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PubMed2006

Graemlin: general and robust alignment of multiple large interaction networks.

The recent proliferation of protein interaction networks has motivated research into network alignment: the cross-species comparison of conserved functional modules. Previous studies have laid the foundations for such comparisons and demonstrated their power on a select set of sparse interaction networks. Recently, however, new computational techniques have produced hundreds of predicted interaction networks with interconnection densities that push existing alignment algorithms to their limits. To find conserved functional modules in these new networks, we have developed Graemlin, the first algorithm capable of scalable multiple network alignment. Graemlin's explicit model of functional evolution allows both the generalization of existing alignment scoring schemes and the location of conserved network topologies other than protein complexes and metabolic pathways. To assess Graemlin's performance, we have developed the first quantitative benchmarks for network alignment, which allow comparisons of algorithms in terms of their ability to recapitulate the KEGG database of conserved functional modules. We find that Graemlin achieves substantial scalability gains over previous methods while improving sensitivity.

Algorithms↗
PubMed2001

Microscopic self-organization in networks.

We report our numerical studies on microscopic self-organization of a reaction system in three types of differently connected networks: a regular network, a small-world network, and a random network. Our simulation results show that the topology of the network has an important effect on the communication among reaction molecules, and plays an important role in microscopic self-organization. The correlation length among reacting molecules in a random or a small-world network is much shorter compared with that in a regular one. As a result, it is much easier to obtain microscopic self-organization in a small-world or a random network. We also observed a phase transition from a stochastic state to a synchronized state when we increased the randomness of a small-world network.

Journal Article↗
PubMed2003

Connectivity strategies to enhance the capacity of weight-bearing networks.

The connectivity properties of a weight-bearing network are exploited to enhance its capacity. We study a 2D network of sites where the weight-bearing capacity of a given site depends on the capacities of the sites connected to it in the layers above. The network consists of clusters, viz., a set of sites connected with each other with the largest such collection of sites being denoted as the maximal cluster. New connections are made between sites in successive layers using two distinct strategies. The key element of our strategies consists of adding as many disjoint clusters as possible to the sites on the trunk T of the maximal cluster. In the first strategy the reconnections start from the last layer upwards and stop when no new sites are added. In the second case, the reconnections start from the top layer and go all the way down to the last layer. The new networks can bear much higher weights than the original networks and have much lower failure rates. The first strategy leads to a greater enhancement of stability, whereas the second leads to a greater enhancement of capacity compared to the original networks. The original network used here is a typical example of the branching hierarchical class. However, the application of strategies similar to ours can yield useful results in other types of networks as well.

Journal Article↗
PubMed2003

Lattice Boltzmann simulation of fluid flow in fracture networks with rough, self-affine surfaces.

Using the lattice Boltzmann method, we study fluid flow in a two-dimensional (2D) model of fracture network of rock. Each fracture in a square network is represented by a 2D channel with rough, self-affine internal surfaces. Various parameters of the model, such as the connectivity and the apertures of the fractures, the roughness profile of their surface, as well as the Reynolds number for flow of the fluid, are systematically varied in order to assess their effect on the effective permeability of the fracture network. The distribution of the fractures' apertures is approximated well by a log-normal distribution, which is consistent with experimental data. Due to the roughness of the fractures' surfaces, and the finite size of the networks that can be used in the simulations, the fracture network is anisotropic. The anisotropy increases as the connectivity of the network decreases and approaches the percolation threshold. The effective permeability K of the network follows the power law K approximately (beta), where is the average aperture of the fractures in the network and the exponent beta may depend on the roughness exponent. A crossover from linear to nonlinear flow regime is obtained at a Reynolds number Re approximately O(1), but the precise numerical value of the crossover Re depends on the roughness of the fractures' surfaces.

Journal Article↗
PubMed2004

L -percolations of complex networks.

Given a complex network, its L-paths correspond to sequences of L+1 distinct nodes connected through L distinct edges. The L-conditional expansion of a complex network can be obtained by connecting all its pairs of nodes which are linked through at least one L-path, and the respective conditional L-expansion of the original network is defined as the intersection between the original network and its L-expansion. Such expansions are verified to act as filters enhancing the network connectivity, consequently contributing to the identification of communities in small-world models. It is shown in this paper for L=2 and 3, in both analytical and experimental fashions, that an evolving complex network with a fixed number of nodes undergoes successive phase transitions--the so-called L-percolations, giving rise to Eulerian giant clusters. It is also shown that the critical values of such percolations are a function of the network size and that the network percolates for L=3 before L=2 .

Journal Article↗
PubMed2004

Finding community structure in very large networks.

The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O (md log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m approximately n and d approximately log n, in which case our algorithm runs in essentially linear time, O (n log(2) n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web site of a large on-line retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 x 10(6) edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.

Journal Article↗
PubMed2005

Graph operations and synchronization of complex networks.

The effects of graph operations on the synchronization of coupled dynamical systems are studied. The operations range from addition or deletion of links to various ways of combining networks and generating larger networks from simpler ones. Methods from graph theory are used to calculate or estimate the eigenvalues of the Laplacian operator, which determine the synchronizability of continuous or discrete time dynamics evolving on the network. Results are applied to explain numerical observations on random, scale-free, and small-world networks. An interesting feature is that, when two networks are combined by adding links between them, the synchronizability of the resulting network may worsen as the synchronizability of the individual networks is improved. Similarly, adding links to a network may worsen its synchronizability, although it decreases the average distance in the graph.

Journal Article↗
PubMed2005

Spectral measures of bipartivity in complex networks.

We introduce a quantitative measure of network bipartivity as a proportion of even to total number of closed walks in the network. Spectral graph theory is used to quantify how close to bipartite a network is and the extent to which individual nodes and edges contribute to the global network bipartivity. It is shown that the bipartivity characterizes the network structure and can be related to the efficiency of semantic or communication networks, trophic interactions in food webs, construction principles in metabolic networks, or communities in social networks.

Journal Article↗
PubMed2005

Diffusion in scale-free networks with annealed disorder.

The scale-free (SF) networks that have been studied so far contained quenched disorder generated by random dilution which does not vary with the time. In practice, if a SF network is to represent, for example, the worldwide web, then the links between its various nodes may temporarily be lost and reestablished again later on. This gives rise to SF networks with annealed disorder. Even if the disorder is quenched, it may be more realistic to generate it by a dynamical process that is happening in the network. In this paper, we study diffusion in SF networks with annealed disorder generated by various scenarios, as well as in SF networks with quenched disorder which, however, is generated by the diffusion process itself. Several quantities of the diffusion process are computed, including the mean number of distinct sites visited, the mean number of returns to the origin, and the mean number of connected nodes that are accessible to the random walkers at any given time. The results, including (1) greatly reduced growth with the time of the mean number of distinct sites visited, (2) blocking of the random walkers, (3) the existence of a phase diagram that separates the region in which diffusion is possible from one in which diffusion is impossible, and (4) a transition in the structure of the networks at which the mean number of distinct sites visited vanishes, indicate completely different behavior for the computed quantities than those in SF networks with quenched disorder generated by simple random dilution.

Journal Article↗
PubMed2006

Statistical self-similar properties of complex networks.

It has been shown that many complex networks shared distinctive features, which differ in many ways from the random and the regular networks. Although these features capture important characteristics of complex networks, their applicability depends on the type of networks. To unravel ubiquitous characteristics that complex networks may have in common, we adopt the clustering coefficient as the probability measure, and present a systematic analysis of various types of complex networks from the perspective of statistical self-similarity. We find that the probability distribution of the clustering coefficient is best characterized by the multifractal; moreover, the support of the measure had a fractal dimension. These two features enable us to describe complex networks in a unified way; at the same time, offer unforeseen possibilities to comprehend complex networks.

Journal Article↗
PubMed2006

Fractal-like tree networks reducing the thermal conductivity.

The effective thermal conductivity of composites with embedded self-similar H-shaped fractal-like tree networks is studied. It is found that the effective thermal conductivity of the composites with these networks is related to the structures of the networks and the ratio of the component thermal conductivities: the longer the branches, the lower the thermal conductivity; the smaller the ratio (beta) of successive branch diameters, the lower the thermal conductivity; the denser the network, the lower the thermal conductivity. It is also found that the thermal conductivity of the H-shaped fractal-like tree networks does not obey Murray's law. The present results show that a network embedded in a composite plays an important role, and the thermal conductivity of the network itself may be less than that of the original material by several orders of magnitude. Fractal-like tree networks can significantly reduce the thermal conductivity compared to an equivalent single cylinder.

Journal Article↗
PubMed2006

Dynamic behaviors in directed networks.

Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the Watts-Strogatz undirected network and then change undirected edges to directed arcs with a given probability, still preserving the connectivity of the network. A generalized clustering coefficient for directed networks is defined and used to investigate the interplay between the synchronization behavior and underlying structural properties of directed networks. We observe that the directedness of complex networks plays an important role in emerging dynamical behaviors, which is also confirmed by a numerical study of the sociological game theoretic voter model on directed networks.

Journal Article↗
PubMed2006

Emergent criticality from coevolution in random Boolean networks.

The coevolution of network topology and dynamics is studied in an evolutionary Boolean network model that is a simple model of a gene regulatory network. We find that a critical state emerges spontaneously resulting from the interplay between topology and dynamics during the evolution. The final evolved state is shown to be independent of initial conditions. The network appears to be driven to a random Boolean network with uniform in-degree of 2 in the large-network limit. However, for biologically realized network sizes, significant finite-size effects are observed including a broad in-degree distribution and an average in-degree connections between 2 and 3. These results may be important for explaining the properties of gene regulatory networks.

Cell Physiological Phenomena↗
PubMed2006

Analysis of an evolving email network.

In this paper we study an evolving email network model first introduced by Wang and De Wilde, to the best of our knowledge. The model is analyzed by formulating the network topology as a random process and studying the dynamics of the process. Our analytical results show a number of steady state properties about the email traffic between different nodes and the aggregate networking behavior (i.e., degree distribution, clustering coefficient, average path length, and phase transition), and also confirm the empirical results obtained by Wang and De Wilde. We also conducted simulations confirming the analytical results. Extensive simulations were run to evaluate email traffic behavior at the link and network levels, phase transition phenomena, and also studying the behavior of email traffic in a hierarchical network. The methods established here are also applicable to many other practical networks including sensor networks and social networks.

Journal Article↗
PubMed2005

Estimating time-dependent gene networks from time series microarray data by dynamic linear models with Markov switching.

In gene network estimation from time series microarray data, dynamic models such as differential equations and dynamic Bayesian networks assume that the network structure is stable through all time points, while the real network might changes its structure depending on time, affection of some shocks and so on. If the true network structure underlying the data changes at certain points, the fitting of the usual dynamic linear models fails to estimate the structure of gene network and we cannot obtain efficient information from data. To solve this problem, we propose a dynamic linear model with Markov switching for estimating time-dependent gene network structure from time series gene expression data. Using our proposed method, the network structure between genes and its change points are automatically estimated. We demonstrate the effectiveness of the proposed method through the analysis of Saccharomyces cerevisiae cell cycle time series data.

Algorithms↗
PubMed2004

Long-term characterization of firing dynamics of spontaneous bursts in cultured neural networks.

Extracellular action potentials were recorded from developing dissociated rat neocortical networks continuously for up to 49 days in vitro using planar multielectrode arrays. Spontaneous neuronal activity emerged toward the end of the first week in vitro and from then on exhibited periods of elevated firing rates, lasting for a few days up to weeks, which were largely uncorrelated among different recording sites. On a time scale of seconds to minutes, network activity typically displayed an ongoing repetition of distinctive firing patterns, including short episodes of synchronous firing at many sites (network bursts). Network bursts were highly variable in their individual spatio-temporal firing patterns but showed a remarkably stable underlying probabilistic structure (obtained by summing consecutive bursts) on a time scale of hours. On still longer time scales, network bursts evolved gradually, with a significant broadening (to about 2 s) in the third week in vitro, followed by a drastic shortening after about one month in vitro. Bursts at this age were characterized by highly synchronized onsets reaching peak firing levels within less than ca. 60 ms. This pattern persisted for the rest of the culture period. Throughout the recording period, active sites showed highly persistent temporal relationships within network bursts. These longitudinal recordings of network firing have, thus, brought to light a reproducible pattern of complex changes in spontaneous firing dynamics of bursts during the development of isolated cortical neurons into synaptically interconnected networks.

Action Potentials↗
PubMed2005

New MPLS network management techniques based on adaptive learning.

The combined use of the differentiated services (DiffServ) and multiprotocol label switching (MPLS) technologies is envisioned to provide guaranteed quality of service (QoS) for multimedia traffic in IP networks, while effectively using network resources. These networks need to be managed adaptively to cope with the changing network conditions and provide satisfactory QoS. An efficient strategy is to map the traffic from different DiffServ classes of service on separate label switched paths (LSPs), which leads to distinct layers of MPLS networks corresponding to each DiffServ class. In this paper, three aspects of the management of such a layered MPLS network are discussed. In particular, an optimal technique for the setup of LSPs, capacity allocation of the LSPs and LSP routing are presented. The presented techniques are based on measurement of the network state to adapt the network configuration to changing traffic conditions.

Algorithms↗
PubMed2004

Tracking a maneuvering target using neural fuzzy network.

A fast target maneuver detecting and highly accurate tracking technique using a neural fuzzy network based on Kalman filter is proposed in this paper. In the automatic target tracking system, there exists an important and difficult problem: how to detect the target maneuvers and fast response to avoid miss-tracking? The traditional maneuver detection algorithms, such as variable dimension filter (VDF) and input estimation (IE) etc., are computation intensive and difficult to implement in real time. To solve this problem, neural network algorithms have been issued recently. However, the normal neural networks such as backpropagation networks usually produce the extra problems of low convergence speed and/or large network size. Furthermore, the way to decide the network structure is heuristic. To overcome these defects and to make use of neural learning ability, a developed standard Kalman filter with a self-constructing neural fuzzy inference network (KF-SONFIN) algorithm for target tracking is presented in this paper. By generating possible target trajectories including maneuver information to train the SONFIN, the trained SONFIN can detect when the maneuver occurred, the magnitude of maneuver values and when the maneuver disappeared. Without having to change the structure of Kalman filter nor modeling the maneuvering target, this new algorithm, SONFIN, can always find itself an economic network size with a fast learning process. Simulation results show that the KF-SONFIN is superior to the traditional IE and VDF methods in estimation accuracy.

Journal Article↗