Small-world Network Model Research Articles

Study on the optimal supervision strategy of government low-carbon subsidy and the corresponding efficiency and stability in the small-world network context

The optimal strategy for the government to supervise low-carbon subsidy is studied in this paper, as well as the problem of supervision efficiency and supervision stability. Firstly, the evolutionary game models are constructed in un-supervision and supervision cases respectively, based on agents of the government and enterprises, and three supervision strategies and related rules are given. Secondly, the supervision efficiency and supervision stability are discussed based on the established small-world network model, then the optimal supervision strategy and the corresponding optimal supervision probability are obtained. Moreover, parameter sensitivity analysis is carried out based on benefit stability. The simulation results show that: (1) the optimal strategy for the government to supervise low-carbon subsidy is random supervision of enterprises who declare high subsidy, with the optimal probability of supervision 0.48, and the overall optimal supervision probability 0.24. (2) the supervision efficiency and supervision stability can not achieve at the same time. However, in order to maximize the revenues of both agents, the measure of efficiency first and stability second can be considered. (3) when there is more noise in the environment, the average revenues of both agents are lower, and the benefit stability is worse. When the supervision cost is higher, the result is the same as the case with more noise in the environment. However, the increase in punishment cost does not necessarily lead to the increase in revenue. When punishment cost increases to a certain extent, and continues to increase, the revenues of both agents reduce first, and then increase, and the benefit stability becomes worse first, and then better. Finally, the related policy recommendations and future work are presented.

Collective behavior of large-scale neural networks with GPU acceleration.

In this paper, the collective behaviors of a small-world neuronal network motivated by the anatomy of a mammalian cortex based on both Izhikevich model and Rulkov model are studied. The Izhikevich model can not only reproduce the rich behaviors of biological neurons but also has only two equations and one nonlinear term. Rulkov model is in the form of difference equations that generate a sequence of membrane potential samples in discrete moments of time to improve computational efficiency. These two models are suitable for the construction of large scale neural networks. By varying some key parameters, such as the connection probability and the number of nearest neighbor of each node, the coupled neurons will exhibit types of temporal and spatial characteristics. It is demonstrated that the implementation of GPU can achieve more and more acceleration than CPU with the increasing of neuron number and iterations. These two small-world network models and GPU acceleration give us a new opportunity to reproduce the real biological network containing a large number of neurons.

Exploiting Small World Networks for Energy Efficiency in Network of Multi-Clock-Rate Wireless Devices

While state-of-the-art in wireless communication is highly spectrum efficient, it is still wanting in terms of energy efficiency. Sleep scheduling techniques provide limited gains due to the large fraction of time spent by wireless devices in idle-listening. The use of multi-clock-rate sampling devices (MCDs) in conjunction with frequency agnostic preamble detection promises significant improvements in energy efficiency by downclocking the receiver to save energy. In this paper, we consider a wireless ad hoc network of MCDs, and model it as a small world network. We propose a new energy efficient small world network model for a network of MCDs, which considers the battery energy of the wireless nodes, the multi-hop transmission distance, and downclocking level of the devices. Results show that the proposed model is more energy efficient than the Newman and Watts model.

The common transcriptional subnetworks of the grape berry skin in the late stages of ripening

BackgroundWine grapes are important economically in many countries around the world. Defining the optimum time for grape harvest is a major challenge to the grower and winemaker. Berry skins are an important source of flavor, color and other quality traits in the ripening stage. Senescent-like processes such as chloroplast disorganization and cell death characterize the late ripening stage.ResultsTo better understand the molecular and physiological processes involved in the late stages of berry ripening, RNA-seq analysis of the skins of seven wine grape cultivars (Cabernet Franc, Cabernet Sauvignon, Merlot, Pinot Noir, Chardonnay, Sauvignon Blanc and Semillon) was performed. RNA-seq analysis identified approximately 2000 common differentially expressed genes for all seven cultivars across four different berry sugar levels (20 to 26 °Brix). Network analyses, both a posteriori (standard) and a priori (gene co-expression network analysis), were used to elucidate transcriptional subnetworks and hub genes associated with traits in the berry skins of the late stages of berry ripening. These independent approaches revealed genes involved in photosynthesis, catabolism, and nucleotide metabolism. The transcript abundance of most photosynthetic genes declined with increasing sugar levels in the berries. The transcript abundance of other processes increased such as nucleic acid metabolism, chromosome organization and lipid catabolism. Weighted gene co-expression network analysis (WGCNA) identified 64 gene modules that were organized into 12 subnetworks of three modules or more and six higher order gene subnetworks. Some gene subnetworks were highly correlated with sugar levels and some subnetworks were highly enriched in the chloroplast and nucleus. The petal R package was utilized independently to construct a true small-world and scale-free complex gene co-expression network model. A subnetwork of 216 genes with the highest connectivity was elucidated, consistent with the module results from WGCNA. Hub genes in these subnetworks were identified including numerous members of the core circadian clock, RNA splicing, proteolysis and chromosome organization. An integrated model was constructed linking light sensing with alternative splicing, chromosome remodeling and the circadian clock.ConclusionsA common set of differentially expressed genes and gene subnetworks from seven different cultivars were examined in the skin of the late stages of grapevine berry ripening. A densely connected gene subnetwork was elucidated involving a complex interaction of berry senescent processes (autophagy), catabolism, the circadian clock, RNA splicing, proteolysis and epigenetic regulation. Hypotheses were induced from these data sets involving sugar accumulation, light, autophagy, epigenetic regulation, and fruit development. This work provides a better understanding of berry development and the transcriptional processes involved in the late stages of ripening.

Spatial connections in regional climate model rainfall outputs at different temporal scales: Application of network theory

Understanding the spatial and temporal variability of rainfall has always been a great challenge, and the impacts of climate change further complicate this issue. The present study employs the concepts of complex networks to study the spatial connections in rainfall, with emphasis on climate change and rainfall scaling. Rainfall outputs (during 1961–1990) from a regional climate model (i.e. Weather Research and Forecasting (WRF) model that downscaled the European Centre for Medium-range Weather Forecasts, ECMWF ERA-40 reanalyses) over Southeast Asia are studied, and data corresponding to eight different temporal scales (6-hr, 12-hr, daily, 2-day, 4-day, weekly, biweekly, and monthly) are analyzed. Two network-based methods are applied to examine the connections in rainfall: clustering coefficient (a measure of the network’s local density) and degree distribution (a measure of the network’s spread). The influence of rainfall correlation threshold (T) on spatial connections is also investigated by considering seven different threshold levels (ranging from 0.5 to 0.8). The results indicate that: (1) rainfall networks corresponding to much coarser temporal scales exhibit properties similar to that of small-world networks, regardless of the threshold; (2) rainfall networks corresponding to much finer temporal scales may be classified as either small-world networks or scale-free networks, depending upon the threshold; and (3) rainfall spatial connections exhibit a transition phase at intermediate temporal scales, especially at high thresholds. These results suggest that the most appropriate model for studying spatial connections may often be different at different temporal scales, and that a combination of small-world and scale-free network models might be more appropriate for rainfall upscaling/downscaling across all scales, in the strict sense of scale-invariance. The results also suggest that spatial connections in the studied rainfall networks in Southeast Asia are weak, especially when more stringent conditions are imposed (i.e. when T is very high), except at the monthly scale.

A small-world network model for the simulation of fire spread onboard naval vessels

This work is devoted to the development of a small-world network model to predict real-time fire spread onboard naval vessels. This model takes into account short-range and long-range connections between neighboring and remote network compartments. Fire ignition and flashover, as well as fire transmissions through the walls and ventilation ducts are simulated using time-dependent normal probability density functions. Mean durations of fire transmission through the walls and ducts are determined by a three-zone model and a one-dimensional CFD code, respectively. Specific experiments are conducted in a steel room, representative of a naval vessel compartment, in order to validate the zone model. Then a proof of concept is developed by applying the network model to a full-scale vessel mockup composed of 113 compartments on 7 decks. A statistical study is conducted to produce fire risk maps, classifying the vessel compartments according to their propensity to burn.

Hybrid control of delay induced hopf bifurcation of dynamical small-world network.

In this paper, we focus on the Hopf bifurcation control of a small-world network model with time-delay. With emphasis on the relationship between the Hopf bifurcation and the time-delay, we investigate the effect of time-delay by choosing it as the bifurcation parameter. By using tools from control and bifurcation theory, it is proved that there exists a critical value of time-delay for the stability of the model. When the time-delay passes through the critical value, the model loses its stability and a Hopf bifurcation occurs. To enhance the stability of the model, we propose an improved hybrid control strategy in which state feedback and parameter perturbation are used. Through linear stability analysis, we show that by adjusting the control parameter properly, the onset of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point of the model. Finally, numerical simulations are given to verify the theoretical analysis.

Scaling of weighted spectral distribution in weighted small-world networks**Project supported by the National Natural Science Foundation of China (Grant Nos. 61402485, 61573262, and 61303061).

Many real-world systems can be modeled by weighted small-world networks with high clustering coefficients. Recent studies for rigorously analyzing the weighted spectral distribution (WSD) have focused on unweighted networks with low clustering coefficients. In this paper, we rigorously analyze the WSD in a deterministic weighted scale-free small-world network model and find that the WSD grows sublinearly with increasing network order (i.e., the number of nodes) and provides a sensitive discrimination for each input of this model. This study demonstrates that the scaling feature of the WSD exists in the weighted network model which has high and order-independent clustering coefficients and reasonable power-law exponents.

The most common friend first immunization**Project supported by the National Natural Science Foundation of China (Grant No. 61263019), the Program for International Science and Technology Cooperation Projects of Gansu Province, China (Grant No. 144WCGA166), and the Program for Longyuan Young Innovation Talents and the Doctoral Foundation of Lanzhou University of Technology, China.

In this paper, a standard susceptible-infected-recovered-susceptible(SIRS) epidemic model based on the Watts–Strogatz (WS) small-world network model and the Barabsi–Albert (BA) scale-free network model is established, and a new immunization scheme — “the most common friend first immunization” is proposed, in which the most common friend’s node is described as being the first immune on the second layer protection of complex networks. The propagation situations of three different immunization schemes — random immunization, high-risk immunization, and the most common friend first immunization are studied. At the same time, the dynamic behaviors are also studied on the WS small-world and the BA scale-free network. Moreover, the analytic and simulated results indicate that the immune effect of the most common friend first immunization is better than random immunization, but slightly worse than high-risk immunization. However, high-risk immunization still has some limitations. For example, it is difficult to accurately define who a direct neighbor in the life is. Compared with the traditional immunization strategies having some shortcomings, the most common friend first immunization is effective, and it is nicely consistent with the actual situation.

Вычисление областей устойчивости дискретных моделей больших нейронных сетей типа small world

The article is devoted to description of discrete models of small world networks with a large number of neurons with a certain parameter p varying from 0 to 1. For p=0 have model, regular neural networks, which is a ring network in which each neuron interacts with several neighbors on the ring. In the case p=1 have a model with randomly distributed connections. When the values of $p$ not exceeding 0.1 have the Watts-Strogatz small world network. Such a neural network can be models of different neural structures in living organisms, for example, the hippocampus of the mammalian brain. This paper examines the dynamics of change areas of stability of such neural networks when 0\leq p \leq 0.1. Numerical experiments show an increase in sustainability in the transition from a regular network to small world.

A small-world network model of facial emotion recognition.

Various models have been proposed to increase understanding of the cognitive basis of facial emotions. Despite those efforts, interactions between facial emotions have received minimal attention. If collective behaviours relating to each facial emotion in the comprehensive cognitive system could be assumed, specific facial emotion relationship patterns might emerge. In this study, we demonstrate that the frameworks of complex networks can effectively capture those patterns. We generate 81 facial emotion images (6 prototypes and 75 morphs) and then ask participants to rate degrees of similarity in 3240 facial emotion pairs in a paired comparison task. A facial emotion network constructed on the basis of similarity clearly forms a small-world network, which features an extremely short average network distance and close connectivity. Further, even if two facial emotions have opposing valences, they are connected within only two steps. In addition, we show that intermediary morphs are crucial for maintaining full network integration, whereas prototypes are not at all important. These results suggest the existence of collective behaviours in the cognitive systems of facial emotions and also describe why people can efficiently recognize facial emotions in terms of information transmission and propagation. For comparison, we construct three simulated networks--one based on the categorical model, one based on the dimensional model, and one random network. The results reveal that small-world connectivity in facial emotion networks is apparently different from those networks, suggesting that a small-world network is the most suitable model for capturing the cognitive basis of facial emotions.

Generalized Byram's formula for arbitrary fire front geometries

The expression proposed a half century ago by Byram allowing the estimation of wild land fire front heat flux was extensively used in fire research and by firefighters. However, this formula does not account for wild land fuel heterogeneity and local weather changes. Its validity is limited to stationary spreads, and fails in describing the behavior of curved fronts and non-spreading fires. A new formula is derived to generalize heat flux estimation to any fire front with arbitrary geometry. Heat flux is found to depend on the front local radius as well as its convexity/concavity. The front curvature induces also a quadratic dependence on the rate of spread. The derived equation is validated by numerical simulations using the small world network model for line and curved fronts. Extensions of generalized Byram formula including fractal dimension of the front and wind speed effect are also proposed.

Comparative effects of avoidance and immunization on epidemic spreading in a dynamic small-world network with community structure

Considering the actual behavior of people’s short-term travel, we propose a dynamic small-world community network model with tunable community strength which has constant local links and time varying long-range jumps. Then an epidemic model of susceptible-infected-recovered is established based on the mean-field method to evaluate the inhibitory effects of avoidance and immunization on epidemic spreading. And an approximate formula for the epidemic threshold is obtained by mathematical analysis. The simulation results show that the epidemic threshold decreases with the increase of inner-community motivation rate and inter-community long-range motivation rate, while it increases with the increase of immunization rate or avoidance rate. It indicates that the inhibitory effect on epidemic spreading of immunization works better than that of avoidance.

A new small-world network created by Cellular Automata

In this paper, we generate small-world networks by the Cellular Automaton based on starting with one-dimensional regular networks. Besides the common properties of small-world networks with small average shortest path length and large clustering coefficient, the small-world networks generated in this way have other properties: (i) The edges which are cut in the regular network can be controlled that whether the edges are reconnected or not, and (ii) the number of the edges of the small-world network model equals the number of the edges of the original regular network. In other words, the average degree of the small-world network model equals to the average degree of the original regular network.

Multi-agent Simulation for Promoting Clean Energy Vehicles from the Perspective of Concern for the Environment and Local Interactions

Clean energy vehicles (CEVs) such as EV or PHV should be promoted for the reduction of greenhouse gas emissions in the transportation sector. However, it is important to note that social interactions affect the promotion of CEVs. Therefore, a multiagent simulation system for promoting CEVs has been developed in the present study from the perspective of not only concern for the environment but also for local interaction processes in terms of social conformity. Intention of holding CEV is described with the database of the questionnaire survey about purchasing vehicles. The social network of the artificial society is described as a small-world network model. The time series changes of the numbers of clean energy vehicles and the volume of greenhouse gas emissions are estimated by the proposed multiagent simulation. Finally, it can be concluded that the proposed multiagent simulation with local interaction is useful for promoting the planning of CEVs.

Corona graphs as a model of small-world networks

We introduce recursive corona graphs as a model of small-world networks. We investigate analytically the critical characteristics of the model, including order and size, degree distribution, average path length, clustering coefficient, and the number of spanning trees, as well as Kirchhoff index. Furthermore, we study the spectra for the adjacency matrix and the Laplacian matrix for the model. We obtain explicit results for all the quantities of the recursive corona graphs, which are similar to those observed in real-life networks.

A Small-world Network Model of Facial Emotion Recognition

Various models have been proposed to increase understanding of the cognitive basis of facial emotions. Despite those efforts, interactions between facial emotions have received minimal attention. If collective behaviours relating to each facial emotion in the comprehensive cognitive system could be assumed, specific facial emotion relationship patterns might emerge. In this study, we demonstrate that the frameworks of complex networks can effectively capture those patterns. We generate 81 facial emotion images (6 prototypes and 75 morphs) and then ask participants to rate degrees of similarity in 3240 facial emotion pairs in a paired comparison task. A facial emotion network constructed on the basis of similarity clearly forms a small-world network, which features an extremely short average network distance and close connectivity. Further, even if two facial emotions have opposing valences, they are connected within only two steps. In addition, we show that intermediary morphs are crucial for maintaining ...

Development of a network based model to simulate the between-farm transmission of the porcine reproductive and respiratory syndrome virus

Contact structure within a population can significantly affect the outcomes of infectious disease spread models. The objective of this study was to develop a network based simulation model for the between-farm spread of porcine reproductive and respiratory syndrome virus to assess the impact of contact structure on between-farm transmission of PRRS virus. For these farm level models, a hypothetical population of 500 swine farms following a multistage production system was used. The contact rates between farms were based on a study analyzing movement of pigs in Canada, while disease spread parameters were extracted from published literature. Eighteen distinct scenarios were designed and simulated by varying the mode of transmission (direct versus direct and indirect contact), type of index herd (farrowing, nursery and finishing), and the presumed network structures among swine farms (random, scale-free and small-world). PRRS virus was seeded in a randomly selected farm and 500 iterations of each scenario were simulated for 52 weeks. The median epidemic size by the end of the simulated period and percentage die-out for each scenario, were the key outcomes captured. Scenarios with scale-free network models resulted in the largest epidemic sizes, while scenarios with random and small-world network models resulted in smaller and similar epidemic sizes. Similarly, stochastic die-out percentage was least for scenarios with scale-free networks followed by random and small-world networks. Findings of the study indicated that incorporating network structures among the swine farms had a considerable impact on the spread of PRRS virus, highlighting the importance of understanding and incorporating realistic contact structures when developing infectious disease spread models for similar populations.

Simulation Analysis of Knowledge Transfer Behaviour Based on Small World Network Model

Simulation Analysis of Knowledge Transfer Behaviour Based on Small World Network Model

A Survivability Clustering Algorithm for Ad Hoc Network Based on a Small-World Model

In Ad hoc network, nodes have the characteristics of limited energy, self-organizing and multi-hop. For the purpose of improving the survivability of Ad hoc network effectively, this paper proposes a new algorithm named EMDWCA (Based on Energy, Mobility and Degrees of the nodes on-demand Weighted Clustering Algorithm). The LEACH algorithm is used to cluster the Ad hoc network in the first election, but the EMDWCA is used in the second election. By considering the appearances, disappearances, and communication link failures of the mobile nodes, this algorithm constructs the topology of Ad hoc network based on a small-world network model. To make sure that nodes can still communicate in the following election cycles, it improves the stability of the network topology and overall network invulnerability. The network is analyzed and simulation experiments are performed in order to compare the performance of this new clustering algorithm with the weighted clustering algorithm (WCA) in terms of the correctness, effectiveness, and invulnerability of the networks. The final result proves that the proposed algorithm provides better performance than the original WCA algorithm.