Explore the vast range of titles available.

We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have proposed 'SAFE' rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into the optimization. We propose strong rules that are very simple and yet screen out far more predictors than the SAFE rules. This great practical improvement comes at a price: the strong rules are not foolproof and can mistakenly discard active predictors, i.e. predictors that have non-zero coefficients in the solution. We therefore combine them with simple checks of the Karush-Kuhn-Tucker conditions to ensure that the exact solution to the convex problem is delivered. Of course, any (approximate) screening method can be combined with the Karush-Kuhn-Tucker conditions to ensure the exact solution; the strength of the strong rules lies in the fact that, in practice, they discard a very large number of the inactive predictors and almost never commit mistakes. We also derive conditions under which they are foolproof. Strong rules provide substantial savings in computational time for a variety of statistical optimization problems.

The leaf economics spectrum (LES) describes multivariate correlations that constrain leaf traits of plant species primarily to a single axis of variation if data are normalized by leaf mass. We show that these traits are approximately distributed proportional to leaf area instead of mass, as expected for a light- and carbon dioxide-collecting organ. Much of the structure in the mass-normalized LES results from normalizing area-proportional traits by mass. Mass normalization induces strong correlations among area-proportional traits because of large variation among species in leaf mass per area (LMA). The high LMA variance likely reflects its functional relationship with leaf life span. A LES that is independent of mass- or area-normalization and LMA reveals physiological relationships that are inconsistent with those in global vegetation models designed to address climate change.

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions. Significance Growth and division of individual cells are the fundamental events underlying many biological processes, including the development of organisms, the growth of tumors, and pathogen–host interactions. Quantitative studies of bacteria can provide insights into single-cell growth and division but are challenging owing to the intrinsic noise in these processes. Now, by using a unique combination of measurement and analysis technologies, together with mathematical modeling, we discover quantitative features that are conserved across physiological conditions. These universal behaviors reflect the physical principle that a single timescale governs noisy bacterial growth and division despite the complexity of underlying molecular mechanisms.

Reproducibility is essential to reliable scientific discovery in high-throughput experiments. In this work we propose a unified approach to measure the reproducibility of findings identified from replicate experiments and identify putative discoveries using reproducibility. Unlike the usual scalar measures of reproducibility, our approach creates a curve, which quantitatively assesses when the findings are no longer consistent across replicates. Our curve is fitted by a copula mixture model, from which we derive a quantitative reproducibility score, which we call the \"irreproducible discovery rate\" (IDR) analogous to the FDR. This score can be computed at each set of paired replicate ranks and permits the principled setting of thresholds both for assessing reproducibility and combining replicates. Since our approach permits an arbitrary scale for each replicate, it provides useful descriptive measures in a wide variety of situations to be explored. We study the performance of the algorithm using simulations and give a heuristic analysis of its theoretical properties. We demonstrate the effectiveness of our method in a ChIP-seq experiment.

Many cities in North America formed at obstacles to water navigation, where continued transport required overland hauling or portage. Portage sites attracted commerce and supporting services, and places where the falls provided water power attracted manufacturing during early industrialization. We examine portage sites in the U.S. South, Mid-Atlantic, and Midwest, including those on the fall line, a geomorphological feature in the southeastern United States marking the final rapids on rivers before the ocean. Although their original advantages have long since become obsolete, we document the continuing importance of historical portage sites. We interpret these results as path dependence and contrast explanations based on sunk costs interacting with decreasing versus increasing returns to scale.

Aim: The area under the receiver operating characteristic (ROC) curve (AUC) is a widely used statistic for assessing the discriminatory capacity of species distribution models. Here, I used simulated data to examine the interdependence of the AUC and classical discrimination measures (sensitivity and specificity) derived for the application of a threshold. I shall further exemplify with simulated data the implications of using the AUC to evaluate potential versus realized distribution models. Innovation: After applying the threshold that makes sensitivity and specificity equal, a strong relationship between the AUC and these two measures was found. This result is corroborated with real data. On the other hand, the AUC penalizes the models that estimate potential distributions (the regions where the species could survive and reproduce due to the existence of suitable environmental conditions), and favours those that estimate realized distributions (the regions where the species actually lives). Main conclusions: Firstly, the independence of the AUC from the threshold selection may be irrelevant in practice. This result also emphasizes the fact that the AUC assumes nothing about the relative costs of errors of omission and commission. However, in most real situations this premise may not be optimal. Measures derived from a contingency table for different cost ratio scenarios, together with the ROC curve, may be more informative than reporting just a single AUC value. Secondly, the AUC is only truly informative when there are true instances of absence available and the objective is the estimation of the realized distribution. When the potential distribution is the goal of the research, the AUC is not an appropriate performance measure because the weight of commission errors is much lower than that of omission errors.

Polynomial regression with response surface analysis is a sophisticated statistical approach that has become increasingly popular in multisource feedback research (e.g., self-observer rating discrepancy). The approach allows researchers to examine the extent to which combinations of two predictor variables relate to an outcome variable, particularly in the case when the discrepancy (difference) between the two predictor variables is a central consideration. We believe this approach has potential for application to a wide variety of research questions. To enhance interest and use of this technique, we provide ideas for future research directions that might benefit from the application of this analytic tool. We also walk through a step-by-step example of how to conduct polynomial regression and response surface analysis and provide all the tools you will need to do the analyses and graph the results (including SPSS syntax, formulas, and a downloadable Excel spreadsheet). Our example involves how discrepancies in perceived supervisor and organizational support relate to affective commitment. Finally, we discuss how this approach is a better, more informative alternative to difference scores and can be applied to the examination of twoway interactions in moderated regression.

In everyday life, many people believe that two heads are better than one. Our ability to solve problems together appears to be fundamental to the current dominance and future survival of the human species. But are two heads really better than one? We addressed this question in the context of a collective low-level perceptual decision-making task. For two observers of nearly equal visual sensitivity, two heads were definitely better than one, provided they were given the opportunity to communicate freely, even in the absence of any feedback about decision outcomes. But for observers with very different visual sensitivities, two heads were actually worse than the better one. These seemingly discrepant patterns of group behavior can be explained by a model in which two heads are Bayes optimal under the assumption that individuals accurately communicate their level of confidence on every trial.

The present two-part review aims to put the different phenomena that have been called \"beta diversity\" over the years into a common conceptual framework and to explain what each of them measures. The first part (Tuomisto 2010) discussed basic definitions of \"beta diversity\". Each arises from a different way of combining a definition of \"diversity\" with a definition of its alpha component and with a mathematical relationship between the alpha and gamma components. This second part assumes that an appropriate basic definition of a beta component (which may or may not be true beta diversity) has been chosen, and the focus here will be on how to quantify it for a given dataset. About twenty different approaches have been used for this purpose. It turns out that only two of these approaches accurately quantify the selected beta component: one does so for the entire dataset, and the other for two sampling units at a time. The other approaches actually quantify other phenomena, such as mean species turnover between sampling units, compositional gradient length (with or without reference to an external gradient), distinctness of a focal sampling unit, rate of species accumulation with increasing sampling effort, rate of compositional turnover along an external gradient, or the rate of decay in compositional similarity with increasing geographical distance. Although most of these phenomena can be expressed as a function of a beta component of diversity, they do not equal a beta component of diversity. Many of these derived variables are not even numerically correlated with the beta component on which they are based, which needs to be taken into account when interpreting the results. The effects of sampling decisions when results are extrapolated beyond the available data will also be discussed.

The subject of collective attention is central to an information age where millions of people are inundated with daily messages. It is thus of interest to understand how attention to novel items propagates and eventually fades among large populations. We have analyzed the dynamics of collective attention among 1 million users of an interactive web site, digg.com, devoted to thousands of novel news stories. The observations can be described by a dynamical model characterized by a single novelty factor. Our measurements indicate that novelty within groups decays with a stretched-exponential law, suggesting the existence of a natural time scale over which attention fades.