Bayesian model-based clustering for multiple network data

There is increasing appetite for analysing multiple network data. This is different to analysing traditional data sets, where now each observation in the data comprises a network. Recent technological advancements have allowed the collection of this type of data in a range of different applications. This has inspired researchers to develop statistical models that most accurately describe the probabilistic mechanism that generates a network population and use this to make inferences about the underlying structure of the network data. Only a few studies developed to date consider the heterogeneity that can exist in a network population. We propose a Mixture of Measurement Error Models for identifying clusters of networks in a network population, with respect to similarities detected in the connectivity patterns among the networks' nodes. Extensive simulation studies show our model performs well in both clustering multiple network data and inferring the model parameters. We further apply our model on two real world multiple network data sets resulting from the fields of Computing (Human Tracking Systems) and Neuroscience

Bayesian Modelling and Inference for Multiple Network Data

There is a growing need for analysing network data due to their prevalence in applications arising from various scientific fields. A broad literature has been developed for the statistical analysis of networks as single observations, while the formulation of statistical frameworks for modelling multiple network data has only recently been considered by researchers. This thesis contributes to the statistical analysis of multiple network data sets, where now each observation in the data comprises a network rather than a scalar quantity. Our first contribution is the development of a Bayesian model-based approach for clustering multiple network data with respect to similarities detected in the connectivity patterns among the networks' nodes. Our model-based approach allows us to interpret the clusters with respect to a parameterisation, notably, through a network representative for each cluster. Our framework can also be formulated to detect networks in a population that are different from a majority group of networks. Extensive simulation studies show our model performs well in both clustering multiple network data and inferring the model parameters. We further apply our model on two real-world multiple network data sets resulting from the fields of Computing (Human Tracking Systems) and Neuroscience. Our second contribution is twofold. First, we introduce a new network distance metric that measures dissimilarities between networks with respect to their cycles, motivated by an ecological application. Second, we propose a new Markov Chain Monte Carlo (MCMC) scheme for inferring the parameters of the intractable Spherical Network Family (SNF) model for multiple network data. Specifically, we introduce an Importance Sampling (IS) step within a Metropolis-Hastings (MH) algorithm that allows the approximation of the intractable normalising constant of the SNF model within the MH ratio. We explore the behaviour of the newly proposed distance metric and the performance of our MCMC scheme through simulation studies, and apply our algorithm on a real-world ecological application

The GNAR-edge model: a network autoregressive model for networks with time-varying edge weights

In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications, such complex systems can be associated with some underlying network describing pairwise relationships among the quantities. Accounting for the underlying network structure for the analysis of this type of multivariate time series is required for assessing estimation error and can be particularly informative for forecasting. Our work is motivated by a dataset consisting of time series of industry-to-industry transactions. In this example, pairwise relationships between Standard Industrial Classification (SIC) codes can be represented using a network, with SIC codes as nodes and pairwise transactions between SIC codes as edges, while the observed time series of the amounts of the transactions for each pair of SIC codes can be regarded as time-varying weights on the edges. Inspired by Knight et al. (2020, J. Stat. Softw., 96, 1–36), we introduce the GNAR-edge model which allows modelling of multiple time series utilizing the network structure, assuming that each edge weight depends not only on its past values, but also on past values of its neighbouring edges, for a range of neighbourhood stages. The method is validated through simulations. Results from the implementation of the GNAR-edge model on the real industry-to-industry data show good fitting and predictive performance of the model. The predictive performance is improved when sparsifying the network using a lead–lag analysis and thresholding edges according to a lead–lag score

The GNAR-edge model: A network autoregressive model for networks with time-varying edge weights

In economic and financial applications, there is often the need for analysing multivariate time series, comprising of time series for a range of quantities. In some applications such complex systems can be associated with some underlying network describing pairwise relationships among the quantities. Accounting for the underlying network structure for the analysis of this type of multivariate time series is required for assessing estimation error and can be particularly informative for forecasting. Our work is motivated by a dataset consisting of time series of industry-to-industry transactions. In this example, pairwise relationships between Standard Industrial Classification (SIC) codes can be represented using a network, with SIC codes as nodes and pairwise transactions between SIC codes as edges, while the observed time series of the amounts of the transactions for each pair of SIC codes can be regarded as time-varying weights on the edges. Inspired by Knight et al. (2020), we introduce the GNAR-edge model which allows modelling of multiple time series utilising the network structure, assuming that each edge weight depends not only on its past values, but also on past values of its neighbouring edges, for a range of neighbourhood stages. The method is validated through simulations. Results from the implementation of the GNAR-edge model on the real industry-to-industry data show good fitting and predictive performance of the model. The predictive performance is improved when sparsifying the network using a lead-lag analysis and thresholding edges according to a lead-lag score

Όψεις της μαθηματικής επίγνωσης σχετικά με την απόδειξη στην Άλγεβρα του Λυκείου

Στην παρούσα μελέτη διερευνάται η επίγνωση των μαθητών/τριών της Α΄ Λυκείου σχετικά με το ρόλο και τις λειτουργίες της απόδειξης στα μαθηματικά, όπως αυτή εμφανίζεται στο μάθημα της Άλγεβρας. Στόχος της έρευνας είναι να μελετηθεί το πώς αποτυπώνεται η επίγνωση για την απόδειξη, ποια η σχέση της με διαφορετικούς τύπους αποδείξεων και αποδεικτικών επιχειρημάτων και ποιες οι ποιοτικές διαφοροποιήσεις στην επίγνωση μαθητών και μαθητριών υψηλής επίδοσης στην απόδειξη. Επικεντρωνόμαστε στην επίγνωση των παιδιών για τις δικές τους γνώσεις για την αποδεικτική διαδικασία και προϊόν, καθώς και στην εφαρμογή αυτής της γνώσης στον έλεγχο αποδείξεων και αποδεικτικών διαδικασιών από τους ίδιους. Θα μελετηθούν οι αποφάσεις και οι πράξεις των παιδιών σε σχέση με τις ανάγκες και τους στόχους τους στην απόδειξη, ως εντοπισμός των ευρύτερων θεωρήσεων τους για τα μαθηματικά. Για την παραπάνω διερεύνηση πραγματοποιήθηκε εμπειρική έρευνα με μικτή μεθοδολογία που περιλάμβανε ένα ερωτηματολόγιο με οκτώ μέρη για τους μαθητές/τριες της Α΄ Λυκείου. Τα μέρη του ερωτηματολογίου εξέταζαν την αυτό-αποτελεσματικότητα (self-efficacy) των μαθητές/τριών για τα Μαθηματικά και την απόδειξη, τις απόψεις και στάσεις τους για τα Μαθηματικά και τη μαθηματική τους ταυτότητα. Σε συνδυασμό με τη συμπλήρωση του ερωτηματολογίου, πραγματοποιήθηκαν τρεις συνεντεύξεις σε επιλεγμένους μαθητές και μαθήτριες (βάσει εννοιακών και στατιστικών κριτηρίων) ώστε να ερμηνευτούν τα διαφορετικά χαρακτηριστικά τους συναρτήσει των δομικών συστατικών της επίγνωσης. Τα αποτελέσματα κατέδειξαν συγκλίσεις και αποκλίσεις με την υπάρχουσα βιβλιογραφία και αναδείχθηκε η πολυπλοκότητα της έννοιας της μαθηματικής επίγνωσης, που δε θα φαινόταν αν περιοριζόμασταν στη συλλογή ποσοτικών δεδομένων.In the present study the awareness of the students of the first grade of Lyceum is investigated, with regards to the role and functions of mathematical proof, as shown by the course of Algebra. The research aim is to study how awareness of proof is impressed, what’s the relationship between awareness and different types of proofs and proving arguments and what are the quantitative differences in the awareness of students with high performance. We focus on awareness of children about their own knowledge of proving process and proof as a product, as well in the application of this knowledge in regulation of proofs and proving processes by themselves. Decisions and actions of children will be studied in relation to the needs and goals of proof, as identification of the broader considerations about mathematics. For the above investigation empirical research was conducted, with mixed methodology included an eight-part questionnaire for students of the first grade of Lyceum. The parts of the questionnaire examined students’ mathematical self-efficacy, proof self-efficacy, their attitudes and values in mathematics and their mathematical identity. In conjunction with the completion of the questionnaire, three interviews were conducted, to selected students (based on conceptual and statistical criteria) to interpret the different characteristics of the function of the structural components of awareness. The results showed convergences and divergences with literature and highlighted the complexity of the concept of mathematical awareness, which it wouldn’t be appeared if we were limited to the collection of quantitative data

Expression of a hindlimb-determining factor Pitx1 in the forelimb of the lizard Pogona vitticeps during morphogenesis

With over 9000 species, squamates, which include lizards and snakes, are the largest group of reptiles and second-largest order of vertebrates, spanning a vast array of appendicular skeletal morphology. As such, they provide a promising system for examining developmental and molecular processes underlying limb morphology. Using the central bearded dragon (Pogona vitticeps) as the primary study model, we examined limb morphometry throughout embryonic development and characterized the expression of three known developmental genes (GHR, Pitx1 and Shh) from early embryonic stage through to hatchling stage via reverse transcription quantitative polymerase chain reaction (RT-qPCR) and immunohistochemistry (IHC). In this study, all genes were found to be transcribed in both the forelimbs and hindlimbs of P. vitticeps. While the highest level of GHR expression occurred at the hatchling stage, Pitx1 and Shh expression was greatest earlier during embryogenesis, which coincides with the onset of the differentiation between forelimb and hindlimb length. We compared our finding of Pitx1 expression-a hindlimb-determining gene-in the forelimbs of P. vitticeps to that in a closely related Australian agamid lizard, Ctenophorus pictus, where we found Pitx1 expression to be more highly expressed in the hindlimb compared with the forelimb during early and late morphogenesis-a result consistent with that found across other tetrapods. Expression of Pitx1 in forelimbs has only rarely been documented, including via in situ hybridization in a chicken and a frog. Our findings from both RT-qPCR and IHC indicate that further research across a wider range of tetrapods is needed to more fully understand evolutionary variation in molecular processes underlying limb morphology.Jane Melville, Sumitha Hunjan, Felicity McLean, Georgia Mantziou, Katja Boysen and Laura J. Parr

Predictors of Childhood Exposure to Parental Secondhand Smoke in the House and Family Car

Childhood exposure to secondhand smoke (SHS) is a serious threat to public health and can be influenced by parental lifestyle habits and beliefs. Taking the above into account we aimed at locating predictors of parental induced exposure to SHS in the house and family car among 614 children who visited the emergency department of two large pediatric hospitals in Athens, Greece. The multivariate analysis revealed that the factors found to mediate household exposure to paternal SHS were the number of cigarettes smoked per day (O.R 1.13, p<0.001) while, having a non-smoking spouse had a protective effect (O.R 0.44, p=0.026). Maternally induced household SHS exposure was related to cigarette consumption. For both parents, child exposure to SHS in the family car was related to higher numbers of cigarettes smoked (p<0.001), and for fathers was also more often found in larger families. Additionally, lower educated fathers were more likely to have a spouse that exposes their children to SHS inside the family car (O.R 1.38 95%C.I: 1.04–1.84, p=0.026). Conclusively, efforts must be made to educate parents on the effects of home and household car exposure to SHS, where smoke free legislation may be difficult to apply

Predictors of children's secondhand smoke exposure at home: a systematic review and narrative synthesis of the evidence

BACKGROUND: Children's exposure to secondhand smoke (SHS) has been causally linked to a number of childhood morbidities and mortalities. Over 50% of UK children whose parents are smokers are regularly exposed to SHS at home. No previous review has identified the factors associated with children's SHS exposure in the home. AIM: To identify by systematic review, the factors which are associated with children's SHS exposure in the home, determined by parent or child reports and/or biochemically validated measures including cotinine, carbon monoxide or home air particulate matter. METHODS: Electronic searches of MEDLINE, EMBASE, PsychINFO, CINAHL and Web of Knowledge to July 2014, and hand searches of reference lists from publications included in the review were conducted. FINDINGS: Forty one studies were included in the review. Parental smoking, low socioeconomic status and being less educated were all frequently and consistently found to be independently associated with children's SHS exposure in the home. Children whose parents held more negative attitudes towards SHS were less likely to be exposed. Associations were strongest for parental cigarette smoking status; compared to children of non-smokers, those whose mothers or both parents smoked were between two and 13 times more likely to be exposed to SHS. CONCLUSION: Multiple factors are associated with child SHS exposure in the home; the best way to reduce child SHS exposure in the home is for smoking parents to quit. If parents are unable or unwilling to stop smoking, they should instigate smoke-free homes. Interventions targeted towards the socially disadvantaged parents aiming to change attitudes to smoking in the presence of children and providing practical support to help parents smoke outside the home may be beneficial