Cluster integrable systems are a broad class of modelled on bipartite dimer models the torus. Many discrete dynamics arise by applying sequences local transformations, which form cluster modular group system. This was recently characterized first author and Inchiostro. There exist some that make use non-local transformations associated with geometric \(R\)-matrices. In this article we character...

Consider testing the null hypothesis that a single structural equation has specified coefficients. The alternative hypothesis is that the relevant part of the reduced form matrix has proper rank, that is, that the equation is identified. The usual linear model with normal disturbances is invariant with respect to linear transformations of the endogenous and of the exogenous variables. When the ...

Recently, Aguilar-Ruiz [2005] considers a data matrix containing both scaling and shifting factors and shows that the mean squared residue [Cheng and Church, 2000], called RESIDUE(II) in this paper, is useful to discover shifting patterns, but not appropriate to find scaling patterns. This finding draws our attention on the weakness of RESIDUE(II) measure and the need of new approaches to disco...

nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

In this paper two fast algorithms that use orthogonal similarity transformations to convert a symmetric rationally generated Toeplitz matrix to tridiagonal form are developed, as a means of finding the eigenvalues of the matrix efficiently. The reduction algorithms achieve cost efficiency by exploiting the rank structure of the input Toeplitz matrix. The proposed algorithms differ in the choice...

The usual procedure to compute the determinant is the so-called Gaussian elimination. We can view this as the transformation of the matrix into a lower triangular matrix with column operations. These transformations do not change the determinant but in the triangular matrix, the computation of the determinant is more convenient: we must only multiply the diagonal elements to obtain it. (It is a...