Lightweight MPI Communicators with Applications to Perfectly Balanced Quicksort

MPI uses the concept of communicators to connect groups of processes. It provides nonblocking collective operations on communicators to overlap communication and computation. Flexible algorithms demand flexible communicators. E.g., a process can work on different subproblems within different process groups simultaneously, new process groups can be created, or the members of a process group can change. Depending on the number of communicators, the time for communicator creation can drastically increase the running time of the algorithm. Furthermore, a new communicator synchronizes all processes as communicator creation routines are blocking collective operations. We present RBC, a communication library based on MPI, that creates range-based communicators in constant time without communication. These RBC communicators support (non)blocking point-to-point communication as well as (non)blocking collective operations. Our experiments show that the library reduces the time to create a new communicator by a factor of more than 400 whereas the running time of collective operations remains about the same. We propose Janus Quicksort, a distributed sorting algorithm that avoids any load imbalances. We improved the performance of this algorithm by a factor of 15 for moderate inputs by using RBC communicators. Finally, we discuss different approaches to bring nonblocking (local) communicator creation of lightweight (range-based) communicators into MPI

The Convenient Setting for Quasianalytic Denjoy--Carleman Differentiable Mappings

For quasianalytic Denjoy--Carleman differentiable function classes $C^Q$ where the weight sequence $Q=(Q_k)$ is log-convex, stable under derivations, of moderate growth and also an $\mathcal L$-intersection (see 1.6), we prove the following: The category of $C^Q$-mappings is cartesian closed in the sense that $C^Q(E,C^Q(F,G))\cong C^Q(E\times F, G)$ for convenient vector spaces. Applications to manifolds of mappings are given: The group of $C^Q$-diffeomorphisms is a regular $C^Q$-Lie group but not better.Comment: 29 pages. Some typos corrected; J. Functional Analysis (2011

Antigen receptor variable region repertoires expressed by T cells infiltrating thyroid, retroorbital, and pretibial tissue in Graves' disease

To date, it has remained unclear whether T cells infiltrating thyroid, retroorbital, and pretibial tissue of patients with Graves' ophthalmopathy and pretibial dermopathy represent a primary immune response that is directed against certain antigenic determinants shared among these involved tissues. To characterize these T cells at the molecular level, we compared the T cell antigen receptor (TcR) variable (V) region gene usage in thyroid, retroorbital, pretibial tissue, and peripheral blood mononuclear cells of two patients with Graves' disease, ophthalmopathy, and pretibial dermopathy. Ribonucleic acid was extracted, reverse transcribed, and amplified using the PCR and 22 V alpha and 23 V beta gene-specific oligonucleotide primers. The resulting TcR V alpha and V beta transcripts were verified by Southern hybridization analysis using TcR C region-specific, digoxigenin-labeled oligonucleotide probes. In addition, complementarity determining regions 3 and junctional regions of TcR V beta genes were sequenced. Marked similarities of intrathyroidal, retroorbital, and pretibial TcR V alpha and V beta gene repertoires were noted with respect to the degree of TcR V gene restriction and the patterns of individual V genes expressed. Sequence analysis of junctional domains of V beta families revealed oligoclonality of intrahyroidal, retroorbital, and pretibial T cells. In addition, certain conserved junctional motifs were shared by T cells derived the thyroid gland and the extrathyroidal sites. Our results suggest that in the two patients with Graves' disease and extrathyroidal manifestations studied, similar antigenic determinants may have contributed to the recruitment and oligoclonal expansion of T cells both within the thyroid gland and at the involved extrathyroidal sites