Newman-Watts Small-world Networks Research Articles

Free running period affected by network structures of suprachiasmatic nucleus neurons exposed to constant light

Exposed to the natural light-dark cycle, 24 h rhythms exist in behavioral and physiological processes of living beings. Interestingly, under constant darkness or constant light, living beings can maintain a robust endogenous rhythm with a free running period (FRP) close to 24 h. In mammals, the circadian rhythm is coordinated by a master clock located in the suprachiasmatic nucleus (SCN) of the brain, which is composed of about twenty thousand self-oscillating neurons. These SCN neurons form a heterogenous network to output a robust rhythm. Thus far, the exact network topology of the SCN neurons is unknown. In this article, we examine the effect of the SCN network structure on the FRP when exposed to constant light by a Poincaré model. Four typical network structures are considered, including a nearest-neighbor coupled network, a Newman–Watts small world network, an ErdÖs–Rényi random network and a Barabási–Albert (BA) scale free network. The results show that the FRP is longest in the BA network, because the BA network is characterized by the most heterogeneous structure among these four types of networks. These findings are not affected by the average node degree of the SCN network or the value of relaxation rate of the SCN neuronal oscillators. Our findings contribute to the understanding of how the network structure of the SCN neurons influences the FRP.

Dynamical mechanism of tacit knowledge dissemination based on newman-watts network

Exploring the mechanism of tacit knowledge dissemination is the basis of tacit knowledge management. This paper explores the mechanism of tacit knowledge dissemination in Newman-Watts small-world networks using the SIR model. The introduction of diffusion in the traditional diffusion model does not change the stability of the system. Therefore, It cannot explain the dissemination process. We replace the diffusion term with the adjacency matrix of the network to achieve dissemination. The results indicate that the diffusion of tacit knowledge subjects and the entropy of the network (NSE) play a crucial role in generating periodic and local dissemination behaviors. This model can guide significance for effectively accelerating tacit knowledge dissemination and improving the core competitiveness of the enterprise.

Dynamical reciprocity in interacting games: Numerical results and mechanism analysis.

We study the evolution of two mutually interacting pairwise games on different topologies. On two-dimensional square lattices, we reveal that the game-game interaction can promote the cooperation prevalence in all cases, and the cooperation-defection phase transitions even become absent and fairly high cooperation is expected when the interaction becomes very strong. A mean-field theory is developed that points out dynamical routes arising therein. Detailed analysis shows indeed that there are rich categories of interactions in either the individual or bulk scenario: invasion, neutral, and catalyzed types; their combination puts cooperators at a persistent advantage position, which boosts the cooperation. The robustness of the revealed reciprocity is strengthened by the studies of model variants, including the public goods game, asymmetrical or time-varying interactions, games of different types, games with timescale separation, different updating rules, etc. The structural complexities of the underlying population, such as Newman-Watts small world networks, Erdős-Rényi random networks, and Barabási-Albert networks, also do not alter the working of the dynamical reciprocity. In particular, as the number of games engaged increases, the cooperation level continuously improves in general. However, our analysis shows that the dynamical reciprocity works only in structured populations, otherwise the game-game interaction has no any impact on the cooperation at all. In brief, our work uncovers a cooperation mechanism in the structured populations, which indicates the great potential for human cooperation since concurrent issues are so often seen in the real world.

Requirements for the containment of COVID-19 disease outbreaks through periodic testing, isolation, and quarantine

We employ individual-based Monte Carlo computer simulations of a stochastic SEIR model variant on a two-dimensional Newman–Watts small-world network to investigate the control of epidemic outbreaks through periodic testing and isolation of infectious individuals, and subsequent quarantine of their immediate contacts. Using disease parameters informed by the COVID-19 pandemic, we investigate the effects of various crucial mitigation features on the epidemic spreading: fraction of the infectious population that is identifiable through the tests; testing frequency; time delay between testing and isolation of positively tested individuals; and the further time delay until quarantining their contacts as well as the quarantine duration. We thus determine the required ranges for these intervention parameters to yield effective control of the disease through both considerable delaying the epidemic peak and massively reducing the total number of sustained infections.

Pattern transition of neuronal networks induced by chemical autapses with random distribution

Abstract The difference of congenital inheritance and acquired development makes the autaptic distribution in different brain regions variant. To investigate the physiological regulation of autaptic structures on the nervous system, the effects of chemical autapses with random distribution on the dynamics of Newman-Watts small-world neuronal networks are systematically analyzed with the help of three network metrics. The autaptic occurring probability is first introduced to characterize the random distribution of autaptic structures. Numerical results show that the random distribution of chemical autapses can markedly modulate the electrophysiological activities of neuronal networks owing to the self-feedback function of excitatory autapses, not only promoting the transmission of neural signals, but also inducing the network-level stochastic resonance and the transition of network dynamics. Particularly, the autaptic random distribution can make subthreshold or chaotic neuronal networks generate the phase synchronization phenomena and eventually evolve into the synchronous periodic discharge state, which provides a strategy to achieve the complete synchronization through pattern transition. This study reveals the ability of the stochastic characteristics of autaptic structures to alter the evolution of network spatiotemporal patterns, which could contribute to the application of autaptic structures in physiological experiments or artificial neural networks.

Synchronization of Chaotic-Oscillation Permanent Magnet Synchronous Generators Networks via Adaptive Impulsive Control

This brief presents an adaptive impulsive control scheme for the chaotic-oscillation permanent magnet synchronous generators networks based on theories of complex networks. First, the parameter conditions of the chaotic permanent magnet synchronous generator model are presented, and the coupled dynamic networks is constructed based on Newman-Watts small-world network algorithm. After then, the adaptive impulsive control theory of complex networks is analyzed. Based on the equidistant impulsive control scheme and the adaptive feedback control scheme, a suitable impulsive control gain matrix, impulsive time and the adaptive feedback controller are designed to illustrate the synchronization of the chaotic-oscillation wind generator networks. Theoretical analysis and simulation results demonstrate that the designed adaptive impulsive controllers are efficient to improve the stability and convergence time of the network.

WSBP/NWBP small-world neural network and its performance for wind power forecasting

A small-world neural network has stronger generalization ability with high transfer efficiency than that of the regular neural networks. This paper presents two novel small-world neural networks, the Watts-Strogatz small-world based on a BP neural network (WSBP) and a Newman-Watts small-world neural network based on a BP neural network (NWBP), related to previous research of complex networks. The algorithms are developed separately by adopting WS and NW small-world networks as their topological structures, and their derivation and convergence criterion are progressively discussed. After that, the proposed models are subsequently tested by two typical nonlinear functions which confirm their significant improvement over the regular BP networks and other algorithms. Finally, a wind power prediction system is advanced to verify their generalization abilities, and show that the models are practically feasible and effective with improved accuracy and acceptable forecasting errors caused by wind fluctuation and randomness with a time scale up to 24 h.

Roles of Clustering Coefficient for the Network Reconstruction

It is important to establish relations between the network reconstruction and the topological dynamical structure of networks. In this article, we quantify the effect for two types of network topologies on the performance of network reconstruction. First, we generate two network modes with variable clustering coefficient based on Holme-Kim model and Newman-Watts small-world model, then we reconstruct the artificial networks by using a novel framework calledL1-norm minimization algorithm based on a theory called compressive sensing (CS), a framework for recovering sparse signals. The results of the simulation experiment show that the accuracy rate for the network reconstruction is a monotonically increasing function of the clustering coefficient in Holme-Kim model, whereas the opposite occurs in Newman-Watts small-world network. And this yet demonstrates that the larger the network size, the higher the accuracy rate. Morever, we compare the results of CS with orthogonal matching pursuit (OMP), a greedy algorithm. The results show that the accuracy rate ofL1-norm minimization method is 10% higher than that of OMP, and OMP yields 1.2 times the computation speed ofL1-norm minimization. Our work demonstrates that the topological structure of network has influence on the accurate reconstruction and it is helpful for offering proper method for the network reconstruction.

How synaptic plasticity influences spike synchronization and its transitions in complex neuronal network.

There is evidence that synaptic plasticity is a vital feature of realistic neuronal systems. This study, describing synaptic plasticity by a modified Oja learning rule, focuses on the effect of synapse learning rate on spike synchronization and its relative transitions in a Newman-Watts small-world neuronal network. The individual dynamics of each neuron is modeled by a simple Rulkov map that produces spiking behavior. Numerical results have indicated that large coupling can lead to a spatiotemporally synchronous pattern of spiking neurons; in addition, this kind of spike synchronization can emerge intermittently by turning information transmission delay between coupled neurons. Interestingly, with the advent of synaptic plasticity, spike synchronization is gradually destroyed by increasing synapse learning rate; moreover, the phenomenon of intermittent synchronization transitions becomes less and less obvious and it even disappears for relative larger learning rate. Further simulations confirm that spike synchronization as well as synchronization transitions is largely independent of network size. Meanwhile, we detect that large shortcuts probability can facilitate spike synchronization, but it is disadvantageous for delay-induced synchronization transitions.

Effects of autapse and ion channel block on the collective firing activity of Newman–Watts small-world neuronal networks

An autapse is a special kind of synapse established between the axon and dendrites of the same neuron. In the present study, we have investigated the cooperative effects of autapse and ion channel block on the collective firing regularity of Newman–Watts small-world networks of stochastic Hodgkin–Huxley neurons. We obtain autaptic time delay induced multi-coherence resonance (MCR) phenomenon in the absence of ion channel block. When the ion channel block is considered, we find that this autaptic delay induced MCR phenomenon enhances with the increasing of potassium channel block, whereas it weakens with the increasing of sodium channel block at weak and intermediate autaptic conductance regimes. However, at strong autaptic conductance regime neither sodium nor potassium channel block have a significant effect on the collective firing regularity of the network. Besides, we investigate the effects of the coupling strength, the network randomness and the cell size on the regularity. We obtain an optimal coupling strength value and an optimal cell size leading to a more prominent MCR effect. We also show that the MCR phenomenon increases with the increasing of network randomness in potassium channel block, but it needs to a minimum network randomness for its appearing in case of sodium channel block.

Dynamic network structured immune particle swarm optimisation with small-world topology

Particle swarm optimisation (PSO) has attracted much attention and is used to wide applications in different fields in recent years because of its simple concept, easy implementation and quick convergence. However, it suffers from premature convergence since the population's diversity loses quickly. In this paper, a novel and efficient variant of PSO named DNIPSO is proposed which help the diversity of the swarm be preserved via the Newman-Watts small world network topology and the immune learning operator. Initially the topology of the population is the regular network. Then the Newman-Watts small world topology is formed gradually and the swarm evolves simultaneously. The optimisation process contains the population structure dynamics and particle immune learning two parts which mutually promoted effectively in whole population. Furthermore, the immune operator which is based on the clonal selection theory achieves a trade-off between exploration and exploitation abilities. Numerical experiments both on continuous unconstrained and constrained benchmark functions are used to test the performance of DNIPSO. Simulation results show it is effective and robust.

An evolutionary analysis of low-carbon strategies based on the government–enterprise game in the complex network context

Low-carbon development patterns have gradually attracted more attention because of strong shocks to society and the economy from environmental problems. Developing a low-carbon economy is essential for every country to improve sustainable economic development, and doing so is at the forefront of low-carbon research. Policy and government intervention play a key role in the development of a low-carbon economy. Using game-based learning theory for reference, this paper builds an evolutionary model of low-carbon strategies based on the game between the government and enterprises in the context of a complex network. It then studies the effects of government incentives on enterprises regarding the diffusion of low-carbon policies and how enterprises compete and transform in the Newman-Watts small-world network. We introduce government policy encouragement as a factor in the decision-making process of companies' adoption of a low-carbon strategy, thus enriching the literature on the diffusion of low-carbon strategies. The model proposed in this paper can be used as a tool to evaluate the diffusion and application of low-carbon strategies among companies. The findings suggest that enterprises’ expectation of government incentives including subsidy and regulation determines whether low-carbon strategies can be diffused, and the diffusion speed. The more quick enterprises adjust their expectations in the government–enterprise game, the more enterprises will learn and follow to adopt effective low-carbon strategy. When enterprises attach great importance to the expected earnings from government incentives, the less effective low-carbon strategy adopted initially can be replaced by another more effective one.

Quantification of degeneracy in Hodgkin–Huxley neurons on Newman–Watts small world network

Degeneracy is a fundamental source of biological robustness, complexity and evolvability in many biological systems. However, degeneracy is often confused with redundancy. Furthermore, the quantification of degeneracy has not been addressed for realistic neuronal networks. The objective of this paper is to characterize degeneracy in neuronal network models via quantitative mathematic measures. Firstly, we establish Hodgkin–Huxley neuronal networks with Newman–Watts small world network architectures. Secondly, in order to calculate the degeneracy, redundancy and complexity in the ensuing networks, we use information entropy to quantify the information a neuronal response carries about the stimulus – and mutual information to measure the contribution of each subset of the neuronal network. Finally, we analyze the interdependency of degeneracy, redundancy and complexity – and how these three measures depend upon network architectures. Our results suggest that degeneracy can be applied to any neuronal network as a formal measure, and degeneracy is distinct from redundancy. Qualitatively degeneracy and complexity are more highly correlated over different network architectures, in comparison to redundancy. Quantitatively, the relationship between both degeneracy and redundancy depends on network coupling strength: both degeneracy and redundancy increase with complexity for small coupling strengths; however, as coupling strength increases, redundancy decreases with complexity (in contrast to degeneracy, which is relatively invariant). These results suggest that the degeneracy is a general topologic characteristic of neuronal networks, which could be applied quantitatively in neuroscience and connectomics.

The circadian rhythm induced by the heterogeneous network structure of the suprachiasmatic nucleus.

In mammals, the master clock is located in the suprachiasmatic nucleus (SCN), which is composed of about 20 000 nonidentical neuronal oscillators expressing different intrinsic periods. These neurons are coupled through neurotransmitters to form a network consisting of two subgroups, i.e., a ventrolateral (VL) subgroup and a dorsomedial (DM) subgroup. The VL contains about 25% SCN neurons that receive photic input from the retina, and the DM comprises the remaining 75% SCN neurons which are coupled to the VL. The synapses from the VL to the DM are evidently denser than that from the DM to the VL, in which the VL dominates the DM. Therefore, the SCN is a heterogeneous network where the neurons of the VL are linked with a large number of SCN neurons. In the present study, we mimicked the SCN network based on Goodwin model considering four types of networks including an all-to-all network, a Newman-Watts (NW) small world network, an Erdös-Rényi (ER) random network, and a Barabási-Albert (BA) scale free network. We found that the circadian rhythm was induced in the BA, ER, and NW networks, while the circadian rhythm was absent in the all-to-all network with weak cellular coupling, where the amplitude of the circadian rhythm is largest in the BA network which is most heterogeneous in the network structure. Our finding provides an alternative explanation for the induction or enhancement of circadian rhythm by the heterogeneity of the network structure.

Autaptic pacemaker mediated propagation of weak rhythmic activity across small-world neuronal networks

We study the effects of an autapse, which is mathematically described as a self-feedback loop, on the propagation of weak, localized pacemaker activity across a Newman–Watts small-world network consisting of stochastic Hodgkin–Huxley neurons. We consider that only the pacemaker neuron, which is stimulated by a subthreshold periodic signal, has an electrical autapse that is characterized by a coupling strength and a delay time. We focus on the impact of the coupling strength, the network structure, the properties of the weak periodic stimulus, and the properties of the autapse on the transmission of localized pacemaker activity. Obtained results indicate the existence of optimal channel noise intensity for the propagation of the localized rhythm. Under optimal conditions, the autapse can significantly improve the propagation of pacemaker activity, but only for a specific range of the autaptic coupling strength. Moreover, the autaptic delay time has to be equal to the intrinsic oscillation period of the Hodgkin–Huxley neuron or its integer multiples. We analyze the inter-spike interval histogram and show that the autapse enhances or suppresses the propagation of the localized rhythm by increasing or decreasing the phase locking between the spiking of the pacemaker neuron and the weak periodic signal. In particular, when the autaptic delay time is equal to the intrinsic period of oscillations an optimal phase locking takes place, resulting in a dominant time scale of the spiking activity. We also investigate the effects of the network structure and the coupling strength on the propagation of pacemaker activity. We find that there exist an optimal coupling strength and an optimal network structure that together warrant an optimal propagation of the localized rhythm.

Autaptic activity-induced synchronization transitions in Newman-Watts network of Hodgkin-Huxley neurons.

In this paper, we numerically study the effect of autapse on the synchronization of Newman-Watts small-world Hodgkin-Huxley neuron network. It is found that the neurons exhibit synchronization transitions as autaptic self-feedback delay is varied, and the phenomenon becomes strongest when autaptic self-feedback strength is optimal. This phenomenon also changes with the change of coupling strength and network randomness and become strongest when they are optimal. There are similar synchronization transitions for electrical and chemical autapse, but the synchronization transitions for chemical autapse occur more frequently and are stronger than those for electrical synapse. The underlying mechanisms are briefly discussed in quality. These results show that autaptic activity plays a subtle role in the synchronization of the neuronal network. These findings may find potential implications of autapse for the information processing and transmission in neural systems.

Effect of small-world topology on wave propagation on networks of excitable elements

We study excitation waves on a Newman–Watts small-world network model of coupled excitable elements. Depending on the global coupling strength, we find differing resilience to the added long-range links and different mechanisms of propagation failure. For high coupling strengths, we show agreement between the network and a reaction-diffusion model with additional mean-field term. Employing this approximation, we are able to estimate the critical density of long-range links for propagation failure.

Effects of spike-time-dependent plasticity on the stochastic resonance of small-world neuronal networks.

The phenomenon of stochastic resonance in Newman-Watts small-world neuronal networks is investigated when the strength of synaptic connections between neurons is adaptively adjusted by spike-time-dependent plasticity (STDP). It is shown that irrespective of the synaptic connectivity is fixed or adaptive, the phenomenon of stochastic resonance occurs. The efficiency of network stochastic resonance can be largely enhanced by STDP in the coupling process. Particularly, the resonance for adaptive coupling can reach a much larger value than that for fixed one when the noise intensity is small or intermediate. STDP with dominant depression and small temporal window ratio is more efficient for the transmission of weak external signal in small-world neuronal networks. In addition, we demonstrate that the effect of stochastic resonance can be further improved via fine-tuning of the average coupling strength of the adaptive network. Furthermore, the small-world topology can significantly affect stochastic resonance of excitable neuronal networks. It is found that there exists an optimal probability of adding links by which the noise-induced transmission of weak periodic signal peaks.

Time delay and long-range connection induced synchronization transitions in Newman-Watts small-world neuronal networks.

The synchronization transitions in Newman-Watts small-world neuronal networks (SWNNs) induced by time delay and long-range connection (LRC) probability have been investigated by synchronization parameter and space-time plots. Four distinct parameter regions, that is, asynchronous region, transition region, synchronous region, and oscillatory region have been discovered at certain LRC probability as time delay is increased. Interestingly, desynchronization is observed in oscillatory region. More importantly, we consider the spatiotemporal patterns obtained in delayed Newman-Watts SWNNs are the competition results between long-range drivings (LRDs) and neighboring interactions. In addition, for moderate time delay, the synchronization of neuronal network can be enhanced remarkably by increasing LRC probability. Furthermore, lag synchronization has been found between weak synchronization and complete synchronization as LRC probability is a little less than 1.0. Finally, the two necessary conditions, moderate time delay and large numbers of LRCs, are exposed explicitly for synchronization in delayed Newman-Watts SWNNs.

Effect of gap junctions on the firing patterns and synchrony for different external inputs in the striatal fast-spiking neuron network.

Gap junctions are the mechanism for striatal fast-spiking interneurons (FSIs) to interconnect with each other and play an important role in determining the physiological functioning of the FSIs. To investigate the effect of gap junctions on the firing activities and synchronization of the network for different external inputs, a simple network with least connections and a Newman-Watts small-world network were constructed. Our research shows that both properties of neural networks are related to the conductance of the gap junctions, as well as the frequency and correlation of the external inputs. The effect of gap junctions on the synchronization of network is different for inputs with different frequencies and correlations. The addition of gap junctions can promote the network synchrony in some conditions but suppress it in others, and they can inhibit the firing activities in most cases. Both the firing rate and synchronization of the network increase along with the increase of the electrical coupling strength for inputs with low frequency and high correlation. Thus, the network of coupled FSIs can act as a detector for synchronous synaptic input from cortex and thalamus.