Empirical Bayes Method for Boltzmann Machines

The framework of the empirical Bayes method allows the estimation of the values of the hyperparameters in the Boltzmann machine by maximizing a specific likelihood function referred to as the empirical Bayes likelihood function. However, the maximization is computationally difficult because the empirical Bayes likelihood function involves intractable integrations of the partition function. The method presented in this chapter avoids this computational problem by using the replica method and the Plefka expansion, which is quite simple and fast because it does not require any iterative procedures and gives reasonable estimates under certain conditions.

Hydrostatic Stress and Fatigue Crack Growth of Notched Ti6Al4V in Aggressive Media

The behavior of structures, machine or components made of composite materials or light high-performance alloys is still a great concern for applications in which high strength-to-mas-ratio is a fundamental requirement. Procedures to detect flaws of small initial cracks and evaluate fatigue crack growth are nowadays essentials for high performance flying or ground machines (airplanes, automobiles,...). Structural reliability and structural health monitoring are considered in this paper and the surface replica method is deepened. Numerical FEM models were developed to assist the surface replica method analysis of the results. Ti6Al4V alloy was considered. This paper is a short technical communication.

Foam Replica Method in the Manufacturing of Bioactive Glass Scaffolds: Out-of-Date Technology or Still Underexploited Potential?

Since 2006, the foam replica method has been commonly recognized as a valuable technology for the production of highly porous bioactive glass scaffolds showing three-dimensional, open-cell structures closely mimicking that of natural trabecular bone. Despite this, there are important drawbacks making the usage of foam-replicated glass scaffolds a difficult achievement in clinical practice; among these, certainly the high operator-dependency of the overall manufacturing process is one of the most crucial, limiting the scalability to industrial production and, thus, the spread of foam-replicated synthetic bone substitutes for effective use in routine management of bone defect. The present review opens a window on the versatile world of the foam replica technique, focusing the dissertation on scaffold properties analyzed in relation to various processing parameters, in order to better understand which are the real issues behind the bottleneck that still puts this technology on the Olympus of the most used techniques in laboratory practice, without moving, unfortunately, to a more concrete application. Specifically, scaffold morphology, mechanical and mass transport properties will be reviewed in detail, considering the various templates proposed till now by several research groups all over the world. In the end, a comprehensive overview of in vivo studies on bioactive glass foams will be provided, in order to put an emphasis on scaffold performances in a complex three-dimensional environment.

Entanglement between two disjoint universes

We use the replica method to compute the entanglement entropy of a universe without gravity entangled in a thermofield-double-like state with a disjoint gravitating universe. Including wormholes between replicas of the latter gives an entropy functional which includes an “island” on the gravitating universe. We solve the back-reaction equations when the cosmological constant is negative to show that this island coincides with a causal shadow region that is created by the entanglement in the gravitating geometry. At high entanglement temperatures, the island contribution to the entropy functional leads to a bound on entanglement entropy, analogous to the Page behavior of evaporating black holes. We demonstrate that the entanglement wedge of the non-gravitating universe grows with the entanglement temperature until, eventually, the gravitating universe can be entirely reconstructed from the non-gravitating one.

Evaluation of Internal Fit and Marginal Adaptation of Provisional Crowns Fabricated with Three Different Techniques

Different techniques have been used to construct provisional crowns to protect prepared teeth. The purpose of this in vitro study was to assess the internal fit and marginal discrepancy of provisional crowns made by different methods. A total of 48 provisional crowns were constructed and divided into three groups (n = 16) according to the fabrication methods: fabricated manually-group MAN; computer-aided design/computer aided manufacturing technology-group CAM; and 3-dimensional (3D)-printed technology-group 3DP. The same standard tessellation language (STL) file was used for both CAD/CAM and 3D-printed group. The silicone-checked method was used to measure the internal gap distance. The marginal discrepancy was measured by using the polyvinyl siloxane (PVS) replica method and swept-source optical coherence tomography (OCT) scanning technique. Data were analyzed with one-way analysis of variance (ANOVA) nonparametric Kruskal-Wallis and Tukey tests at α = 0.05. At the central pit and axial walls, the gap distance mean values of group CAM were higher than those from group MAN and 3DP. The group 3DP was statistically significantly higher in gap distance at the location of occlusion than group MAN and group CAM (p < 0.05). The total gap distances assessed by silicone-checked method revealed there were no statistically significant differences between the tested groups (p > 0.05). The total mean values of absolute and horizontal marginal discrepancy of the group 3DP obtained by using the PVS-replica method and OCT scanning technique were significantly higher than the group MAN and CAM (p < 0.05). Regression correlation results of marginal discrepancy indicated a positive correlation (r = 0.902) between PVS-replica method and OCT scanning technique. The manually fabricated provisional crowns presented better internal fit and a smaller marginal discrepancy. Between different assessment techniques for marginal adaptation, PVS-replica method and OCT scanning technique have a positive correlation.

Evaluation of Cavitation Damage in a Pipe Bend Made of 0.5Cr-0.5Mo-0.3V Steel by Optical Metallography and Replica Method

Prolongation of the service life of key components of fossil-fuelled power plants beyond their original design limit must be accompanied by thorough and extensive monitoring of the actual material state and particularly creep damage. The extent of cavitation is nowadays routinely tested in-situ by using replica method and its quantification is based on practices stated in VGB-TW 507, NORDTEST NT TR 302 derived from the original Neubauer's classification of cavitation damage. Evaluation of cavitation damage based on the measurement of the number of cavities and/or creep micro-cracks has become a routine activity, but in cases when steel contains large amount of non-metallic inclusions, they can be wrongly identified as cavities and to invalidate the result of calculation of cavitation damage. Comparative analysis of cavitation damage was performed in a pipe bend and its weldment made of a low-alloy 0.5Cr-0.5Mo-0.3V steel creep exposed at 540 °C for more than 225,000 hours by using OM (SEM) and replica method and revealed the comparative extent of cavitation damage decreasing from the outer to inner surface of the pipe wall.