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PubMed2001

Scaling properties of scale-free evolving networks: continuous approach.

The scaling behavior of scale-free evolving networks, arising in areas such as communications, scientific citations, collaborations, etc., is studied. We derive universal scaling relations describing properties of such networks, and indicate the limits of their validity. We show that the main properties of scale-free evolving networks may be described in the framework of a simple continuous approach. The simplest models of networks, growing according to a mechanism of preferential attachment of links to nodes, are used. We consider different forms of this preference, and demonstrate that the range of preferential attachments producing scale-free networks is wide. We also obtain scaling relations for networks with nonlinear, accelerating growth, and describe the temporal evolution of the arising distributions. Size effects-the cutoffs of these distributions-introduce restrictions for the observation of power-law dependences. Mainly we discuss the so-called degree distribution, i.e., the distribution of the number of connections of nodes. A scaling form of the distribution of links between pairs of individual nodes for a growing network of citations is also studied. We describe the effects of differences between nodes. The "aging" of nodes changes the exponents of the distributions. The appearance of a single node with high fitness changes the degree distribution of a network dramatically. If its fitness exceeds some threshold value, this node captures a finite part of all links of the network. We show that permanent random damage to a growing scale-free network-a permanent deletion of some links-radically changes the values of the scaling exponents. Results of other kinds of permanent damage are described.

Journal Article↗
PubMed2002

Dynamic stability conditions for Lotka-Volterra recurrent neural networks with delays.

The Lotka-Volterra model of neural networks, derived from the membrane dynamics of competing neurons, have found successful applications in many "winner-take-all" types of problems. This paper studies the dynamic stability properties of general Lotka-Volterra recurrent neural networks with delays. Conditions for nondivergence of the neural networks are derived. These conditions are based on local inhibition of networks, thereby allowing these networks to possess a multistability property. Multistability is a necessary property of a network that will enable important neural computations such as those governing the decision making process. Under these nondivergence conditions, a compact set that globally attracts all the trajectories of a network can be computed explicitly. If the connection weight matrix of a network is symmetric in some sense, and the delays of the network are in L2 space, we can prove that the network will have the property of complete stability.

Journal Article↗
PubMed2003

Subgraphs in random networks.

Understanding the subgraph distribution in random networks is important for modeling complex systems. In classic Erdos networks, which exhibit a Poissonian degree distribution, the number of appearances of a subgraph G with n nodes and g edges scales with network size as approximately N(n-g). However, many natural networks have a non-Poissonian degree distribution. Here we present approximate equations for the average number of subgraphs in an ensemble of random sparse directed networks, characterized by an arbitrary degree sequence. We find scaling rules for the commonly occurring case of directed scale-free networks, in which the outgoing degree distribution scales as P(k) approximately k(-gamma). Considering the power exponent of the degree distribution, gamma, as a control parameter, we show that random networks exhibit transitions between three regimes. In each regime, the subgraph number of appearances follows a different scaling law, approximately Nalpha, where alpha=n-g+s-1 for gamma<2, alpha=n-g+s+1-gamma for 2 gamma(c), where s is the maximal outdegree in the subgraph, and gamma(c)=s+1. We find that certain subgraphs appear much more frequently than in Erdos networks. These results are in very good agreement with numerical simulations. This has implications for detecting network motifs, subgraphs that occur in natural networks significantly more than in their randomized counterparts.

Journal Article↗
PubMed2004

Aggregation process on complex networks.

We study the dynamics of the aggregation of particles and the evolution of the mass distribution, on a complex network which is built following the Watts-Strogatz model. The particles perform random walks following the links on the network, and aggregate when they meet other particles. On disordered networks the density of particles decays as t(-1), while on regular networks it decays as t(-1/2). For intermediate levels of network disorder the dynamics follows that of regular networks at intermediate density, and for low density the disorder of the network becomes relevant and the density decays as t(-1). The crossover time between these two regimes scales with network disorder as t approximately p(-2). We study also an annealed model for the aggregation process, in which the quenched disorder of the network is replaced by stochastic long range jumps in the particle dynamics. The annealed model is found to obey a different scaling with network disorder, with a crossover time t approximately p(-1).

Biophysics↗
PubMed2004

Effect of disorder strength on optimal paths in complex networks.

We study the transition between the strong and weak disorder regimes in the scaling properties of the average optimal path l(opt) in a disordered Erdos-Rényi (ER) random network and scale-free (SF) network. Each link i is associated with a weight tau(i) identical withexp (a r(i) ) , where r(i) is a random number taken from a uniform distribution between 0 and 1 and the parameter a controls the strength of the disorder. We find that for any finite a , there is a crossover network size N* (a) at which the transition occurs. For N< /=4 , and l(opt) approximately N (lambda-3) (/ (lambda-1) ) for SF networks with 3 >N* (a) the scaling behavior is in the weak disorder regime, with l(opt) approximately ln N for ER networks and SF networks with lambda>3 . In order to study the transition we propose a measure which indicates how close or far the disordered network is from the limit of strong disorder. We propose a scaling ansatz for this measure and demonstrate its validity. We proceed to derive the scaling relation between N* (a) and a . We find that N* (a) approximately a(3) for ER networks and for SF networks with lambda>/=4 , and N* (a) approximately a (lambda-1) (/ (lambda-3) ) for SF networks with 3<lambda<4 .

Journal Article↗
PubMed2005

Spectral analysis and the dynamic response of complex networks.

The eigenvalues and eigenvectors of the connectivity matrix of complex networks contain information about its topology and its collective behavior. In particular, the spectral density rho(lambda) of this matrix reveals important network characteristics: random networks follow Wigner's semicircular law whereas scale-free networks exhibit a triangular distribution. In this paper we show that the spectral density of hierarchical networks follows a very different pattern, which can be used as a fingerprint of modularity. Of particular importance is the value rho(0), related to the homeostatic response of the network: it is maximum for random and scale-free networks but very small for hierarchical modular networks. It is also large for an actual biological protein-protein interaction network, demonstrating that the current leading model for such networks is not adequate.

Journal Article↗
PubMed2005

Onset of traffic congestion in complex networks.

Free traffic flow on a complex network is key to its normal and efficient functioning. Recent works indicate that many realistic networks possess connecting topologies with a scale-free feature: the probability distribution of the number of links at nodes, or the degree distribution, contains a power-law component. A natural question is then how the topology influences the dynamics of traffic flow on a complex network. Here we present two models to address this question, taking into account the network topology, the information-generating rate, and the information-processing capacity of individual nodes. For each model, we study four kinds of networks: scale-free, random, and regular networks and Cayley trees. In the first model, the capacity of packet delivery of each node is proportional to its number of links, while in the second model, it is proportional to the number of shortest paths passing through the node. We find, in both models, that there is a critical rate of information generation, below which the network traffic is free but above which traffic congestion occurs. Theoretical estimates are given for the critical point. For the first model, scale-free networks and random networks are found to be more tolerant to congestion. For the second model, the congestion condition is independent of network size and topology, suggesting that this model may be practically useful for designing communication protocols.

Journal Article↗
PubMed2005

Synchronized clusters in coupled map networks. I. Numerical studies.

We study the synchronization of coupled maps on a variety of networks including regular one- and two-dimensional networks, scale-free networks, small world networks, tree networks, and random networks. For small coupling strengths nodes show turbulent behavior but form phase synchronized clusters as coupling increases. When nodes show synchronized behavior, we observe two interesting phenomena. First, there are some nodes of the floating type that show intermittent behavior between getting attached to some clusters and evolving independently. Second, we identify two different ways of cluster formation, namely self-organized clusters which have mostly intracluster couplings and driven clusters which have mostly intercluster couplings. The synchronized clusters may be of dominant self-organized type, dominant driven type, or mixed type depending on the type of network and the parameters of the dynamics. We define different states of the coupled dynamics by considering the number and type of synchronized clusters. For the local dynamics governed by the logistic map we study the phase diagram in the plane of the coupling constant (epsilon) and the logistic map parameter (mu). For large coupling strengths and nonlinear coupling we find that the scale-free networks and the Caley tree networks lead to better cluster formation than the other types of networks with the same average connectivity. For most of our study we use the number of connections of the order of the number of nodes. As the number of connections increases the number of nodes forming clusters and the size of the clusters in general increase.

Journal Article↗
PubMedDate not supplied

Phylogenetic networks: modeling, reconstructibility, and accuracy.

Phylogenetic networks model the evolutionary history of sets of organisms when events such as hybrid speciation and horizontal gene transfer occur. In spite of their widely acknowledged importance in evolutionary biology, phylogenetic networks have so far been studied mostly for specific data sets. We present a general definition of phylogenetic networks in terms of directed acyclic graphs (DAGs) and a set of conditions. Further, we distinguish between model networks and reconstructible ones and characterize the effect of extinction and taxon sampling on the reconstructibility of the network. Simulation studies are a standard technique for assessing the performance of phylogenetic methods. A main step in such studies entails quantifying the topological error between the model and inferred phylogenies. While many measures of tree topological accuracy have been proposed, none exist for phylogenetic networks. Previously, we proposed the first such measure, which applied only to a restricted class of networks. In this paper, we extend that measure to apply to all networks, and prove that it is a metric on the space of phylogenetic networks. Our results allow for the systematic study of existing network methods, and for the design of new accurate ones.

Algorithms↗
PubMed2006

The impact of a social network intervention on retention in Belgian therapeutic communities: a quasi-experimental study.

BACKGROUND: Although numerous studies recognize the importance of social network support in engaging substance abusers into treatment, there is only limited knowledge of the impact of network involvement and support during treatment. The primary objective of this research was to enhance retention in Therapeutic Community treatment utilizing a social network intervention. AIMS: The specific goals of this study were (1) to determine whether different pre-treatment factors predicted treatment retention in a Therapeutic Community; and (2) to determine whether participation of significant others in a social network intervention predicted treatment retention. DESIGN, SETTING AND PARTICIPANTS: Consecutive admissions to four long-term residential Therapeutic Communities were assessed at intake (n = 207); the study comprised a mainly male (84.9%) sample of polydrug (41.1%) and opiate (20.8%) abusers, of whom 64.4% had ever injected drugs. Assessment involved the European version of the Addiction Severity Index (EuropASI), the Circumstances, Motivation, Readiness scales (CMR), the Dutch version of the family environment scale (GKS/FES) and an in-depth interview on social network structure and perceived social support. Network members of different cohorts were assigned to a social network intervention, which consisted of three elements (a video, participation at an induction day and participation in a discussion session). FINDINGS: Hierarchical regression analyses showed that client-perceived social support (F1,198 = 10.9, P = 0.001) and treatment motivation and readiness (F1,198 = 8.8; P = 0.003) explained a significant proportion of the variance in treatment retention (model fit: F7,197 = 4.4; P = 0.000). By including the variable 'significant others' participation in network intervention' (network involvement) in the model, the fit clearly improved (F1,197 = 6.2; P = 0.013). At the same time, the impact of perceived social support decreased (F1,197 = 2.9; P = 0.091). CONCLUSIONS: Participation in the social network intervention was associated with improved treatment retention controlling for other client characteristics. This suggests that the intervention may be of benefit in the treatment of addicted individuals.

Adult↗
PubMed1991

The servant idiotype network.

Network Antigens are idiotopic markers which are expressed on antibodies of a given specificity. These Network Antigen Idiotopes are part of specific immune responses and are selected through the process of antigen-driven maturation. Their natural role in immunity is the regulation of the response via idiotypic network interaction. The biological power of Network Antigens can be harnessed by generating monoclonal Ab2s against polyclonal disease-derived and specific Ab1. Because network antigens play an important biological role in immunity, it becomes difficult to call the Idiotype Network selfish. We believe that the organization and selection of a small antibody repertoire, which is needed to maintain a disease free existence, is accomplished by the idiotypic network. Furthermore, if we better understand the blueprint of this network we can begin to take advantage of the primed state of clones in the network to intervene, either to stimulate beneficial responses, or to suppress harmful immunities using antibodies which recognize the key organizer and controllers in the network.

Animals↗
PubMed2006

Mapping the environmental coverage of the INDEPTH demographic surveillance system network in rural Africa.

OBJECTIVES: The INDEPTH DSS network was founded in 1998 to provide an international network of field sites for continuous demographic evaluation of populations and their health. Results from the network have been used to derive estimates of mortality, morbidity and health equity. Spatial extrapolation and logical summaries of these findings are dependent on the network covering a representative sample of the environments in a region and their interrelationships being known. Here, we investigate how comprehensive is the coverage of the network of rural DSS sites in Africa in terms of the range of ecological zones found across the continent. METHODS: We used satellite imagery to define an environmental signature for each INDEPTH DSS site, and then calculate Euclidean distances from these signatures to the environmental signatures of every image pixel across Africa. These distances were then mapped and a gridded population surface used to mask uninhabited areas to illustrate the extent of the environmental coverage of the INDEPTH network. Environmental similarities between DSS sites were also calculated, hierarchically clustered and visualized as a dendrogram to examine between site relationships. Finally, an ecozonation of Africa was used to analyse the per-ecozone environmental similarity of the INDEPTH DSS network. RESULTS AND CONCLUSIONS: The current INDEPTH DSS network in Africa spans all the major environmental zones, but within these zones the environmental coverage of the network varies. These variations were mapped by ecozone. These maps provide valuable information in determining the confidence with which relationships derived from rural INDEPTH DSS sites can be extended to other areas. The results also indicate suites of sites that form environmentally cohesive groups and from which data can be logically summarized. Finally, the results highlight areas where the location of new INDEPTH DSS sites would increase significantly the environmental coverage of the network.

Africa↗
PubMed2001

Antenna arrays in the SIGMA-eye applicator: interactions and transforming networks.

OBJECTIVES: In multiantenna applicators such as the SIGMA-60 or SIGMA-Eye, which consist of 4 or 12 pairs of antennas shunt to 4 or 12 amplifiers ("antenna couplets"), phases and amplitudes in the feed points of these antennas under certain conditions can significantly differ from the values selected at the multichannel amplifier (forward parameters), mainly due to coupling. In the SIGMA-Eye, this interaction is particularly affected by the transforming networks between the generators and the feed points, thus hampering the control of the feed point parameters. In this work, we perform measurements at existing applicators, present a formalism to describe the facts numerically, and investigate modifications of the transforming networks to improve the performance. METHODS AND MATERIALS: We prepared an experimental setup for the SIGMA-Eye applicator that is fed by forward waves of a 12-channel amplifier system. In this setup, we made the water bolus, the interior of the tissue-equivalent phantom, and the entire transforming network accessible for measuring probes. Then, we constructed various alternative transforming networks such as Pawsey loops, LC matching networks, and power dividers and compared them with the original matching network of the SIGMA-Eye applicator. In particular, we utilized a high-resistive probe to determine the disturbances and influences caused by some channels with respect to some selected feed points of the SIGMA-Eye dipoles. RESULTS: In the original SIGMA-Eye applicator, the influences of coupling channels on the phases and voltages in the feed point of a particular antenna are largest for adjacent longitudinal channels. Here, the +/- 10 degrees phase shift and +/- 30% voltage change were observed if the reference channel (i.e., the disturbed channel) and disturbing channel are equally powered. The changes eminently increased to -30 degrees to + 100 degrees phase shift and -80% to +50% voltage change if the reference channel is fed with much lower power (four to eight-fold) than the disturbing channel. The disturbance from distant channels is less but still significant, reaching shifts of -10 degrees to +50 degrees and -50% to +20%, respectively. Using Pawsey loops instead of the original ferrite rings in the SIGMA-Eye network, the efficacy of the baluns was improved by a more than a factor of 4. Using an LC matching network, dependencies on frequency and external arrangements can be reduced significantly. Applying a power divider circuit, the coupling between antennas combined to one channel is considerably diminished (down to <-25 dB). CONCLUSION: Coupling between resonators (pairs of antennas including the matching network) reduces the control of the SIGMA-Eye applicator, i.e., it causes deviations between the selection of forward parameters at the amplifier and the total actual parameters in the feed points of the antennas. Modified transformation networks can improve the control, in particular by reducing sheath currents and asymmetries. There is a linear but variable relationship between selected (amplifiers) and actually given (feed points) parameters. This linear mapping (described by a matrix) and its characteristics need further investigation.

Hyperthermia, Induced↗
PubMed2006

Inference of scale-free networks from gene expression time series.

Quantitative time-series observation of gene expression is becoming possible, for example by cell array technology. However, there are no practical methods with which to infer network structures using only observed time-series data. As most computational models of biological networks for continuous time-series data have a high degree of freedom, it is almost impossible to infer the correct structures. On the other hand, it has been reported that some kinds of biological networks, such as gene networks and metabolic pathways, may have scale-free properties. We hypothesize that the architecture of inferred biological network models can be restricted to scale-free networks. We developed an inference algorithm for biological networks using only time-series data by introducing such a restriction. We adopt the S-system as the network model, and a distributed genetic algorithm to optimize models to fit its simulated results to observed time series data. We have tested our algorithm on a case study (simulated data). We compared optimization under no restriction, which allows for a fully connected network, and under the restriction that the total number of links must equal that expected from a scale free network. The restriction reduced both false positive and false negative estimation of the links and also the differences between model simulation and the given time-series data.

Algorithms↗
PubMed2004

Single-neuron discharge properties and network activity in dissociated cultures of neocortex.

Cultures of neurons from rat neocortex exhibit spontaneous, temporally patterned, network activity. Such a distributed activity in vitro constitutes a possible framework for combining theoretical and experimental approaches, linking the single-neuron discharge properties to network phenomena. In this work, we addressed the issue of closing the loop, from the identification of the single-cell discharge properties to the prediction of collective network phenomena. Thus, we compared these predictions with the spontaneously emerging network activity in vitro, detected by substrate arrays of microelectrodes. Therefore, we characterized the single-cell discharge properties to Gauss-distributed noisy currents, under pharmacological blockade of the synaptic transmission. Such stochastic currents emulate a realistic input from the network. The mean (m) and variance (s(2)) of the injected current were varied independently, reminiscent of the extended mean-field description of a variety of possible presynaptic network organizations and mean activity levels, and the neuronal response was evaluated in terms of the steady-state mean firing rate (f). Experimental current-to-spike-rate responses f(m, s(2)) were similar to those of neurons in brain slices, and could be quantitatively described by leaky integrate-and-fire (IF) point neurons. The identified model parameters were then used in numerical simulations of a network of IF neurons. Such a network reproduced a collective activity, matching the spontaneous irregular population bursting, observed in cultured networks. We finally interpret such a collective activity and its link with model details by the mean-field theory. We conclude that the IF model is an adequate minimal description of synaptic integration and neuronal excitability, when collective network activities are considered in vitro.

Action Potentials↗
PubMed2005

Distal gap junctions and active dendrites can tune network dynamics.

Gap junctions allow direct electrical communication between CNS neurons. From theoretical and modeling studies, it is well known that although gap junctions can act to synchronize network output, they can also give rise to many other dynamic patterns including antiphase and other phase-locked states. The particular network pattern that arises depends on cellular, intrinsic properties that affect firing frequencies as well as the strength and location of the gap junctions. Interneurons or GABAergic neurons in hippocampus are diverse in their cellular characteristics and have been shown to have active dendrites. Furthermore, parvalbumin-positive GABAergic neurons, also known as basket cells, can contact one another via gap junctions on their distal dendrites. Using two-cell network models, we explore how distal electrical connections affect network output. We build multi-compartment models of hippocampal basket cells using NEURON and endow them with varying amounts of active dendrites. Two-cell networks of these model cells as well as reduced versions are explored. The relationship between intrinsic frequency and the level of active dendrites allows us to define three regions based on what sort of network dynamics occur with distal gap junction coupling. Weak coupling theory is used to predict the delineation of these regions as well as examination of phase response curves and distal dendritic polarization levels. We find that a nonmonotonic dependence of network dynamic characteristics (phase lags) on gap junction conductance occurs. This suggests that distal electrical coupling and active dendrite levels can control how sensitive network dynamics are to gap junction modulation. With the extended geometry, gap junctions located at more distal locations must have larger conductances for pure synchrony to occur. Furthermore, based on simulations with heterogeneous networks, it may be that one requires active dendrites if phase-locking is to occur in networks formed with distal gap junctions.

Action Potentials↗
PubMed1999

Network structure and hospital financial performance in New York State: 1991-1995.

As networks have proliferated, questions have arisen regarding which structure is optimal. To obtain an answer from the hospital perspective, the authors conducted a survey of New York State hospitals to determine how network integration, complexity, and financial risk sharing relate to measures of financial performance during the period of 1991-1995. Of the 64 hospitals indicating a network affiliation by 1995, 67.2 percent listed some network risk-sharing activity. The least integrated networks were associated with the smallest improvements in throughput, and the most complex were associated with the largest negative changes in operating margins. During the first 2 years of network membership, hospitals joining risk-sharing networks experienced operating margin gains averaging 12 percentage points higher than hospitals joining networks without risk sharing; however, this difference dissipated in later years. Networks with higher levels of integration, lower levels of complexity, and which involve some risk-sharing between affiliates are most likely to experience improved hospital financial performance during the network's initial years.

Delivery of Health Care, Integrated↗
PubMed2006

Development and implementation of an algorithm for detection of protein complexes in large interaction networks.

BACKGROUND: After complete sequencing of a number of genomes the focus has now turned to proteomics. Advanced proteomics technologies such as two-hybrid assay, mass spectrometry etc. are producing huge data sets of protein-protein interactions which can be portrayed as networks, and one of the burning issues is to find protein complexes in such networks. The enormous size of protein-protein interaction (PPI) networks warrants development of efficient computational methods for extraction of significant complexes. RESULTS: This paper presents an algorithm for detection of protein complexes in large interaction networks. In a PPI network, a node represents a protein and an edge represents an interaction. The input to the algorithm is the associated matrix of an interaction network and the outputs are protein complexes. The complexes are determined by way of finding clusters, i. e. the densely connected regions in the network. We also show and analyze some protein complexes generated by the proposed algorithm from typical PPI networks of Escherichia coli and Saccharomyces cerevisiae. A comparison between a PPI and a random network is also performed in the context of the proposed algorithm. CONCLUSION: The proposed algorithm makes it possible to detect clusters of proteins in PPI networks which mostly represent molecular biological functional units. Therefore, protein complexes determined solely based on interaction data can help us to predict the functions of proteins, and they are also useful to understand and explain certain biological processes.

Algorithms↗