MLD Relations of Pisot Substitution Tilings

We consider 1-dimensional, unimodular Pisot substitution tilings with three intervals, and discuss conditions under which pairs of such tilings are locally isomorhphic (LI), or mutually locally derivable (MDL). For this purpose, we regard the substitutions as homomorphisms of the underlying free group with three generators. Then, if two substitutions are conjugated by an inner automorphism of the free group, the two tilings are LI, and a conjugating outer automorphism between two substitutions can often be used to prove that the two tilings are MLD. We present several examples illustrating the different phenomena that can occur in this context. In particular, we show how two substitution tilings can be MLD even if their substitution matrices are not equal, but only conjugate in $GL(n,\mathbb{Z})$. We also illustrate how the (in our case fractal) windows of MLD tilings can be reconstructed from each other, and discuss how the conjugating group automorphism affects the substitution generating the window boundaries.Comment: Presented at Aperiodic'09 (Liverpool

Geometrical Models for Substitutions

International audienceWe consider a substitution associated with the Arnoux-Yoccoz interval exchange transformation (IET) related to the tribonacci substitution. We construct the so-called stepped lines associated with the fixed points of the substitution in the abelianization (symbolic) space. We analyze various projections of the stepped line, recovering the Rauzy fractal, a Peano curve related to work in [Arnoux 88], another Peano curve related to the work of [McMullen 09] and [Lowenstein et al. 07], and also the interval exchange transformation itself

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Symbolic approach and induction in the Heisenberg group

We associate a homomorphism in the Heisenberg group to each hyperbolic unimodular automorphism of the free group on two generators. We show that the first return-time of some flows in "good" sections, are conjugate to niltranslations, which have the property of being self-induced.Comment: 18 page

Impacts of changes in groundwater recharge on the isotopic composition and geochemistry of seasonally ice-covered lakes: insights for sustainable management

Lakes are under increasing pressure due to widespread anthropogenic impacts related to rapid development and population growth. Accordingly, many lakes are currently undergoing a systematic decline in water quality. Recent studies have highlighted that global warming and the subsequent changes in water use may further exacerbate eutrophication in lakes. Lake evolution depends strongly on hydrologic balance, and therefore on groundwater connectivity. Groundwater also influences the sensitivity of lacustrine ecosystems to climate and environmental changes, and governs their resilience. Improved characterization of groundwater exchange with lakes is needed today for lake preservation, lake restoration, and sustainable management of lake water quality into the future. In this context, the aim of the present paper is to determine if the future evolution of the climate, the population, and the recharge could modify the geochemistry of lakes (mainly isotopic signature and quality via phosphorous load) and if the isotopic monitoring of lakes could be an efficient tool to highlight the variability of the water budget and quality. Small groundwater-connected lakes were chosen to simulate changes in water balance and water quality expected under future climate change scenarios, namely representative concentration pathways (RCPs) 4.5 and 8.5. Contemporary baseline conditions, including isotope mass balance and geochemical characteristics, were determined through an intensive field-based research program prior to the simulations. Results highlight that future lake geochemistry and isotopic composition trends will depend on four main parameters: location (and therefore climate conditions), lake catchment size (which impacts the intensity of the flux change), lake volume (which impacts the range of variation), and lake G index (i.e., the percentage of groundwater that makes up total lake inflows), the latter being the dominant control on water balance conditions, as revealed by the sensitivity of lake isotopic composition. Based on these model simulations, stable isotopes appear to be especially useful for detecting changes in recharge to lakes with a G index of between 50 and 80 %, but response is non-linear. Simulated monthly trends reveal that evolution of annual lake isotopic composition can be dampened by opposing monthly recharge fluctuations. It is also shown that changes in water quality in groundwater-connected lakes depend significantly on lake location and on the intensity of recharge change

Ultraschallmikroskopie im oberen Aerodigestivtrakt: Erste klinische Erfahrungen

Zusammenfassung: Hintergrund: Erste klinische Erfahrungen mit der Ultraschallmikroskopie im Bereich der oberen Luft- und Speisewege werden beschrieben. Patienten und Methoden: In der vorliegenden Pilotstudie wurden 20 gesunde Probanden und 10 Patienten, die aufgrund einer Veränderung von Mundhöhle, Rachen oder Kehlkopf operiert wurden, mit einem neuen Prototyp eines Ultraschallmikroskops untersucht. Ergebnisse: Insgesamt konnten 24 normale und 6 pathologische Befunde im Bereich des oberen Aerodigestivtrakts erhoben werden. Dabei handelte es sich einerseits um normale Schleimhaut von Mundboden, Wange, Gaumen und Stimmlippe, andererseits um Karzinome des Mundbodens, der aryepiglottischen Falte und der Stimmlippe. Des Weiteren wurden ein Papillom des Gaumenbogens und 2Epiglottiszysten ultraschallmikroskopisch untersucht. Schlussfolgerung: Unsere Untersuchungen zeigen, dass die Ultraschallmikroskopie der Hohlorgane in den Bereich des Möglichen gerückt ist. Hierbei unterscheiden sich pathologische Läsionen deutlich von normalem Epithel. Zur Erkennung von Gesetzmäßigkeiten bei Veränderungen von Mundhöhle, Rachen und Kehlkopf sind jedoch weitere Untersuchungen mit wesentlich größeren Fallzahlen nöti

Experimental investigation of the mechanical stiffness of periodic framework-patterned elastomers

Recent advances in the cataloguing of three-dimensional nets mean a systematic search for framework structures with specific properties is now feasible. Theoretical arguments about the elastic deformation of frameworks suggest characteristics of mechanically isotropic networks. We explore these concepts on both isotropic and anisotropic networks by manufacturing porous elastomers with three different periodic net geometries. The blocks of patterned elastomers are subjected to a range of mechanical tests to determine the dependence of elastic moduli on geometric and topological parameters. We report results from axial compression experiments, three-dimensional X-ray computed tomography imaging and image-based finite-element simulations of elastic properties of framework-patterned elastomers

Split-rib reconstruction of the frontal sinus: two cases and literature review

Abstract Background: Large defects of the anterior wall of the frontal sinus require closure using either autologous or foreign material. In cases of osteomyelitis, the reconstruction must be resistant to bacterial infection. Split-rib osteoplasty can be used in different sites. Methods: Two patients with malignant sinonasal tumours underwent repeated treatment, and subsequently developed osteomyelitis of the frontal bone. After adequate therapy, a large defect of the anterior wall persisted. Reconstruction was performed using the split-rib method. The literature on this topic was reviewed. Results: Both patients' treatment were successful. No complications occurred. A PubMed search on the topic of rib reconstruction of the frontal sinus and skull was performed; 18 publications matched the inclusion criteria. From these sources, we noted that 182 reconstructions yielded good results with few complications. Conclusion: Large defects of the anterior wall of the frontal sinus can be closed successfully using autologous split-rib grafting. Aesthetic outcome is good and donor site morbidity is minima

Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

An algorithm to identify automorphisms which arise from self-induced interval exchange transformations

We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval exchange transformation in case of success.Comment: 26 pages, 8 figures. v2: the article has been reorganized to make for a more linear read. A few paragraphs have been added for clarit