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Computing Dimensionally Parametrized Determinant Formulas
, 1997
"... We are interested in dimensionally parametrized determinant formulas for specially structured matrices. Applications of this question occur in the study of arbitrary dimensional geometric predicates. We will investigate determinant formulas for two important matrix classes and discuss the implementa ..."
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We are interested in dimensionally parametrized determinant formulas for specially structured matrices. Applications of this question occur in the study of arbitrary dimensional geometric predicates. We will investigate determinant formulas for two important matrix classes and discuss
On the determinant formulas by Borodin
 Okounkov, Baik, Deift and Rains. math.FA/0101008 ; http://xxx.lanl.gov/abs
"... We give alternative proofs to (block case versions of) some formulas for Toeplitz and Fredholm determinants established recently by the authors of the title. Our proof of the BorodinOkounkov formula is very short and direct. The proof of the BaikDeiftRains formulas is based on standard manipulati ..."
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Cited by 8 (0 self)
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We give alternative proofs to (block case versions of) some formulas for Toeplitz and Fredholm determinants established recently by the authors of the title. Our proof of the BorodinOkounkov formula is very short and direct. The proof of the BaikDeiftRains formulas is based on standard
Determinant formula for the sixvertex model with reflecting end
 J. Math. Phys
, 1998
"... Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end. ..."
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Cited by 25 (0 self)
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Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.
Determining Optical Flow
 ARTIFICIAL INTELLIGENCE
, 1981
"... Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent veloc ..."
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Cited by 2379 (9 self)
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Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantized rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.
A Fredholm determinant formula for Toeplitz determinants
"... The purpose of this note is to explain how the results of [13] apply to a question raised by A. Its and, independently, P. Deift during the MSRI workshop ..."
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Cited by 76 (10 self)
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The purpose of this note is to explain how the results of [13] apply to a question raised by A. Its and, independently, P. Deift during the MSRI workshop
DETERMINANT FORMULAS FOR CLASS NUMBERS IN FUNCTION FIELDS
"... Abstract. In this paper, by extending Kucera’s idea to the function field case, we obtain several determinant formulas involving the real class number and the relative class number of any subfield of cyclotomic function fields. We also provide several examples using these determinant formulas. 1. ..."
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Abstract. In this paper, by extending Kucera’s idea to the function field case, we obtain several determinant formulas involving the real class number and the relative class number of any subfield of cyclotomic function fields. We also provide several examples using these determinant formulas. 1.
Determinant Formulas for the Toda and Discrete Toda Equations
, 1999
"... Abstract: Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the τ functions for the Painlevé equations is also discussed. 1 ..."
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Abstract: Determinant formulas for the general solutions of the Toda and discrete Toda equations are presented. Application to the τ functions for the Painlevé equations is also discussed. 1
Improved algorithms for optimal winner determination in combinatorial auctions and generalizations
, 2000
"... Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NPcomplete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper present ..."
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Cited by 598 (55 self)
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Combinatorial auctions can be used to reach efficient resource and task allocations in multiagent systems where the items are complementary. Determining the winners is NPcomplete and inapproximable, but it was recently shown that optimal search algorithms do very well on average. This paper
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination
 Biometrika
, 1995
"... Markov chain Monte Carlo methods for Bayesian computation have until recently been restricted to problems where the joint distribution of all variables has a density with respect to some xed standard underlying measure. They have therefore not been available for application to Bayesian model determi ..."
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Cited by 1330 (24 self)
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determination, where the dimensionality of the parameter vector is typically not xed. This article proposes a new framework for the construction of reversible Markov chain samplers that jump between parameter subspaces of di ering dimensionality, which is exible and entirely constructive. It should therefore
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1,173,859