Numerical simulation of a binary communication channel: Comparison between a replica calculation and an exact solution

The mutual information of a single-layer perceptron with $N$ Gaussian inputs and $P$ deterministic binary outputs is studied by numerical simulations. The relevant parameters of the problem are the ratio between the number of output and input units, $\alpha = P/N$, and those describing the two-point correlations between inputs. The main motivation of this work refers to the comparison between the replica computation of the mutual information and an analytical solution valid up to $\alpha \sim O(1)$. The most relevant results are: (1) the simulation supports the validity of the analytical prediction, and (2) it also verifies a previously proposed conjecture that the replica solution interpolates well between large and small values of $\alpha$.Comment: 6 pages, 8 figures, LaTeX fil

Equilibrium properties of a Josephson junction ladder with screening effects

In this paper we calculate the ground state phase diagram of a Josephson Junction ladder when screening field effects are taken into account. We study the ground state configuration as a function of the external field, the penetration depth and the anisotropy of the ladder, using different approximations to the calculation of the induced fields. A series of tongues, characterized by the vortex density $\omega$, is obtained. The vortex density of the ground state, as a function of the external field, is a Devil's staircase, with a plateau for every rational value of $\omega$. The width of each of these steps depends strongly on the approximation made when calculating the inductance effect: if the self-inductance matrix is considered, the $\omega=0$ phase tends to occupy all the diagram as the penetration depth decreases. If, instead, the whole inductance matrix is considered, the width of any step tends to a non-zero value in the limit of very low penetration depth. We have also analyzed the stability of some simple metastable phases: screening fields are shown to enlarge their stability range.Comment: 16 pp, RevTex. Figures available upon request at [email protected] To be published in Physical Review B (01-Dec-96

Renormalization Group Study of the soliton mass on the (lambda Phi^4)_{1+1} lattice model

We compute, on the $(\lambda \Phi^4)_{1+1}$ model on the lattice, the soliton mass by means of two very different numerical methods. First, we make use of a ``creation operator'' formalism, measuring the decay of a certain correlation function. On the other hand we measure the shift of the vacuum energy between the symmetric and the antiperiodic systems. The obtained results are fully compatible. We compute the continuum limit of the mass from the perturbative Renormalization Group equations. Special attention is paid to ensure that we are working on the scaling region, where physical quantities remain unchanged along any Renormalization Group Trajectory. We compare the continuum value of the soliton mass with its perturbative value up to one loop calculation. Both quantities show a quite satisfactory agreement. The first is slightly bigger than the perturbative one; this may be due to the contributions of higher order corrections.Comment: 19 pages, preprint DFTUZ/93/0

Static chaos and scaling behaviour in the spin-glass phase

We discuss the problem of static chaos in spin glasses. In the case of magnetic field perturbations, we propose a scaling theory for the spin-glass phase. Using the mean-field approach we argue that some pure states are suppressed by the magnetic field and their free energy cost is determined by the finite-temperature fixed point exponents. In this framework, numerical results suggest that mean-field chaos exponents are probably exact in finite dimensions. If we use the droplet approach, numerical results suggest that the zero-temperature fixed point exponent $\theta$ is very close to $\frac{d-3}{2}$. In both approaches $d=3$ is the lower critical dimension in agreement with recent numerical simulations.Comment: 28 pages + 6 figures, LateX, figures uuencoded at the end of fil

Numerical study of a short-range p-spin glass model in three dimensions

In this work we study numerically a short range p-spin glass model in three dimensions. The behaviour of the model appears to be remarkably different from mean field predictions. In fact it shares some features typical of models with full replica-symmetry breaking (FRSB). Nevertheless, we believe that the transition that we study is intrinsically different from the FRSB and basically due to non-perturbative contributions. We study both the statics and the dynamics of the system which seem to confirm our conjectures.Comment: 20 pages, 15 figure

Discrete breathers in dc biased Josephson-junction arrays

We propose a method to excite and detect a rotor localized mode (rotobreather) in a Josephson-junction array biased by dc currents. In our numerical studies of the dynamics we have used experimentally realizable parameters and included self-inductances. We have uncovered two families of rotobreathers. Both types are stable under thermal fluctuations and exist for a broad range of array parameters and sizes including arrays as small as a single plaquette. We suggest a single Josephson-junction plaquette as an ideal system to experimentally investigate these solutions.Comment: 5 pages, 5 figure, to appear June 1, 1999 in PR

ProOpDB: Prokaryotic Operon DataBase

The Prokaryotic Operon DataBase (ProOpDB, http://operons.ibt.unam.mx/OperonPredictor) constitutes one of the most precise and complete repositories of operon predictions now available. Using our novel and highly accurate operon identification algorithm, we have predicted the operon structures of more than 1200 prokaryotic genomes. ProOpDB offers diverse alternatives by which a set of operon predictions can be retrieved including: (i) organism name, (ii) metabolic pathways, as defined by the KEGG database, (iii) gene orthology, as defined by the COG database, (iv) conserved protein domains, as defined by the Pfam database, (v) reference gene and (vi) reference operon, among others. In order to limit the operon output to non-redundant organisms, ProOpDB offers an efficient method to select the most representative organisms based on a precompiled phylogenetic distances matrix. In addition, the ProOpDB operon predictions are used directly as the input data of our Gene Context Tool to visualize their genomic context and retrieve the sequence of their corresponding 5′ regulatory regions, as well as the nucleotide or amino acid sequences of their genes

The influence of critical behavior on the spin glass phase

We have argued in recent papers that Monte Carlo results for the equilibrium properties of the Edwards-Anderson spin glass in three dimensions, which had been interpreted earlier as providing evidence for replica symmetry breaking, can be explained quite simply within the droplet model once finite size effects and proximity to the critical point are taken into account. In this paper, we show that similar considerations are sufficient to explain the Monte Carlo data in four dimensions. In particular, we study the Parisi overlap and the link overlap for the four-dimensional Ising spin glass in the Migdal-Kadanoff approximation. Similar to what is seen in three dimensions, we find that temperatures well below those studied in Monte Carlo simulations have to be reached before the droplet model predictions become apparent. We also show that the double-peak structure of the link overlap distribution function is related to the difference between domain-wall excitations that cross the entire system and droplet excitations that are confined to a smaller region.Comment: 8 pages, 8 figure

Absence of stable collinear configurations in Ni(001)ultrathin films: canted domain structure as ground state

Brillouin light scattering (BLS) measurements were performed for (17-120) Angstrom thick Cu/Ni/Cu/Si(001) films. A monotonic dependence of the frequency of the uniform mode on an in-plane magnetic field H was observed both on increasing and on decreasing H in the range (2-14) kOe, suggesting the absence of a metastable collinear perpendicular ground state. Further investigation by magneto-optical vector magnetometry (MOKE-VM) in an unconventional canted-field geometry provided evidence for a domain structure where the magnetization is canted with respect to the perpendicular to the film. Spin wave calculations confirm the absence of stable collinear configurations.Comment: 6 pages, 3 figures (text, appendix and 1 figure added

4D Spin Glasses in Magnetic Field Have a Mean Field like Phase

By using numerical simulations we show that the 4D $J=\pm 1$ Edwards Anderson spin glass in magnetic field undergoes a mean field like phase transition. We use a dynamical approach: we simulate large lattices (of volume $V$) and work out the behavior of the system in limit where both $t$ and $V$ go to infinity, but where the limit $V \to \infty$ is taken first. By showing that the dynamic overlap $q$ converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with the ones obtained by mean field computations.Comment: Physrev format, 5 ps figures include