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Compatible Differential Constraints to an Infinite Chain of Transport Equations for
"... We study an infinite chain of transport equations for cumulants which appears in modeling the dynamics of a momentumless turbulent planar wake. The method of compatible differential constraints for formulating its integrability properties is applied. The compatibility conditions obtained make it po ..."
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We study an infinite chain of transport equations for cumulants which appears in modeling the dynamics of a momentumless turbulent planar wake. The method of compatible differential constraints for formulating its integrability properties is applied. The compatibility conditions obtained make
Nonlinear total variation based noise removal algorithms
, 1992
"... A constrained optimization type of numerical algorithm for removing noise from images is presented. The total variation of the image is minimized subject to constraints involving the statistics of the noise. The constraints are imposed using Lagrange multipliers. The solution is obtained using the g ..."
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Cited by 2271 (51 self)
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the gradientprojection method. This amounts to solving a time dependent partial differential equation on a manifold determined by the constraints. As t ~ 0o the solution converges to a steady state which is the denoised image. The numerical algorithm is simple and relatively fast. The results appear
Randomized kinodynamic planning
 THE INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2001; 20; 378
, 2001
"... This paper presents the first randomized approach to kinodynamic planning (also known as trajectory planning or trajectory design). The task is to determine control inputs to drive a robot from an initial configuration and velocity to a goal configuration and velocity while obeying physically based ..."
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Cited by 626 (35 self)
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space that has both firstorder differential constraints and obstaclebased global constraints. The state space serves the same role as the configuration space for basic path planning; however, standard randomized pathplanning techniques do not directly apply to planning trajectories in the state space
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5411 (68 self)
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was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory
Alloy: A Lightweight Object Modelling Notation
, 2001
"... Alloy is a little language for describing structural properties. It offers a declaration syntax compatible with graphical object models, and a setbased formula syntax powerful enough to express complex constraints and yet amenable to a fully automatic semantic analysis. Its meaning is given by tr ..."
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Cited by 459 (17 self)
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Alloy is a little language for describing structural properties. It offers a declaration syntax compatible with graphical object models, and a setbased formula syntax powerful enough to express complex constraints and yet amenable to a fully automatic semantic analysis. Its meaning is given
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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volatility of 20 % and subsequently a lower one, computed by a forward relationship to accommodate the oneyear volatility. We now have a single process, compatible with the two option prices. From the term structure of implied volatilities we can infer a timedependent instantaneous volatility, because
Probing the Pareto frontier for basis pursuit solutions
, 2008
"... The basis pursuit problem seeks a minimum onenorm solution of an underdetermined leastsquares problem. Basis pursuit denoise (BPDN) fits the leastsquares problem only approximately, and a single parameter determines a curve that traces the optimal tradeoff between the leastsquares fit and the ..."
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Cited by 365 (5 self)
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and the onenorm of the solution. We prove that this curve is convex and continuously differentiable over all points of interest, and show that it gives an explicit relationship to two other optimization problems closely related to BPDN. We describe a rootfinding algorithm for finding arbitrary points
Informationtheoretic metric learning
 in NIPS 2006 Workshop on Learning to Compare Examples
, 2007
"... We formulate the metric learning problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. Via a surprising equivalence, we show that this problem can be solved as a lowrank kernel learning problem. Spe ..."
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Cited by 359 (15 self)
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We formulate the metric learning problem as that of minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. Via a surprising equivalence, we show that this problem can be solved as a lowrank kernel learning problem
Direct Reduction and Differential Constraints
, 1994
"... . Direct reductions of partial differential equations to systems of ordinary differential equations are in onetoone correspondence with compatible differential constraints. The differential constraint method is applied to prove that a parabolic evolution equation admits infinitely many characteris ..."
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Cited by 37 (2 self)
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. Direct reductions of partial differential equations to systems of ordinary differential equations are in onetoone correspondence with compatible differential constraints. The differential constraint method is applied to prove that a parabolic evolution equation admits infinitely many
Towards a theory of differential constraints of a hydrodynamic hierarchy
 J. Nonlinear Math. Phys
, 2002
"... We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinitedimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative ..."
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Cited by 29 (1 self)
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We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinitedimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems
Results 1  10
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