bacteria in the semihumid and semiarid disturbed mining areas.