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PubMed2006

Linear relation on the correlation in complex networks.

Correlation in complex networks follows a linear relation between the degree of a node and the total degrees of its neighbors for six different classes of real networks. This general linear relation is an extension of the Aboav-Weaire law in two-dimensional cellular structures and provides a simple and different perspective on the correlation in complex networks, which is complementary to an existing description using Pearson correlation coefficients and a power law fit. Analytical expression for this linear relation for three standard models of complex networks: the Erdos-Renyi, Watts-Strogatz, and Barabasi-Albert networks is provided. The slope and intercept of this linear relation are described by a single parameter a together with the first and second moment of the degree distribution of the network. The assortivity of the network can be related to the sign of the intercept.

Journal Article↗
PubMed2006

Degree-dependent intervertex separation in complex networks.

We study the mean length (l)(k) of the shortest paths between a vertex of degree k and other vertices in growing networks, where correlations are essential. In a number of deterministic scale-free networks we observe a power-law correction to a logarithmic dependence, (l)(k) = A ln[N/k((gamma-1)/2)]-Ck(gamma-1)/N+ in a wide range of network sizes. Here N is the number of vertices in the network, gamma is the degree distribution exponent, and the coefficients A and C depend on a network. We compare this law with a corresponding (l)(k) dependence obtained for random scale-free networks growing through the preferential attachment mechanism. In stochastic and deterministic growing trees with an exponential degree distribution, we observe a linear dependence on degree, (l)(k)approximately A ln N-Ck. We compare our findings for growing networks with those for uncorrelated graphs.

Journal Article↗
PubMed2006

Degree landscapes in scale-free networks.

We generalize the degree-organizational view of real-world networks with broad degree distributions in a landscape analog with mountains (high-degree nodes) and valleys (low-degree nodes). For example, correlated degrees between adjacent nodes correspond to smooth landscapes (social networks), hierarchical networks to one-mountain landscapes (the Internet), and degree-disassortative networks without hierarchical features to rough landscapes with several mountains. To quantify the topology, we here measure the widths of the mountains and the separation between different mountains. We also generate ridge landscapes to model networks organized under constraints imposed by the space the networks are embedded in, associated to spatial or in molecular networks to functional localization.

Journal Article↗
PubMed2006

Exact solutions for models of evolving networks with addition and deletion of nodes.

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied. In the real world, however, many networks, including the web, not only add vertices but also lose them. Here we formulate models of the time evolution of such networks and give exact solutions for a number of cases of particular interest. For the case of net growth and so-called preferential attachment--in which newly appearing vertices attach to previously existing ones in proportion to vertex degree--we show that the resulting networks have power-law degree distributions, but with an exponent that diverges as the growth rate vanishes. We conjecture that the low exponent values observed in real-world networks are thus the result of vigorous growth in which the rate of addition of vertices far exceeds the rate of removal. Were growth to slow in the future--for instance, in a more mature future version of the web--we would expect to see exponents increase, potentially without bound.

Journal Article↗
PubMed2006

Muller's ratchet in random graphs and scale-free networks.

Muller's ratchet is an evolutionary process that has been implicated in the extinction of asexual species, the evolution of mitochondria, the degeneration of the Y chromosome, the evolution of sex and recombination and the evolution of microbes. Here we study the speed of Muller's ratchet in a population subdivided into many small subpopulations connected by migration, and distributed on a network. We compare the speed of the ratchet in two distinct types of topologies: scale free networks and random graphs. The difference between the topologies is noticeable when the average connectivity of the network and the migration rate is large. In this situation we observe that the ratchet clicks faster in scale free networks than in random graphs. So contrary to intuition, scale free networks are more prone to loss of genetic information than random graphs. On the other hand, we show that scale free networks are more robust to the random extinction than random graphs. Since these complex networks have been shown to describe well real-life systems, our results open a framework for studying the evolution of microbes and disease epidemics.

Algorithms↗
PubMed2006

Evolving Apollonian networks with small-world scale-free topologies.

We propose two types of evolving networks: evolutionary Apollonian networks (EANs) and general deterministic Apollonian networks (GDANs), established by simple iteration algorithms. We investigate the two networks by both simulation and theoretical prediction. Analytical results show that both networks follow power-law degree distributions, with distribution exponents continuously tuned from 2 to 3. The accurate expression of clustering coefficient is also given for both networks. Moreover, the investigation of the average path length of EAN and the diameter of GDAN reveals that these two types of networks possess small-world feature. In addition, we study the collective synchronization behavior on some limitations of the EAN.

Journal Article↗
PubMed2006

Dynamics of networking agents competing for high centrality and low degree.

We model a system of networking agents that seek to optimize their centrality in the network while keeping their cost, the number of connections they are participating in, low. Unlike other game-theory based models for network evolution, the success of the agents is related only to their position in the network. The agents use strategies based on local information to improve their chance of success. Both the evolution of strategies and network structure are investigated. We find a dramatic time evolution with cascades of strategy change accompanied by a change in network structure. On average the network self-organizes to a state close to the transition between a fragmented state and a state with a giant component. Furthermore, with increasing system size both the average degree and the level of fragmentation decreases.

Journal Article↗
PubMedDate not supplied

Motif search in graphs: application to metabolic networks.

The classic view of metabolism as a collection of metabolic pathways is being questioned with the currently available possibility of studying whole networks. Novel ways of decomposing the network into modules and motifs that could be considered as the building blocks of a network are being suggested. In this work, we introduce a new definition of motif in the context of metabolic networks. Unlike in previous works on (other) biochemical networks, this definition is not based only on topological features. We propose instead to use an alternative definition based on the functional nature of the components that form the motif, which we call a reaction motif. After introducing a formal framework motivated by biological considerations, we present complexity results on the problem of searching for all occurrences of a reaction motif in a network and introduce an algorithm that is fast in practice in most situations. We then show an initial application to the study of pathway evolution. Finally, we give some general features of the observed number of occurrences in order to highlight some structural features of metabolic networks.

Algorithms↗
PubMed2004

A one-layer recurrent neural network for support vector machine learning.

This paper presents a one-layer recurrent neural network for support vector machine (SVM) learning in pattern classification and regression. The SVM learning problem is first converted into an equivalent formulation, and then a one-layer recurrent neural network for SVM learning is proposed. The proposed neural network is guaranteed to obtain the optimal solution of support vector classification and regression. Compared with the existing two-layer neural network for the SVM classification, the proposed neural network has a low complexity for implementation. Moreover, the proposed neural network can converge exponentially to the optimal solution of SVM learning. The rate of the exponential convergence can be made arbitrarily high by simply turning up a scaling parameter. Simulation examples based on benchmark problems are discussed to show the good performance of the proposed neural network for SVM learning.

Journal Article↗
PubMed2006

Self-adaptation in next-generation Internet networks: how to react to traffic changes while respecting QoS?

Next-generation network infrastructure should support different services and several levels of quality of service (QoS) and resilience. The main requirements for such multiservice networks are flexibility, effective utilization of network resources, and ability to react to traffic demand changes with time. These requisites lead to the fact that next-generation networks should, to some extend, be "self-adapting," to cope with the need of promptly reacting to traffic demand changes, in an effective way, while taking into account the different requirements in terms of QoS. This paper sketches the reference network scenario and discusses the subject of self-adapting networks, attempting to focus on the key issues that need to be solved to realize future infrastructures. As a relevant example, this paper briefly reports a system developed by the authors' laboratory that implements a traffic engineering solution able to fulfill the mentioned requirements. This system could be regarded as a first concrete step toward the realization of self-adapting networks. In addition, some relevant results that were obtained either by simulation or by experiments on a real test bed are reported to discuss the main characteristics of such a system and assess the feasibility of the concept. Finally, the paper reviews the main hot issues that need to be addressed, in the authors' opinion, by the international research community.

Journal Article↗
PubMed2005

Who's there and who cares: age as an indicator of social support networks for caregivers among people living with motor neurone disease.

This paper explores the social support networks available to the informal carers of people living with motor neurone disease (MND). An ethnographic case study was undertaken using eco mapping, observation and conversational interviews to collect data from 18 primary carers of people living with MND. Interviews took place in participants' homes in metropolitan, regional and rural locations. Participants discussed the content of their support network and drew lines between individuals to indicate the type and strength of relationship. Changes to the network were depicted on eco maps during subsequent interviews. While health policy-makers assume that healthy social capital exists in Australian communities and that social cohesion will ensure active and available support networks in times of illness or disability, data from this exploratory study indicated that this was not consistently the case. Support networks varied in size and composition; however, age was identified as a discriminator of the availability and consistency of support. People in older age groups identified more diverse but consistent support systems while people in younger age groups reported more fluctuations in the strength of relationships and declines in support as caregiving became more demanding. Individual assessment of support networks at regular intervals in the caregiving trajectory is vital for all carers. However carers in younger age groups may need specific support to manage the psychological crises that occur and more access to paid care. Older carers may need consistent support to handle more of the instrumental aspects of care and assistance to mobilise their support networks. Community workers should be alert to the possible need for crisis intervention when tensions in relationships threaten carers' ability to provide effective care.

Age Factors↗
PubMed2005

Quantitative analysis of keratin filament networks in scanning electron microscopy images of cancer cells.

The keratin filament network is an important part of the cytoskeleton. It is involved in the regulation of shape and viscoelasticity of epithelial cells. The morphology of keratin networks depends on post-translational modifications of keratin monomers. In-vitro studies indicated that network characteristics, such as filament crosslink density, determines the biophysical properties of the filament network. This report presents a quantitative method for the morphological analysis of keratin filament networks. Visualization of filaments was based on prefixation extraction of epithelial cells and scanning electron microscopy (SEM). SEM images were processed by a skeletonization algorithm to obtain a graph structure that represents individual filaments as well as their connections. This method was applied to investigate the effects of transforming growth factor alpha (TGFalpha) on the morphology of keratin networks in pancreatic cancer cells. TGFalpha contributes to pancreatic cancer progression and activates signalling pathways phosphorylating keratin monomers. Using this new method, a significant alteration to the keratin network morphology could be detected in response to TGFalpha.

Cell Transformation, Neoplastic↗
PubMed2005

Reconfiguration of multiple motor networks by short- and long-term actions of an identified modulatory neuron.

The pyloric and gastric motor pattern-generating networks in the stomatogastric ganglion of the lobster Homarus gammarus are reconfigured into a new functional circuit by burst discharge in an identified pair of modulatory projection interneurons, originally named the pyloric suppressor (PS) neurons because of their inhibitory effects on pyloric network activity. Here we elucidate the actions of the PS neurons on individual members of the neighbouring gastric circuit, as well as describing their ability to alter synaptic coupling between the two networks. PS neuron firing has two distinct effects on gastric network activity: an initial short-lasting action mediated by transient inhibition of most gastric motoneurons, followed by a long-lasting circuit activation associated with a prolonged PS-evoked depolarization of the medial gastric (MG) motoneuron and the single network interneuron, Int1. These long-lasting effects are voltage-dependent, and experiments with hyperpolarizing current injection and photoablation suggest that excitation of both the MG neuron and Int1 is critical for PS-elicited gastric network rhythmicity. In parallel, PS neuron discharge persistently (lasting several minutes) enhances the strength of an inhibitory synaptic influence of the MG neuron on the pyloric dilator (PD)-anterior burster (AB) pacemaker neurons, thereby facilitating operational fusion of the two networks. Therefore, a single modulatory neuron may influence disparate populations of neurons via a range of very different and highly target-specific mechanisms: conventional transient synaptic drive and up- or down-modulation of membrane properties and synaptic efficacy. Moreover, distinctly different time courses of these actions allow different circuit configurations to be specified sequentially by a given modulatory input.

Animals↗
PubMed1988

Maternal social networks and mother-infant interactions in full-term and very low birthweight, preterm infants.

The relation between maternal social networks and mother-infant interactions at 6 months of age was examined in 34 mother-preterm and 20 mother-full-term dyads. All preterm infants were of very low birthweight and experienced medical complications. Mothers were interviewed regarding their social networks; ratings of maternal behaviors were derived from videotaped mother-infant interactions. There were few between-group differences in mean levels of network variables; however, the association between network structure and maternal sensitivity differed in the 2 groups. A larger number of ties between the mother's family of origin and the mother's friends related to higher maternal sensitivity in full-terms but to lower maternal sensitivity in preterms. The birth of a full-term infant is typically a positive event around which a tightly knit network can coalesce to support the mother. It is less clear that the birth of a preterm infant is a positive event, leaving network members unsure of their roles and how to respond. Under the latter circumstances, fewer ties among network members may decrease the likelihood of ambiguous or stressful communications.

Adaptation, Psychological↗
PubMed2005

Regulation of metabolic networks: understanding metabolic complexity in the systems biology era.

Metabolism is one of the best recognised networks within biological systems, but our understanding of metabolic regulation has been limited by a failure to consider regulation within the context of the whole network. With recent advances in theoretical aspects of network thinking and a postgenomic landscape in which our ability to quantify molecular changes at a systems level is unsurpassed, the time is ripe for the development of a new level of understanding of the regulation of plant metabolic networks. Theoretical advances such as the formal description of 'scale-free' networks have provided explanations for network behaviour (such as robustness). In parallel, the appreciation of the importance of new levels of the metabolic regulatory hierarchy (such as protein-protein interaction) and the continuing development of global profiling technologies is generating a system-wide molecular data set of increasing resolution. In this review we will argue that the integration of these different aspects of metabolic research will bring about a step change in our understanding of the regulation of metabolic networks in plants.

Gene Expression Profiling↗
PubMed1984

A framework and themes for social network intervention.

This paper is concerned with the development and application of social network concepts in clinical practice. A framework of network levels and sets for ordering data and observations is proposed; the phenomenon of truncated networks is considered and two emphases in network intervention (gathering and connecting forms) are proposed to conceptualize network characteristics and practice that follows from such characteristics. A number of current examples of network practice are placed within the framework, and several advantages of utilizing a network perspective as a complement to existing models of family therapy are noted.

Adaptation, Psychological↗
PubMed1994

Associations between the mental health and social networks of children and parents in single-parent families. A comparison between a clinical group and a control group.

The parents and children in single-parent families were studied. A group of 39 children ages 9-16 years who had been patients at a child and adolescent psychiatric clinic and a control group with an equal number of children were interviewed together with their single parent regarding social network and mental health. The networks of children and parents in the control group were more similar to each other than the networks of parents and children in the patient group. The crosswise influence of parents' mental health, children's behavioral disturbances and social networks showed associations between parents' mental health and children's behavioural disturbances, between parents's social networks and children's behavioural disturbances and between parents' mental health and their social networks. There was, on the other hand, no association between parents' mental health and the social networks of their children.

Adolescent↗
PubMed1995

Legislative and policy strategies for supporting rural health network development: lessons from the 103rd Congress.

There was considerable support in most major health reform bills considered by the 103rd Congress for the development of rural integrated service networks. The demise of comprehensive health reform, together with the pace of current market-driven changes in the health care system, suggests the need to assess the impact of specific policy strategies considered in the last Congress on rural integrated service network development. Toward this end, this article evaluates the rural health policy strategies of the major bills in relation to three essential preconditions for the development of rural integrated service networks: (1) the need for a more stable financial base for rural providers; (2) the need for administrative, service and clinical capacity to mount a successful network; and finally, (3) the need for appropriate market areas to ensure fair competition among networks and plans. Key policy strategies for supporting rural network development include reform of insurance and payment policies, expansion of targeted support and technical assistance to the underserved, limited-capacity rural areas, and policies governing purchasing groups or alliances that will ensure appropriate treatment of rural providers and networks.

Comprehensive Health Care↗