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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 309 (26 self)
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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
A RIEMANNHILBERT PROBLEM IN A RIEMANN SURFACE ∗
"... Abstract One of the inspirations behind Peter Lax’s interest in dispersive integrable systems, as the small dispersion parameter goes to zero, comes from systems of ODEs discretizing 1dimensional compressible gas dynamics [17]. For example, an understanding of the asymptotic behavior of the Toda la ..."
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the method used was the method of Lax and Levermore [16], reducing the asymptotic problem to the solution of a minimization problem with constraints (an “equilibrium measure ” problem). Later, it was found that the asymptotic method of Deift and Zhou (analysis of the associated RiemannHilbert factorization
THE OSTROVSKY–VAKHNENKO EQUATION BY A RIEMANN–HILBERT APPROACH
"... Abstract. We present an inverse scattering transform approach for the equation utxx − 3ux + 3uxuxx + uuxxx = 0. This equation can be viewed as the short wave model for the Degasperis–Procesi equation or the differentiated Ostrovsky–Vakhnenko equation. The approach is based on an associated Riemann–H ..."
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Abstract. We present an inverse scattering transform approach for the equation utxx − 3ux + 3uxuxx + uuxxx = 0. This equation can be viewed as the short wave model for the Degasperis–Procesi equation or the differentiated Ostrovsky–Vakhnenko equation. The approach is based on an associated Riemann–Hilbert
Noncommutative Monopoles and RiemannHilbert Problems
, 2003
"... The Bogomolny equations for YangMillsHiggs monopoles follow from a system of linear equations which may be solved through a parametric RiemannHilbert problem. We extend this approach to noncommutative R³ and use it to (re)construct noncommutative Dirac, WuYang, and BPS monopole configurations in ..."
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Cited by 8 (0 self)
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The Bogomolny equations for YangMillsHiggs monopoles follow from a system of linear equations which may be solved through a parametric RiemannHilbert problem. We extend this approach to noncommutative R³ and use it to (re)construct noncommutative Dirac, WuYang, and BPS monopole configurations
Analysis, Modeling and Generation of SelfSimilar VBR Video Traffic
, 1994
"... We present a detailed statistical analysis of a 2hour long empirical sample of VBR video. The sample was obtained by applying a simple intraframe video compression code to an action movie. The main findings of our analysis are (1) the tail behavior of the marginal bandwidth distribution can be accu ..."
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Cited by 546 (6 self)
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be accurately described using "heavytailed" distributions (e.g., Pareto); (2) the autocorrelation of the VBR video sequence decays hyperbolically (equivalent to longrange dependence) and can be modeled using selfsimilar processes. We combine our findings in a new (nonMarkovian) source model
Graphical models, exponential families, and variational inference
, 2008
"... The formalism of probabilistic graphical models provides a unifying framework for capturing complex dependencies among random variables, and building largescale multivariate statistical models. Graphical models have become a focus of research in many statistical, computational and mathematical fiel ..."
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Cited by 800 (26 self)
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fields, including bioinformatics, communication theory, statistical physics, combinatorial optimization, signal and image processing, information retrieval and statistical machine learning. Many problems that arise in specific instances — including the key problems of computing marginals and modes
Bundle Adjustment  A Modern Synthesis
 VISION ALGORITHMS: THEORY AND PRACTICE, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 555 (12 self)
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This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics
The Geometry of Dissipative Evolution Equations: The Porous Medium Equation
"... We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition and the ..."
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Cited by 413 (11 self)
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We show that the porous medium equation has a gradient flow structure which is both physically and mathematically natural. In order to convince the reader that it is mathematically natural, we show the time asymptotic behavior can be easily understood in this framework. We use the intuition
Ehrenpreis Type Representations and Their RiemannHilbert Nonlinearisation
, 2003
"... We review a new method for studying boundary value problems for evolution PDEs. This method yields explicit results for a large class of evolution equations which include: (a) Linear equations with constant coe#cients, (b) certain classes of linear equations with variable coe#cients, and (c) integra ..."
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We review a new method for studying boundary value problems for evolution PDEs. This method yields explicit results for a large class of evolution equations which include: (a) Linear equations with constant coe#cients, (b) certain classes of linear equations with variable coe#cients, and (c
Results 1  10
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63,690