AGWAN: A Generative Model for Labelled, Weighted Graphs

Real-world graphs or networks tend to exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Much effort has been directed into creating realistic and tractable models for unlabelled graphs, which has yielded insights into graph structure and evolution. Recently, attention has moved to creating models for labelled graphs: many real-world graphs are labelled with both discrete and numeric attributes. In this paper, we presentAgwan (Attribute Graphs: Weighted and Numeric), a generative model for random graphs with discrete labels and weighted edges. The model is easily generalised to edges labelled with an arbitrary number of numeric attributes. We include algorithms for fitting the parameters of the Agwanmodel to real-world graphs and for generating random graphs from the model. Using real-world directed and undirected graphs as input, we compare our approach to state-of-the-art random labelled graph generators and draw conclusions about the contribution of discrete vertex labels and edge weights to graph structure.

From ideal reactor concepts to reality:The novel drum reactor for photocatalytic wastewater treatment

This article reports the development of a novel drum photocatalytic reactor for treating dye effluent streams. The parameters for operation including drum rotation speed, light source distance, catalyst loading and H2O2 doping have been investigated using methylene blue as a model pollutant. Effluent can be generated by a number of domestic and industrial sources, including pharmaceutical, oil and gas, agricultural, food and chemical sectors. The work reported here proposes the application of semiconductor photocatalysis as a final polishing step for the removal of hydrocarbons from effluents sources, initial studies have proved effective in removing residual hydrocarbons from the effluent.

2D Monolayer MoS2–Carbon Interoverlapped Superstructure: Engineering Ideal Atomic Interface for Lithium Ion Storage: Engineering Ideal Atomic Interface for Lithium Ion Storage

A novel strategy for the controlled synthesis of 2D MoS<inf>2</inf>/C hybrid nanosheets consisting of the alternative layer-by-layer interoverlapped single-layer MoS<inf>2</inf> and mesoporous carbon (m-C) is demonstrated. Such special hybrid nanosheets with a maximized MoS<inf>2</inf>/m-C interface contact show very good performance for lithium-ion batteries in terms of high reversible capacity, excellent rate capability, and outstanding cycling stability.

Irish language education and the national ideal: The dynamics of nationalism in Northern Ireland

Since the beginning of the Northern Ireland conflict in the late 1960s, Irish nationalism has been identified as a prominent force in the political culture of the state. Recent studies have suggested, however, that the ‘Nationalist’ population has become increasingly content within the new political framework created by the peace process and the aspiration for Irish unity diminished. In placing the Northern Ireland situation within the theoretical framework of nationalism, this paper will analyse how these changing priorities have been possible. Through an analysis of Irish language study in Northern Ireland's schools, the paper will examine how the political ideals espoused by the nationalist Sinn Féin Party reflected the priorities of the ‘nationalist community’. It will be contended that the relationship between the ideology and ‘the people’ is much more complex than is often allowed for and that educational inequalities are a significant contributing factor to this.

Generating Realistic Labelled, Weighted Random Graphs

Generative algorithms for random graphs have yielded insights into the structure and evolution of real-world networks. Most networks exhibit a well-known set of properties, such as heavy-tailed degree distributions, clustering and community formation. Usually, random graph models consider only structural information, but many real-world networks also have labelled vertices and weighted edges. In this paper, we present a generative model for random graphs with discrete vertex labels and numeric edge weights. The weights are represented as a set of Beta Mixture Models (BMMs) with an arbitrary number of mixtures, which are learned from real-world networks. We propose a Bayesian Variational Inference (VI) approach, which yields an accurate estimation while keeping computation times tractable. We compare our approach to state-of-the-art random labelled graph generators and an earlier approach based on Gaussian Mixture Models (GMMs). Our results allow us to draw conclusions about the contribution of vertex labels and edge weights to graph structure.

Energy of line graphs

The energy of a graph is equal to the sum of the absolute values of its eigenvalues. The energy of a matrix is equal to the sum of its singular values. We establish relations between the energy of the line graph of a graph G and the energies associated with the Laplacian and signless Laplacian matrices of G. © 2010 Elsevier B.V. All rights reserved.

Efficient edge domination in regular graphs

An induced matching of a graph G is a matching having no two edges joined by an edge. An efficient edge dominating set of G is an induced matching M such that every other edge of G is adjacent to some edge in M. We relate maximum induced matchings and efficient edge dominating sets, showing that efficient edge dominating sets are maximum induced matchings, and that maximum induced matchings on regular graphs with efficient edge dominating sets are efficient edge dominating sets. A necessary condition for the existence of efficient edge dominating sets in terms of spectra of graphs is established. We also prove that, for arbitrary fixed p ≥ 3, deciding on the existence of efficient edge dominating sets on p-regular graphs is NP-complete. © 2008 Elsevier B.V. All rights reserved.

Spectral characterization of families of split graphs

An upper bound for the sum of the squares of the entries of the principal eigenvector corresponding to a vertex subset inducing a k-regular subgraph is introduced and applied to the determination of an upper bound on the order of such induced subgraphs. Furthermore, for some connected graphs we establish a lower bound for the sum of squares of the entries of the principal eigenvector corresponding to the vertices of an independent set. Moreover, a spectral characterization of families of split graphs, involving its index and the entries of the principal eigenvector corresponding to the vertices of the maximum independent set is given. In particular, the complete split graph case is highlighted.

The Jordan canonical form for a class of weighted directed graphs

Recently, Cardon and Tuckfield (2011) [1] have described the Jordan canonical form for a class of zero-one matrices, in terms of its associated directed graph. In this paper, we generalize this result to describe the Jordan canonical form of a weighted adjacency matrix A in terms of its weighted directed graph.

Spectra of graphs obtained by a generalization of the join graph operation

Taking a Fiedler’s result on the spectrum of a matrix formed from two symmetric matrices as a motivation, a more general result is deduced and applied to the determination of adjacency and Laplacian spectra of graphs obtained by a generalized join graph operation on families of graphs (regular in the case of adjacency spectra and arbitrary in the case of Laplacian spectra). Some additional consequences are explored, namely regarding the largest eigenvalue and algebraic connectivity.

A recursive construction of the regular exceptional graphs with least eigenvalue -2

In spectral graph theory a graph with least eigenvalue 2 is exceptional if it is connected, has least eigenvalue greater than or equal to 2, and it is not a generalized line graph. A ðk; tÞ-regular set S of a graph is a vertex subset, inducing a k-regular subgraph such that every vertex not in S has t neighbors in S. We present a recursive construction of all regular exceptional graphs as successive extensions by regular sets.

Determination of (0,2)-regular sets in graphs and applications

In this paper, relevant results about the determination of (k,t)-regular sets, using the main eigenvalues of a graph, are reviewed and some results about the determination of (0,2)-regular sets are introduced. An algorithm for that purpose is also described. As an illustration, this algorithm is applied to the determination of maximum matchings in arbitrary graphs.

The Structure of Design Processes: ideal and reality in Bruce Archer’s 1968 doctoral thesis

The paper centres on a single document, the 1968 doctoral thesis of L Bruce Archer. It traces the author’s earlier publications and the sources that informed and inspired his thinking, as a way of understanding the trajectory of his ideas and the motivations for his work at the Royal College of Art from 1962. Analysis of the thesis suggests that Archer’s ambition for a rigorous ‘science of design’ inspired by algorithmic approaches was increasingly threatened with disruption by his experience of large, complex design projects. His attempts to deal with this problem are shown to involve a particular interpretation of cybernetics. The paper ends with Archer’s own retrospective view and a brief account of his dramatically changed opinions. Archer is located as both a theorist and someone intensely interested in the commercial world of industrial design.

Perceived Social Pressures and the Internalization of the Mesomorphic Ideal: the Role of Drive for Muscularity and Autonomy in Physically Active Men

BACKGROUND: Researchers have tested the beliefs of sportspeople and sports medicine specialists that cognitive strategies influence strength performance. Few investigators have synthesised the literature. OBJECTIVES: The specific objectives were to review evidence regarding (a) the cognitive strategy-strength performance relationship; (b) participant skill level as a moderator; and (c) cognitive, motivational, biomechanical/physiological, and emotional mediators. METHOD: Studies were sourced via electronic databases, reference lists of retrieved articles, and manual searches of relevant journals. Studies had to be randomised or counterbalanced experiments with a control group or condition, repeated measures, and a quality control score above 0.5 (out of 1). Cognitive strategies included goal setting, imagery, self-talk, preparatory arousal, and free choice. Dependent variables included maximal strength, local muscular endurance, or muscular power. RESULTS: Globally, cognitive strategies were reliability associated with increased strength performance (results ranged from 61 to 65 %). Results were mixed when examining the effects of specific strategies on particular dependent variables, although no intervention had an overall negative influence. Indeterminate relationships emerged regarding hypothesised mediators (except cognitive variables) and participant skill level as a moderator. CONCLUSIONS: Although cognitive strategies influence strength performance, there are knowledge gaps regarding specific types of strength, especially muscular power. Cognitive variables, such as concentration, show promise as possible mediators.