Loop Quasi-Invariant Chunk Motion by peeling with statement composition

Several techniques for analysis and transformations are used in compilers. Among them, the peeling of loops for hoisting quasi-invariants can be used to optimize generated code, or simply ease developers' lives. In this paper, we introduce a new concept of dependency analysis borrowed from the field of Implicit Computational Complexity (ICC), allowing to work with composed statements called Chunks to detect more quasi-invariants. Based on an optimization idea given on a WHILE language, we provide a transformation method - reusing ICC concepts and techniques - to compilers. This new analysis computes an invariance degree for each statement or chunks of statements by building a new kind of dependency graph, finds the maximum or worst dependency graph for loops, and recognizes if an entire block is Quasi-Invariant or not. This block could be an inner loop, and in that case the computational complexity of the overall program can be decreased. We already implemented a proof of concept on a toy C parser 1 analysing and transforming the AST representation. In this paper, we introduce the theory around this concept and present a prototype analysis pass implemented on LLVM. In a very near future, we will implement the corresponding transformation and provide benchmarks comparisons.Comment: In Proceedings DICE-FOPARA 2017, arXiv:1704.0516

Quebec's Green Future: The Lowest-Cost Route to Green Gas Reductions

The authors say Quebec’s efforts to reduce greenhouse gas (GHG) emissions must face some key facts. First, the possibilities of an effective reduction of GHG emissions through the substitution of one energy source for another are limited in Quebec. Second, Quebec’s era of low-cost hydroelectric production is finished. And third, low domestic electricity prices favour heavy usage and limit Quebec’s capacity to export clean hydroelectricity. This Backgrounder is also available in French.economic growth and innovation, greenhouse gas emissions (GHG), Quebec, carbon tax

Rational BV-algebra in String Topology

Let $M$ be a 1-connected closed manifold and $LM$ be the space of free loops on $M$. In \cite{C-S} M. Chas and D. Sullivan defined a structure of BV-algebra on the singular homology of $LM$, H_\ast(LM; \bk). When the field of coefficients is of characteristic zero, we prove that there exists a BV-algebra structure on \hH^\ast(C^\ast (M); C^\ast (M)) which carries the canonical structure of Gerstenhaber algebra. We construct then an isomorphism of BV-algebras between \hH^\ast (C^\ast (M); C^\ast (M)) and the shifted H_{\ast+m} (LM; {\bk}). We also prove that the Chas-Sullivan product and the BV-operator behave well with the Hodge decomposition of $H_\ast (LM)$

On the cohomology algebra of free loop spaces

Let $X$ be a simply connected space and $\Bbb K$ be any field. The normalized singular cochains $N^*(X; {\Bbb K})$ admit a natural strongly homotopy commutative algebra structure, which induces a natural product on the Hochschild homology $HH_* N^*X$ of the space $X$. We prove that, endowed with this product, $HH_*N^*X$ is isomorphic to the cohomology algebra of the free loop space of $X$ with coefficients in $\Bbb K$. We also show how to construct a simpler Hochschild complex which allows direct computation.Comment: 21 pages, to appear in Topolog

https://www.researchgate.net/publication/329529188_Comparative_Performance_Prediction_of_Historical_Thames_A_Rater_Class_Designs

The Thames A-Rater fleet is a unique class both in appearance and in its combination of historic and modern technologies. With high aspect ratio, carbon fibre rigs fitted onto wooden hulls, many of which have survived two World Wars, the class is a demonstration of the evolution of sailing technology. In more recent decades, various attempts have been made to expand the class with new composite boats. However, due to the strict rules issued by the class association, new hulls must be exact replicas of existing A-Raters, with a 1.5 inch tolerance. Furthermore, as only one linesplan exists in the public domain, the expansion of the fleet is extremely limited. Consequently, in order to ensure the conservation of some of these historic designs, the lines of several vessels were taken off and used to create accurate linesplan and 3D models. The comparative performance of the various crafts was then assessed through a Velocity Prediction Programme, focused on the specific environmental conditions of the vessels' main operating area, eventually ascertaining the hull with the best racing potential by design

String topology on Gorenstein spaces

The purpose of this paper is to describe a general and simple setting for defining $(g,p+q)$-string operations on a Poincar\'e duality space and more generally on a Gorenstein space. Gorenstein spaces include Poincar\'e duality spaces as well as classifying spaces or homotopy quotients of connected Lie groups. Our presentation implies directly the homotopy invariance of each $(g,p+q)$-string operation as well as it leads to explicit computations.Comment: 30 pages and 2 figure