Copyright, Culture, and Community in Virtual Worlds

Communities that interact on-line through computer games and other virtual worlds are mediated by the audiovisual content of the game interface. Much of this content is subject to copyright law, which confers on the copyright owner the legal right to prevent certain unauthorized uses of the content. Such exclusive rights impose a limiting factor on the development of communities that are situated around the interface content, because the rights, privileges, and\ud exceptions associated with copyright generally tend to disregard the cultural significance of copyrighted content. This limiting effect of copyright is well illustrated by examination of the copied content appropriated by virtual diaspora communities from the game Uru: Ages of Myst. Reconsideration of current copyright law would be required in order to accommodate the cohesion of on-line\ud communities and related cultural uses of copyrighted content

Separable Concave Optimization Approximately Equals Piecewise-Linear Optimization

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of the polyhedron and linear in 1/epsilon. For many practical concave cost problems, the resulting piecewise-linear cost problem can be formulated as a well-studied discrete optimization problem. As a result, a variety of polynomial-time exact algorithms, approximation algorithms, and polynomial-time heuristics for discrete optimization problems immediately yield fully polynomial-time approximation schemes, approximation algorithms, and polynomial-time heuristics for the corresponding concave cost problems. We illustrate our approach on two problems. For the concave cost multicommodity flow problem, we devise a new heuristic and study its performance using computational experiments. We are able to approximately solve significantly larger test instances than previously possible, and obtain solutions on average within 4.27% of optimality. For the concave cost facility location problem, we obtain a new 1.4991+epsilon approximation algorithm.Comment: Full pape

Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optimization problem. Our technique preserves constant factor approximation ratios, as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. Using our technique, we obtain a new 1.61-approximation algorithm for the concave cost facility location problem. For inventory problems, we obtain a new exact algorithm for the economic lot-sizing problem with general concave ordering costs, and a 4-approximation algorithm for the joint replenishment problem with general concave individual ordering costs

On Quantifying Dependence: A Framework for Developing Interpretable Measures

We present a framework for selecting and developing measures of dependence when the goal is the quantification of a relationship between two variables, not simply the establishment of its existence. Much of the literature on dependence measures is focused, at least implicitly, on detection or revolves around the inclusion/exclusion of particular axioms and discussing which measures satisfy said axioms. In contrast, we start with only a few nonrestrictive guidelines focused on existence, range and interpretability, which provide a very open and flexible framework. For quantification, the most crucial is the notion of interpretability, whose foundation can be found in the work of Goodman and Kruskal [Measures of Association for Cross Classifications (1979) Springer], and whose importance can be seen in the popularity of tools such as the $R^2$ in linear regression. While Goodman and Kruskal focused on probabilistic interpretations for their measures, we demonstrate how more general measures of information can be used to achieve the same goal. To that end, we present a strategy for building dependence measures that is designed to allow practitioners to tailor measures to their needs. We demonstrate how many well-known measures fit in with our framework and conclude the paper by presenting two real data examples. Our first example explores U.S. income and education where we demonstrate how this methodology can help guide the selection and development of a dependence measure. Our second example examines measures of dependence for functional data, and illustrates them using data on geomagnetic storms.Comment: Published in at http://dx.doi.org/10.1214/12-STS405 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Quasinormal Modes of Kerr Black Holes in Four and Higher Dimensions

We analytically calculate to leading order the asymptotic form of quasinormal frequencies of Kerr black holes in four, five and seven dimensions. All the relevant quantities can be explicitly expressed in terms of elliptical integrals. In four dimensions, we confirm the results obtained by Keshest and Hod by comparing the analytic results to the numerical ones.Comment: 14 pages, 7 figure