Finitely generated ideal languages and synchronizing automata

We study representations of ideal languages by means of strongly connected synchronizing automata. For every finitely generated ideal language L we construct such an automaton with at most 2^n states, where n is the maximal length of words in L. Our constructions are based on the De Bruijn graph.Comment: Submitted to WORDS 201

How dense can one pack spheres of arbitrary size distribution?

We present the first systematic algorithm to estimate the maximum packing density of spheres when the grain sizes are drawn from an arbitrary size distribution. With an Apollonian filling rule, we implement our technique for disks in 2d and spheres in 3d. As expected, the densest packing is achieved with power-law size distributions. We also test the method on homogeneous and on empirical real distributions, and we propose a scheme to obtain experimentally accessible distributions of grain sizes with low porosity. Our method should be helpful in the development of ultra-strong ceramics and high performance concrete.Comment: 5 pages, 5 figure

A Hamiltonian approach for explosive percolation

We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We show that the following two ingredients are essential for obtaining an abrupt (first-order) transition in the fraction of the system occupied by the largest cluster: (i) the size of all growing clusters should be kept approximately the same, and (ii) the inclusion of merging bonds (i.e., bonds connecting vertices in different clusters) should dominate with respect to the redundant bonds (i.e., bonds connecting vertices in the same cluster). Moreover, in the extreme limit where only merging bonds are present, a complete enumeration scheme based on tree-like graphs can be used to obtain an exact solution of our model that displays a first-order transition. Finally, the proposed mechanism can be viewed as a generalization of standard percolation that discloses an entirely new family of models with potential application in growth and fragmentation processes of real network systems.Comment: 4 pages, 4 figure

Influence of the external pressure on the quantum correlations of molecular magnets

The study of quantum correlations in solid state systems is a large avenue for research and their detection and manipulation are an actual challenge to overcome. In this context, we show by using first-principles calculations on the prototype material KNaCuSi$_{4}$O$_{10}$ that the degree of quantum correlations in this spin cluster system can be managed by external hydrostatic pressure. Our results open the doors for research in detection and manipulation of quantum correlations in magnetic systems with promising applications in quantum information science

Fault detection in the Tennessee Eastman benchmark process using dynamic principal components analysis based on decorrelated residuals (DPCA-DR)

Current multivariate control charts for monitoring large scale industrial processes are typically based on latent variable models, such as principal component analysis (PCA) or its dynamic counterpart when variables present auto-correlation (DPCA). In fact, it is usually considered that, under such conditions, DPCA is capable to effectively deal with both the cross- and auto-correlated nature of data. However, it can easily be verified that the resulting monitoring statistics (T2 and Q, also referred by SPE) still present significant auto-correlation. To handle this issue, a set of multivariate statistics based on DPCA and on the generation of decorrelated residuals were developed, that present low auto-correlation levels, and therefore are better positioned to implement SPC in a more consistent and stable way (DPCA-DR). The monitoring performance of these statistics was compared with that from other alternative methodologies for the well-known Tennessee Eastman process benchmark. From this study, we conclude that the proposed statistics had the highest detection rates on 19 out of the 21 faults, and are statistically superior to their PCA and DPCA counterparts. DPCA-DR statistics also presented lower auto-correlation, which simplifies their implementation and improves their reliability