Eigenvalues Research Papers - Academia.edu (original) (raw)

Page 1. Segmentation of Retinal Blood Vessels Based on the Second Directional Derivative and Region Growing M. Elena Martinez-Pkrez'; Alun D. Hughes2, Alice V. Stanton2, Simon A. Thorn2, Ani1 A.... more

Page 1. Segmentation of Retinal Blood Vessels Based on the Second Directional Derivative and Region Growing M. Elena Martinez-Pkrez'; Alun D. Hughes2, Alice V. Stanton2, Simon A. Thorn2, Ani1 A. Bharath' and Kim H. Parker' ...

In this paper two fast algorithms that use orthogonal simila rity transformations to convert a symmetric rationally generated Toeplitz matrix to tridiagonal form a re developed, as a means of finding the eigenvalues of the matrix... more

In this paper two fast algorithms that use orthogonal simila rity transformations to convert a symmetric rationally generated Toeplitz matrix to tridiagonal form a re developed, as a means of finding the eigenvalues of the matrix efficiently. The reduction algorithms achieve cost e fficiency by exploiting the rank structure of the input Toeplitz matrix. The proposed algorithms differ in the choi ce of the generator set for the rank structure of the input Toeplitz matrix.

Abstract-We present a steady-state analysis of high-repetition-rate passively mode-locked semiconductor lasers. The analysis includes effects of amplitude-to-phase coupling in both gain and absorber sections. A many-mode eigenvalue... more

Abstract-We present a steady-state analysis of high-repetition-rate passively mode-locked semiconductor lasers. The analysis includes effects of amplitude-to-phase coupling in both gain and absorber sections. A many-mode eigenvalue approach is pre-sented to obtain supermode ...

We derive closed form expressions and limiting formulae for a variety of functions of a permutation resulting from repeated riffle shuffles. The results allow new formulae and approximations for the number of permutations inS n with given... more

We derive closed form expressions and limiting formulae for a variety of functions of a permutation resulting from repeated riffle shuffles. The results allow new formulae and approximations for the number of permutations inS n with given cycle type and number of descents. The theorems are derived from a bijection discovered by Gessel. A self-contained proof of Gessel's result is given.

In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving... more

In a recent paper (S. Kumar, A. Pandey, Phys. Rev. E, 79, 2009, p. 026211) we considered Jacobi family (including Laguerre and Gaussian cases) of random matrix ensembles and reported exact solutions of crossover problems involving time-reversal symmetry breaking. In the present paper we give details of the work. We start with Dyson’s Brownian motion description of random matrix ensembles

The transmission of vibrations between coupled subsystems is treated by using coupling eigenvalues and eigenvectors. It is demonstrated through a basic equation that coupling eigenvalues and eigenvectors characterize the energy exchanges... more

The transmission of vibrations between coupled subsystems is treated by using coupling eigenvalues and eigenvectors. It is demonstrated through a basic equation that coupling eigenvalues and eigenvectors characterize the energy exchanges between subsystems due to the coupling. The coupling eigenvalue relates to the coupling strength and coupling eigenvectors to the coupling transmission path. In addition, in the case of several couplings, a simplified method is presented in which only the prevailing modal path between subsystems is used. The results obtained by using this method compare well with the reference calculation. The transmission of vibrations by coupling can be calculated with a small number of variables and offers a new perspective in the range of medium frequency.

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we... more

The map which takes a square matrix to its tropical eigenvalue-eigenvector pair is piecewise linear. We determine the cones of linearity of this map. They are simplicial but they do not form a fan. Motivated by statistical ranking, we also study the restriction of that cone decomposition to the subspace of skew-symmetric matrices.

... Reina Mercedes, Seville 41012, Spain (Received 23 January 1995; revised version received 13 February 1995; accepted 2 March 1995) A method to calculate the ... 1, we can express the kth layer as: ak(Zk) = Tk(Zk)hk(O) + Rk(Zk) (10)... more

... Reina Mercedes, Seville 41012, Spain (Received 23 January 1995; revised version received 13 February 1995; accepted 2 March 1995) A method to calculate the ... 1, we can express the kth layer as: ak(Zk) = Tk(Zk)hk(O) + Rk(Zk) (10) where matrix T and vector R are given in ...

For most unsymmetric matrices it is difficult to compute many accurate eigenvalues using the prim- itive form of the unsymmetric Lanczos algorithm (ULA). In this paper we propose a modification of the ULA. It is related to ideas used in... more

For most unsymmetric matrices it is difficult to compute many accurate eigenvalues using the prim- itive form of the unsymmetric Lanczos algorithm (ULA). In this paper we propose a modification of the ULA. It is related to ideas used in (J. Chem. Phys. 122 (2005), 244107 (11 pages)) to compute resonance lifetimes. Using the refined ULA we suggest, the calculation

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also... more

Brizolis asked the question: does every prime p have a pair (g,h) such that h is a fixed point for the discrete logarithm with base g? The first author previously extended this question to ask about not only fixed points but also two-cycles, and gave heuristics (building on work of Zhang, Cobeli, Zaharescu, Campbell, and Pomerance) for estimating the number of such pairs given certain conditions on g and h. In this paper we extend these heuristics and prove results for some of them, building again on the aforementioned work. We also make some new conjectures and prove some average versions of the results.

Face recognition has been largely used in biometric field as a security measure at air ports, passport verif ication, criminals ' list verification, visa processing, and so on. Various literature studies suggested different... more

Face recognition has been largely used in biometric field as a security measure at air ports, passport verif ication, criminals ' list verification, visa processing, and so on. Various literature studies suggested different approaches for face recognition systems and most of these studies have limitations with low performance rates. Eigenfaces and principle component analysis (PCA) can be considered as most important face recognition approaches in the literature. There is a need to develop algorithms and approaches that overcome these disadvantages and improve performance of face recognition systems. At the same time, there is a lack of literature studies which are related to face recognition systems based on EigenFaces and PCA. Therefore, this work includes a comparative study of literature researches related to Eigenfaces and PCA for face recognition systems. The main steps, strengths and limitations of each study will be discussed. Many recommendations were suggested in this...

We investigate the manifold M of real symmetric n × n matrices having a multiple eigenvalue. We present an algorithm to derive a minimal-degree equation system for M, and give its result equations for n = 3. We prove that 1) M is prime... more

We investigate the manifold M of real symmetric n × n matrices having a multiple eigenvalue. We present an algorithm to derive a minimal-degree equation system for M, and give its result equations for n = 3. We prove that 1) M is prime and has co-dimension 2, 2) each matrix in M having n − 1 of different eigenvalues

The aim of this paper is to use the so-called Cayley transform to compute the LS category of Lie groups and homogeneous spaces by giving explicit categorical open coverings. When applied to U(n), U(2n)/Sp(n)U(2n)/Sp(n)U(2n)/Sp(n) and U(n)/O(n)U(n)/O(n)U(n)/O(n) this method... more

The aim of this paper is to use the so-called Cayley transform to compute the LS category of Lie groups and homogeneous spaces by giving explicit categorical open coverings. When applied to U(n), U(2n)/Sp(n)U(2n)/Sp(n)U(2n)/Sp(n) and U(n)/O(n)U(n)/O(n)U(n)/O(n) this method is simpler than those formerly known. We also show that the Cayley transform is related to height functions in Lie groups, allowing to give a local linear model of the set of critical points. As an application we give an explicit covering of Sp(2)Sp(2)Sp(2) by categorical open sets. The obstacles to generalize these results to Sp(n)Sp(n)Sp(n) are discussed.