Rankin-Cohen brackets on quasimodular forms

We give the algebra of quasimodular forms a collection of Rankin-Cohen operators. These operators extend those defined by Cohen on modular forms and, as for modular forms, the first of them provide a Lie structure on quasimodular forms. They also satisfy a ``Leibniz rule'' for the usual derivation. Rankin-Cohen operators are useful for proving arithmetic identities. In particular we give an interpretation of the Chazy equation and explain why such an equation has to exist.Comment: 17 page

A stochastic individual based model for the growth of a stand of Japanese knotweed including mowing as a management technique

Invasive alien species are a growing threat for environment and health. They also have a major economic impact, as they can damage many infrastructures. The Japanese knotweed (Fallopia japonica), present in North America, Northern and Central Europe as well as in Australia and New Zealand, is listed by the World Conservation Union as one of the world's worst invasive species. So far, most models have dealt with how the invasion spreads without management. This paper aims at providing a model able to study and predict the dynamics of a stand of Japanese knotweed taking into account mowing as a management technique. The model we propose is stochastic and individual-based, which allows us taking into account the behaviour of individuals depending on their size and location, as well as individual stochasticity. We set plant dynamics parameters thanks to a calibration with field data, and study the influence of the initial population size, the mean number of mowing events a year and the management project duration on mean area and mean number of crowns of stands. In particular, our results provide the sets of parameters for which it is possible to obtain the stand eradication, and the minimal duration of the management project necessary to achieve this latter

Optimal configurations of lines and a statistical application

Motivated by the construction of confidence intervals in statistics, we study optimal configurations of $2^d-1$ lines in real projective space $RP^{d-1}$. For small $d$, we determine line sets that numerically minimize a wide variety of potential functions among all configurations of $2^d-1$ lines through the origin. Numerical experiments verify that our findings enable to assess efficiently the tightness of a bound arising from the statistical literature.Comment: 13 page

On the Covariance of ICP-based Scan-matching Techniques

This paper considers the problem of estimating the covariance of roto-translations computed by the Iterative Closest Point (ICP) algorithm. The problem is relevant for localization of mobile robots and vehicles equipped with depth-sensing cameras (e.g., Kinect) or Lidar (e.g., Velodyne). The closed-form formulas for covariance proposed in previous literature generally build upon the fact that the solution to ICP is obtained by minimizing a linear least-squares problem. In this paper, we show this approach needs caution because the rematching step of the algorithm is not explicitly accounted for, and applying it to the point-to-point version of ICP leads to completely erroneous covariances. We then provide a formal mathematical proof why the approach is valid in the point-to-plane version of ICP, which validates the intuition and experimental results of practitioners.Comment: Accepted at 2016 American Control Conferenc

The topology of the space of symplectic balls in rational 4-manifolds

We study in this paper the rational homotopy type of the space of symplectic embeddings of the standard ball $B^4(c) \subset \R^4$ into 4-dimensional rational symplectic manifolds. We compute the rational homotopy groups of that space when the 4-manifold has the form $M_{\lambda}= (S^2 \times S^2, \mu \omega_0 \oplus \omega_0)$ where $\omega_0$ is the area form on the sphere with total area 1 and $\mu$ belongs to the interval $[1,2]$. We show that, when $\mu$ is 1, this space retracts to the space of symplectic frames, for any value of $c$. However, for any given $1 < \mu < 2$, the rational homotopy type of that space changes as $c$ crosses the critical parameter $c_{crit} = \mu - 1$, which is the difference of areas between the two $S^2$ factors. We prove moreover that the full homotopy type of that space changes only at that value, i.e the restriction map between these spaces is a homotopy equivalence as long as these values of $c$ remain either below or above that critical value.Comment: Typos corrected, 2 minor corrections in the text. Numbering consistant with the published versio

The role of recent experience and weight on hen's agonistic behaviour during dyadic conflict resolution.

Recent victory or defeat experiences and 2-hour familiarity with the meeting place were combined with size differences in order to better understand their effects on the behaviour leading to the establishment of dyadic dominance relationships between hens not previously acquainted with each other. Three kinds of encounters were videotaped: (i) a previous winner unfamiliar with the meeting place met a previous loser familiar for 2 hours with the meeting place (n = 12 dyads); (ii) as in (i) but both were unfamiliar with the meeting place (n=12); (iii) as in (i) but the previous winner was familiar with the meeting place while the previous loser was unfamiliar (n=13). The weight asymmetry was combined with these three types of encounters by selecting hens of various weight differences: in 29 dyads the recent loser was heavier than the recent winner and in 8 dyads it was the reverse. Recent experience had a major influence upon both agonistic behaviour and dominance outcome. Hens that were familiar with the meeting site initiated attacks more frequently than their unfamiliar opponent but did not win significantly more often. Recent experience and site familiarity could be used to identify 80% of future initiators. Once the first aggressive behaviour had been initiated, it led to victory of its initiator in 92% of cases. Weight was not found to influence agonistic behaviour nor dominance outcome. However, hens with superior comb and wattles areas won significantly more initial meetings than opponents with smaller ones. In the final encounters, victory also went more frequently to the bird showing larger comb and wattles, which happened also to be the previous dominant in a majority of cases. The use of higher-order partial correlations as an ex post facto control for comb and wattles indicates that they were not influential upon agonistic behaviour nor on dominance outcome, but were simply co-selected with the selection of victorious and defeated birds in the first phase of the experiment designed to let hens acquire recent victory/defeat experience

An analysis of the benefits of signal injection for low-speed sensorless control of induction motors

We analyze why low-speed sensorless control of the IM is intrinsically difficult, and what is gained by signal injection. The explanation relies on the control-theoretic concept of observability applied to a general model of the saturated IM. We show that the IM is not observable when the stator speed is zero in the absence of signal injection, but that observability is restored thanks to signal injection and magnetic saturation. The analysis also reveals that existing sensorless algorithms based on signal injection may perform poorly for some IMs under particular operating conditions. The approach is illustrated by simulations and experimental data