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786
Reachability Problems in Quaternion Matrix and Rotation Semigroups
"... Abstract. We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric in ..."
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Cited by 5 (2 self)
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Abstract. We examine computational problems on quaternion matrix and rotation semigroups. It is shown that in the ultimate case of quaternion matrices, in which multiplication is still associative, most of the decision problems for matrix semigroups are undecidable in dimension two. The geometric
Reachability problems in lowdimensional iterative maps
"... Abstract. In this paper we analyse the dynamics of onedimensional piecewise maps (PAMs). We show that onedimensional PAMs are equivalent to pseudobilliard or so called “strange billiard ” systems. We also show that the more general class of rational functions leads to undecidability of reachabili ..."
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Cited by 1 (0 self)
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of reachability problem for onedimensional piecewise maps with a finite number of intervals.
Fast maximum margin matrix factorization for collaborative prediction
 In Proceedings of the 22nd International Conference on Machine Learning (ICML
, 2005
"... Maximum Margin Matrix Factorization (MMMF) was recently suggested (Srebro et al., 2005) as a convex, infinite dimensional alternative to lowrank approximations and standard factor models. MMMF can be formulated as a semidefinite programming (SDP) and learned using standard SDP solvers. However, cu ..."
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Cited by 248 (6 self)
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Maximum Margin Matrix Factorization (MMMF) was recently suggested (Srebro et al., 2005) as a convex, infinite dimensional alternative to lowrank approximations and standard factor models. MMMF can be formulated as a semidefinite programming (SDP) and learned using standard SDP solvers. However
From Post Systems to the Reachability Problems for Matrix Semigroups and Multicounter Automata
 Developments in Language Theory, LNCS 3340
, 2004
"... Abstract. The main result of this paper is the reduction of PCP(n) to the vector reachability problem for a matrix semigroup generated by n 4 \Theta 4 integral matrices. It follows that the vector reachability problem is undecidable for a semigroup generated by 7 integral matrices of dimension 4. Th ..."
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Cited by 2 (1 self)
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Abstract. The main result of this paper is the reduction of PCP(n) to the vector reachability problem for a matrix semigroup generated by n 4 \Theta 4 integral matrices. It follows that the vector reachability problem is undecidable for a semigroup generated by 7 integral matrices of dimension 4
Sparse subspace clustering
 In CVPR
, 2009
"... We propose a method based on sparse representation (SR) to cluster data drawn from multiple lowdimensional linear or affine subspaces embedded in a highdimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all oth ..."
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Cited by 241 (14 self)
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We propose a method based on sparse representation (SR) to cluster data drawn from multiple lowdimensional linear or affine subspaces embedded in a highdimensional space. Our method is based on the fact that each point in a union of subspaces has a SR with respect to a dictionary formed by all
On the Computational Complexity of Matrix Semigroup Problems
"... Abstract. Most computational problems for matrix semigroups and groups are inherently difficult to solve and even undecidable starting from dimension three. The questions about the decidability and complexity of problems for twodimensional matrix semigroups remain open and are directly linked with ..."
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Cited by 2 (1 self)
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Abstract. Most computational problems for matrix semigroups and groups are inherently difficult to solve and even undecidable starting from dimension three. The questions about the decidability and complexity of problems for twodimensional matrix semigroups remain open and are directly linked
LowDimensional Models for PCA and Regression LowDimensional Models for PCA and Regression
"... This thesis examines two separate statistical problems for which lowdimensional models are effective. In the first part of this thesis, we examine the Robust Principal Components Analysis (RPCA) problem: given a matrix X that is the sum of a lowrank matrix L * and a sparse noise matrix S * , reco ..."
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This thesis examines two separate statistical problems for which lowdimensional models are effective. In the first part of this thesis, we examine the Robust Principal Components Analysis (RPCA) problem: given a matrix X that is the sum of a lowrank matrix L * and a sparse noise matrix
Membership and Reachability Problems for Rowmonomial Transformations
"... Abstract. In this paper we study the membership and vector reachability problems for labelled transition systems with rowmonomial transformations. We show the decidability of these problems for rowmonomial martix semigroups over rationals and extend these results to the wider class of matrix semig ..."
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Cited by 2 (1 self)
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Abstract. In this paper we study the membership and vector reachability problems for labelled transition systems with rowmonomial transformations. We show the decidability of these problems for rowmonomial martix semigroups over rationals and extend these results to the wider class of matrix
c ○ World Scientific Publishing Company REACHABILITY PROBLEMS IN LOWDIMENSIONAL ITERATIVE MAPS
"... In this paper we analyze the dynamics of onedimensional piecewise maps (PAMs). We show that onedimensional PAMs are equivalent to pseudobilliard or so called “strange billiard ” systems. We also show that the more general class of rational functions leads to undecidability of reachability problem ..."
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In this paper we analyze the dynamics of onedimensional piecewise maps (PAMs). We show that onedimensional PAMs are equivalent to pseudobilliard or so called “strange billiard ” systems. We also show that the more general class of rational functions leads to undecidability of reachability
Reachability Of Fuzzy Matrix Period
, 1997
"... The computational complexity of the matrix period reachability (MPR) problem in a fuzzy algebra B is studied. Given an n n matrix A with elements in B, the problem is to decide whether there is an nvector x such that the sequence of matrix powers A; A²; A³ ; : : : has the same period length as the ..."
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Cited by 2 (0 self)
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The computational complexity of the matrix period reachability (MPR) problem in a fuzzy algebra B is studied. Given an n n matrix A with elements in B, the problem is to decide whether there is an nvector x such that the sequence of matrix powers A; A²; A³ ; : : : has the same period length
Results 1  10
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786