Derived Mackey functors and CpnC_{p^n}-equivariant cohomology

We establish a novel approach to computing $G$-equivariant cohomology for a finite group $G$, and demonstrate it in the case that $G = C_{p^n}$. For any commutative ring spectrum $R$, we prove a symmetric monoidal reconstruction theorem for genuine $G$-$R$-modules, which records them in terms of their geometric fixedpoints as well as gluing maps involving their Tate cohomologies. This reconstruction theorem follows from a symmetric monoidal stratification (in the sense of \cite{AMR-strat}); here we identify the gluing functors of this stratification in terms of Tate cohomology. Passing from genuine $G$-spectra to genuine $G$-$\mathbb{Z}$-modules (a.k.a. derived Mackey functors) provides a convenient intermediate category for calculating equivariant cohomology. Indeed, as $\mathbb{Z}$-linear Tate cohomology is far simpler than $\mathbb{S}$-linear Tate cohomology, the above reconstruction theorem gives a particularly simple algebraic description of genuine $G$-$\mathbb{Z}$-modules. We apply this in the case that $G = C_{p^n}$ for an odd prime $p$, computing the Picard group of genuine $G$-$\mathbb{Z}$-modules (and therefore that of genuine $G$-spectra) as well as the $RO(G)$-graded and Picard-graded $G$-equivariant cohomology of a point.Comment: improved introduction; minor notational changes and reorganizatio

American Literary Environmentalism, 1637-1872.

The American environment is a mythic narrative that has served to mystify the social and economic relationships linking people and place. This study examines the early writing of the environment, from the 1637 Pequot War to the creation of the first national parks in the late nineteenth century. Chapter 1 draws on the work of Michel Foucault and Edward Said to theorize literary environmentalism as a knowledge-power formation that functions as a domestic Orientalism. Chapter 2 theorizes the narratological and psychosociological bases of environmental constructions generally before analyzing two colonial texts whose literary environmentalism is paradigmatic: John Underhill\u27s Newes from America (1638), which writes the New England wilderness via tropes of gender and race that explicitly link the environment\u27s description to its possession, and Mary Rowlandson\u27s The Soveraignty and Goodness of God (1682), which recapitulates but also complicates these figures. Chapter 3 analyzes James Fenimore Cooper\u27s The Last of the Mohicans (1826), paying particular attention to how its wilderness serves to naturalize the regeneration of a racially pure American civilization. Chapter 4 analyzes three works related by their linked constructions of Yosemite Valley. Lafayette Bunnell\u27s account of the Mariposa Indian War (1851-1852), The History of the Discovery of the Yosemite, utilizes an aesthetic discourse to justify the ethnic cleansing that accompanied the discovery of Yosemite. Frederick Law Olmsted\u27s 1865 management report on the new Yosemite Park implicates the national park idea in an urban-industrial ideology of social sanitation through outdoor recreation. Clarence King\u27s Mountaineering in the Sierra Nevada (1872) links environmentalism and literary realism to the exigencies of a fast-maturing corporate capitalism. My concluding chapter analyzes the idea of the postnatural in two contemporary ecocritical texts, Bill McKibben\u27s The End of Nature and Rebecca Solnit\u27s Savage Dreams. McKibben\u27s work recapitulates the early colonialist and capitalist trope of the virgin wilderness, while Savage Dreams refuses the concept of an originary nature and adopts a more promising mode for a genuinely revisionist environmental writing, one that refuses to seek in nature the sorts of lessons and remedies available only through a conscious engagement with this nation\u27s own cultures

Stratified noncommutative geometry

We introduce a theory of stratifications of noncommutative stacks (i.e. presentable stable $\infty$-categories), and we prove a reconstruction theorem that expresses them in terms of their strata and gluing data. This reconstruction theorem is compatible with symmetric monoidal structures, and with more general operadic structures such as $E_n$-monoidal structures. We also provide a suite of fundamental operations for constructing new stratifications from old ones: restriction, pullback, quotient, pushforward, and refinement. Moreover, we establish a dual form of reconstruction, which is closely related to reflection functors and Verdier duality. Our main application is to equivariant stable homotopy theory: for any compact Lie group $G$, we give a symmetric monoidal stratification of genuine $G$-spectra, that expresses them in terms of their geometric fixedpoints (as homotopy-equivariant spectra) and gluing data therebetween (which are given by proper Tate constructions). We also prove an adelic reconstruction theorem; this applies not just to ordinary schemes but in the more general context of tensor-triangular geometry, where we obtain a symmetric monoidal stratification over the Balmer spectrum. We discuss the particular example of chromatic homotopy theory: the adelic stratification of the $\infty$-category of spectra.Comment: Added material on: reflection functors; Verdier duality; t-structures; alignment ("noncommutative general position"); the pullback and refinement operations; central co/augmented idempotents; non-presentable stratifications; categorical fixedpoints; gluing functors for $G$ nonabelian; naive $G$-spectra. (A version with improved formatting is available at https://etale.site/writing/strat.pdf.

Pseudo-Random Number Generation on GP-GPU

International audienceRandom number generation is a key element of stochastic simulations. It has been widely studied for sequential applications purposes, enabling us to reliably use pseudo-random numbers in this case. Unfortunately, we cannot be so enthusiastic when dealing with parallel stochastic simulations. Many applications still neglect random stream parallelization, leading to potentially biased results. Particular parallel execution platforms, such as Graphics Processing Units (GPUs), add their constraints to those of Pseudo-Random Number Generators (PRNGs) used in parallel. It results in a situation where potential biases can be combined to performance drops when parallelization of random streams has not been carried out rigorously. Here, we propose criteria guiding the design of good GPU-enabled PRNGs. We enhance our comments with a study of the techniques aiming to correctly parallelize random streams, in the context of GPU-enabled stochastic simulations

Reliable Initialization of GPU-enabled Parallel Stochastic Simulations Using Mersenne Twister for Graphics Processors

International audienceParallel stochastic simulations tend to exploit more and more computing power and they are now also developed for General Purpose Graphics Process Units (GP-GPUs). Conse-quently, they need reliable random sources to feed their applications. We propose a survey of the current Pseudo Random Numbers Generators (PRNG) available on GPU. We give a particular focus to the recent Mersenne Twister for Graphics Processors (MTGP) that has just been released. Our work provides empirically checked statuses designed to initialize a particular configuration of this generator, in order to prevent any potential bias introduced by the parallelization of the PRNG

Prototyping Parallel Simulations on Manycore Architectures Using Scala: A Case Study

International audienceAt the manycore era, every simulation practitioner can take advantage of the com-puting horsepower delivered by the available high performance computing devices. From multicoreCPUs (Central Processing Unit) to thousand-thread GPUs (Graphics Processing Unit), severalarchitectures are now able to offer great speed-ups to simulations. However, it is often tricky toharness them properly, and even more complicated to implement a few declinations of the samemodel to compare the parallelizations. Thus, simulation practitioners would mostly benefit of asimple way to evaluate the potential benefits of choosing one platform or another to parallelizetheir simulations. In this work, we study the ability of the Scala programming language to fulfillthis need. We compare the features of two frameworks in this study: Scala Parallel Collections andScalaCL. Both of them provide facilities to set up a data-parallelism approach on Scala collections.The capabilities of the two frameworks are benchmarked with three simulation models as well asa large set of parallel architectures. According to our results, these two Scala frameworks shouldbe considered by the simulation community to quickly prototype parallel simulations, and choosethe target platform on which investing in an optimized development will be rewarding

ShoveRand: a Model-Driven Framework to Easily Generate Random Numbers on GP-GPU

International audienceStochastic simulations are often sensitive to the randomness source that characterizes the statistical quality of their results. Consequently, we need highly reliable Random Number Generators (RNGs) to feed such applications. Recent developments try to shrink the computation time by using more and more General Purpose Graphics Processing Units (GP-GPUs) to speed-up stochastic simulations. Such devices bring new parallelization possibilities, but they also introduce new programming difficulties. Since RNGs are at the base of any stochastic simulation, they also need to be ported to GP-GPU. There is still a lack of well-designed implementations of quality-proven RNGs on GP-GPU platforms. In this paper, we introduce ShoveRand, a framework defining common rules to generate random numbers uniformly on GP-GPU. Our framework is designed to cope with any GPU-enabled development platform and to expose a straightforward interface to users. We also provide an existing RNG implementation with this framework to demonstrate its efficiency in both development and ease of use