An evolving network model with community structure

Many social and biological networks consist of communities—groups of nodes within which connections are dense, but between which connections are sparser. Recently, there has been considerable interest in designing algorithms for detecting community structures in real-world complex networks. In this paper, we propose an evolving network model which exhibits community structure. The network model is based on the inner-community preferential attachment and inter-community preferential attachment mechanisms. The degree distributions of this network model are analysed based on a mean-field method. Theoretical results and numerical simulations indicate that this network model has community structure and scale-free properties

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Finding and evaluating community structure in networks

We propose and study a set of algorithms for discovering community structure in networks -- natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.Comment: 16 pages, 13 figure

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Employing with conviction: The experiences of employers who actively recruit criminalised people

Atherton, P., & Buck, G. Employing with conviction: The experiences of employers who actively recruit criminalised people. Probation Journal, 68(2), pp. 186-205. Copyright © [2021] (Copyright Holder). Reprinted by permission of SAGE Publications.In England and Wales, criminal reoffending costs £18 billion annually. Securing employment can support desistance from crime, but only 17% of ex-prisoners are employed a year after release. Understanding the motivations of employers who do recruit criminalised people therefore represents an important area of inquiry. This article draws upon qualitative interviews with twelve business leaders in England who proactively employ criminalised people. Findings reveal that inclusive recruitment can be (indirectly) encouraged by planning policies aimed to improve social and environmental well-being and that employers often work creatively to meet employees’ additional needs, resulting in commercial benefits and (re)settlement opportunities

Comparing community structure identification

We compare recent approaches to community structure identification in terms of sensitivity and computational cost. The recently proposed modularity measure is revisited and the performance of the methods as applied to ad hoc networks with known community structure, is compared. We find that the most accurate methods tend to be more computationally expensive, and that both aspects need to be considered when choosing a method for practical purposes. The work is intended as an introduction as well as a proposal for a standard benchmark test of community detection methods.Comment: 10 pages, 3 figures, 1 table. v2: condensed, updated version as appears in JSTA

Predicting Expected Absolute Chemotherapy Treatment Benefit in Women With Early-Stage Breast Cancer Using EndoPredict, an Integrated 12-Gene Clinicomolecular Assay.

PURPOSE: Previous studies have shown EndoPredict (EPclin), a test that integrates 12-gene expression data with nodal status and tumor size, to be predictive for risk of distant recurrence in women with estrogen receptor-positive, human epidermal growth factor receptor 2-negative early-stage breast cancer. Here, we modeled expected absolute chemotherapy benefit on the basis of EPclin test results. METHODS: The effect of chemotherapy was modeled using previously validated 10-year risk of distant recurrence as a function of EPclin score for patients treated without chemotherapy. Average relative chemotherapy benefit to reduce breast cancer distant recurrence was evaluated using a published meta-analysis from the Early Breast Cancer Trialists' Collaborative Group. Absolute chemotherapy benefit differences were estimated across a range of interaction strengths between relative chemotherapy benefit and EPclin score. The average absolute benefit was calculated for patients with high and low EPclin scores using the distribution of scores in 2,185 samples tested by Myriad Genetics. RESULTS: The average expected absolute benefit of chemotherapy treatment for patients with a low EPclin score was 1.8% in the absence of interaction and 1.5% for maximal interaction. Conversely, the expected average absolute chemotherapy benefit for patients with a high EPclin score was 5.3% and 7.3% for no interaction and maximal interaction, respectively. CONCLUSION: For women with estrogen receptor-positive, human epidermal growth factor receptor 2-negative early-stage breast cancer, a high EPclin score identified which patients would benefit most from adjuvant chemotherapy in terms of absolute reduction of distant recurrence, regardless of the amount of interaction between EPclin and relative chemotherapy benefit. A high degree of prognostic discrimination for distant recurrence is more important for identifying patients likely to benefit most from chemotherapy than an interaction between EPclin and treatment-relative benefit

Minding impacting events in a model of stochastic variance

We introduce a generalisation of the well-known ARCH process, widely used for generating uncorrelated stochastic time series with long-term non-Gaussian distributions and long-lasting correlations in the (instantaneous) standard deviation exhibiting a clustering profile. Specifically, inspired by the fact that in a variety of systems impacting events are hardly forgot, we split the process into two different regimes: a first one for regular periods where the average volatility of the fluctuations within a certain period of time is below a certain threshold and another one when the local standard deviation outnumbers it. In the former situation we use standard rules for heteroscedastic processes whereas in the latter case the system starts recalling past values that surpassed the threshold. Our results show that for appropriate parameter values the model is able to provide fat tailed probability density functions and strong persistence of the instantaneous variance characterised by large values of the Hurst exponent is greater than 0.8, which are ubiquitous features in complex systems.Comment: 18 pages, 5 figures, 1 table. To published in PLoS on