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3,800
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 1475 (29 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 580 (6 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 <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 ..."
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Cited by 508 (32 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 436 (12 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.
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 305 (17 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.
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 238 (32 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
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 220 (3 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.
Interval estimation for a binomial proportion
 Statist. Sci
, 2001
"... Abstract. We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standardWaldconfidence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that t ..."
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Cited by 185 (2 self)
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Abstract. We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standardWaldconfidence interval has previously been remarkedon in the literature (Blyth andStill, Agresti andCoull, Santner andothers). We begin by showing that the chaotic coverage properties of the Waldinterval are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects andcannot be trusted. This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examinedfor its coverage probability andits length. Basedon this analysis, we recommendthe Wilson interval or the equaltailedJeffreys prior interval for small n andthe interval suggestedin Agresti andCoull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval. Key words and phrases: Bayes, binomial distribution, confidence intervals, coverage probability, Edgeworth expansion, expected length, Jeffreys prior, normal approximation, posterior.
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 182 (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.