1. Relative Entropy Between Markov Transition Rate Matrices - Matrices Kesidis Walrand
We derive the relativeentropybetween two Markov transition rate matrices from sample path considerations. This relativeentropyisinterpreted as a #level 2.5" large deviations action functional. That is, the level two large deviations action functional for empirical distributions of continuous-time Markovchains can be derived from the relativeentropy using the contraction mapping principle #4#. 1 Introduction In this note we derive the relativeentropybetween two Markov transition rate matrices. We use the relativeentropy to obtain an expression for the probability that a Markov chain with a given transition matrix behaves as if it had another transition rate matrix over a long period of time #large deviations#. 2 The Main Result Consider a stationary Markovchain X with...

2. On the Recognition of Permuted Supnick and Incomplete Monge Matrices - Diskrete Optimierung; Monge Matrices; Vladimir Deineko; Vladimir Deineko; Rüdiger Rudolf; Rudiger Rudolf; Gerhard J. Woeginger; Gerhard J. Woeginger
. Incomplete Monge matrices are a generalization of standard Monge matrices: the values of some entries are not specified and the Monge property only must hold for all specified entries. We derive several combinatorial properties of incomplete Monge matrices and prove that the problem of recognizing permuted incomplete Monge matrices is NP-complete. For the special case of permuted Supnick matrices , we derive a fast recognition algorithm and thereby identify a special case of the n-vertex travelling salesman problem which can be solved in O(n 2 log n) time. Keywords. Monge matrices, Supnick matrices, permutations, travelling salesman problem. 1 Introduction...

3. Graph Embeddings, Symmetric Real Matrices, and Generalized Inverses - Graph Embeddings,Symmetric Real Matrices,Stephen Guattery
Graph embedding techniques for bounding eigenvalues of associated matrices have a wide range of applications. The bounds produced by these techniques are not in general tight, however, and maybeo#byalog 2 n factor for some graphs. Guattery and Miller showed that, by adding edge directions to the graph representation, they could construct an embedding called the current flow embedding, which embeds each edge of the guest graph as an electric current flow in the host graph. They also showed how this embedding can be used to construct matrices whose nonzero eigenvalues had a one-to-one correspondence to the reciprocals of the eigenvalues of the generalized Laplacians. For the Laplacians of...

4. On the Recognition of Permuted Supnick and Incomplete Monge Matrices - Monge Matrices,Vladimir Deineko,Rudiger Rudolf,Gerhard J. Woeginger
. Incomplete Monge matrices are a generalization of standard Monge matrices: the values of some entries are not specified and the Monge property only must hold for all specified entries. We derive several combinatorial properties of incomplete Monge matrices and prove that the problem of recognizing permuted incomplete Monge matrices is NP-complete. For the special case of permuted Supnick matrices , we derive a fast recognition algorithm and thereby identify a special case of the n-vertex travelling salesman problem which can be solved in O(n 2 log n) time. Keywords. Monge matrices, Supnick matrices, permutations, travelling salesman problem. 1 Introduction An m Theta n matrix C is called a Monge matrix if...

5. On a new positive extension problem for block Toeplitz matrices - Toeplitz Matrices,D. Alpay,V. Bolotnikov,Ph. Loubaton
In this paper we consider positive extension problems for block Toeplitz matrices when the specified entries form a stalactite type pattern. These problems do not seem in general to be amenable by the classical methods (they correspond to bitangential interpolation problems in the class of Carath'eodory functions of a kind usually not solvable by the classical methods of interpolation). We solve these problems by reduction to a tangential interpolation with symmetries in a Carath'eodory class. 1 Introduction In the present paper we study new extension problems for block Toeplitz matrices. Let us first recall the simplest extension problem for such matrices. Problem 1.1 Given matrices S 0 ; : :...

6. Spectral inequalities and equalities involving products of matrices - Chi-kwong Li; Yiu-tung Poon
Let A1,..., Ak be n × n matrices. We studied inequalities and equalities involving eigenvalues, diagonal entries, and singular values of A0 = A1 · · · Ak and those of A1,..., Ak. It is shown that the matrices attaining equalities often have special reducible structure. The results are then applied to study normality and reducibility of matrices, extending some results and answering some questions of Miranda, Wang and Zhang.

7. Spectral Inequalities and Equalities Involving Products of Matrices - Chi-Kwong Li Department; Chi-kwong Li; Yiu-tung Poon
Let A 1 ; : : : ; A k be n \Theta n matrices. We studied inequalities and equalities involving eigenvalues, diagonal entries, and singular values of A 0 = A 1 \Delta \Delta \Delta A k and those of A 1 ; : : : ; A k . It is shown that the matrices attaining equalities often have special reducible structure. The results are then applied to study normality and reducibility of matrices, extending some results and answering some questions of Miranda, Wang and Zhang. Keywords: matrices, eigenvalues, singular values. AMS Classifications: 15A42, 15A18 1 Introduction Let...

8. On the Weighing Matrices of Order 4n and Weight 4n-2 and 2n-1 - Marc Gysin; Jennifer Seberry
We give algorithms and constructions for mathematicaland computer searches which allow us to establish the existence of W (4n; 4n \Gamma 2) and W (4n; 2n \Gamma 1) for many orders 4n less than 4000. We compare these results with the orders for which W (4n; 4n) and W (4n; 2n) are known. We use new algorithms based on the theory of cyclotomy to obtain new T -matrices of order 43 and JM-matrices which yield W (4n; 4n \Gamma 2) for n = 5; 7; 9; 11; 13; 17; 19; 25;31; 37; 41; 43; 61; 71; 73; 157. Key words...

9. RAIRO Operations Research Will be set by the publisher A NOTE ON TREE REALIZATIONS OF MATRICES ∗ - Alain Hertz; Sacha Varone
Abstract. It is well known that each tree metric M has a unique realization as a tree, and that this realization minimizes the total length of the edges among all other realizations of M. We extend this result to the class of symmetric matrices M with zero diagonal, positive entries, and such that mij + mkl ≤ max{mik + mjl, mil + mjk} for all distinct i, j, k, l.

10. A Scalable Method for Estimating Network Traffic Matrices from Link Counts - Matrices From Link Counts,Jin Cao,Scott V,Er Wiel,Bin Yu,Zhengyuan Zhu
Traffic matrices are extremely useful for network configuration, management, engineering, and pricing. Direct measurement is, however, expensive in general and impossible in some cases. This paper proposes a scalable algorithm for statistically estimating a traffic matrix from the readily available link counts. It relies on a divide-andconquer strategy to lower the computational cost without losing estimation accuracy. The proposed algorithm is tested on a real network with 18 nodes. The estimates are comparable to the direct estimates but require dramatically less computation.

11. A Scalable Method for Estimating Network Traffic Matrices from Link Counts - Matrices From Link Counts,Jin Cao,Scott V,Er Wiel,Bin Yu,Zhengyuan Zhu
Traffic matrices are extremely useful for network configuration, management, engineering, and pricing. Direct measurement is, however, expensive in general and impossible in some cases. This paper proposes a scalable algorithm for statistically estimating a traffic matrix from the readily available link counts. It relies on a divide-andconquer strategy to lower the computational cost without losing estimation accuracy. The proposed algorithm is tested on a real network with 18 nodes. The estimates are comparable to the direct estimates but require dramatically less computation.

12. A Scalable Method for Estimating Network Traffic Matrices from Link Counts - Matrices From Link Counts,Jin Cao,Scott V,Er Wiel,Bin Yu,Zhengyuan Zhu
Traffic matrices are extremely useful for network configuration, management, engineering, and pricing. Direct measurement is, however, expensive in general and impossible in some cases. This paper proposes a scalable algorithm for statistically estimating a traffic matrix from the readily available link counts. It relies on a divide-andconquer strategy to lower the computational cost without losing estimation accuracy. The proposed algorithm is tested on a real network with 18 nodes. The estimates are comparable to the direct estimates but require dramatically less computation.

13. A look-ahead Bareiss algorithm for general Toeplitz matrices - Toeplitz Matrices,Roland W. Freund
this paper, an extension of the Bareiss algorithm to general Toeplitz systems is presented. Using look-ahead techniques, the proposed algorithm can skip over arbitrary blocks of singular or ill-conditioned submatrices, and at the same time, it still fully exploits the Toeplitz structure. Implementation details and operations counts are given, and numerical experiments are reported. We also discuss special versions of the proposed look-ahead Bareiss algorithm for Hermitian indefinite Toeplitz systems and banded Toeplitz systems.

14. Boundary-Based Corner Detection Using Eigenvalues of Covariance Matrices - D. M. Tsai; H. T. Hou; H. J. Su
covariance matrices

15. A Metric for Covariance Matrices - Wolfgang Förstner; Boudewijn Moonen; Fdpdq Gdq; Carl Friedrich Gauss
The paper presents a metric for positive definite covariance matrices. It is a natural expression involving traces and joint eigenvalues of the matrices. It is shown to be the distance coming from a canonical invariant Riemannian metric on the space Sym + (n; R) of real symmetric positive definite matrices In contrast to known measures, collected e. g. in Grafarend 1972, the metric is invariant under affine transformations and inversion. It can be used for evaluating covariance matrices or for optimization of measurement designs.

16. Random Walks, Totally Unimodular Matrices, and a Randomised Dual Simplex Algorithm - Unimodular Matrices,Martin Dyer,Leeds U. K
We discuss the application of random walks to generating a random basis of a totally unimodular matrix and to solving a linear program with such a constraint matrix. We also derive polynomial upper bounds on the combinatorial diameter of an associated polyhedron. Supported by NATO grant RG0088/89 y Supported by NSF grants CCR-8900112, CCR-9024935 and NATO grant RG0088/89 1 1

17. Aspectos fisiopatológicos y moleculares en la remodelación de la matriz extracelular vascular - Erijman,Mauricio O.; Litovsky,Silvio
En la remodelación arterial, como en otros tejidos del organismo, la matriz extracelular cumple un papel importante. La complejidad en la constitución de la matriz hace de la remodelación un fenómeno difícil de reproducir experimentalmente. En el caso de las arterias es clave la modificación de la relación músculo liso-matriz que produzca el cambio en el músculo liso del fenotipo contráctil al secretor. Para que ocurran los cambios en la matriz y en el músculo liso es determinante la activación de los genes productores de las proteasas que modificarán las relaciones célula-célula y célula-matriz.

18. Aspectos fisiopatológicos y moleculares en la remodelación de la matriz extracelular vascular - Erijman,Mauricio O.; Litovsky,Silvio
En la remodelación arterial, como en otros tejidos del organismo, la matriz extracelular cumple un papel importante. La complejidad en la constitución de la matriz hace de la remodelación un fenómeno difícil de reproducir experimentalmente. En el caso de las arterias es clave la modificación de la relación músculo liso-matriz que produzca el cambio en el músculo liso del fenotipo contráctil al secretor. Para que ocurran los cambios en la matriz y en el músculo liso es determinante la activación de los genes productores de las proteasas que modificarán las relaciones célula-célula y célula-matriz.

19. Caracterización de matrices normales usando valores propios - Sarria Zapata, Humberto; Cuida Gómez, María Astrid; Alvarez Polo, Yolima
A matrix A, is called normal if AA_ = A_A, where A_ is the conjugate transpose of A. In this article we present new proofs for some characterizations of the normal matrices, in terms of their eigenvalues.

20. Decision Questions on Integer Matrices - Tero Harju; Turku Centre; Computer Science
We give a survey of simple undecidability results and open problems concerning matrices of low order with integer entries. Connections to the theory of finite automata (with multiplicities) are also provided.

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