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SMOOTH SOLUTIONS FOR THE DYADIC MODEL
"... ABSTRACT. We consider the dyadic model, which is a toy model to test issues of well–posedness and blow–up for the Navier–Stokes and Euler equations. We prove well–posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier–Stokes. Likewise we prov ..."
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Cited by 8 (5 self)
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ABSTRACT. We consider the dyadic model, which is a toy model to test issues of well–posedness and blow–up for the Navier–Stokes and Euler equations. We prove well–posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier–Stokes. Likewise we
Learning with local and global consistency
 Advances in Neural Information Processing Systems 16
, 2004
"... We consider the general problem of learning from labeled and unlabeled data, which is often called semisupervised learning or transductive inference. A principled approach to semisupervised learning is to design a classifying function which is sufficiently smooth with respect to the intrinsic stru ..."
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Cited by 666 (21 self)
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structure collectively revealed by known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data. 1
Smooth Stabilization Implies Coprime Factorization
, 1989
"... This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. I ..."
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Cited by 459 (62 self)
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This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations
Topology of the Set of Smooth Solutions to the Liouville Equation
, 2008
"... We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic. 1 1 ..."
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We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic. 1 1
A solution to Plato’s problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge
 PSYCHOLOGICAL REVIEW
, 1997
"... How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LS ..."
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Cited by 1772 (10 self)
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How do people know as much as they do with as little information as they get? The problem takes many forms; learning vocabulary from text is an especially dramatic and convenient case for research. A new general theory of acquired similarity and knowledge representation, latent semantic analysis (LSA), is presented and used to successfully simulate such learning and several other psycholinguistic phenomena. By inducing global knowledge indirectly from local cooccurrence data in a large body of representative text, LSA acquired knowledge about the full vocabulary of English at a comparable rate to schoolchildren. LSA uses no prior linguistic or perceptual similarity knowledge; it is based solely on a general mathematical learning method that achieves powerful inductive effects by extracting the right number of dimensions (e.g., 300) to represent objects and contexts. Relations to other theories, phenomena, and problems are sketched.
Smooth Solution to the 1Dimensional Spin Equations
"... Abstract In this paper, the global existence and uniqueness of a smooth solution to the periodic initialvalue problem of the spin equations of antiferromagnets in 1 dimension are proved. ..."
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Abstract In this paper, the global existence and uniqueness of a smooth solution to the periodic initialvalue problem of the spin equations of antiferromagnets in 1 dimension are proved.
New results in linear filtering and prediction theory
 Trans. ASME, Ser. D, J. Basic Eng
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
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Cited by 585 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Symmetry and Related Properties via the Maximum Principle
, 1979
"... We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting plan ..."
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Cited by 539 (4 self)
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We prove symmetry, and some related properties, of positive solutions of second order elliptic equations. Our methods employ various forms of the maximum principle, and a device of moving parallel planes to a critical position, and then showing that the solution is symmetric about the limiting
Results 1  10
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793,345