Sparse universal graphs for planarity

We show that for every integer $n\geq 1$ there exists a graph $G_n$ with $(1+o(1))n$ vertices and $n^{1 + o(1)}$ edges such that every $n$-vertex planar graph is isomorphic to a subgraph of $G_n$. The best previous bound on the number of edges was $O(n^{3/2})$, proved by Babai, Chung, Erd\H{o}s, Graham, and Spencer in 1982. We then show that for every integer $n\geq 1$ there is a graph $U_n$ with $n^{1 + o(1)}$ vertices and edges that contains induced copies of every $n$-vertex planar graph. This significantly reduces the number of edges in a recent construction of the authors with Dujmovi\'c, Gavoille, and Micek.Comment: v2: added new result about induced-universal graph

Tight bound for the Erd\H{o}s-P\'osa property of tree minors

Let $T$ be a tree on $t$ vertices. We prove that for every positive integer $k$ and every graph $G$, either $G$ contains $k$ pairwise vertex-disjoint subgraphs each having a $T$ minor, or there exists a set $X$ of at most $t(k-1)$ vertices of $G$ such that $G-X$ has no $T$ minor. The bound on the size of $X$ is best possible and improves on an earlier $f(t)k$ bound proved by Fiorini, Joret, and Wood (2013) with some very fast growing function $f(t)$. Moreover, our proof is very short and simple

C’est tous les jours qu’il faut faire la révolution

Gwénaël Morin a passé un an aux Laboratoires d’Aubervilliers, à mettre en place, faire vivre et évoluer son « Théâtre Permanent ». Adossée à une triple ambition (transmettre en continu, répéter tous les jours et jouer tous les soirs) et à une exigence de gratuité, l’expérience du Théâtre Permanent se présentait comme un véritable outil artistique d'affirmation et d'intensification du théâtre, c’est-à-dire comme la réalisation et l’épuisement d’un projet politique et artistique mis à l’épreuve..

The Excluded Tree Minor Theorem Revisited

We prove that for every tree $T$ of radius $h$, there is an integer $c$ such that every $T$-minor-free graph is contained in $H\boxtimes K_c$ for some graph $H$ with pathwidth at most $2h-1$. This is a qualitative strengthening of the Excluded Tree Minor Theorem of Robertson and Seymour (GM I). We show that radius is the right parameter to consider in this setting, and $2h-1$ is the best possible bound

Mapping Bioclimatic Indices by Downscaling MODIS Land Surface Temperature: Case Study of the Saint-Emilion Area

Thermal conditions, influenced by the local environment, impact the development of the vine and determine the composition of the grapes. Bioclimatic indices, based on cumulative air temperatures, are modelled and mapped using statistical methods integrating local factors. Air temperature data from sensors networks are limited in space and time. We evaluated the potential of land surface temperature (LST) to identify comparable spatial distribution, and not to replace air temperature, by using a support vector machine algorithm to compare bioclimatic indices calculated from air temperature or LST. This study focused on the 2012–2018 period in the Saint-Emilion winegrowing area of France. The use of several digital elevation models with high spatial resolution (i.e., GMTED10 (1000, 500 and 250 m) and SRTM (90 and 30 m)) enabled LST to be downscaled at each resolution. The same topographic variables (elevation, slope, orientation coordinates) were used as predictors, and identical algorithms and cross-validation parameters were implemented in both mapping methods. Bioclimatic indices were calculated from daily air temperature, daily LST or weekly LST. The results of the daily and weekly downscaling of the MODIS time series at several spatial resolutions are encouraging for application to viticulture and have allowed to identify an optimal resolution between 500 m and 250 m limiting bias

Sparse universal graphs for planarity

We show that for every integer $n\geq 1$ there exists a graph $G_n$ with $n^{1 + o(1)}$ edges such that every $n$-vertex planar graph is isomorphic to a subgraph of $G_n$. The best previous bound on the number of edges was $O(n^{3/2})$, proved by Babai, Erd\H{o}s, Chung, Graham, and Spencer in 1982

Evaluation de la relation entre températures de l'air et températures de surface issues du satellite Modis : Application aux vignobles de la vallée de Waipara (Nouvelle Zélande)

International audienc

Estimation des températures de l'air à partir des températures de surfaces modis dans les vignobles de la vallée de Waipara (Nouvelle Zélande)

International audienc

Pyrosequencing assessment of prokaryotic and eukaryotic diversity in biofilm communities from a French river.

International audienceDespite the recent and significant increase in the study of aquatic microbial communities, little is known about the microbial diversity of complex ecosystems such as running waters. This study investigated the biodiversity of biofilm communities formed in a river with 454 Sequencing™. This river has the particularity of integrating both organic and microbiological pollution, as receiver of agricultural pollution in its upstream catchment area and urban pollution through discharges of the wastewater treatment plant of the town of Billom. Different regions of the small subunit (SSU) ribosomal RNA gene were targeted using nine pairs of primers, either universal or specific for bacteria, eukarya, or archaea. Our aim was to characterize the widest range of rDNA sequences using different sets of polymerase chain reaction (PCR) primers. A first look at reads abundance revealed that a large majority (47-48%) were rare sequences (<5 copies). Prokaryotic phyla represented the species richness, and eukaryotic phyla accounted for a small part. Among the prokaryotic phyla, Proteobacteria (beta and alpha) predominated, followed by Bacteroidetes together with a large number of nonaffiliated bacterial sequences. Bacillariophyta plastids were abundant. The remaining bacterial phyla, Verrucomicrobia and Cyanobacteria, made up the rest of the bulk biodiversity. The most abundant eukaryotic phyla were annelid worms, followed by Diatoms, and Chlorophytes. These latter phyla attest to the abundance of plastids and the importance of photosynthetic activity for the biofilm. These findings highlight the existence and plasticity of multiple trophic levels within these complex biological systems

Mapping Bioclimatic Indices by Downscaling MODIS Land Surface Temperature: Case Study of the Saint-Emilion Area

International audienc