Based on the document-centric view of XML, we present the query language XIRQL. Current proposals for XML query languages lack most IR-related features, which are weighting and ranking, relevance-oriented search, datatypes with vague predicates, and semantic relativism. XIRQL integrates these features by using ideas from logic-based 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.

Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) non-Gaussian 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.

Abstract. The use of simulation for high-dimensional intractable computations has revolutionized applied mathematics. Designing, improving and understanding the new tools leads to (and leans on) fascinating mathematics, from representation theory through micro-local analysis. 1.

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 Tracy-Widom law. In addition, we conjecture a precise value for the time constant in the general first and last passage problems. 1.

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 sub-noise containing the Gaussian part of its noise. Thus, the coalescing motion cannot be described by a white noise.

It is proved that the moments of the width of Galton-Watson 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.

this paper was to provide a summary of the stateof -the-art theory on Bayesian model selection and the application of MCMC algorithms. It has been shown how applications of considerable complexity can be handled successfully within this framework. Several methods for dealing with the use of default, improper priors in the Bayesian model selection 506 Andrieu, Doucet et al. framework has been shown. Special care has been taken to pinpoint the subtleties of jumping from one parameter space to another, and in general, to show the construction of MCMC samplers in such scenarios. The focus in the paper was on the reversible jump MCMC algorithm as this is the most widely used of all existing methods; it is easy to use, flexible and has nice properties. Many references have been cited, with the emphasis being given to articles with signal processing applications. A Notation

Abstract. 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. Key words and phrases: Random Matrix, empirical distribution of the eigenvalues, Stieltjes

We present two randomized algorithms, one for message passing and the other for shared memory, that, with probability 1, schedule multiparty interactions in a strongly fair manner. Both algorithms improve upon a previous result by Joung and Smolka (proposed in a shared-memory model, along with a straightforward conversion to the message-passing paradigm) in the following aspects: First, processes' speeds as well as communication delays need not be bounded by any predetermined constant. Secondly, our algorithms are completely decentralized, and the sharedmemory solution makes use of only single-writer variables. Finally, both algorithms are symmetric in the sense that all processes execute the same code, and no unique identifiers are used to distinguish processes. 1 Introduction Since Hoare introduced CSP [13], interactions and nondeterminism have become two fundamental features in many programming languages for distributed computing (e.g., Ada [34], Script [11], Action Systems [3], IP ...

ABSTRACT. We study the question, “For which reals x does there exist a measure µ such that x is random relative to µ? ” We show that for every nonrecursive x, there is a measure which makes x random without concentrating on x. We give several conditions on x equivalent to there being continuous measure which makes x random. We show that for all but countably many reals x these conditions apply, so there is a continuous measure which makes x random. There is a meta-mathematical aspect of this investigation. As one requires higher arithmetic levels in the degree of randomness, one must make use of more iterates of the power set of the continuum to show that for all but countably many x’s there is a continuous µ which makes x random to that degree. 1.