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Register a new userA comparison of partisan-gerrymandering measures
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Gregory S. Warrington
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We compare and contrast fourteen measures that have been proposed for the purpose of quantifying partisan gerrymandering. We consider measures that, rather than examining the shapes of districts, utilize only the partisan vote distribution among districts. The measures considered are t
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Many people believe that it is disadvantageous for members aligning with a minority party to cluster in cities, as this makes it easier for the majority party to gerrymander district boundaries to diminish the representation of the minority. We examine this effect by exhaustively computing the average representation for every possible $5times 5$ grid of population placement and district boundaries. We show that, in fact, it is advantageous for the minority to arrange themselves in clusters, as it is positively correlated with representation. We extend this result to more general cases by considering the dual graph of districts, and we also propose and analyze metaheuristic algorithms that allow us to find strong lower bounds for maximum expected representation.
We study empirically how the fame of WWI fighter-pilot aces, measured in numbers of web pages mentioning them, is related to their achievement, measured in numbers of opponent aircraft destroyed. We find that on the average fame grows exponentially with achievement; the correlation coefficient between achievement and the logarithm of fame is 0.72. The number of people with a particular level of achievement decreases exponentially with the level, leading to a power-law distribution of fame. We propose a stochastic model that can explain the exponential growth of fame with achievement. Next, we hypothesize that the same functional relation between achievement and fame that we found for the aces holds for other professions. This allows us to estimate achievement for professions where an unquestionable and universally accepted measure of achievement does not exist. We apply the method to Nobel Prize winners in Physics. For example, we obtain that Paul Dirac, who is a hundred times less famous than Einstein contributed to physics only two times less. We compare our results with Landaus ranking.
Though competitive analysis has been a very useful performance measure for the quality of online algorithms, it is recognized that it sometimes fails to distinguish between algorithms of different quality in practice. A number of alternative measures have been proposed, but, with a few exceptions, these have generally been applied only to the online problem they were developed in connection with. Recently, a systematic study of performance measures for online algorithms was initiated [Boyar, Irani, Larsen: Eleventh International Algorithms and Data Structures Symposium 2009], first focusing on a simple server problem. We continue this work by studying a fundamentally different online problem, online search, and the Reservation Price Policies in particular. The purpose of this line of work is to learn more about the applicability of various performance measures in different situations and the properties that the different measures emphasize. We investigate the following analysis techniques: Competitive, Relative Worst Order, Bijective, Average, Relative Interval, Random Order, and Max/Max. In addition to drawing conclusions on this work, we also investigate the measures sensitivity to integral vs. real-valued domains, and as a part of this work, generalize some of the known performance measures. Finally, we have established the first optimality proof for Relative Interval Analysis.
Diseases spread over temporal networks of interaction events between individuals. Structures of these temporal networks hold the keys to understanding epidemic propagation. One early concept of the literature to aid in discussing these structures is concurrency -- quantifying individuals tendency to form time-overlapping partnerships. Although conflicting evaluations and an overabundance of operational definitions have marred the history of concurrency, it remains important, especially in the area of sexually transmitted infections. Today, much of theoretical epidemiology uses more direct models of contact patterns, and there is an emerging body of literature trying to connect methods to the concurrency literature. In this review, we will cover the development of the concept of concurrency and these new approaches.
This chapter introduces OpenStreetMap - a crowd-sourced, worldwide mapping project and geospatial data repository - to illustrate its usefulness in quickly and easily analyzing and visualizing planning and design outcomes in the built environment. It demonstrates the OSMnx toolkit for automatically downloading, modeling, analyzing, and visualizing spatial big data from OpenStreetMap. We explore patterns and configurations in street networks and buildings around the world computationally through visualization methods - including figure-ground diagrams and polar histograms - that help compress urban complexity into comprehensible artifacts that reflect the human experience of the built environment. Ubiquitous urban data and computation can open up new urban form analyses from both quantitative and qualitative perspectives.
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