Computing meaningful clusters of nodes is crucial to analyze large networks. In this paper, we present a pairwise node similarity measure that allows to extract roles, i.e. group of nodes sharing similar flow patterns within a network. We propose a low rank iterative scheme to approximate the similarity measure for very large networks. Finally, we show that our low rank similarity score success...

The general linear model y = Xβ + ε with correlated error variables can be transformed by means of the generalized singular value decomposition to a very simple model (canonical form) where the least squares solution is obvious. The method works also if X and the covariance matrix of the error variables do not have full rank or are nearly rank deficient (rank-k approximation). By backtransforma...

The general linear model y = Xβ + ε with correlated error variables can be transformed by means of the generalized singular value decomposition to a very simple model (canonical form) where the least squares solution is obvious. The method works also if X and the covariance matrix of the error variables do not have full rank or are nearly rank deficient (rank-k approximation). By backtransforma...

Let A be a unital maximal full algebra of operator fields with base space [0, 1] and fibre algebras {At}t∈[0,1]k . We show that the stable rank of A is bounded above by the quantity supt∈[0,1]ksr(C([0, 1] )⊗ At). Here the symbol “sr” means stable rank. Using the above estimate, we compute the stable ranks of the C-algebras of the (possibly higher rank) discrete Heisenberg groups.

We characterize bijections on matrix spaces (operator algebras) preserving full rank (invertibility) of differences of matrix (operator) pairs in

This paper proposes a class of full space diversity full rate space-time turbo codes. Both parallel concatenated and serially concatenated codes are designed. The full space diversity design is facilitated by a rank theory. Compared with space-time trellis codes, the simulations show the space-time turbo codes have excellent performance in both quasi-static fading channels and time varying fadi...

It is an open problem if an elementary p-group of rank k ≥ 3 does admit full-rank normalized factorization into two of its subsets such that one of the factors has p elements. The paper provides an answer in the p ≤ 7 special case.

For a higher-rank graph Λ with sources we detail a construction that creates a row-finite higher-rank graph Λ that does not have sources and contains Λ as a subgraph. Furthermore, when Λ is row-finite the Cuntz-Krieger algebra of Λ, C(Λ) is a full corner of C(Λ), the Cuntz-Krieger algebra of Λ.

The multivariate reduced rank regression model plays an important role in econometrics. Examples include co-integration analysis and models with a factor structure. Geweke (1996) provided the foundations for a Bayesian analysis of this model. Unfortunately several of the full conditional posterior distributions, which forms the basis for constructing a Gibbs sampler for the poster distribution,...