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1,751
Monte Carlo Statistical Methods
, 1998
"... This paper is also the originator of the Markov Chain Monte Carlo methods developed in the following chapters. The potential of these two simultaneous innovations has been discovered much latter by statisticians (Hastings 1970; Geman and Geman 1984) than by of physicists (see also Kirkpatrick et al. ..."
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Cited by 900 (23 self)
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This paper is also the originator of the Markov Chain Monte Carlo methods developed in the following chapters. The potential of these two simultaneous innovations has been discovered much latter by statisticians (Hastings 1970; Geman and Geman 1984) than by of physicists (see also Kirkpatrick et al. 1983). 5.5.5 ] PROBLEMS 211
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erent ..."
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Cited by 376 (4 self)
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We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erential or di#erence equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between di#erent classes of orthogonal polynomials listed in the Askeyscheme. In chapter 3 we list the qanalogues of the polynomials in the Askeyscheme. We give their definition, orthogonality relation, three term recurrence relation, second order di#erence equation, forward and backward shift operator, Rodriguestype formula and generating functions. In chapter 4 we give the limit relations between those basic hypergeometric orthogonal polynomials. Finally, in chapter 5 we...
On the distribution of the length of the longest increasing subsequence of random permutations
 J. Amer. Math. Soc
, 1999
"... Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1
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Cited by 347 (28 self)
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Let SN be the group of permutations of 1, 2,...,N. If π ∈ SN,wesaythat π(i1),...,π(ik) is an increasing subsequence in π if i1 <i2 <·· · <ikand π(i1) < π(i2) < ···<π(ik). Let lN (π) be the length of the longest increasing subsequence. For example, if N =5andπis the permutation 5 1 3 2 4 (in oneline notation:
Modeling annotated data
 In Proc. of the 26th Intl. ACM SIGIR Conference
, 2003
"... We consider the problem of modeling annotated data—data with multiple types where the instance of one type (such as a caption) serves as a description of the other type (such as an image). We describe three hierarchical probabilistic mixture models that are aimed at such data, culminating in the Cor ..."
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Cited by 332 (11 self)
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We consider the problem of modeling annotated data—data with multiple types where the instance of one type (such as a caption) serves as a description of the other type (such as an image). We describe three hierarchical probabilistic mixture models that are aimed at such data, culminating in the CorrLDA model, a latent variable model that is effective at modeling the joint distribution of both types and the conditional distribution of the annotation given the primary type. We take an empirical Bayes approach to finding parameter estimates and conduct experiments in heldout likelihood, automatic annotation, and textbased image retrieval using the Corel database of images and captions. 1
Optimal inapproximability results for MAXCUT and other 2variable CSPs?
, 2005
"... In this paper we show a reduction from the Unique Games problem to the problem of approximating MAXCUT to within a factor of ffGW + ffl, for all ffl> 0; here ffGW ss.878567 denotes the approximation ratio achieved by the GoemansWilliamson algorithm [25]. This implies that if the Unique Games ..."
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Cited by 173 (24 self)
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In this paper we show a reduction from the Unique Games problem to the problem of approximating MAXCUT to within a factor of ffGW + ffl, for all ffl> 0; here ffGW ss.878567 denotes the approximation ratio achieved by the GoemansWilliamson algorithm [25]. This implies that if the Unique Games
Ripple Joins for Online Aggregation
"... We present a new family of join algorithms, called ripple joins, for online processing of multitable aggregation queries in a relational database management system (dbms). Such queries arise naturally in interactive exploratory decisionsupport applications. Traditional offline join algorithms are ..."
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Cited by 157 (11 self)
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We present a new family of join algorithms, called ripple joins, for online processing of multitable aggregation queries in a relational database management system (dbms). Such queries arise naturally in interactive exploratory decisionsupport applications. Traditional offline join algorithms are designed to minimize the time to completion of the query. In contrast, ripple joins are designed to minimize the time until an acceptably precise estimate of the query result is available, as measured by the length of a confidence interval. Ripple joins are adaptive, adjusting their behavior during processing in accordance with the statistical properties of the data. Ripple joins also permit the user to dynamically trade off the two key performance factors of online aggregation: the time between successive updates of the running aggregate, and the amount by which the confidenceinterval length decreases at each update. We show how ripple joins can be implemented in an existing dbms using iterators, and we give an overview of the methods used to compute confidence intervals and to adaptively optimize the ripple join "aspectratio" parameters. In experiments with an initial implementation of our algorithms in the postgres dbms, the time required to produce reasonably precise online estimates was up to two orders of magnitude smaller than the time required for the best offline join algorithms to produce exact answers.
Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons
, 1999
"... The dynamics of networks of sparsely connected excitatory and inhibitory integrateand re neurons is studied analytically. The analysis reveals a very rich repertoire of states, including: Synchronous states in which neurons re regularly; Asynchronous states with stationary global activity and very ..."
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Cited by 147 (11 self)
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The dynamics of networks of sparsely connected excitatory and inhibitory integrateand re neurons is studied analytically. The analysis reveals a very rich repertoire of states, including: Synchronous states in which neurons re regularly; Asynchronous states with stationary global activity and very irregular individual cell activity; States in which the global activity oscillates but individual cells re irregularly, typically at rates lower than the global oscillation frequency. The network can switch between these states, provided the external frequency, or the balance between excitation and inhibition, is varied. Two types of network oscillations are observed: In the `fast' oscillatory state, the network frequency is almost fully controlled by the synaptic time scale. In the `slow' oscillatory state, the network frequency depends mostly on the membrane time constant. Finite size eects in the asynchronous state are also discussed.
On Nonreflecting Boundary Conditions
 J. COMPUT. PHYS
, 1995
"... Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated ..."
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Cited by 128 (1 self)
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Improvements are made in nonreflecting boundary conditions at artificial boundaries for use with the Helmholtz equation. First, it is shown how to remove the difficulties that arise when the exact DtN (DirichlettoNeumann) condition is truncated for use in computation, by modifying the truncated condition. Second, the exact DtN boundary condition is derived for elliptic and spheroidal coordinates. Third, approximate local boundary conditions are derived for these coordinates. Fourth, the truncated DtN condition in elliptic and spheroidal coordinates is modified to remove difficulties. Fifth, a sequence of new and more accurate local boundary conditions is derived for polar coordinates in two dimensions. Numerical results are presented to demonstrate the usefulness of these improvements.
Fast Algorithms for Manipulating Formal Power Series
"... The classical algorithms require order n ~ operations to compute the first n terms in the reversion of a power series or the composition of two series, and order nelog n operations if the fast Founer transform is used for power series multiplication In this paper we show that the composition and r ..."
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Cited by 106 (9 self)
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The classical algorithms require order n ~ operations to compute the first n terms in the reversion of a power series or the composition of two series, and order nelog n operations if the fast Founer transform is used for power series multiplication In this paper we show that the composition and reversion problems are equivalent (up to constant factors), and we give algorithms which require only order (n log n) ~/2 operations In many cases of practical importance only order n log n operations are required, these include certain special functions of power series and power series solution of certain differential equations Applications to rootfinding methods which use inverse interpolation and to queueing theory are described, some results on multivariate power series are stated, and several open questions are mentioned.