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34
XIRQL: A Query Language for Information Retrieval in XML Documents
, 2001
"... Based on the documentcentric view of XML, we present the query language XIRQL. Current proposals for XML query languages lack most IRrelated features, which are weighting and ranking, relevanceoriented search, datatypes with vague predicates, and semantic relativism. XIRQL integrates these featur ..."
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Cited by 153 (6 self)
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Based on the documentcentric view of XML, we present the query language XIRQL. Current proposals for XML query languages lack most IRrelated features, which are weighting and ranking, relevanceoriented search, datatypes with vague predicates, and semantic relativism. XIRQL integrates these features by using ideas from logicbased probabilistic IR models, in combination with concepts from the database area. For processing XIRQL queries, a path algebra is presented, that also serves as a starting point for query optimization.
On Advances in Statistical Modeling of Natural Images
 Journal of Mathematical Imaging and Vision
, 2003
"... Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modelin ..."
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Cited by 98 (5 self)
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Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) nonGaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns. Two categories of results are considered: (i) studies of probability models of images or image decompositions (such as Fourier or wavelet decompositions), and (ii) discoveries of underlying image manifolds while restricting to natural images. Applications of these models in areas such as texture analysis, image classification, compression, and denoising are also considered.
THE MARKOV CHAIN MONTE CARLO REVOLUTION
"... Abstract. The use of simulation for highdimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through microlocal analysis. 1. ..."
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Cited by 18 (1 self)
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Abstract. The use of simulation for highdimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through microlocal analysis. 1.
A GUE central limit theorem and universality of directed first and last passage site percolation
 Int. Math. Res. Not
, 2005
"... Abstract. We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles exhibit universal fluctuations given by the TracyWidom law. In addition, we conjecture a pre ..."
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Cited by 14 (1 self)
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Abstract. We prove a GUE central limit theorem for random variables with finite fourth moment. We apply this theorem to prove that the directed first and last passage percolation problems in thin rectangles exhibit universal fluctuations given by the TracyWidom law. In addition, we conjecture a precise value for the time constant in the general first and last passage problems. 1.
Flows, coalescence and noise
, 2002
"... We are interested in stationary "fluid" random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flo ..."
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Cited by 10 (3 self)
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We are interested in stationary "fluid" random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exists a coalescing flow and a flow of kernels solution of the SDE, a classification is given: All solutions of the SDE can be obtained by filtering a coalescing motion with respect to a subnoise containing the Gaussian part of its noise. Thus, the coalescing motion cannot be described by a white noise.
A CLT for Informationtheoretic statistics of Gram random matrices with a given variance profile
, 2008
"... Consider a N × n random matrix Yn = (Y n ij) where the entries are given by Y n σij(n) ij = √ X n n ij, the Xn ij being centered, independent and identically distributed random variables with unit variance and (σij(n); 1 ≤ i ≤ N,1 ≤ j ≤ n) being an array of numbers we shall refer to as a variance ..."
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Cited by 10 (5 self)
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Consider a N × n random matrix Yn = (Y n ij) where the entries are given by Y n σij(n) ij = √ X n n ij, the Xn ij being centered, independent and identically distributed random variables with unit variance and (σij(n); 1 ≤ i ≤ N,1 ≤ j ≤ n) being an array of numbers we shall refer to as a variance profile. We study in this article the fluctuations of the random variable log det (YnY ∗ n + ρIN) where Y ∗ is the Hermitian adjoint of Y and ρ> 0 is an additional parameter. We prove that when centered and properly rescaled, this random variable satisfies a Central Limit Theorem (CLT) and has a Gaussian limit whose parameters are identified. A complete description of the scaling parameter is given; in particular it is shown that an additional term appears in this parameter in the case where the 4 th moment of the Xij’s differs from the 4 th moment of a Gaussian random variable. Such a CLT is of interest in the field of wireless communications.
The Width of GaltonWatson Trees Conditioned by the Size
, 2004
"... It is proved that the moments of the width of GaltonWatson trees of size n and with ospring variance are asymptotically given by ( n) mp where mp are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a ti ..."
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Cited by 7 (1 self)
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It is proved that the moments of the width of GaltonWatson trees of size n and with ospring variance are asymptotically given by ( n) mp where mp are the moments of the maximum of the local time of a standard scaled Brownian excursion. This is done by combining a weak limit theorem and a tightness estimate. The method is quite general and we state some further applications. 1.
A necessary and sufficient condition for the tailtriviality of a recursive tree process. Sankhyā 68
, 2006
"... Given a recursive distributional equation (RDE) and a solution µ of it, we consider the tree indexed invariant process called the recursive tree process (RTP) with marginal µ. We introduce a new type of bivariate uniqueness property which is different from the one defined by Aldous and Bandyopadhyay ..."
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Cited by 5 (3 self)
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Given a recursive distributional equation (RDE) and a solution µ of it, we consider the tree indexed invariant process called the recursive tree process (RTP) with marginal µ. We introduce a new type of bivariate uniqueness property which is different from the one defined by Aldous and Bandyopadhyay [5], and we prove that this property is equivalent to tailtriviality for the RTP, thus obtaining a necessary and sufficient condition to determine tailtriviality for a RTP in general. As an application we consider Aldous ’ construction of the frozen percolation process on a infinite regular tree [3] and show that the associated RTP has a trivial tail. AMS 2000 subject classification: 60K35, 60G10, 60G20. Key words and phrases: Bivariate uniqueness, distributional identities, endogeny,
The Skorokhod embedding problem and its offspring
, 2004
"... This is a survey about the Skorokhod embedding problem. It presents all known solutions together with their properties and some applications. Some of the solutions are just described, while others are studied in detail and their proofs are presented. A certain unification of proofs, based on onedi ..."
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Cited by 5 (2 self)
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This is a survey about the Skorokhod embedding problem. It presents all known solutions together with their properties and some applications. Some of the solutions are just described, while others are studied in detail and their proofs are presented. A certain unification of proofs, based on onedimensional potential theory, is made. Some new facts which appeared in a natural way when different solutions were crossexamined, are reported. Azéma and Yor’s and Root’s solutions are studied extensively. A possible use of the latter is suggested together with a conjecture.