The Experts below are selected from a list of 549 Experts worldwide ranked by ideXlab platform
Michael S. Hsiao - One of the best experts on this subject based on the ideXlab platform.
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ICCD - Implicit Search-Space Aware Cofactor Expansion: A Novel Preimage Computation Technique
2006 International Conference on Computer Design, 2006Co-Authors: Kameshwar Chandrasekar, Michael S. HsiaoAbstract:In this paper, we introduce a novel preimage computation technique that directly computes the circuit Cofactors without an explicit search for any satisfiable solution. We use an implicit search on the primary inputs of a sequential circuit to compute all the circuit Cofactors for the target preimage. In order to alleviate the computational cost, aggressive learning techniques are introduced that reason on the search-states by analyzing the relations among circuit Cofactors. Such analysis generates search-state induced clauses that directly help to prune the Cofactor space during preimage computation and to perform non-chronological backtracking. Experimental results show that a significant improvement can be achieved in both performance and capacity as compared to the existing techniques.
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Implicit Search-Space Aware Cofactor Expansion: A Novel Preimage Computation Technique
2006 International Conference on Computer Design, 2006Co-Authors: Kameshwar Chandrasekar, Michael S. HsiaoAbstract:In this paper, we introduce a novel preimage computation technique that directly computes the circuit Cofactors without an explicit search for any satisfiable solution. We use an implicit search on the primary inputs of a sequential circuit to compute all the circuit Cofactors for the target preimage. In order to alleviate the computational cost, aggressive learning techniques are introduced that reason on the search-states by analyzing the relations among circuit Cofactors. Such analysis generates search-state induced clauses that directly help to prune the Cofactor space during preimage computation and to perform non-chronological backtracking. Experimental results show that a significant improvement can be achieved in both performance and capacity as compared to the existing techniques.
Kameshwar Chandrasekar - One of the best experts on this subject based on the ideXlab platform.
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ICCD - Implicit Search-Space Aware Cofactor Expansion: A Novel Preimage Computation Technique
2006 International Conference on Computer Design, 2006Co-Authors: Kameshwar Chandrasekar, Michael S. HsiaoAbstract:In this paper, we introduce a novel preimage computation technique that directly computes the circuit Cofactors without an explicit search for any satisfiable solution. We use an implicit search on the primary inputs of a sequential circuit to compute all the circuit Cofactors for the target preimage. In order to alleviate the computational cost, aggressive learning techniques are introduced that reason on the search-states by analyzing the relations among circuit Cofactors. Such analysis generates search-state induced clauses that directly help to prune the Cofactor space during preimage computation and to perform non-chronological backtracking. Experimental results show that a significant improvement can be achieved in both performance and capacity as compared to the existing techniques.
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Implicit Search-Space Aware Cofactor Expansion: A Novel Preimage Computation Technique
2006 International Conference on Computer Design, 2006Co-Authors: Kameshwar Chandrasekar, Michael S. HsiaoAbstract:In this paper, we introduce a novel preimage computation technique that directly computes the circuit Cofactors without an explicit search for any satisfiable solution. We use an implicit search on the primary inputs of a sequential circuit to compute all the circuit Cofactors for the target preimage. In order to alleviate the computational cost, aggressive learning techniques are introduced that reason on the search-states by analyzing the relations among circuit Cofactors. Such analysis generates search-state induced clauses that directly help to prune the Cofactor space during preimage computation and to perform non-chronological backtracking. Experimental results show that a significant improvement can be achieved in both performance and capacity as compared to the existing techniques.
Christoph Koutschan - One of the best experts on this subject based on the ideXlab platform.
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ISSAC - Zeilberger's holonomic ansatz for Pfaffians
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12, 2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger's approach is based on the Laplace Expansion (Cofactor Expansion) of the determinant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper "Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary.
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Zeilberger’s Holonomic Ansatz for Pfaffians
2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger’s holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger’s approach is based on the Laplace Expansion (Cofactor Expansion) of the determinant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper“Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants ” by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary. Categories and Subject Descriptors G.2.1 [Discrete Mathematics]: Combinatorics—Recurrences and difference equations; G.4 [Mathematical Software]: Algorithm design and analysi
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Zeilberger's Holonomic Ansatz for Pfaffians
arXiv: Combinatorics, 2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger's approach is based on the Laplace Expansion (Cofactor Expansion) of the determinant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper "Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary.
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Zeilberger’s holonomic ansatz for Pfaffians
ACM, 2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger’s holonomic ansatz for symbolic de-terminant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determi-nants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger’s approach is based on the Laplace Expansion (Cofactor Expansion) of the deter-minant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper“Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants ” by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary. Categories and Subject Descriptor
Masao Ishikawa - One of the best experts on this subject based on the ideXlab platform.
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ISSAC - Zeilberger's holonomic ansatz for Pfaffians
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12, 2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger's approach is based on the Laplace Expansion (Cofactor Expansion) of the determinant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper "Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary.
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Zeilberger’s Holonomic Ansatz for Pfaffians
2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger’s holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger’s approach is based on the Laplace Expansion (Cofactor Expansion) of the determinant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper“Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants ” by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary. Categories and Subject Descriptors G.2.1 [Discrete Mathematics]: Combinatorics—Recurrences and difference equations; G.4 [Mathematical Software]: Algorithm design and analysi
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Zeilberger's Holonomic Ansatz for Pfaffians
arXiv: Combinatorics, 2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger's holonomic ansatz for symbolic determinant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determinants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger's approach is based on the Laplace Expansion (Cofactor Expansion) of the determinant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper "Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants" by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary.
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Zeilberger’s holonomic ansatz for Pfaffians
ACM, 2012Co-Authors: Masao Ishikawa, Christoph KoutschanAbstract:A variation of Zeilberger’s holonomic ansatz for symbolic de-terminant evaluations is proposed which is tailored to deal with Pfaffians. The method is also applicable to determi-nants of skew-symmetric matrices, for which the original approach does not work. As Zeilberger’s approach is based on the Laplace Expansion (Cofactor Expansion) of the deter-minant, we derive our approach from the Cofactor Expansion of the Pfaffian. To demonstrate the power of our method, we prove, using computer algebra algorithms, some conjectures proposed in the paper“Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel determinants ” by Ishikawa, Tagawa, and Zeng. A minor summation formula related to partitions and Motzkin paths follows as a corollary. Categories and Subject Descriptor
Gérard Subsol - One of the best experts on this subject based on the ideXlab platform.
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Orientations of Simplices Determined by Orderings on the Coordinates of their Vertices
arXiv: Discrete Mathematics, 2016Co-Authors: Emeric Gioan, Kevin Sol, Gérard SubsolAbstract:Provided n points in an (n-1)-dimensional affine space, and one ordering of the points for each coordinate, we address the problem of testing whether these orderings determine if the points are the vertices of a simplex (i.e. are affinely independent), regardless of the real values of the coordinates. We also attempt to determine the orientation of this simplex. In other words, given a matrix whose columns correspond to affine points, we want to know when the sign (or the non-nullity) of its determinant is implied by orderings given to each row for the values of the row. We completely solve the problem in dimensions 2 and 3. We provide a direct combinatorial characterization, along with a formal calculus method. It can also be viewed as a decision algorithm, and is based on testing the existence of a suitable inductive Cofactor Expansion of the determinant. We conjecture that our method generalizes in higher dimensions. This work aims to be part of a study on how oriented matroids encode shapes of 3-dimensional landmark-based objects. Specifically, applications include the analysis of anatomical data for physical anthropology and clinical research.
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CCCG - Orientations of Simplices Determined by Orderings on the Coordinates of their Vertices
2011Co-Authors: Emeric Gioan, Kevin Sol, Gérard SubsolAbstract:We address the problem of testing when orderings on coordinates of n points in an (n-1)-dimensional affine space, one ordering for each coordinate, suffice to determine if these points are the vertices of a simplex (i.e. are affinely independent), and the orientation of this simplex, independently of the real values of the coordinates. In other words, we want to know when the sign (or the non-nullity) of the determinant of a matrix whose columns correspond to affine points is determined by orderings given on the values on each row. We completely solve the problem in dimensions 2 and 3, providing a direct combinatorial characterization, together with a formal calculus method, that can be seen also as a decision algorithm, which relies on testing the existence of a suitable inductive Cofactor Expansion of the determinant. We conjecture that the method we use generalizes in higher dimensions. The motivation for this work is to be part of a study on how oriented matroids encode shapes of 3-dimensional objects, with applications in particular to the analysis of anatomical data for physical anthropology and clinical research.
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Orientations of Simplices Determined by Orderings on the Coordinates of their Vertices
2011Co-Authors: Emeric Gioan, Kevin Sol, Gérard SubsolAbstract:We address the problem of testing when orderings on coordinates of n points in an (n-1)-dimensional affine space, one ordering for each coordinate, suffice to determine if these points are the vertices of a simplex (i.e. are affinely independent), and the orientation of this simplex, independently of the real values of the coordinates. In other words, we want to know when the sign (or the non-nullity) of the determinant of a matrix whose columns correspond to affine points is determined by orderings given on the values on each row. We completely solve the problem in dimensions 2 and 3, providing a direct combinatorial characterization, together with a formal calculus method, that can be seen also as a decision algorithm, which relies on testing the existence of a suitable inductive Cofactor Expansion of the determinant. We conjecture that the method we use generalizes in higher dimensions. The motivation for this work is to be part of a study on how oriented matroids encode shapes of 3-dimensional objects, with applications in particular to the analysis of anatomical data for physical anthropology and clinical research.