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342
On determining a Riemannian manifold from the DirichlettoNeumann map, Annales Scientifiques de L’École Normale Supérieure
"... ABSTRACT. – We study the inverse problem of determining a Riemannian manifold from the boundary data of harmonic functions. This problem arises in electrical impedance tomography, where one tries to find an unknown conductivity inside a given body from voltage and current measurements made at the bo ..."
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Cited by 82 (39 self)
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ABSTRACT. – We study the inverse problem of determining a Riemannian manifold from the boundary data of harmonic functions. This problem arises in electrical impedance tomography, where one tries to find an unknown conductivity inside a given body from voltage and current measurements made
FishScales: Representing Fuzzy Manifolds
 IN PROCEEDINGS OF THE 6TH IEEE INTERNATIONAL CONFERENCE ON COMPUTER VISION (ICCV ’98
, 1998
"... We address the problem of automatically reconstructing mmanifolds of unknown topology from unorganized points in metric pspaces obtained from a noisy measurement process. The point set is first approximated by a collection of oriented primitive fuzzy sets over a range of resolutions. Hierarchical ..."
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Cited by 22 (4 self)
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We address the problem of automatically reconstructing mmanifolds of unknown topology from unorganized points in metric pspaces obtained from a noisy measurement process. The point set is first approximated by a collection of oriented primitive fuzzy sets over a range of resolutions
Signal Recovery on Incoherent Manifolds
"... Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear submanifold of a highdimensional ambient space. We introduce SPIN, a firstorder projected gradient method to recover the signal com ..."
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Cited by 7 (1 self)
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Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear submanifold of a highdimensional ambient space. We introduce SPIN, a firstorder projected gradient method to recover the signal
Vectorvalued Manifold Regularization
"... We consider the general problem of learning an unknown functional dependency, f: X ↦ → Y, between a structured input space X and a structured output space Y, fromlabeled and unlabeled examples. We formulate this problem in terms of datadependent regularization in Vectorvalued Reproducing Kernel Hi ..."
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Cited by 9 (4 self)
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We consider the general problem of learning an unknown functional dependency, f: X ↦ → Y, between a structured input space X and a structured output space Y, fromlabeled and unlabeled examples. We formulate this problem in terms of datadependent regularization in Vectorvalued Reproducing Kernel
Projecting to a slow manifold: Singularly perturbed systems and legacy codes
, 2005
"... We consider dynamical systems possessing an attracting, invariant “slow manifold ” that can be parameterized by a few observable variables. We present a procedure that, given a process for integrating the system step by step and a set of values of the observables, finds the values of the remaining ..."
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Cited by 56 (18 self)
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time derivatives are zero provides an estimate of the unknown variables that is an mthorder approximation to a point on the slow manifold in a sense to be defined. We then show how this criterion can be applied approximately when the system is defined by a legacy code rather than directly through
Identification of Unknown Functions in Dynamic Systems
"... Abstract — We consider the problem of representing a complex process by a simple model, in order to perform advanced control for instance. In many cases, the main dynamic of the process is well known and some knowledgebased equations can be written, but some parts of the process are unknown. In thi ..."
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Abstract — We consider the problem of representing a complex process by a simple model, in order to perform advanced control for instance. In many cases, the main dynamic of the process is well known and some knowledgebased equations can be written, but some parts of the process are unknown
MULTISCALE MANIFOLD REPRESENTATION AND MODELING
, 2005
"... Many real world data sets can be viewed as points in a higherdimensional space that lie concentrated around a lowerdimensional manifold structure. We propose a new multiscale representation for such point clouds based on lifting and perfect matching. The result is an adaptive wavelet transform tha ..."
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that decomposes a point cloud into manifold approximations and details at multiple scales. We illustrate with several examples that the transform can extract an unknown smooth manifold from noisy point cloud samples using simple wavelet thresholding ideas.
Geometry of CalabiYau manifolds
"... CalabiYau manifolds are certain higher dimensional generalisations of Riemann surfaces of genus one. Calabi Yau manifolds of dimension two form the wellstudied class of K3surfaces. It turns out that there exist a myriad of topologically different CalabiYau threefolds. However, their classificati ..."
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, their classification is unknown and even the question if there exist finitely or infinitely many of them is an open problem. The unexpected and only partially explained phenomenon of mirror symmetry has led to large research efforts over the last decades. In the course the basic theory of CalabiYau manifolds
The DirichlettoNeumann map for complete Riemannian manifolds with boundary
 Comm. Geom. Anal
"... Abstract. We study the problem of determining a complete Riemannian manifold with boundary from the Cauchy data of harmonic functions. This problem arises in electrical impedance tomography, where one tries to ¯nd an unknown conductivity inside a given body from measurements done on the boundary of ..."
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Cited by 50 (28 self)
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Abstract. We study the problem of determining a complete Riemannian manifold with boundary from the Cauchy data of harmonic functions. This problem arises in electrical impedance tomography, where one tries to ¯nd an unknown conductivity inside a given body from measurements done on the boundary
ON AFFINE AND RIEMANNIAN MANIFOLDS
"... According to folklore (a precise criterion in the language of exterior differential systems may be found in [2]), a generic overdetermined partial differential equation may be rewritten as a first order ‘closed system ’ in which all first partial derivatives of the dependent variables are expressed ..."
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in terms of the variables themselves. To do this, one must introduce extra dependent variables for unknown derivatives until all derivatives of the original and extra variables can be determined as consequences of the original equation. This is the wellknown procedure of ‘prolongation’. Particular
Results 11  20
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342