About the Stabilization of a Nonlinear Perturbed Difference Equation

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order than that of the nominal difference equation. In the general case, the controller consists of two combined parts, namely, the feedback nominal controller which stabilizes the nominal (i.e., perturbation-free) difference equation plus an incremental controller which completes the stabilization in the presence of perturbed or unmodeled dynamics in the uncontrolled difference equation. A stabilization variant consists of using a single controller to stabilize both the nominal difference equation and also the perturbed one under a small-type characterization of the perturbed dynamics. The study is based on Banach fixed point principle, and it is also valid with slight modification for the stabilization of unstable oscillatory solutions.

Best Proximity Points of Generalized Semicyclic Impulsive Self-Mappings: Applications to Impulsive Differential and Difference Equations

This paper is devoted to the study of convergence properties of distances between points and the existence and uniqueness of best proximity and fixed points of the so-called semicyclic impulsive self-mappings on the union of a number of nonempty subsets in metric spaces. The convergences of distances between consecutive iterated points are studied in metric spaces, while those associated with convergence to best proximity points are set in uniformly convex Banach spaces which are simultaneously complete metric spaces. The concept of semicyclic self-mappings generalizes the well-known one of cyclic ones in the sense that the iterated sequences built through such mappings are allowed to have images located in the same subset as their pre-image. The self-mappings under study might be in the most general case impulsive in the sense that they are composite mappings consisting of two self-mappings, and one of them is eventually discontinuous. Thus, the developed formalism can be applied to the study of stability of a class of impulsive differential equations and that of their discrete counterparts. Some application examples to impulsive differential equations are also given.

How central are clients in sexual networks created by commercial sex?

Sex workers are traditionally considered important vectors of transmission of sexually transmitted infections (STI). The role of clients is commonly overlooked, partially due to the lack of evidence on clients' position in the sexual network created by commercial sex. Contrasting the diffusion importance of sex workers and their clients in the map of their sexual encounters in two Web-mediated communities, we find that from diffusion perspective, clients are as important as sex workers. Their diffusion importance is closely linked to the geography of the sexual encounters: as a result of different movement patterns, travelling clients shorten network distances between distant network neighborhoods and thus facilitate contagion among them more than sex workers, and find themselves more often in the core of the network by which they could contribute to the persistence of STIs in the community. These findings position clients into the set of the key actors and highlight the role of human mobility in the transmission of STIs in commercial sexual networks.

Identification of Sex and Female’s Reproductive Stage in Commercial Fish Species through the Quantification of Ribosomal Transcripts in Gonads

The estimation of maturity and sex of fish stocks in European waters is a requirement of the EU Data Collection Framework as part of the policy to improve fisheries management. On the other hand, research on fish biology is increasingly focused in molecular approaches, researchers needing correct identification of fish sex and reproductive stage without necessarily having in house the histological know-how necessary for the task. Taking advantage of the differential gene transcription occurring during fish sex differentiation and gametogenesis, the utility of 5S ribosomal RNA (5S rRNA) and General transcription factor IIIA (gtf3a) in the molecular identification of sex and gametogenic stage was tested in different economically-relevant fish species from the Bay of Biscay. Gonads of 9 fish species (, Atlantic, Atlantic-chub and horse mackerel, blue whiting, bogue, European anchovy, hake and pilchard and megrim), collected from local commercial fishing vessels were histologically sexed and 5S and 18S rRNA concentrations were quantified by capillary electrophoresis to calculate a 5S/18S rRNA index. Degenerate primers permitted cloning and sequencing of gtf3a fragments in 7 of the studied species. 5S rRNA and gtf3a transcript levels, together with 5S/18S rRNA index, distinguished clearly ovaries from testis in all of the studied species. The values were always higher in females than in males. 5S/18S rRNA index values in females were always highest when fish were captured in early phases of ovary development whilst, in later vitellogenic stages, the values decreased significantly. In megrim and European anchovy, where gonads in different oogenesis stages were obtained, the 5S/18S rRNA index identified clearly gametogenic stage. This approach, to the sexing and the quantitative non-subjective identification of the maturity stage of female fish, could have multiple applications in the study of fish stock dynamics, fish reproduction and fecundity and fish biology in general.