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International audience; Restricted Boltzmann machines (RBMs) are energy-based neural networks which are commonly used as the building blocks for deep-architecture neural architectures. In this work, we derive a deterministic framework for the training, evaluation, and use of RBMs based upon the Thouless-Anderson-Palmer (TAP) mean-field approximation of widely connected systems with weak interactions coming from spin-glass theory. While the TAP approach has been extensively studied for fully visible binary spin systems, our construction is generalized to latent-variable models, as well as to arbitrarily distributed real-valued spin systems with bounded support. In our numerical experiments, we demonstrate the effective deterministic training of our proposed models and are able to show interesting features of unsupervised learning which could not be directly observed with sampling. Additionally, we demonstrate how to utilize our TAP-based framework for leveraging trained RBMs as joint priors in denoising problems.

International audience; Pressure-controlled displacement of an oil-water interface is studied in dense packings of functionalized glass beads with well-defined spatial wettability correlations. An enhanced dissipation is observed if the typical extension ξ of the same-type wetting domains is smaller than the average bead diameter d. Three-dimensional imaging using x-ray microtomography shows that the frequencies nðsÞ of residual droplet volumes s for different ξ collapse onto the same curve. This indicates that the additional dissipation for small ξ is due to contact line pinning rather than an increase of capillary break-up and coalescence events.

Electrons at noble metal surfaces can be confined within terraces leading to one-dimensional surface states. These can be studied with angle-resolved photoemission from vicinal surfaces with regular arrays of (111)-oriented terraces. Here we show the case of Au(23 23 21), which is vicinal to Au(111) and displays L=56Å wide terraces. The surface state band appears broken up into three quantum well levels that match to those of the infinite quantum well of the same width L. Their parallel momentum dependent photoemission intensity allows mapping the probability density of the confined wave function in reciprocal space using angle-resolved photoemission. By Fourier transformation, their respective experimental wave functions in real space are obtained and compared to the case of the infinite quantum-well, showing excellent agreement. Final state step superlattice diffraction effects have also been observed. Finally, we observe the quenching of the characteristic spin-orbit coupling of Au(111) in the confinement direction. This is another indication of the one-dimensional character of the surface state, as confirmed with first order perturbation theory., A.Mu., F.J.G. de A., E.V.C., Y.M.K., and J.E.O. are supported by the Universidad del Pais Vasco Grant No. 1/UPV/EHU/00057.240-EA-8078/2000. V.R. and S.R. are supported by the CNRS-ULTIMATECH program, the CRIF and the Universite de Paris 7. A. Ma. was supported by Contract No. HPMF-CT-2000-00565. The experiments at the SRC were supported by NSF Grants No. DMR-0084402, DMR9704196, and DMR-9815416.

Surface states at vicinal Au(788) and Au(322) have been investigated with angle-resolved photoemission and synchrotron radiation. Both surfaces are characterized by highly regular one-dimensional step arrays with relatively wide (∼3.9 Å) or narrow (∼1.3 Å) terraces in Au(788) and Au(322), respectively. Depending on the terrace size we observe that surface electrons behave in a completely different way. In Au(788) terraces become one-dimensional, lateral quantum wells that confine surface electrons between adjacent steps. In Au(322) surface electrons propagate across the step array forming two-dimensional superlattice bands. By tuning photon energy and angle we probe fundamental properties of the electron wave functions in both cases., A.Mu. and J.E.O. are supported by the Universidad del Pais Vasco (1/UPV/EHU/00057.240-EA-8078/2000). V.R. and S.R. are supported by the CNRS-ULTIMATECH program, the CRIF and the Universite de Paris 7. V. P.-D. is supported by the Comunidad Autonoma de Madrid (Project No. 07N/0042/98) and the DGICYT (Spain Grant No. PB97-1199).

STM images show that vicinal Au(788) surfaces are made up of a uniform array of (111)-oriented terraces of similar width (∼3.8nm). This uniformity makes it possible to study the electronic structure of the resulting step superlattice by angle-resolved photoemission. We show that for this terrace array the surface state appears to be broken up into one-dimensional quantum-well levels, indicating total electron confinement within the terraces. The angular resolution allows the probability density of the terrace quantum well state to be mapped in reciprocal space, complementing nicely the wave function measured in real space by STM., A. Mu., F. J. G. de A., and J. E. O. are supported by the Universidad del País Vasco (1/UPV/EHU/00057.240-EA8078/2000) and the Max Planck Research Award Program. V. R. and S. R. are supported by the CNRS-ULTIMATECH program, the CRIF, and the Université de Paris 7. A. Ma. is supported by a Marie Curie Fellowship of the European Union, under Contract No. HPMF-CT-2000-00565. V. P.-D. is supported by the Comunidad Autónoma de Madrid (Project No. 07N/0042/98) and the DGICYT (Spain) (Grant No. PB-97-1199).