159 research outputs found
The Narayana Distribution
No full text: The Narayana distribution is N n;k = 1 n i n k\Gamma1 ji n k j for 1 k n. This paper concerns structures counted by the Narayana distribution and bijective relationships between them. Here the statistic counting pairs of ascent steps on Catalan paths is prominently considered. Defining the n th Narayana polynomial as N n (w) = P 1kn N n;k w k , for n 1, the paper gives a combinatorial proof of a three term recurrence for these polynomials. It examines the Schroder numbers and the Kirkman numbers and establishes a sequence of bijections linking dissections of polygons to large Schroder paths. keywords: Catalan numbers, lattice paths, Schroder numbers AMS Subject Classification: 05A15 email: [email protected] Note to typesetter: the symbol L is a calligraphic L. It should be set as either a calligraphic L or a script L. Thanks. 1 2 1. introduction Using the steps V = (0; 1) and H = (1; 0), the set of Catalan paths, Cat n , is the set of lattice paths from (0; ..
QPACE: Quantum Chromodynamics Parallel Computing on the Cell Broadband Engine
No full textApplication-driven computers for Lattice Gauge Theory simulations have often been based on system-on-chip designs, but the development costs can be prohibitive for academic project budgets. An alternative approach uses compute nodes based on a commercial processor tightly coupled to a custom-designed network processor. Preliminary analysis shows that this solution offers good performance, but it also entails several challenges, including those arising from the processor's multicore structure and from implementing the network processor on a field-programmable gate array
Hilbert series of the Grassmannian and -Narayana numbers
No full textsummary:We compute the Hilbert series of the complex Grassmannian using invariant theoretic methods. This is made possible by showing that the denominator of the -Hilbert series is a Vandermonde-like determinant. We show that the -polynomial of the Grassmannian coincides with the -Narayana polynomial. A simplified formula for the -polynomial of Schubert varieties is given. Finally, we use a generalized hypergeometric Euler transform to find simplified formulae for the -Narayana numbers, i.e.~the -polynomial of the Grassmannian
Narayana numbers and Schur-Szegö composition
No full textIn the present paper we find a new interpretation of Narayana polynomials N-n(x) which are the generating polynomials for the Narayana numbers N-n,N-k = 1/nC(n)(k-1)C(n)(k) where C-j(i) stands for the usual binomial coefficient, i.e. C-j(i) = j!/i!(j-i)!. They count Dyck paths of length n and with exactly k peaks, see e.g. [R.A. Sulanke, The Narayana distribution, in: Lattice Path Combinatorics and Applications (Vienna, 1998), J. Statist. Plann. Inference 101 (1-2) (2002) 311-326 (special issue)] and they appeared recently in a number of different combinatorial situations, see for e.g. [. Doslic, D. Syrtan, D. Veljan, Enumerative aspects of secondary structures, Discrete Math. 285 (2004) 67-82; A. Sapounakis, I. Tasoulas, P. Tsikouras, Counting strings in Dyck paths, Discrete Math. 307 (2007) 2909-2924; F. Yano, H. Yoshida, Some set partitions statistics in non-crossing partitions and generating functions, Discrete Math. 307 (2007) 3147-3160]. Strangely enough Narayana polynomials also occur as limits as n -> infinity of the sequences of eigenpolynomials of the Schur-Szego composition map sending (n - 1)-tuples of polynomials of the form (x +1)(n-1) (x + a) to their Schur-Szego product, see below. We present below a relation between Narayana polynomials and the classical Gegenbauer polynomials which implies, in particular, an explicit formula for the density and the distribution function of the asymptotic root-counting measure of the polynomial sequence {N-n(x)}
QPACE - a QCD parallel computer based on cell processors
No full textQPACE is a novel parallel computer which has been developed to be primarily
used for lattice QCD simulations. The compute power is provided by the IBM
PowerXCell 8i processor, an enhanced version of the Cell processor that is used in the Playstation 3. The QPACE nodes are interconnected by a custom,
application optimized 3-dimensional torus network implemented on an FPGA. To achieve the very high packaging density of 26 TFlops per rack a new water
cooling concept has been developed and successfully realized. In this paper we give an overview of the architecture and highlight some important technical details of the system. Furthermore, we provide initial performance results and report on the installation of 8 QPACE racks providing an aggregate peak performance of 200 TFlops
Status of the QPACE Project
No full textWe give an overview of the QPACE project, which is pursuing the development of a massively parallel, scalable supercomputer for LQCD. The machine is a three-dimensional torus of identical processing nodes, based on the PowerXCell 8i processor. The nodes are connected by an FPGA-based, application-optimized network processor attached to the PowerXCell 8i processor. We present a performance analysis of lattice QCD codes on QPACE and corresponding hardware benchmarks
QPACE: power-efficient parallel architecture based on IBM PowerXCell 8i
No full textQPACE is a novel massively parallel architecture optimized for lattice QCD simulations. Each node comprises an IBM PowerXCell-8i processor. The nodes are interconnected by a custom 3-dimensional torus network implemented on an FPGA. The architecture was systematically optimized with respect to power consumption. This put QPACE in the number one spot on the Green500 List published in November 2009. In this paper we give an overview of the architecture and highlight the steps taken to improve power efficiency
Generalizing the Convex Hull of a Sample: The R Package alphahull
No full textThis paper presents the R package alphahull which implements the ñ-convex hull and the ñ-shape of a finite set of points in the plane. These geometric structures provide an informative overview of the shape and properties of the point set. Unlike the convex hull, the ñ-convex hull and the ñ-shape are able to reconstruct non-convex sets. This flexibility make them specially useful in set estimation. Since the implementation is based on the intimate relation of theses constructs with Delaunay triangulations, the R package alphahull also includes functions to compute Voronoi and Delaunay tesselations. The usefulness of the package is illustrated with two small simulation studies on boundary length estimation.
A programming environment to control switching networks based on STC104 packet routing chip
No full textIntroduction This work is part of a test project for the third level trigger and on-line full event reconstruction for the HERA-B experiment[1]. The high event rate (10 MHz - corresponding to the bunch crossing rate) with multiple interactions per bunch crossing will produce more than 10 7 particles per second per square centimeter in the innermost detector region. The event rate is expected to be reduced by about five orders of magnitude by a three-level trigger system. The 1 AIHENP'96 SE-142 2 Corresponding author. Tel.:+49 3762 77 350, fax: +49 3762 77 330 , e-mail: [email protected] Preprint submitted to Elsevier Preprint 11 November first and second level trigger will operate on a limited range of data, due to the hard time constraints for these systems. In the data acquisition scheme the event building is performed after the second level trigger decision. The events are then routed to the third level trigger, a
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