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

A designed phenylalanyl-tRNA synthetase variant allows efficient in vivo incorporation of aryl ketone functionality into proteins

Incorporation of non-natural amino acids into proteins in vivo expands the scope of protein synthesis and design. p-Acetylphenylalanine was incorporated into recombinant dihydrofolate reductase (DHFR) in Escherichia coli via a computationally designed mutant form of the phenylalanyl-tRNA synthetase of the host. DHFR outfitted with ketone functionality can be chemoselectively ligated with hydrazide reagents under mild conditions

Système d’indicateurs sur les addictions : Chiffres-clé sur la consommation de substances psychoactives chez les jeunes de 11 à 24 ans dans le canton de Vaud

Le Département de la santé et de l’action sociale (DSAS) du canton de Vaud est chargé de la mise en oeuvre de la politique de prévention et de lutte contre les méfaits des addictions. Afin d’assurer le pilotage de cette politique, le DSAS souhaite disposer d’indicateurs fiables lui permettant d’évaluer les besoins, de planifier l’offre de prise en charge médico-sociale et d’évaluer les effets des projets et programmes soutenus financièrement. Le monitorage porte sur cinq thèmes : (1) la situation épidémiologique du canton de Vaud en matière de consommation de substances et de comportements addictifs ; (2) le repérage et les interventions précoces dans la population jeune ; (3) la prise en charge médico-sociale ; (4) la réduction des risques, et (5) la répression et la régulation du marché. Ce document propose une synthèse des indicateurs retenus concernant la situation épidémiologique du canton de Vaud en matière de consommation d’alcool, de tabac et de cannabis chez les jeunes de 11 à 24 ans

Green's Relations in Finite Transformation Semigroups

We consider the complexity of Green's relations when the semigroup is given by transformations on a finite set. Green's relations can be defined by reachability in the (right/left/two-sided) Cayley graph. The equivalence classes then correspond to the strongly connected components. It is not difficult to show that, in the worst case, the number of equivalence classes is in the same order of magnitude as the number of elements. Another important parameter is the maximal length of a chain of components. Our main contribution is an exponential lower bound for this parameter. There is a simple construction for an arbitrary set of generators. However, the proof for constant alphabet is rather involved. Our results also apply to automata and their syntactic semigroups.Comment: Full version of a paper submitted to CSR 2017 on 2016-12-1

Optimization in task--completion networks

We discuss the collective behavior of a network of individuals that receive, process and forward to each other tasks. Given costs they store those tasks in buffers, choosing optimally the frequency at which to check and process the buffer. The individual optimizing strategy of each node determines the aggregate behavior of the network. We find that, under general assumptions, the whole system exhibits coexistence of equilibria and hysteresis.Comment: 18 pages, 3 figures, submitted to JSTA

Most Complex Regular Right-Ideal Languages

A right ideal is a language L over an alphabet A that satisfies L = LA*. We show that there exists a stream (sequence) (R_n : n \ge 3) of regular right ideal languages, where R_n has n left quotients and is most complex under the following measures of complexity: the state complexities of the left quotients, the number of atoms (intersections of complemented and uncomplemented left quotients), the state complexities of the atoms, the size of the syntactic semigroup, the state complexities of the operations of reversal, star, and product, and the state complexities of all binary boolean operations. In that sense, this stream of right ideals is a universal witness.Comment: 19 pages, 4 figures, 1 tabl