tt-Martin boundary of killed random walks in the quadrant

We compute the $t$-Martin boundary of two-dimensional small steps random walks killed at the boundary of the quarter plane. We further provide explicit expressions for the (generating functions of the) discrete $t$-harmonic functions. Our approach is uniform in $t$, and shows that there are three regimes for the Martin boundary.Comment: 18 pages, 2 figures, to appear in S\'eminaire de Probabilit\'e

User-assisted reverse modeling with evolutionary algorithms

This paper presents a system for user-assisted reverse modeling: from digitized point-cloud to solid models ready to be used in a CAD modeling system. Our approach consists in the following steps: segmentation, fitting, and constructive model discovery. Each of these steps are based on evolutionary algorithms. The obtained objects can then be further edited or parameterized by users and fitted to adapt their shape to different point-clouds

On the functions counting walks with small steps in the quarter plane

Models of spatially homogeneous walks in the quarter plane ${\bf Z}_+^{2}$ with steps taken from a subset $\mathcal{S}$ of the set of jumps to the eight nearest neighbors are considered. The generating function $(x,y,z)\mapsto Q(x,y;z)$ of the numbers $q(i,j;n)$ of such walks starting at the origin and ending at $(i,j) \in {\bf Z}_+^{2}$ after $n$ steps is studied. For all non-singular models of walks, the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are continued as multi-valued functions on ${\bf C}$ having infinitely many meromorphic branches, of which the set of poles is identified. The nature of these functions is derived from this result: namely, for all the 51 walks which admit a certain infinite group of birational transformations of ${\bf C}^2$, the interval $]0,1/|\mathcal{S}|[$ of variation of $z$ splits into two dense subsets such that the functions $x \mapsto Q(x,0;z)$ and $y\mapsto Q(0,y;z)$ are shown to be holonomic for any $z$ from the one of them and non-holonomic for any $z$ from the other. This entails the non-holonomy of $(x,y,z)\mapsto Q(x,y;z)$, and therefore proves a conjecture of Bousquet-M\'elou and Mishna.Comment: 40 pages, 17 figure

On the dynamical behavior of the ABC model

We consider the ABC dynamics, with equal density of the three species, on the discrete ring with $N$ sites. In this case, the process is reversible with respect to a Gibbs measure with a mean field interaction that undergoes a second order phase transition. We analyze the relaxation time of the dynamics and show that at high temperature it grows at most as $N^2$ while it grows at least as $N^3$ at low temperature

Acacia auriculiformis production in the Mampu agroforestry zone on the Batéké plateau, Democratic Republic of Congo

peer reviewedThe Mampu agroforestry zone on the Batéké plateau in the Democratic Republic of Congo, which has been managed with Acacia auriculiformis shade trees for over twenty years by local communities, supplies subsistence products and fuel wood to Kinshasa. Thanks to international grant funding, this agroforestry system, which integrates traditional slashand- burn cultivation, has been replicated in many places across the RDC, but its performance has never been assessed. The aim of this study was to estimate Acacia auriculiformis production in terms of total biomass and usable biomass for charcoal (stems and branches more than 4 cm in diameter) as part of the agroforestry system. To do so, two local allometric equations for total and usable biomass were adjusted from destructive testing data. Using existing inventory data (n = 112 plots), we identified significant structural heterogeneity throughout the rotation period (8-10 years) but also among plots of the same age. Despite this heterogeneity, which may be accounted for by environmental conditions on site and/or by differences in the handling of plot management techniques, production is comparable to that observed at other sites, averaging 145 tonnes per hectare over 10 years. The Mampu agroforestry system has many advantages, including direct services creating rural employment and combined production of subsistence goods and charcoal, but also indirect services such as avoided deforestation and carbon sequestration. The system's sustainability and dissemination should nevertheless be discussed

Note sur le comportement sexuel des juments en milieu tropical

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Combining astrometry and JUICE -- Europa Clipper radio science to improve the ephemerides of the Galilean moons

The upcoming JUICE and Europa Clipper missions to Jupiter's Galilean satellites will provide radio science tracking measurements of both spacecraft. Such data are expected to significantly help estimating the moons' ephemerides and related dynamical parameters. However, the two missions will yield an imbalanced dataset, with no flybys planned at Io, condensed over less than six years. Current ephemerides' solutions for the Galilean moons, on the other hand, rely on ground-based astrometry collected over more than a century which, while being less accurate, bring very valuable constraints on the long-term dynamics of the system. An improved solution for the Galilean satellites' complex dynamics could however be achieved by exploiting the existing synergies between these different observation sets. To quantify this, we merged simulated JUICE and Clipper radio science data with existing ground-based astrometric and radar observations, and performed the inversion. Our study specifically focusses on the resulting formal uncertainties in the moons' states, as well as Io's and Jupiter's tidal dissipation parameters. Adding astrometry stabilises the moons' state solution, especially beyond the missions' timelines. It furthermore reduces the uncertainties in $1/Q$ (inverse of the tidal quality factor) by a factor two to four for Jupiter, and about 30-35\% for Io. Among all data types, classical astrometry data prior to 1960 proved particularly beneficial. We also show that ground observations of Io add the most to the solution, confirming that ground observations can fill the lack of radio science data for this specific moon. We obtained a noticeable solution improvement when exploiting the complementarity between all different observation sets. These promising simulation results thus motivate future efforts to achieve a global solution from actual JUICE and Clipper radio science data

Combining astrometry and JUICE-Europa Clipper radio science to improve the ephemerides of the Galilean moons

Context. The upcoming JUICE and Europa Clipper missions targeting Jupiter s Galilean satellites will provide radio science tracking measurements of both spacecraft. Such data are expected to significantly help estimating the moons ephemerides and related dynamical parameters (e.g. tidal dissipation parameters). However, the two missions will yield an imbalanced dataset, with no flybys planned at Io, condensed over less than six years. Current ephemerides solutions for the Galilean moons, on the other hand, rely on ground-based astrometry collected over more than a century which, while being less accurate, bring very valuable constraints on the long-term dynamics of the system. Aims. An improved solution for the Galilean satellites complex dynamics could however be achieved by exploiting the existing synergies between these different observation sets. Methods. To quantify this, we merged simulated radio science data from both JUICE and Europa Clipper spacecraft with existing ground-based astrometric and radar observations, and performed the inversion in different configurations: either adding all available ground observations or individually assessing the contribution of different data subsets. Our discussion specifically focusses on the resulting formal uncertainties in the moons states, as well as Io s and Jupiter s tidal dissipation parameters. Results. Adding astrometry stabilises the moons state solution, especially beyond the missions timelines. It furthermore reduces the uncertainties in 1/Q (inverse of the tidal quality factor) by a factor two to four for Jupiter, and about 30- 35% for Io. Among all data types, classical astrometry data prior to 1960 proved particularly beneficial. Overall, we also show that ground observations of Io add the most to the solution, confirming that ground observations can fill the lack of radio science data for this specific moon. Conclusions. We obtained a noticeable solution improvement when making use of the complementarity between all different observation sets. The promising results obtained with simulations thus motivate future efforts to achieve a global solution from actual JUICE and Clipper radio science measurements

Three osculating walkers

We consider three directed walkers on the square lattice, which move simultaneously at each tick of a clock and never cross. Their trajectories form a non-crossing configuration of walks. This configuration is said to be osculating if the walkers never share an edge, and vicious (or: non-intersecting) if they never meet. We give a closed form expression for the generating function of osculating configurations starting from prescribed points. This generating function turns out to be algebraic. We also relate the enumeration of osculating configurations with prescribed starting and ending points to the (better understood) enumeration of non-intersecting configurations. Our method is based on a step by step decomposition of osculating configurations, and on the solution of the functional equation provided by this decomposition