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Using Cayley Menger determinants
 In Proceedings of the 2004 ACM symposium on Solid modeling
, 2003
"... This paper shows the Menger Cayley determinant is more convenient to solve the Stewart platform; classical Menger Cayley determinants are presented; new Menger Cayley determinants, for some asymmetric problems, are given. 1 The Stewart platform problem ..."
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Cited by 2 (1 self)
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This paper shows the Menger Cayley determinant is more convenient to solve the Stewart platform; classical Menger Cayley determinants are presented; new Menger Cayley determinants, for some asymmetric problems, are given. 1 The Stewart platform problem
THE CAYLEYMENGER DETERMINANT IS IRREDUCIBLE FOR n ≥ 3
, 2008
"... Abstract. We prove that the CayleyMenger determinant of an ndimensional simplex is an absolutely irreducible polynomial for n≥3. We also study the irreducibility of polynomials associated to related geometric constructions. n (n + 1) Let {dij: 0 ≤ i < j ≤ n} be a set of variables and consider t ..."
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Cited by 6 (0 self)
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Abstract. We prove that the CayleyMenger determinant of an ndimensional simplex is an absolutely irreducible polynomial for n≥3. We also study the irreducibility of polynomials associated to related geometric constructions. n (n + 1) Let {dij: 0 ≤ i < j ≤ n} be a set of variables and consider
Using CayleyMenger Determinants for Geometric Constraint Solving
, 2004
"... We use CayleyMenger Determinants (CMDs) to obtain an intrinsic formulation of geometric constraints. First, we show that classical CMDs are very convenient to solve the Stewart platform problem. Second, issues like distances between points, distances between spheres, cocyclicity and cosphericity of ..."
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Cited by 5 (1 self)
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We use CayleyMenger Determinants (CMDs) to obtain an intrinsic formulation of geometric constraints. First, we show that classical CMDs are very convenient to solve the Stewart platform problem. Second, issues like distances between points, distances between spheres, cocyclicity and cosphericity
Application of Linear Algebra: Notes on Talk given to Princeton University Math Club on CayleyMenger Determinant and Generalized Ndimensional Pythagorean Theorem
, 2003
"... This is the notes for my November 2003 talk for the Princeton University Math Club on Higher Dimensional Geometry. The focus of the talk is Ndimensional content calculation of simplexes, which leads to the proof of the CayleyMenger Determinants. From the CayleyMenger Determinants, I attempt to th ..."
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This is the notes for my November 2003 talk for the Princeton University Math Club on Higher Dimensional Geometry. The focus of the talk is Ndimensional content calculation of simplexes, which leads to the proof of the CayleyMenger Determinants. From the CayleyMenger Determinants, I attempt
Coordinatefree Formulation of a 321 Wirebased Tracking Device using CayleyMenger Determinants
 in Proc. IEEE Int. Conf. Robot. Automat
, 2003
"... This paper deals with the problem of estimating the pose of a rigid moving object by measuring the length of six wires attached to it. Among all possible locations for the attachments on the moving object, the "321" configuration exhibits the highest number of favorable properties. A clo ..."
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Cited by 5 (4 self)
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closedform coordinatefree solution to the forward kinematics of this particular configuration is given in terms of CayleyMenger determinants. The proposed formulation is mathematically more tractable compared to previous ones because all terms are determinants with geometric meaning. This accommodates
Using Linear Algebra for Intelligent Information Retrieval
 SIAM REVIEW
, 1995
"... Currently, most approaches to retrieving textual materials from scientific databases depend on a lexical match between words in users' requests and those in or assigned to documents in a database. Because of the tremendous diversity in the words people use to describe the same document, lexical ..."
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Cited by 672 (18 self)
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, lexical methods are necessarily incomplete and imprecise. Using the singular value decomposition (SVD), one can take advantage of the implicit higherorder structure in the association of terms with documents by determining the SVD of large sparse term by document matrices. Terms and documents represented
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real
Closedform solution of absolute orientation using unit quaternions
 J. Opt. Soc. Am. A
, 1987
"... Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares pr ..."
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Cited by 973 (4 self)
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Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. I present here a closedform solution to the leastsquares problem for three or more points. Currently various empirical, graphical, and numerical iterative methods are in use. Derivation of the solution is simplified by use of unit quaternions to represent rotation. I emphasize a symmetry property that a solution to this problem ought to possess. The best translational offset is the difference between the centroid of the coordinates in one system and the rotated and scaled centroid of the coordinates in the other system. The best scale is equal to the ratio of the rootmeansquare deviations of the coordinates in the two systems from their respective centroids. These exact results are to be preferred to approximate methods based on measurements of a few selected points. The unit quaternion representing the best rotation is the eigenvector associated with the most positive eigenvalue of a symmetric 4 X 4 matrix. The elements of this matrix are combinations of sums of products of corresponding coordinates of the points. 1.
Results 1  10
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