Binary Patterns in Binary Cube-Free Words: Avoidability and Growth

The avoidability of binary patterns by binary cube-free words is investigated and the exact bound between unavoidable and avoidable patterns is found. All avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the growth rates of the avoiding languages are studied. All such languages, except for the overlap-free language, are proved to have exponential growth. The exact growth rates of languages avoiding minimal avoidable patterns are approximated through computer-assisted upper bounds. Finally, a new example of a pattern-avoiding language of polynomial growth is given.Comment: 18 pages, 2 tables; submitted to RAIRO TIA (Special issue of Mons Days 2012

Number of Holes in Unavoidable Sets of Partial Words I

Partial words are sequences over a finite alphabet that may contain some undefined positions called holes. We consider unavoidable sets of partial words of equal length. We compute the minimum number of holes in sets of size three over a binary alphabet (summed over all partial words in the sets). We also construct all sets that achieve this minimum. This is a step towards the difficult problem of fully characterizing all unavoidable sets of partial words of size three

Random subshifts of finite type

Let $X$ be an irreducible shift of finite type (SFT) of positive entropy, and let $B_n(X)$ be its set of words of length $n$. Define a random subset $\omega$ of $B_n(X)$ by independently choosing each word from $B_n(X)$ with some probability $\alpha$. Let $X_{\omega}$ be the (random) SFT built from the set $\omega$. For each $0\leq \alpha \leq1$ and $n$ tending to infinity, we compute the limit of the likelihood that $X_{\omega}$ is empty, as well as the limiting distribution of entropy for $X_{\omega}$. For $\alpha$ near 1 and $n$ tending to infinity, we show that the likelihood that $X_{\omega}$ contains a unique irreducible component of positive entropy converges exponentially to 1. These results are obtained by studying certain sequences of random directed graphs. This version of "random SFT" differs significantly from a previous notion by the same name, which has appeared in the context of random dynamical systems and bundled dynamical systems.Comment: Published in at http://dx.doi.org/10.1214/10-AOP636 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analysis of measurement and simulation errors in structural system identification by observability techniques

This is the peer reviewed version of the following article: [Lei, J., Lozano-Galant, J. A., Nogal, M., Xu, D., and Turmo, J. (2017) Analysis of measurement and simulation errors in structural system identification by observability techniques. Struct. Control Health Monit., 24: . doi: 10.1002/stc.1923.], which has been published in final form at http://onlinelibrary.wiley.com/wol1/doi/10.1002/stc.1923/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.During the process of structural system identification, errors are unavoidable. This paper analyzes the effects of measurement and simulation errors in structural system identification based on observability techniques. To illustrate the symbolic approach of this method a simply supported beam is analyzed step-by-step. This analysis provides, for the very first time in the literature, the parametric equations of the estimated parameters. The effects of several factors, such as errors in a particular measurement or in the whole measurement set, load location, measurement location or sign of the errors, on the accuracy of the identification results are also investigated. It is found that error in a particular measurement increases the errors of individual estimations, and this effect can be significantly mitigated by introducing random errors in the whole measurement set. The propagation of simulation errors when using observability techniques is illustrated by two structures with different measurement sets and loading cases. A fluctuation of the observed parameters around the real values is proved to be a characteristic of this method. Also, it is suggested that a sufficient combination of different load cases should be utilized to avoid the inaccurate estimation at the location of low curvature zones.Peer ReviewedPostprint (author's final draft