Invariance: a Theoretical Approach for Coding Sets of Words Modulo Literal (Anti)Morphisms

Let $A$ be a finite or countable alphabet and let $\theta$ be literal (anti)morphism onto $A^*$ (by definition, such a correspondence is determinated by a permutation of the alphabet). This paper deals with sets which are invariant under $\theta$ ($\theta$-invariant for short).We establish an extension of the famous defect theorem. Moreover, we prove that for the so-called thin $\theta$-invariant codes, maximality and completeness are two equivalent notions. We prove that a similar property holds in the framework of some special families of $\theta$-invariant codes such as prefix (bifix) codes, codes with a finite deciphering delay, uniformly synchronized codes and circular codes. For a special class of involutive antimorphisms, we prove that any regular $\theta$-invariant code may be embedded into a complete one.Comment: To appear in Acts of WORDS 201

Association between lumbar disc degeneration and biochemical markers of bone and cartilage remodelling

peer reviewe

Deposition rate controls nucleation and growth during amorphous/nanocrystalline competition in sputtered Zr-Cr thin films

Dual-phase Zr-based thin films synthesized by magnetron co-sputtering and showing competitive growth between amorphous and crystalline phases have been reported recently. In such films, the amorphous phase grows as columns, while the crystalline phase grows as separated cone-shaped crystalline regions made of smaller crystallites. In this paper, we investigate this phenomenon and propose a model for the development of the crystalline regions during thin film growth. We evidence using X-ray diffraction (XRD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM), that this competitive selfseparation also exists in co-sputtered Zr-Cr thin films with Cr contents of ~84-86 at.%, corresponding to the transition between the amorphous and crystalline compositions, and in the Zr-V system. Then, to assess the sturdiness of this phenomenon, its existence and geometrical characteristics are evaluated when varying the film composition and the deposition rate. The variation of geometrical features, such as the crystalline cone angle, the size and density of crystallites, is discussed. Is it shown that a variation in the deposition rate changes the nucleation and growth kinetics of the crystallites. The surface coverage by the crystalline phase at a given thickness is also calculated for each deposition rate. Moreover, comparison is made between Zr-Cr, Zr-V, Zr-Mo and Zr-W dual-phase thin films to compare their nucleation and growth kinetics

Language Emptiness of Continuous-Time Parametric Timed Automata

Parametric timed automata extend the standard timed automata with the possibility to use parameters in the clock guards. In general, if the parameters are real-valued, the problem of language emptiness of such automata is undecidable even for various restricted subclasses. We thus focus on the case where parameters are assumed to be integer-valued, while the time still remains continuous. On the one hand, we show that the problem remains undecidable for parametric timed automata with three clocks and one parameter. On the other hand, for the case with arbitrary many clocks where only one of these clocks is compared with (an arbitrary number of) parameters, we show that the parametric language emptiness is decidable. The undecidability result tightens the bounds of a previous result which assumed six parameters, while the decidability result extends the existing approaches that deal with discrete-time semantics only. To the best of our knowledge, this is the first positive result in the case of continuous-time and unbounded integer parameters, except for the rather simple case of single-clock automata

Formation of a metastable nanostructured mullite during Plasma Electrolytic Oxidation of aluminium in “soft” regime condition

International audienceThis paper demonstrates the possibility of producing a lamellar ceramic nanocomposite at the topmost surface of oxide coatings grown with the Plasma Electrolytic Oxidation process (PEO). PEO was conducted on aluminium in a silicate-rich electrolyte under the so-called "soft" regime. Nanoscale characterisation showed that the transition from the "arcs" to the "soft" regime was concomitant with the gradual formation of a 1:1 mullite/alumina lamellar nanocomposite (≈120 nm thick) that filled the cavity of the PEO "pancake" structure. Combined with plasma diagnostic techniques, a three-step growth mechanism was proposed: (i) local melting of alumina under the PEO micro-discharges (≈3200 K at high heating rate ≈3 × 10 8 K·s −1); (ii) progressive silicon enrichment of the melt coming from the electrolyte; and (iii) quenching of the melt at a cooling rate of ≈3.3 × 10 7 K·s −1 as the micro-discharge extinguishes. Under such severe cooling conditions, the solidification process was non-equilibrium as predicted by the metastable SiO 2-Al 2 O 3 binary phase diagram. This resulted in phase separation where pure alumina lamellae alternate periodically with 1:1 mullite lamellae

Enumeration and Decidable Properties of Automatic Sequences

We show that various aspects of k-automatic sequences -- such as having an unbordered factor of length n -- are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the appearance function, and the repetitivity index. We also give some new characterizations of the class of k-regular sequences. Many results extend to other sequences defined in terms of Pisot numeration systems

Recommendations for The Conduct of Economic Evaluations in Osteoporosis: Outcomes of An Experts’ Consensus Meeting Organized by The European Society for Clinical and Economic Aspects of Osteoporosis, Osteoarthritis and Musculoskeletal Diseases (ESCEO) And the US Branch of The International Osteoporosis Foundation

Summary Economic evaluations are increasingly used to assess the value of health interventions, but variable quality and heterogeneity limit the use of these evaluations by decision-makers. These recommendations provide guidance for the design, conduct, and reporting of economic evaluations in osteoporosis to improve their transparency, comparability, and methodologic standards. Introduction This paper aims to provide recommendations for the conduct of economic evaluations in osteoporosis in order to improve their transparency, comparability, and methodologic standards. Methods A working group was convened by the European Society for Clinical and Economic Aspects of Osteoporosis and Osteoarthritis to make recommendations for the design, conduct, and reporting of economic evaluations in osteoporosis, to define an osteoporosis-specific reference case to serve a minimum standard for all economic analyses in osteoporosis, to discuss methodologic challenges and initiate a call for research. A literature review, a face-to-face meeting in New York City (including 11 experts), and a review/approval by a larger group of experts worldwide (including 23 experts in total) were conducted. Results Recommendations on the type of economic evaluation, methods for economic evaluation, modeling aspects, base-case analysis and population, excess mortality, fracture costs and disutility, treatment characteristics, and model validation were provided. Recommendations for reporting economic evaluations in osteoporosis were also made and an osteoporosis-specific checklist was designed that includes items to report when performing an economic evaluation in osteoporosis. Further, 12 minimum criteria for economic evaluations in osteoporosis were identified and 12 methodologic challenges and need for further research were discussed. Conclusion While the working group acknowledges challenges and the need for further research, these recommendations are intended to supplement general and national guidelines for economic evaluations, improve transparency, quality, and comparability of economic evaluations in osteoporosis, and maintain methodologic standards to increase their use by decision-makers