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.

Social networks and occupational choice: the endogenous formation of attitudes and beliefs about tax compliance

The paper analyses the emergence of group-specific attitudes and beliefs about tax compliance when individuals interact in a social network. It develops a model in which taxpayers possess a range of individual characteristics – including attitude to risk, potential for success in self-employment, and the weight attached to the social custom for honesty – and make an occupational choice based on these characteristics. Occupations differ in the possibility for evading tax. The social network determines which taxpayers are linked, and information about auditing and compliance is transmitted at meetings between linked taxpayers. Using agent-based simulations, the analysis demonstrates how attitudes and beliefs endogenously emerge that differ across sub-groups of the population. Compliance behaviour is different across occupational groups, and this is reinforced by the development of group-specific attitudes and beliefs. Taxpayers self-select into occupations according to the degree of risk aversion, the subjective probability of audit is sustained above the objective probability, and the weight attached to the social custom differs across occupations. These factors combine to lead to compliance levels that differ across occupations.

Interpretation bias in preschool children at risk for anxiety: a prospective study

A story-stem paradigm was used to assess interpretation bias in preschool children. Data were available for 131 children. Interpretation bias, behavioural inhibition (BI) and anxiety were assessed when children were aged between 3 years 2 months and 4 years 5 months. Anxiety was subsequently assessed 12-months, 2-years and 5-years later. A significant difference in interpretation bias was found between participants who met criteria for an anxiety diagnosis at baseline, with clinically anxious participants more likely to complete the ambiguous story-stems in a threat-related way. Threat interpretations significantly predicted anxiety symptoms at 12-month follow-up, after controlling for baseline symptoms, but did not predict anxiety symptoms or diagnoses at either 2-year or 5- year follow-up. There was little evidence for a relationship between BI and interpretation bias. Overall, the pattern of results was not consistent with the hypothesis that interpretation bias plays a role in the development of anxiety. Instead, some evidence for a role in the maintenance of anxiety over relatively short periods of time was found. The use of a story-stem methodology to assess interpretation bias in young children is discussed along with the theoretical and clinical implications of the findings.

Temperament, family environment and anxiety in preschool children

This research examines the relationship between behavioural inhibition (BI), family environment (overinvolved and negative parenting, parental anxiety and parent-child attachment) and anxiety in a sample of 202 preschool children. Participants were aged between 3 years 2 months and 4 years 5 months, 101 were male. A thorough methodology was used that incorporated data from multiple observations of behaviour, diagnostic interviews and questionnaire measures. The results showed that children categorised as behaviourally inhibited were significantly more likely to meet criteria for a range of anxiety diagnoses. Furthermore, a wide range of family environment factors, including maternal anxiety, parenting and attachment were significantly associated with BI, with inhibited children more likely to experience adverse family environment factors. No interactions between temperament and family environment were found for child anxiety. However, a significant relationship between current maternal anxiety and child anxiety was found consistently even after controlling for BI. Additionally, there was some evidence of a relationship between maternal negativity and child anxiety, after controlling for BI. The results may suggest that temperament and family environment operate as additive, rather than interactive risk factors for child anxiety. This is discussed in the context of theoretical models of child anxiety and directions for future research.

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.

Shared cognition in childhood anxiety: interpretation bias in preschool children and their parents

Although interpretation bias has been associated with the development and/or maintenance of childhood anxiety, its origins remain unclear. The present study is the first to examine intergenerational transmission of this bias from parents to their preschool-aged children via the verbal information pathway. A community sample of fifty parent–child pairs was recruited. Parents completed measures of their own trait anxiety and interpretation bias, their child’s anxiety symptoms, and a written story-stem measure, to capture the way parents tell their children stories. Interpretation bias was assessed in preschool-aged children (aged between 2 years 7 months and 5 years 8 months) using an extended story-stem paradigm. Young children’s interpretation bias was not significantly associated with their own anxiety symptoms. Neither was there evidence for a significant association between parent and child interpretation bias. However, parents who reported they would tell their child one or more threatening story endings in the written story-stem task had significantly higher anxiety than those who did not include any threatening story endings. In turn, children whose parents did not include any threatening endings in their written stories had significantly lower threat interpretations on the child story-stem paradigm, compared to those with parents who included at least one threatening story ending. The results suggest that parental verbal information could play a role in the development of interpretation bias in young children.

Risk-taking and inhibitory control in behaviourally inhibited and disinhibited preschool children

The temperament style Behavioural Inhibition (BI) has been implicated as a risk factor for the development of internalising disorders such as anxiety. Of interest is what factors influence the developmental trajectories of both inhibited and disinhibited children and the development of psychopathology. One such factor is risk-taking behaviour. Using the computer based Balloon Analogue Risk Task, we assessed risk taking behaviour in behaviourally inhibited (n = 27) and behaviourally disinhibited (n = 43) children. This is the first study to examine the relationship between BI, executive functioning and risk-taking. The results indicated Behavioural Inhibition was not related to risk-taking but that inhibitory control predicted reward focused results. These findings illustrate how inhibitory control affects risk-taking and risk avoidance in both inhibited and disinhibited children.

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.

Vitamin A deficiency in preschool children of Recife, Northeast of Brazil

Vitamin A deficiency in preschool children of Recife, Northeast of Brazil. The purpose of the study was to evaluate the extent of vitamin A deficiency (VAD) among preschool children in the city of Recife, Northeast Brazil. The sample comprised 344 children of both sexes, 24 to 60 months old, in 18 public day care centres in the city of Recife, in 2007. The nutritional status of vitamin A was assessed by biochemical (serum retinol) and dietetic (vitamin A rich-food consumption) indicators and the pondo-stature status through anthropometric indicators weight-for-age, height-for-age and weight-for-height. The prevalence of hyporetinolemia (<0.70 mu mol / L) was 7.7% (IC95% 4.88 - 11.81), which characterizes the VAD as a light-type public health problem, according to World Health Organization criteria. On the other hand, 29.6% (IC95% 24.22 - 35.63) of children had acceptable or marginal levels (0.70 to 1.04 mu mol/L) of retinol. Regarding the vitamin A rich-food intake, values below the EAR (Estimated Average Requirement) - 210 mu g/day for children of 1 to 3 years old and 275 mu g/day for children of 4 to 8 years old - were 8.1% and 21.3% respectively. The prevalence of anthropometrical deficits (<-2 scores -Z) in preschool children were 2.5% for the indicator weight-for-age, 8.6% for height-for-age and 1.5% for weight-for-height. The research findings point out to the importance of institutionalization for the appropriate nutritional status of children and maintenance of adequate reserves of vitamin A. However, more studies are needed focusing on non-institutionalized preschool, or children living outside the privileged environment of public day care centres.

Fortified food made by the extrusion of a mixture of chickpea, corn and bovine lung controls iron-deficiency anaemia in preschool children

A fortified food that was rich in protein, vitamins and iron made of chickpea, bovine lung and corn was developed with the aim of controlling iron-deficiency anaemia in children from poorer areas. It was tested in Teresina, State of Piaui, Northeastern Brazil, on a population with high anaemia prevalence. Two local daycare units with similar characteristics were selected and the children at one of them received a 30 g pack three times a week, representing a total iron daily intake of 6.96 mg. The other daycare unit was followed as a control. The capillary haemoglobin concentration was determined for the children at both daycare units, at the beginning of the study and after a two-month intervention period. The mean haemoglobin concentration in the test group at the beginning of the intervention was 11.8 g/dL, which increased to 13.1 g/dL at the end of the intervention. In the control group these figures remained practically constant (11.6-11.8 g/dL). These represented a dramatic and significant drop in anaemia prevalence, from 61.5% to 11.5% in the test group, and an insignificant reduction (63.1-57.7%) in the control group. The acceptance of the fortified snack was excellent and no undesirable effects were observed. (C) 2007 Published by Elsevier Ltd.

Motivations for knowledge sharing in virtual social networks: a comparative study between Brazil and France

Sociedades pós-modernas caracterizam-se pela transição de economias baseadas em ativos tangíveis para economias de conhecimento, onde indivíduos vivenciam uma imprescindível conectividade, mas ao mesmo tempo, experimentam um enfraquecimento das estruturas sociais, que tem generado uma crescente necessidade de se criar bases cognitivas e afetivas para a vida (Rheingold, 1992; Wasko & Farah, 2005; Arvidsson, 2008). Nesse cenário se desenvolve o fenômeno das redes sociais virtuais, agregando milhões de pessoas que compartilham mensagens de texto, imagens e vídeos todos os dias (Nielsen, 2012) fazendo com que organizações privadas foquem cada vez mais seus investimentos para acompanhar as novas tendências (McWilliam, 2000; Reichheld & Schefter, 2000; Yoo, Suh & Lee, 2002; Arvidsson, 2008). Consequentemente, uma das mais importantes questões que vem ganhando importância no meio academico e entre profissionais da área é justamente: por que as pessoas compartilham conhecimento online? (Monge, Fulk, Kalman, Flanigan, Parnassa & Rumsey, 1998; Lin, 2001) Por meio de uma metodologia de estudo de caso conduzida no Brasil e na França, este estudo objetiva produzir uma relevante revisão teórica acerca do tema, trazendo novas idéias de diferentes contextos, e propondo um modelo para avaliar as principais motivações que conduzem indivíduos a compartilhar conhecimento em redes sociais virtuais. Essas razões foram estruturadas em cinco dimensões: capital estrutural, cognitivo e relacional, motivações pessoais e razões monetárias (Nahapiet & Ghoshal, 1998; Wasko & Faraj, 2005; Chiu et al, 2006). As evidências sugerem que o processo de participar e compartilhar conhecimento em redes sociais virtuais é resultado de uma complexa combinação de motivações de orientação pessoal e coletiva, que parecem variar pouco de acordo com os diferentes objetivos e contextos dessas comunidades, onde as razões financeiras parecem ser secundárias.