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

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

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

Further insights into the beck hopelessness scale (BHS). Unidimensionality among psychiatric inpatients

Short versions of the Beck Hopelessness Scale have all been created according the Classical Test Theory, but the use and the application of this theory has been repeatedly criticized. In the current study, the Item Response Theory approach was employed to refine and shorten the BHS in order to build a reasonably coherent unidimensional scale whose items/symptoms can be treated as ordinal indicators of the theoretical concept of hopelessness, scaled along a single continuum. In a sample of 492 psychiatrically hospitalized, adult patients (51.2% females), predominantly with a diagnosis of Bipolar Disorder type II, the BHS was submitted to Mokken Scale Analysis. A final set of the nine best-fitting items satisfied the assumptions of local independency, monotonicity, and invariance of the item ordering. Using the ROC curve method, the IRT-based 9-item BHS showed good discriminant validity in categorizing psychiatric inpatients with high/medium suicidal risk and patients with and without suicide attempts. With high sensitivity (&gt;.90), this newly developed scale could be used as a valid screening tool for suicidal risk assessment in psychiatric inpatients

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

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

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

Estimations of length-weight relationships and consumption rates of odontocetes in the Mediterranean Sea from stranding data

Stranding data provide fundamental information on biometric traits of cetaceans useful to increase knowledge on ecological traits and their consumption patterns. In this study, the length weight (L-W) relationships through the power regression model (W = a ×Lb ) were calculated for three dolphin species (the striped dolphin, the common bottlenose dolphin and the Risso’s dolphin) in several Mediterranean subregions and at the scale of the entire basin. Length (L) and weight (W) data were collected from stranding records during the period from 1983 to 2021 acquired from several databases and the literature. Starting from L-W relationships, a bootstrap method was applied to estimate the mean body weights, the daily ingested biomass (IB) and annual food consumption (AFC) rates of different dolphin species. In particular, four different equations were used to estimate the IB rates. Prey consumption by dolphin species was calculated through AFC rates and the available diet information (expressed in weight fractions) of dolphin species for different Mediterranean subregions. Considering the L-W relationships in the Mediterranean Sea, b coefficient values were equal to 2.578, 2.975 and 2.988 for the striped, the common bottlenose and the Risso’s dolphin, respectively. At the Mediterranean scale, the AFC values estimated were 3913 kg (CI 2469–5306) for the Risso’s dolphin, 2571 kg (1372–3963) for the common bottlenose dolphin and 1118 kg (531–1570) for the striped dolphin. Prey consumption pattern showed a clear partitioning among the investigated species, where the common bottlenose dolphin exploits neritic demersal and pelagic fishes (e.g. eel fishes, sparids), the striped dolphin exploits mesopelagic fishes and myctophids, and the Risso’s dolphin was specialized on bathyal cephalopods of Histioteuthidae family. The results obtained in this study provide new information for the investigated species in several Mediterranean subregions providing a first consistent baseline to support the population dynamics modelling. At the same time, the wide uncertainty ranges of some parameters, as well as the lack of information for some species, stress the necessity of improving the data collection associated to stranding events, especially in the southern Mediterranean areas

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