Optimal Capacity of the Blume-Emery-Griffiths perceptron

A Blume-Emery-Griffiths perceptron model is introduced and its optimal capacity is calculated within the replica-symmetric Gardner approach, as a function of the pattern activity and the imbedding stability parameter. The stability of the replica-symmetric approximation is studied via the analogue of the Almeida-Thouless line. A comparison is made with other three-state perceptrons.Comment: 10 pages, 8 figure

A spherical Hopfield model

We introduce a spherical Hopfield-type neural network involving neurons and patterns that are continuous variables. We study both the thermodynamics and dynamics of this model. In order to have a retrieval phase a quartic term is added to the Hamiltonian. The thermodynamics of the model is exactly solvable and the results are replica symmetric. A Langevin dynamics leads to a closed set of equations for the order parameters and effective correlation and response function typical for neural networks. The stationary limit corresponds to the thermodynamic results. Numerical calculations illustrate our findings.Comment: 9 pages Latex including 3 eps figures, Addition of an author in the HTML-abstract unintentionally forgotten, no changes to the manuscrip

Measurement of mesoscopic High-TcT_c superconductors using Si mechanical micro-oscillators

In a superconducting mesoscopic sample, with dimensions comparable to the London penetration depth, some properties are qualitatively different to those found in the bulk material. These properties include magnetization, vortex dynamics and ordering of the vortex lattice. In order to detect the small signals produced by this kind of samples, new instruments designed for the microscale are needed. In this work we use micromechanical oscillators to study the magnetic properties of a Bi$_2$Sr$_2$CaCu$_2$O$_{8 + \delta}$ disk with a diameter of 13.5 microns and a thickness of 2.5 microns. The discussion of our results is based on the existence and contribution of inter and intra layer currents.Comment: 4 pages, 6 figure

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

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

Minimalist AdaBoost for blemish identification in potatoes

We present a multi-class solution based on minimalist Ad- aBoost for identifying blemishes present in visual images of potatoes. Using training examples we use Real AdaBoost to rst reduce the fea- ture set by selecting ve features for each class, then train binary clas- siers for each class, classifying each testing example according to the binary classier with the highest certainty. Against hand-drawn ground truth data we achieve a pixel match of 83% accuracy in white potatoes and 82% in red potatoes. For the task of identifying which blemishes are present in each potato within typical industry dened criteria (10% coverage) we achieve accuracy rates of 93% and 94%, respectively

Structure of Flux Line Lattices with Weak Disorder at Large Length Scales

Dislocation-free decoration images containing up to 80,000 vortices have been obtained on high quality Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$ superconducting single crystals. The observed flux line lattices are in the random manifold regime with a roughening exponent of 0.44 for length scales up to 80-100 lattice constants. At larger length scales, the data exhibit nonequilibrium features that persist for different cooling rates and field histories.Comment: 4 pages, 3 gif images, to appear in PRB rapid communicatio