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

The "Placing" of Identity in Nomadic Societies: Aboriginal Landscapes of the Northwestern Plains of North America

Nomadic Northwestern Plains First Nations expressed fundamental symbols semiotically across media. Landscapes were transformational assemblages of signs and symbols; circle and power axis signified the cosmos. Ritual monuments were linked through animal ceremonialism to cosmic renewal. Animals were limitless if appropriate ritual was maintained. Formalized circular household plans signified the cosmos with the horizon-bounded outer landscape "read" by extension as consistent with the constructed inner world. Cyclic time had spatial parallels, with sites as cyclic iterations of prototypic place and performance. This aboriginal life-world was a web of overlapping territories with mobile centres and radiating itineraries. Sharing of resources and ritual sites, and transient co-residence of groups were facilitated by hand-signs that reinforced sym bolic "unity-within-diversity." These characteristics all had definable landscape correlates and consequences. Monuments were "of" a site, not "upon" it: deriving substance and power from location, they became "natural" elements. Résumé Les premières nations nomades des plaines du Nord-Ouest exprimaient sémiotiquement leurs symboles fondamentaux par divers canaux. Les pay sages étaient des assemblages en transformation de signes et de symboles et le cercle et l'axe de puissance représentaient le cosmos. Les monuments rituels étaient liés au renouveau cosmique par des cérémonies mettant en scène des animaux. Ceux-ci étaient considérés inépuisables si on observait le rituel adéquat. Les habitats circulaires représentaient le cosmos et le paysage extérieur délimité par l'horizon pouvait par extension être « lu » comme conforme aux structures du monde intérieur. Les cycles du temps avaient leurs pendants spatiaux, des circuits cycliques de prototypes d'emplacements et d'activités. Ce monde autochtone était une toile de territoires qui se chevauchaient, avec des centres mobiles autour desquels rayonnaient des trajets. Le partage des ressources et des lieux rituels et la coexistence passagère des groupes étaient facilités par le langage gestuel qui renforçait une symbolique « unité dans la diversité ». Ces caractéristiques avaient toutes des corrélations et des conséquences définissables dans le paysage. Les monuments étaient d'un emplacement, pas superposés à lui, et tiraient substance et force du lieu. Ils devenaient des éléments « naturels »

Helmeted Muskox (Bootherium bombifrons) from Near Fort Saskatchewan, Alberta: Dating Evidence for Redeposition in Late Pleistocene Alluvium

Superimposition and intersection of preglacial and postglacial valley systems on the Canadian plains indicates that some of the recovered Quaternary vertebrate fossils may be redeposited. To test this proposition, an accelerator mass spectrometer (AMS) date was obtained on bone from a previously described helmeted muskox skull from near Fort Saskatchewan, Alberta. The specimen, identified as Bootherium bombifrons = Symbos cavifrons was previously thought to be Late Pleistocene (postglacial) in age but showed evidence of transport. A date of 30 570 ± 250 14C yrs BP indicates that it is of Middle Wisconsinan (pre-Last Glacial Maximum) age and therefore was ultimately derived from the Empress Formation (Saskatchewan Gravels and Sands) in the Edmonton area. Other vertebrate fossils must be assessed carefully in this light and direct dating is recommended wherever possible to facilitate both stratigraphic and paleontological studies.La surimposition et l’entrecroisement des réseaux fluviatiles pré- et postglaciaires dans les Prairies indiquent que certains fossiles de vertébrés du Quaternaire pourraient avoir fait l’objet d’un remaniement. Pour tester l’hypothèse, nous avons daté, à l'aide d'un accélérateur de particules (SMA), un os provenant d'un crâne d'ovibos casqué (antérieurement décrit) trouvé près de Fort Saskatchewan. Identifié comme un Bootherium bombifrons = Symbos cavifrons, le spécimen, qu'on avait daté du Pléistocène supérieur (postglaciaire), portait des traces de transport. La date de 30 570 ± 250 ans 14C BP obtenue par SMA, indique qu'il daterait plutôt du Wisconsinien moyen (avant le dernier maximum glaciaire) et qu'il proviendrait, par conséquent, de la Formation d’Empress (Graviers et Sables de la Saskatchewan), dans la région d'Edmonton. À la lumière de ce résultat, d'autres fossiles de vertébrés devraient être réétudiés et, dans la mesure du possible, faire l'objet d'une datation directe, afin de favoriser les études stratigraphiques et paléontologiques