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2,474
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 1021 (25 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 401 (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 360 (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 344 (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 178 (28 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
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 174 (13 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.
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 166 (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.
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 163 (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.
Efficient estimation of stochastic volatility using noisy observations: A multiscale approach
, 2004
"... With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed asset returns contain error or noise, for example, in the form ..."
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Cited by 112 (12 self)
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With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility consistently and efficiently, when the observed asset returns contain error or noise, for example, in the form of microstructure noise. The former (consistency) has been addressed heavily in the recent literature, however, the resulting estimator is not quite efficient. In Zhang, Mykland, and AïtSahalia (2003), the best estimator converges to the true volatility only at the rate of n −1/6. In this paper, we propose an efficient estimator which converges to the true at the rate of n −1/4, which is the best attainable. The estimator remains valid when the observation noise is dependent. Some key words and phrases: consistency, dependent noise, discrete observation, efficiency, Ito process, microstructure noise, observation error, rate of convergence, realized volatility