A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

Loanword Phonology, Lexical Exceptions, Morphologically Driven Underapplication, and the Nature of Positionally Biased Constraints

In this paper we provide a formal account for underapplication of vowel reduction to schwa in Majorcan Catalan loanwords and learned words. On the basis of the comparison of these data with those concerning productive derivation and verbal inflection, which show analogous patterns, in this paper we also explore the existing and not yet acknowledged correlation between those processes that exhibit a particular behaviour in the loanword phonology with respect to the native phonology of the language, those processes that show lexical exceptions and those processes that underapply due to morphological reasons. In light of the analysis of the very same data and taking into account the aforementioned correlation, we show how there might exist a natural diachronic relation between two kinds of Optimality Theory constraints which are commonly used but, in principle, mutually exclusive: positional faithfulness and contextual markedness constraints. Overall, phonological productivity is proven to be crucial in three respects: first, as a context of the grammar, given that «underapplication» is systematically found in what we call the productive phonology of the dialect (including loanwords, learned words, productive derivation and verbal inflection); second, as a trigger or blocker of processes, in that the productivity or the lack of productivity of a specific process or constraint in the language is what explains whether it is challenged or not in any of the depicted situations, and, third, as a guiding principle which can explain the transition from the historical to the synchronic phonology of a linguistic variety.

Topological phases in small quantum Hall samples

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect it is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

Uncovering the functional constraints underlying the genomic organisation of the Odorant-Binding Protein genes

Animal olfactory systems have a critical role for the survival and reproduction of individuals. In insects, the odorant-binding proteins (OBPs) are encoded by a moderately sized gene family, and mediate the first steps of the olfactory processing. Most OBPs are organized in clusters of a few paralogs, which are conserved over time. Currently, the biological mechanism explaining the close physical proximity among OBPs is not yet established. Here, we conducted a comprehensive study aiming to gain insights into the mechanisms underlying the OBP genomic organization. We found that the OBP clusters are embedded within large conserved arrangements. These organizations also include other non-OBP genes, which often encode proteins integral to plasma membrane. Moreover, the conservation degree of such large clusters is related to the following: 1) the promoter architecture of the confined genes, 2) a characteristic transcriptional environment, and 3) the chromatin conformation of the chromosomal region. Our results suggest that chromatin domains may restrict the location of OBP genes to regions having the appropriate transcriptional environment, leading to the OBP cluster structure. However, the appropriate transcriptional environment for OBP and the other neighbor genes is not dominated by reduced levels of expression noise. Indeed, the stochastic fluctuations in the OBP transcript abundance may have a critical role in the combinatorial nature of the olfactory coding process.

The Besançon Galaxy Model renewed. I. Constraints on the Galactic thin disc evolution from Tycho data

Context. The understanding of Galaxy evolution can be facilitated by the use of population synthesis models, which allow to test hypotheses on the star formation history, star evolution, as well as chemical and dynamical evolution of the Galaxy. Aims. The new version of the Besanc¸on Galaxy Model (hereafter BGM) aims to provide a more flexible and powerful tool to investigate the Initial Mass Function (IMF) and Star Formation Rate (SFR) of the Galactic disc. Methods. We present a new strategy for the generation of thin disc stars which assumes the IMF, SFR and evolutionary tracks as free parameters. We have updated most of the ingredients for the star count production and, for the first time, binary stars are generated in a consistent way. We keep in this new scheme the local dynamical self-consistency as in Bienayme et al (1987). We then compare simulations from the new model with Tycho-2 data and the local luminosity function, as a first test to verify and constrain the new ingredients. The effects of changing thirteen different ingredients of the model are systematically studied. Results. For the first time, a full sky comparison is performed between BGM and data. This strategy allows to constrain the IMF slope at high masses which is found to be close to 3.0, excluding a shallower slope such as Salpeter"s one. The SFR is found decreasing whatever IMF is assumed. The model is compatible with a local dark matter density of 0.011 M pc−3 implying that there is no compelling evidence for significant amount of dark matter in the disc. While the model is fitted to Tycho2 data, a magnitude limited sample with V<11, we check that it is still consistent with fainter stars. Conclusions. The new model constitutes a new basis for further comparisons with large scale surveys and is being prepared to become a powerful tool for the analysis of the Gaia mission data.

Fiscal sustainability across government tiers: an assessment of soft budget constraints

This paper analyses how fiscal adjustment comes about when both central and sub-national governments are involved in consolidation. We test sustainability of public debt with a fiscal rule for both the federal and regional government. Results for the German Länder show that lower tier governments bear a relatively smaller part of the burden of debt consolidation, if they consolidate at all. Most of the fiscal adjustment occurs via central government debt. In contrast, both the US federal and state levels contribute to consolidation of public finances.

The age of the"Grande Coupure" mammal turnover: New constraints from the Eocene Oligocene record of the Eastern Ebro Basin (NE Spain.)

The Grande Coupure represents a major terrestrial faunal turnover recorded in Eurasia associated with the overall climate shift at the Eocene-Oligocene transition. During this event, a large number of European Eocene endemic mammals became extinct and new Asian immigrants appeared. The absolute age of the Grande Coupure, however, has remained controversial for decades. The Late Eocene-Oligocene continental record of the Eastern Ebro Basin (NE Spain) constitutes a unique opportunity to build a robust magnetostratigraphy- based chronostratigraphy which can contribute with independent age constraints for this important turnover. This study presents new magnetostratigraphic data of a 495-m-thick section (Moià-Santpedor) that ranges from 36.1 Ma to 33.3 Ma. The integration of the new results with previous litho- bio- and magnetostratigraphic records of the Ebro Basin yields accurate ages for the immediately pre- and post-Grand Coupure mammal fossil assemblages found in the study area, bracketing the Grande Coupure to an age embracing the Eocene-Oligocene transition, with a maximum allowable lag of 0.5 Myr with respect to this boundary. The shift to drier conditions that accompanied the global cooling at the Eocene-Oligocene transition probably determined the sedimentary trends in the Eastern Ebro Basin. The occurrence and expansion of an amalgamated-channel sandstone unit is interpreted as the forced response of the fluvial fan system to the transient retraction of the central-basin lake systems. The new results from the Ebro Basin allow us to revisit correlations for the controversial Eocene-Oligocene record of the Hampshire Basin (Isle of Wight, UK), and their implications for the calibration of the Mammal Palaeogene reference levels MP18 to MP21.

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits