Behavioral fractality in marine copepods: Endogenous rhythms versus exogenous stressors

The presence of endogenous rhythms in the swimming behavior of five common species of copepods (i.e. minute marine crustaceans) was investigated through comparisons of the scaling properties of their three-dimensional trajectories and cumulative probability distribution functions of move lengths recorded during the day and at night. Beside clear inter-specific differences in their behavioral scaling properties, the five species exhibited an increase in path tortuosity at night, consistent with an increase in food foraging activity. Given the absence of food under all experimental conditions, this suggests the presence of an endogenous swimming rhythm consistent with the widely reported pattern of ascent at dusk resulting in copepods entering the food-rich surface layer at night. The impact of the stress exerted on swimming behavior by changes in the light regime (i.e. light and dark conditions respectively experienced at night and during the day) and the related copepod behavioral adaptivity was also investigated. The low and high fractal dimensions respectively observed during daytime in the dark and during night-time under conditions of simulated daytime indicate that these organisms have the ability to adjust the complexity of their swimming path depending on exogenous factors, independent of their actual endogenous rhythms. The scaling exponents of the cumulative probability distribution function of move lengths exhibit a significant decrease during daylight hours under simulated night-time conditions and during the night under simulated daytime conditions, suggesting an increase in the stress levels experienced by the five species considered. It is finally shown that the stress exerted on endogenous behavioral diel variability by exogenous cues has a species-specific effect on copepods.     

Multiple scale analysis of complex networks using the empirical mode decomposition method

Empirical mode decomposition (EMD) method can decompose any complicated data into finite ‘intrinsic mode functions’ (IMFs). In this paper, we use EMD method to analyze and discuss the structural properties of complex networks. A random-walk method is used to collect the data series of network systems. Utilizing the EMD method, we decompose the obtained data into finite IMFs under different spatial scales. The analysis results show that EMD method is an effective tool for capturing the topological properties of network systems under different spatial scales, such as the modular structures of network systems and their energy densities.     

The exponential degree distribution in complex networks: Non-equilibrium network theory, numerical simulation and empirical data

The exponential degree distribution has been found in many real world complex networks, based on which, the random growing process has been introduced to analyze the formation principle of such kinds of networks. Inspired from the non-equilibrium network theory, we construct the network according to two mechanisms: growing and adjacent random attachment. By using the Kolmogorov-Smirnov Test (KST), for the same number of nodes and edges, we find the simulation results are remarkably consistent with the predictions of the non-equilibrium network theory, and also surprisingly match the empirical databases, such as the Worldwide Marine Transportation Network (WMTN), the Email Network of University at Rovira i Virgili (ENURV) in Spain and the North American Power Grid Network (NAPGN). Our work may shed light on interpreting the exponential degree distribution and the evolution mechanism of the complex networks.     

On the distributions of Laplacian eigenvalues versus node degrees in complex networks

In this paper, the important issue of Laplacian eigenvalue distributions is investigated through theory-guided extensive numerical simulations, for four typical complex network models, namely, the ER random-graph networks, WS and NW small-world networks, and BA scale-free networks. It is found that these four types of complex networks share some common features, particularly similarities between the Laplacian eigenvalue distributions and the node degree distributions.     

Finding community structures in complex networks using mixed integer optimisation

The detection of community structure has been used to reveal the relationships between individual objects and their groupings in networks. This paper presents a mathematical programming approach to identify the optimal community structures in complex networks based on the maximisation of a network modularity metric for partitioning a network into modules. The overall problem is formulated as a mixed integer quadratic programming (MIQP) model, which can then be solved to global optimality using standard optimisation software. The solution procedure is further enhanced by developing special symmetry-breaking constraints to eliminate equivalent solutions. It is shown that additional features such as minimum/maximum module size and balancing among modules can easily be incorporated in the model. The applicability of the proposed optimisation-based approach is demonstrated by four examples. Comparative results with other approaches from the literature show that the proposed methodology has superior performance while global optimum is guaranteed.     

Link prediction in complex networks: A survey

Link prediction in complex networks has attracted increasing attention from both physical and computer science communities. The algorithms can be used to extract missing information, identify spurious interactions, evaluate network evolving mechanisms, and so on. This article summaries recent progress about link prediction algorithms, emphasizing on the contributions from physical perspectives and approaches, such as the random-walk-based methods and the maximum likelihood methods. We also introduce three typical applications: reconstruction of networks, evaluation of network evolving mechanism and classification of partially labeled networks. Finally, we introduce some applications and outline future challenges of link prediction algorithms.     

复杂网络中带有应急恢复机理的级联动力学分析

提出带有应急恢复机理的网络级联故障模型,研究模型在最近邻耦合网络,Erdos-Renyi随机网络,Watts-Strogatz小世界网络和Barabasi-Albert无标度网络四种网络拓扑下的网络级联动力学行为.给出了应急恢复机理和网络效率的定义,并研究了模型中各参数对网络效率和网络节点故障率在级联故障过程中变化情况的影响.结果表明,模型中应急恢复概率的增大减缓了网络效率的降低速度和节点故障率的增长速度,并且提高了网络的恢复能力.而且网络中节点负载容量越大,网络效率降低速度和节点故障率的增长速度越慢.同时,随着节点过载故障概率的减小,网络效率的降低速度和节点故障率的增长速度也逐渐减缓.此外,对不同网络拓扑中网络效率和网络节点故障率在级联故障过程中的变化情况进行分析,结果发现网络拓扑节点度分布的异质化程度的增大,提高了级联故障所导致的网络效率的降低速度和网络节点故障率的增长速度.以上结果分析了复杂网络中带有应急恢复机理的网络级联动力学行为,为实际网络中级联故障现象的控制和防范提供了参考.     

Link prediction in complex networks: a clustering perspective

Link prediction is an open problem in the complex network, which attracts much research interest currently. However, little attention has been paid to the relation between network structure and the performance of prediction methods. In order to fill this vital gap, we try to understand how the network structure affects the performance of link prediction methods in the view of clustering. Our experiments on both synthetic and real-world networks show that as the clustering grows, the accuracy of these methods could be improved remarkably, while for the sparse and weakly clustered network, they perform poorly. We explain this through the distinguishment caused by increased clustering between the score distribution of positive and negative instances. Our finding also sheds light on the problem of how to select appropriate approaches for different networks with various densities and clusterings.     

EAMCD: an efficient algorithm based on minimum coupling distance for community identification in complex networks

Community structure is an important feature in many real-world networks, which can help us understand structure and function in complex networks better. In recent years, there have been many algorithms proposed to detect community structure in complex networks. In this paper, we try to detect potential community beams whose link strengths are greater than surrounding links and propose the minimum coupling distance (MCD) between community beams. Based on MCD, we put forward an optimization heuristic algorithm (EAMCD) for modularity density function to welded these community beams into community frames which are seen as a core part of community. Using the principle of random walk, we regard the remaining nodes into the community frame to form a community. At last, we merge several small community frame fragments using local greedy strategy for the modularity density general function. Real-world and synthetic networks are used to demonstrate the effectiveness of our algorithm in detecting communities in complex networks.     

Synchronization in weighted complex networks: Heterogeneity and synchronizability

Synchronization in different types of weighted networks based on a scale-free weighted network model is investigated. It has been argued that heterogeneity suppresses synchronization in unweighted networks [T. Nishikawa, A.E. Motter, Y.C. Lai, F.C. Hoppensteadt, Phys. Rev. Lett. 91 (2003) 014101]. However, it is shown in this work that as the network becomes more heterogeneous, the synchronizability of Type I symmetrically weighted networks, and Type I and Type II asymmetrically weighted networks is enhanced, while the synchronizability of Type II symmetrically weighted networks is weakened.     

Advances in dynamic temporal networks: Understanding the temporal dynamics of complex adaptive networks

Complex networks have been extensively studied in the past 15 years and with increasing details. However, research on the temporal dynamics of complex networks is largely a new territory yet to map out. The present volume presents a collection of papers dealing with various aspects of the problem and this editorial introduces the field as well as the papers.     

Consistent empirical physical formula construction for recoil energy distribution in HPGe detectors by using artificial neural networks

The gamma-ray tracking technique is a highly efficient detection method in experimental nuclear structure physics. On the basis of this method, two gamma-ray tracking arrays, AGATA in Europe and GRETA in the USA, are currently being tested. The interactions of neutrons in these detectors lead to an unwanted background in the gamma-ray spectra. Thus, the interaction points of neutrons in these detectors have to be determined in the gamma-ray tracking process in order to improve photo-peak efficiencies and peak-to-total ratios of the gamma-ray peaks. In this paper, the recoil energy distributions of germanium nuclei due to inelastic scatterings of 1–5 MeV neutrons were first obtained by simulation experiments. Secondly, as a novel approach, for these highly nonlinear detector responses of recoiling germanium nuclei, consistent empirical physical formulas (EPFs) were constructed by appropriate feedforward neural networks (LFNNs). The LFNN-EPFs are of explicit mathematical functional form. Therefore, the LFNN-EPFs can be used to derive further physical functions which could be potentially relevant for the determination of neutron interactions in gamma-ray tracking process.     

Computing communities in complex networks using the Dirichlet processing Gaussian mixture model with spectral clustering

Community detection becomes a significant tool for the complex network analysis. The study of the community detection algorithms has received an enormous amount of attention. It is still an open question whether a highly accurate and efficient algorithm is found in most data sets. We propose the Dirichlet Processing Gaussian Mixture Model with Spectral Clustering algorithm for detecting the community structures. The combination of traditional spectral algorithm and new non-parametric Bayesian model provides high accuracy and quality. We compare the proposed algorithm with other existing community detecting algorithms using different real-world data sets and computer-generated synthetic data sets. We show that the proposed algorithm results in high modularity, and better accuracy in a wide range of networks. We find that the proposed algorithm works best for the large size of the data sets.     

Identifying an influential spreader from a single seed in complex networks via a message-passing approach

Identifying the most influential spreaders is one of outstanding problems in physics of complex systems. So far, many approaches have attempted to rank the influence of nodes but there is still the lack of accuracy to single out influential spreaders. Here, we directly tackle the problem of finding important spreaders by solving analytically the expected size of epidemic outbreaks when spreading originates from a single seed. We derive and validate a theory for calculating the size of epidemic outbreaks with a single seed using a message-passing approach. In addition, we find that the probability to occur epidemic outbreaks is highly dependent on the location of the seed but the size of epidemic outbreaks once it occurs is insensitive to the seed. We also show that our approach can be successfully adapted into weighted networks.     

Introduction to Focus Issue: synchronization and cascading processes in complex networks

The study of collective dynamics in complex networks has emerged as a next frontier in the science of networks. This Focus Issue presents the latest developments on this exciting front, focusing in particular on synchronous and cascading dynamics, which are ubiquitous forms of network dynamics found in a wide range of physical, biological, social, and technological systems.     

Predicting criticality and dynamic range in complex networks: effects of topology

The collective dynamics of a network of coupled excitable systems in response to an external stimulus depends on the topology of the connections in the network. Here we develop a general theoretical approach to study the effects of network topology on dynamic range, which quantifies the range of stimulus intensities resulting in distinguishable network responses. We find that the largest eigenvalue of the weighted network adjacency matrix governs the network dynamic range. When the largest eigenvalue is exactly one, the system is in a critical state and its dynamic range is maximized. Further, we examine higher order behavior of the steady state system, which predicts that networks with more homogeneous degree distributions should have higher dynamic range. Our analysis, confirmed by numerical simulations, generalizes previous studies in terms of the largest eigenvalue of the adjacency matrix.     

Dynamical motifs: building blocks of complex dynamics in sparsely connected random networks

Spatiotemporal network dynamics is an emergent property of many complex systems that remains poorly understood. We suggest a new approach to its study based on the analysis of dynamical motifs-small subnetworks with periodic and chaotic dynamics. We simulate randomly connected neural networks and, with increasing density of connections, observe the transition from quiescence to periodic and chaotic dynamics. This transition is explained by the appearance of dynamical motifs in the structure of these networks. We also observe domination of periodic dynamics in simulations of spatially distributed networks with local connectivity and explain it by the absence of chaotic and the presence of periodic motifs in their structure.     

Onset of synchronization in weighted complex networks: the effect of weight-degree correlation

By numerical simulations, we investigate the onset of synchronization of networked phase oscillators under two different weighting schemes. In scheme-I, the link weights are correlated to the product of the degrees of the connected nodes, so this kind of networks is named as the weight-degree correlated (WDC) network. In scheme-II, the link weights are randomly assigned to each link regardless of the node degrees, so this kind of networks is named as the weight-degree uncorrelated (WDU) network. Interestingly, it is found that by increasing a parameter that governs the weight distribution, the onset of synchronization in WDC network is monotonically enhanced, while in WDU network there is a reverse in the synchronization performance. We investigate this phenomenon from the viewpoint of gradient network, and explain the contrary roles of coupling gradient on network synchronization: gradient promotes synchronization in WDC network, while deteriorates synchronization in WDU network. The findings highlight the fact that, besides the link weight, the correlation between the weight and the node degree is also important to the network dynamics.     

Optimal communication schemes in a complex network: From trees to bottleneck networks

The robustness of a communication scheme in a complex network may depend on the location of distinguished nodes. We collect different approaches to the idea of vulnerability and we give methods that help us to decide the good spots for the leader nodes. More specifically, we present a constructive method that yields the best location in a communication scheme for a leader node in the case that the underlying network is tree-shaped and show how it can be used for more general networks. In order to do that we consider a local approach via the bottleneck tree associated to a given node, as well as a uniform a approach by means of the so-called bottleneck network for several communication topologies.