Sylvie Marcos

The propagator method for source bearing estimation

Abstract This paper investigates the propagator method as a possible alternative to the MUSIC method for source bearing estimation with arrays consisting of a large number of sensors. Indeed, the propagator method (PM) is a subspace-based method which does not require the eigendecomposition of the cross-spectral matrix (CSM) of the received signals. The propagator is a linear operator which only depends on the steering vectors and which can be easily extracted from the data. We here propose a new version of the propagator method referred to as the orthonormal propagator method (OPM). The performance of the PM and the OPM is theoretically analysed in terms of the mean squared error on the source bearing estimates and in terms of computational complexity. The performance results are then compared to those of MUSIC. We find that at high and medium signal-to-noise ratio, the OPM performs quite like MUSIC with a complexity reduced by the ratio of the number of sources to the number of sensors. Simulations are presented to strengthen the theoretical results. At low signal-to-noise ratio, the OPM can also perform like MUSIC when the assumed number of sources is slightly overestimated.

Systematics of nuclear matter and finite nuclei properties in a non-linear relativistic mean field approach

Abstract A phenomenological non-linear relativistic mean field approach is used to investigate primarily the properties of nuclear matter. The dimensionless parameters are adjusted using different empirical quantities which are discussed in detail: saturation conditions, the incompressibility parameter, symmetry energy and surface energy. Particular attention is paid to the cubic and quartic terms in the self-interaction part of the scalar field. The effective parameters are then used to study doubly magic finite nuclei in the Dirac-Hartree approximation. Different ground-state properties, binding energies, rms radii, density distributions, are then systematically analyzed and discussed. A remarkable agreement with experimental quantities is found and further possibilities are suggested.

Single-particle magnetic moments in a relativistic shell model

Abstract Starting from the original σ + ω model of Walecka, single-particle properties of finite nuclei are derived in the Dirac-Hartree approximation. In such a model, large relativistic corrections are found for the single-particle Dirac magnetic moment, whose origin is found to be closely connected with the effective nucleon mass in nuclei yielding a reasonable value of the spin-orbit splitting. A phenomenological model, which takes into account tensor as well as space-like vector potentials, is found to reduce considerably the amount of relativistic corrections. A possible connection with the Dirac-Hartree-Fock approximation is discussed.

Performances analysis of the propagator method for source bearing estimation

This paper investigates the performances of the propagator method (PM) in terms of the mean squared error (MSE) on the bearing estimates and in terms of the computational complexity. The propagator method (PM) is a subspace-based method which does not require any eigendecomposition of the cross-spectral matrix (CSM) of the received signals or any singular value decomposition (SVD) of the data matrix. We show that the performance of the PM are more sensitive to the fact that the basis of the noise subspace is not orthonormal than to the presence of noise in the data. We therefore propose a new version of the PM referred to as the orthonormal propagator method (OPM). We show that at high and medium signal-to-noise ratio, the OPM performs like MUSIC with a complexity reduced by the number of sources to the number of sensors ratio. The OPM can also perform like MUSIC at low SNR when the assumed number of sources is slightly overdetermined.<<ETX>>

A unified framework for gradient algorithms used for filter adaptation and neural network training

In this paper we present in a unified framework the gradient algorithms employed in the adaptation of linear time filters (TF) and the supervised training of (non-linear) neural networks (NN). the optimality criteria used to optimize the parameters H of the filter or network are the least squares (LS) and least mean squares (LMS) in both contexts. They respectively minimize the total or the mean squares of the error e(k) between an (output) reference sequence d(k) and the actual system output y(k) corresponding to the input X(k). Minimization is performed iteratively by a gradient algorithm. the index k in (TF) is time and it runs indefinitely. Thus iterations start as soon as reception of X(k) begins. the recursive algorithm for the adaptation H(k – 1) H(k) of the parameters is implemented each time a new input X(k) is observed. When training a (NN) with a finite number of examples, the index k denotes the example and it is upper-bounded. Iterative (block) algorithms wait until all K examples are received to begin the network updating. However, K being frequently very large, recursive algorithms are also often preferred in (NN) training, but they raise the question of ordering the examples X(k). Except in the specific case of a transversal filter, there is no general recursive technique for optimizing the LS criterion. However, X(k) is normally a random stationary sequence; thus LS and LMS are equivalent when k becomes large. Moreover, the LMS criterion can always be minimized recursively with the help of the stochastic LMS gradient algorithm, which has low computational complexity. In (TF), X(k) is a sliding window of (time) samples, whereas in the supervised training of (NN) with arbitrarily ordered examples, X(k – 1) and X(k) have nothing to do with each other. When this (major) difference is rubbed out by plugging a time signal at the network input, the recursive algorithms recently developed for (NN) training become similar to those of adaptive filtering. In this context the present paper displays the similarities between adaptive cascaded linear filters and trained multilayer networks. It is also shown that there is a close similarity between adaptive recursive filters and neural networks including feedback loops. The classical filtering approach is to evaluate the gradient by ‘forward propagation’, whereas the most popular (NN) training method uses a gradient backward propagation method. We show that when a linear (TF) problem is implemented by an (NN), the two approaches are equivalent. However, the backward method can be used for more general (non-linear) filtering problems. Conversely, new insights can be drawn in the (NN) context by the use of a gradient forward computation. The advantage of the (NN) framework, and in particular of the gradient backward propagation approach, is evidently to have a much larger spectrum of applications than (TF), since (i) the inputs are arbitrary and (ii) the (NN) can perform non-linear (TF).

Neural network training schemes for non-linear adaptive filtering and modelling

There are a wide variety of cost functions, techniques for estimating their gradient, and adaptive algorithms for updating the coefficients of neural networks used as nonlinear adaptive filters. The authors discuss the various algorithms which result from various choices of criteria and of gradient estimation techniques. New algorithms are introduced, and the relations between the present work, the real-time recurrent learning algorithm, and the teacher forcing technique are discussed. The authors show that the training algorithms suggested recently for feedback networks are very closely related to and in some cases identical to the algorithms used classically for adapting recursive filters.<<ETX>>

The warm breath

Abstract The Hot Modified Thomas-Fermi (HMTF) method has been used in a sum rule approach to estimate the evolution of the energy peak and width of the isoscalar monopole resonance with the excitation energy represented by a nuclear temperature T . Isothermal and isentropic calculations are reported.

A CONNECTION BETWEEN THE RELATIVISTIC MEAN FIELD APPROACH AND EFFECTIVE INTERACTIONS

Abstract Starting first from the relativistic mean field approach of finite nuclei, the Dirac equation is reduced to a Schrodinger equation which resembles very much the Hartree-Fock-Skyrme equation. As an alternative, a low density expansion of the energy in nuclear matter is performed and both approaches are compared. The connection with effective hamiltonians is discussed, as well as the possible relation between realistic parameters and effective ones.

Low-entropy adiabats for stellar collapse☆

Abstract The equation of state of hot, dense matter is computed along two adiabats ( s =1.0 k and s = 1.5 k ) using the nuclear Thomas-Fermi model.

Relativistic mean field approach to the scattering of antinucleons and nucleons by nuclei

Abstract A realistic mean field approach based on the Walecka theory for nuclear matter is used to derive the optical potential for nucleon and antinucleon-nucleus systems. The total and reaction cross sections are calculated in the WKB approximation for different nuclei ranging from carbon to lead and for incident energies between 0.1 and 2 GeV.