A new algebraic invariant for weak equivalence of sofic subshifts

It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. Two independent approaches are used: ζ-semigroups as recognition structures for sofic subshifts, and relatively free profinite semigroups. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally defined by pseudovarieties of finite semigroups are closed under weak equivalence. Among such classes are the classes of almost finite type subshifts and aperiodic subshifts. The algebraic invariant is compared with other robust conjugacy invariants.Research programme AutoMathA of ESF; Pessoa bilateral project Egide/Grices 11113YM "Automata, profinite semigroups and symbolic dynamics"; FCT, grant SFRH/BD/24200/2005; POCI 2010; FS

A new algebraic invariant for weak equivalence of sofic subshifts

It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. Two independent approaches are used: ζ-semigroups as recognition structures for sofic subshifts, and relatively free profinite semigroups. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally defined by pseudovarieties of finite semigroups are closed under weak equivalence. Among such classes are the classes of almost finite type subshifts and aperiodic subshifts. The algebraic invariant is compared with other robust conjugacy invariants.Research programme AutoMathA of ESF; Pessoa bilateral project Egide/Grices 11113YM "Automata, profinite semigroups and symbolic dynamics"; FCT, grant SFRH/BD/24200/2005; POCI 2010; FS

On Varieties of Ordered Automata

The Eilenberg correspondence relates varieties of regular languages to pseudovarieties of finite monoids. Various modifications of this correspondence have been found with more general classes of regular languages on one hand and classes of more complex algebraic structures on the other hand. It is also possible to consider classes of automata instead of algebraic structures as a natural counterpart of classes of languages. Here we deal with the correspondence relating positive $\mathcal C$-varieties of languages to positive $\mathcal C$-varieties of ordered automata and we present various specific instances of this correspondence. These bring certain well-known results from a new perspective and also some new observations. Moreover, complexity aspects of the membership problem are discussed both in the particular examples and in a general setting

Chemoenzymatic Probes for Detecting and Imaging Fucose-α(1-2)-galactose Glycan Biomarkers

The disaccharide motif fucose-α(1-2)-galactose (Fucα(1-2)Gal) is involved in many important physiological processes, such as learning and memory, inflammation, asthma, and tumorigenesis. However, the size and structural complexity of Fucα(1-2)Gal-containing glycans have posed a significant challenge to their detection. We report a new chemoenzymatic strategy for the rapid, sensitive detection of Fucα(1-2)Gal glycans. We demonstrate that the approach is highly selective for the Fucα(1-2)Gal motif, detects a variety of complex glycans and glycoproteins, and can be used to profile the relative abundance of the motif on live cells, discriminating malignant from normal cells. This approach represents a new potential strategy for biomarker detection and expands the technologies available for understanding the roles of this important class of carbohydrates in physiology and disease

-variety.

Open problems on regular languages: an historical perspectiv

First order formulas with modular predicates

Two results by Schützenberger (1965) and by Mc-Naughton and Papert (1971) lead to a precise description of the expressive power of first order logic on words interpreted as ordered colored structures. In this paper, we study the expressive power of existential formulas and of Boolean combinations of existential formulas in a logic enriched by modular numerical predicates. We first give a combinatorial description of the corresponding regular languages, and then give an algebraic characterization in terms of their syntactic morphisms. It follows that one can effectively decide whether a given regular language is captured by one of these two fragments of first order logic. The proofs rely on nontrivial techniques of semigroup theory: stamps, derived categories and wreath products. 1

A new algebraic invariant for weak equivalence of sofic subshifts

It is studied how taking the inverse image by a sliding block code affects the syntactic semigroup of a sofic subshift. The main tool are ζ-semigroups, considered as recognition structures for sofic subshifts. A new algebraic invariant is obtained for weak equivalence of sofic subshifts, by determining which classes of sofic subshifts naturally defined by pseudovarieties of finite semigroups are closed under weak equivalence. Among such classes are the classes of almost finite type subshifts and aperiodic subshifts. The algebraic invariant is compared with other robust conjugacy invariants

Analyse parodontale en prothèse fixée à visée esthétique

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