In theory, plasmids can only be maintained in a population when the rate of horizontal gene transfer is larger than the combined effect of segregational loss and the decrease of fitness associated with plasmid carriage. Recent advances in genome sequencing have shown, however, that a large fraction of plasmids do not carry the genes necessary for conjugation or mobilization. So, how are so-called non-transmissible plasmids able to persist? In order to address this question, we examined a previously published evolutionary model based on the interaction between P. aeruginosa and the non-transmissible plasmid pNUK73. Both our in silico and in vitro results demonstrated that, although compensatory adaptation can decrease the rate of plasmid decay, the conditions for the maintenance of a non-transmissible plasmid are very stringent if the genes it carries are not beneficial to the bacterial host. This result suggests that apparently non-transmissible plasmids may still experience episodes of horizontal gene transfer occurring at very low frequencies, and that these scattered transmission events are sufficient to stabilize these plasmids. We conclude by discussing different genomic and microbiological approaches that could allow for the detection of these rare transmission events and thus to obtain a reliable estimate of the rate of horizontal gene transfer.

We investigate the transmission properties of quasiperiodic or aperiodic structures based on graphene arranged according to the Cantor sequence. In particular, we have found self-similar behaviour in the transmission spectra, and most importantly, we have calculated the scalability of the spectra. To do this, we implement and propose scaling rules for each one of the fundamental parameters: generation number, height of the barriers and length of the system. With this in mind we have been able to reproduce the reference transmission spectrum, applying the appropriate scaling rule, by means of the scaled transmission spectrum. These scaling rules are valid for both normal and oblique incidence, and as far as we can see the basic ingredients to obtain self-similar characteristics are: relativistic Dirac electrons, a self-similar structure and the non-conservation of the pseudo-spin. This constitutes a reduction of the number of conditions needed to observe self-similarity in graphene-based structures, see Díaz-

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