Stability of the Mezard-Parisi solution for random manifolds

The eigenvalues of the Hessian associated with random manifolds are constructed for the general case of $R$ steps of replica symmetry breaking. For the Parisi limit $R\to\infty$ (continuum replica symmetry breaking) which is relevant for the manifold dimension $D<2$, they are shown to be non negative.Comment: LaTeX, 15 page

Replica Fourier Transforms on Ultrametric Trees, and Block-Diagonalizing Multi-Replica Matrices

The analysis of objects living on ultrametric trees, in particular the block-diagonalization of 4-replica matrices $M^{\alpha \beta ; \gamma \delta}$, is shown to be dramatically simplified through the introduction of properly chosen operations on those objects. These are the Replica Fourier Transforms on ultrametric trees. Those transformations are defined and used in the present work.Comment: Latex file, 14 page

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

Application of the quantum spin glass theory to image restoration

Quantum fluctuation is introduced into the Markov random fields (MRF's) model for image restoration in the context of Bayesian approach. We investigate the dependence of the quantum fluctuation on the quality of BW image restoration by making use of statistical mechanics. We find that the maximum posterior marginal (MPM) estimate based on the quantum fluctuation gives a fine restoration in comparison with the maximum a posterior (MAP) estimate or the thermal fluctuation based MPM estimate.Comment: 19 pages, 9 figures, 1 table, RevTe

Thermodynamic properties of extremely diluted symmetric Q-Ising neural networks

Using the replica-symmetric mean-field theory approach the thermodynamic and retrieval properties of extremely diluted {\it symmetric} $Q$-Ising neural networks are studied. In particular, capacity-gain parameter and capacity-temperature phase diagrams are derived for $Q=3, 4$ and $Q=\infty$. The zero-temperature results are compared with those obtained from a study of the dynamics of the model. Furthermore, the de Almeida-Thouless line is determined. Where appropriate, the difference with other $Q$-Ising architectures is outlined.Comment: 16 pages Latex including 6 eps-figures. Corrections, also in most of the figures have been mad

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

Consumers’ acceptance and preferences for nutrition-modified and functional dairy products: a systematic review

This systematic literature review collects and summarizes research on consumer acceptance and preferences for nutrition-modified and functional dairy products, to reconcile, and expand upon, the findings of previous studies. We find that female consumers show high acceptance for some functional dairy products, such as yogurt enriched with calcium, fiber and probiotics. Acceptance for functional dairy products increases among consumers with higher diet/health related knowledge, as well as with aging. General interest in health, food-neophobia and perceived self-efficacy seem also to contribute shaping the acceptance for functional dairy products. Furthermore, products with “natural” matches between carriers and ingredients have the highest level of acceptance among consumers. Last, we find that brand familiarity drives consumers with low interest in health to increase their acceptance and preference for health enhanced dairy products, such as probiotic yogurts, or those with a general function claim

Functional renormalization group at large N for random manifolds

We introduce a method, based on an exact calculation of the effective action at large N, to bridge the gap between mean field theory and renormalization in complex systems. We apply it to a d-dimensional manifold in a random potential for large embedding space dimension N. This yields a functional renormalization group equation valid for any d, which contains both the O(epsilon=4-d) results of Balents-Fisher and some of the non-trivial results of the Mezard-Parisi solution thus shedding light on both. Corrections are computed at order O(1/N). Applications to the problems of KPZ, random field and mode coupling in glasses are mentioned

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