Table of contents

A general method for building and training a multilayer neural network functioning as a parity machine is proposed. It is composed of two basic steps: a growth step in which two hidden layers are built and a pruning step in which any redundant units are removed. A perceptron-type algorithm is used to learn the connection strengths in order to minimize a classification error. The first hidden layer is built by adding units as they are needed, until the zero error convergence is achieved. We then show that the problem of mapping these internal representations onto the desired output is the n-parity problem. So, the second hidden layer is built by a geometrical design procedure with no learning. The used pruning process can remove sometimes all the units of the second hidden layer. The final architecture can then have one or two hidden layers.

The first investigation of the quasi-classical regime of thin plate vibrations in the high-frequency regime is presented. Using an efficient numerical scheme to compute many eigenfrequencies of a stadium-shaped plate, we find that the distribution of level spacings and the spectrum rigidity follow the GOE (Gaussian orthogonal ensemble) random matrix statistics. An asymptotic equivalence between the spectrum of a clamped plate and that of a membrane with a mixed boundary condition is derived. We also present examples of eigenmodes which present scars and give their quantization.

A binary aqueous suspension of large (L) and small (S) nearly-hard-sphere colloidal polystyrene spheres is shown to segregate spontaneously into L-rich and S-rich regions for suitable choices of volume fraction and size ratio. This is the first observation of such purely entropic phase separation of chemically identical species in which at least one component remains fluid. Simple theoretical arguments are presented to make this effect plausible.

We have studied the time dependences of density in the compacts of ultrafine metal particles under high external pressure. An anomalously slow relaxation of density (a log(t) behaviour) was found that confirms the analogy between granular materials and glassy systems pointed out earlier.

In this work Rényi's entropies of diffusion-limited aggregates are studied as a function of the number of particles N constituting the aggregate. We found that these aggregates exhibit a multifractal behaviour for finite size. The multifractality is lost very slowly when the aggregate grows, and finally aggregates become monofractal when N → ∞.

Robust scaling relations are observed in a model for fragmentation of fractal and nonfractal objects on square and triangular lattices with initial mass M₀ up to 6.4 millions, initial average coordination q₀ up to 10 and space dimension d varying from 1 to 5. For a diverse class of attacks simulating temperature variation we find that ∼ M₀/q₀ and ∼ ² independent of topology, lattice symmetry, and dimension of the object, where is the maximum number of fragments and the maximum number of diverse mass fragments generated during fragmentation.

The electric behaviour of the quasi-one-dimensional charge density wave (CDW) compound K_0.3MoO₃ is investigated at liquid-helium temperatures. At a threshold voltage, an abrupt increase in the conductivity takes place. The onset of this transition in conductivity is marked by a hysteresis. In the low-conducting branch of this hysteresis an intermittently spiking current signal in time domain has been found. 1/f^a noise and a power law scaling of the firing and waiting times as well as for spike sizes are characteristic for this critical dynamics. The results indicate critical behaviour which is self-organized.

The field extension with respect to the commutativity is considered. The relations of extended fields with ordinary ones are given. Some physical examples of such extensions are described.

The fluorescence of a single r.f.-trapped and cooled Ba⁺ ion, induced by the light of two lasers, shows a null at the S_1/2-D_3/2 resonance of the frequency difference. We have measured the Zeeman effect and power broadening of this "dark line", and also the shift of the associated "bright" line, which is related to the Raman light shift. A 75 kHz wide dark line was observed. Such a resonance might be used to control a 147 THz standard frequency free of systematic shifts in excess of 10^-15.

Radiative muon capture into ground hydrogenic states has been computed without the soft-photon approximation, for muons of energy above 1 keV. The process can be interpreted as the "stochastic" component of the continuum-to-bound transition as it comprises sudden events analogous to bremstrahlung. The results are compared with other calculations. Experimental signals and possible implications are discussed.

An electron beam generated by a GaAs photocathode, activated in negative electron affinity conditions, was studied under two different accelerating regimes. The energy spread of the beam, after an adiabatic acceleration is lower than after a fast acceleration. For the first time a longitudinal plasma parameter greater than one has been obtained for an electron beam.

We introduce a lattice Boltzmann model for the simulation of two immiscible fluids in three dimensions. The model is an extension of ideas used in the construction of a previous two-dimensional immiscible lattice Boltzmann model. We derive a theoretical value of the surface tension from consideration of the microscopic collision rules and verify this value with measurements from simulations.

We study the morphology of vicinal surfaces close to the reconstructing Au(111) and the nonreconstructing Pb(111) face. Molecular-dynamics simulations with many-body potentials for gold and lead have been conducted, using (534) as a test vicinal at T ∼ 0.8T_m, where T_m is the bulk melting temperature. It is found that, as a result of surface reconstruction, the gold vicinal surface undergoes faceting, while in lead the vicinal surface remains stable. Our results explain the origin of sharp edges on the equilibrium crystal shape of gold and smooth edges on lead.

In this letter, we shall present a generalization to quantum transport of the self-scattering technique commonly used in semi-classical transport simulations. The proposed Quantum Monte Carlo method originates from a perturbative expansion of the Liouville-von Neumann equation. Following the lines of Chambers' approach to semi-classical transport, an approximate imaginary self-energy ℏ/τ₀ is introduced which plays a role analogous to that of the maximum scattering rate in the traditional Monte Carlo method. At each perturbative order, the exact correction to 1/τ₀ is evaluated. The corresponding Monte Carlo algorithm for the study of quantum transport results to be very similar to the traditional one: by means of this "quantum self-scattering" technique, we again deal with the generation of "free flights" and "interaction processes", as in the semi-classical case. In particular, these similarities are found to be very useful for the analysis of quantum phenomena which give rise to deviations from semi-classical results.

We follow the cluster formation when depositing less than 2 monolayers Cu onto a monocrystalline αAl₂O₃ (0001) stoichiometric surface, by combining XPS and X-ray absorption spectroscopy at the Cu K edge (EXAFS, XANES). An estimate of the evolution of cluster size with copper deposition is given from XANES and EXAFS data. The variation of the Cu Auger parameter, measured from the XPS spectra, shows a continuous increase, attributed to the continuous increase of cluster size with copper deposition.

Recent results obtained by neutron diffraction measurements for x ∼ 3/8 do not support the existence of any superstructure (SS) composed of parallel full and empty CuO chains, as predicted by several models for O ordering. Assuming a screened Coulomb interaction between any two O ions of the basal plane, we looked for the SS of the lowest free energy. We obtained a SS that, compared with the one proposed in the experimental work, fits the observed intensities much better. If the reduction of the repulsion between those second-neighbour O atoms with a Cu atom in between due to charge-transfer effects is included, all diffraction patterns that have been observed so far (x ∼ 1/8, 1/2, 3/8, 4/7, 3/5, 5/8, 2/3, 3/4 and 7/8) can be explained.