Weighted alpha-rate dominating sets in social networks

We are looking into variants of a domination set problem in social networks. While randomised algorithms for solving the minimum weighted domination set problem and the minimum alpha and alpha-rate domination problem on simple graphs are already present in the literature, we propose here a randomised algorithm for the minimum weighted alpha-rate domination set problem which is, to the best of our knowledge, the first such algorithm. A theoretical approximation bound based on a simple randomised rounding technique is given. The algorithm is implemented in Python and applied to a UK Twitter mentions networks using a measure of individuals’ influence (klout) as weights. We argue that the weights of vertices could be interpreted as the costs of getting those individuals on board for a campaign or a behaviour change intervention. The minimum weighted alpha-rate dominating set problem can therefore be seen as finding a set that minimises the total cost and each individual in a network has at least alpha percentage of its neighbours in the chosen set. We also test our algorithm on generated graphs with several thousand vertices and edges. Our results on this real-life Twitter networks and generated graphs show that the implementation is reasonably efficient and thus can be used for real-life applications when creating social network based interventions, designing social media campaigns and potentially improving users’ social media experience.

Social networks, migration, and care in Tanzania

This paper explores the impacts of the HIV/AIDS epidemic on children and families in northern Tanzania using the concept of social resilience.1 The study is based on the findings of childfocused research with street children and children and families from HIV/AIDS-affected households. The paper illustrates the coping strategies that children and young people, and parents and caregivers adopt at the household level. In particular, it examines how the burden of care affects different generations of women and highlights their resilience, together with the importance of social networks and the fluidity of movement between rural and urban areas. The research suggests that migrating to urban areas to seek a living in the informal sector represents a survival strategy adopted by some children and young people orphaned by AIDS when their families and communities are unable or unwilling to support them. The paper concludes by exploring parents’, caregivers’, children’s, and young people’s views on the forms of social support that would promote their resilience and thereby help to mitigate the impacts of the epidemic at the household level.

Using learning networks to understand complex systems: a case study of biological, geophysical and social research in the Amazon

Developing high-quality scientific research will be most effective if research communities with diverse skills and interests are able to share information and knowledge, are aware of the major challenges across disciplines, and can exploit economies of scale to provide robust answers and better inform policy. We evaluate opportunities and challenges facing the development of a more interactive research environment by developing an interdisciplinary synthesis of research on a single geographic region. We focus on the Amazon as it is of enormous regional and global environmental importance and faces a highly uncertain future. To take stock of existing knowledge and provide a framework for analysis we present a set of mini-reviews from fourteen different areas of research, encompassing taxonomy, biodiversity, biogeography, vegetation dynamics, landscape ecology, earth-atmosphere interactions, ecosystem processes, fire, deforestation dynamics, hydrology, hunting, conservation planning, livelihoods, and payments for ecosystem services. Each review highlights the current state of knowledge and identifies research priorities, including major challenges and opportunities. We show that while substantial progress is being made across many areas of scientific research, our understanding of specific issues is often dependent on knowledge from other disciplines. Accelerating the acquisition of reliable and contextualized knowledge about the fate of complex pristine and modified ecosystems is partly dependent on our ability to exploit economies of scale in shared resources and technical expertise, recognise and make explicit interconnections and feedbacks among sub-disciplines, increase the temporal and spatial scale of existing studies, and improve the dissemination of scientific findings to policy makers and society at large. Enhancing interaction among research efforts is vital if we are to make the most of limited funds and overcome the challenges posed by addressing large-scale interdisciplinary questions. Bringing together a diverse scientific community with a single geographic focus can help increase awareness of research questions both within and among disciplines, and reveal the opportunities that may exist for advancing acquisition of reliable knowledge. This approach could be useful for a variety of globally important scientific questions.

Interventions in social networks: impact on mood and network dynamics

Results from two studies on longitudinal friendship networks are presented, exploring the impact of a gratitude intervention on positive and negative affect dynamics in a social network. The gratitude intervention had been previously shown to increase positive affect and decrease negative affect in an individual but dynamic group effects have not been considered. In the first study the intervention was administered to the whole network. In the second study two social networks are considered and in each only a subset of individuals, initially low/high in negative affect respectively received the intervention as `agents of change'. Data was analyzed using stochastic actor based modelling techniques to identify resulting network changes, impact on positive and negative affect and potential contagion of mood within the group. The first study found a group level increase in positive and a decrease in negative affect. Homophily was detected with regard to positive and negative affect but no evidence of contagion was found. The network itself became more volatile along with a fall in rate of change of negative affect. Centrality measures indicated that the best broadcasters were the individuals with the least negative affect levels at the beginning of the study. In the second study, the positive and negative affect levels for the whole group depended on the initial levels of negative affect of the intervention recipients. There was evidence of positive affect contagion in the group where intervention recipients had low initial level of negative affect and contagion in negative affect for the group where recipients had initially high level of negative affect.

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

Inclusion, social networks and resilience: strategies, practices and outcomes for disabled children and their families

This paper explores the strategies of service providers and the benefits reported by disabled children and their parents/carers in three Children's Fund programmes in England. Based on National Evaluation of the Children's Fund research, we discuss how different understandings of ‘inclusion’ informed the diverse strategies and approaches service providers adopted. While disabled children and families perceived the benefits of services predominantly in terms of building individual children's resilience and social networks, the paper highlights the need for holistic approaches which have a broad view of inclusion, support children's networks and tackle disabling barriers within all the spheres of children's lives.

Dynamics of brand competition: Effects of unobserved social networks

Brand competition is modelled using an agent based approach in order to examine the long run dynamics of market structure and brand characteristics. A repeated game is designed where myopic firms choose strategies based on beliefs about their rivals and consumers. Consumers are heterogeneous and can observe neighbour behaviour through social networks. Although firms do not observe them, the social networks have a significant impact on the emerging market structure. Presence of networks tends to polarize market share and leads to higher volatility in brands. Yet convergence in brand characteristics usually happens whenever the market reaches a steady state. Scale-free networks accentuate the polarization and volatility more than small world or random networks. Unilateral innovations are less frequent under social networks.

Facebook faith - social networking in a faith based community

This paper views the increasing social networking as an efficient emerging ministry to the moveable generation. Through social network such as Facebook, ministry from a pastoral perspective can become more authentic and meaningful. Ministry is relational. Social Networking sites provide a strong platform to being part in other people’s life. Social networking and living online builds community beyond geographical boarders. Young adults and youths digital identity often reflects their faith, this is supported by research which suggests a practice of more openness to share and expose private issues online. Spiritual and religious views are freely shared, creating sacred spaces in the midst of life practising a holistic faith identity in a secular community. Providing a strong platform for information flow, Social Network is attractive in a postmodern society where inviting people to join in events are perceived as non threatening, making church community events transparent and available to people who do not attend church, inviting spiritual friendships and relationships. Social Networking strengthens relationship in a non hierarchical manner and invites the minister into lives where there previously would have been barriers, engaging in prayer and bible study as well as pastoral care through social networking, thus relationships deepens via social networking making people real. It has been observed that, although community building happens on the net, church affiliation loyalty remains to the local community. Therefore presence ministry though social networks emerges as a core form of ministry, where relations to youth who move from local church to university campuses are kept alive. The asynchronous nature of communication within social networking eases the minister in her work. The minister is able to engage with many individuals at the same time. Before the minister could visit one person at a time, now she visits 5-6 individuals at any given time. Therefore social networking not only increases the quality of the work, but also empowers the minister to be more efficient.

Social networks and positive and negative affect

We followed 100 university students in the UK for one week, instructing them to record all face-to-face, phone and digital contacts during the day as well as their positive and negative affect. We wanted to see how positive and negative affect spread around a social network while taking into account participants’ socio-demographic data, personality, general health and gratitude scores. We focused on the participants’ connections with those in their class; excluding friends and family outside this group. The data was analysed using actor-based models implemented in SIENA. Results show differences between positive and negative affect dynamics in this environment and an influence of personality traits on the average number and rate of communication.

Sustainable horticultural supply chain: the case of local food networks in the United Kingdom

In the UK there is widespread support from Government, media and consumers for local food networks. These have the potential to provide a more sustainable supply chain and are well suited to the unique production and consumption characteristics of horticultural products. In terms of food marketing, local food is in its relative infancy and is still without any formal definition. This lack of clarity hampers research activities. Although the profile of local food buyers and their expectations has been explored, our knowledge of its social, economic and environmental aspects is minimal. This research contributes by exploring the structure and scope of local food activities in the UK in terms of profiling those specialised retail outlets who provide consumers with the opportunity to purchase locally grown horticultural products.

Technological change and the challenges for regional development: building social capital in less-favoured regions

The relevance of regional policy for less favoured regions (LFRs) reveals itself when policy-makers must reconcile competitiveness with social cohesion through the adaptation of competition or innovation policies. The vast literature in this area generally builds on an overarching concept of ‘social capital’ as the necessary relational infrastructure for collective action diversification and policy integration, in a context much influenced by a dynamic of industrial change and a necessary balance between the creation and diffusion of ‘knowledge’ through learning. This relational infrastructure or ‘social capital’ is centred on people’s willingness to cooperate and ‘envision’ futures as a result of “social organization, such as networks, norms and trust that facilitate action and cooperation for mutual benefit” (Putnam, 1993: 35). Advocates of this interpretation of ‘social capital’ have adopted the ‘new growth’ thinking behind ‘systems of innovation’ and ‘competence building’, arguing that networks have the potential to make both public administration and markets more effective as well as ‘learning’ trajectories more inclusive of the development of society as a whole. This essay aims to better understand the role of ‘social capital’ in the production and reproduction of uneven regional development patterns, and to critically assess the limits of a ‘systems concept’ and an institution-centred approach to comparative studies of regional innovation. These aims are discussed in light of the following two assertions: i) learning behaviour, from an economic point of view, has its determinants, and ii) the positive economic outcomes of ‘social capital’ cannot be taken as a given. It is suggested that an agent-centred approach to comparative research best addresses the ‘learning’ determinants and the consequences of social networks on regional development patterns. A brief discussion of the current debate on innovation surveys has been provided to illustrate this point.

Social networks: evolving graphs with memory dependent edges

The plethora, and mass take up, of digital communication tech- nologies has resulted in a wealth of interest in social network data collection and analysis in recent years. Within many such networks the interactions are transient: thus those networks evolve over time. In this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges, which may appear and disappear according to their recent history. We consider time discrete and time continuous variants of the model. We consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence. In particular we show that such networks may continue evolving forever, or else may quench and become static (containing immortal and/or extinct edges). This depends on the ex- istence or otherwise of certain infinite products and series involving age dependent model parameters. To test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data, and we apply these concepts to three real networks: summary data on mobile phone use from a developing region; online social-business network data from China; and disaggregated mobile phone communications data from a reality mining experiment in the US. In each case we show that there is evidence for memory dependent dynamics, such as that embodied within the class of models proposed here.

Evolving social networks, attitudes and beliefs and counter terrorism

'The Princeton Companion to Applied Mathematics' is an introduction to applied mathematics for students, teachers, and professionals. This article is for the "Application Areas" part of the book, which comprises articles on connections between applied mathematics and other disciplines.

Bayesian parameter estimation for latent Markov random fields and social networks

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalising constant. This problem has received much attention, but very little of this has focussed on the important practical case where the data consists of noisy or incomplete observations of the underlying hidden structure. This paper specifically addresses this problem, comparing two alternative methodologies. In the first of these approaches particle Markov chain Monte Carlo (Andrieu et al., 2010) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray et al., 2006) for avoiding the calculation of the intractable normalising constant (a proof showing that this combination targets the correct distribution in found in a supplementary appendix online). This approach is compared with approximate Bayesian computation (Pritchard et al., 1999). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the paper targets an approximation to the true posterior due to the use of MCMC to simulate from the latent graphical model, in lieu of being able to do this exactly in general. The supplementary appendix also describes the nature of the resulting approximation.