The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Differential-Difference Equations. By Richard Bellman and Kenneth L. Cooke. Pp. xvi, 465. 1963. (Academic Press)

The populations of many species of animals and plants are age-structured, i.e. the individuals present at any one time were born over a range of different times, and their fertility and survival depend on age. The properties of such populations are important for interpreting experiments and observations on the genetics of populations for animal and plant breeding, and for understanding the evolution of features of life-histories such as senescence and time of reproduction. In this new edition Brian Charlesworth provides a comprehensive review of the basic mathematical theory of the demography and genetics of age-structured populations. The mathematical level of the book is such that it will be accessible to anyone with a knowledge of basic calculus and linear algebra.

Evolution in age-structured populations

We describe a collection of algorithms that we developed and implemented to facilitate the automatic recovery of the modular structure of a software system from its source code. We treat automatic modularization as an optimization problem. Our algorithms make use of traditional hill-climbing and genetic algorithms.

Using automatic clustering to produce high-level system organizations of source code

The geometry of an Archimedes screw is governed by certain external parameters (its outer radius, length, and slope) and certain internal parameters (its inner radius, number of blades, and the pitch of the blades). The external parameters are usually determined by the location of the screw and how much water is to be lifted. The internal parameters, however, are free to be chosen to optimize the performance of the screw. In this paper the inner radius and pitch that maximize the volume of water lifted in one turn of the screw are found. The optimal parameter values found are compared with the values used in a screw described by the Roman architect and engineer Vitruvius in the first century B.C., and with values used in the design of modern Archimedes screws.

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The Turn of the Screw: Optimal Design of an Archimedes Screw

Innovative approaches are needed to combat the illegal trade in wildlife. Here, we used network analysis and a new database, HealthMap Wildlife Trade, to identify the key nodes (countries) that support the illegal wildlife trade. We identified key exporters and importers from the number of shipments a country sent and received and from the number of connections a country had to other countries over a given time period. We used flow betweenness centrality measurements to identify key intermediary countries. We found the set of nodes whose removal from the network would cause the maximum disruption to the network. Selecting six nodes would fragment 89.5% of the network for elephants, 92.3% for rhinoceros, and 98.1% for tigers. We then found sets of nodes that would best disseminate an educational message via direct connections through the network. We would need to select 18 nodes to reach 100% of the elephant trade network, 16 nodes for rhinoceros, and 10 for tigers. Although the choice of locations for interventions should be customized for the animal and the goal of the intervention, China was the most frequently selected country for network fragmentation and information dissemination. Identification of key countries will help strategize illegal wildlife trade interventions.

https://www.healthmap.org/wildlifetrade/paper.pdf

Quantitative methods of identifying the key nodes in the illegal wildlife trade network.

Archimedes screws have become increasingly popular throughout Europe to drive hydropower plants using residual flow from a stream or river. This heightened usage of such screws during the past few years is attributable to their robustness, simplicity, and fish friendliness. Presently the dimensioning of a hydropower site equipped with an Archimedes screw is dependent mainly on the experience of the design engineer. This is so because there is no appropriate theory for the optimal hydraulic design of screws used at hydropower sites, especially for the water-inflow conditions. In this paper, a new analytical model for the water inflow is derived, and the optimal values of the inflow parameters are determined to achieve a planned inflow to the screw.

Analytical Model for Water Inflow of an Archimedes Screw Used in Hydropower Generation

A computational geometry technique is utilized to detect, diagnose, and/or mitigate fault detection during the execution of a software application. Runtime measurements are collected and processed to generate a geometric enclosure that represents the normal, non-failing, operating space of the application being monitored. When collected runtime measurements are classified as being inside or on the perimeter of the geometric enclosure, the application is considered to be in a normal, non-failing, state. When collected runtime measurements are classified as being outside of the geometric enclosure, the application is considered to be in an anomalous, failing, state. In an example embodiment, the geometric enclosure is a convex hull generated in N-dimensional Euclidean space. Appropriate action (e.g., restart the software, turn off access to a network port) can be taken depending on where the measurement values lie in the space.

Chris Rorres

Papers

Using automatic clustering to produce high-level system organizations of source code

The Turn of the Screw: Optimal Design of an Archimedes Screw

Quantitative methods of identifying the key nodes in the illegal wildlife trade network.

Analytical Model for Water Inflow of an Archimedes Screw Used in Hydropower Generation

Detection, diagnosis, and mitigation of software faults