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130
Computing iceberg queries efficiently
 In Proc. of the 24th VLDB Conf
, 1998
"... Many applications compute aggregate functions... ..."
The curious history of Faà di Bruno’s formula
 Amer. Math. Monthly
, 2002
"... the best known answer is Faà di Bruno’s Formula. If g and f are functions with a sufficient number of derivatives, then dm g ( f (t)) = dtm � m! b1! b2!···bm! g(k) � � ′ b1 � ′ ′ f (t) f (t) ( f (t)) ..."
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Cited by 114 (0 self)
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the best known answer is Faà di Bruno’s Formula. If g and f are functions with a sufficient number of derivatives, then dm g ( f (t)) = dtm � m! b1! b2!···bm! g(k) � � ′ b1 � ′ ′ f (t) f (t) ( f (t))
Mellin transforms and asymptotics: Finite differences and Rice's integrals
, 1995
"... High order differences of simple number sequences may be analysed asymptotically by means of integral representations, residue calculus, and contour integration. This technique, akin to Mellin transform asymptotics, is put in perspective and illustrated by means of several examples related to combin ..."
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Cited by 103 (8 self)
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High order differences of simple number sequences may be analysed asymptotically by means of integral representations, residue calculus, and contour integration. This technique, akin to Mellin transform asymptotics, is put in perspective and illustrated by means of several examples related to combinatorics and the analysis of algorithms like digital tries, digital search trees, quadtrees, and distributed leader election.
Convoluted generalized white noise, Schwinger functions and their continuation to Wightman functions
, 2008
"... We construct Euclidean random fields X over IR d, by convoluting generalized white noise F with some integral kernels G, as X = G ∗ F. We study properties of Schwinger (or moment) functions of X. In particular, we give a general equivalent formulation of the cluster property in terms of truncated Sc ..."
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Cited by 27 (15 self)
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We construct Euclidean random fields X over IR d, by convoluting generalized white noise F with some integral kernels G, as X = G ∗ F. We study properties of Schwinger (or moment) functions of X. In particular, we give a general equivalent formulation of the cluster property in terms of truncated Schwinger functions which we then apply to the above fields. We present a partial negative result on the reflection positivity of convoluted generalized white noise. Furthermore, by representing the kernels Gα of the pseudo–differential operators (− ∆ + m 2 0) −α for α ∈ (0,1) and m0> 0 as Laplace transforms we perform the analytic continuation of the (truncated) Schwinger functions of X = Gα ∗ F, obtaining the corresponding (truncated) Wightman distributions on Minkowski space which satisfy the relativistic postulates on invariance, spectral property, locality and cluster property.
Associated polynomials and uniform methods for the solution of linear problems
 SIAM Review
, 1966
"... 2. Brief survey of results 279 3. The basic orthonormality relation 279 ..."
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Cited by 26 (0 self)
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2. Brief survey of results 279 3. The basic orthonormality relation 279
COMBINATORIAL MODELS OF CREATION–ANNIHILATION
 SÉMINAIRE LOTHARINGIEN DE COMBINATOIRE 65 (2011), ARTICLE B65C
, 2011
"... Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB − BA = 1. This study surveys the relationships between classical combinatorial structures and the reduction to normal form of operator ..."
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Cited by 18 (3 self)
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Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB − BA = 1. This study surveys the relationships between classical combinatorial structures and the reduction to normal form of operator polynomials in such an algebra. The connection is achieved through suitable labelled graphs, or “diagrams”, that are composed of elementary “gates”. In this way, many normal form evaluations can be systematically obtained, thanks to models that involve set partitions, permutations, increasing trees, as well as weighted lattice paths. Extensions to qanalogues, multivariate frameworks, and urn models are also briefly discussed.
On the distribution of the sum of n nonidentically distributed uniform random variables
 Annals of the Institute of Statistical Mathematics
"... integrals. Abstract. The distribution of the sum of independent identically distributed uniform random variables is wellknown. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit ..."
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Cited by 18 (1 self)
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integrals. Abstract. The distribution of the sum of independent identically distributed uniform random variables is wellknown. However, it is sometimes necessary to analyze data which have been drawn from different uniform distributions. By inverting the characteristic function, we derive explicit formulæ for the distribution of the sum of n nonidentically distributed uniform random variables in both the continuous and the discrete case. The results, though involved, have a certain elegance. As examples, we derive from our general formulæ some special cases which have appeared in the literature.
From Useful Algorithms for Slowly Convergent Series to Physical Predictions Based on Divergent Perturbative Expansions
, 707
"... This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has hitherto not received the attention it actually deserves. T ..."
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Cited by 17 (2 self)
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This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has hitherto not received the attention it actually deserves. The unifying concept for convergence acceleration methods is that in many cases, one can reach much faster convergence than by adding a particular series term by term. In some cases, it is even possible to use a divergent input series, together with a suitable sequence transformation, for the construction of numerical methods that can be applied to the calculation of special functions. This review both aims to provide some practical guidance as well as a groundwork for the study of specialized literature. As a second topic, we review some recent developments in the field of Borel resummation, which is generally recognized as one of the most versatile methods for the summation of factorially divergent (perturbation) series. Here, the focus is on algorithms which make optimal use of all information contained in a finite set of perturbative coefficients. The unifying concept for the various aspects of the Borel method investigated here is