The diagonal of the multiplihedra and the tensor product of A-infinity morphisms

We define a cellular approximation for the diagonal of the Forcey--Loday realizations of the multiplihedra, and endow them with a compatible topological cellular operadic bimodule structure over the Loday realizations of the associahedra. This provides us with a model for topological and algebraic A-infinity morphisms, as well as a universal and explicit formula for their tensor product. We study the monoidal properties of this newly defined tensor product and conclude by outlining several applications, notably in algebraic and symplectic topology.Comment: v2 : correction of the formula for the polytopal diagonal of the multiplihedra + minor corrections ; 39 pages, 11 figures, comments are welcom

Magnetic Field Enhanced Coherence Length in Cold Atomic Gases

We study the effect of an external magnetic field on coherent backscattering of light from a cool rubidium vapor. We observe that the backscattering enhancement factor can be {\it increased} with $B$. This surprising behavior shows that the coherence length of the system can be increased by applying a magnetic field, in sharp contrast with ususal situations. This is mainly due to the lifting of the degeneracy between Zeeman sublevels. We find good agreement between our experimental data and a full Monte-Carlosimulation, taking into account the magneto-optical effects and the geometry of the atomic cloud

A Strong Call-By-Need Calculus

We present a call-by-need ?-calculus that enables strong reduction (that is, reduction inside the body of abstractions) and guarantees that arguments are only evaluated if needed and at most once. This calculus uses explicit substitutions and subsumes the existing strong-call-by-need strategy, but allows for more reduction sequences, and often shorter ones, while preserving the neededness. The calculus is shown to be normalizing in a strong sense: Whenever a ?-term t admits a normal form n in the ?-calculus, then any reduction sequence from t in the calculus eventually reaches a representative of the normal form n. We also exhibit a restriction of this calculus that has the diamond property and that only performs reduction sequences of minimal length, which makes it systematically better than the existing strategy. We have used the Abella proof assistant to formalize part of this calculus, and discuss how this experiment affected its design

Solving a Continent-Scale Inventory Routing Problem at Renault

This paper is the fruit of a partnership with Renault. Their backward logistic requires to solve a continent-scale multi-attribute inventory routing problem (IRP). With an average of 30 commodities, 16 depots, and 600 customers spread across a continent, our instances are orders of magnitude larger than those in the literature. Existing algorithms do not scale. We propose a large neighborhood search (LNS). To make it work, (1) we generalize existing split delivery vehicle routing problem and IRP neighborhoods to this context, (2) we turn a state-of-the art matheuristic for medium-scale IRP into a large neighborhood, and (3) we introduce two novel perturbations: the reinsertion of a customer and that of a commodity into the IRP solution. We also derive a new lower bound based on a flow relaxation. In order to stimulate the research on large-scale IRP, we introduce a library of industrial instances. We benchmark our algorithms on these instances and make our code open-source. Extensive numerical experiments highlight the relevance of each component of our LNS

Optic Flow-Based Nonlinear Control and Sub-optimal Guidance for Lunar Landing

International audience— A sub-optimal guidance and nonlinear control scheme based on Optic Flow (OF) cues ensuring soft lunar land-ing using two minimalistic bio-inspired visual motion sensors is presented here. Unlike most previous approaches, which rely on state estimation techniques and multiple sensor fusion methods, the guidance and control strategy presented here is based on the sole knowledge of a minimum sensor suite (including OF sensors and an IMU). Two different tasks are addressed in this paper: the first one focuses on the computation of an optimal trajectory and the associated control sequences, and the second one focuses on the design and theoretical stability analysis of the closed loop using only OF and IMU measurements as feedback information. Simulations performed on a lunar landing scenario confirm the excellent performances and the robustness to initial uncertainties of the present guidance and control strategy

Bio-inspired Landing Approaches and Their Potential Use On Extraterrestrial Bodies

International audienceAutomatic landing on extraterrestrial bodies is still a challenging and hazardous task. Here we propose a new type of autopilot designed to solve landing problems, which is based on neurophysiological, behavioral, and biorobotic findings on flying insects. Flying insects excel in optic flow sensing techniques and cope with highly parallel data at a low energy and computational cost using lightweight dedicated motion processing circuits. In the first part of this paper, we present our biomimetic approach in the context of a lunar landing scenario, assuming a 2-degree-of-freedom spacecraft approaching the moon, which is simulated with the PANGU software. The autopilot we propose relies only on optic flow (OF) and inertial measurements, and aims at regulating the OF generated during the landing approach, by means of a feedback control system whose sensor is an OF sensor. We put forward an estimation method based on a two-sensor setup to accurately estimate the orientation of the lander's velocity vector, which is mandatory to control the lander's pitch in a near optimal way with respect to the fuel consumption. In the second part, we present a lightweight Visual Motion Sensor (VMS) which draws on the results of neurophysiological studies on the insect visual system. The VMS was able to perform local 1-D angular speed measurements in the range 1.5°/s - 25°/s. The sensor was mounted on an 80 kg unmanned helicopter and test-flown outdoors over various fields. The OF measured onboard was shown to match the ground-truth optic flow despite the dramatic disturbances and vibrations experienced by the sensor