Action minimizing orbits in the n-body problem with simple choreography constraint

In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in \RR^d under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, where $\tau = 2\pi / n$. In this setting, we first prove that for every d,n \in \NN and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit

Visite de l'entreprise "Les Charpentiers des Alpes et de Provence". Production de lamellé-collé à Vitrolles (Bouches-du-Rhône)

Compte rendu de la visite de l'entreprise "Les Charpentiers des Alpes et de Provence". Production de lamellé-collé à Vitrolles (Bouches-du-Rhône) suivi du compte rendu des discussions : quels bois la forêt méditerranéenne peut-elle produire ? Organisées dans le cadre de Foresterranée'87

Valorisation des bois de chênes méditerranéens par le tranchage : chênes verts, chênes pubescents, chênes-lièges

International audienc

Effects of particle composition on thorium scavenging in the North Atlantic

Author Posting. © The Author(s), 2018. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Geochimica et Cosmochimica Acta 233 (2018): 115-134, doi:10.1016/j.gca.2018.04.035.The dependence of thorium scavenging by particles on particle composition is examined at selected stations of the U.S. GEOTRACES North Atlantic Section (GA03). Scavenging is here described by the apparent, first-order rate constant of Th adsorption onto particles (k1), as estimated from an inversion of Th radioisotope and radioactive parent data. Our k1 estimates are regressed against particle phase data using two different models. Model I considers biogenic particles (POC+PIC+bSi), lithogenic particles, Mn (oxyhydr)oxides, and Fe (oxyhydr)oxides as regressors, and k1 as the regressand. Model II considers ln(POC+PIC+bSi), ln(lithogenic particles), ln(Mn (oxyhydr)oxides), and ln(Fe (oxyhydr)oxides) as regressors, and ln(k1) as the regressand, where ln() denotes the natural logarithm. Thus, models I and II posit that the effects of particle phases on k1 are, respectively, additive and multiplicative. These models are applied to three groups of stations: (i) all selected stations, (ii) stations west of theMauritanian upwelling region (“western stations”), and (iii) stations within that region (“eastern stations”). We find that model II appears to better describe the effect of particle composition on k1 than model I. Particle composition explains a larger fraction of the variance of k1 for the eastern stations (R2 = 0.60 for model I and 0.67 for model II) than for the western stations (R2 = 0.26 for model I and 0.39 for model II). When considering all stations, the variance of k1 explained by particle composition is intermediate (R2 = 0.50 for model I and 0.51 for model II). According to model II, the variance of k1 explained by particle composition is predominantly due to biogenic particles at the eastern stations and to Mn (oxyhydr)oxides at the western stations. Additionally, we find that particle composition does not explain a significantly different proportion of variance of k1 than particle concentration. It is thus concluded that, at our selected stations, (i) biogenic particles andMn (oxyhydr)oxides more strongly influence Th scavenging than any other phases considered, and (ii) particle composition and particle concentration have comparable effects on this process.We acknowledge the U.S. National Science Foundation for supporting this study (grant OCE-1232578) and the U.S. GEOTRACES North Atlantic section ship time, sampling, and data analysis

Improved linkage analysis of Quantitative Trait Loci using bulk segregants unveils a novel determinant of high ethanol tolerance in yeast

Background: Bulk segregant analysis (BSA) coupled to high throughput sequencing is a powerful method to map genomic regions related with phenotypes of interest. It relies on crossing two parents, one inferior and one superior for a trait of interest. Segregants displaying the trait of the superior parent are pooled, the DNA extracted and sequenced. Genomic regions linked to the trait of interest are identified by searching the pool for overrepresented alleles that normally originate from the superior parent. BSA data analysis is non-trivial due to sequencing, alignment and screening errors. Results: To increase the power of the BSA technology and obtain a better distinction between spuriously and truly linked regions, we developed EXPLoRA (EXtraction of over-rePresented aLleles in BSA), an algorithm for BSA data analysis that explicitly models the dependency between neighboring marker sites by exploiting the properties of linkage disequilibrium through a Hidden Markov Model (HMM). Reanalyzing a BSA dataset for high ethanol tolerance in yeast allowed reliably identifying QTLs linked to this phenotype that could not be identified with statistical significance in the original study. Experimental validation of one of the least pronounced linked regions, by identifying its causative gene VPS70, confirmed the potential of our method. Conclusions: EXPLoRA has a performance at least as good as the state-of-the-art and it is robust even at low signal to noise ratio's i.e. when the true linkage signal is diluted by sampling, screening errors or when few segregants are available

Module networks revisited: computational assessment and prioritization of model predictions

The solution of high-dimensional inference and prediction problems in computational biology is almost always a compromise between mathematical theory and practical constraints such as limited computational resources. As time progresses, computational power increases but well-established inference methods often remain locked in their initial suboptimal solution. We revisit the approach of Segal et al. (2003) to infer regulatory modules and their condition-specific regulators from gene expression data. In contrast to their direct optimization-based solution we use a more representative centroid-like solution extracted from an ensemble of possible statistical models to explain the data. The ensemble method automatically selects a subset of most informative genes and builds a quantitatively better model for them. Genes which cluster together in the majority of models produce functionally more coherent modules. Regulators which are consistently assigned to a module are more often supported by literature, but a single model always contains many regulator assignments not supported by the ensemble. Reliably detecting condition-specific or combinatorial regulation is particularly hard in a single optimum but can be achieved using ensemble averaging.Comment: 8 pages REVTeX, 6 figure

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field