On analysis of complex network dynamics – changes in local topology

Social networks created based on data gathered in various computer systems are structures that constantly evolve. The nodes and their connections change because they are influenced by the external to the network events.. In this work we present a new approach to the description and quantification of patterns of complex dynamic social networks illustrated with the data from the Wroclaw University of Technology email dataset. We propose an approach based on discovery of local network connection patterns (in this case triads of nodes) as well as we measure and analyse their transitions during network evolution. We define the Triad Transition Matrix (TTM) containing the probabilities of transitions between triads, after that we show how it can help to discover the dynamic patterns of network evolution. One of the main issues when investigating the dynamical process is the selection of the time window size. Thus, the goal of this paper is also to investigate how the size of time window influences the shape of TTM and how the dynamics of triad number change depending on the window size. We have shown that, however the link stability in the network is low, the dynamic network evolution pattern expressed by the TTMs is relatively stable, and thus forming a background for fine-grained classification of complex networks dynamics. Our results open also vast possibilities of link and structure prediction of dynamic networks. The future research and applications stemming from our approach are also proposed and discussed

Foundations and modelling of dynamic networks using Dynamic Graph Neural Networks: A survey

Dynamic networks are used in a wide range of fields, including social network analysis, recommender systems, and epidemiology. Representing complex networks as structures changing over time allow network models to leverage not only structural but also temporal patterns. However, as dynamic network literature stems from diverse fields and makes use of inconsistent terminology, it is challenging to navigate. Meanwhile, graph neural networks (GNNs) have gained a lot of attention in recent years for their ability to perform well on a range of network science tasks, such as link prediction and node classification. Despite the popularity of graph neural networks and the proven benefits of dynamic network models, there has been little focus on graph neural networks for dynamic networks. To address the challenges resulting from the fact that this research crosses diverse fields as well as to survey dynamic graph neural networks, this work is split into two main parts. First, to address the ambiguity of the dynamic network terminology we establish a foundation of dynamic networks with consistent, detailed terminology and notation. Second, we present a comprehensive survey of dynamic graph neural network models using the proposed terminologyComment: 28 pages, 9 figures, 8 table

Splitting of liftings in products of probability spaces

We prove that if (X,\mathfrakA,P) is an arbitrary probability space with countably generated \sigma-algebra \mathfrakA, (Y,\mathfrakB,Q) is an arbitrary complete probability space with a lifting \rho and \hat R is a complete probability measure on \mathfrakA \hat \otimes_R \mathfrakB determined by a regular conditional probability {S_y:y\in Y} on \mathfrakA with respect to \mathfrakB, then there exist a lifting \pi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R) and liftings \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\pi(E)]^y=\sigma_y\bigl([\pi(E)]^y\bigr). Assuming the absolute continuity of R with respect to P\otimes Q, we prove the existence of a regular conditional probability {T_y:y\in Y} and liftings \varpi on (X\times Y,\mathfrakA \hat \otimes_R \mathfrakB,\hat R), \rho' on (Y,\mathfrakB,\hat Q) and \sigma_y on (X,\hat \mathfrakA_y,\hat S_y), y\in Y, such that, for every E\in\mathfrakA \hat \otimes_R \mathfrakB and every y\in Y, [\varpi(E)]^y=\sigma_y\bigl([\varpi(E)]^y\bigr) and \varpi(A\times B)=\bigcup_{y\in\rho'(B)}\sigma_y(A)\times{y}\qquadif A\times B\in\mathfrakA\times\mathfrakB. Both results are generalizations of Musia\l, Strauss and Macheras [Fund. Math. 166 (2000) 281-303] to the case of measures which are not necessarily products of marginal measures. We prove also that liftings obtained in this paper always convert \hat R-measurable stochastic processes into their \hat R-measurable modifications.Comment: Published at http://dx.doi.org/10.1214/009117904000000018 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Link Prediction Based on Subgraph Evolution in Dynamic Social Networks

We propose a new method for characterizing the dynamics of complex networks with its application to the link prediction problem. Our approach is based on the discovery of network subgraphs (in this study: triads of nodes) and measuring their transitions during network evolution. We define the Triad Transition Matrix (TTM) containing the probabilities of transitions between triads found in the network, then we show how it can help to discover and quantify the dynamic patterns of network evolution. We also propose the application of TTM to link prediction with an algorithm (called TTM-predictor) which shows good performance, especially for sparse networks analyzed in short time scales. The future applications and research directions of our approach are also proposed and discussed

A Landscape Lullaby? The Function of (Post-) Pastoral Elements in Kazuo Ishiguro's Never Let Me Go

Published in 2005, Kazuo Ishiguro’s novel Never Let Me Go presents a vision of a society where clones are raised to donate their vital organs. Because of the dystopian elements in the narration, one might expect a setting in a futuristic environment. Instead, the story takes place mainly in pastoral visions of the English countryside. This distinct setting creates a stark contrast to the characters’ harsh reality, which is gradually revealed throughout the narrative. In this article, I argue that the novel complicates the pastoral and offers new perspectives on the relationship of humans and nature by incorporating post-pastoral elements. In order to investigate the contrast between the dystopian reality and its peaceful setting, the pastoral initially provides a useful lens. The concept is an “ancient cultural tool” often found in literature, which is used to express humanity’s relationship to the land and natural surroundings (Gifford, “Post-Pastoral” 15; “Reading Strategies” 45). It is extended by approaches like the anti-pastoral and the post-pastoral. By primarily following Terry Gifford’s theoretical understandings, I will use these concepts for an analysis of the novel’s descriptions of nature, choice of language and narrative structure. I will mainly focus on the depiction of Hailsham, a boarding school for clones, because this offers insights into the characters’ ways of handling their fate and the importance of their childhood surroundings throughout their lives

Review Essay: Gendered Bodies and Necropolitical States

Bromwich, Rebecca. 2015. Looking for Ashley: Re-reading What the Smith Case Reveals about the Governance of Girls, Mothers and Families in Canada. Bradford, ON: Demeter Press.Dean, Amber. 2015. Remembering Vancouver’s Disappeared Women: Settler Colonialism and The Difficulty of Inheritance. Toronto, ON: University of Toronto Press.