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A Note on a One-Parameter Family of Catalan-Like Numbers

by Paul Barry
"... We study a family of sequences of Catalan-like numbers based on the series reversion process. Properties of these sequences are derived, including continued fraction expansions, associated orthogonal polynomials and associated Aigner matrices, which turn out to be Riordan arrays. 1 ..."
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We study a family of sequences of Catalan-like numbers based on the series reversion process. Properties of these sequences are derived, including continued fraction expansions, associated orthogonal polynomials and associated Aigner matrices, which turn out to be Riordan arrays. 1

On a one-parameter family of Riordan arrays and the weight distribution of MDS codes

by Paul Barry, Patrick Fitzpatrick
"... We use the formalism of the Riordan group to study a one-parameter family of lower-triangular matrices related to the weight distribution of maximum distance separable codes. We obtain factorization results for these matrices. We then derive alternative expressions for the weight distribution of MDS ..."
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We use the formalism of the Riordan group to study a one-parameter family of lower-triangular matrices related to the weight distribution of maximum distance separable codes. We obtain factorization results for these matrices. We then derive alternative expressions for the weight distribution

Parametric Integer Programming

by Paul Feautrier - RAIRO Recherche Op'erationnelle , 1988
"... When analysing computer programs (especially numerical programs in which arrays are used extensively), one is often confronted with integer programming problems. These problems have three peculiarities: ffl feasible points are ranked according to lexicographic order rather than the usual linear ec ..."
Abstract - Cited by 206 (22 self) - Add to MetaCart
When analysing computer programs (especially numerical programs in which arrays are used extensively), one is often confronted with integer programming problems. These problems have three peculiarities: ffl feasible points are ranked according to lexicographic order rather than the usual linear

Parametric Catalan numbers and Catalan triangles

by Tian-xiao He - Linear Algebra Appl
"... Here presented a generalization of Catalan numbers and Cata-lan triangles associated with two parameters based on the se-quence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan n ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
Here presented a generalization of Catalan numbers and Cata-lan triangles associated with two parameters based on the se-quence characterization of Bell-type Riordan arrays. Among the generalized Catalan numbers, a class of large generalized Catalan numbers and a class of small generalized Catalan

Maximizing Performance in a Striped Disk Array

by Peter M. Chen, David A. Patterson , 1990
"... Improvements in disk speeds have not kept up with improvements in processor and memory speeds. One way to correct the resulting speed mismatch is to stripe data across many disks. In this paper, we address how to stripe data to get maximum performance from the disks. Specifically, we examine how to ..."
Abstract - Cited by 140 (10 self) - Add to MetaCart
Improvements in disk speeds have not kept up with improvements in processor and memory speeds. One way to correct the resulting speed mismatch is to stripe data across many disks. In this paper, we address how to stripe data to get maximum performance from the disks. Specifically, we examine how

The Catalan numbers

by unknown authors
"... Abstract. Catalan numbers C(n) = 1 n+1 n enumerate binary trees and Dyck paths. The distribution of paths with respect to their number k of factors is given by ballot numbers B(n, k) = n−k � � n+k n+k n. These integers are known to satisfy simple recurrence, which may be visualised in a “Catalan ..."
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triangle”, a lower-triangular two-dimensional array. It is surprising that the extension of this construction to 3 dimensions generates integers B3(n, k, l) that give a 2-parameter distribution of C3(n) = 1 � � 3n 2n+1 n, which may be called oder-3 Fuss-Catalan numbers, and enumerate ternary trees

Coil sensitivity encoding for fast MRI. In:

by Klaas P Pruessmann , Markus Weiger , Markus B Scheidegger , Peter Boesiger - Proceedings of the ISMRM 6th Annual Meeting, , 1998
"... New theoretical and practical concepts are presented for considerably enhancing the performance of magnetic resonance imaging (MRI) by means of arrays of multiple receiver coils. Sensitivity encoding (SENSE) is based on the fact that receiver sensitivity generally has an encoding effect complementa ..."
Abstract - Cited by 193 (3 self) - Add to MetaCart
-coil array in brain imaging. With an array of five coils double-oblique heart images were obtained in one-third of conventional scan time. Magn Reson Med 42:952-962, 1999. 1999 Wiley-Liss, Inc. Key words: MRI; sensitivity encoding; SENSE; fast imaging; receiver coil array Among today's many medical

An end-to-end discriminative approach to machine translation

by Percy Liang, Alexandre Bouchard-côté, Dan Klein, Ben Taskar - In Proceedings of the Joint International Conference on Computational Linguistics and Association of Computational Linguistics (COLING/ACL , 2006
"... We present a perceptron-style discriminative approach to machine translation in which large feature sets can be exploited. Unlike discriminative reranking approaches, our system can take advantage of learned features in all stages of decoding. We first discuss several challenges to error-driven disc ..."
Abstract - Cited by 161 (3 self) - Add to MetaCart
-driven discriminative approaches. In particular, we explore different ways of updating parameters given a training example. We find that making frequent but smaller updates is preferable to making fewer but larger updates. Then, we discuss an array of features and show both how they quantitatively increase BLEU score

A determinant property of Catalan numbers

by M. E. Mays, Jerzy Wojciechowski - Discrete Math
"... Catalan numbers arise in a family of persymmetric arrays with determinant 1. The demonstration ..."
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Catalan numbers arise in a family of persymmetric arrays with determinant 1. The demonstration

PASCAL, CATALAN, AND GENERAL SEQUENCE

by V. E. Hoggatt, Marjre Bckwell
"... the first coiumn of matrix inverses of matrices containing certain columns of Pascal's triangle, and which also can be obtained from certain diagonals of Pascal's triangle [1], [2]. These sequences S,- are also the solutions for certain ballot problems, which counting process also yields t ..."
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their convolution arrays. The convolution triangles for the sequences 5 / contain determinants with special values and occur in matrix products yielding Pascal's triangle. Surprisingly enough, we can also find determinant properties which hold for any convolution array. 1. OW THE CATALAN WUIV1BERS AMD BALLOT
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