Resolvent smoothness and local decay at low energies for the standard model of non-relativistic QED

We consider an atom interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. The nucleus is supposed to be fixed. We prove smoothness of the resolvent and local decay of the photon dynamics for quantum states in a spectral interval I just above the ground state energy. Our results are uniform with respect to I. Their proofs are based on abstract Mourre's theory, a Mourre inequality established in [FGS1], Hardy-type estimates in Fock space, and a low-energy dyadic decomposition.Comment: 31 page

Polynomial-Time Algorithms for Quadratic Isomorphism of Polynomials: The Regular Case

Let $\mathbf{f}=(f\_1,\ldots,f\_m)$ and $\mathbf{g}=(g\_1,\ldots,g\_m)$ be two sets of $m\geq 1$ nonlinear polynomials over $\mathbb{K}[x\_1,\ldots,x\_n]$ ($\mathbb{K}$ being a field). We consider the computational problem of finding -- if any -- an invertible transformation on the variables mapping $\mathbf{f}$ to $\mathbf{g}$. The corresponding equivalence problem is known as {\tt Isomorphism of Polynomials with one Secret} ({\tt IP1S}) and is a fundamental problem in multivariate cryptography. The main result is a randomized polynomial-time algorithm for solving {\tt IP1S} for quadratic instances, a particular case of importance in cryptography and somewhat justifying {\it a posteriori} the fact that {\it Graph Isomorphism} reduces to only cubic instances of {\tt IP1S} (Agrawal and Saxena). To this end, we show that {\tt IP1S} for quadratic polynomials can be reduced to a variant of the classical module isomorphism problem in representation theory, which involves to test the orthogonal simultaneous conjugacy of symmetric matrices. We show that we can essentially {\it linearize} the problem by reducing quadratic-{\tt IP1S} to test the orthogonal simultaneous similarity of symmetric matrices; this latter problem was shown by Chistov, Ivanyos and Karpinski to be equivalent to finding an invertible matrix in the linear space $\mathbb{K}^{n \times n}$ of $n \times n$ matrices over $\mathbb{K}$ and to compute the square root in a matrix algebra. While computing square roots of matrices can be done efficiently using numerical methods, it seems difficult to control the bit complexity of such methods. However, we present exact and polynomial-time algorithms for computing the square root in $\mathbb{K}^{n \times n}$ for various fields (including finite fields). We then consider \\#{\tt IP1S}, the counting version of {\tt IP1S} for quadratic instances. In particular, we provide a (complete) characterization of the automorphism group of homogeneous quadratic polynomials. Finally, we also consider the more general {\it Isomorphism of Polynomials} ({\tt IP}) problem where we allow an invertible linear transformation on the variables \emph{and} on the set of polynomials. A randomized polynomial-time algorithm for solving {\tt IP} when $\mathbf{f}=(x\_1^d,\ldots,x\_n^d)$ is presented. From an algorithmic point of view, the problem boils down to factoring the determinant of a linear matrix (\emph{i.e.}\ a matrix whose components are linear polynomials). This extends to {\tt IP} a result of Kayal obtained for {\tt PolyProj}.Comment: Published in Journal of Complexity, Elsevier, 2015, pp.3

ACME vs PDDL: support for dynamic reconfiguration of software architectures

On the one hand, ACME is a language designed in the late 90s as an interchange format for software architectures. The need for recon guration at runtime has led to extend the language with speci c support in Plastik. On the other hand, PDDL is a predicative language for the description of planning problems. It has been designed in the AI community for the International Planning Competition of the ICAPS conferences. Several related works have already proposed to encode software architectures into PDDL. Existing planning algorithms can then be used in order to generate automatically a plan that updates an architecture to another one, i.e., the program of a recon guration. In this paper, we improve the encoding in PDDL. Noticeably we propose how to encode ADL types and constraints in the PDDL representation. That way, we can statically check our design and express PDDL constraints in order to ensure that the generated plan never goes through any bad or inconsistent architecture, not even temporarily.Comment: 6\`eme \'edition de la Conf\'erence Francophone sur les Architectures Logicielles (CAL 2012), Montpellier : France (2012

Sparse and Non-Negative BSS for Noisy Data

Non-negative blind source separation (BSS) has raised interest in various fields of research, as testified by the wide literature on the topic of non-negative matrix factorization (NMF). In this context, it is fundamental that the sources to be estimated present some diversity in order to be efficiently retrieved. Sparsity is known to enhance such contrast between the sources while producing very robust approaches, especially to noise. In this paper we introduce a new algorithm in order to tackle the blind separation of non-negative sparse sources from noisy measurements. We first show that sparsity and non-negativity constraints have to be carefully applied on the sought-after solution. In fact, improperly constrained solutions are unlikely to be stable and are therefore sub-optimal. The proposed algorithm, named nGMCA (non-negative Generalized Morphological Component Analysis), makes use of proximal calculus techniques to provide properly constrained solutions. The performance of nGMCA compared to other state-of-the-art algorithms is demonstrated by numerical experiments encompassing a wide variety of settings, with negligible parameter tuning. In particular, nGMCA is shown to provide robustness to noise and performs well on synthetic mixtures of real NMR spectra.Comment: 13 pages, 18 figures, to be published in IEEE Transactions on Signal Processin

An Observer-Based Design for Cogging Forces Cancellation in Permanent Magnet Linear Motors

International audienceThis paper adresses the high precision positioning issue of permanent magnet (PM) linear motors, in presence of spatially periodic forces, also known as cogging. Using an internal model representation of this perturbation, an observer- based controller only relying on position measurements is derived. The observation error is not autonomous, and the stability analysis of the resulting closed loop system is regarded as the stability of two interconnected systems. For the motor to quickly track a desired trajectory, while being robust to large magnitude cogging forces, a small-gain like theorem is derived and used to tune the gains of the control law in an explicit way. The experimental results obtained through this method are then showed and compared with those of a PID controller

Active estimation of the initial phase for brushless synchronous motors

International audienceThis paper addresses the initial phase estimation problem for brushless synchronous motors. Only displacement measurements are used (no current) and friction, load and motor parameters are supposed to be unknown. Because of friction, the system is modelled by a differential equation with discontinuous right-hand side. Specific open-loop inputs are designed (active method) to get the initial phase as a function of the magnitude of the displacements along the corresponding trajectories. The estimation relies on a complete classification of the possible dynamical behaviours of the considered discontinuous right-hand side system with periodic input, whatever values the unknown parameters may take. We propose an approximated formula of the initial phase. Some experimental results are given, together with a comparison of our method to a classical procedur

Basic and supplementary sensory feedback in handwriting

International audienceThe mastering of handwriting is so essential in our society that it is important to try to find new methods for facilitating its learning and rehabilitation. The ability to control the graphic movements clearly impacts on the quality of the writing. This control allows both the programming of letter formation before movement execution and the online adjustments during execution, thanks to diverse sensory feedback (FB). New technologies improve existing techniques or enable new methods to supply the writer with real-time computer-assisted FB. The possibilities are numerous and various. Therefore, two main questions arise: (1) What aspect of the movement is concerned and (2) How can we best inform the writer to help them correct their handwriting? In a first step, we report studies on FB naturally used by the writer. The purpose is to determine which information is carried by each sensory modality, how it is used in handwriting control and how this control changes with practice and learning. In a second step, we report studies on supplementary FB provided to the writer to help them to better control and learn how to write. We suggest that, depending on their contents, certain sensory modalities will be more appropriate than others to assist handwriting motor control. We emphasize particularly the relevance of auditory modality as online supplementary FB on handwriting movements. Using real-time supplementary FB to assist in the handwriting process is probably destined for a brilliant future with the growing availability and rapid development of tablets

Hybridization of Nonlinear and Mixed-Integer Linear Programming for Aircraft Separation With Trajectory Recovery

International audienceThe approach presented in this article aims at finding a solution to the problem of conflict-free motion planning for multiple aircraft on the same flight level with trajectory recovery. One contribution of this work is to develop three consistent models, from a continuous-time representation to a discrete-time linear approximation. Each of these models guarantees separation at all times as well as trajectory recovery, but they are not equally difficult to solve. A new hybrid algorithm is thus developed in order to use the optimal solution of a mixed integer linear program as a starting point when solving a nonlinear formulation of the problem. The significance of this process is that it always finds a solution when the linear model is feasible while still taking into account the nonlinear nature of the problem. A test bed containing numerous data sets is then generated from three virtual scenarios. A comparative analysis with three different initialisations of the nonlinear optimisation validates the efficiency of the hybrid method