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

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

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

Critical connectedness of thin arithmetical discrete planes

An arithmetical discrete plane is said to have critical connecting thickness if its thickness is equal to the infimum of the set of values that preserve its $2$-connectedness. This infimum thickness can be computed thanks to the fully subtractive algorithm. This multidimensional continued fraction algorithm consists, in its linear form, in subtracting the smallest entry to the other ones. We provide a characterization of the discrete planes with critical thickness that have zero intercept and that are $2$-connected. Our tools rely on the notion of dual substitution which is a geometric version of the usual notion of substitution acting on words. We associate with the fully subtractive algorithm a set of substitutions whose incidence matrix is provided by the matrices of the algorithm, and prove that their geometric counterparts generate arithmetic discrete planes.Comment: 18 pages, v2 includes several corrections and is a long version of the DGCI extended abstrac

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

Triangulations and Severi varieties

We consider the problem of constructing triangulations of projective planes over Hurwitz algebras with minimal numbers of vertices. We observe that the numbers of faces of each dimension must be equal to the dimensions of certain representations of the automorphism groups of the corresponding Severi varieties. We construct a complex involving these representations, which should be considered as a geometric version of the (putative) triangulations

Subset currents on free groups

We introduce and study the space of \emph{subset currents} on the free group $F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite Borel measure on the space $\mathfrak C_N$ of all closed subsets of $\partial F_N$ consisting of at least two points. While ordinary geodesic currents generalize conjugacy classes of nontrivial group elements, a subset current is a measure-theoretic generalization of the conjugacy class of a nontrivial finitely generated subgroup in $F_N$, and, more generally, in a word-hyperbolic group. The concept of a subset current is related to the notion of an "invariant random subgroup" with respect to some conjugacy-invariant probability measure on the space of closed subgroups of a topological group. If we fix a free basis $A$ of $F_N$, a subset current may also be viewed as an $F_N$-invariant measure on a "branching" analog of the geodesic flow space for $F_N$, whose elements are infinite subtrees (rather than just geodesic lines) of the Cayley graph of $F_N$ with respect to $A$.Comment: updated version; to appear in Geometriae Dedicat

Observation of confined current ribbon in JET plasmas

we report the identification of a localised current structure inside the JET plasma. It is a field aligned closed helical ribbon, carrying current in the same direction as the background current profile (co-current), rotating toroidally with the ion velocity (co-rotating). It appears to be located at a flat spot in the plasma pressure profile, at the top of the pedestal. The structure appears spontaneously in low density, high rotation plasmas, and can last up to 1.4 s, a time comparable to a local resistive time. It considerably delays the appearance of the first ELM.Comment: 10 pages, 6 figure

Trayectorias laborales de jóvenes trabajadores de la actividad vitivinícola : departamento Maipú, Mendoza

La presente investigación tuvo como eje los vínculos entre educación y trabajo en la vitivinicultura mendocina desde 1990 . El objetivo general fue comprender los procesos de incorporación de jóvenes de ambos sexos al mundo del trabajo y su vínculo con las estrategias de formación y los esquemas de percepción en el mercado vitivinícola mendocino desde los 90. Se analizaron e identificaron los tipos de trayectorias educativas, laborales y transiciones existentes en los jóvenes. También los condicionantes de género que operan desde la perspectiva de las mujeres jóvenes. Se buscó comprender las formas que adquieren, cómo se manifiestan y varían las perspectivas acerca del trabajo, de las exigencias laborales y las condiciones del mercado de trabajo a lo largo de las trayectorias educativas y laborales y cuáles son los principales elementos constitutivos de las trayectorias de inserción, qué factores están asociados a sus variaciones y cómo se vinculan con las expectativas y estrategias de formación de inserción laboral.Fil: Martín, María Eugenia. CONICET (Consejo Nacional de Investigaciones Científicas y Técnicas) - Universidad Nacional de CuyoFil: Zamarbide, Gabriela. Universidad Nacional de Cuy