Exact Green Function for Neutral Pauli-Dirac Particle with Anomalous Magnetic Momentum in Linear Magnetic Field

We consider Pauli--Dirac fermion submitted to an inhomogeneous magnetic field. It is showed that the propagator of the neutral Dirac particle with an anomalous magnetic moment in an external linear magnetic field is the causal Green function $S^{c}(x_{b},x_{a})$ of the Pauli--Dirac equation. The corresponding Green function is calculated via path integral method in global projection, giving rise to the exact eigenspinors expressions. The neutral particle creation probability corresponding to our system is analyzed, which is obtained as function of the introduced field $B'$ and the additional spin magnetic moment $\mu$.Comment: 12 page

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

Path integral of the hydrogen atom, the Jacobi's principle of least action and one-dimensional quantum gravity

A path integral evaluation of the Green's function for the hydrogen atom initiated by Duru and Kleinert is studied by recognizing it as a special case of the general treatment of the separable Hamiltonian of Liouville-type. The basic dynamical principle involved is identified as the Jacobi's principle of least action for given energy which is reparametrization invariant, and thus the appearance of a gauge freedom is naturally understood. The separation of variables in operator formalism corresponds to a choice of gauge in path integral, and the Green's function is shown to be gauge independent if the operator ordering is properly taken into account. Unlike the conventional Feynman path integral,which deals with a space-time picture of particle motion, the path integral on the basis of the Jacobi's principle sums over orbits in space. We illustrate these properties by evaluating an exact path integral of the Green's function for the hydrogen atom in parabolic coordinates, and thus avoiding the use of the Kustaanheimo-Stiefel transformation. In the present formulation , the Hamiltonian for Stark effect is converted to the one for anharmonic oscillators with an unstable quartic coupling. We also study the hydrogen atom path integral from a view point of one-dimensional quantum gravity coupled to matter fields representing the electron coordinates. A simple BRST analysis of the problem with an evaluation of Weyl anomaly is presented .Comment: 29pages. Manuscript has been substantially modified and extended , to emphasize the gauge theoretical aspects of the problem. The title itself has been changed accordingl

CURIOUS: Intrinsically Motivated Modular Multi-Goal Reinforcement Learning

In open-ended environments, autonomous learning agents must set their own goals and build their own curriculum through an intrinsically motivated exploration. They may consider a large diversity of goals, aiming to discover what is controllable in their environments, and what is not. Because some goals might prove easy and some impossible, agents must actively select which goal to practice at any moment, to maximize their overall mastery on the set of learnable goals. This paper proposes CURIOUS, an algorithm that leverages 1) a modular Universal Value Function Approximator with hindsight learning to achieve a diversity of goals of different kinds within a unique policy and 2) an automated curriculum learning mechanism that biases the attention of the agent towards goals maximizing the absolute learning progress. Agents focus sequentially on goals of increasing complexity, and focus back on goals that are being forgotten. Experiments conducted in a new modular-goal robotic environment show the resulting developmental self-organization of a learning curriculum, and demonstrate properties of robustness to distracting goals, forgetting and changes in body properties.Comment: Accepted at ICML 201

Algebraic treatment of the confluent Natanzon potentials

Using the so(2,1) Lie algebra and the Baker, Campbell and Hausdorff formulas, the Green's function for the class of the confluent Natanzon potentials is constructed straightforwardly. The bound-state energy spectrum is then determined. Eventually, the three-dimensional harmonic potential, the three-dimensional Coulomb potential and the Morse potential may all be considered as particular cases.Comment: 9 page

Combinaison de codeurs par algorithme génétique : Application à la vérification du locuteur

Le domaine de la vérification du locuteur regroupe les applications pour lesquelles on désire identifier l'identité d'une personne à partir de sa voix. Le champ d'application couvre de nombreux secteurs tels que l'accès sécurisé, les transactions téléphoniques, la surveillance, l'indexation audio ou encore l'expertise judiciaire. Notre étude porte sur l'étape d'extraction de caractéristiques du système de reconnaissance du locuteur. Ce module a pour fonction d'extraire du signal de parole les informations pertinentes du point de vue de la discrimination inter-locuteur. Nous proposons dans cet article d'utiliser un algorithme génétique pour optimiser un système d'extraction de caractéristiques adapté à la reconnaissance du locuteur. La méthode proposée permet d'obtenir une amélioration significative du taux de reconnaissance sur la base Nist SRE 2005