Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed binary patterns. We show that the number of such sequences increases exponentially with their length and that the growth rate, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive a new algorithm for determi...

We study the largest number of sequences with the property that any two sequences do not contain specified pairs of patterns. We show that this number increases exponentially with the length of the sequences and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We illustrate a new heuristic for computing the joint spectral...

Certain magnetic recording applications call for a large number of sequences whose differences do not include certain disallowed patterns. We show that the number of such sequences increases exponentially with their length and that the exponent, or capacity, is the logarithm of the joint spectral radius of an appropriately defined set of matrices. We derive new algorithms for determining the jo...

Reenement equations play an important role in computer graphics and wavelet analysis. In this paper we investigate multivariate reenement equations associated with a dila-tion matrix and a nitely supported reenement mask. We characterize the L p-convergence of a subdivision scheme in terms of the p-norm joint spectral radius of a collection of matrices associated with the reenement mask. In par...

Abstract In this paper we study ergodic optimization and multifractal behavior of Lyapunov exponents for matrix cocycles. We show that the restricted variational principle holds generic cocycles [in sense (Bonatti Viana in Ergod Theory Dyn Syst 24(5):1295–1330, 2004)] over mixing subshifts finite type. also spectrum is equal to closure set where entropy positive such Moreover, continuity at bou...