A new proof for the decidability of D0L ultimate periodicity

We give a new proof for the decidability of the D0L ultimate periodicity problem based on the decidability of p-periodicity of morphic words adapted to the approach of Harju and Linna.Comment: In Proceedings WORDS 2011, arXiv:1108.341

The Critical Exponent is Computable for Automatic Sequences

The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable. Our results also apply to variants of the critical exponent, such as the initial critical exponent of Berthe, Holton, and Zamboni and the Diophantine exponent of Adamczewski and Bugeaud. Our work generalizes or recovers previous results of Krieger and others, and is applicable to other situations; e.g., the computation of the optimal recurrence constant for a linearly recurrent k-automatic sequence.Comment: In Proceedings WORDS 2011, arXiv:1108.341

The complexity of tangent words

In a previous paper, we described the set of words that appear in the coding of smooth (resp. analytic) curves at arbitrary small scale. The aim of this paper is to compute the complexity of those languages.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Infinite permutations vs. infinite words

I am going to compare well-known properties of infinite words with those of infinite permutations, a new object studied since middle 2000s. Basically, it was Sergey Avgustinovich who invented this notion, although in an early study by Davis et al. permutations appear in a very similar framework as early as in 1977. I am going to tell about periodicity of permutations, their complexity according to several definitions and their automatic properties, that is, about usual parameters of words, now extended to permutations and behaving sometimes similarly to those for words, sometimes not. Another series of results concerns permutations generated by infinite words and their properties. Although this direction of research is young, many people, including two other speakers of this meeting, have participated in it, and I believe that several more topics for further study are really promising.Comment: In Proceedings WORDS 2011, arXiv:1108.341

Physics of Solar Prominences: II - Magnetic Structure and Dynamics

Observations and models of solar prominences are reviewed. We focus on non-eruptive prominences, and describe recent progress in four areas of prominence research: (1) magnetic structure deduced from observations and models, (2) the dynamics of prominence plasmas (formation and flows), (3) Magneto-hydrodynamic (MHD) waves in prominences and (4) the formation and large-scale patterns of the filament channels in which prominences are located. Finally, several outstanding issues in prominence research are discussed, along with observations and models required to resolve them.Comment: 75 pages, 31 pictures, review pape

High-resolution characterization of deformation induced martensite in large areas of fatigued austenitic stainless steel using deep learning

Abstract This paper aims to demonstrate a novel technique enabling the accurate visualization and fast mapping of deformation-induced α′-martensite produced during cyclic straining of a metastable austenitic stainless steel, refined by reversion annealing to different grain sizes. The technique is based on energy and angular separation of the signal electrons in a scanning electron microscope (SEM). Collection of the inelastic backscattered electrons emitted under high take-off angles from a sample surface results in the acquisition of micrographs with high sensitivity to structural defects, such as dislocations, grain boundaries, and other imperfections. The areas with a high density of lattice imperfections reduce the penetration depth of the primary electrons, and simultaneously affect the signal electrons leaving the specimen. This results in an increase in the inelastic backscattered electrons yielded from the vicinity of α′-martensite, and a bright halo surrounds this phase. The α′-martensite phase can thus be separated from the austenitic matrix in SEM micrographs. In this work, we propose a deep learning method for a precise α′-martensite mapping within a large area. Various deep learning-based methods have been tested, and the best result measured by both Dice loss and IoU scores has been achieved using the U-Net architecture extended by the ResNet encoder