Many linear macroeconomic models can be cast in the …rst-order form, AEtyt+1 = Byt +CEtxt; if the matrix A is permitted to be singular. For this singular linear di¤erence system under rational expectations, we show there is a unique stable solution under two requirements: (i) the determinental polynomial jAz ¡ Bj is not zero for some value of z, and (ii) a rank condition is satis…ed which is a ...

In Semantic Role Labeling (SRL), it is reasonable to globally assign semantic roles due to strong dependencies among arguments. Some relations between arguments significantly characterize the structural information of argument structure. In this paper, we concentrate on thematic hierarchy that is a rank relation restricting syntactic realization of arguments. A loglinear model is proposed to ac...

We show that for every forest T the linear rank-width of T is equal to the path-width of T , and the linear clique-width of T equals the path-width of T plus two, provided that T contains a path of length three. It follows that both linear rank-width and linear clique-width of forests can be computed in linear time. Using our characterization of linear rank-width of forests, we determine the se...

We consider the problem of designing a linear transformation , of rank , which projects the features of a classifier onto such as to achieve minimum Bayes error (or probability of misclassification). Two avenues will be explored: the first is to maximize the -average divergence between the class densities and the second is to minimize the union Bhattacharyya bound in the range of . While both a...

We consider the problem of designing a linear transformation 2 IR , of rank p n, which projects the features of a classi er x 2 IR onto y = x 2 IR such as to achieve minimum Bayes error (or probability of misclassi cation). Two avenues will be explored: the rst is to maximize the -average divergence between the class densities and the second is to minimize the union Bhattacharyya bound in the r...

Rank-Based methods for iid linear models have been developed over the past 30 years. However, little work has been done in the area of mixed models. In this paper, we discuss a transformation approach to modeling a particular mixed model: one with an arbitrary number of fixed effects and covariates but only one random effect. Discussion of the asymptotic theory is given and the results of a sim...

We study the Lattice Isomorphism Problem (LIP), in which given two lattices L1 and L2 the goal is to decide whether there exists an orthogonal linear transformation mapping L1 to L2. Our main result is an algorithm for this problem running in time nO(n) times a polynomial in the input size, where n is the rank of the input lattices. A crucial component is a new generalized isolation lemma, whic...

In numerical linear algebra much attention has been paid to matrices that are sparse, i.e., containing a lot of zeros. For example, to compute the eigenvalues of a general dense symmetric matrix, this matrix is first reduced to a similar tridiagonal one using an orthogonal similarity transformation. The subsequent QR-algorithm performed on this n×n tridiagonal matrix, takes the sparse structure...

Various efficient generalized sphere decoding (GSD) algorithms have been proposed to approach optimal ML performance for underdetermined linear systems, by transforming the original problem into the full-column-rank one so that standard SD can be fully applied. However, their design parameters are heuristically set based on observation or the possibility of an ill-conditioned transformed matrix...