Pattern-recalling processes in quantum Hopfield networks far from saturation

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of 'heat bath' that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the 'temperature'. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantum-mechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which non-extensive number $p$ of patterns are embedded via asymmetric Hebbian connections, namely, $p/N \to 0$ for the number of neuron $N \to \infty$ ('far from saturation'), we evaluate the recalling processes for one of the built-in patterns under the influence of quantum-mechanical noise.Comment: 10 pages, 3 figures, using jpconf.cls, Proc. of Statphys-Kolkata VI

An Efficient Method of Summarizing Documents Using Impression Measurements

Automatic generic document summarization based on unsupervised schemes is a very useful approach because it does not require training data. Although techniques using latent semantic analysis (LSA) and non-negative matrix factorization (NMF) have been applied to determine topics of documents, there are no researches on reduction of matrix and speeding up of computation of the NMF method. In order to achieve this scheme, this paper utilizes the generic impressive expressions from newspapers to extract important sentences as summary. Therefore, it has no stemming processes and no filtering of stop words. Generally, novels are typical documents providing sentimental impression for readers. However, newspapers deliver different impressions for new knowledge because they inform readers about current events, informative articles and diverse features. The proposed method introduces impressive expressions for newspapers and their measurements are applied to the NMF method. From 100 KB text data of experimental results by the proposed method, it turns out that the matrix size reduces by 80 % and the computation of the NMF method becomes 7 times faster than with the original method, without degrading the relevancy of extracted sentences

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

Image restoration using the chiral Potts spin-glass

We report on the image reconstruction (IR) problem by making use of the random chiral q-state Potts model, whose Hamiltonian possesses the same gauge invariance as the usual Ising spin glass model. We show that the pixel representation by means of the Potts variables is suitable for the gray-scale level image which can not be represented by the Ising model. We find that the IR quality is highly improved by the presence of a glassy term, besides the usual ferromagnetic term under random external fields, as very recently pointed out by Nishimori and Wong. We give the exact solution of the infinite range model with q=3, the three gray-scale level case. In order to check our analytical result and the efficiency of our model, 2D Monte Carlo simulations have been carried out on real-world pictures with three and eight gray-scale levels.Comment: RevTex 13 pages, 10 figure

On-Line AdaTron Learning of Unlearnable Rules

We study the on-line AdaTron learning of linearly non-separable rules by a simple perceptron. Training examples are provided by a perceptron with a non-monotonic transfer function which reduces to the usual monotonic relation in a certain limit. We find that, although the on-line AdaTron learning is a powerful algorithm for the learnable rule, it does not give the best possible generalization error for unlearnable problems. Optimization of the learning rate is shown to greatly improve the performance of the AdaTron algorithm, leading to the best possible generalization error for a wide range of the parameter which controls the shape of the transfer function.)Comment: RevTeX 17 pages, 8 figures, to appear in Phys.Rev.

On-line learning of non-monotonic rules by simple perceptron

We study the generalization ability of a simple perceptron which learns unlearnable rules. The rules are presented by a teacher perceptron with a non-monotonic transfer function. The student is trained in the on-line mode. The asymptotic behaviour of the generalization error is estimated under various conditions. Several learning strategies are proposed and improved to obtain the theoretical lower bound of the generalization error.Comment: LaTeX 20 pages using IOP LaTeX preprint style file, 14 figure

Mineralization of hydroxyapatite upon a unique xanthan gum hydrogel by an alternate soaking process

We previously reported a xanthan gum (Xan) hydrogel showing excellent mechanical properties. Mineralization of hydroxyapatite (Hap) upon the Xan hydrogel would provide a unique biomaterial applicable for bone tissue engineering. Here, we show the mineralization of Hap upon the Xan hydrogel by means of an alternate soaking process. Hap was gradually grown upon the Xan-matrix surface with increasing number of soaking cycles due to the ionic interactions between calcium cations and carboxyl groups. Interestingly, the mineralization induced a microstructure change in the gel-matrix from a layered structure to a porous structure. The mechanical properties of the resulting Hap–Xan composite hydrogels were further investigated by a tensile test, where the Hap–Xan composite hydrogel with an appropriate amount of Hap (Xan/Hap = 2.7) was capable of approximately 370% elongation

Identification of Very Red Counterparts of SiO Maser and OH/IR Objects in the GLIMPSE Survey

Using the 3.6/4.5/5.8/8.0 micron images with 1.2 arcsec pixel resolution from the Spitzer/GLIMPSE survey, we investigated 23 masing and 18 very red objects that were not identified in the 2MASS survey. Counterparts for all selected objects were found in the GLIMPSE images. Color indices in these IR bands suggest the presence of a high-extinction layer of more than a few tenths of a solar mass in front of the central star. Furthermore, radio observations in the SiO and H2O maser lines found characteristic maser-line spectra of the embedded objects, e.g., the SiO J=1-0 line intensity in the v=2 state stronger than that of the v=1 state, or very widespread H2O maser emission spectra. This indicates that these objects are actually enshrouded by very thick circumstellar matter, some of which cannot be ascribed to the AGB wind of the central star. Individually interesting objects are discussed, including two newly found water fountains and an SiO source with nebulosity.Comment: High resolution figures available at ftp://ftp.nro.nao.ac.jp/nroreport/no653.pdf.gz. ApJ No. 655 no.1 issue in pres