Multiplicative versus additive noise in multi-state neural networks

The effects of a variable amount of random dilution of the synaptic couplings in Q-Ising multi-state neural networks with Hebbian learning are examined. A fraction of the couplings is explicitly allowed to be anti-Hebbian. Random dilution represents the dying or pruning of synapses and, hence, a static disruption of the learning process which can be considered as a form of multiplicative noise in the learning rule. Both parallel and sequential updating of the neurons can be treated. Symmetric dilution in the statics of the network is studied using the mean-field theory approach of statistical mechanics. General dilution, including asymmetric pruning of the couplings, is examined using the generating functional (path integral) approach of disordered systems. It is shown that random dilution acts as additive gaussian noise in the Hebbian learning rule with a mean zero and a variance depending on the connectivity of the network and on the symmetry. Furthermore, a scaling factor appears that essentially measures the average amount of anti-Hebbian couplings.Comment: 15 pages, 5 figures, to appear in the proceedings of the Conference on Noise in Complex Systems and Stochastic Dynamics II (SPIE International

Stationary states of a spherical Minority Game with ergodicity breaking

Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003) displays a phase with broken ergodicity and dependence of the macroscopic stationary state on initial conditions. The model thus bears more similarity with the original MG. Still, all order parameters including the volatility can computed in the ergodic phases without making any approximations. We also study the effects of market impact correction on the phase diagram. Finally we discuss a continuous-time version of the model as well as the differences between on-line and batch update rules. Our analytical results are confirmed convincingly by comparison with numerical simulations. In an appendix we extend the analysis of the earlier spherical MG to a model with general time-step, and compare the dynamics and statics of the two spherical models.Comment: 26 pages, 8 figures; typo correcte

Multi-State Image Restoration by Transmission of Bit-Decomposed Data

We report on the restoration of gray-scale image when it is decomposed into a binary form before transmission. We assume that a gray-scale image expressed by a set of Q-Ising spins is first decomposed into an expression using Ising (binary) spins by means of the threshold division, namely, we produce (Q-1) binary Ising spins from a Q-Ising spin by the function F(\sigma_i - m) = 1 if the input data \sigma_i \in {0,.....,Q-1} is \sigma_i \geq m and 0 otherwise, where m \in {1,....,Q-1} is the threshold value. The effects of noise are different from the case where the raw Q-Ising values are sent. We investigate which is more effective to use the binary data for transmission or to send the raw Q-Ising values. By using the mean-field model, we first analyze the performance of our method quantitatively. Then we obtain the static and dynamical properties of restoration using the bit-decomposed data. In order to investigate what kind of original picture is efficiently restored by our method, the standard image in two dimensions is simulated by the mean-field annealing, and we compare the performance of our method with that using the Q-Ising form. We show that our method is more efficient than the one using the Q-Ising form when the original picture has large parts in which the nearest neighboring pixels take close values.Comment: latex 24 pages using REVTEX, 10 figures, 4 table

Machined Versus Cast Abutments for Single Dental Implants: A 3-year within-Patient Multicentre Randomized Controlled Trial

PURPOSE: To compare clinical outcomes of machined titanium abutments (machined group) versus cast cobalt-chrome abutments (cast group). MATERIALS AND METHODS: Thirty-one partially edentulous subjects received two single non-adjacent implant-supported crowns each at three centres. Three and a half months after implant placement, implants were randomized at impression taking to receive one machined and one cast abutment according to a within-patient study design. Four patients dropped out and one patient lost one implant before randomization, so only 26 patients had their implants randomized. Outcome measures were: prosthesis and implant failures, any complications, and radiographic peri-implant marginal bone level changes. Patients were followed up for 3 years after loading. RESULTS: After randomization, three patients dropped out. One implant failed and two crowns on cast abutments were lost, but differences in implant and prosthesis failures were not statistically different (McNemar test P = 1.000; difference in proportions = 0.04 and P = 0.500; difference in proportions = 0.08, respectively). Two minor complications occurred in the cast group versus one in the machined group, the difference not being statistically different (McNemar test P = 1.000; difference in proportions = 0.04; 95% CI 0.18 to 22.06). Both groups presented statistically significant peri-implant marginal bone loss from implant placement to 3 years after loading, respectively -0.72 ± 0.90 mm (P = 0.001) for machined and -0.60 ± 0.61 mm (P <0.001) for cast abutments, with no statistically significant differences between the two groups (mean difference -0.12 mm; 95% CI -0.57 to 0.34; P = 0.624). Both groups gradually lost marginal peri-implant bone from loading (baseline) to 3 years after loading, but this was not statistically significant; machined lost -0.05 ± 0.12 mm while cast lost -0.14 ± 0.11 mm, a difference that was not statistically significant (mean difference 0.06 mm; 95% CI -0.24 to 0.35; P = 0.708). CONCLUSIONS: The present clinical data suggest that implant prognosis up to 3 years after loading is not affected by the choice of machined or cast abutments

Metastability and paramagnetism in superconducting mesoscopic disks

A projected order parameter is used to calculate, not only local minima of the Ginzburg-Landau energy functional, but also saddle points or energy barriers responsible for the metastabilities observed in superconducting mesoscopic disks (Geim et al. Nature {\bf 396}, 144 (1998)). We calculate the local minima magnetization and find the energetic instability points between vortex configurations with different vorticity. We also find that, for any vorticity, the supercurrent can reverse its flow direction on decreasing the magnetic field before one vortex can escape.Comment: Modified version as to appear in Phys. Rev. Let

Image restoration using the Q-Ising spin glass

We investigate static and dynamic properties of gray-scale image restoration (GSIR) by making use of the Q-Ising spin glass model, whose ladder symmetry allows to take in account the distance between two spins. We thus give an explicit expression of the Hamming distance between the original and restored images as a function of the hyper-parameters in the mean field limit. Finally, numerical simulations for real-world pictures are carried out to prove the efficiency of our model.Comment: 27pages, 13figures, revte

The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles

It is shown that an exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite-step sequence processing model which has retarded self-interactions. We have also derived the stationary state equations by means of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must assume that crosstalk noise of an input to spins obeys a Gaussian distribution. On the other hand, the path-integral method does not require such a Gaussian approximation of crosstalk noise. We have found that both the signal-to-noise analysis and the path-integral analysis give the completely same result with respect to the stationary state in the case where the dynamics is deterministic, when we assume the Maxwell construction ansatz. We have shown the dependence of storage capacity (alpha_c) on the number of patterns per one limit cycle (l). Storage capacity monotonously increases with the number of steps, and converges to alpha_c=0.269 at l ~= 10. The original properties of the finite-step sequence processing model appear as long as the number of steps of the limit cycle has order l=O(1).Comment: 24 pages, 3 figure