A Variational Perspective on Accelerated Methods in Optimization

Accelerated gradient methods play a central role in optimization, achieving optimal rates in many settings. While many generalizations and extensions of Nesterov's original acceleration method have been proposed, it is not yet clear what is the natural scope of the acceleration concept. In this paper, we study accelerated methods from a continuous-time perspective. We show that there is a Lagrangian functional that we call the \emph{Bregman Lagrangian} which generates a large class of accelerated methods in continuous time, including (but not limited to) accelerated gradient descent, its non-Euclidean extension, and accelerated higher-order gradient methods. We show that the continuous-time limit of all of these methods correspond to traveling the same curve in spacetime at different speeds. From this perspective, Nesterov's technique and many of its generalizations can be viewed as a systematic way to go from the continuous-time curves generated by the Bregman Lagrangian to a family of discrete-time accelerated algorithms.Comment: 38 pages. Subsumes an earlier working draft arXiv:1509.0361

Determinants for Bullying Victimization among 11–16-Year-Olds in 15 Low- and Middle-Income Countries:\ud A Multi-Level Study

Bullying is an issue of public health importance among adolescents worldwide. The present study aimed at explaining differences in bullying rates among adolescents in 15 low- and middle-income countries using globally comparable indicators of social and economic well-being. Using data derived from the Global School-based Health Survey, we performed bivariate analyses to examine differences in bullying rates by country and by bullying type. We then constructed a multi-level model using four fixed variables (age, gender, hunger and truancy) at the individual level, random effects at the classroom and\ud school levels and four fixed variables at the country level (Gini coefficient, per capita Gross Domestic Project, homicide rate and pupil to teacher ratio). Bullying rates differed significantly by classroom, school and by country, with Egypt (34.2%) and Macedonia (3.6%) having the highest and lowest rates, respectively. Eleven-year-olds were the most likely of the studied age groups to report being bullied, as was being a male. Hunger and truancy were found to significantly predict higher rates of bullying. None of the explanatory variables at the country level remained in the final model. While self-reported bullying varied significantly between countries, the variance between classrooms better explained these differences. Our findings suggest that classroom settings should be considered when designing approaches aimed at bullying prevention.\u

A Genetic Locus Regulates the Expression of Tissue-Specific mRNAs from Multiple Transcription Units

129 GIX- mice, unlike animals of the congeneic partner strain GIX+, do not express significant amounts of the retroviral antigens gp70 and p30. Evidence is presented indicating that the GIX phenotype is specified by a distinct regulatory gene acting on multiple transcription units to control the levels of accumulation of specific mRNA species. The steady-state levels of retroviral-homologous mRNA from the tissues of GIX+ and GIX- mice were examined by blot hybridization using as probes DNA fragments from cloned murine leukemia viruses. RNA potentially encoding viral antigens was reduced or absent in GIX- mice, even though no differences in integrated viral genomes were detected between these congeneic strains by DNA blotting. Tissue-specific patterns of accumulation of these RNA species were detected in brain, epididymis, liver, spleen, and thymus, and several distinct RNA species were found to be coordinately regulated with the GIX phenotype. Measurements of RNA synthesis suggest a major role for transcriptional control in the regulation of some retroviral messages

Reconciling diverse lacustrine and terrestrial system response to penultimate deglacial warming in southern Europe

Unlike the most recent deglaciation, the regional expression of climate changes during the penultimate deglaciation remains understudied, even though it led into a period of excess warmth with estimates of global average temperature 1–2 °C, and sea level ∼6 m, above pre-industrial values. We present the first complete high-resolution southern European diatom record capturing the penultimate glacial-interglacial transition, from Lake Ioannina (northwest Greece). It forms part of a suite of proxies selected to assess the character and phase relationships of terrestrial and aquatic ecosystem response to rapid climate warming, and to resolve apparent conflicts in proxy evidence for regional paleohydrology. The diatom data suggest a complex penultimate deglaciation driven primarily by multiple oscillations in lake level, and provide firm evidence for the regional influence of abrupt changes in North Atlantic conditions. There is diachroneity in lake and terrestrial ecosystem response to warming at the onset of the last interglacial, with an abrupt increase in lake level occurring ∼2.7 k.y. prior to sustained forest expansion with peak precipitation. We identify the potentially important role of direct input of snow melt and glacial meltwater transfer to the subterranean karst system in response to warming, which would cause rising regional groundwater levels. This explanation, and the greater sensitivity of diatoms to subtle changes in temperature, reconciles the divergent lacustrine and terrestrial proxy evidence and highlights the sensitivity of lakes situated in mountainous karstic environments to past climate warming

Your Place in Space: Classroom Experiment on Spatial Location Theory

The authors detail an urban economics experiment that is easily run in the classroom. The experiment has a flexible design that allows the instructor to explore how congestion, zoning, public transportation, and taxation levels determine the bid-rent function. Heterogeneous agents in the experiment compete for land use utilizing a simple auction mechanism. Using the data that is collected, a bid-rent function is derived, and the experimental treatment is altered over the course of three sessions to uncover core concepts in urban economics. Moreover, this provides a tangible experience that can be used to help undergraduates relate to urban issues such as the steep rent gradient found around many larger colleges and universities.

Advances in Data Combination, Analysis and Collection for System Reliability Assessment

The systems that statisticians are asked to assess, such as nuclear weapons, infrastructure networks, supercomputer codes and munitions, have become increasingly complex. It is often costly to conduct full system tests. As such, we present a review of methodology that has been proposed for addressing system reliability with limited full system testing. The first approaches presented in this paper are concerned with the combination of multiple sources of information to assess the reliability of a single component. The second general set of methodology addresses the combination of multiple levels of data to determine system reliability. We then present developments for complex systems beyond traditional series/parallel representations through the use of Bayesian networks and flowgraph models. We also include methodological contributions to resource allocation considerations for system relability assessment. We illustrate each method with applications primarily encountered at Los Alamos National Laboratory.Comment: Published at http://dx.doi.org/10.1214/088342306000000439 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org