Results 1  10
of
155
ANFIS: adaptivenetworkbased fuzzy inference
 IEEE Transactions on Systems Man and Cybernetics
, 1993
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Illposed problems in early vision
 Proceedings of the IEEE
, 1988
"... The first processing stage in computational vision, also called early vision, consists of decoding twodimensional images in terms of properties of 30 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detect ..."
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Cited by 195 (13 self)
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The first processing stage in computational vision, also called early vision, consists of decoding twodimensional images in terms of properties of 30 surfaces. Early vision includes problems such as the recovery of motion and optical flow, shape from shading, surface interpolation, and edge detection. These are inverse problems, which are often illposed or illconditioned. We review here the relevant mathematical results on illposed and illconditioned problems and introduce the formal aspects of regularization theory in the linear and nonlinear case. Specific topics in early vision and their regularization are then analyzed rigorously, characterizing existence, uniqueness, and stability of solutions.
Exponential integrability and transportation cost related to logarithmic Sobolev inequalities
 J. FUNCT. ANAL
, 1999
"... We study some problems on exponential integrability, concentration of measure, and transportation cost related to logarithmic Sobolev inequalities. On the real line, we then give a characterization of those probability measures which satisfy these inequalities. ..."
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Cited by 102 (6 self)
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We study some problems on exponential integrability, concentration of measure, and transportation cost related to logarithmic Sobolev inequalities. On the real line, we then give a characterization of those probability measures which satisfy these inequalities.
Method of invariant manifolds and regularization of acoustic spectra. Transport Theory and Stat
 Phys
, 1994
"... A new approach to the problem of reduced description for Boltzmanntype systems is developed. It involves a direct solution of two main problems: thermodynamici ty and dynamic invariance of reduced description. A universal construction is introduced, which gives a thermodynamic parameterization of a ..."
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Cited by 18 (12 self)
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A new approach to the problem of reduced description for Boltzmanntype systems is developed. It involves a direct solution of two main problems: thermodynamici ty and dynamic invariance of reduced description. A universal construction is introduced, which gives a thermodynamic parameterization of an almost arbitrary approximation. Newtontype procedures of successive approximations are developed which correct dynamic noninvariance. The method is applied to obtain corrections to the local Maxwell manifold uSlng parametrics expansions instead of Taylor series into powers of Knudsen number. In particular, the high frequency acoustic spectra is obtained. 1.
Numerical Solution of the Nonlinear PoissonBoltzmann Equation: Developing More Robust and Efficient Methods
 J. Comput. Chem
, 1995
"... this paper, we consider numerical solution of the nonlinear PoissonBoltzmann equation (PBE), the fundamental equation arising in the DebyeHuckel theory [1] of continuum molecular eletrostatics. In the case of a 1 : 1 electrolyte, this equation can be written as (#(r)#u(r)) + # (r) sinh(u(r) ..."
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Cited by 18 (5 self)
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this paper, we consider numerical solution of the nonlinear PoissonBoltzmann equation (PBE), the fundamental equation arising in the DebyeHuckel theory [1] of continuum molecular eletrostatics. In the case of a 1 : 1 electrolyte, this equation can be written as (#(r)#u(r)) + # (r) sinh(u(r)) = 4#e c kBT z i #(r r i ), u(#) = 0, (1) a threedimensional second order nonlinear partial differential equation governing the dimensionless electrostatic potential u(r) = e c #(r)/k 1 B T 1 , where #(r) is the electrostatic potential at a field position r. The importance of this equation for modeling biomolecules is wellestablished; more detailed discussions of the use of the PoissonBoltzmann equation may be found in the survey articles of Briggs and McCammon [2] and Sharp and Honig [3]
On Duality Theory of Conic Linear Problems
 in SemiInfinite Programming
, 2000
"... In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate du ..."
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Cited by 15 (0 self)
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In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate duality approach where the questions of "no duality gap" and existence of optimal solutions are related to properties of the corresponding optimal value function. We discuss in detail applications of the abstract duality theory to the problem of moments, linear semiinfinite and continuous linear programming problems. Key words: Conic linear programs, Lagrangian and conjugate duality, optimal value function, problem of moments, semiinfinite programming, continuous linear programming. AMS subject classification: 49N15, 90C34, 90C46 # Work performed at Argonne National Laboratory while a Faculty Research Participant. Program administered by the Argonne Division of Educational Programs with fun...
023 "Time Series Modelling with Semiparametric Factor Dynamics" by Szymon Borak, Wolfgang Härdle, Enno Mammen and Byeong
, 2007
"... Highdimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the lowdimensional time series analysis. Such highdimensional problems occur frequently in many different fi ..."
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Cited by 15 (5 self)
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Highdimensional regression problems which reveal dynamic behavior are typically analyzed by time propagation of a few number of factors. The inference on the whole system is then based on the lowdimensional time series analysis. Such highdimensional problems occur frequently in many different fields of science. In this paper we address the problem of inference when the factors and factor loadings are estimated by semiparametric methods. This more flexible modelling approach poses an important question: Is it justified, from inferential point of view, to base statistical inference on the estimated times series factors? We show that the difference of the inference based on the estimated time series and ‘true ’ unobserved time series is asymptotically negligible. Our results justify fitting vector autoregressive processes to the estimated factors, which allows one to study the dynamics of the whole highdimensional system with a lowdimensional representation. We illustrate the theory with a simulation study. Also, we apply the method to a study of the dynamic behavior of implied volatilities and to the analysis of functional magnetic resonance imaging (fMRI) data.
Algebras of singular integral operators with PC coefficients in rearrangementinvariant spaces with Muckenhoupt weights
 J. Operator Theory
"... Abstract. We prove necessary conditions for the Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. These conditions are formulated in terms of indices of submultiplicative functions associated with local properties of the space, of ..."
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Cited by 14 (1 self)
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Abstract. We prove necessary conditions for the Fredholmness of singular integral operators with piecewise continuous coefficients on weighted Banach function spaces. These conditions are formulated in terms of indices of submultiplicative functions associated with local properties of the space, of the curve, and of the weight. As an example, we consider weighted Nakano spaces L p(·) w (weighted Lebesgue spaces with variable exponent). Moreover, our necessary conditions become also sufficient for weighted Nakano spaces over nice curves whenever w is a Khvedelidze weight, and the variable exponent p(t) satisfies the estimate p(τ) − p(t)  ≤ A/( − log τ − t). 1.
A characterization of Lipschitzian stability in optimal control
 In: Calculus of Variations and Optimal Control
, 1999
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