Elementary Derivative Tasks and Neural Net Multiscale Analysis of Tasks

Neural nets are known to be universal approximators. In particular, formal neurons implementing wavelets have been shown to build nets able to approximate any multidimensional task. Such very specialized formal neurons may be, however, difficult to obtain biologically and/or industrially. In this paper we relax the constraint of a strict ``Fourier analysis'' of tasks. Rather, we use a finite number of more realistic formal neurons implementing elementary tasks such as ``window'' or ``Mexican hat'' responses, with adjustable widths. This is shown to provide a reasonably efficient, practical and robust, multifrequency analysis. A training algorithm, optimizing the task with respect to the widths of the responses, reveals two distinct training modes. The first mode induces some of the formal neurons to become identical, hence promotes ``derivative tasks''. The other mode keeps the formal neurons distinct.Comment: latex neurondlt.tex, 7 files, 6 figures, 9 pages [SPhT-T01/064], submitted to Phys. Rev.

Existence of a Density Functional for an Intrinsic State

A generalization of the Hohenberg-Kohn theorem proves the existence of a density functional for an intrinsic state, symmetry violating, out of which a physical state with good quantum numbers can be projected.Comment: 6 page

Is friction responsible for the reduction of fusion rates far below the Coulomb barrier?

The fusion of two interacting heavy ions traditionally has been interpreted in terms of the penetration of the projectile into the target. Observed rates well below the Coulomb barrier are considerably lower than estimates obtained from penetration factors. One approach in the analysis of the data invokes coupling to non-elastic channels in the scattering as the source of the depletion. Another is to analyze those data in terms of tunneling in semi-classical models, with the observed depletion being taken as evidence of a ``friction'' under the barrier. A complementary approach is to consider such tunneling in terms of a fully quantal model. We investigate tunneling with both one-dimensional and three-dimensional models in a fully quantal approach to investigate possible sources for such a friction. We find that the observed phenomenon may not be explained by friction. However, we find that under certain conditions tunneling may be enhanced or diminished by up to 50%, which finds analogy with observation, without the invocation of a friction under the barrier.Comment: 18 pages, 15 figures embedde

Existence of Density Functionals for Excited States and Resonances

We show how every bound state of a finite system of identical fermions, whether a ground state or an excited one, defines a density functional. Degeneracies created by a symmetry group can be trivially lifted by a pseudo-Zeeman effect. When complex scaling can be used to regularize a resonance into a square integrable state, a DF also exists.Comment: 4 pages, no figure

Entanglement of localized states

We derive exact expressions for the mean value of Meyer-Wallach entanglement Q for localized random vectors drawn from various ensembles corresponding to different physical situations. For vectors localized on a randomly chosen subset of the basis, tends for large system sizes to a constant which depends on the participation ratio, whereas for vectors localized on adjacent basis states it goes to zero as a constant over the number of qubits. Applications to many-body systems and Anderson localization are discussed.Comment: 6 pages, 4 figure

Intermediate quantum maps for quantum computation

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production, and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically, and yields pseudorandom operators with original properties, enabling for example to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.Comment: 4 pages, 4 figures, research done at http://www.quantware.ups-tlse.fr

Adaptation to altered interaural time differences in a virtual reality environment

Interaural time differences (ITDs) are important cues for determining the azimuth location of a sound source and need to be accurately reproduced, in a virtual reality (VR) environment, to achieve a realistic sense of sound location for the listener. ITDs are usually included in head related transfer functions (HRTFs) used for audio rendering, and can be individualised to match the user’s head size (e.g. longer ITDs are needed for larger head sizes). In recent years, studies have shown that it is possible to train subjects to adapt and improve their performance in sound localisation skills to non-individualized HRTFs. The analysis of such improvements has focused mainly on adaptation to monoaural spectral cues rather than binaural cues such as ITDs. In this work listeners are placed in a VR environment and are asked to localise the source of a noise burst in the horizontal plane. Using a generic non-individualized HRTF with its ITD modified to match the head size of each participant, test and training phases are alternated, with the latter providing continuous auditory feedback. The experiment is then repeated with ITDs simulating larger (150%) and smaller (50%) head sizes. Comparing localisation accuracy before and after training, it is observed that while training seems to improve sound localisation performance, this varies according to the simulated head size and target location