Catching the head, tail, and everything in between: a streaming algorithm for the degree distribution

The degree distribution is one of the most fundamental graph properties of interest for real-world graphs. It has been widely observed in numerous domains that graphs typically have a tailed or scale-free degree distribution. While the average degree is usually quite small, the variance is quite high and there are vertices with degrees at all scales. We focus on the problem of approximating the degree distribution of a large streaming graph, with small storage. We design an algorithm headtail, whose main novelty is a new estimator of infrequent degrees using truncated geometric random variables. We give a mathematical analysis of headtail and show that it has excellent behavior in practice. We can process streams will millions of edges with storage less than 1% and get extremely accurate approximations for all scales in the degree distribution. We also introduce a new notion of Relative Hausdorff distance between tailed histograms. Existing notions of distances between distributions are not suitable, since they ignore infrequent degrees in the tail. The Relative Hausdorff distance measures deviations at all scales, and is a more suitable distance for comparing degree distributions. By tracking this new measure, we are able to give strong empirical evidence of the convergence of headtail

Efficient Estimation of Heat Kernel PageRank for Local Clustering

Given an undirected graph G and a seed node s, the local clustering problem aims to identify a high-quality cluster containing s in time roughly proportional to the size of the cluster, regardless of the size of G. This problem finds numerous applications on large-scale graphs. Recently, heat kernel PageRank (HKPR), which is a measure of the proximity of nodes in graphs, is applied to this problem and found to be more efficient compared with prior methods. However, existing solutions for computing HKPR either are prohibitively expensive or provide unsatisfactory error approximation on HKPR values, rendering them impractical especially on billion-edge graphs. In this paper, we present TEA and TEA+, two novel local graph clustering algorithms based on HKPR, to address the aforementioned limitations. Specifically, these algorithms provide non-trivial theoretical guarantees in relative error of HKPR values and the time complexity. The basic idea is to utilize deterministic graph traversal to produce a rough estimation of exact HKPR vector, and then exploit Monte-Carlo random walks to refine the results in an optimized and non-trivial way. In particular, TEA+ offers practical efficiency and effectiveness due to non-trivial optimizations. Extensive experiments on real-world datasets demonstrate that TEA+ outperforms the state-of-the-art algorithm by more than four times on most benchmark datasets in terms of computational time when achieving the same clustering quality, and in particular, is an order of magnitude faster on large graphs including the widely studied Twitter and Friendster datasets.Comment: The technical report for the full research paper accepted in the SIGMOD 201

A model for differentiating school shooters characteristics

Purpose The current study aimed to explore the potential for developing a model for differentiating school shooters based on their characteristics (or risk factors) before the attack took place. Design/methodology/approach Data on forty school shootings was compiled from the National School Safety Center’s Report on School Associated Violent Deaths (SAVD) and media accounts. Content analysis of the cases produced a set of 18 variables relating to offenders’ characteristics (or risk factors). Data were subjected to Smallest Space Analysis (SSA), a non-metric multidimensional scaling procedure. Findings Results revealed three distinct themes: Disturbed School Shooter, Rejected School Shooter, and Criminal School Shooter. Further analysis identified links between these themes with the family background of the offender. Research limitations/implications These findings have both significant theoretical implications in our understanding of school shooters and the crime in general. They offer potential for practical applications in terms of prevention and intervention strategies. A key limitation relates to the quality of data. Originality/Value This is the first study to develop a model for differentiating school shooter characteristic

Edward Carpenter: The Forgotten Birth Control Advocate. The Progression of His Advocacy and its Culmination

Edward Carpenter is remembered as an English Poet, Socialist, sex-reformer and gay rights activist. This work aims to illuminate another avenue of Carpenter’s ventures, birth control. The previously overlooked avenue of Carpenter’s interest is the focus of this work. Through analysis of selected work by Carpenter, such as his 1894 pamphlets, can his ideology and advocacy begin to be shaped and understood. This becomes further evident through his professional relationships with birth control pioneers such as Marie Stopes and Margaret Sanger. Carpenter’s advocacy is made further evident through the analysis of his unpublished manuscript ‘Birth Control and Bisexuality’. What becomes clear in this work is that Carpenter was advocating for birth control throughout his early work and, by the 1920s, was actively writing about the subject. Whether or not intentional, Carpenter was dropping breadcrumbs of birth control advocacy in early writing and later on was explicit and deliberate in his advocacy

Covid and care: how to make job support schemes better

Rishi Sunak’s job support schemes were ambitious – at least initially. But did they work? In fact, argue the LSE COVID and Care Research Group, they were conceived with a particular kind of worker in mind: an able-bodied white British national who could easily work from home. Future support schemes need to reflect the large numbers of people in precarious, informal work

A Critical Assessment of Trait versus Situationalist Positions and the NEO Personality Inventory (NEO-PI-R)

Over time, the concept of personality has stimulated considerable theorising and debate amongst researchers. Thought to be characteristics within an individual that account for consistent patterns of thought, feelings and behaviours, the quest to understand individual differences between human beings has led to the increased uptake of psychological measurement tools, known as psychometric tests. Many variations of psychometric tests that have been devised to date attempt to operationalise the theoretical principles of Trait theory and the dimensions therein. Typically, these are applied within occupational, educational and clinical settings, where such personality measures are considered increasingly useful in the evaluation of individuals either being assessed, or due to begin working within an organisation. However, despite researchers implementing psychometric tests such as the NEO Personality Inventory (NEO-PI-R; Costa and McCrae, 1992a) reporting high levels of construct validity for the measure (Widiger and Trull, 1997), criticism surrounding the reliability of findings obtained from applications of the tool, resulting from the general lack of agreement around the trait dimensions that underpin psychometric testing, remain important. Another highly contented issue surrounding the basis of such tests are the stability and situationalist arguments, which criticise such methods as inaccurately representing a true picture of the individual due to failing to take the full environmental influences upon people into account. Such issues are undoubtedly more complex than such a summarisation can accredit, and upon paying systematic and critical consideration to the related assessments, a greater depth of analysis may be drawn