Interpolating the Sherrington-Kirkpatrick replica trick

The interpolation techniques have become, in the past decades, a powerful approach to lighten several properties of spin glasses within a simple mathematical framework. Intrinsically, for their construction, these schemes were naturally implemented into the cavity field technique, or its variants as the stochastic stability or the random overlap structures. However the first and most famous approach to mean field statistical mechanics with quenched disorder is the replica trick. Among the models where these methods have been used (namely, dealing with frustration and complexity), probably the best known is the Sherrington-Kirkpatrick spin glass: In this paper we are pleased to apply the interpolation scheme to the replica trick framework and test it directly to the cited paradigmatic model: interestingly this allows to obtain easily the replica-symmetric control and, synergically with the broken replica bounds, a description of the full RSB scenario, both coupled with several minor theorems. Furthermore, by treating the amount of replicas $n\in(0,1]$ as an interpolating parameter (far from its original interpretation) this can be though of as a quenching temperature close to the one introduce in off-equilibrium approaches and, within this viewpoint, the proof of the attended commutativity of the zero replica and the infinite volume limits can be obtained.Comment: This article is dedicated to David Sherrington on the occasion of his seventieth birthda

Thermodynamics and Universality for Mean Field Quantum Spin Glasses

We study aspects of the thermodynamics of quantum versions of spin glasses. By means of the Lie-Trotter formula for exponential sums of operators, we adapt methods used to analyze classical spin glass models to answer analogous questions about quantum models.Comment: 17 page

Path integrals and symmetry breaking for optimal control theory

This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a linear equation. The transformation is similar to the transformation used to relate the classical Hamilton-Jacobi equation to the Schr\"odinger equation. As a result of the linearity, the usual backward computation can be replaced by a forward diffusion process, that can be computed by stochastic integration or by the evaluation of a path integral. It is shown, how in the deterministic limit the PMP formalism is recovered. The significance of the path integral approach is that it forms the basis for a number of efficient computational methods, such as MC sampling, the Laplace approximation and the variational approximation. We show the effectiveness of the first two methods in number of examples. Examples are given that show the qualitative difference between stochastic and deterministic control and the occurrence of symmetry breaking as a function of the noise.Comment: 21 pages, 6 figures, submitted to JSTA

Cephalopod paralarvae and upwelling conditions off Galician waters (NW Spain)

A total of 103 cephalopod paralarvae were sampled during June 1995 in Galician waters (NW Spain). Samples were taken with Bongo nets of 300 and 500 m mesh size at 48 sampling stations along 10 transverse transects ranging from 80 to 600 m water depth. Paralarvae of loliginid squid were most abundant (40%). TheRhynchoteuthion paralarvae of ommastrephid squid accounted for 25%, whereas sepiolids comprised 23% of the total sample. Octopods were scarce, at only 6.6%. Other cephalopod families accounted for 5%. Sizes of paralarvae ranged from 1.0 to 7.1 mm mantle length. Temperature and salinity distribution showed the presence of an intense upwelling during the survey period. The sampling data obtained before and during the presence of upwelled water off Rias of Pontevedra and Vigo (southern zone) showed that paralarval cephalopod abundance and distribution were closely related to the upwelled Eastern North-Atlantic Central Water (ENACW)

Investigacion y/o innovación. Un proyecto en y para el centro educativo

Algunos de los cambios acaecidos en el campo de la epistemología de la investigación, nos obliga a revisar con un sentido más crítico mucho de lo que normalmente se investiga en la educación. La existencia de tener presente estos cambios nace de la comprobación de nuevos paradigmas en la educación; de los que la investigación tiene que ser más seriamente consciente.Una de las variables que puede incidir de forma más o menos directa es el grado de autonomía y desarrollo profesional de los profesores investigadores. Una investigación centrada en el puesto de trabajo ( Centro docente), centrada en un Proyecto, centrada en la práctica, centrada en los problemas prácticos de su clase y realizada en un concepto específico, como miembro de un colectivo (Departamento o Claustro) y que una vez planteadas las necesidades específicas de la investigación, para que el profesorado participe en el diseño, en la realización y en la evaluación de la misma.Con este documento pretendemos exponer los momentos, las finalidades y las orientaciones llevadas a cabo en un proyecto de trabajo desde la investigación-acción

Griffiths Inequalities for Ising Spin Glasses on the Nishimori Line

The Griffiths inequalities for Ising spin glasses are proved on the Nishimori line with various bond randomness which includes Gaussian and $\pm J$ bond randomness. The proof for Ising systems with Gaussian bond randomness has already been carried out by Morita et al, which uses not only the gauge theory but also the properties of the Gaussian distribution, so that it cannot be directly applied to the systems with other bond randomness. The present proof essentially uses only the gauge theory, so that it does not depend on the detail properties of the probability distribution of random interactions. Thus, the results obtained from the inequalities for Ising systems with Gaussian bond randomness do also hold for those with various bond randomness, especially with $\pm J$ bond randomness.Comment: 13pages. Submitted to J. Phys. Soc. Jp

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation

Horizontal Resorption of Fresh-Frozen Corticocancellous Bone Blocks in the Reconstruction of the Atrophic Maxilla at 5 Months

BACKGROUND: Reliable implant-supported rehabilitation of an alveolar ridge needs sufficient volume of bone. In order to achieve a prosthetic-driven positioning, bone graft techniques may be required. PURPOSE: This prospective cohort study aims to clinically evaluate the amount of resorption of corticocancellous fresh-frozen allografts bone blocks used in the reconstruction of the severe atrophic maxilla. MATERIALS AND METHODS: Twenty-two partial and totally edentulous patients underwent bone augmentation procedures with fresh-frozen allogenous blocks from the iliac crest under local anesthesia. Implants were inserted into the grafted sites after a healing period of 5 months. Final fixed prosthesis was delivered ± 4 months later. Ridge width analysis and measurements were performed with a caliper before and after grafting and at implant insertion. Bone biopsies were performed in 16 patients. RESULTS: A total of 98 onlay block allografts were used in 22 patients with an initial mean alveolar ridge width of 3.41 ± 1.36 mm. Early exposure of blocks was observed in four situations and one of these completely resorbed. Mean horizontal bone gain was 3.63 ± 1.28 mm (p < .01). Mean buccal bone resorption between allograph placement and the reopening stage was 0.49 ± 0.54 mm, meaning approximately 7.1% (95% confidence interval: [5.6%, 8.6%]) of total ridge width loss during the integration period. One hundred thirty dental implants were placed with good primary stability (≥ 30 Ncm). Four implants presented early failure before the prosthetic delivery (96.7% implant survival). All patients were successfully rehabilitated. Histomorphometric analysis revealed 20.9 ± 5.8% of vital bone in close contact to the remaining grafted bone. A positive strong correlation (adjusted R2  = 0.44, p = .003) was found between healing time and vital bone percentage. CONCLUSIONS: Augmentation procedures performed using fresh-frozen allografts from the iliac crest are a suitable alternative in the reconstruction of the atrophic maxilla with low resorption rate at 5 months, allowing proper stability of dental implants followed by fixed prosthetic rehabilitation

Replica bounds for diluted non-Poissonian spin systems

In this paper we extend replica bounds and free energy subadditivity arguments to diluted spin-glass models on graphs with arbitrary, non-Poissonian degree distribution. The new difficulties specific of this case are overcome introducing an interpolation procedure that stresses the relation between interpolation methods and the cavity method. As a byproduct we obtain self-averaging identities that generalize the Ghirlanda-Guerra ones to the multi-overlap case.Comment: Latex file, 15 pages, 2 eps figures; Weak point revised and corrected; Misprints correcte