The FC-rank of a context-free language

We prove that the finite condensation rank (FC-rank) of the lexicographic ordering of a context-free language is strictly less than $\omega^\omega$

Isomorphisms of scattered automatic linear orders

We prove that the isomorphism of scattered tree automatic linear orders as well as the existence of automorphisms of scattered word automatic linear orders are undecidable. For the existence of automatic automorphisms of word automatic linear orders, we determine the exact level of undecidability in the arithmetical hierarchy

Repeated summer drought and re-watering during the first growing year of oak (Quercus petraea) delay autumn senescence and bud burst in the following spring

Climate change predicts harsher summer droughts for mid-latitudes in Europe. To enhance our understanding of the putative impacts on forest regeneration, we studied the response of oak seedlings (Quercus petraea) to water deficit. Potted seedlings originating from three locally sourced provenances were subjected to two successive drought periods during the first growing season each followed by a plentiful re watering. Here, we describe survival and phenological responses after the second drought treatment, applying general linear mixed modeling. From the 441 drought treated seedlings 189 subsisted with higher chances of survival among smaller plants and among single plants per pot compared to doubles. Remarkably, survival was independent of the provenance, although relatively more plants had died off in two provenances compared to the third one with mean plant height being higher in one provenance and standard deviation of plant height being higher in the other. Timing of leaf senescence was clearly delayed after the severe drought treatment followed by re-watering, with two seedlings per pot showing a lesser retardation compared to single plants. This delay can be interpreted as a compensation time in which plants recover before entering the subsequent developmental process of leaf senescence, although it renders seedlings more vulnerable to early autumn frosts because of the delayed hardening of the shoots. Onset of bud flush in the subsequent spring still showed a significant but small delay in the drought treated group, independent of the number of seedlings per pot, and can be considered as an after effect of the delayed senescence. In both phenological models significant differences among the three provenances were detected independent from the treatment. The only provenance that is believed to be local of origin, displayed the earliest leaf senescence and the latest flushing, suggesting an adaptation to the local maritime climate. This provenance also displayed the highest standard deviation of plant height, which can be interpreted as an adaptation to variable and unpredictable weather conditions, favoring smaller plants in drought-prone summers and higher plants in more normal growing seasons

Multivariate Approaches to Classification in Extragalactic Astronomy

Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still largely in use, together with numerous mono-or bivariate classifications most often made by eye. However, a classification must be driven by the data, and sophisticated multivariate statistical tools are used more and more often. In this paper we review these different approaches in order to situate them in the general context of unsupervised and supervised learning. We insist on the astrophysical outcomes of these studies to show that multivariate analyses provide an obvious path toward a renewal of our classification of galaxies and are invaluable tools to investigate the physics and evolution of galaxies.Comment: Open Access paper. http://www.frontiersin.org/milky\_way\_and\_galaxies/10.3389/fspas.2015.00003/abstract\>. \<10.3389/fspas.2015.00003 \&g

Impossibility results on stability of phylogenetic consensus methods

We answer two questions raised by Bryant, Francis and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say, gene evolution trees) into a resulting, "consensus" tree (say, a species tree). Various stability criteria have been explored in this context, seeking to model desirable consistency properties of consensus methods as the experimental data is updated (e.g., more taxa, or more trees, are mapped). However, such stability conditions can be incompatible with some basic regularity properties that are widely accepted to be essential in any meaningful consensus method. Here, we prove that such an incompatibility does arise in the case of extension stability on binary trees and in the case of associative stability. Our methods combine general theoretical considerations with the use of computer programs tailored to the given stability requirements