Profinite completion and double-dual : isomorphisms and counter-examples

We define, for any group $G$, finite approximations ; with this tool, we give a new presentation of the profinite completion $\hat{\pi} : G \to \hat{G}$ of an abtract group $G$. We then prove the following theorem : if $k$ is a finite prime field and if $V$ is a $k$-vector space, then, there is a natural isomorphism between $\hat{V}$ (for the underlying additive group structure) and the additive group of the double-dual $V^{**}$. This theorem gives counter-examples concerning the iterated profinite completions of a group. These phenomena don't occur in the topological case

Self-interfering wavepackets

We study the propagation of non-interacting polariton wavepackets. We show how two qualitatively different concepts of mass that arise from the peculiar polariton dispersion lead to a new type of particle-like object from non-interacting fields---much like self-accelerating beams---shaped by the Rabi coupling out of Gaussian initial states. A divergence and change of sign of the diffusive mass results in a "mass wall" on which polariton wavepackets bounce back. Together with the Rabi dynamics, this yield propagation of ultrafast subpackets and ordering of a spacetime crystal.Comment: (no movies part of this preprint

Expressing Bayesian Fusion as a Product of Distributions: Application to Randomized Hough Transform

Data fusion is a common issue of mobile robotics, computer assisted medical diagnosis or behavioral control of simulated character for instance. However data sources are often noisy, opinion for experts are not known with absolute precision, and motor commands do not act in the same exact manner on the environment. In these cases, classic logic fails to manage efficiently the fusion process. Confronting different knowledge in an uncertain environment can therefore be adequately formalized in the bayesian framework. Besides, bayesian fusion can be expensive in terms of memory usage and processing time. This paper precisely aims at expressing any bayesian fusion process as a product of probability distributions in order to reduce its complexity. We first study both direct and inverse fusion schemes. We show that contrary to direct models, inverse local models need a specific prior in order to allow the fusion to be computed as a product. We therefore propose to add a consistency variable to each local model and we show that these additional variables allow the use of a product of the local distributions in order to compute the global probability distribution over the fused variable. Finally, we take the example of the Randomized Hough Transform. We rewrite it in the bayesian framework, considering that it is a fusion process to extract lines from couples of dots in a picture. As expected, we can find back the expression of the Randomized Hough Transform from the literature with the appropriate assumptions

Expressing Bayesian Fusion as a Product of Distributions: Application in Robotics

More and more fields of applied computer science involve fusion of multiple data sources, such as sensor readings or model decision. However incompleteness of the models prevent the programmer from having an absolute precision over their variables. Therefore bayesian framework can be adequate for such a process as it allows handling of uncertainty.We will be interested in the ability to express any fusion process as a product, for it can lead to reduction of complexity in time and space. We study in this paper various fusion schemes and propose to add a consistency variable to justify the use of a product to compute distribution over the fused variable. We will then show application of this new fusion process to localization of a mobile robot and obstacle avoidance

Microring resonator refractive index sensor with integrated spectrometer

We present a SOI ring based sensor read-out system. The novelty of the architecture lies in the capability to sense the shifts of multiple peaks simultaneously with an integrated AWG spectrometer

A Hitchhiker's Guide to Statistical Comparisons of Reinforcement Learning Algorithms

Consistently checking the statistical significance of experimental results is the first mandatory step towards reproducible science. This paper presents a hitchhiker's guide to rigorous comparisons of reinforcement learning algorithms. After introducing the concepts of statistical testing, we review the relevant statistical tests and compare them empirically in terms of false positive rate and statistical power as a function of the sample size (number of seeds) and effect size. We further investigate the robustness of these tests to violations of the most common hypotheses (normal distributions, same distributions, equal variances). Beside simulations, we compare empirical distributions obtained by running Soft-Actor Critic and Twin-Delayed Deep Deterministic Policy Gradient on Half-Cheetah. We conclude by providing guidelines and code to perform rigorous comparisons of RL algorithm performances.Comment: 8 pages + supplementary materia

CLIC: Curriculum Learning and Imitation for object Control in non-rewarding environments

In this paper we study a new reinforcement learning setting where the environment is non-rewarding, contains several possibly related objects of various controllability, and where an apt agent Bob acts independently, with non-observable intentions. We argue that this setting defines a realistic scenario and we present a generic discrete-state discrete-action model of such environments. To learn in this environment, we propose an unsupervised reinforcement learning agent called CLIC for Curriculum Learning and Imitation for Control. CLIC learns to control individual objects in its environment, and imitates Bob's interactions with these objects. It selects objects to focus on when training and imitating by maximizing its learning progress. We show that CLIC is an effective baseline in our new setting. It can effectively observe Bob to gain control of objects faster, even if Bob is not explicitly teaching. It can also follow Bob when he acts as a mentor and provides ordered demonstrations. Finally, when Bob controls objects that the agent cannot, or in presence of a hierarchy between objects in the environment, we show that CLIC ignores non-reproducible and already mastered interactions with objects, resulting in a greater benefit from imitation

The ATLAS liquid argon hadronic end-cap calorimeter: construction and selected beam test results

ATLAS has chosen for its Hadronic End-Cap Calorimeter (HEC) the copper-liquid argon sampling technique with flat plate geometry and GaAs pre-amplifiers in the argon. The contruction of the calorimeter is now approaching completion. Results of production quality checks are reported and their anticipated impact on calorimeter performance discussed. Selected results, such as linearity, electron and pion energy resolution, uniformity of energy response, obtained in beam tests both of the Hadronic End-Cap Calorimeter by itself, and in the ATLAS configuration where the HEC is in combination with the Electromagnetic End-Cap Calorimeter (EMEC) are described.Comment: 4 pages, 2 figures,IPRD04 conferenc