Modularity and community detection in bipartite networks

The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity. The bipartite modularity is presented in terms of a modularity matrix B; some key properties of the eigenspectrum of B are identified and used to describe an algorithm for identifying modules in bipartite networks. The algorithm is based on the idea that the modules in the two parts of the network are dependent, with each part mutually being used to induce the vertices for the other part into the modules. We apply the algorithm to real-world network data, showing that the algorithm successfully identifies the modular structure of bipartite networks.Comment: RevTex 4, 11 pages, 3 figures, 1 table; modest extensions to conten

Train‐the‐trainer: Methodology to learn the cognitive interview

Research has indicated that police may not receive enough training in interviewing cooperative witnesses, specifically in use of the cognitive interview (CI). Practically, for the CI to be effective in real‐world investigations, police investigators must be trained by law enforcement trainers. We conducted a three‐phase experiment to examine the feasibility of training experienced law enforcement trainers who would then train others to conduct the CI. We instructed Federal Bureau of Investigation and local law enforcement trainers about the CI (Phase I); law enforcement trainers from both agencies (n = 4, 100% male, mean age = 50 years) instructed university students (n = 25, 59% female, mean age = 21 years) to conduct either the CI or a standard law enforcement interview (Phase II); the student interviewers then interviewed other student witnesses (n = 50, 73% female, mean age = 22 years), who had watched a simulated crime (phase III). Compared with standard training, interviews conducted by those trained by CI‐trained instructors contained more information and at a higher accuracy rate and with fewer suggestive questions.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147804/1/jip1518_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147804/2/jip1518.pd

The Peculiar Phase Structure of Random Graph Bisection

The mincut graph bisection problem involves partitioning the n vertices of a graph into disjoint subsets, each containing exactly n/2 vertices, while minimizing the number of "cut" edges with an endpoint in each subset. When considered over sparse random graphs, the phase structure of the graph bisection problem displays certain familiar properties, but also some surprises. It is known that when the mean degree is below the critical value of 2 log 2, the cutsize is zero with high probability. We study how the minimum cutsize increases with mean degree above this critical threshold, finding a new analytical upper bound that improves considerably upon previous bounds. Combined with recent results on expander graphs, our bound suggests the unusual scenario that random graph bisection is replica symmetric up to and beyond the critical threshold, with a replica symmetry breaking transition possibly taking place above the threshold. An intriguing algorithmic consequence is that although the problem is NP-hard, we can find near-optimal cutsizes (whose ratio to the optimal value approaches 1 asymptotically) in polynomial time for typical instances near the phase transition.Comment: substantially revised section 2, changed figures 3, 4 and 6, made minor stylistic changes and added reference

Researching the use of force: The background to the international project

This article provides the background to an international project on use of force by the police that was carried out in eight countries. Force is often considered to be the defining characteristic of policing and much research has been conducted on the determinants, prevalence and control of the use of force, particularly in the United States. However, little work has looked at police officers’ own views on the use of force, in particular the way in which they justify it. Using a hypothetical encounter developed for this project, researchers in each country conducted focus groups with police officers in which they were encouraged to talk about the use of force. The results show interesting similarities and differences across countries and demonstrate the value of using this kind of research focus and methodology

Tropical tele-connections to the Mediterranean climate and weather

Some strong natural fluctuations of climate in the Eastern Mediterranean (EM) region are shown to be connected to the major tropical systems. Potential relations between EM rainfall extremes to tropical systems, e.g. El Niño, Indian Monsoon and hurricanes, are demonstrated. For a specific event, high resolution modelling of the severe flood on 3-5 December 2001 in Israel suggests a relation to hurricane Olga. In order to understand the factors governing the EM climate variability in the summer season, the relationship between extreme summer temperatures and the Indian Monsoon was examined. Other tropical factors like the Red-Sea Trough system and the Saharan dust are also likely to contribute to the EM climate variability

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