On the Sandpile group of the cone of a graph

In this article, we give a partial description of the sandpile group of the cone of the cartesian product of graphs in function of the sandpile group of the cone of their factors. Also, we introduce the concept of uniform homomorphism of graphs and prove that every surjective uniform homomorphism of graphs induces an injective homomorphism between their sandpile groups. As an application of these result we obtain an explicit description of a set of generators of the sandpile group of the cone of the hypercube of dimension d.Comment: 20 pages, 11 figures. The title was changed, other impruvements were made throughout the article. To appear in Linear Algebra and Its Application

Limiting shapes for deterministic centrally seeded growth models

We study the rotor router model and two deterministic sandpile models. For the rotor router model in $\mathbb{Z}^d$, Levine and Peres proved that the limiting shape of the growth cluster is a sphere. For the other two models, only bounds in dimension 2 are known. A unified approach for these models with a new parameter $h$ (the initial number of particles at each site), allows to prove a number of new limiting shape results in any dimension $d \geq 1$. For the rotor router model, the limiting shape is a sphere for all values of $h$. For one of the sandpile models, and $h=2d-2$ (the maximal value), the limiting shape is a cube. For both sandpile models, the limiting shape is a sphere in the limit $h \to -\infty$. Finally, we prove that the rotor router shape contains a diamond.Comment: 18 pages, 3 figures, some errors corrected and more explanation added, to appear in Journal of Statistical Physic

Challenges for biodiversity research in Europe.

In 2010, the international year of biodiversity, new policies for preserving biodiversity in Europe and worldwide will be developed as targets set by older policies, such as to halt biodiversity loss in the EU by 2010, were not met. This paper aims at sharing the expertise LERU's members harbour to set the right priorities for new biodiversity policies

Post-AGB stars with hot circumstellar dust: binarity of the low-amplitude pulsators

While the first binary post-AGB stars were serendipitously discovered, the distinct characteristics of their Spectral Energy Distribution (SED) allowed us to launch a more systematic search for binaries. We selected post-AGB objects which show a broad dust excess often starting already at H or K, pointing to the presence of a gravitationally bound dusty disc in the system. We started a very extensive multi-wavelength study of those systems and here we report on our radial velocity and photometric monitoring results for six stars of early F type, which are pulsators of small amplitude. To determine the radial velocity of low signal-to-noise time-series, we constructed dedicated auto-correlation masks. The radial velocity variations were subjected to detailed analysis to differentiate between pulsational variability and variability due to orbital motion. Finally orbital minimalisation was performed to constrain the orbital elements. All of the six objects are binaries, with orbital periods ranging from 120 to 1800 days. Five systems have non-circular orbits. The mass functions range from 0.004 to 0.57 solar mass and the companions are likely unevolved objects of (very) low initial mass. We argue that these binaries must have been subject to severe binary interaction when the primary was a cool supergiant. Although the origin of the circumstellar disc is not well understood, the disc is generally believed to be formed during this strong interaction phase. The eccentric orbits of these highly evolved objects remain poorly understood. With the measured orbits and mass functions we conclude that the circumbinary discs seem to have a major impact on the evolution of a significant fraction of binary systems.Comment: 13 pages, 15 figures, accepted for Astronomy and Astrophysic

Founder effects drive the genetic structure of passively dispersed aquatic invertebrates

Populations of passively dispersed organisms in continental aquatic habitats typically show high levels of neutral genetic differentiation despite their high dispersal capabilities. Several evolutionary factors, including founder events, local adaptation, and life cycle features such as high population growth rates and the presence of propagule banks, have been proposed to be responsible for this paradox. Here, we have modeled the colonization process to assess the impact of migration rate, population growth rate, population size, local adaptation and life-cycle features on the population genetic structure in these organisms. Our simulations show that the strongest effect on population structure are persistent founder effects, resulting from the interaction of a few population founders, high population growth rates, large population sizes and the presence of diapausing egg banks. In contrast, the role of local adaptation, genetic hitchhiking and migration is limited to small populations in these organisms. Our results indicate that local adaptation could have different impact on genetic structure in different groups of zooplankters

Long term photometric monitoring with the Mercator telescope. Frequencies and mode identification of variable O-B stars

Aims. We selected a large sample of O-B stars that were considered as (candidate) slowly pulsating B, beta Cep, and Maia stars after the analysis of their hipparcos data. We analysed our new seven passband geneva data collected for these stars during the first three years of scientific operations of the mercator telescope. We performed a frequency analysis for 28 targets with more than 50 high-quality measurements to improve their variability classification. For the pulsating stars, we tried both to identify the modes and to search for rotationally split modes. Methods: We searched for frequencies in all the geneva passbands and colours by using two independent frequency analysis methods and we applied a 3.6 S/N-level criterion to locate the significant peaks in the periodograms. The modes were identified by applying the method of photometric amplitudes for which we calculated a large, homogeneous grid of equilibrium models to perform a pulsational stability analysis. When both the radius and the projected rotational velocity of an object are known, we determined a lower limit for the rotation frequency to estimate the expected frequency spacings in rotationally split pulsation modes. Results: We detected 61 frequencies, among which 33 are new. We classified 21 objects as pulsating variables (7 new confirmed pulsating stars, including 2 hybrid beta Cep/SPB stars), 6 as non-pulsating variables (binaries or spotted stars), and 1 as photometrically constant. All the Maia candidates were reclassified into other variability classes. We performed mode identification for the pulsating variables for the first time. The most probable l value is 0, 1, 2, and 4 for 1, 31, 9, and 5 modes, respectively, including only 4 unambiguous identifications. For 7 stars we cannot rule out that some of the observed frequencies belong to the same rotationally split mode. For 4 targets we may begin to resolve close frequency multiplets. Based on observations collected with the p7 photometer attached to the Flemish 1.2-m mercator telescope situated at the Roque de los Muchachos observatory on La Palma (Spain). Section [see full textsee full text], including Figs. is only available in electronic form at http://www.aanda.org, and Tables 2 and 3 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/463/243Peer reviewe

Heritability and Artificial Selection on Ambulatory Dispersal Distance in Tetranychus urticae: Effects of Density and Maternal Effects

Dispersal distance is understudied although the evolution of dispersal distance affects the distribution of genetic diversity through space. Using the two-spotted spider mite, Tetranychus urticae, we tested the conditions under which dispersal distance could evolve. To this aim, we performed artificial selection based on dispersal distance by choosing 40 individuals (out of 150) that settled furthest from the home patch (high dispersal, HDIS) and 40 individuals that remained close to the home patch (low dispersal, LDIS) with three replicates per treatment. We did not observe a response to selection nor a difference between treatments in life-history traits (fecundity, survival, longevity, and sex-ratio) after ten generations of selection. However, we show that heritability for dispersal distance depends on density. Heritability for dispersal distance was low and non-significant when using the same density as the artificial selection experiments while heritability becomes significant at a lower density. Furthermore, we show that maternal effects may have influenced the dispersal behaviour of the mites. Our results suggest primarily that selection did not work because high density and maternal effects induced phenotypic plasticity for dispersal distance. Density and maternal effects may affect the evolution of dispersal distance and should be incorporated into future theoretical and empirical studies