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A minimal model based on network incorporating individual interactions is proposed to study the non-Poisson statistical properties of human behavior: individuals in system interact with their neighbors, the probability of an individual acting correlates to its activity, and all the individuals involved in action will change their activities randomly. The model reproduces varieties of spatial–temporal patterns observed in empirical studies of human daily communications, providing insight into various human activities and embracing a range of realistic social interacting systems, particularly, intriguing bimodal phenomenon. This model bridges priority queueing theory and punctuated equilibrium dynamics, and our modeling and analysis is likely to shed light on non-Poisson phenomena in many complex systems. [ABSTRACT FROM AUTHOR]

In society, many problems can be understood as multitasking process with multiplayer (MPM). Choosing different strategies or different orders in processing tasks, an individual will spend a different amount of time to complete all the tasks. Therefore, a good strategy or a good order can help an individual work more efficiently. In this paper, we propose a model to study the optimization problems of MPM. The average time spent for all the tasks by an individual is calculated in each strategy, and we find the random choice strategy can make an individual spend less time in completing all tasks. The correlation coefficient between the order of each task processed by an individual and the corresponding time spent for all the tasks by the individual is also calculated. Then the internal statistics law between the order and the corresponding time is found and explains why the random choice strategy is better. Finally, we research the change of the queue length in each task with the time. These results have certain significance on theory and practical application on MPM. [ABSTRACT FROM AUTHOR]

Abstract: When planning for the evacuation guidance, how to efficiently set the trained evacuation leaders is an important problem which has great impact on the evacuation process. This paper investigates the effect of the number and positions of evacuation leaders on the evacuation dynamics in rooms with limited visibility range. In the improved social force model, only the trained leaders exactly know the exit positions, and the others could only follow the guidance according to the positions and directions of evacuation leaders. According to the simulation results, only one or two leaders could get remarkable effect for a single-exit configuration. But for configurations with multi-exits, evacuation leaders would make the dynamic slower unless the guidance sufficiently utilizes every exit. The results indicate that, we should set as many leaders as the number of exits in the center of the multi-exits regular squared room, and when emergencies occur, each leader heads to a different exit. Moreover, if we do like this, the evacuation would be even faster than that with 20 random-position-leaders. This work may shed some light on the drawing up of emergency scheme for large public-gathering places like stadiums and shopping malls. [Copyright &y& Elsevier]

Abstract: We empirically study the activity pattern of individual blog-posting and observe the interevent time distributions decay as power-laws at both individual and population level. As different from previous studies, we find significant short-term memory in it. Moreover, the memory coefficient first decays in a power law and then turns to an exponential form. Our findings produce evidence for the strong short-term memory in human dynamics and challenge previous models. Accordingly, we propose a simple model based on temporal preference, which can well reproduce both the heavy-tailed nature and the strong memory effects. This work helps in understanding the temporal regularities of online human behaviors. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the data of industries in China and find that the frequency distributions of fixed assets and fixed-assets’ investment of industries obey power laws. We show that these power-law modes can be explained by the rules of the Simon Model, rather than the existing investment theories such as the classical investment theory or acceleration principle. Moreover, the mechanism of the investment distribution may be similar to the forest-fire model of self-organizing criticality. By introducing the complex system methods, this research changes the traditional opinion of the investment and gains some meaningful understanding in the dynamics of industries and the economic cycle. [Copyright &y& Elsevier]

Abstract: The interactions between investors and investments are of significant importance to understand the dynamics of financial markets. An evolutionary model is proposed to investigate the dynamic behaviors of investors and investments in a market ecology. The investors are divided into two groups, active ones and passive ones, distinguished by different selection capabilities based on the partial information, while the investments are simply categorized as good ones and bad ones. Without external influence, the system consisting of both investors and investments can self-organize to a quasi-stationary state according to their own strategies associating with the gains of market information. The model suggests that the partial information asymmetry of investors and various qualities of investments commonly give rise to a diverse dynamic behavior of the system by quantifying the fraction of active investors and of good investment at the quasi-stationary state. [Copyright &y& Elsevier]

Abstract: Conditional interactions are common in both human and animal societies. To understand the impacts of this feature on the evolution of cooperation, we propose a modified public goods game combined with conditional interactions in terms of the aspiration payoffs. Through simulations, we find that the function of the fraction of cooperators and the synergy factor is non-monotonic. This indicates that a large synergy factor is not always in favor of the promotion of cooperation. In addition, for a high aspiration, the typical coexistence state of cooperators and defectors could disappear, and the system demonstrates a sharp transition from the complete defection state to the complete cooperation state as the synergy factor increases. Furthermore, an interesting critical phenomenon is found in a finite system, i.e., the system can randomly evolve into a complete defection state or a complete cooperation state. An explanation of these evolutionary outcomes is provided in this paper, which is in agreement with the simulation results. [Copyright &y& Elsevier]

Abstract: Within most real biological or social systems, age plays an important role in the vitality of individuals. For instance, individuals become more and more weak with age, while young individuals may prosper even under poor living conditions. In this paper, we find that aging as a coevolutionary process promotes cooperation more effectively than quenched heterogeneous distributions of age. By studying the average age of defectors and cooperators along the boundaries separating the domains of the two strategies, we reveal the significance of coevolutionary rules for the successful evolution of cooperation amongst selfish and unrelated individuals. [Copyright &y& Elsevier]

Abstract: We propose a nonlinear voter model to study the emergence of global consensus in opinion dynamics. In our model, agent i agrees with one of binary opinions with the probability that is a power function of the number of agents holding this opinion among agent i and its nearest neighbors, where an adjustable parameter α controls the effect of herd behavior on consensus. We find that there exists an optimal value of α leading to the fastest consensus for lattices, random graphs, small-world networks and scale-free networks. Qualitative insights are obtained by examining the spatiotemporal evolution of the opinion clusters. [Copyright &y& Elsevier]

Abstract: In this paper, we study the statistical properties of bookmarking behaviors in Delicious.com. We find that the inter-event time () distributions of bookmarking decay in a power-like manner as increases at both individual and population levels. Remarkably, we observe a significant change in the exponent when the inter-event time increases from the intra-day range to the inter-day range. In addition, the dependence of the exponent on individual activity is found to be different in the two ranges. Instead of monotonically increasing with activity, the inter-day exponent peaks around 3. These results suggest that the mechanisms driving human actions are different in the intra-day and inter-day ranges. We further show that the global distributions of less active users are closer to an exponential distribution than those of more active users. Moreover, a universal behavior in the inter-day range is observed by considering the rescaled variable . Finally, the possible causes of these phenomena are discussed. [Copyright &y& Elsevier]

Abstract: We propose a negotiation strategy to address the effect of geography on the dynamics of naming games over small-world networks. Communication and negotiation frequencies between two agents are determined by their geographical distance in terms of a parameter characterizing the correlation between interaction strength and the distance. A finding is that there exists an optimal parameter value leading to fastest convergence to global consensus on naming. Numerical computations and a theoretical analysis are provided to substantiate our findings. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we study an aspiration-induced migration model, in which each individual plays the prisoner’s dilemma game with those being within a circle of radius centered on himself/herself. An individual will migrate to a randomly chosen place with the velocity if his/her payoff is below the aspiration level. We report that cooperative behavior is favored when the aspiration level and interaction radius are moderate, and the migration velocity is slow. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a recommendation algorithm based on the resource-allocation progresses on bipartite networks. In this model, each node is assigned an attraction that is proportional to the power of its degree, where the exponent is an adjustable parameter that controls the configuration of attractions. In the resource-allocation process, each transmitter distributes its each neighbor a fragment of resource that is proportional to the attraction of the neighbor. Based on a benchmark database, we find that decreasing the attractions that the nodes with higher degrees are assigned can further improve the algorithmic accuracy. More significantly, numerical results show that the optimal configuration of attractions subject to accuracy can also generate more diverse and less popular recommendations. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce a modified collaborative filtering (MCF) algorithm, which has remarkably higher accuracy than the standard collaborative filtering. In the MCF, instead of the cosine similarity index, the user–user correlations are obtained by a diffusion process. Furthermore, by considering the second-order correlations, we design an effective algorithm that depresses the influence of mainstream preferences. Simulation results show that the algorithmic accuracy, measured by the average ranking score, is further improved by 20.45% and 33.25% in the optimal cases of MovieLens and Netflix data. More importantly, the optimal value depends approximately monotonously on the sparsity of the training set. Given a real system, we could estimate the optimal parameter according to the data sparsity, which makes this algorithm easy to be applied. In addition, two significant criteria of algorithmic performance, diversity and popularity, are also taken into account. Numerical results show that as the sparsity increases, the algorithm considering the second-order correlation can outperform the MCF simultaneously in all three criteria. [Copyright &y& Elsevier]

Abstract: The optimal information feedback has a significant effect on many socioeconomic systems like stock market and traffic systems aiming to make full use of resources. In this paper, we studied dynamics of traffic flow with real-time information provided and the influence of a feedback strategy named prediction feedback strategy is introduced, based on a two-route scenario in which dynamic information can be generated and displayed on the board to guide road users to make a choice. Our model incorporates the effects of adaptability into the cellular automaton models of traffic flow and simulation results adopting this optimal information feedback strategy have demonstrated high efficiency in controlling spatial distribution of traffic patterns compared with the other three information feedback strategies, i.e., vehicle number and flux. [Copyright &y& Elsevier]

Abstract: We introduce a preferential selection mechanism into a spatial public goods game where players are located on a square lattice. Each individual chooses one of its neighbors as a reference with a probability proportional to , where is the neighbor’s payoff and (≥0) is a tunable parameter. It is shown that the introduction of such a preferential selection can remarkably promote the emergence of cooperation over a wide range of the multiplication factor. We find that the mean payoffs of cooperators along the boundary are higher than that of defectors and cooperators form larger clusters as increases. The extinction thresholds of cooperators and defectors for different values of noise are also investigated. [Copyright &y& Elsevier]

Abstract: In this paper, we study the capacity of a highway with two on-ramps by using a cellular automata traffic flow model. We investigate how to improve the system capacity by assigning traffic flow to the two ramps. The system phase diagram is presented and different regions are classified. It is shown that in region I, in which both ramps are in free flow and the main road upstream of the ramps is in congestion, assigning a higher proportion of the demand to the upstream on-ramp could improve the overall flow, which is consistent with previous studies. This is explained through studying the spatiotemporal patterns and analytical investigations. In contrast, optimal assignment has not been observed in other regions. We point out that our result is robust and model independent under certain conditions. [Copyright &y& Elsevier]

Abstract: The naming game model characterizes the main evolutionary features of languages or more generally of communication systems. Very recently, the combination of complex networks and the naming game has received much attention and the influences of various topological properties on the corresponding dynamical behavior have been widely studied. In this paper, we investigate the naming game on small-world geographical networks. The small-world geographical networks are constructed by randomly adding links to two-dimensional regular lattices, and it is found that the convergence time is a nonmonotonic function of the geographical distance of randomly added shortcuts. This phenomenon indicates that, although a long geographical distance of the added shortcuts favors consensus achievement, too long a geographical distance of the added shortcuts inhibits the convergence process, making it even slower than the moderates. [Copyright &y& Elsevier]

Abstract: In recent years, the well-developed Vicsek model has attracted more and more attention. Unfortunately, in-depth research on its convergence speed is not yet completed. In this paper, we investigate some key factors governing the convergence speed of the Vicsek model with the assistance of extensive numerical simulations. A significant phenomenon surfaces that the convergence time scales obeys a power law with , with and being the horizon radius and the number of particles, respectively. To further accelerate the convergence procedure, we propose a kind of improved Vicsek model with self-driven particles governed by variational speeds, which can remarkably shorten the convergence time of the standard Vicsek model. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel method to compute the similarity between congeneric nodes in bipartite networks. Different from the standard cosine similarity, we take into account the influence of a node’s degree. Substituting this new definition of similarity for the standard cosine similarity, we propose a modified collaborative filtering (MCF). Based on a benchmark database, we demonstrate the great improvement of algorithmic accuracy for both user-based MCF and object-based MCF. [Copyright &y& Elsevier]

Abstract: We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node’s packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node is proportional to , where is the degree of node and is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal . [Copyright &y& Elsevier]

Abstract: In this paper we present an empirical study of a few practical systems described by cooperation networks, and propose a model to understand the results obtained. We study four non-social systems, which are the Bus Route Networks of Beijing and Yangzhou, the Travel Route Network of China, Huai-Yang recipes of Chinese cooked food, and a social system, which is the Collaboration Network of Hollywood Actors. In order to explain the results related to the degree distribution, act-degree distribution and act-size distribution (especially about the degree distribution, which may be better fitted using a stretched exponential distribution (SED)), we suggest a simple model to show a possible evolutionary mechanism for the emergence of such networks. The analytic and numerical results obtained from the model are in good agreement with the empirical results. [Copyright &y& Elsevier]

Recently, the open review process has attracted the attention of more and more researchers. In order to deeply and quantitatively understand the process, we employ statistical analysis methods, combining human dynamics theory with the assortative mixing analysis of networks to study the process. Our results present the burst characteristics and preference characteristics of authors and reviewers during the review process. Simultaneously, these results demonstrate the irrelevance between the popularity of the manuscript research topic and the manuscript acceptance rate. Moreover, using the assortative mixing analysis method confirmed that the keywords network basically has obvious assortativity. Furthermore, these results suggest that although no inevitable connection between keywords and the acceptance rate of the manuscript, the combination of keywords in the manuscript is influential. Our research results provide useful points for the design of the review system and paper submission. Future work should analyze more data from other disciplines or deconstruct the underlying mechanism of the open review process. • We present the burst and preference characteristics of authors and reviewers. • We demonstrate the irrelevance between the popularity of the manuscript research topic and the manuscript acceptance rate. • We find the combination of keywords in the manuscript is influential. • We investigate the assortative mixing in acceptance–rejection keywords network, and the result suggests that it has strong assortativity. [ABSTRACT FROM AUTHOR]

In this study, a new cellular automata traffic flow model with dual cruise-control limit, where the vehicles with their velocities v = 1 , 5 are not affected by noise and the slow-to-start rule is also introduced for standing vehicles with just one free cell, is established. Computer simulations are used to identify three typical phases from the fundamental diagram: free flow, synchronized flow, and wide moving jam. However, in the original cruise-control limit cellular automata traffic model, there are only two kinds of traffic phases, namely, free flow and congested traffic flow. Furthermore, in the "linear" synchronous flow region, the ratio of flow to density depends on the randomization probability. The synchronous flow with scattered data is firstly found under the dense distribution. Compared to the previous models, the rules of our model are simpler, but it can present many features of Kerner's three-phase theory, in particular, 2 Z -characteristic for phase transitions. • A new cellular automata model with dual cruise-control limit is established. • The slow-to-start rule is incorporated in the model. • A scattered synchronous flow is firstly found in the dense distribution. • The slope of the "linear" synchronous flow depends on the randomization probability. • The typical characteristics of three-phase traffic flow can be simulated. [ABSTRACT FROM AUTHOR]

Background: To report on corneal endothelial regeneration, graft clarity, and vision recovery when using endothelium-free grafts., Methods: We evaluated the donor's cell viability using trypan blue staining and dual staining with calcein acetoxy methyl ester and ethidium homodimer-1. To preserve eyeball integrity, we performed therapeutic penetrating keratoplasty using cryopreserved donor tissue without endothelium on 195 consecutive patients who suffered from corneal perforation due to progressive primary corneal disease such as herpes simplex keratitis, fungal keratitis, ocular thermal burns, keratoconus, and phlyctenular keratoconjunctivitis. Of these, 18 eyes recovered corneal graft clarity and underwent periodic slit-lamp microscopy, A-scan pachymetry, and in vivo confocal microscopy to observe the clinical manifestations, variations in corneal thickness, and repopulation of the corneal endothelial cells on the donor grafts., Results: No viable cells were detected in the cryopreserved corneas. After the therapeutic penetrating keratoplasty, notable corneal graft edema was observed in all 18 eyes for 1-4 months, and no corneal endothelial cells were detected on the grafts during this period. Thereafter, we observed gradual and progressive regression and final resolution of the stromal edema, with complete recovery of corneal graft clarity. Through periodic confocal microscopy, we observed the corneal endothelium's regenerating process, along with single cells bearing multiple nuclei and cell division-like morphology. The regenerated endothelium on the grafts reached a mean cell density of 991 cells/mm 2 . Remarkable vision rehabilitation was achieved in all 18 patients., Conclusions: We obtained conclusive evidence that host-derived endothelial cells can regenerate a new endothelium over the endothelium-free graft, which possesses normal functions for corneal clarity and vision recovery., (© 2022. The Author(s).)

It is a longstanding debate on the absence of threshold for susceptible-infected-susceptible (SIS) model on networks with finite second order moment of degree distribution. The eigenvector localization of the adjacency matrix for a network gives rise to the inactive Griffiths phase featuring slow decay of the activity localized around highly connected nodes due to the dynamical fluctuation. We show how it dramatically changes our understanding of the SIS model, opening up new possibilities for the debate. We derive the critical condition for Griffiths to active phase transition: on average, an infected node can further infect another one in the characteristic lifespan of the star subgraph composed of the node and its nearest neighbors. The system approaches the critical point of avoiding the irreversible dynamical fluctuation and the trap of absorbing state. As a signature of the phase transition, the infection density of a node is not only proportional to its degree, but also proportional to the exponentially growing lifespan of the star. And the divergence of the average lifespan of the stars is responsible for the vanishing threshold in the thermodynamic limit. The eigenvector localization exponentially reinforces the infection of highly connected nodes, while it inversely suppresses the infection of small-degree nodes.

Covering a network with minimum number of boxes is critical for using the renormalization technique to explore the network configuration space in a multiscale fashion. Here, we propose a versatile methodology composed of flexible representation and sampling of boxes, which have so far received scant attention, and the strategy of selecting boxes to cover the network. It is exemplified via random box sampling strategies and greedy methods to select boxes. We show that the key to substantially reduce the number of boxes is to give the selection priority to those boxes containing nodes that are not included in boxes bigger than themselves. Our algorithm achieves the improvement of diminishing the number of boxes amounting to nearly 25% compared with these well known algorithms.

In the course of development, sleep, or mental disorders, certain neurons in the brain display spontaneous spike-burst activity. The synaptic plasticity evoked by such activity is here studied in the presence of spike-timing-dependent plasticity (STDP). In two chemically coupled bursting model neurons, the spike-burst activity can translate the STDP related to pre- and postsynaptic spike activity into burst-timing-dependent plasticity (BTDP), based on the timing of bursts of pre- and postsynaptic neurons. The resulting BTDP exhibits exponential decays with the same time scales as those of STDP. In weakly coupled bursting neuron networks, the synaptic modification driven by the spike-burst activity obeys a power-law distribution. The model can also produce a power-law distribution of synaptic weights. Here, the considered bursting behavior is made of stereotypical groups of spikes, and bursting is evenly spaced by long intervals.

Objective: To investigate the effects of corneal thickness distribution and apex position on postoperative refractive status after full-bed deep anterior lamellar keratoplasty (FBDALK)., Methods: This is a retrospective analysis of patients who were diagnosed with advanced keratoconus between 2011 and 2014 in our hospital. The base of the cone in all patients did not exceed the central cornea at a 6-mm range. The FBDALK was performed by a same surgeon. All patients had a complete corneal suture removal and the follow-up records were intact. Patients who had graft-bed misalignment or who were complicated with a cataract or glaucoma were excluded. Uncorrected visual acuity (UCVA), best spectacle corrected visual acuity (BSCVA), and Pentacam examination data were recorded at two years postoperatively. The recorded data included the superior-inferior (S-I) and nasal-temporal (N-T) corneal thickness differences in 2, 4, 6, and 8 mm diameter concentric circles with the corneal apex as the center (S-I 2 mm , S-I 4 mm , S-I 6 mm , S-I 8 mm , N-T 2 mm , N-T 4 mm , N-T 6 mm , and N-T 8 mm ), the linear, X-axis, and Y-axis distance between the corneal pupillary center and the cornea apex, total corneal astigmatism at a zone of 3 mm diameter from the corneal apex (TA 3 mm ), the astigmatic vector values J 0 and J 45 , and the corneal total higher-order aberration for 3 and 6 mm pupil diameters (HOA 3 mm and HOA 6 mm ). Statistical analysis was performed by SPSS 15.0., Results: A total of 47 eyes of 46 patients met the criteria and were included in this study. The mean follow-up time was (28±7) months. The mean UCVA was 0.45±0.23 (logMAR) (MAR: minimum angle of resolution) and the mean BSCVA was 0.19±0.15 (logMAR), which were all significantly positively correlated with postoperative TA 3 mm and HOA 3 mm . The mean S-I corneal thickness differences were (44.62±37.74) μm, and the mean N-T was (38.57±32.29) μm. S-I 2 mm was significantly positively correlated with J 0 (r=0.31), J 45 (r=0.42), HOA 3 mm (r=0.37), and HOA 6 mm (r=0.48). S-I 4 mm and S-I 8 mm were significantly positively correlated with HOA 3 mm (r=0.30, r=0.40) and HOA 6 mm (r=0.46, r=0.35). The X-axis distance between corneal pupillary center and corneal apex was significantly positively correlated with J 45 (r=0.29)., Conclusions: In patients with advanced keratoconus after FBDALK, the unevenly distributed thickness at corneal pupillary area and the misalignment of corneal apex and pupillary center might cause significant regular and irregular astigmatism, which affected the postoperative visual quality.

Controlling complex networked systems is a real-world puzzle that remains largely unsolved. Despite recent progress in understanding the structural characteristics of network control energy, target state and system dynamics have not been explored. We examine how varying the final state mixture affects the control energy of canonical and conformity-incorporated dynamical systems. We find that the control energy required to drive a network to an identical final state is lower than that required to arrive a non-identical final state. We also demonstrate that it is easier to achieve full control in a conformity-based dynamical network. Finally we determine the optimal control strategy in terms of the network hierarchical structure. Our work offers a realistic understanding of the control energy within the final state mixture and sheds light on controlling complex systems.

By defining a new measure to community structure, exclusive modularity, and based on cavity method of statistical physics, we develop a mathematically principled method to determine the completeness of community structure, which represents whether a partition that is either annotated by experts or given by a community-detection algorithm, carries complete information about community structure in the network. Our results demonstrate that the expert partition is surprisingly incomplete in some networks such as the famous political blogs network, indicating that the relation between meta-data and community structure in real-world networks needs to be re-examined. As a byproduct we find that the exclusive modularity, which introduces a null model based on the degree-corrected stochastic block model, is of independent interest. We discuss its applications as principled ways of detecting hidden structures, finding hierarchical structures without removing edges, and obtaining low-dimensional embedding of networks.

In real networks, the dependency between nodes is ubiquitous; however, the dependency is not always complete and homogeneous. In this paper, we propose a percolation model with weak and heterogeneous dependency; i.e., dependency strengths could be different between different nodes. We find that the heterogeneous dependency strength will make the system more robust, and for various distributions of dependency strengths both continuous and discontinuous percolation transitions can be found. For Erdős-Rényi networks, we prove that the crossing point of the continuous and discontinuous percolation transitions is dependent on the first five moments of the dependency strength distribution. This indicates that the discontinuous percolation transition on networks with dependency is determined not only by the dependency strength but also by its distribution. Furthermore, in the area of the continuous percolation transition, we also find that the critical point depends on the first and second moments of the dependency strength distribution. To validate the theoretical analysis, cases with two different dependency strengths and Gaussian distribution of dependency strengths are presented as examples.

Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two k cliques means that they share at least l1 makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for l=1. More interesting, our analysis shows that at the critical point, the order parameter ϕ(c) for l>1 is neither 0 nor 1, but a constant depending on k and l. All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation.

The bidirectional selection between two classes widely emerges in various social lives, such as commercial trading and mate choosing. Until now, the discussions on bidirectional selection in structured human society are quite limited. We demonstrated theoretically that the rate of successfully matching is affected greatly by individuals' neighborhoods in social networks, regardless of the type of networks. Furthermore, it is found that the high average degree of networks contributes to increasing rates of successful matches. The matching performance in different types of networks has been quantitatively investigated, revealing that the small-world networks reinforces the matching rate more than scale-free networks at given average degree. In addition, our analysis is consistent with the modeling result, which provides the theoretical understanding of underlying mechanisms of matching in complex networks.

Objective: To investigate the characteristics of the size and distribution of primary iris-ciliary body cysts and its associated with the change of anterior chamber angle., Methods: It was a cross sectional study. Patients with shallow anterior chambers found in routine health examinations were evaluated with UBM scan. Any primary iris-ciliary body cysts detected were recorded in the parameters of quantity, size, location, and quadrant. The shape of the angle in the UBM was compared to the surrounding area of angle without the cyst, and also whether the angle was narrowed or closed was recorded. The factors related to the corresponding narrowed or closed angle were analyzed., Results: The 502 cysts were detected in 134 (29.32%) of the 457 patients, which were all primary iris-ciliary body cysts. The cysts were located in the iridociliary sulcus (41.24%) and pars plicata (58.37%) and distributions were 44.22% situated at the inferotemporal quadrant, 26.88% at the inferonasal quadrant, 23.11% at the superotemporal quadrant and 5.38% at the superonasal quadrant. The largest base size of the cysts was 0.6289 +/- 0.2329 mm and most were mid-sized cysts (86.05%). The incidence of the cysts with corresponding chamber angle narrowing or closure in the iridociliary sulcus was 82.13% (170/207), and in the pars plicata was 22.87% (67/293). The difference between them was statistical significant (chi2 = 170.83, P < 0.01). The relationship between the cyst size and the proportion of the cysts which caused corresponding angles narrowing or closure was analyzed by way of rectilinear correlation, and it was found to be a positive correlation (r = 0.9939, P < 0.01)., Conclusions: The incidence of primary iris-ciliary body cysts in the normal population is high and some may cause corresponding angle narrowing or closure; The location and size of the cysts are the factors to induce narrowing or closure of the angle in the corresponding area.

It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature.