The Experts below are selected from a list of 318 Experts worldwide ranked by ideXlab platform
Ron Kimmel - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian Operator for Spectral Shape Analysis
IEEE transactions on visualization and computer graphics, 2018Co-Authors: Yoni Choukroun, Alon Shtern, Alexander M. Bronstein, Ron KimmelAbstract:Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami Operator. In this paper, we propose to adapt the classical Hamiltonian Operator from quantum mechanics to the field of shape analysis. To this end, we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present general optimization approaches for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested Operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.
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Sparse Approximation of 3D Meshes Using the Spectral Geometry of the Hamiltonian Operator
Journal of Mathematical Imaging and Vision, 2018Co-Authors: Yoni Choukroun, Gautam Pai, Ron KimmelAbstract:The discrete Laplace Operator is ubiquitous in spectral shape analysis, since its eigenfunctions are provably optimal in representing smooth functions defined on the surface of the shape. Indeed, subspaces defined by its eigenfunctions have been utilized for shape compression, treating the coordinates as smooth functions defined on the given surface. However, surfaces of shapes in nature often contain geometric structures for which the general smoothness assumption may fail to hold. At the other end, some explicit mesh compression algorithms utilize the order by which vertices that represent the surface are traversed, a property which has been ignored in spectral approaches. Here, we incorporate the order of vertices into an Operator that defines a novel spectral domain. We propose a method for representing 3D meshes using the spectral geometry of the Hamiltonian Operator, integrated within a sparse approximation framework. We adapt the concept of a potential function from quantum physics and incorporate vertex ordering information into the potential, yielding a novel data-dependent Operator. The potential function modifies the spectral geometry of the Laplacian to focus on regions with finer details of the given surface. By sparsely encoding the geometry of the shape using the proposed data-dependent basis, we improve compression performance compared to previous results that use the standard Laplacian basis and spectral graph wavelets.
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Hamiltonian Operator for spectral shape analysis
arXiv: Graphics, 2016Co-Authors: Yoni Choukroun, Alon Shtern, Alexander M. Bronstein, Ron KimmelAbstract:Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami Operator. In this paper, we propose to adapt the classical Hamiltonian Operator from quantum mechanics to the field of shape analysis. To this end we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present a general optimization approach for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested Operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.
Alatancang - One of the best experts on this subject based on the ideXlab platform.
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Generalized Inverse of Upper Triangular Infinite Dimensional Hamiltonian Operators
Algebra Colloquium, 2013Co-Authors: Junjie Huang, Xiang Guo, Yonggang Huang, AlatancangAbstract:In this paper, we deal with the generalized inverse of upper triangular infinite dimensional Hamiltonian Operators. Based on the structure Operator matrix J in infinite dimensional symplectic spaces, it is shown that the generalized inverse of an infinite dimensional Hamiltonian Operator is also Hamiltonian. Further, using the decomposition of spaces, an upper triangular Hamiltonian Operator can be written as a new Operator matrix of order 3, and then an explicit expression of the generalized inverse is given.
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Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operator
Acta Mathematicae Applicatae Sinica, 2011Co-Authors: Wu Deyu, AlatancangAbstract:In this paper,the adjoint Operator of infinite dimensional Hamiltonian Operator is studied by method of perturbation theory and the sufficient conditions under which the infinite dimensional Hamiltonian Operator is symplectic self-adjoint are given.
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Symplectic eigenfunction expansion theorem for elasticity of rectangular planes with two simply-supported opposite sides ⁄
Applied Mathematics and Mechanics, 2010Co-Authors: Guo Lin Hou, AlatancangAbstract:The eigenvalue problem of the Hamiltonian Operator associated with plane elasticity problems is investigated. The eigenfunctions of the Operator are directly solved with mixed boundary conditions for the displacement and stress in a rectangular region. The completeness of the eigenfunctions is then proved, providing the feasibility of using separation of variables to solve the problems. A general solution is obtained with the symplectic eigenfunction expansion theorem.
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Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators
Journal of Mathematical Research and Exposition, 2009Co-Authors: Wang, Hua, Alatancang, Huang, DunAbstract:In this paper,by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian Operator H,a necessary and sufficient condition is obtained on the symmetry of σp(A) and σp1(-A*) with respect to the imaginary axis.Then the symmetry of the point spectrum of H is given,and several examples are presented to illustrate the results.
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Spectral Description of a Class of Infinite-Dimensional Hamiltonian Operators and Its Application to Plane Elasticity Equations Without Body Force
Communications in Theoretical Physics, 2008Co-Authors: Fan Xiao-ying, AlatancangAbstract:In this paper, the results of spectral description and invertihility of upper triangle infinite-dimensional Hamiltonian Operators with a diagonal domain are given. By the above results, it is proved that the infinite-dimensional Hamiltonian Operator associated with plane elasticity equations without the body force is invertible, and the spectrum of which is non-empty and is a subset of R.
Alatancang Chen - One of the best experts on this subject based on the ideXlab platform.
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Symmetry of the Quadratic Numerical Range and Spectral Inclusion Properties of Hamiltonian Operator Matrices
Mathematical Notes, 2018Co-Authors: Junjie Huang, J. Liu, Alatancang ChenAbstract:This paper studies Hamiltonian Operator matrices with unbounded entries. Their quadratic numerical range is shown to be symmetric with respect to the imaginary axis under certain assumptions. Spectral inclusion properties are found.
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On the ascent of infinite dimensional Hamiltonian Operators
Chinese Physics B, 2015Co-Authors: Alatancang ChenAbstract:In this paper, the ascent of 2× 2 infinite dimensional Hamiltonian Operators and a class of 4× 4 infinite dimensional Hamiltonian Operators are studied, and the conditions under which the ascent of 2× 2 infinite dimensional Hamiltonian Operator is 1 and the ascent of a class of 4× 4 infinite dimensional Hamiltonian Operators that arises in study of elasticity is 2 are obtained. Concrete examples are given to illustrate the effectiveness of criterions.
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Eigenvalue problem of Hamiltonian Operator matrices
Journal of Inequalities and Applications, 2015Co-Authors: Hua Wang, Junjie Huang, Alatancang ChenAbstract:This paper deals with the eigenvalue problem of Hamiltonian Operator matrices with at least one invertible off-diagonal entry. The ascent and the algebraic multiplicity of their eigenvalues are determined by using the properties of the eigenvalues and associated eigenvectors. The necessary and sufficient condition is further given for the eigenvector (root vector) system to be complete in the Cauchy principal value sense.
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Symplectic approach for the plane elasticity problem of quasicrystals with point group 10 mm
Applied Mathematical Modelling, 2015Co-Authors: Hua Wang, Junjie Huang, Alatancang ChenAbstract:Abstract The symplectic approach is introduced into the plane elasticity problem of quasicrystals with point group 10 mm. The basic equations of the problem are equivalently written as the Hamiltonian dual equations. It is shown that the generalized eigenvector system of the corresponding Hamiltonian Operator matrix is complete in the Cauchy Principal Value (CPV) sense. The analytical solution and related numerical results of the problem are then given.
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On invertible nonnegative Hamiltonian Operator matrices
Acta Mathematica Sinica English Series, 2014Co-Authors: Guo Hai Jin, Guo Lin Hou, Alatancang ChenAbstract:Some new characterizations of nonnegative Hamiltonian Operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian Operator to be invertible are obtained, so that the main results in the previously published papers are corollaries of the new theorems. Most of all we want to stress the method of proof. It is based on the connections between Pauli Operator matrices and nonnegative Hamiltonian matrices.
Yoni Choukroun - One of the best experts on this subject based on the ideXlab platform.
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Hamiltonian Operator for Spectral Shape Analysis
IEEE transactions on visualization and computer graphics, 2018Co-Authors: Yoni Choukroun, Alon Shtern, Alexander M. Bronstein, Ron KimmelAbstract:Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami Operator. In this paper, we propose to adapt the classical Hamiltonian Operator from quantum mechanics to the field of shape analysis. To this end, we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present general optimization approaches for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested Operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.
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Sparse Approximation of 3D Meshes Using the Spectral Geometry of the Hamiltonian Operator
Journal of Mathematical Imaging and Vision, 2018Co-Authors: Yoni Choukroun, Gautam Pai, Ron KimmelAbstract:The discrete Laplace Operator is ubiquitous in spectral shape analysis, since its eigenfunctions are provably optimal in representing smooth functions defined on the surface of the shape. Indeed, subspaces defined by its eigenfunctions have been utilized for shape compression, treating the coordinates as smooth functions defined on the given surface. However, surfaces of shapes in nature often contain geometric structures for which the general smoothness assumption may fail to hold. At the other end, some explicit mesh compression algorithms utilize the order by which vertices that represent the surface are traversed, a property which has been ignored in spectral approaches. Here, we incorporate the order of vertices into an Operator that defines a novel spectral domain. We propose a method for representing 3D meshes using the spectral geometry of the Hamiltonian Operator, integrated within a sparse approximation framework. We adapt the concept of a potential function from quantum physics and incorporate vertex ordering information into the potential, yielding a novel data-dependent Operator. The potential function modifies the spectral geometry of the Laplacian to focus on regions with finer details of the given surface. By sparsely encoding the geometry of the shape using the proposed data-dependent basis, we improve compression performance compared to previous results that use the standard Laplacian basis and spectral graph wavelets.
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Hamiltonian Operator for spectral shape analysis
arXiv: Graphics, 2016Co-Authors: Yoni Choukroun, Alon Shtern, Alexander M. Bronstein, Ron KimmelAbstract:Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami Operator. In this paper, we propose to adapt the classical Hamiltonian Operator from quantum mechanics to the field of shape analysis. To this end we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present a general optimization approach for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested Operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.
M. Gregoratti - One of the best experts on this subject based on the ideXlab platform.
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The Hamiltonian Operator Associated with Some Quantum Stochastic Evolutions
Communications in Mathematical Physics, 2006Co-Authors: M. GregorattiAbstract:We consider the Hamiltonian Operator associated to the quantum stochastic differential equation introduced by Hudson and Parthasarathy to describe a quantum mechanical evolution in the presence of a “quantum noise”. We characterize such a Hamiltonian in the case of arbitrary multiplicity and bounded coefficients: we find an essentially self-adjoint restriction of the Operator and, in particular, we provide an explicit construction of a dense set of vectors belonging to its domain.
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ON THE Hamiltonian Operator ASSOCIATED TO SOME QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS
Infinite Dimensional Analysis Quantum Probability and Related Topics, 2000Co-Authors: M. GregorattiAbstract:We consider the quantum stochastic differential equation introduced by Hudson and Parthasarathy to describe the stochastic evolution of an open quantum system together with its environment. We study the (unbounded) Hamiltonian Operator generating the unitary group connected, as shown by Frigerio and Maassen, to the solution of the equation. We find a densely defined restriction of the Hamiltonian Operator; in some special cases we prove that this restriction is essentially self-adjoint and in one particular case we get the whole Hamiltonian with its full domain.
