Different approaches to community detection

A precise definition of what constitutes a community in networks has remained elusive. Consequently, network scientists have compared community detection algorithms on benchmark networks with a particular form of community structure and classified them based on the mathematical techniques they employ. However, this comparison can be misleading because apparent similarities in their mathematical machinery can disguise different reasons for why we would want to employ community detection in the first place. Here we provide a focused review of these different motivations that underpin community detection. This problem-driven classification is useful in applied network science, where it is important to select an appropriate algorithm for the given purpose. Moreover, highlighting the different approaches to community detection also delineates the many lines of research and points out open directions and avenues for future research.Comment: 14 pages, 2 figures. Written as a chapter for forthcoming Advances in network clustering and blockmodeling, and based on an extended version of The many facets of community detection in complex networks, Appl. Netw. Sci. 2: 4 (2017) by the same author

Using risk to inform overtopping protection decisions

Presented at the Protections 2016: 2nd international seminar on dam protection against overtopping: concrete dams, embankment dams, levees, tailings dams held on 7th-9th September, 2016, at Colorado State University in Fort Collins, Colorado, USA. The increasing demand for dam and levee safety and flood protection has motivated new research and advancements and a greater need for cost-effective measures in overtopping protection as a solution for overtopping concerns at levees and dams. This seminar will bring together leading experts from practice, research, development, and implementation for two days of knowledge exchange followed by a technical tour of the Colorado State University Hydraulic Laboratory with overtopping flume and wave simulator. This seminar will focus on: Critical issues related to levees and dams; New developments and advanced tools; Overtopping protection systems; System design and performance; Applications and innovative solutions; Case histories of overtopping events; Physical modeling techniques and recent studies; and Numerical modeling methods.Includes bibliographical references.The decision to implement overtopping protection as a dam safety modification alternative can be difficult. The decision involves a conscious decision to allow a dam to overtop for floods above a threshold flood. If a large flood occurs that initiates dam overtopping, there is no turning back, and the dam and the overtopping protection must be able to resist the overtopping flows. The chance of intervention being successful for a dam that is already overtopping, should erosion initiate, would be very unlikely. There is more of a comfort level among many dam engineers in providing conventional solutions to a dam overtopping issue. These traditional measures include raising the dam crest to provide additional surcharge space to store a portion of the flood inflows or providing additional spillway capacity to more closely match the peak flood inflows. There is often the perception among experienced dam engineers that these traditional measures provide a safer solution and pose less risk than an overtopping solution. This paper will present scenarios that demonstrate that in some cases, overtopping protection may be just as safe or the safer alternative, by exposing the downstream population to equal or less risk of dam failure during a large flood event. These scenarios will consist of an embankment dam where a replacement gated spillway alternative will be compared to overtopping protection and a concrete dam where raising of the dam will be compared to providing overtopping protection for the dam foundation

Finding local community structure in networks

Although the inference of global community structure in networks has recently become a topic of great interest in the physics community, all such algorithms require that the graph be completely known. Here, we define both a measure of local community structure and an algorithm that infers the hierarchy of communities that enclose a given vertex by exploring the graph one vertex at a time. This algorithm runs in time O(d*k^2) for general graphs when $d$ is the mean degree and k is the number of vertices to be explored. For graphs where exploring a new vertex is time-consuming, the running time is linear, O(k). We show that on computer-generated graphs this technique compares favorably to algorithms that require global knowledge. We also use this algorithm to extract meaningful local clustering information in the large recommender network of an online retailer and show the existence of mesoscopic structure.Comment: 7 pages, 6 figure

О горно-геологическом образовании в Томском политехническом университете на рубеже тысячелетий

Рассматривается история развития горно-геологического образования в Томском политехническом университете

Finding community structure in very large networks

The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(m d log n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in which case our algorithm runs in essentially linear time, O(n log^2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400,000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers

A measure of centrality based on the spectrum of the Laplacian

We introduce a family of new centralities, the k-spectral centralities. k-Spectral centrality is a measurement of importance with respect to the deformation of the graph Laplacian associated with the graph. Due to this connection, k-spectral centralities have various interpretations in terms of spectrally determined information. We explore this centrality in the context of several examples. While for sparse unweighted networks 1-spectral centrality behaves similarly to other standard centralities, for dense weighted networks they show different properties. In summary, the k-spectral centralities provide a novel and useful measurement of relevance (for single network elements as well as whole subnetworks) distinct from other known measures.Comment: 12 pages, 6 figures, 2 table

Practical and Rigorous Uncertainty Bounds for Gaussian Process Regression

Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important applications, like learning-based control with safety guarantees, frequentist uncertainty bounds are required. Although such rigorous bounds are available for Gaussian Processes, they are too conservative to be useful in applications. This often leads practitioners to replacing these bounds by heuristics, thus breaking all theoretical guarantees. To address this problem, we introduce new uncertainty bounds that are rigorous, yet practically useful at the same time. In particular, the bounds can be explicitly evaluated and are much less conservative than state of the art results. Furthermore, we show that certain model misspecifications lead to only graceful degradation. We demonstrate these advantages and the usefulness of our results for learning-based control with numerical examples.Comment: Contains supplementary material and corrections to the original versio

Foundations for the Integration of Enterprise Wikis and Specialized Tools for Enterprise Architecture Management

Organizations are challenged with rapidly changing business requirements and an ever-increasing volume respectively variety of information. Enterprise Architecture (EA) and its respective management function are considered as means to overcome these challenges. Appropriate tool support to this end is an elementary success factor to guide the EA management (EAM) initiative. Nevertheless, practitioners perceive currently available tools specialized for EAM as not sufficient in their organizations. Major reasons are inflexible data models as well as missing integration with processes and their focus on expert users. Regarding these limitations Enterprise Wikis provide practice proven solutions already exploited by organizations. These Enterprise Wikis are able to extend the capabilities of existing EA tools to cope with unstructured information and leverage a better utilization of structured EA information. In this paper we present the foundations for an integration of specialized EAM tools and Enterprise Wikis. We elaborate scenarios for both tool species using a practitioner survey and differentiate four integration cases

Asymptotic behavior of the number of Eulerian orientations of graphs

We consider the class of simple graphs with large algebraic connectivity (the second-smallest eigenvalue of the Laplacian matrix). For this class of graphs we determine the asymptotic behavior of the number of Eulerian orientations. In addition, we establish some new properties of the Laplacian matrix, as well as an estimate of a conditionality of matrices with the asymptotic diagonal predominanceComment: arXiv admin note: text overlap with arXiv:1104.304