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

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

Ultimate periodicity of b-recognisable sets : a quasilinear procedure

It is decidable if a set of numbers, whose representation in a base b is a regular language, is ultimately periodic. This was established by Honkala in 1986. We give here a structural description of minimal automata that accept an ultimately periodic set of numbers. We then show that it can verified in linear time if a given minimal automaton meets this description. This thus yields a O(n log(n)) procedure for deciding whether a general deterministic automaton accepts an ultimately periodic set of numbers.Comment: presented at DLT 201

Approche socio-anthropologique pour l’évaluation de la vulnérabilité sociale des zones protégées par les digues fluviales du Rhône aval

National audienceCette communication présente un modèle d’évaluation de la vulnérabilité sociale au risque inondation dans les zones protégées par des digues. Ce modèle articule trois échelles d’analyse. Une échelle macrosociologique porte sur les tendances économiques et socio-démographiques afin d’évaluer la vulnérabilité de grandes unités territoriales cohérentes. L’échelle mésoscopique fait référence à l’espace de groupes sociaux et de regroupements humains cohérents. À cette échelle, on privilégie le recours à l’enquête par questionnaires auprès de ménages en zone inondable. La méthodologie proposée s’oriente en particulier vers une approche comportementaliste afin d’évaluer la propension des individus à s’exposer au risque, en fonction également de leurs capacités d’adaptation, de leurs connaissances de l’inondation, des actions préventives adoptées par les ménages, etc. Enfin, à l’échelle microsociologique, au moyen d’entretiens semi-directifs, l’approche développée tente de cerner les conditions et restrictions à la mise en ½uvre de méthodes quantitatives pour l’évaluation de la vulnérabilité sociale. / A three-scaled model is assumed to estimate the social vulnerability of leveed areas. A macro scale refers to the economic and socio-demographic trends that allow to assess the vulnerability of coherent large urban areas. A meso scale refers to homogeneous communities or social groups. At this scale, the assessment of vulnerability proceeds by questionnaire surveys of households in flood risk areas. The methodology especially adopts a behavioural approach trying to estimate the propensity of people to self-exposure to risks, risk-taking practices, adaptive capacities, knowledge of flood process, the mitigation actions undertaken by householders, etc. At a micro scale, thanks to semi-structured interviews the methodology tries to assess the conditions and the restrictions to an assessment of vulnerability by means of quantitative methods

Canonical Representatives of Morphic Permutations

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over $\{0,\ldots,q-1\}$ as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defined by a sequence of numbers from [0, 1], such that the frequency of its elements in any interval is equal to the length of that interval. We show that a canonical representative exists if and only if the word is uniquely ergodic, and that is why we use the term ergodic permutations. We also discuss ways to construct the canonical representative of a permutation defined by a morphic word and generalize the construction of Makarov, 2009, for the Thue-Morse permutation to a wider class of infinite words.Comment: Springer. WORDS 2015, Sep 2015, Kiel, Germany. Combinatorics on Words: 10th International Conference. arXiv admin note: text overlap with arXiv:1503.0618

Multifractal eigenstates of quantum chaos and the Thue-Morse sequence

We analyze certain eigenstates of the quantum baker's map and demonstrate, using the Walsh-Hadamard transform, the emergence of the ubiquitous Thue-Morse sequence, a simple sequence that is at the border between quasi-periodicity and chaos, and hence is a good paradigm for quantum chaotic states. We show a family of states that are also simply related to Thue-Morse sequence, and are strongly scarred by short periodic orbits and their homoclinic excursions. We give approximate expressions for these states and provide evidence that these and other generic states are multifractal.Comment: Substantially modified from the original, worth a second download. To appear in Phys. Rev. E as a Rapid Communicatio

Using the Hadamard and related transforms for simplifying the spectrum of the quantum baker's map

We rationalize the somewhat surprising efficacy of the Hadamard transform in simplifying the eigenstates of the quantum baker's map, a paradigmatic model of quantum chaos. This allows us to construct closely related, but new, transforms that do significantly better, thus nearly solving for many states of the quantum baker's map. These new transforms, which combine the standard Fourier and Hadamard transforms in an interesting manner, are constructed from eigenvectors of the shift permutation operator that are also simultaneous eigenvectors of bit-flip (parity) and possess bit-reversal (time-reversal) symmetry.Comment: Version to appear in J. Phys. A. Added discussions; modified title; corrected minor error

Retention mechanisms and binding states of deuterium implanted into beryllium

doi:10.1088/1367-2630/11/4/043023 Abstract. The retention of 1 keV D+ ions implanted into clean and oxidized single crystalline Be at room and elevated temperatures is investigated by a combination of in situ analytical techniques including temperature programmed desorption (TPD), nuclear reaction analysis, low-energy ion spectroscopy (LEIS) and x-ray photoelectron spectroscopy. For the first time, the whole temperature regime for deuterium release and the influence of thin oxide films on the release processes are clarified. The cleaned and annealed Be sample has residual oxygen concentration equivalent to 0.2monolayer (ML) BeO in the near-surface region as the only contamination. LEIS shows that Be from the volume covers thin BeO surface layers above an annealing temperature of 1000K by segregation, forming a pure Be-terminated surface, which is stable at lower temperatures until again oxidized by residual gas. No deuterium is retained in the sample above 950K. By analyzing TPD spectra, active retention mechanisms and six energetically different binding states are identified. Activation energies (EA