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Females and males are known to be different in the prevalences of multiple psychiatric disorders, while the underlying neural mechanisms are unclear. Based on non-invasive neuroimaging techniques and graph theory, many researchers have tried to use a small-world network model to elucidate sex differences in the brain. This manuscript aims to compile the related research findings from the past few years and summarize the sex differences in human brain networks in both normal and psychiatric populations from the perspective of small-world properties. We reviewed published reports examining altered small-world properties in both the functional and structural brain networks between males and females. Based on four patterns of altered small-world properties proposed: randomization, regularization, stronger small-worldization, and weaker small-worldization, we found that current results point to a significant trend toward more regularization in normal females and more randomization in normal males in functional brain networks. On the other hand, there seems to be no consensus to date on the sex differences in small-world properties of the structural brain networks in normal populations. Nevertheless, we noticed that the sample sizes in many published studies are small, and future studies with larger samples are warranted to obtain more reliable results. Moreover, the number of related studies conducted in psychiatric populations is still limited and more investigations might be needed. We anticipate that these conclusions will contribute to a deeper understanding of the sex differences in the brain, which may be also valuable for developing new methods in the treatment of psychiatric disorders. [ABSTRACT FROM AUTHOR]

Let G be a graph with vertex set V (G) and edge set E(G). For a set M of vertices and an edge e of a graph G, let P (M, e) be the set of pairs (x, y) with a vertex x of M and a vertex y of V (G) such that dG(x, y) ≠dG−e(x, y). Given a vertex x, an edge e is said to be monitored by x if there exists a vertex v in G such that (x, v) ∈P ({x}, e), and the collection of such edges is EM(x). A set M of vertices of a graph G is distance-edge-monitoring (DEM for short) set if every edge e of G is monitored by some vertex of M, that is, the set P (M, e) is nonempty. The DEM number dem(G) of a graph G is defined as the smallest size of such a set in G. The vertices of M represent distance probes in a network modeled by G; when the edge e fails, the distance from x to y increases, and thus we are able to detect the failure. In this paper, we first give some bounds or exact values of line graphs of trees, grids, complete bipartite graphs, and obtain the exact values of DEM numbers for some graphs and their line graphs, including the friendship and wheel graphs. Next, for each n, m > 1, we obtain that there exists a graph Gn,m such that dem(Gn,m) = n and dem(L(Gn,m)) = 4 or 2n + t, for each integer t≥ 0. In the end, the DEM number for the line graph of a small-world network (DURT) is given. [ABSTRACT FROM AUTHOR]

Background: The alternations of brain responses to a strong desire to void were unclear, and the gender differences under the strong desire to void remain controversial. The present study aims to identify the functional brain network's topologic property changes evoked by a strong desire to void in healthy male and female adults with synchronous urodynamics using a graph theory analysis. Methods: The bladders of eleven healthy males and eleven females were filled via a catheter using a specific infusion and withdrawal pattern. A resting-state functional magnetic resonance imaging (fMRI) was performed on the enrolled subjects, scanning under both the empty bladder and strong desire to void states. An automated anatomical labeling (AAL) atlas was used to identify the ninety cortical and subcortical regions. Pearson's correlation calculations were performed to establish a brain connection matrix. A paired t-test (p < 0.05) and Bonferroni correction were applied to identify the significant statistical differences in topological properties between the two states, including small-world network property parameters [gamma (γ) and lambda (λ)], characteristic path length (Lp), clustering coefficient (Cp), global efficiency (Eglob), local efficiency (Eloc), and regional nodal efficiency (Enodal). Results: The final data suggested that females and males had different brain response patterns to a strong desire to void, compared with an empty bladder state. Conclusions: More brain regions involving emotion, cognition, and social work were active in females, and males might obtain a better urinary continence via a compensatory mechanism. [ABSTRACT FROM AUTHOR]

During both sleep and awake immobility, hippocampal place cells reactivate time-compressed versions of sequences representing recently experienced trajectories in a phenomenon known as replay. Intriguingly, spontaneous sequences can also correspond to forthcoming trajectories in novel environments experienced later, in a phenomenon known as preplay. Here, we present a model showing that sequences of spikes correlated with the place fields underlying spatial trajectories in both previously experienced and future novel environments can arise spontaneously in neural circuits with random, clustered connectivity rather than pre-configured spatial maps. Moreover, the realistic place fields themselves arise in the circuit from minimal, landmark-based inputs. We find that preplay quality depends on the network’s balance of cluster isolation and overlap, with optimal preplay occurring in small-world regimes of high clustering yet short path lengths. We validate the results of our model by applying the same place field and preplay analyses to previously published rat hippocampal place cell data. Our results show that clustered recurrent connectivity can generate spontaneous preplay and immediate replay of novel environments. These findings support a framework whereby novel sensory experiences become associated with preexisting “pluripotent” internal neural activity patterns.

Networks haven been widely used to understand the spread of infectious disease. This study examines the properties of small-world networks in modeling infectious disease on campus. Two different small-world models are developed and the behaviors of infectious disease in the models are observed through numerical simulations. The results show that the behavior pattern of infectious disease in a small-world network is different from those in a regular network or a random network. The spread of the infectious disease increases as the proportion of long-distance connections p increasing, which indicates that reducing the contact among people is an effective measure to control the spread of infectious disease. The probability of node position exchange in a network (p2) had no significant effect on the spreading speed, which suggests that reducing human mobility in closed environments does not help control infectious disease. However, the spreading speed is proportional to the number of shared nodes (s), which means reducing connections between different groups and dividing students into separate sections will help to control infectious disease. In the end, the simulating speed of the small-world network is tested and the quadratic relationship between simulation time and the number of nodes may limit the application of the SW network in areas with large populations.

The coronavirus (COVID-19) pandemic began in late 2019, unleashing a severe human health crisis that lasted three years and caused immeasurable economic losses worldwide. Although the World Health Organization declared the end of its emergency phase in May 2023, formulating measures by predicting transmission trends of the epidemic is one of the crucial ways to monitor and contain this disease. On the other hand, epidemiological studies have shown that the spatial structure of the population is a vital factor in the spread of epidemics. When infectious diseases invade a region, epidemics are often transmitted through connectivity between hosts. Therefore, in this study, we propose a small-world network model to simulate the transmission of the COVID-19 epidemic. However, the small-world network is organized by Gaussian distributed wiring that satisfies the frequency-distance rule in human mobility theory. Based on its nonlinear dynamic properties, an epidemic prediction model is developed. We performed numerical simulations and evaluated the accuracy of the prediction model. The results show that a high level of accuracy was achieved. The prediction model is examined using the MoH Malaysia COVID-19 dataset. When compared, our model showed lower fitting errors and was closer to the actual curves than the SIR model.

The present view on heartbeat initiation is that a primary pacemaker cell or a group of cells in the sinoatrial node (SAN) center paces the rest of the SAN and the atria. However, recent high-resolution imaging studies show a more complex paradigm of SAN function that emerges from heterogeneous signaling, mimicking brain cytoarchitecture and function. Here, we developed and tested a new conceptual numerical model of SAN organized similarly to brain networks featuring a modular structure with small-world topology. In our model, a lower rate module leads action potential (AP) firing in the basal state and during parasympathetic stimulation, whereas a higher rate module leads during β-adrenergic stimulation. Such a system reproduces the respective shift of the leading pacemaker site observed experimentally and a wide range of rate modulation and robust function while conserving energy. Since experimental studies found functional modules at different scales, from a few cells up to the highest scale of the superior and inferior SAN, the SAN appears to feature hierarchical modularity, i.e., within each module, there is a set of sub-modules, like in the brain, exhibiting greater robustness, adaptivity, and evolvability of network function. In this perspective, our model offers a new mainframe for interpreting new data on heterogeneous signaling in the SAN at different scales, providing new insights into cardiac pacemaker function and SAN-related cardiac arrhythmias in aging and disease.

The aim of this study was to investigate the inner link between the small-world brain network and inhibitory control. Functional near-infrared spectroscopy (fNIRS) was used to construct a neurofeedback (NF) training system and regulate the frontal small-world brain network. The small-world network downregulation group (DOWN, n = 17) and the small-world network upregulation group (UP, n = 17) received five days of fNIRS-NF training and performed the color–word Stroop task before and after training. The behavioral and functional brain network topology results of both groups were analyzed by a repeated-measures analysis of variance (ANOVA), which showed that the upregulation training helped to improve inhibitory control. The upregulated small-world brain network exhibits an increase in the brain network regularization, links widely dispersed brain resources, and reduces the lateralization of brain functional networks between hemispheres. This suggests an inherent correlation between small-world functional brain networks and inhibitory control; moreover, dynamic optimization under cost efficiency trade-offs provides a neural basis for inhibitory control. Inhibitory control is not a simple function of a single brain region or connectivity but rather an emergent property of a broader network. [ABSTRACT FROM AUTHOR]

The coronavirus (COVID-19) pandemic began in late 2019, unleashing a severe human health crisis that lasted three years and caused immeasurable economic losses worldwide. Although the World Health Organization declared the end of its emergency phase in May 2023, formulating measures by predicting transmission trends of the epidemic is one of the crucial ways to monitor and contain this disease. On the other hand, epidemiological studies have shown that the spatial structure of the population is a vital factor in the spread of epidemics. When infectious diseases invade a region, epidemics are often transmitted through connectivity between hosts. Therefore, in this study, we propose a small-world network model to simulate the transmission of the COVID-19 epidemic. However, the small-world network is organized by Gaussian distributed wiring that satisfies the frequency-distance rule in human mobility theory. Based on its nonlinear dynamic properties, an epidemic prediction model is developed. We performed numerical simulations and evaluated the accuracy of the prediction model. The results show that a high level of accuracy was achieved. The prediction model is examined using the MoH Malaysia COVID-19 dataset. When compared, our model showed lower fitting errors and was closer to the actual curves than the SIR model. [ABSTRACT FROM AUTHOR]

The Sun is an external object that significantly impacts the earth's atmosphere and space weather conditions. Flares and coronal mass ejections are large-scale solar atmospheric features that mainly emerge at active regions above the sunspots and have influenced the earth. The sunspots, considered signatures of solar activity, are fascinating features related to the internal dynamics and activity of the Sun. The appearance of the sunspots in the photosphere shows the complexity of the magnetic field on the Sun. The frequency and size of sunspots change over time which show periods (e.g., eleven years periodicity) that may be a sign of the complex Sun. The time series of the sunspot numbers have been recorded for several centuries, and this time series is significantly changed over time. The complex network approach is a way to investigate the inherent property of complex time series, such as the sunspots time series. In this study, the growing complex network with the visibility condition is constructed using the time series of the sunspots (time and numbers) for 1922 to 2016 collected by SILSO. We compute the complex network parameters such degree of nodes, shortest path length, and clustering coefficients. We examine the sunspot complex network's scale-free, small-world, and assortative properties. We show that the degree distribution of the complex network for the time series of the sunspots obeys a power-law distribution function. We applied a method via maximum likelihood estimation in the Bayesian framework to obtain the power indicated. Therefore, the degree exponent is obtained larger than three, so the complex network for the time series of the sunspots is small- world and scale-free. The power-low behavior is an essential characteristic of self-organized or self-organized criticality systems. Limited productivity is a crucial property for these complex systems. The small word behavior indicates that the large sunspot numbers in the time series are clustered with several small values neighbors and linked with distinct large values in the time series. The small-world network represents a small characteristic path length with a high clustering coefficient. The scale-free and small-word behavior for the network of the sunspots time series may imply that the sunspots and sunspot groups forming via complex non-linear dynamics. Changing the magnetic polarity of the sunspots during the solar cycle can be a characteristic of such complex systems. The limited predictability in sunspots' time series, e.g., the intensity of activity within a solar cycle, may also be another sign of the complex Sun. The behavior of the degree of node distribution, clustering coefficient, and shortest path length indicates that the time series of sunspots is a non-random system. We showed that the degree of correlation is a function of the network size and can be considered as an assortative, dis-assortative, or neutral network. [ABSTRACT FROM AUTHOR]

This study takes diffusion capacity, absorptive capacity, and relationship strength as the main influencing factors, constructs models of knowledge flow in small‐world networks and scale‐free networks, and uses numerical simulation to observe the flow characteristics of explicit knowledge and tacit knowledge in different networks. The knowledge of explicit flow in different networks exhibits the phenomenon of knowledge emergence, but this phenomenon is more obvious in a small‐world network. The flow of tacit knowledge in a small‐world network has a better effect. In a scale‐free network, the quantity and frequency of knowledge flow are significantly higher than those in a small‐world network. The reason for this phenomenon is the differences in the response, connection and structure of different networks. The quantity and frequency of the flow of explicit knowledge in the same network are significantly higher than those of tacit knowledge. The reason for this phenomenon is the different types of knowledge flow in different modes, with different levels of flow difficulty and flow sustainability. First, this study visually compares the differences in flow between the two types of knowledge. Second, flow models of the two types of knowledge are constructed, and the flow characteristics of the two types of knowledge in different networks are simulated. Finally, the reasons for the differences in flow between the two types of knowledge are explained by using loosely coupled theory. [ABSTRACT FROM AUTHOR]

The fractal and small-word properties are two important properties of complex networks. In this paper, we propose a new random rewiring method to transform fractal networks into small-world networks. We theoretically prove that the proposed method can retain the degree of all nodes (hence the degree distribution) and the connectivity of the network. Further, we also theoretically prove that our method also retains the tree structure of tree graphs. Our method can transform many different types of fractal networks into small-world networks while the degree distribution and connectivity of these networks remain unchanged, demonstrating the generality of small-world networks. In addition, the method also works for other types of complex networks. The rewiring method proposed in this paper can be used in a broader range of applications of network analysis. [ABSTRACT FROM AUTHOR]

The effect of synaptic plasticity on the synchronization mechanism of the cerebral cortex has been a hot research topic over the past two decades. There are a great deal of literatures on excitatory pyramidal neurons, but the mechanism of interaction between the inhibitory interneurons is still under exploration. In this study, we consider a complex network consisting of excitatory (E) pyramidal neurons and inhibitory (I) interneurons interacting with chemical synapses through spike-timing-dependent plasticity (STDP). To study the effects of eSTDP and iSTDP on synchronization and oscillation behaviors emerged in an excitatory–inhibitory balanced network, we analyzed three different cases, a small-world network of purely excitatory neurons with eSTDP, a small-world network of purely inhibitory neurons with iSTDP and a small-world network with excitatory–inhibitory balanced neurons. By varying the number of inhibitory interneurons, and that of connected edges in a small-world network, and the coupling strength, these networks exhibit different synchronization and oscillation behaviors. We found that the eSTDP facilitates synchronization effectively, while iSTDP has no significant impact on it. In addition, eSTDP and iSTDP restrict the balance of the excitatory–inhibitory balanced neuronal network together and play a fundamental role in maintaining network stability and synchronization. They also can be used to guide the treatment and further research of neurodegenerative diseases. [ABSTRACT FROM AUTHOR]

In this paper, synchronization and encrypted communication transmissions of analog and digital messages in a deterministic small-world network (DSWN) are presented. In the first instance, we use a network with 3 coupled nodes in a nearest-neighbor (NN) topology, then the amount of nodes is increased until reaching a DSWN with 24 nodes. The synchronization and encrypted communication transmissions using a DSWN are presented experimentally by using Chua's chaotic circuit as node, in both analog and digital electronic implementations, where for the continuous version (CV) we use operational amplifiers (OA), and in the discretized version (DV) we use Euler's numerical algorithm implemented in an embedded system by using an Altera/Intel FPGA and external digital-to-analog converters. [ABSTRACT FROM AUTHOR]

Coherence resonance (CR), stochastic synchronization (SS), and spike-timing-dependent plasticity (STDP) are ubiquitous dynamical processes in biological neural networks. Whether there exists an optimal network and STDP configuration at which CR and SS are both pronounced is a fundamental question of interest that is still elusive. We expect such a configuration to enable the brain to make synergistic and optimal use of these phenomena to process information efficiently. This paper considers a small-world network of excitable Hodgkin–Huxley neurons driven by channel noise and STDP with an asymmetric Hebbian time window. Numerical results indicate specific network topology and STDP parameter intervals in which CR and SS can be simultaneously enhanced. Our results imply that an optimally tuned inherent background noise, STDP rule, and network topology can play a constructive role in enhancing both the time precision of firing and the synchronization in neural systems. [ABSTRACT FROM AUTHOR]

In the practice of COVID-19 prevention and control in China, the home quarantine policy directly connects and manages the residents, which plays a significant role in preventing the spread of the epi-demic in the community. We evaluate the effectiveness of current home quarantine policy in the actual execution process based on the evolutionary game relationship between the community and res-idents. This paper establishes a double-layer coupled complex network game model, and uses the multi-agent modeling method to study the game relationship between the community and residents in the context of home quarantine policies. The results show that initial strategy of the community with strict supervision and reasonable government reward allocation will increase the proportion of the residents complying with the quarantine rule. When 80% of the communities chose to supervise strictly at the beginning, people are more likely to follow the rules. While when the residents can only get 20% of the government's reward, the proportion of choosing to violate the quarantine rules is much higher than that when they can get 80% of the reward. Besides, the structure of small-world network and environmental noise will also affect the residents' strategy. As the probability of reconnection of the small-world network rises from 0.2 to 0.8, the proportion of residents who choose to comply with the strategy becomes much higher. When the environmental noise reaches 0.5, the ratio of residents who choose to violate the strategy is higher than the ratio of complianc. The study is helpful to provide the basis for the government to formulate the quarantine policy and propose an optimization for making effective quarantine measures. In this way, the government can adjust the parameters to make residents achieve the possible level of compliance with quarantine policies as high as possible to contain the spread of the epidemic. [ABSTRACT FROM AUTHOR]

Inspired by the nervous system working mechanism of a biological brain, brain-like intelligence has been a research frontier in the field of artificial intelligence. Under external stimulation, biological brains have self-adaptive advantages. Drawing from the advantage of biological brains, it is meaningful to investigate the anti-interference ability of brain-like models. In this study, we proposed a spiking neural network with small-world topology (SWSNN), where Izhikevich neuron models and synaptic plasticity models with excitatory and inhibitory synapses are introduced to represent nodes and edges of the network, respectively. The anti-interference ability of the SWSNN against pulse noise is investigated, and the anti-interference ability of SNNs with different topologies are compared. The simulation results indicate that: (i) our SWSNN has anti-interference ability against pulse noise, which is supported from different perspectives based on two indices. Furthermore, the chain reaction of firing rates, synaptic weights and topological characteristics forms neural information processing in the SWSNN under pulse noise. In addition, the synaptic weights are significantly relevant to the anti-interference ability, which implies that an intrinsic factor of the anti-interference ability is the dynamic regulation of synaptic plasticity. (ii) Our SWSNN outperforms the random and regular SNNs that are not complex networks in terms of anti-interference performance. For complex network, the anti-interference performance of SWSNN is superior to that of scale-free SNN, and the anti-interference superiority of the SWSNN is more obvious with the increase of amplitude of pulse noise. The topological characteristics of the network are further discussed, and the results imply that the topology is a factor that affects the anti-interference performance of the SWSNN. [ABSTRACT FROM AUTHOR]

Introduction: Age-related decline in episodic memory performance in otherwise healthy older adults is indisputably evident. Yet, it has been shown that under certain conditions episodic memory performance in healthy older adults' barely deviates from those seen in young adults. Here we report on the quality of object encoding in an ecologically valid, virtual-reality based memory assessment in a sample of healthy older and younger adults with comparable memory performance. Methods: We analyzed encoding by establishing both a serial and semantic clustering index and an object memory association network. Results: As expected, semantic clustering was superior in older adults without need for additional allocation of executive resources whereas young adults tended more to rely on serial strategies. The association networks suggested a plethora of obvious but also less obvious memory organization principles, some of which indicated converging approaches between the groups as suggested by a subgraph analysis and some of which indicated diverging approaches as suggested by the respective network interconnectivity. A higher interconnectivity was observed in the older adults' association networks. Discussion: We interpreted this as a consequence of superior semantic memory organization (extent to which effective semantic strategies diverged within the group). In conclusion, these results might indicate a diminished need for compensatory cognitive effort in healthy older adults when encoding and recalling everyday objects under ecologically valid conditions. Due to an enhanced and multimodal encoding model, superior crystallized abilities might be sufficient to counteract an age-related decline in various other and specific cognitive domains. This approach might potentially elucidate age-related changes in memory performance in both healthy and pathological aging. [ABSTRACT FROM AUTHOR]

In this work, we consider a phenomenological two-dimensional discrete model coupled in a structure of a clustered network to investigate the suppression of neuronal synchronization in a complex network. We constructed a network according to a weighted human connectivity matrix and an adjacency matrix that carries small-world properties. The coupling between neurons is inserted through a chemical synapse term and a neuronal activation function. The neuronal synchronization is measured by the Kuramoto order parameter. We intend to achieve the suppression of burst phase synchronization, and for that, we use a mathematical tool, based on the technique of deep brain stimulation, which consists of applying an external signal to the network after a certain time, causing the bursts to desynchronize. Our results are efficient when applying the feedback method both in the global network and in the cortical regions. We have seen that for cortical regions, synchronization is more difficult to suppress, however, by slightly increasing the perturbation, we are able to achieve the desired effect. This shows that it is possible to use the control efficiently in isolated cortical areas, therefore, we present a new alternative to conventional methods, avoiding to apply the control to the entire network to obtain the same results. [ABSTRACT FROM AUTHOR]

Meteorological droughts often propagate to agricultural (and other) droughts, both spatially and temporally. The present study proposes a novel complex networks-based cascading spatial drought network to examine the spatial propagation of meteorological droughts in a region to agricultural droughts in other regions. This is done through: (1) establishing stable homogeneous drought communities; (2) investigating inter-community drought propagation; (3) locating drought sources; and (4) evaluating drought connections within major crop belts. The approach is implemented to study droughts in the Indian-subcontinent during the period 1948–2022. Monthly precipitation and root-zone soil moisture data from GLDAS (Global Land Data Assimilation System) are used to compute the standardized precipitation index (SPI) for meteorological droughts and standardized soil moisture index (SSI) for agricultural droughts. Primarily, the drought network is demarcated into several subsets of network communities within which clusters of localized propagation take place. Multi-community subgraphs combining different communities are also formed to understand the long-distance inter-community drought linkages. Using network centrality measures, such as degree, closeness, and clustering coefficient, network properties of scale-freeness, small-worldness, and presence of rich-clubs are checked. Although the overall network does not exhibit any of these properties, certain subgraphs have significant small-worldness, rich-clubs, and partial scale-freeness. Some of the crucial nodes that support these network properties lie in the monsoon pathways (in the Western Ghats), and others have a strong association with El Niño Southern Oscillation (ENSO) teleconnections, thus validating the ability of the drought network to capture seasonal and climatic features. Additionally, subgraphs of nodes with high productivity of different food crops are created to study drought propagation within crop belts. Barring potential shortcomings related to data dependencies, the cascading spatial drought network helps identify an impending agricultural drought that could strengthen our ability to forecast droughts. • A novel spatial network to track meteorological to agricultural droughts is designed. • Homogenous drought communities are formed and drought hubs are identified. • Several multi-community subgraphs reveal significant rich-club and small-world properties. • Network measures are compared with agricultural productivity to understand drought propagation in crop-belts. [ABSTRACT FROM AUTHOR]

The aim of this study was to investigate the inner link between the small-world brain network and inhibitory control. Functional near-infrared spectroscopy (fNIRS) was used to construct a neurofeedback (NF) training system and regulate the frontal small-world brain network. The small-world network downregulation group (DOWN, n = 17) and the small-world network upregulation group (UP, n = 17) received five days of fNIRS-NF training and performed the color–word Stroop task before and after training. The behavioral and functional brain network topology results of both groups were analyzed by a repeated-measures analysis of variance (ANOVA), which showed that the upregulation training helped to improve inhibitory control. The upregulated small-world brain network exhibits an increase in the brain network regularization, links widely dispersed brain resources, and reduces the lateralization of brain functional networks between hemispheres. This suggests an inherent correlation between small-world functional brain networks and inhibitory control; moreover, dynamic optimization under cost efficiency trade-offs provides a neural basis for inhibitory control. Inhibitory control is not a simple function of a single brain region or connectivity but rather an emergent property of a broader network.

With the development of information society and network technology, people increasingly depend on information found on the Internet. At the same time, the models of information diffusion on the Internet are changing as well. However, these models experience the problem due to the fast development of network technologies. There is no thorough research in regards to the latest models and their applications and advantages. As a result, it is essential to have a comprehensive study of information diffusion models.The primary goal of this research is to provide a comparative study on the existing models such as the Ising model, Sznajd model, SIR model, SICR model, Game theory and social networking services models. We discuss several of their applications with the existing limitations and further categorizations. Vulnerabilities and privacy challenges of information diffusion models are extensively explored. Furthermore, categorization including strengths and weaknesses are discussed. Finally, limitations and recommendations are suggested with diverse solutions for the improvement of the information diffusion models and envisioned future research directions.

Objective: The risk of falling increases in diabetic peripheral neuropathy (DPN) patients. As a central part, Basal ganglia play an important role in motor and balance control, but whether its involvement in DPN is unclear. Methods: TenpatientswithconfirmedDPN, tendiabetespatientswithoutDPN, and ten healthy age-matched controls(HC) were recruited to undergo magnetic resonance imaging(MRI) to assess brain structure and zone adaptability. Multiscale entropy and small-world network analysis were then used to assess the complexity of the hemodynamic response signal, reflecting the adaptability of the basal ganglia. Results: There was no significant difference in brain structure among the three groups, except the duration of diabetes in DPN patients was longer (p < 0.05). The complexity of basal ganglia was significantly decreased in the DPN group compared with the non-DPN and HC group (p < 0.05), which suggested their poor adaptability. Conclusion: In the sensorimotor loop, peripheral and early central nervous lesions exist simultaneously in DPN patients. Multiscale Entropy and Small-world Network Analysis could detect basal ganglia dysfunction prior to structural changes in MRI, potentially valuable tools for early non-invasive screening and follow-up. [ABSTRACT FROM AUTHOR]

During both sleep and awake immobility, hippocampal place cells reactivate time-compressed versions of sequences representing recently experienced trajectories in a phenomenon known as replay. Intriguingly, spontaneous sequences can also correspond to forthcoming trajectories in novel environments experienced later, in a phenomenon known as preplay. Here, we present a model showing that sequences of spikes correlated with the place fields underlying spatial trajectories in both previously experienced and future novel environments can arise spontaneously in neural circuits with random, clustered connectivity rather than pre-configured spatial maps. Moreover, the realistic place fields themselves arise in the circuit from minimal, landmark-based inputs. We find that preplay quality depends on the network's balance of cluster isolation and overlap, with optimal preplay occurring in small-world regimes of high clustering yet short path lengths. We validate the results of our model by applying the same place field and preplay analyses to previously published rat hippocampal place cell data. Our results show that clustered recurrent connectivity can generate spontaneous preplay and immediate replay of novel environments. These findings support a framework whereby novel sensory experiences become associated with preexisting "pluripotent" internal neural activity patterns., Competing Interests: JB, HG, JS, SJ, PM No competing interests declared, (© 2024, Breffle et al.)

We study an extension of the Bornholdt spin-market model using configurable network topology. The distribution of returns was studied using the probability plot correlation coefficient and indicates three different behaviors for the tails of the distribution of returns. The price volatility was studied by fitting the magnetization with a Wiener process and a power-law behavior was found for the volatility as a function of the levels of randomness and connectivity of the network. Both parameters have opposing effects on the risk as inferred from the Shannon entropy of the magnetization. Also, we show that trading can spatially auto-organize depending on the conditions of the control space. Finally, we show that there is a range of values of the control space that renders a model that reproduces real-market data. [ABSTRACT FROM AUTHOR]

The problem of whether we can execute free acts or not is central in philosophical thought, and it has been studied by numerous scholars throughout the centuries. Recently, neurosciences have entered this topic contributing new data and insights into the neuroanatomical basis of cognitive processes. With the advent of connectomics, a more refined landscape of brain connectivity can be analysed at an unprecedented level of detail. Here, we identify the connectivity network involved in the movement process from a connectomics point of view, from its motivation through its execution until the sense of agency develops. We constructed a "volitional network" using data derived from the Brainnetome Atlas database considering areas involved in volitional processes as known in the literature. We divided this process into eight processes and used Graph Theory to measure several structural properties of the network. Our results show that the volitional network is small-world and that it contains four communities. Nodes of the right hemisphere are contained in three of these communities whereas nodes of the left hemisphere only in two. Centrality measures indicate the nucleus accumbens is one of the most connected nodes in the network. Extensive connectivity is observed in all processes except in Decision (to move) and modulation of Agency, which might correlate with a mismatch mechanism for perception of Agency. [ABSTRACT FROM AUTHOR]

A striking discovery in the field of network science is that the majority of real networked systems have some universal structural properties. In general, they are simultaneously sparse, scale-free, small-world, and loopy. In this article, we investigate the second-order consensus of dynamic networks with such universal structures subject to white noise at vertices. We focus on the network coherence HSO characterized in terms of the $\mathcal {H}_{2}$ -norm of the vertex systems, which measures the mean deviation of vertex states from their average value. We first study numerically the coherence of some representative real-world networks. We find that their coherence HSO scales sublinearly with the vertex number $N$. We then study analytically HSO for a class of iteratively growing networks—pseudofractal scale-free webs (PSFWs), and obtain an exact solution to HSO, which also increases sublinearly in $N$ , with an exponent much smaller than 1. To explain the reasons for this sublinear behavior, we finally study HSO for Sierpinśki gaskets, for which HSO grows superlinearly in $N$ , with a power exponent much larger than 1. Sierpinśki gaskets have the same number of vertices and edges as the PSFWs but do not display the scale-free and small-world properties. We thus conclude that the scale-free, small-world, and loopy topologies are jointly responsible for the observed sublinear scaling of HSO. [ABSTRACT FROM AUTHOR]

• Continuous deterministic models underestimate the effectiveness of contact tracing. • Small-world network models provide a better alternative. • Contact tracing can greatly reduce the spread of the original strain of SARS-CoV-2. • For the Delta variant contact tracing remains effective although to a lesser extent. • Every effort is needed to expand the contact tracing pool to make it work. Most of the mathematical modeling studies on COVID-19 transmission are based on continuous deterministic models that do not consider the characteristics of social networks. The effect of contact tracing on mitigating COVID-19, and other infectious diseases in general, is studied in a small-world network. This network has its advantages over the commonly used continuous deterministic mathematical models in that the characteristics of social networks can be properly incorporated. Simulation results show that for the original strain of SARS-CoV-2, contact tracing can play an important role in reducing and delaying the peak daily new cases. New cases can be reduced by using symptom onset to isolate tracked individuals, but the benefit can be greatly enhanced by testing asymptomatic and presymptomatic individuals on the sixth to eighth day of infection. For the delta variant, or other variants of much higher infectivity, contact tracing alone cannot significantly lower the number of daily new cases but is able to delay the peaks greatly, thus affording more time to explore and implement pharmaceutical interventions. Contact tracing can be a very powerful tool to combat COVID-19 caused by the original strain or any variant of SARS-CoV-2. In order to make contact tracing effective, every effort is needed to expand the pool of contact tracing and provide all necessary support to the self-quarantined. [ABSTRACT FROM AUTHOR]

While the construction industry has brought substantial economic benefits to society, it has also generated substantial construction and demolition waste (CDW). Illegal dumping, which refers to dumping CDW in an unauthorized non-filling location, has become widespread in many countries and regions. Illegally dumping CDW destroys the environment, causing groundwater pollution and forest fires and causing significant economic impacts. However, there is a lack of research on the decision-making behaviours and logical rules of the main participants, construction contractors and the government in the illegal CDW dumping process. This paper constructs an evolutionary game model on a small-world network considering government supervision to portray the decision-making behaviours of illegal dumping participants and conducts a numerical simulation based on empirical equations to propose an effective supervision strategy for the government to manage illegal CDW dumping efficiently. It is found that the illegal dumping behaviours of contractors are mainly affected by the intensity of government supervision, the cost of fines and the income of illegal dumping; while for government, a supervision strategy is found to be necessary, and a supervision intensity of approximately 0.7 is the optimal supervision probability given supervision efficiency. Notably, under a low-level supervision probability, increasing the penalty alone does not curb illegal dumping, and a certain degree of supervision must be maintained. The results show that in addition to setting fines for illegal dumping, the government must enforce a certain level of supervision and purify the market environment to steadily reduce illegal dumping. [ABSTRACT FROM AUTHOR]

In this paper, we numerically investigate two distinct phenomena, coherence resonance (CR) and self-induced stochastic resonance (SISR), in multiplex neural networks in the presence of spike-timing-dependent plasticity (STDP). The high degree of CR achieved in one layer network turns out to be more robust than that of SISR against variations in the network topology and the STDP parameters. This behavior is the opposite of the one presented by Yamakou and Jost (Phys. Rev. E 100, 022313, 2019), where SISR is more robust than CR against variations in the network parameters but in the absence of STDP. Moreover, the degree of SISR in one layer network increases with a decreasing (increasing) depression temporal window (potentiation adjusting rate) of STDP. However, the poor degree of SISR in one layer network can be significantly enhanced by multiplexing this layer with another one exhibiting a high degree of CR or SISR and suitable inter-layer STDP parameter values. In addition, for all inter-layer STDP parameter values, the enhancement strategy of SISR based on the occurrence of SISR outperforms the one based on CR. Finally, the optimal enhancement strategy of SISR based on the occurrence of SISR (CR) occurs via long-term potentiation (long-term depression) of the inter-layer synaptic weights.

• Complex networks can assess river networks' structure and change at node scales. • Small-world" properties of the plain reticular river network were disclosed. • Global efficiency has advantages in assessing river connectivity. • Betweenness centrality measures the river's ability to control water transport. • Hub nodes shift from spatial dispersion to north-to-south cluster along the river. eticular river networks, characterized by a dense pattern of rivers and loop structures, are primarily found in lower river delta plains and are being modified due to rapid population growth and urbanization. This change impacts the distribution of water resources and could result in more frequent and severe floods. Therefore, accurately characterizing the structure of river networks is crucial. In this study, the structure and its changes of a typical plain reticular river network in the Lixia River hinterland area (LRHA), China, were evaluated in the 1960s, 1970s, 1980s, 2009, and 2016 using complex network theory tools at global and local scales. First, we constructed a complex network model by generalizing river sources, outlets, and confluences as nodes and channels as edges. By comparing with the equivalent random networks, it is found that the river networks of LRHA have large clustering coefficients and short characteristic path lengths. These characteristics classify it as a small-world network within complex networks, which is notably efficient for water and material transportation. Second, at the global scale, the global efficiency in complex network theory considers the interconnectivity between nodes and assesses the potential paths between them, effectively reflecting the connectivity status of the river network. At the local scale, the betweenness centrality of a complex network can reflect the control ability of water and material transportation at river nodes. After the 1970s, constructing several new mainstem rivers gradually shifted nodes with high betweenness centrality towards the north–south flowing rivers. In addition, we used Moran's I to quantify the spatial clustering of the network's indicators and found that degree and betweenness centrality exhibited higher spatial clustering, with mean Moran's I values of 0.398 and 0.300, respectively. Finally, we compared the structure of river networks in urban versus rural areas and the mainstem versus tributary streams. We found that urban river networks and mainstem rivers exhibit a higher degree of betweenness centrality, resulting in a greater capacity to regulate water and material cycles within the river network. According to the research findings, complex network theory has been proven to effectively evaluate the structure of reticular river networks at various scales. It enhances our comprehension of the river network's structure and assists managers in gaining a deeper understanding of how the river network structure influences the distribution of water resources. [ABSTRACT FROM AUTHOR]

In this paper, synchronization and encrypted communication transmissions of analog and digital messages in a deterministic small-world network (DSWN) are presented. In the first instance, we use a network with 3 coupled nodes in a nearest-neighbor (NN) topology, then the amount of nodes is increased until reaching a DSWN with 24 nodes. The synchronization and encrypted communication transmissions using a DSWN are presented experimentally by using Chua’s chaotic circuit as node, in both analog and digital electronic implementations, where for the continuous version (CV) we use operational amplifiers (OA), and in the discretized version (DV) we use Euler’s numerical algorithm implemented in an embedded system by using an Altera/Intel FPGA and external digital-to-analog converters.

Purpose: Age-related hearing loss (ARHL), associated with the function of speech perception decreases characterized by bilateral sensorineural hearing loss at high frequencies, has become an increasingly critical public health problem. This study aimed to investigate the topological features of the brain functional network and structural dysfunction of the central nervous system in ARHL using graph theory. Methods: Forty-six patients with ARHL and forty-five age, sex, and education-matched healthy controls were recruited to undergo a resting-state functional magnetic resonance imaging (fMRI) scan in this study. Graph theory was applied to analyze the topological properties of the functional connectomes by studying the local and global organization of neural networks. Results: Compared with healthy controls, the patient group showed increased local efficiency (Eloc) and clustering coefficient (Cp) of the small-world network. Besides, the degree centrality (Dc) and nodal efficiency (Ne) values of the left inferior occipital gyrus (IOG) in the patient group showed a decrease in contrast with the healthy control group. In addition, the intra-modular interaction of the occipital lobe module and the inter-modular interaction of the parietal occipital module decreased in the patient group, which was positively correlated with Dc and Ne. The intra-modular interaction of the occipital lobe module decreased in the patient group, which was negatively correlated with the Eloc. Conclusion: Based on fMRI and graph theory, we indicate the aberrant small-world network topology in ARHL and dysfunctional interaction of the occipital lobe and parietal lobe, emphasizing the importance of dysfunctional left IOG. These results suggest that early diagnosis and treatment of patients with ARHL is necessary, which can avoid the transformation of brain topology and decreased brain function. [ABSTRACT FROM AUTHOR]

Stroke is a neurological condition that impacts activity performance and quality of life for survivors. While neurological impairments after the event explain the performance of patients in specific activities, the origin of such impairments has traditionally been explained as a consequence of structural and functional damage to the nervous system. However, there are important mechanisms related to energy efficiency (trade-off between biological functions and energy consumption) at different levels that can be related to these impairments and restrictions: first, at the neuronal level, where the availability of energy resources is the initial cause of the event, as well as determines the possibilities of spontaneous recovery. Second, at the level of neural networks, where the "small world" operation of the network is compromised after the stroke, implicating a high energetic cost and inefficiency in the information transfer, which is related to the neurological recovery and clinical status. Finally, at the behavioral level, the performance limitations are related to the highest cost of energy or augmented energy expenditure during the tasks to maintain the stability of the segment, system, body, and finally, the behavior of the patients. In other words, the postural homeostasis. In this way, we intend to provide a synthetic vision of the energy impact of stroke, from the particularities of the operation of the nervous system, its implications, as one of the determinant factors in the possibilities of neurological, functional, and behavioral recovery of our patients. [ABSTRACT FROM AUTHOR]

The external segment of globus pallidus (GPe) is a network of oscillatory neurons connected by inhibitory synapses. We studied the intrinsic dynamic and the response to a shared brief inhibitory stimulus in a model GPe network. Individual neurons were simulated using a phase resetting model based on measurements from mouse GPe neurons studied in slices. The neurons showed a broad heterogeneity in their firing rates and in the shapes and sizes of their phase resetting curves. Connectivity in the network was set to match experimental measurements. We generated statistically equivalent neuron heterogeneity in a small-world model, in which 99% of connections were made with near neighbors and 1% at random, and in a model with entirely random connectivity. In both networks, the resting activity was slowed and made more irregular by the local inhibition, but it did not show any periodic pattern. Cross-correlations among neuron pairs were limited to directly connected neurons. When stimulated by a shared inhibitory input, the individual neuron responses separated into two groups: one with a short and stereotyped period of inhibition followed by a transient increase in firing probability, and the other responding with a sustained inhibition. Despite differences in firing rate, the responses of the first group of neurons were of fixed duration and were synchronized across cells. [ABSTRACT FROM AUTHOR]

Simulation modelling has gained ground over the years since it can provide various scenarios applied to any scientific area. In this study, a stochastic cellular automata model is proposed, in which agents fall into three distinct categories (adopters, non-adopters and denials). Based on Hofstede's cultural dimension individualism, we characterize three major international markets, as perfectly clustered (collective) to perfectly random (individualistic). We investigate innovation diffusion speed, in each network topology. At each time step, the decision of non-adopters to purchase innovative products, is affected by their immediate neighborhood (von Neumman). The speed of diffusion is evaluated using time at which sales reach 50% of market. Effects of simulation parameters on speed of diffusion, are assessed using a log-normal accelerated failure time model. Results demonstrate that diffusion of innovative products accelerates when innovators of a virtual economic system are placed according to a random network and when amount of innovators and imitators in the economic system increases. Slower innovative products' diffusion process is a result of a large amount of denials and of how imitators are placed in the in the virtual economic system. Diffusion in small-world virtual economic systems lead to small time inflexion points very close to those of a random networked market. [ABSTRACT FROM AUTHOR]

There are several methods for categorizing images, the most of which are statistical, geometric, model-based and structural methods. In this paper, a new method for describing images based on complex network models is presented. Each image contains a number of key points that can be identified through standard edge detection algorithms. To understand each image better, we can use these points to create a graph of the image. In order to facilitate the use of graphs, generated graphs are created in the form of a complex network of small-worlds. Complex grid features such as topological and dynamic features can be used to display image-related features. After generating this information, it normalizes them and uses them as suitable features for categorizing images. For this purpose, the generated information is given to the neural network. Based on these features and the use of neural networks, comparisons between new images are performed. The results of the article show that this method has a good performance in identifying similarities and finally categorizing them. [ABSTRACT FROM AUTHOR]

This paper repurposes the classic insight from network theory that long-distance connections drive disease propagation into a strategy for controlling a second wave of Covid-19. We simulate a scenario in which a lockdown is first imposed on a population and then partly lifted while long-range transmission is kept at a minimum. Simulated spreading patterns resemble contemporary distributions of Covid- 19 across EU member states, German and Italian regions, and through New York City, providing some model validation. Results suggest that our proposed strategy may significantly reduce peak infection. We also find that post-lockdown flare-ups remain local longer, aiding geographical containment. These results suggest a tailored policy in which individuals who frequently travel to places where they interact with many people are offered greater protection, tracked more closely, and are regularly tested. This policy can be communicated to the general public as a simple and reasonable principle: Stay nearby or get checked.

Social Internet of Things (SIoT) is a new standard resulting from the integration of the Internet of Things (IoT) and social networking. IoT is a visionary, one-paradigm, whereas social networks are platforms where voluminous collaborations between humans exist. The SIoT is defined as a social network of objects that are not only smarter but also socially conscious. Fundamental requirements of both IoT and SIoT networks include efficient service search and the discovery of object mechanisms. Therefore, our paper proposes a simple model for social networks to discover the object or services by using a small-world network. Our proposed model comprised a set of objects, and where each object is looking for a service. The service search is initiated in different hops by an object using a service query message to the nearest object. If the requested object is identified immediately or at the first hop, a permanent link is established between the service requester and the service provider otherwise the search process is repeated until the service is discovered. In this study, we integrate the SIoT with the small world concept for the building of our model. Our proposed model guarantees that the object containing the information is in a bounded path length and is treatable owing to the structure of small-world networks. The process of search is efficient because it is initiated only when an object asks for another object or service. Our intention here is to increase the navigability of the network. We carefully performed numerical analyses for our model and presented the simulation results based on efficiencies such as average path length, clustering coefficient, service execution time, and the giant component. After conducting various experiments, we conclude that our proposed model is efficient and reflects the real network structures of small-world networks, therefore, it can be suitable for social networks.

Stroke is a neurological condition that impacts activity performance and quality of life for survivors. While neurological impairments after the event explain the performance of patients in specific activities, the origin of such impairments has traditionally been explained as a consequence of structural and functional damage to the nervous system. However, there are important mechanisms related to energy efficiency (trade-off between biological functions and energy consumption) at different levels that can be related to these impairments and restrictions: first, at the neuronal level, where the availability of energy resources is the initial cause of the event, as well as determines the possibilities of spontaneous recovery. Second, at the level of neural networks, where the “small world” operation of the network is compromised after the stroke, implicating a high energetic cost and inefficiency in the information transfer, which is related to the neurological recovery and clinical status. Finally, at the behavioral level, the performance limitations are related to the highest cost of energy or augmented energy expenditure during the tasks to maintain the stability of the segment, system, body, and finally, the behavior of the patients. In other words, the postural homeostasis. In this way, we intend to provide a synthetic vision of the energy impact of stroke, from the particularities of the operation of the nervous system, its implications, as one of the determinant factors in the possibilities of neurological, functional, and behavioral recovery of our patients.