Covariant spinor representation of iosp(d,2/2)iosp(d,2/2) and quantization of the spinning relativistic particle

A covariant spinor representation of $iosp(d,2/2)$ is constructed for the quantization of the spinning relativistic particle. It is found that, with appropriately defined wavefunctions, this representation can be identified with the state space arising from the canonical extended BFV-BRST quantization of the spinning particle with admissible gauge fixing conditions after a contraction procedure. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the $iosp(d,2/2)$ algebra.Comment: Updated version with references included and covariant form of equation 1. 23 pages, no figure

Integrity bases for local invariants of composite quantum systems

Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in $F(q)$ corrected and conclusions modified accordingl

An investigation of the performance portability of OpenCL

This paper reports on the development of an MPI/OpenCL implementation of LU, an application-level benchmark from the NAS Parallel Benchmark Suite. An account of the design decisions addressed during the development of this code is presented, demonstrating the importance of memory arrangement and work-item/work-group distribution strategies when applications are deployed on different device types. The resulting platform-agnostic, single source application is benchmarked on a number of different architectures, and is shown to be 1.3–1.5× slower than native FORTRAN 77 or CUDA implementations on a single node and 1.3–3.1× slower on multiple nodes. We also explore the potential performance gains of OpenCL’s device fissioning capability, demonstrating up to a 3× speed-up over our original OpenCL implementation

Comparison of Fatty Acid Composition, Phytochemical Profiles and Antioxidant Activities in Four Flax (Linum usitatissimum L.) Varieties

Abstract The present study was intendant to evaluate variations among flaxseed varities in terms of fatty acid composition, phytochemical profiles, and antioxidant activities determined by oxygen radical absorbance capacity (ORAC), 2,2-Diphenyl-1-picrylhydrazyl (DPPH) and ferrous ion reducing antioxidant power (FRAP) assays. Significant variations in the fatty acid composition, phenolic acids and lignan were observed in flaxseed varieties from different countries. Among these flaxseed verities, the unsaturated fatty acids accounted over four fifths of total fatty acid contents. The highest ratio of linolenic acid of total fatty acid was observed in USPEA, whereas the lowest one was found in Yexiao. USPEA showed the most contents of total phenolics, as well as flaxseed lignans. In general, total phenolics appeared to be the main contributors in the antioxidant capacity of flaxseed, which presented significant positive correlation. Our study revealed that both cultivar and origin of seeds significantly affect fatty acid composition, phenolic acids, lignans and subsequent antioxidant activities in flaxseed. The results provide new aspects of breeding resources of flaxseed cultivars by presenting their quality specification and possible commercial value

Predictive analysis of a hydrodynamics application on large-scale CMP clusters

We present the development of a predictive performance model for the high-performance computing code Hydra, a hydrodynamics benchmark developed and maintained by the United Kingdom Atomic Weapons Establishment (AWE). The developed model elucidates the parallel computation of Hydra, with which it is possible to predict its runtime and scaling performance on varying large-scale chip multiprocessor (CMP) clusters. A key feature of the model is its granularity; with the model we are able to separate the contributing costs, including computation, point-to-point communications, collectives, message buffering and message synchronisation. The predictions are validated on two contrasting large-scale HPC systems, an AMD Opteron/ InfiniBand cluster and an IBM BlueGene/P, both of which are located at the Lawrence Livermore National Laboratory (LLNL) in the US. We validate the model on up to 2,048 cores, where it achieves a > 85% accuracy in weak-scaling studies. We also demonstrate use of the model in exposing the increasing costs of collectives for this application, and also the influence of node density on network accesses, therefore highlighting the impact of machine choice when running this hydrodynamics application at scale

Covariance, correlation and entanglement

Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on covariance. This works for two- and three-component systems but produces ambiguities for multicomponent systems of composite dimension. Its relationship to angular momentum dispersion for symmetric symmetric spin states is described.Comment: 30 pages, Latex, to appear in J Phys

Syzygies of torsion bundles and the geometry of the level l modular variety over M_g

We formulate, and in some cases prove, three statements concerning the purity or, more generally the naturality of the resolution of various rings one can attach to a generic curve of genus g and a torsion point of order l in its Jacobian. These statements can be viewed an analogues of Green's Conjecture and we verify them computationally for bounded genus. We then compute the cohomology class of the corresponding non-vanishing locus in the moduli space R_{g,l} of twisted level l curves of genus g and use this to derive results about the birational geometry of R_{g, l}. For instance, we prove that R_{g,3} is a variety of general type when g>11 and the Kodaira dimension of R_{11,3} is greater than or equal to 19. In the last section we explain probabilistically the unexpected failure of the Prym-Green conjecture in genus 8 and level 2.Comment: 35 pages, appeared in Invent Math. We correct an inaccuracy in the statement of Prop 2.

Polynomial super-gl(n) algebras

We introduce a class of finite dimensional nonlinear superalgebras $L = L_{\bar{0}} + L_{\bar{1}}$ providing gradings of $L_{\bar{0}} = gl(n) \simeq sl(n) + gl(1)$. Odd generators close by anticommutation on polynomials (of degree $>1$) in the $gl(n)$ generators. Specifically, we investigate `type I' super-$gl(n)$ algebras, having odd generators transforming in a single irreducible representation of $gl(n)$ together with its contragredient. Admissible structure constants are discussed in terms of available $gl(n)$ couplings, and various special cases and candidate superalgebras are identified and exemplified via concrete oscillator constructions. For the case of the $n$-dimensional defining representation, with odd generators $Q_{a}, \bar{Q}{}^{b}$, and even generators ${E^{a}}_{b}$, $a,b = 1,...,n$, a three parameter family of quadratic super-$gl(n)$ algebras (deformations of $sl(n/1)$) is defined. In general, additional covariant Serre-type conditions are imposed, in order that the Jacobi identities be fulfilled. For these quadratic super-$gl(n)$ algebras, the construction of Kac modules, and conditions for atypicality, are briefly considered. Applications in quantum field theory, including Hamiltonian lattice QCD and space-time supersymmetry, are discussed.Comment: 31 pages, LaTeX, including minor corrections to equation (3) and reference [60

Hopf algebras and characters of classical groups

Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at SSPCM'07, Myczkowce, Poland, Sept 200