Using Zero-Result SERPs to Teach Users to Search

In certain locales, search-query diversity is poor despite substantial search traffic and/or rapid traffic growth. Consequently, in such locales, the full utility of a search engine remains unknown or unleveraged by the user base. This disclosure describes techniques to provide example search queries along with zero-result search engine result pages (SERPs). The example queries can include queries that are popular in the locale, queries that are contextually relevant to the user’s initial query, etc. The search examples provide user education for the use of a search engine and the possibilities of search, resulting in greater user engagement and retention

On Large Rational Solutions of Cubic Thue Equations: What Thue Did to Pell

In 1659, John Pell and Johann Rahn wrote a text which explained how to find all integer solutions to the quadratic equation u2 - d v2 = 1. In 1909, Axel Thue showed that the cubic equation u3 - d v3 = 1 has finitely many integer solutions, so it remains to examine their rational solutions. We explain how to find large rational solutions i.e., a sequence of rational points (un, vn) which increase without bound as n increases without bound. Such cubic equations are birationally equivalent to elliptic curves of the form y2 = x3 - D. The rational points on an elliptic curve form an abelian group, so a large rational point (u,v) maps to a rational point (x,y) of approximate order 3. Following an idea of Zagier, we explain how to compute such rational points using continued fractions of elliptic logarithms. We divide our discussion into two parts. The first concerns Pell\u27s quadratic equation. We give an informal discussion of the history of the equation, illuminate the relation with the theory of groups, and review known results on properties of integer solutions through the use of continued fractions. The second concerns the more general equation uN - d vN = 1. We explain why N = 3 is the most interesting exponent, present the relation with elliptic curves, and investigate properties of rational solutions through the use of elliptic integrals. This project was completed at Miami University, in Oxford, OH as part of the Summer Undergraduate Mathematical Sciences Institute (SUMSRI)

Lifetime history of indoor tanning in young people: a retrospective assessment of initiation, persistence, and correlates

<p>Abstract</p> <p>Background</p> <p>Despite educational and public health campaigns to convey the risks of indoor tanning, many individuals around the world continue to engage in this behavior. Few descriptive studies of indoor tanning have collected information pertaining to the lifetime history of indoor tanning, thereby limiting our ability to understand indoor tanning patterns and potentially target interventions for individuals who not only initiate, but continue to persistently engage in indoor tanning.</p> <p>Methods</p> <p>In-person interviews elicited detailed retrospective information on lifetime history of indoor tanning among white individuals (n = 401) under age 40 seen by a dermatologist for a minor benign skin condition. These individuals were controls in a case-control study of early-onset basal cell carcinoma. Outcomes of interest included ever indoor tanning in both males and females, as well as persistent indoor tanning in females - defined as females over age 31 who tanned indoors at least once in the last three or all four of four specified age periods (ages 11-15, 16-20, 21-30 and 31 or older). Multivariate logistic regression was used to identify sociodemographic and lifestyle correlates of ever and persistent indoor tanning in females.</p> <p>Results</p> <p>Approximately three-quarters (73.3%) of females and 38.3% of males ever tanned indoors, with a median age of initiation of 17.0 and 21.5, respectively. Among indoor tanners, 39.3% of females and 21.7% of males reported being burned while indoor tanning. Female ever indoor tanners were younger, had darker color eyes, and sunbathed more frequently than females who never tanned indoors. Using unique lifetime exposure data, 24.7% of female indoor tanners 31 and older persistently tanned indoors starting as teenagers. Female persistent indoor tanners drank significantly more alcohol, were less educated, had skin that tanned with prolonged sun exposure, and sunbathed outdoors more frequently than non-persistent tanners.</p> <p>Conclusions</p> <p>Indoor tanning was strikingly common in this population, especially among females. Persistent indoor tanners had other high-risk behaviors (alcohol, sunbathing), suggesting that multi-faceted behavioral interventions aimed at health promotion/disease prevention may be needed in this population.</p

A Partitioning Deletion/Substitution/Addition Algorithm for Creating Survival Risk Groups

As an extension of the partDSA package (Molinaro, Lostritto, and Weston 2009), we present the partDSA Survival package to accommodate survival outcomes. The algorithmic methodology of partDSA is described in Molinaro, Lostritto, and van der Laan (2010), and the extension of partDSA to survival outcomes is described in Lostritto, Strawderman, and Molinaro (2011). PartDSA creates a piecewise constant model for predicting an outcome of interest from a complex interaction of covariates. This model consists of ”and/or ” boolean statements on covariates such that each statement defines a group of observations which are assigned a constant predicted value. The creation of a partDSA model is guided by a specified loss function, and in the case of a survival outcome this loss function must be modified to accommodate a censored outcome. The functionality of partDSA for categorical and continuous outcomes is described in the partDSA vignette and here we describe the new functionality for survival data

Novel Aggregate Deletion/Substitution/Addition Learning Algorithms for Recursive Partitioning

<p>Many complex diseases are caused by a variety of both genetic and environmental factors acting in conjunction. To help understand these relationships, nonparametric methods that use aggregate learning have been developed such as <i>random forests</i> and <i>conditional forests</i>. Molinaro et al. (<a href="#cit0020" target="_blank">2010</a>) described a powerful, single model approach called <i>partDSA</i> that has the advantage of producing interpretable models. We propose two extensions to the <i>partDSA</i> algorithm called <i>bagged partDSA</i> and <i>boosted partDSA</i>. These algorithms achieve higher prediction accuracies than individual <i>partDSA</i> objects through aggregating over a set of <i>partDSA</i> objects. Further, by using <i>partDSA</i> objects in the ensemble, each base learner creates decision rules using both “and” and “or” statements, which allows for natural logical constructs. We also provide four variable ranking techniques that aid in identifying the most important individual factors in the models. In the regression context, we compared bagged partDSA and boosted partDSA to random forests and conditional forests. Using simulated and real data, we found that bagged partDSA had lower prediction error than the other methods if the data were generated by a simple logic model, and that it performed similarly for other generating mechanisms. We also found that <i>boosted partDSA</i> was effective for a particularly complex case. Taken together these results suggest that the new methods are useful additions to the ensemble learning toolbox. We implement these algorithms as part of the partDSA R package. Supplementary materials for this article are available online.</p

partDSA: deletion/substitution/addition algorithm for partitioning the covariate space in prediction

Motivation: Until now, much of the focus in cancer has been on biomarker discovery and generating lists of univariately significant genes, as well as epidemiological and clinical measures. These approaches, although significant on their own, are not effective for elucidating the synergistic qualities of the numerous components in complex diseases. These components do not act one at a time, but rather in concert with numerous others. A compelling need exists to develop analytically sound and computationally advanced methods that elucidate a more biologically meaningful understanding of the mechanisms of cancer initiation and progression by taking these interactions into account