The Experts below are selected from a list of 570 Experts worldwide ranked by ideXlab platform
Liam Maguire - One of the best experts on this subject based on the ideXlab platform.
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Selecting Critical Patterns Based on Local Geometrical and Statistical Information
IEEE transactions on pattern analysis and machine intelligence, 2011Co-Authors: Liam MaguireAbstract:Pattern selection methods have been traditionally developed with a dependency on a specific classifier. In contrast, this paper presents a method that selects critical patterns deemed to carry essential information applicable to train those types of classifiers which require spatial information of the training data set. Critical patterns include those edge patterns that define the boundary and those border patterns that separate classes. The proposed method selects patterns from a new perspective, primarily based on their location in input space. It determines class edge patterns with the assistance of the approximated Tangent Hyperplane of a class surface. It also identifies border patterns between classes using local probability. The proposed method is evaluated on benchmark problems using popular classifiers, including multilayer perceptrons, radial basis functions, support vector machines, and nearest neighbors. The proposed approach is also compared with four state-of-the-art approaches and it is shown to provide similar but more consistent accuracy from a reduced data set. Experimental results demonstrate that it selects patterns sufficient to represent class boundary and to preserve the decision surface.
Andrew Jackson - One of the best experts on this subject based on the ideXlab platform.
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The evolution of a magnetic field subject to Taylor′s constraint using a projection operator
Geophysical Journal International, 2011Co-Authors: Philip W. Livermore, Glenn R. Ierley, Andrew JacksonAbstract:SUMMARY In the rapidly rotating, low-viscosity limit of the magnetohydrodynamic equations as relevant to the conditions in planetary cores, any generated magnetic field likely evolves while simultaneously satisfying a particular continuous family of invariants, termed Taylor’s constraint. It is known that, analytically, any magnetic field will evolve subject to these constraints through the action of a time-dependent coaxially cylindrical geostrophic flow. However, severe numerical problems limit the accuracy of this procedure, leading to rapid violation of the constraints. By judicious choice of a certain truncated Galerkin representation of the magnetic field, Taylor’s constraint reduces to a finite set of conditions of size O(N), significantly less than the O(N3) degrees of freedom, where N denotes the spectral truncation in both solid angle and radius. Each constraint is homogeneous and quadratic in the magnetic field and, taken together, the constraints define the finite-dimensional Taylor manifold whose Tangent plane can be evaluated. The key result of this paper is a description of a stable numerical method in which the evolution of a magnetic field in a spherical geometry is constrained to the manifold by projecting its rate of change onto the local Tangent Hyperplane. The Tangent plane is evaluated by contracting the vector of spectral coefficients with the Taylor tensor, a large but very sparse 3-D array that we define. We demonstrate by example the numerical difficulties in finding the geostrophic flow numerically and how the projection method can correct for inaccuracies. Further, we show that, in a simplified system using projection, the normalized measure of Taylorization, τ, may be maintained smaller than O(10−10) (where τ= 0 is an exact Taylor state) over 1/10 of a dipole decay time, eight orders of magnitude smaller than analogous measures applied to recent low Ekman-number geodynamo models.
Valerio Scarani - One of the best experts on this subject based on the ideXlab platform.
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Nonlocal games and optimal steering at the boundary of the quantum set
Physical Review A, 2016Co-Authors: Yi-zheng Zhen, Koon Tong Goh, Yu-lin Zheng, Wen-fei Cao, Kai Chen, Valerio ScaraniAbstract:The boundary between classical and quantum correlations is well characterized by linear constraints called Bell inequalities. It is much harder to characterize the boundary of the quantum set itself in the space of no-signaling correlations. For the points on the quantum boundary that violate maximally some Bell inequalities, J. Oppenheim and S. Wehner [Science 330, 1072 (2010)] pointed out a complex property: Alice's optimal measurements steer Bob's local state to the eigenstate of an effective operator corresponding to its maximal eigenvalue. This effective operator is the linear combination of Bob's local operators induced by the coefficients of the Bell inequality, and it can be interpreted as defining a fine-grained uncertainty relation. It is natural to ask whether the same property holds for other points on the quantum boundary, using the Bell expression that defines the Tangent Hyperplane at each point. We prove that this is indeed the case for a large set of points, including some that were believed to provide counterexamples. The price to pay is to acknowledge that the Oppenheim-Wehner criterion does not respect equivalence under the no-signaling constraint: for each point, one has to look for specific forms of writing the Bell expressions.
Philip W. Livermore - One of the best experts on this subject based on the ideXlab platform.
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The evolution of a magnetic field subject to Taylor′s constraint using a projection operator
Geophysical Journal International, 2011Co-Authors: Philip W. Livermore, Glenn R. Ierley, Andrew JacksonAbstract:SUMMARY In the rapidly rotating, low-viscosity limit of the magnetohydrodynamic equations as relevant to the conditions in planetary cores, any generated magnetic field likely evolves while simultaneously satisfying a particular continuous family of invariants, termed Taylor’s constraint. It is known that, analytically, any magnetic field will evolve subject to these constraints through the action of a time-dependent coaxially cylindrical geostrophic flow. However, severe numerical problems limit the accuracy of this procedure, leading to rapid violation of the constraints. By judicious choice of a certain truncated Galerkin representation of the magnetic field, Taylor’s constraint reduces to a finite set of conditions of size O(N), significantly less than the O(N3) degrees of freedom, where N denotes the spectral truncation in both solid angle and radius. Each constraint is homogeneous and quadratic in the magnetic field and, taken together, the constraints define the finite-dimensional Taylor manifold whose Tangent plane can be evaluated. The key result of this paper is a description of a stable numerical method in which the evolution of a magnetic field in a spherical geometry is constrained to the manifold by projecting its rate of change onto the local Tangent Hyperplane. The Tangent plane is evaluated by contracting the vector of spectral coefficients with the Taylor tensor, a large but very sparse 3-D array that we define. We demonstrate by example the numerical difficulties in finding the geostrophic flow numerically and how the projection method can correct for inaccuracies. Further, we show that, in a simplified system using projection, the normalized measure of Taylorization, τ, may be maintained smaller than O(10−10) (where τ= 0 is an exact Taylor state) over 1/10 of a dipole decay time, eight orders of magnitude smaller than analogous measures applied to recent low Ekman-number geodynamo models.
Yi-zheng Zhen - One of the best experts on this subject based on the ideXlab platform.
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Nonlocal games and optimal steering at the boundary of the quantum set
Physical Review A, 2016Co-Authors: Yi-zheng Zhen, Koon Tong Goh, Yu-lin Zheng, Wen-fei Cao, Kai Chen, Valerio ScaraniAbstract:The boundary between classical and quantum correlations is well characterized by linear constraints called Bell inequalities. It is much harder to characterize the boundary of the quantum set itself in the space of no-signaling correlations. For the points on the quantum boundary that violate maximally some Bell inequalities, J. Oppenheim and S. Wehner [Science 330, 1072 (2010)] pointed out a complex property: Alice's optimal measurements steer Bob's local state to the eigenstate of an effective operator corresponding to its maximal eigenvalue. This effective operator is the linear combination of Bob's local operators induced by the coefficients of the Bell inequality, and it can be interpreted as defining a fine-grained uncertainty relation. It is natural to ask whether the same property holds for other points on the quantum boundary, using the Bell expression that defines the Tangent Hyperplane at each point. We prove that this is indeed the case for a large set of points, including some that were believed to provide counterexamples. The price to pay is to acknowledge that the Oppenheim-Wehner criterion does not respect equivalence under the no-signaling constraint: for each point, one has to look for specific forms of writing the Bell expressions.
