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25,273
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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to the correct marginals. However, on the QMR network, the loopy be liefs oscillated and had no obvious relation ship to the correct posteriors. We present some initial investigations into the cause of these oscillations, and show that some sim ple methods of preventing them lead to the wrong results
HyTech: A Model Checker for Hybrid Systems
 Software Tools for Technology Transfer
, 1997
"... A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing conti ..."
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Cited by 473 (6 self)
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A hybrid system is a dynamical system whose behavior exhibits both discrete and continuous change. A hybrid automaton is a mathematical model for hybrid systems, which combines, in a single formalism, automaton transitions for capturing discrete change with differential equations for capturing
HOMOGENIZATION AND TWOSCALE CONVERGENCE
, 1992
"... Following an idea of G. Nguetseng, the author defines a notion of "twoscale" convergence, which is aimed at a better description of sequences of oscillating functions. Bounded sequences in L2(f) are proven to be relatively compact with respect to this new type of convergence. A corrector ..."
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Cited by 451 (14 self)
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type theorem (i.e., which permits, in some cases, replacing a sequence by its "twoscale " limit, up to a strongly convergent remainder in L2(12)) is also established. These results are especially useful for the homogenization of partial differential equations with periodically oscillating
Pricing with a Smile
 Risk Magazine
, 1994
"... prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility. If the model were perfect, this implied value would be the same for all option market prices, but reality shows this is not the case. Implied Black–Scholes vol ..."
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Cited by 445 (1 self)
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the former is the quadratic mean of the latter. The spot process S is then governed by the following stochastic differential equation: dS �rt () dt��() t dW
On the distribution of the largest eigenvalue in principal components analysis
 ANN. STATIST
, 2001
"... Let x �1 � denote the square of the largest singular value of an n × p matrix X, all of whose entries are independent standard Gaussian variates. Equivalently, x �1 � is the largest principal component variance of the covariance matrix X ′ X, or the largest eigenvalue of a pvariate Wishart distribu ..."
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Cited by 422 (4 self)
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is defined in terms of the Painlevé II differential equation and can be numerically evaluated and tabulated in software. Simulations showthe approximation to be informative for n and p as small as 5. The limit is derived via a corresponding result for complex Wishart matrices using methods from random matrix
Differentialdifference equations
, 1963
"... are solved, where either f(x) or g(x) is specified in certain intervals in the range 0 ^ x < oo, with up to four intervals. r(f) may be different for different intervals. It is shown that the solution is closely allied to that of a type of FourierBessel series with mixed boundary values so that ..."
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Cited by 331 (0 self)
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are solved, where either f(x) or g(x) is specified in certain intervals in the range 0 ^ x < oo, with up to four intervals. r(f) may be different for different intervals. It is shown that the solution is closely allied to that of a type of FourierBessel series with mixed boundary values so
A review of algebraic multigrid
, 2001
"... Since the early 1990s, there has been a strongly increasing demand for more efficient methods to solve large sparse, unstructured linear systems of equations. For practically relevant problem sizes, classical onelevel methods had already reached their limits and new hierarchical algorithms had to b ..."
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Cited by 347 (11 self)
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to be developed in order to allow an efficient solution of even larger problems. This paper gives a review of the first hierarchical and purely matrixbased approach, algebraic multigrid (AMG). AMG can directly be applied, for instance, to efficiently solve various types of elliptic partial differential equations
A Spectral Method in Time for InitialValue Problems
, 2012
"... A timespectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this generalized weighted residual method (GWRM). The approximate solutions obtained are thus a ..."
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A timespectral method for solution of initial value partial differential equations is outlined. Multivariate Chebyshev series are used to represent all temporal, spatial and physical parameter domains in this generalized weighted residual method (GWRM). The approximate solutions obtained are thus
A steepest descent method for oscillatory Riemann–Hilbert problems: asymptotics for the MKdV equation
 Ann. of Math
, 1993
"... In this announcement we present a general and new approach to analyzing the asymptotics of oscillatory RiemannHilbert problems. Such problems arise, in particular, in evaluating the longtime behavior of nonlinear wave equations solvable by the inverse scattering method. We will restrict ourselves ..."
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Cited by 303 (27 self)
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equations solvable by the inverse scattering method, such as the KdV, nonlinear Schrödinger (NLS), and Boussinesq equations, etc., and also to “integrable ” ordinary differential equations such as the Painlevé transcendents. As described, for example, in [IN] or [BC], the inverse scattering method
How to break MD5 and other hash functions
 In EUROCRYPT
, 2005
"... Abstract. MD5 is one of the most widely used cryptographic hash functions nowadays. It was designed in 1992 as an improvement of MD4, and its security was widely studied since then by several authors. The best known result so far was a semi freestart collision, in which the initial value of the has ..."
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Cited by 317 (7 self)
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Abstract. MD5 is one of the most widely used cryptographic hash functions nowadays. It was designed in 1992 as an improvement of MD4, and its security was widely studied since then by several authors. The best known result so far was a semi freestart collision, in which the initial value
Results 11  20
of
25,273