Accelerating networks: Effects of preferential connections

Networks are commonly observed structures in complex systems with interacting and interdependent parts that self-organize. For nonlinearly growing networks, when the total number of connections increases faster than the total number of nodes, the network is said to accelerate. We propose a systematic model for the dynamics of growing networks represented by distribution kinetics equations. We define the nodal-linkage distribution, construct a population dynamics equation based on the association-dissociation process, and perform the moment calculations to describe the dynamics of such networks. For nondirectional networks with finite numbers of nodes and connections, the moments are the total number of nodes, the total number of connections, and the degree (the average number of connections per node), represented by the average moment. Size independent rate coefficients yield an exponential network describing the network without preferential attachment, and size dependent rate coefficients produce a power law network with preferential attachment. The model quantitatively describes accelerating network growth data for a supercomputer (Earth Simulator), for regulatory gene networks, and for the Internet.     

Public transport networks: empirical analysis and modeling

Public transport networks of fourteen cities of so far unexplored network size are analyzed in standardized graph representations: the simple graph of the network map, the bipartite graph of routes and stations, and both one mode projections of the latter. Special attention is paid to the inter-relations and spatial embedding of transport routes. This systematic approach reveals rich behavior beyond that of the ubiquitous scale-free complex network. We find strong evidence for structures in PTNs that are counter-intuitive and need to be explained, among these a pronounced diversity in the expression of typical network characteristics within the present sample of cities, a surprising geometrical behavior with respect to the two-dimensional geographical embedding and an unexpected attraction between transport routes. A simple model based on these observations reproduces many of the identified PTN properties by growing networks of attractive self-avoiding walks.     

Stability and dynamical properties of material flow systems on random networks

The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are characteristic of flow networks in economic, ecological and biological systems. Based on results from random matrix theory, we work out the phase diagram of such systems defined on extensively connected random graphs, and study in detail how the choice of control policies and the network structure affects stability. We also present results for more complex topologies of the underlying graph, focussing on finitely connected Erdös-Réyni graphs, Small-World Networks and Barabási-Albert scale-free networks. Results indicate that variability of input-output matrix elements, and random structures of the underlying graph tend to make the system less stable, while fast price dynamics or strong responsiveness to stock accumulation promote stability.     

Local Minority Game with Evolutionary Strategies

We study a model of local minority game in the random Kauffman network with evolutionary strategies and propose three methods to update the strategy of poor agents, with lower points in a given generation： namely to update either the Boolean function of their strategies randomly, or their local information of randomly adjacent m agents, or the number m of randomly chosen adjacent agents. The results of extended numerical simulations show that the behaviour of strategies in the three methods may enhance significantly the entire coordination of agents in the system. It is also found that a poor agent tends to use both small m strategies and correlated strategies, and the strategies of agents will finally self-organize into a steady-state distribution for a long time playing of the game.     

Graph kernels,hierarchical clustering,and network community structure: experiments and comparative analysis

There has been a quickly growing interest in properties of complex networks, such as the small world property, power-law degree distribution, network transitivity, and community structure, which seem to be common to many real world networks. In this study, we consider the community property which is also found in many real networks. Based on the diffusion kernels of networks, a hierarchical clustering approach is proposed to uncover the community structure of different extent of complex networks. We test the method on some networks with known community structures and find that it can detect significant community structure in these networks. Comparison with related methods shows the effectiveness of the method.     

Kinetic models for wealth exchange on directed networks

We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models. The nature of asset distribution in such directed networks show varied results, the degree of asset inequality increased with the degree of disorder in the graphs.     

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.     

Formation of electrically active clusterized neural networks

Ordinarily, in vitro neurons self-organize into homogeneous networks of single neurons linked by dendrites and axons. We show that under special conditions they can also self-organize into neuronal clusters, which are linked by bundles of axons. Multielectrode array measurement reveals that the clusterized networks are also electrically active and exhibit synchronized bursting events similar to those observed in the homogeneous networks. From time-lapse recording, we deduced the features required for the neuronal clusterized versus homogeneous self-organization and developed a simple model for testing their validity.     

Spatio-temporal dynamics,patterns formation and turbulence in complex fluids due to electrohydrodynamics instabilities

The complex spatio-temporal dynamics generated by electrohydrodynamics instabilities in a nematic liquid crystal under the action of a driving oscillating electric field is investigated. Quasi-stationary convective structures which are visible at large scales are broken into chaotic patterns at higher driving voltages, thus generating small-scale structures. Scaling analysis reveals that these small-scale structures self-organize in a network of subleading structures which are reminescent of convective rolls. This network persists well inside the chaotic regimes, disappearing only at very high voltages, where stochastic dynamical scattering mode takes place.     

Self-organization of treadmilling filaments

The cytoskeleton is an active network of polar filaments. The activity can lead to the polymerization of filaments at one end and depolymerization at the other. This phenomenon is called treadmilling and is essential for many cellular processes, in particular, the crawling of cells on a substrate. We develop a microscopic theoretical framework for describing systems of treadmilling filaments. We show that such systems can self-organize into structures observed in cell fragments, in particular, asters and moving spots.     

Can a few fanatics influence the opinion of a large segment of a society?

Models that provide insight into how extreme positions regarding any social phenomenon may spread in a society or at the global scale are of great current interest. A realistic model must account for the fact that globalization, internet, and other means of mass communications have given rise to scale-free networks of interactions between people. We propose a novel model which takes into account the nature of the interactions network, and provides some key insights into this phenomenon. These include, (1) the existence of a fundamental difference between a hierarchical network whereby people are influenced by those that are higher in the hierarchy but not by those below them, and a symmetrical network where person-on-person influence works mutually, and (2) that a few “fanatics” can influence a large fraction of the population either temporarily (in the hierarchical networks) or permanently (in symmetrical networks). Even if the “fanatics” disappear, the population may still remain susceptible to the positions originally advocated by them. The model is, however, general and applicable to any phenomenon for which there is a degree of enthusiasm or susceptibility to in the population.     

One-dimensional optical reflectors based on self-organization of polymeric comb-shaped supramolecules

We demonstrate that complexation of dodecylbenzenesulphonic acid, DBSA, to a diblock copolymer of polystyrene- block-poly(4-vinylpyridine), PS- block-P4VP, leads to polymeric supramolecules PS- block-P4VP(DBSA)y (y = 1.0, 1.5, and 2.0), which self-organize with a particularly large lamellar periodicity in excess of 1000 A. The structures consist of alternating PS and P4VP(DBSA)y layers, where the latter contains smaller internal structure, probably lamellar. The DBSA side chains are bonded to the pyridines by protonation and hydrogen bonding and they effectively plasticize the material. In this way relatively well-developed structures are obtained even without annealing or macroscopic alignment. Transmission and reflectance measurements show that a relatively narrow and incomplete bandgap exists for supramolecules of high molecular weight block copolymer at ca. 460 nm.     

Cooperation and community structure in social networks

Situations of conflict giving rise to social dilemmas are widespread in society. One way of studying these important phenomena is by using simplified models of individual behavior under conflicting situations such as evolutionary game theory. Starting from the observation that individuals interact through networks of acquaintances, we study the evolution of cooperation on model and real social networks through well known paradigmatic games. Using a new payoff scheme which leaves replicator dynamics invariant, we find that cooperation is sustainable in such networks, even in the difficult case of the prisoner’s dilemma. The evolution and stability of cooperation implies the condensation of game strategies into the existing community structures of the social network in which clusters of cooperators survive thanks to their higher connectivity towards other fellow cooperators.     

Silicon-riched-oxide cluster assembled nanostructures formed by low energy cluster beam deposition

Free beam of silicon oxide nanoclusters is produced by a gas aggregation source from SiO precursor. Due to the disproportionation reaction during the condensation of SiO vapor the generated clusters are Si-riched. The clusters are collimated to be a fine beam and deposited on the substrate at room temperature. The microstructures of the cluster-based nanofilm are characterized by TEM. It is shown that with appropriate impacting parameters, Si-riched oxide nanofilms assembled from uniformly distributed isolated clusters can be obtained. And the clusters can self-organize into partially densely ordered packing within local domains. XPS spectra are taken to analyze the chemical components of the nanofilms. Photoluminescence from the Si-riched oxide nanofilms has also been observed.     

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.     

Networks of interactions in the secondary and tertiary structure of ribosomal RNA

We construct four different structural networks for both the secondary and tertiary structures of the 16S and 23S ribosomal RNAs (rRNAs) in the high-resolution crystal structures of the Thermus thermophilus 30S and Haloarcula marismortui 50S ribosomal subunits, and investigate topological characteristics of the rRNA structures by determining relevant measures, such as the characteristic path length, the clustering coefficient, and the helix betweenness. This study reveals that the 23S rRNA network is more compact than the 16S rRNA networks, reflecting the more globular overall structure of the 23S rRNA relative to the 16S rRNA. In particular, the large number of tertiary interactions in the 23S rRNA tends to cluster, accounting for its small-world network properties. In addition, although the rRNA networks are not the scale-free network, their helix betweenness has a power-law distribution and is correlated with the phylogenetic conservation of helices. The higher the helix betweenness, the more conserved the helix. These results suggest a potential role of the rRNA network as a new quantitative approach in rRNA research.     

Evolution of networks

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, and so on.     

Modeling the Internet

We model the Internet as a network of interconnected Autonomous Systems which self-organize under an absolute lack of centralized control. Our aim is to capture how the Internet evolves by reproducing the assembly that has led to its actual structure and, to this end, we propose a growing weighted network model driven by competition for resources and adaptation to maintain functionality in a demand and supply balance. On the demand side, we consider the environment, a pool of users which need to transfer information and ask for service. On the supply side, ASs compete to gain users, but to be able to provide service efficiently, they must adapt their bandwidth as a function of their size. Hence, the Internet is not modeled as an isolated system but the environment, in the form of a pool of users, is also a fundamental part which must be taken into account. ASs compete for users and big and small come up, so that not all ASs are identical. New connections between ASs are made or old ones are reinforced according to the adaptation needs. Thus, the evolution of the Internet can not be fully understood if just described as a technological isolated system. A socio-economic perspective must also be considered.     

Long term behavior of lithographically prepared in vitro neuronal networks

We measured the long term spontaneous electrical activity of neuronal networks with different sizes, grown on lithographically prepared substrates and recorded with multi-electrode-array technology. The time sequences of synchronized bursting events were used to characterize network dynamics. All networks exhibit scale-invariant Lévy distributions and long-range correlations. These observations suggest that different-size networks self-organize to adjust their activities over many time scales. As predictions of current models differ from our observations, this calls for revised models.