The design of a parallel dense linear algebra software library: Reduction to Hessenberg,tridiagonal, and bidiagonal form

This paper discusses issues in the design of ScaLAPACK, a software library for performing dense linear algebra computations on distributed memory concurrent computers. These issues are illustrated using the ScaLAPACK routines for reducing matrices to Hessenberg, tridiagonal, and bidiagonal forms. These routines are important in the solution of eigenproblems. The paper focuses on how building blocks are used to create higher-level library routines. Results are presented that demonstrate the scalability of the reduction routines. The most commonly-used building blocks used in ScaLAPACK are the sequencing BLAS, the parallel BLAS (PBLAS) and the Basic Linear Algebra Communication Subprograms (BLACS). Each of the matrix reduction algorithms consists of a series of steps in each of which one block column (orpanel), and/or block row, of the matrix is reduced, followed by an update of the portion of the matrix that has not been factorized so far. This latter phase is performed using Level 3 PBLAS operations and contains the bulk of the computation. However, the panel reduction phase involves a significant amount of communication, and is important in determining the scalability of the algorithm. The simplest way to parallelize the panel reduction phase is to replace the BLAS routines appearing in the LAPACK routine (mostly matrix-vector and matrix-matrix multiplications) with the corresponding PBLAS routines. However, in some cases it is possible to reduce communication startup costs by performing the communication necessary for consecutive BLAS operations in a single communication using a BLACS call. Thus, there is a tradeoff between efficiency and software engineering considerations, such as ease of programming and simplicity of code.Research was supported in part by the Applied Mathematical Sciences Research Program of the Office of Energy Research, U.S. Department of Energy, by the Defense Advanced Research Projects Agency under contract DAAL03-91-C-0047, administered by the Army Research Office, and in part by the Center for Research on Parallel Computing.     

Brauer groups,embedding problems,and nilpotent groups as Galois groups

Let ℚ _ab denote the maximal abelian extension of the rationals ℚ, and let ℚ_abnil denote the maximal nilpotent extension of ℚ _ab . We prove that for every primep, the free pro-p group on countably many generators is realizable as the Galois group of a regular extension of ℚ_abnil(t). We also prove that ℚ_abnil is not PAC (pseudo-algebraically closed). This paper was inspired by the author's participation in a special year on the arithmetic of fields at the Institute for Advanced Studies at the Hebrew University of Jerusalem. I would like to express my appreciation to the Institute for its hospitality, and to the organizers, especially Moshe Jarden. Partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund-Japan Technion Society Research Fund.     

In vivo proton magnetic resonance spectroscopy of alcohol in rhesus monkey brain

Brain alcohol was measured in rhesus monkeys (Macaca mulatta) by proton magnetic resonance spectroscopy (MRS) following acute nasogastric alcohol administration (0.8 g/kg). Monkeys were anesthetized with ketamine and xylazine. A 1.5 T whole body imager and a 3-inch surface coil were used to acquire TE 30 and 270 ms spectra from a 7.5 cc voxel localized with a stimulated echo (STEAM) sequence. Venous blood samples were collected during spectral acquisitions for gas chromatographic determination of temporally concordant blood alcohol levels (BALs). Acute alcohol administration did not alter the resonance areas of N-acetylaspartate/N-acetyl containing compounds (NAA), choline containing compounds, or total creatine. The NAA resonance was used as an internal standard to calculate approximate brain alcohol concentrations, which averaged 27 ± 3% and 27 ± 8% of temporally concordant BALs (T₂-corrected TE 30 and TE 270 ms spectra, respectively). In addition to reconfirming results from prior studies finding incomplete detection of brain alcohol with MRS, these results demonstrate the feasibility of measuring brain alcohol in anesthetized nonhuman primates to examine relationships between alcohol exposure history and MRS-visibility of brain alcohol.     

On the Methyl-Transfer Reaction in Crystalline Methyl 2-(Methylthio)benzenesulfonate: a Thermally Induced Non-Topochemical Solid-State Reaction

The rearrangement of methyl 2-(methylthio)benzenesulfonate ( 1 ) to the zwitterionic 2-(dimethyl-sulfonium)benzenesulfonate ( 2 ) is known to proceed in solution by intermolecular Me transfers. The same rearrangement has been observed to occur in crystalline 1 , but the crystal structure shows that the molecular packing is not conducive to intermolecular Me transfer. The reaction has been carried out with mixed crystals composed of 1 and deuteriomethylated (D₆)- l . By fast-atom-bombardment mass spectroscopy, it has been shown that the product consists of a 1:2:1 mixture of the non-, tri-, and hexadeuterated species, the mixture expected, if the solid-state reaction proceeds by intermolecular Me transfers. From this result, together with the slower rates of conversion in the single crystal compared with the melt, it can be concluded that the reaction must occur not topochemically but rather at defects such as microcavities, surfaces, and other irregularities in the ordered crystal arrangement.     

Elasticity of a magnetic lattice near the magnetic critical point

The isothermal elastic constants and the coefficient of anomalous thermal expansion of a magnetic lattice are discussed. The spin system is described by the Ising model with an exchange coupling depending on lattice spacing. A behavior of the elastic constants and the coefficient of thermal expansion is found which is in qualitative agreement with experiments. The isothermal compressibility remains positive nearT _c and no thermo-mechanical instability occurs (which would lead to a first-order phase transitions), in contrast to earlier theories.