Particles approximations of Vlasov equations with singular forces : Propagation of chaos

We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also provide results for forces with singularity up to $\alpha < d-1$ but with large enough cut-off. This last result thus almost includes the most interesting case of Coulombian or gravitational interaction, but it is also interesting when the strength of the singularity $\alpha$ is larger but close to one, in which case it allows for very small cut-off.Comment: 47 pages. This version: improvement of the presentation, in particular of the deterministic result

Low-Thrust Lyapunov to Lyapunov and Halo to Halo with L2L^2-Minimization

In this work, we develop a new method to design energy minimum low-thrust missions (L2-minimization). In the Circular Restricted Three Body Problem, the knowledge of invariant manifolds helps us initialize an indirect method solving a transfer mission between periodic Lyapunov orbits. Indeed, using the PMP, the optimal control problem is solved using Newton-like algorithms finding the zero of a shooting function. To compute a Lyapunov to Lyapunov mission, we first compute an admissible trajectory using a heteroclinic orbit between the two periodic orbits. It is then used to initialize a multiple shooting method in order to release the constraint. We finally optimize the terminal points on the periodic orbits. Moreover, we use continuation methods on position and on thrust, in order to gain robustness. A more general Halo to Halo mission, with different energies, is computed in the last section without heteroclinic orbits but using invariant manifolds to initialize shooting methods with a similar approach

Stability of trajectories for N -particles dynamics with singular potential

We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain close enough at later times. For potential less singular than the classical electrostatic kernel, we are able to prove such a result, for initial positions/velocities distributed according to the Gibbs equilibrium of the system

Developmental Bayesian Optimization of Black-Box with Visual Similarity-Based Transfer Learning

We present a developmental framework based on a long-term memory and reasoning mechanisms (Vision Similarity and Bayesian Optimisation). This architecture allows a robot to optimize autonomously hyper-parameters that need to be tuned from any action and/or vision module, treated as a black-box. The learning can take advantage of past experiences (stored in the episodic and procedural memories) in order to warm-start the exploration using a set of hyper-parameters previously optimized from objects similar to the new unknown one (stored in a semantic memory). As example, the system has been used to optimized 9 continuous hyper-parameters of a professional software (Kamido) both in simulation and with a real robot (industrial robotic arm Fanuc) with a total of 13 different objects. The robot is able to find a good object-specific optimization in 68 (simulation) or 40 (real) trials. In simulation, we demonstrate the benefit of the transfer learning based on visual similarity, as opposed to an amnesic learning (i.e. learning from scratch all the time). Moreover, with the real robot, we show that the method consistently outperforms the manual optimization from an expert with less than 2 hours of training time to achieve more than 88% of success

Approximation particulaire des équations de Vlasov avec noyaux de force singuliers : la propagation du chaos

We obtain the mean field limit and the propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also provide results for forces with singularity up to $\alpha < d-1$ but with large enough cut-off. This last result thus almost includes the most interesting case of Coulombian or gravitational interaction, but it is also interesting when the strength of the singularity $\alpha$ is larger but close to one, in which case it allows for very small cut-off.Nous montrons la validité de l'approximation par champ moyen et prouvons la propagation du chaos pour un système de particules en interaction par le biais d'une force avec singularité 1/|x|α, avec α<1 en dimension d≥3. Nous traitons également le cas de forces avec troncature et des singularités pouvant aller jusqu'à α<d−1. Ce dernier résultat permet presque d'atteindre les cas d'interaction coulombiennes ou gravitationnelles et requiert seulement de très petits paramètres de troncature lorsque la singularité est proche de α=1

Bayesian Optimization for Developmental Robotics with Meta-Learning by Parameters Bounds Reduction

In robotics, methods and softwares usually require optimizations of hyperparameters in order to be efficient for specific tasks, for instance industrial bin-picking from homogeneous heaps of different objects. We present a developmental framework based on long-term memory and reasoning modules (Bayesian Optimisation, visual similarity and parameters bounds reduction) allowing a robot to use meta-learning mechanism increasing the efficiency of such continuous and constrained parameters optimizations. The new optimization, viewed as a learning for the robot, can take advantage of past experiences (stored in the episodic and procedural memories) to shrink the search space by using reduced parameters bounds computed from the best optimizations realized by the robot with similar tasks of the new one (e.g. bin-picking from an homogenous heap of a similar object, based on visual similarity of objects stored in the semantic memory). As example, we have confronted the system to the constrained optimizations of 9 continuous hyperparameters for a professional software (Kamido) in industrial robotic arm bin-picking tasks, a step that is needed each time to handle correctly new object. We used a simulator to create bin-picking tasks for 8 different objects (7 in simulation and one with real setup, without and with meta-learning with experiences coming from other similar objects) achieving goods results despite a very small optimization budget, with a better performance reached when meta-learning is used (84.3% vs 78.9% of success overall, with a small budget of 30 iterations for each optimization) for every object tested (p-value=0.036).Comment: Accepted at the IEEE International Conference on Development and Learning and Epigenetic Robotics 2020 (ICDL-Epirob 2020

What’s So Special About Patent Law?

The widespread belief that patent law is special has shaped the development of patent law into one of the most specialized areas of the law today. The belief in patent law’s exceptionalism manifests itself as two related presumptions with respect to the judiciary: first, that generalist judges who do not have patent law expertise cannot effectively decide patent cases, and second, that judges can develop necessary expertise through repeated experience with patent cases. Congress showed that it acquiesced to both views when it created the Federal Circuit and the Patent Pilot Program. In recent years, however, the Supreme Court has reminded us that the judiciary’s difficulty with patent cases is not the law, but is instead that patent cases often involve difficult subject matter, which sometimes requires technical or scientific expertise. While Congress’s early attempts to deal with these difficulties focused on courts with legal―rather than technical―expertise, the Supreme Court’s recent pronouncements suggest that they should have been doing the reverse. Moreover, to the extent that it is the underlying technology that makes patent cases difficult, that commends the use of an administrative, rather than a judicial, solution. One potentially viable answer to the judiciary’s problem with patent law has already been partly implemented in the form of the recently created Patent Trial and Appeal Board. This Article proposes expansion of that solution by making that new entity the exclusive forum for deciding issues of patent validity