Random graph models of social networks

Phase transitions in supercritical explosive percolation

Percolation describes the sudden emergence of large-scale connectivity as edges are added to a lattice or random network. In the Bohman-Frieze-Wormald model (BFW) of percolation, edges sampled from a random graph are considered individually and either added to the graph or rejected provided that the fraction of accepted edges is never smaller than a decreasing function with asymptotic value of α, a constant. The BFW process has been studied as a model system for investigating the underlying mechanisms leading to discontinuous phase transitions in percolation. Here we focus on the regime αε[0.6,0.95] where it is known that only one giant component, denoted C(1) , initially appears at the discontinuous phase transition. We show that at some point in the supercritical regime C(1) stops growing and eventually a second giant component, denoted C(2), emerges in a continuous percolation transition. The delay between the emergence of C(1) and C(2) and their asymptotic sizes both depend on the value of α and we establish by several techniques that there exists a bifurcation point α(c)=0.763±0.002. For αε[0.6,α(c)), C(1) stops growing the instant it emerges and the delay between the emergence of C(1) and C(2) decreases with increasing α. For αε(α(c),0.95], in contrast, C(1) continues growing into the supercritical regime and the delay between the emergence of C(1) and C(2) increases with increasing α. As we show, α(c) marks the minimal delay possible between the emergence of C(1) and C(2) (i.e., the smallest edge density for which C(2) can exist). We also establish many features of the continuous percolation of C(2) including scaling exponents and relations.

Epidemiological effects of group size variation in social species

Contact patterns in group-structured populations determine the course of infectious disease outbreaks. Network-based models have revealed important connections between group-level contact patterns and the dynamics of epidemics, but these models typically ignore heterogeneities in within-group composition. Here, we analyse a flexible mathematical model of disease transmission in a hierarchically structured wildlife population, and find that increased variation in group size reduces the epidemic threshold, making social animal populations susceptible to a broader range of pathogens. Variation in group size also increases the likelihood of an epidemic for mildly transmissible diseases, but can reduce the likelihood and expected size of an epidemic for highly transmissible diseases. Further, we introduce the concept of epidemiological effective group size, which we define to be the group size of a hypothetical population containing groups of identical size that has the same epidemic threshold as an observed population. Using data from the Serengeti Lion Project, we find that pride-living Serengeti lions are epidemiologically comparable to a homogeneous population with up to 20 per cent larger prides.

DISCRETE-TIME EPIDEMIC DYNAMICS WITH AWARENESS IN RANDOM NETWORKS

Human behavioral responses fundamentally influence the spread of infectious disease. In this paper, we study a discrete-time SIS epidemic process in random networks. Three forms of individual awareness, namely, local awareness, global awareness and contact awareness, are considered. The effect of awareness is to reduce the risk of infection. Based on the stability theory of matrix difference equation, we derive analytically the epidemic threshold. It is found that both local and contact awareness can raise the epidemic threshold, while the global awareness only decreases the epidemic prevalence. Our results are in line with a recent result using differential equation-based methods.

Temporal characterisation of the network of Danish cattle movements and its implication for disease control: 2000-2009

Social network analysis provides a valuable framework for understanding the dynamics of diseases on networks as well as a means for defining effective control measures. An understanding of the underlying contact pattern for a susceptible population is advisable before embarking on any strategy for disease control. The objective of this study was to characterise the network of Danish cattle movements over a 10-year period from 2000 to 2009 with a view to understanding: (1) cohesiveness of the network, (2) influential holdings and (3) structural vulnerability of the network. Network analyses of data involving all cattle movements in Denmark registered during the period of interest were performed. A total of 50,494 premises participated in 4,204,895 individual movements during the 10-year period. The results pointed to a predominantly scale-free structure of the network; though marked by small-world properties in March-April 2001 as well as in 24 other months during the period October 2006 to December 2009. The network was sparsely connected with markets being the key influential holdings. Its vulnerability to removal of markets suggests that targeting highly connected holdings during epidemics should be the focus of control efforts.

Inferring population-level contact heterogeneity from common epidemic data

Models of infectious disease spread that incorporate contact heterogeneity through contact networks are an important tool for epidemiologists studying disease dynamics and assessing intervention strategies. One of the challenges of contact network epidemiology has been the difficulty of collecting individual and population-level data needed to develop an accurate representation of the underlying host population's contact structure. In this study, we evaluate the utility of common epidemiological measures (R0, epidemic peak size, duration and final size) for inferring the degree of heterogeneity in a population's unobserved contact structure through a Bayesian approach. We test the method using ground truth data and find that some of these epidemiological metrics are effective at classifying contact heterogeneity. The classification is also consistent across pathogen transmission probabilities, and so can be applied even when this characteristic is unknown. In particular, the reproductive number, R0, turns out to be a poor classifier of the degree heterogeneity, while, unexpectedly, final epidemic size is a powerful predictor of network structure across the range of heterogeneity. We also evaluate our framework on empirical epidemiological data from past and recent outbreaks to demonstrate its application in practice and to gather insights about the relevance of particular contact structures for both specific systems and general classes of infectious disease. We thus introduce a simple approach that can shed light on the unobserved connectivity of a host population given epidemic data. Our study has the potential to inform future data-collection efforts and study design by driving our understanding of germane epidemic measures, and highlights a general inferential approach to learning about host contact structure in contemporary or historic populations of humans and animals.

Transmission of equine influenza virus during an outbreak is characterized by frequent mixed infections and loose transmission bottlenecks

The ability of influenza A viruses (IAVs) to cross species barriers and evade host immunity is a major public health concern. Studies on the phylodynamics of IAVs across different scales – from the individual to the population – are essential for devising effective measures to predict, prevent or contain influenza emergence. Understanding how IAVs spread and evolve during outbreaks is critical for the management of epidemics. Reconstructing the transmission network during a single outbreak by sampling viral genetic data in time and space can generate insights about these processes. Here, we obtained intra-host viral sequence data from horses infected with equine influenza virus (EIV) to reconstruct the spread of EIV during a large outbreak. To this end, we analyzed within-host viral populations from sequences covering 90% of the infected yards. By combining gene sequence analyses with epidemiological data, we inferred a plausible transmission network, in turn enabling the comparison of transmission patterns during the course of the outbreak and revealing important epidemiological features that were not apparent using either approach alone. The EIV populations displayed high levels of genetic diversity, and in many cases we observed distinct viral populations containing a dominant variant and a number of related minor variants that were transmitted between infectious horses. In addition, we found evidence of frequent mixed infections and loose transmission bottlenecks in these naturally occurring populations. These frequent mixed infections likely influence the size of epidemics.

Influenza A viruses (IAVs) are major pathogens of humans and animals. Understanding how IAVs spread and evolve at different scales (individual, regional, global) in natural conditions is critical for preventing or managing influenza epidemics. A vast body of knowledge has been generated on the evolution of IAVs at the global scale. Additionally, recent experimental transmission studies have examined the diversity and transmission of influenza viruses within and between hosts. However, most studies on the spread of IAVs during epidemics have been based on consensus viral sequences, an approach that does not have enough discriminatory power to reveal exact transmission pathways. Here, we analyzed multiple within-host viral populations from different horses infected with equine influenza virus (EIV) during the course of an outbreak in a population within a confined area. This provided an opportunity to examine the genetic diversity of the viruses within single animals, the transmission of the viruses between each closely confined population within a yard, and the transmission between horses in different yards. We show that individual horses can be infected by viruses from more than one other horse, which has important implications for facilitating segment reassortment and the evolution of EIV. Additionally, by combining viral sequencing data and epidemiological data we show that the high levels of mixed infections can reveal the underlying epidemiological dynamics of the outbreak, and that epidemic size could be underestimated if only epidemiological data is considered. As sequencing technologies become cheaper and faster, these analyses could be undertaken almost in real-time and help control future outbreaks.

An approach for the identification of targets specific to bone metastasis using cancer genes interactome and gene ontology analysis

Metastasis is one of the most enigmatic aspects of cancer pathogenesis and is a major cause of cancer-associated mortality. Secondary bone cancer (SBC) is a complex disease caused by metastasis of tumor cells from their primary site and is characterized by intricate interplay of molecular interactions. Identification of targets for multifactorial diseases such as SBC, the most frequent complication of breast and prostate cancers, is a challenge. Towards achieving our aim of identification of targets specific to SBC, we constructed a 'Cancer Genes Network', a representative protein interactome of cancer genes. Using graph theoretical methods, we obtained a set of key genes that are relevant for generic mechanisms of cancers and have a role in biological essentiality. We also compiled a curated dataset of 391 SBC genes from published literature which serves as a basis of ontological correlates of secondary bone cancer. Building on these results, we implement a strategy based on generic cancer genes, SBC genes and gene ontology enrichment method, to obtain a set of targets that are specific to bone metastasis. Through this study, we present an approach for probing one of the major complications in cancers, namely, metastasis. The results on genes that play generic roles in cancer phenotype, obtained by network analysis of 'Cancer Genes Network', have broader implications in understanding the role of molecular regulators in mechanisms of cancers. Specifically, our study provides a set of potential targets that are of ontological and regulatory relevance to secondary bone cancer.

Diffusion, annihilation, and chemical reactions in complex networks with spatial constraints

We consider Erdö]s-Rényi-type networks embedded in one-dimensional (de=1) and two-dimensional (de=2) Euclidean space with the link-length distribution p(r)∼r-δ. The dimension d of these networks, as a function of δ, has been studied earlier and has been shown to depend on δ. Here we consider diffusion, annihilation, and chemical reaction processes on these spatially constrained networks and show that their dynamics is controlled by the dimension d of the system. We study, as a function of the exponent δ and the embedding dimension de, the average distance <r>∼t1/dw a random walker has traveled after t time steps as well as the probability of the random walker's return to the origin P0(t). From these quantities we determine the network dimension d and the dimension dw of the random walk as a function of δ. We find that the fraction d/dw governs the number of survivors as a function of time t in the annihilation process (A+A→0) and in the chemical reaction process (A+B→0), showing that the relations derived for ordered and disordered lattices with short-range links remain valid also in the case of complex embedded networks with long-range links.

Social influence and spread dynamics in social networks

Social networks often serve as a critical medium for information dissemination, diffusion of epidemics, and spread of behavior, by shared activities or similarities between individuals. Recently, we have witnessed an explosion of interest in studying social influence and spread dynamics in social networks. To date, relatively little material has been provided on a comprehensive review in this field. This brief survey addresses this issue. We present the current significant empirical studies on real social systems, including network construction methods, measures of network, and newly empirical results. We then provide a concise description of some related social models from both macro- and micro-level perspectives. Due to the difficulties in combining real data and simulation data for verifying and validating real social systems, we further emphasize the current research results of computational experiments. We hope this paper can provide researchers significant insights into better understanding the characteristics of personal influence and spread patterns in large-scale social systems.

A complex systems approach to evaluate HIV prevention in metropolitan areas: preliminary implications for combination intervention strategies

BACKGROUND

HIV transmission among injecting and non-injecting drug users (IDU, NIDU) is a significant public health problem. Continuing propagation in endemic settings and emerging regional outbreaks have indicated the need for comprehensive and coordinated HIV prevention. We describe the development of a conceptual framework and calibration of an agent-based model (ABM) to examine how combinations of interventions may reduce and potentially eliminate HIV transmission among drug-using populations.

METHODOLOGY/PRINCIPAL FINDINGS

A multidisciplinary team of researchers from epidemiology, sociology, geography, and mathematics developed a conceptual framework based on prior ethnographic and epidemiologic research. An ABM was constructed and calibrated through an iterative design and verification process. In the model, "agents" represent IDU, NIDU, and non-drug users who interact with each other and within risk networks, engaging in sexual and, for IDUs, injection-related risk behavior over time. Agents also interact with simulated HIV prevention interventions (e.g., syringe exchange programs, substance abuse treatment, HIV testing) and initiate antiretroviral treatment (ART) in a stochastic manner. The model was constructed to represent the New York metropolitan statistical area (MSA) population, and calibrated by comparing output trajectories for various outcomes (e.g., IDU/NIDU prevalence, HIV prevalence and incidence) against previously validated MSA-level data. The model closely approximated HIV trajectories in IDU and NIDU observed in New York City between 1992 and 2002, including a linear decrease in HIV prevalence among IDUs. Exploratory results are consistent with empirical studies demonstrating that the effectiveness of a combination of interventions, including syringe exchange expansion and ART provision, dramatically reduced HIV prevalence among IDUs during this time period.

CONCLUSIONS/SIGNIFICANCE

Complex systems models of adaptive HIV transmission dynamics can be used to identify potential collective benefits of hypothetical combination prevention interventions. Future work will seek to inform novel strategies that may lead to more effective and equitable HIV prevention strategies for drug-using populations.

Reverse preferential spread in complex networks

Large-degree nodes may have a larger influence on the network, but they can be bottlenecks for spreading information since spreading attempts tend to concentrate on these nodes and become redundant. We discuss that the reverse preferential spread (distributing information inversely proportional to the degree of the receiving node) has an advantage over other spread mechanisms. In large uncorrelated networks, we show that the mean number of nodes that receive information under the reverse preferential spread is an upper bound among any other weight-based spread mechanisms, and this upper bound is indeed a logistic growth independent of the degree distribution.

EpiFire: An open source C++ library and application for contact network epidemiology

BACKGROUND

Contact network models have become increasingly common in epidemiology, but we lack a flexible programming framework for the generation and analysis of epidemiological contact networks and for the simulation of disease transmission through such networks.

RESULTS

Here we present EpiFire, an applications programming interface and graphical user interface implemented in C++, which includes a fast and efficient library for generating, analyzing and manipulating networks. Network-based percolation and chain-binomial simulations of susceptible-infected-recovered disease transmission, as well as traditional non-network mass-action simulations, can be performed using EpiFire.

CONCLUSIONS

EpiFire provides an open-source programming interface for the rapid development of network models with a focus in contact network epidemiology. EpiFire also provides a point-and-click interface for generating networks, conducting epidemic simulations, and creating figures. This interface is particularly useful as a pedagogical tool.

Organization and evolution of synthetic idiotypic networks

We introduce a class of weighted graphs whose properties are meant to mimic the topological features of idiotypic networks, namely, the interaction networks involving the B core of the immune system. Each node is endowed with a bit string representing the idiotypic specificity of the corresponding B cell, and the proper distance between any couple of bit strings provides the coupling strength between the two nodes. We show that a biased distribution of the entries in bit strings can yield fringes in the (weighted) degree distribution, small-world features, and scaling laws, in agreement with experimental findings. We also investigate the role of aging, thought of as a progressive increase in the degree of bias in bit strings, and we show that it can possibly induce mild percolation phenomena, which are investigated too.

Community structure and scale-free collections of Erdős-Rényi graphs

Community structure plays a significant role in the analysis of social networks and similar graphs, yet this structure is little understood and not well captured by most models. We formally define a community to be a subgraph that is internally highly connected and has no deeper substructure. We use tools of combinatorics to show that any such community must contain a dense Erdős-Rényi (ER) subgraph. Based on mathematical arguments, we hypothesize that any graph with a heavy-tailed degree distribution and community structure must contain a scale-free collection of dense ER subgraphs. These theoretical observations corroborate well with empirical evidence. From this, we propose the Block Two-Level Erdős-Rényi (BTER) model, and demonstrate that it accurately captures the observable properties of many real-world social networks.

A stochastic Markov chain model to describe lung cancer growth and metastasis

A stochastic Markov chain model for metastatic progression is developed for primary lung cancer based on a network construction of metastatic sites with dynamics modeled as an ensemble of random walkers on the network. We calculate a transition matrix, with entries (transition probabilities) interpreted as random variables, and use it to construct a circular bi-directional network of primary and metastatic locations based on postmortem tissue analysis of 3827 autopsies on untreated patients documenting all primary tumor locations and metastatic sites from this population. The resulting 50 potential metastatic sites are connected by directed edges with distributed weightings, where the site connections and weightings are obtained by calculating the entries of an ensemble of transition matrices so that the steady-state distribution obtained from the long-time limit of the Markov chain dynamical system corresponds to the ensemble metastatic distribution obtained from the autopsy data set. We condition our search for a transition matrix on an initial distribution of metastatic tumors obtained from the data set. Through an iterative numerical search procedure, we adjust the entries of a sequence of approximations until a transition matrix with the correct steady-state is found (up to a numerical threshold). Since this constrained linear optimization problem is underdetermined, we characterize the statistical variance of the ensemble of transition matrices calculated using the means and variances of their singular value distributions as a diagnostic tool. We interpret the ensemble averaged transition probabilities as (approximately) normally distributed random variables. The model allows us to simulate and quantify disease progression pathways and timescales of progression from the lung position to other sites and we highlight several key findings based on the model.

Structural diversity in social contagion

The concept of contagion has steadily expanded from its original grounding in epidemic disease to describe a vast array of processes that spread across networks, notably social phenomena such as fads, political opinions, the adoption of new technologies, and financial decisions. Traditional models of social contagion have been based on physical analogies with biological contagion, in which the probability that an individual is affected by the contagion grows monotonically with the size of his or her "contact neighborhood"--the number of affected individuals with whom he or she is in contact. Whereas this contact neighborhood hypothesis has formed the underpinning of essentially all current models, it has been challenging to evaluate it due to the difficulty in obtaining detailed data on individual network neighborhoods during the course of a large-scale contagion process. Here we study this question by analyzing the growth of Facebook, a rare example of a social process with genuinely global adoption. We find that the probability of contagion is tightly controlled by the number of connected components in an individual's contact neighborhood, rather than by the actual size of the neighborhood. Surprisingly, once this "structural diversity" is controlled for, the size of the contact neighborhood is in fact generally a negative predictor of contagion. More broadly, our analysis shows how data at the size and resolution of the Facebook network make possible the identification of subtle structural signals that go undetected at smaller scales yet hold pivotal predictive roles for the outcomes of social processes.

Cluster identification based on correlations

The problem addressed is the identification of cooperating agents based on correlations created as a result of the joint action of these and other agents. A systematic method for using correlations beyond second moments is developed. The technique is applied to a didactic example, the identification of alphabet letters based on correlations among the pixels used in an image of the letter. As in this example, agents can belong to more than one cluster. Moreover, the identification scheme does not require that the patterns be known ahead of time.

Unbiased degree-preserving randomization of directed binary networks

Randomizing networks using a naive "accept-all" edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with nontrivial acceptance probabilities for directed graphs, which converges to a strictly uniform measure and is based on edge swaps that conserve all in and out degrees. The acceptance probabilities can also be generalized to define Markov chains that target any alternative desired measure on the space of directed graphs in order to generate graphs with more sophisticated topological features. This is demonstrated by defining a process tailored to the production of directed graphs with specified degree-degree correlation functions. The theory is implemented numerically and tested on synthetic and biological network examples.

Connectivity and thought: the influence of semantic network structure in a neurodynamical model of thinking

Understanding cognition has been a central focus for psychologists, neuroscientists and philosophers for thousands of years, but many of its most fundamental processes remain very poorly understood. Chief among these is the process of thought itself: the spontaneous emergence of specific ideas within the stream of consciousness. It is widely accepted that ideas, both familiar and novel, arise from the combination of existing concepts. From this perspective, thought is an emergent attribute of memory, arising from the intrinsic dynamics of the neural substrate in which information is embedded. An important issue in any understanding of this process is the relationship between the emergence of conceptual combinations and the dynamics of the underlying neural networks. Virtually all theories of ideation hypothesize that ideas arise during the thought process through association, each one triggering the next through some type of linkage, e.g., structural analogy, semantic similarity, polysemy, etc. In particular, it has been suggested that the creativity of ideation in individuals reflects the qualitative structure of conceptual associations in their minds. Interestingly, psycholinguistic studies have shown that semantic networks across many languages have a particular type of structure with small-world, scale free connectivity. So far, however, these related insights have not been brought together, in part because there has been no explicitly neural model for the dynamics of spontaneous thought. Recently, we have developed such a model. Though simplistic and abstract, this model attempts to capture the most basic aspects of the process hypothesized by theoretical models within a neurodynamical framework. It represents semantic memory as a recurrent semantic neural network with itinerant dynamics. Conceptual combinations arise through this dynamics as co-active groups of neural units, and either dissolve quickly or persist for a time as emergent metastable attractors and are recognized consciously as ideas. The work presented in this paper describes this model in detail, and uses it to systematically study the relationship between the structure of conceptual associations in the neural substrate and the ideas arising from this system's dynamics. In particular, we consider how the small-world and scale-free characteristics influence the effectiveness of the thought process under several metrics, and show that networks with both attributes indeed provide significant advantages in generating unique conceptual combinations.

Modularity-based graph partitioning using conditional expected models

Modularity-based partitioning methods divide networks into modules by comparing their structure against random networks conditioned to have the same number of nodes, edges, and degree distribution. We propose a novel way to measure modularity and divide graphs, based on conditional probabilities of the edge strength of random networks. We provide closed-form solutions for the expected strength of an edge when it is conditioned on the degrees of the two neighboring nodes, or alternatively on the degrees of all nodes comprising the network. We analytically compute the expected network under the assumptions of Gaussian and Bernoulli distributions. When the Gaussian distribution assumption is violated, we prove that our expression is the best linear unbiased estimator. Finally, we investigate the performance of our conditional expected model in partitioning simulated and real-world networks.

Network structure and the role of key players in a translational cancer research network: a study protocol

INTRODUCTION

Translational research networks are a deliberate strategy to bridge the gulf between biomedical research and clinical practice through interdisciplinary collaboration, supportive funding and infrastructure. The social network approach examines how the structure of the network and players who hold important positions within it constrain or enable function. This information can be used to guide network management and optimise its operations. The aim of this study was to describe the structure of a translational cancer research network (TCRN) in Australia over its first year, identify the key players within the network and explore these players' opportunities and constraints in maximising important network collaborations.

METHODS AND ANALYSIS

This study deploys a mixed-method longitudinal design using social network analysis augmented by interviews and review of TCRN documents. The study will use network documents and interviews with governing body members to explore the broader context into which the network is embedded as well as the perceptions and expectations of members. Of particular interest are the attitudes and perceptions of clinicians compared with those of researchers. A co-authorship network will be constructed of TCRN members using journal and citation databases to assess the success of past pre-network collaborations. Two whole network social network surveys will be administered 12 months apart and parameters such as density, clustering, centrality and betweenness centrality computed and compared using UCINET and Netdraw. Key players will be identified and interviewed to understand the specific activities, barriers and enablers they face in that role.

ETHICS AND DISSEMINATION

Ethics approvals were obtained from the University of New South Wales, South Eastern Sydney Northern Sector Local Health Network and Calvary Health Care Sydney. Results will be discussed with members of the TCRN, submitted to relevant journals and presented as oral presentations to clinicians, researchers and policymakers.

Health professional networks as a vector for improving healthcare quality and safety: a systematic review

BACKGROUND

While there is a considerable corpus of theoretical and empirical literature on networks within and outside of the health sector, multiple research questions are yet to be answered.

OBJECTIVE

To conduct a systematic review of studies of professionals' network structures, identifying factors associated with network effectiveness and sustainability, particularly in relation to quality of care and patient safety.

METHODS

The authors searched MEDLINE, CINAHL, EMBASE, Web of Science and Business Source Premier from January 1995 to December 2009.

RESULTS

A majority of the 26 unique studies identified used social network analysis to examine structural relationships in networks: structural relationships within and between networks, health professionals and their social context, health collaboratives and partnerships, and knowledge sharing networks. Key aspects of networks explored were administrative and clinical exchanges, network performance, integration, stability and influences on the quality of healthcare. More recent studies show that cohesive and collaborative health professional networks can facilitate the coordination of care and contribute to improving quality and safety of care. Structural network vulnerabilities include cliques, professional and gender homophily, and over-reliance on central agencies or individuals.

CONCLUSIONS

Effective professional networks employ natural structural network features (eg, bridges, brokers, density, centrality, degrees of separation, social capital, trust) in producing collaboratively oriented healthcare. This requires efficient transmission of information and social and professional interaction within and across networks. For those using networks to improve care, recurring success factors are understanding your network's characteristics, attending to its functioning and investing time in facilitating its improvement. Despite this, there is no guarantee that time spent on networks will necessarily improve patient care.

Universal fractal scaling of self-organized networks

There is an abundance of literature on complex networks describing a variety of relationships among units in social, biological, and technological systems. Such networks, consisting of interconnected nodes, are often self-organized, naturally emerging without any overarching designs on topological structure yet enabling efficient interactions among nodes. Here we show that the number of nodes and the density of connections in such self-organized networks exhibit a power law relationship. We examined the size and connection density of 47 self-organizing networks of various biological, social, and technological origins, and found that the size-density relationship follows a fractal relationship spanning over 6 orders of magnitude. This finding indicates that there is an optimal connection density in self-organized networks following fractal scaling regardless of their sizes.

Happy aged people are all alike, while every unhappy aged person is unhappy in its own way

Aging of the world's population represents one of the most remarkable success stories of medicine and of humankind, but it is also a source of various challenges. The aim of the collaborative cross-cultural European study of adult well being (ESAW) is to frame the concept of aging successfully within a causal model that embraces physical health and functional status, cognitive efficacy, material security, social support resources, and life activity. Within the framework of this project, we show here that the degree of heterogeneity among people who view aging in a positive light is significantly lower than the degree of heterogeneity of those who hold a negative perception of aging. We base this conclusion on our analysis of a survey involving 12,478 people aged 50 to 90 from six West European countries. We treat the survey database as a bipartite network in which individual respondents are linked to the actual answers they provide. Taking this perspective allows us to construct a projected network of respondents in which each link indicates a statistically validated similarity of answers profile between the connected respondents, and to identify clusters of individuals independently of demographics. We show that mental and physical well-being are key factors determining a positive perception of aging. We further observe that psychological aspects, like self-esteem and resilience, and the nationality of respondents are relevant aspects to discriminate among participants who indicate positive perception of aging.

Percolation on correlated random networks

We consider a class of random, weighted networks, obtained through a redefinition of patterns in an Hopfield-like model, and, by performing percolation processes, we get information about topology and resilience properties of the networks themselves. Given the weighted nature of the graphs, different kinds of bond percolation can be studied: stochastic (deleting links randomly) and deterministic (deleting links based on rank weights), each mimicking a different physical process. The evolution of the network is accordingly different, as evidenced by the behavior of the largest component size and of the distribution of cluster sizes. In particular, we can derive that weak ties are crucial in order to maintain the graph connected and that, when they are the most prone to failure, the giant component typically shrinks without abruptly breaking apart; these results have been recently evidenced in several kinds of social networks.

Social network analysis in the study of nonhuman primates: a historical perspective

Advances over the last 15 years have made social network analysis (SNA) a powerful tool for the study of nonhuman primate social behavior. Although many SNA-based techniques have been only very recently adopted in primatological research, others have been commonly used by primatologists for decades. The roots of SNA also stem from some of the same conceptual frameworks as the majority of nonhuman primate behavioral research. The rapid development of SNA in recent years has led to questions within the primatological community of where and how SNA fits within this field. We aim to address these questions by providing an overview of the historical relationship between SNA and the study of nonhuman primates. We begin with a brief history of the development of SNA, followed by a detailed description of the network-based visualization techniques, analytical methods and conceptual frameworks which have been employed by primatologists since as early as the 1960s. We also introduce some of the latest advances to SNA, thereby demonstrating that this approach contains novel tools for the study of nonhuman primate social behavior which may be used to shed light on questions that cannot be addressed fully using more conventional methods.

Equal graph partitioning on estimated infection network as an effective epidemic mitigation measure

Controlling severe outbreaks remains the most important problem in infectious disease area. With time, this problem will only become more severe as population density in urban centers grows. Social interactions play a very important role in determining how infectious diseases spread, and organization of people along social lines gives rise to non-spatial networks in which the infections spread. Infection networks are different for diseases with different transmission modes, but are likely to be identical or highly similar for diseases that spread the same way. Hence, infection networks estimated from common infections can be useful to contain epidemics of a more severe disease with the same transmission mode. Here we present a proof-of-concept study demonstrating the effectiveness of epidemic mitigation based on such estimated infection networks. We first generate artificial social networks of different sizes and average degrees, but with roughly the same clustering characteristic. We then start SIR epidemics on these networks, censor the simulated incidences, and use them to reconstruct the infection network. We then efficiently fragment the estimated network by removing the smallest number of nodes identified by a graph partitioning algorithm. Finally, we demonstrate the effectiveness of this targeted strategy, by comparing it against traditional untargeted strategies, in slowing down and reducing the size of advancing epidemics.

Network Sampling and Classification:An Investigation of Network Model Representations

Methods for generating a random sample of networks with desired properties are important tools for the analysis of social, biological, and information networks. Algorithm-based approaches to sampling networks have received a great deal of attention in recent literature. Most of these algorithms are based on simple intuitions that associate the full features of connectivity patterns with specific values of only one or two network metrics. Substantive conclusions are crucially dependent on this association holding true. However, the extent to which this simple intuition holds true is not yet known. In this paper, we examine the association between the connectivity patterns that a network sampling algorithm aims to generate and the connectivity patterns of the generated networks, measured by an existing set of popular network metrics. We find that different network sampling algorithms can yield networks with similar connectivity patterns. We also find that the alternative algorithms for the same connectivity pattern can yield networks with different connectivity patterns. We argue that conclusions based on simulated network studies must focus on the full features of the connectivity patterns of a network instead of on the limited set of network metrics for a specific network type. This fact has important implications for network data analysis: for instance, implications related to the way significance is currently assessed.

Network-based scoring system for genome-scale metabolic reconstructions

Background

Network reconstructions at the cell level are a major development in Systems Biology. However, we are far from fully exploiting its potentialities. Often, the incremental complexity of the pursued systems overrides experimental capabilities, or increasingly sophisticated protocols are underutilized to merely refine confidence levels of already established interactions. For metabolic networks, the currently employed confidence scoring system rates reactions discretely according to nested categories of experimental evidence or model-based likelihood.

Results

Here, we propose a complementary network-based scoring system that exploits the statistical regularities of a metabolic network as a bipartite graph. As an illustration, we apply it to the metabolism of Escherichia coli. The model is adjusted to the observations to derive connection probabilities between individual metabolite-reaction pairs and, after validation, to assess the reliability of each reaction in probabilistic terms. This network-based scoring system uncovers very specific reactions that could be functionally or evolutionary important, identifies prominent experimental targets, and enables further confirmation of modeling results.

Conclusions

We foresee a wide range of potential applications at different sub-cellular or supra-cellular levels of biological interactions given the natural bipartivity of many biological networks.

Using network properties to predict disease dynamics on human contact networks

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations.

Statistically validated networks in bipartite complex systems

Many complex systems present an intrinsic bipartite structure where elements of one set link to elements of the second set. In these complex systems, such as the system of actors and movies, elements of one set are qualitatively different than elements of the other set. The properties of these complex systems are typically investigated by constructing and analyzing a projected network on one of the two sets (for example the actor network or the movie network). Complex systems are often very heterogeneous in the number of relationships that the elements of one set establish with the elements of the other set, and this heterogeneity makes it very difficult to discriminate links of the projected network that are just reflecting system's heterogeneity from links relevant to unveil the properties of the system. Here we introduce an unsupervised method to statistically validate each link of a projected network against a null hypothesis that takes into account system heterogeneity. We apply the method to a biological, an economic and a social complex system. The method we propose is able to detect network structures which are very informative about the organization and specialization of the investigated systems, and identifies those relationships between elements of the projected network that cannot be explained simply by system heterogeneity. We also show that our method applies to bipartite systems in which different relationships might have different qualitative nature, generating statistically validated networks in which such difference is preserved.

Methods for generating complex networks with selected structural properties for simulations: a review and tutorial for neuroscientists

Many simulations of networks in computational neuroscience assume completely homogenous random networks of the Erdös–Rényi type, or regular networks, despite it being recognized for some time that anatomical brain networks are more complex in their connectivity and can, for example, exhibit the “scale-free” and “small-world” properties. We review the most well known algorithms for constructing networks with given non-homogeneous statistical properties and provide simple pseudo-code for reproducing such networks in software simulations. We also review some useful mathematical results and approximations associated with the statistics that describe these network models, including degree distribution, average path length, and clustering coefficient. We demonstrate how such results can be used as partial verification and validation of implementations. Finally, we discuss a sometimes overlooked modeling choice that can be crucially important for the properties of simulated networks: that of network directedness. The most well known network algorithms produce undirected networks, and we emphasize this point by highlighting how simple adaptations can instead produce directed networks.

Poisson Approximation of the Number of Cliques in Random Intersection Graphs

A random intersection graphG(n,m,p) is defined on a setVofnvertices. There is an auxiliary setWconsisting ofmobjects, and each vertexv∈Vis assigned a random subset of objectsWv⊆Wsuch thatw∈Wvwith probabilityp, independently for allv∈Vand allw∈W. Given two verticesv1,v2∈V, we setv1∼v2if and only ifWv1∩Wv2≠ ∅. We use Stein's method to obtain an upper bound on the total variation distance between the distribution of the number ofh-cliques inG(n,m,p) and a related Poisson distribution for any fixed integerh.

Modeling Ideational Creativity in Groups: Connecting Cognitive, Neural, and Computational Approaches

Many creative activities take place in a group context, whether in short-term meetings, work teams, or by means of electronic interaction. The group creative process necessarily involves the exchange of ideas or information. Recent models of group creativity have focused on the cognitive underpinnings of this type of group creative process, primarily based on the group brainstorming literature. The authors describe an elaborated computational version of their cognitive model of group creativity and related computational models, and highlight some plausible neural bases for various involved processes. The major findings and theoretical perspectives in this literature are summarized and some potentially fruitful empirical and theoretical directions are highlighted. It is hoped that this comprehensive treatment can be a basis for integrating the present literature and providing useful predictions for further research on this topic.

Bending of the "9+2" axoneme analyzed by the finite element method

Many data demonstrate that the regulation of the bending polarity of the "9+2" axoneme is supported by the curvature itself, making the internal constraints central in this process, adjusting either the physical characteristics of the machinery or the activity of the enzymes involved in different pathways. Among them, the very integrated Geometric Clutch model founds this regulation on the convenient adjustments of the probability of interaction between the dynein arms and the beta-tubulin monomers of the outer doublet pairs on which they walk. Taking into consideration (i) the deviated bending of the outer doublets pairs (Cibert, C., Heck, J.-V., 2004. Cell Motil. Cytoskeleton 59, 153-168), (ii) the internal tensions of the radial spokes and the tangential links (nexin links, dynein arms), (iii) a theoretical 5 microm long proximal segment of the axoneme and (iv) the short proximal segment of the axoneme, we have reevaluated the adjustments of these intervals using a finite element approach. The movements we have calculated within the axonemal cylinder are consistent with the basic hypothesis that found the Geometric Clutch model, except that the axonemal side where the dynein arms are active increases the intervals between the two neighbor outer doublet pairs. This result allows us to propose a mechanism of bending reversion of the axoneme, involving the concerted ignition of the molecular engines along the two opposite sides of the axoneme delineated by the bending plane.

Emergence of heterogeneity and political organization in information exchange networks

We present a simple model of the emergence of the division of labor and the development of a system of resource subsidy from an agent-based model of directed resource production with variable degrees of trust between the agents. The model has three distinct phases corresponding to different forms of societal organization: disconnected (independent agents), homogeneous cooperative (collective state), and inhomogeneous cooperative (collective state with a leader). Our results indicate that such levels of organization arise generically as a collective effect from interacting agent dynamics and may have applications in a variety of systems including social insects and microbial communities.

When metabolism meets topology: Reconciling metabolite and reaction networks

The search for a systems-level picture of metabolism as a web of molecular interactions provides a paradigmatic example of how the methods used to characterize a system can bias the interpretation of its functional meaning. Metabolic maps have been analyzed using novel techniques from network theory, revealing some non-trivial, functionally relevant properties. These include a small-world structure and hierarchical modularity. However, as discussed here, some of these properties might actually result from an inappropriate way of defining network interactions. Starting from the so-called bipartite organization of metabolism, where the two meaningful subsets (reactions and metabolites) are considered, most current works use only one of the subsets by means of so-called graph projections. Unfortunately, projected graphs often ignore relevant biological and chemical constraints, thus leading to statistical artifacts. Some of these drawbacks and alternative approaches need to be properly addressed.

Hamiltonian approach for explosive percolation

We present a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by D. Achlioptas [Science 323, 1453 (2009)]. We show that the following two ingredients are sufficient for obtaining an abrupt (first-order) transition in the fraction of the system occupied by the largest cluster: (i) the size of all growing clusters should be kept approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds connecting vertices in different clusters) should dominate with respect to the redundant bonds (i.e., bonds connecting vertices in the same cluster). Moreover, in the extreme limit where only merging bonds are present, a complete enumeration scheme based on treelike graphs can be used to obtain an exact solution of our model that displays a first-order transition. Finally, the presented mechanism can be viewed as a generalization of standard percolation that discloses a family of models with potential application in growth and fragmentation processes of real network systems.