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Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
 SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
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Cited by 557 (12 self)
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to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We also argue that most known interior point methods for linear programs can be transformed in a
Detection and Tracking of Point Features
 International Journal of Computer Vision
, 1991
"... The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small interframe displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade i ..."
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Cited by 622 (2 self)
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The factorization method described in this series of reports requires an algorithm to track the motion of features in an image stream. Given the small interframe displacement made possible by the factorization approach, the best tracking method turns out to be the one proposed by Lucas and Kanade
Volume of Fluid (VOF) Method for the Dynamics of Free Boundaries,” Los Alamos Scientific Laboratory report
"... Several methods have been previously used to approximate free boundaries in tinitedifference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efftcient than other method ..."
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Cited by 544 (2 self)
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Several methods have been previously used to approximate free boundaries in tinitedifference numerical simulations. A simple, but powerful, method is described that is based on the concept of a fractional volume of fluid (VOF). This method is shown to be more flexible and efftcient than other
ReactionDiffusion Textures
 Computer Graphics
, 1991
"... We present a method for texture synthesisbased on the simulation of a process of local nonlinear interaction, called reactiondiffusion, which has been proposed as a model of biological pattern formation. We extend traditional reactiondiffusion systems by allowing anisotropic and spatially nonunif ..."
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Cited by 151 (0 self)
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We present a method for texture synthesisbased on the simulation of a process of local nonlinear interaction, called reactiondiffusion, which has been proposed as a model of biological pattern formation. We extend traditional reactiondiffusion systems by allowing anisotropic and spatially nonuniform
A SINGULARLY PERTURBED SEMILINEAR REACTIONDIFFUSION PROBLEM IN
"... Abstract. The semilinear reactiondiffusion equation −ε24u+b(x, u) = 0 with Dirichlet boundary conditions is considered in a convex polygonal domain. The singular perturbation parameter ε is arbitrarily small, and the “reduced equation ” b(x, u0(x)) = 0 may have multiple solutions. An asymptotic ..."
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Abstract. The semilinear reactiondiffusion equation −ε24u+b(x, u) = 0 with Dirichlet boundary conditions is considered in a convex polygonal domain. The singular perturbation parameter ε is arbitrarily small, and the “reduced equation ” b(x, u0(x)) = 0 may have multiple solutions. An asymptotic
Reactiondiffusion and Free Boundary Problems
, 2006
"... 1 Introduction and overview of the Field Reactiondiffusion equations, semilinear diffusion equations and freeboundary problems form an important domain of the theory of partial differential equations that is both very rich and challenging mathematically and is intricately related to numerous appli ..."
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1 Introduction and overview of the Field Reactiondiffusion equations, semilinear diffusion equations and freeboundary problems form an important domain of the theory of partial differential equations that is both very rich and challenging mathematically and is intricately related to numerous
Where the REALLY Hard Problems Are
 IN J. MYLOPOULOS AND R. REITER (EDS.), PROCEEDINGS OF 12TH INTERNATIONAL JOINT CONFERENCE ON AI (IJCAI91),VOLUME 1
, 1991
"... It is well known that for many NPcomplete problems, such as KSat, etc., typical cases are easy to solve; so that computationally hard cases must be rare (assuming P != NP). This paper shows that NPcomplete problems can be summarized by at least one "order parameter", and that the hard p ..."
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Cited by 681 (1 self)
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problems occur at a critical value of such a parameter. This critical value separates two regions of characteristically different properties. For example, for Kcolorability, the critical value separates overconstrained from underconstrained random graphs, and it marks the value at which the probability
Nonlinear component analysis as a kernel eigenvalue problem

, 1996
"... We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all ..."
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Cited by 1554 (85 self)
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We describe a new method for performing a nonlinear form of Principal Component Analysis. By the use of integral operator kernel functions, we can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all
ON THE SINGULARLY PERTURBED SEMILINEAR REACTIONDIFFUSION PROBLEM AND ITS NUMERICAL SOLUTION
"... Abstract. We obtain improved derivative estimates for the solution of the semilinear singularly perturbed reactiondiffusion problem in one dimension. This enables us to modify the transition points between the fine and coarse parts of the Shishkin discretization mesh. We prove that the numerical so ..."
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Abstract. We obtain improved derivative estimates for the solution of the semilinear singularly perturbed reactiondiffusion problem in one dimension. This enables us to modify the transition points between the fine and coarse parts of the Shishkin discretization mesh. We prove that the numerical
Results 1  10
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