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Suppose that $G$ is a simple, vertex-labeled graph and that $S$ is a multiset. Then if there exists a one-to-one mapping between the elements of $S$ and the vertices of $G$, such that edges in $G$ exist if and only if the absolute difference of the corresponding vertex labels exist in $S$, then $G$ is an \emph{autograph}, and $S$ is a \emph{signature} for $G$. While it is known that many common families are graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited. In this paper, we identify the smallest non-autograph: a graph with 6 vertices and 11 edges. Furthermore, we demonstrate that the infinite family of graphs on $n$ vertices consisting of the complement of two non-intersecting cycles contains only non-autographs for $n \geq 8$., Comment: 18 pages

Data science is an emerging interdisciplinary field that combines elements of mathematics, statistics, computer science, and knowledge in a particular application domain for the purpose of extracting meaningful information from the increasingly sophisticated array of data available in many settings. These data tend to be non-traditional, in the sense that they are often live, large, complex, and/or messy. A first course in statistics at the undergraduate level typically introduces students with a variety of techniques to analyze small, neat, and clean data sets. However, whether they pursue more formal training in statistics or not, many of these students will end up working with data that is considerably more complex, and will need facility with statistical computing techniques. More importantly, these students require a framework for thinking structurally about data. We describe an undergraduate course in a liberal arts environment that provides students with the tools necessary to apply data science. The course emphasizes modern, practical, and useful skills that cover the full data analysis spectrum, from asking an interesting question to acquiring, managing, manipulating, processing, querying, analyzing, and visualizing data, as well communicating findings in written, graphical, and oral forms., Comment: 21 pages total including supplementary materials

Reproducibility is increasingly important to statistical research, but many details are often omitted from the published version of complex statistical analyses. A reader's comprehension is limited to what the author concludes, without exposure to the computational process. Often, the industrious reader cannot expand upon or validate the author's results. Even the author may struggle to reproduce their own results upon revisiting them. R Markdown is an authoring syntax that combines the ease of Markdown with the statistical programming language R. An R Markdown document or presentation interweaves computation, output and written analysis to the effect of transparency, clarity and an inherent invitation to reproduce (especially as sharing data is now as easy as the click of a button). It is an open-source tool that can be used either on its own or through the RStudio integrated development environment (IDE). In addition to facilitating reproducible research, R Markdown is a boon to collaboratively-minded data analysts, whose workflow can be streamlined by sharing only one master document that contains both code and content. Statistics educators may also find that R Markdown is helpful as a homework template, for both ease-of-use and in discouraging students from copy-and-pasting results from classmates. Training students in R Markdown will introduce to the workforce a new class of data analysts with an ingrained, foundational inclination toward reproducible research., Comment: 16 pages

Nolan and Temple Lang argue that "the ability to express statistical computations is an essential skill." A key related capacity is the ability to conduct and present data analysis in a way that another person can understand and replicate. The copy-and-paste workflow that is an artifact of antiquated user-interface design makes reproducibility of statistical analysis more difficult, especially as data become increasingly complex and statistical methods become increasingly sophisticated. R Markdown is a new technology that makes creating fully-reproducible statistical analysis simple and painless. It provides a solution suitable not only for cutting edge research, but also for use in an introductory statistics course. We present evidence that R Markdown can be used effectively in introductory statistics courses, and discuss its role in the rapidly-changing world of statistical computation., Comment: 20 pages, plus a 10 page appendix

We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard. Second, we show that RoundRobin, the algorithm in which the sensors simply take turns covering the entire region, has a tight approximation guarantee of 3/2 in both Set Once Strip Cover and the more general Strip Cover problem, in which each radius may be set finitely-many times. Moreover, we show that the more general class of duty cycle algorithms, in which groups of sensors take turns covering the entire region, can do no better. Finally, we give an optimal O(n^2 log n)-time algorithm for the related Set Radius Strip Cover problem, in which all sensors must be activated immediately., Comment: briefly announced at SPAA 2013