Universal countable Borel quasi-orders

In recent years, much work in descriptive set theory has been focused on the Borel complexity of naturally occurring classification problems, in particular, the study of countable Borel equivalence relations and their structure under the quasi-order of Borel reducibility. Following the approach of Louveau and Rosendal for the study of analytic equivalence relations, we study countable Borel quasi-orders. In this paper we are concerned with universal countable Borel quasi-orders, i.e. countable Borel quasi-orders above all other countable Borel quasi-orders with regard to Borel reducibility. We first establish that there is a universal countable Borel quasi-order, and then establish that several countable Borel quasi-orders are universal. An important example is an embeddability relation on descriptive set theoretic trees. Our main result states that embeddability of finitely generated groups is a universal countable Borel quasi-order, answering a question of Louveau and Rosendal. This immediately implies that biembeddability of finitely generated groups is a universal countable Borel equivalence relation. The same techniques are also used to show that embeddability of countable groups is a universal analytic quasi-order. Finally, we show that, up to Borel bireducibility, there are continuum-many distinct countable Borel quasi-orders which symmetrize to a universal countable Borel equivalence relation

Factoring out ordered sections to expose thread-level parallelism

With the rise of multi-core processors, researchers are taking a new look at extending the applicability auto-parallelization techniques. In this paper, we identify a dependence pattern on which autoparallelization currently fails. This dependence pattern occurs for ordered sections, i.e. code fragments in a loop that must be executed atomically and in original program order. We discuss why these ordered sections prohibit current auto-parallelizers from working and we present a technique to deal with them. We experimentally demonstrate the efficacy of the technique, yielding significant overall program speedups

Alignments of mitochondrial genome arrangements: Applications to metazoan phylogeny

Mitochondrial genomes provide a valuable dataset for phylogenetic studies, in particular of metazoan phylogeny because of the extensive taxon sample that is available. Beyond the traditional sequence-based analysis it is possible to extract phylogenetic information from the gene order. Here we present a novel approach utilizing these data based on cyclic list alignments of the gene orders. A progressive alignment approach is used to combine pairwise list alignments into a multiple alignment of gene orders. Parsimony methods are used to reconstruct phylogenetic trees, ancestral gene orders, and consensus patterns in a straightforward approach. We apply this method to study the phylogeny of protostomes based exclusively on mitochondrial genome arrangements. We, furthermore, demonstrate that our approach is also applicable to the much larger genomes of chloroplasts

High performance FORTRAN without templates: An alternative model for distribution and alignment

Language extensions of FORTRAN are being developed which permit the user to map data structures to the individual processors of distributed memory machines. These languages allow a programming style in which global data references are used. Current efforts are focussed on designing a common basis for such languages, the result of which is known as High Performance Fortran (HPF). One of the central debates in the HPF effort revolves around the concept of templates, introduced as an abstract index space to which data could be aligned. A model for the mapping of data which provides the functionality of High Performance Fortran distributions without the use of templates is presented