In this paper, we discuss some properties of joint spectral {radius(jsr)} and  generalized spectral radius(gsr)  for a finite set of upper triangular matrices with entries in a Banach algebra and represent relation between geometric and joint/generalized spectral radius. Some of these are in scalar matrices, but  some are different. For example for a bounded set of scalar matrices,$Sigma$, $r_*...

We construct an identity-based encryption (IBE) scheme from the standard Learning with Errors (LWE) assumption that has compact public-key and achieves adaptive security in the standard model. In particular, our scheme only needs 2 public matrices to support O(log λ)-bit length identity, and O(λ/ log λ) public matrices to support λ-bit length identity. This improves over previous IBE schemes fr...

O R IG IN A L A R T IC L E Ursula Rohr Sgarbieri

The random matrix uniformly distributed over the set of all mby-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random matrices, is studied. It is shown that a k-good random m-by-n matrix with a distribution of minimum support size is uniformly distributed over a maximum-rank-dista...

This paper gives an explicit method for computing the resultant of any sparse unmixed bivariate system with given support. We construct square matrices whose determinant is exactly the resultant. The matrices constructed are of hybrid Sylvester and Bézout type. The results extend those in [14] by giving a complete combinatorial description of the matrix. Previous work by D’Andrea [5] gave pure ...

‎in this paper‎, ‎we prove the nonexistence of two weighing matrices of‎ ‎weight 81‎, ‎namely $cw(88,81)$ and $cw(99,81)$‎. ‎we will apply two‎ ‎very different methods to do so; for the case of $cw(88,81)$‎, ‎we‎  ‎will use almost purely counting methods‎, ‎while for $cw(99,81)$‎, ‎we‎ ‎will use algebraic methods‎.

We establish bounds on the spectral radii for a large class of sparse random matrices, which includes the adjacency matrices of inhomogeneous Erdős-Rényi graphs. For the Erdős-Rényi graph G(n, d/n), our results imply that the smallest and second-largest eigenvalues of the adjacency matrix converge to the edges of the support of the asymptotic eigenvalue distribution provided that d log n. Toget...

Dealing with traffic demand trip matrices to feed models that support traffic management decisions is still a problem that deserves research into finding practical solutions in the short term horizon, before future developments become available. This paper analyzes the role of OD matrices in the framework of Analysis, Modeling and Simulation (AMS), namely when moving from static OD matrices to ...

We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction of Le et al. (2013) as a special case, but also extends to Circulant, Toeplitz and Hankel matrices, and the broader family of structured matrices that are characterized by the concept ...