Multidimensional extension of the Morse--Hedlund theorem

A celebrated result of Morse and Hedlund, stated in 1938, asserts that a sequence $x$ over a finite alphabet is ultimately periodic if and only if, for some $n$, the number of different factors of length $n$ appearing in $x$ is less than $n+1$. Attempts to extend this fundamental result, for example, to higher dimensions, have been considered during the last fifteen years. Let $d\ge 2$. A legitimate extension to a multidimensional setting of the notion of periodicity is to consider sets of \ZZ^d definable by a first order formula in the Presburger arithmetic . With this latter notion and using a powerful criterion due to Muchnik, we exhibit a complete extension of the Morse--Hedlund theorem to an arbitrary dimension $d$ and characterize sets of $\ZZ^d$ definable in in terms of some functions counting recurrent blocks, that is, blocks occurring infinitely often

Syndeticity and independent substitutions

We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the notion of two independent substitutions. Our main result is the following. If a sequence $x$ is generated by two independent substitutions, at least one being of exponential growth, then the factors of $x$ appearing infinitely often in $x$ appear with bounded gaps. As an application, we derive an analogue of Cobham's theorem for two independent substitutions (or abstract numeration systems) one with polynomial growth, the other being exponential

Household Water Demand Estimation using Micro-Level Data

La Reunion Island is facing to specific difficulties in supplying drinking water. In the western part of this french departement drincking water is lacking. In this context, well-suited policies require to know perfectly households consumption behavior. To this end, the household water demand function is estimated. Data have been recorded on a random sample of 2000 consumers by a telephone poll. Water bills have been collected by post, from 200 volunteer households.

Structure de l’île d’Eivissa (Ibiza) et sa place dans le cadre baléare

La présente étude retrace l’évolution des connaissances acquises sur la structure d’Eivissa. Un nouveau découpage structural de cette île est proposé. Deux importants accidents transverses divisent l’île en trois grands compartiments. Au Paléogène, l’île appartenait probablement à un territoire émergé. Une transgression marine débuta au Burdigalien (nannozone NN3) et fut maximale au Langhien inférieur (nannozone NN5). Elle déposa des sédiments rapportés à la Formation de la Cala d’Hort, impliquée dans les écailles tectoniques. Cette formation est surmontée par la Formation de Cap Jueu datée du Langhien supérieur-Serravallien, également impliquée dans les écailles. L’existence d’un olistostrome d’âge aquitano-burdigalien évoquée par des auteurs antérieurs n’est pas retenue, ni celle d’un olistostrome d’âge langhien. Nous ne reconnaissons pas la présence de klippes sédimentaires localisées dans une « avant-fosse langhienne». Nous interprétons ces klippes comme étant des klippes tectoniques. Le sillon subbétique ne passe pas dans les Baléares. Eivissa et Majorque correspondent au prolongement vers le Nord-Est du Prébétique d’Alicante

Geologists of Russian origin in Latin America

Se describe la vida y trayectoria de geólogos que más allá de su nacionalidad (rusa, ucraniana, tártara, alemana, etc.), nacieron en territorios que pertenecieron al Imperio Ruso, la Unión Soviética o la Federación Rusa, y de sus descendientes graduados en geología, todos los cuales vivieron y trabajaron en países de Latinoamérica (en los cuales las lenguas que prevalecen son el español y el portugués). También se incluyen geólogos de la URSS que trabajaron temporariamente en algunos países de Latinoamérica y que con sus publicaciones contribuyeron a la Geología.We describe here the life and career of geologists who beyond their nationality(Russian, Ukrainian, Tatar, German, etc.), were born on the territory of the Russian Empire, the SovietUnion or the Russian Federation and their descendants that became geologists, all of whom lived andworked in Latin-American countries (where Spanish and Portuguese languages prevail). We includealso geologists from USSR who worked temporary in some countries of Latin America and leftcontributions to geology in form of publications.Fil: Tchoumatchenco, Platon. Bulgarian Academy Of Sciences; BulgariaFil: Riccardi, Alberto Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Naturales y Museo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Durand Delga, Michel. Centre National de la Recherche Scientifique; FranciaFil: Alonso, Ricardo. Universidad Nacional de Salta; ArgentinaFil: Wiasemsky, Michel. Centre National de la Recherche Scientifique; FranciaFil: Boltovskoy, Demetrio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Ecología, Genética y Evolución de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Ecología, Genética y Evolución de Buenos Aires; ArgentinaFil: Charrier González, Reynaldo. Sociedad Geologica de Chile; ChileFil: Minina, Elena. State Geological Museum “V.I.Vernadsky”; Rusi

Structure de l’île d’Eivissa (Ibiza) et sa place dans le cadre baléare

La présente étude retrace l’évolution des connaissances acquises sur la structure d’Eivissa. Un nouveau découpage structural de cette île est proposé. Deux importants accidents transverses divisent l’île en trois grands compartiments. Au Paléogène, l’île appartenait probablement à un territoire émergé. Une transgression marine débuta au Burdigalien (nannozone NN3) et fut maximale au Langhien inférieur (nannozone NN5). Elle déposa des sédiments rapportés à la Formation de la Cala d’Hort, impliquée dans les écailles tectoniques. Cette formation est surmontée par la Formation de Cap Jueu datée du Langhien supérieur-Serravallien, également impliquée dans les écailles. L’existence d’un olistostrome d’âge aquitano-burdigalien évoquée par des auteurs antérieurs n’est pas retenue, ni celle d’un olistostrome d’âge langhien. Nous ne reconnaissons pas la présence de klippes sédimentaires localisées dans une « avant-fosse langhienne». Nous interprétons ces klippes comme étant des klippes tectoniques. Le sillon subbétique ne passe pas dans les Baléares. Eivissa et Majorque correspondent au prolongement vers le Nord-Est du Prébétique d’Alicante.El present estudi esbossa l’evolució dels coneixements adquirits sobre l’estructura d’Eivissa. Es proposa un nou tall estructural per aquesta illa. Dos importants accidents transversals divideixen l’illa en tres gran compartiments. Al Paleogen, l’illa probablement pertanyia a un territori emergit. Una transgressió marina que es va iniciar al Burdigalià (nannozona NN3) i arribà a la seva màxima expressió al Languià (nannozona NN5) amb la deposició dels sediments corresponents a la Formació Cala d’Hort que estan implicats en les escates tectòniques. Aquesta formació està coronada per la Formació de Cap Jueu datada com a Languià superior-Serraval·lià, també implicada en l’estructuració en forma d’escates. L’existència d’un olistostroma d’edat aquitano-burdigaliana que ja havia estat descrita per autors anteriors no es conserva, ni la d’un olistostroma d’edat languiana. Per la nostra part, no reconeixem la presència de klippes sedimentàries localitzades dins d’una “avant-fosa languiana”. Interpretem aquestes klippes com a klippes tectòniques. El solc subbètic no té lloc a les Balears. Eivissa i Mallorca es corresponen amb la prolongació vers el nord-est del prebètic d’Alacant.The situation of Eivissa justifies a special interest for its geological characteristics. Being the furstlest west element of the group of islands emerging from the “balearic promontory”, Eivissa makes it possible to evaluate the paleogeographic and tectonic relationships with the external zones of the betic cordilleras. It is now according to E. Suess and P. Fallot (1922), that the Balearic islands make up the structural prolongation of this orogenesis. The present study traces the evolution of the knowledge acquired so far about the geology of the island of Eivissa and its structural place in the Balearic islands. A new structural conception of this island is proposed

Better Sooner Rather Than Later

This article unifies and generalizes fundamental results related to $n$-process asynchronous crash-prone distributed computing. More precisely, it proves that for every $0\leq k \leq n$, assuming that process failures occur only before the number of participating processes bypasses a predefined threshold that equals $n-k$ (a participating process is a process that has executed at least one statement of its code), an asynchronous algorithm exists that solves consensus for $n$ processes in the presence of $f$ crash failures if and only if $f \leq k$. In a very simple and interesting way, the "extreme" case $k=0$ boils down to the celebrated FLP impossibility result (1985, 1987). Moreover, the second extreme case, namely $k=n$, captures the celebrated mutual exclusion result by E.W. Dijkstra (1965) that states that mutual exclusion can be solved for $n$ processes in an asynchronous read/write shared memory system where any number of processes may crash (but only) before starting to participate in the algorithm (that is, participation is not required, but once a process starts participating it may not fail). More generally, the possibility/impossibility stated above demonstrates that more failures can be tolerated when they occur earlier in the computation (hence the title).Comment: 10 page

Submillimetre/TeraHertz Astronomy at Dome C with CEA filled bolometer array

Submillimetre/TeraHertz (e.g. 200, 350, 450 microns) astronomy is the prime technique to unveil the birth and early evolution of a broad range of astrophysical objects. A major obstacle to carry out submm observations from ground is the atmosphere. Preliminary site testing and atmospheric transmission models tend to demonstrate that Dome C could offer the best conditions on Earth for submm/THz astronomy. The CAMISTIC project aims to install a filled bolometer-array camera with 16x16 pixels on IRAIT at Dome C and explore the 200-$\mu$m windows for potential ground-based observations.Comment: 6 page