Inducing a probability distribution in Stochastic Multicriteria Acceptability Analysis

In multiple criteria decision aiding, very often the alternatives are compared by means of a value function compatible with the preferences expressed by the Decision Maker. The problem is that, in general, there is a plurality of compatible value functions, and providing a final recommendation on the problem at hand considering only one of them could be considered arbitrary to some extent. For such a reason, Stochastic Multicriteria Acceptability Analysis gives information in statistical terms by taking into account a sample of models compatible with the provided preferences. These statistics are given assuming the existence of a probability distribution in the space of value functions being defined a priori. In this paper, we propose some methods aiming to build a probability distribution on the space of value functions considering the preference information given by the Decision Maker. To prove the goodness of our proposal we performed an extensive set of simulations. Moreover, a sensitivity analysis on the variables of our procedure has been done as well

Sinus Floor Elevation with Modified Crestal Approach and Single Loaded Short Implants: A Case Report with 4 Years of Follow-Up

Tooth extraction is usually followed by bone reduction. In the maxillary posterior region, this remodelling combined with sinus pneumatisation and periodontal defects may lead to a reduced basal bone height available for implant placement. Sinus floor elevation can be performed with different surgical techniques. Crestal approach has demonstrated to be effective, less invasive, and associated with a reduced morbidity. This article reports a modified sinus floor elevation by means of rotary, noncutting instruments, addition of xenograft, and 2 short-threaded implant placements. The aim of the study was to evaluate the implant’s success and intrasinus radiographical bone gain after 4 years of functional loading. The premolar implant site presented a starting basal bone height of 6 mm, while the molar site was of 2 mm. In the first surgical step, sinus floor elevation was performed mesially and the implant was inserted, and distally only sinus floor elevation was performed. After 6 months, the mesial implant was uncovered and the second implant was inserted; 4 months later, the second fixture was uncovered, and both fixtures were loaded with single provisional screw-retained crowns and later with single screw-retained porcelain fused to metal crowns. Implants integrated successfully, and crestal bone remodelling did not exceed the smooth collar. Bone gain was 3 mm for the mesial implant and more than 5 mm for the distal one

Comparison among Classical, Probabilistic and Quantum Algorithms for Hamiltonian Cycle problem

The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a Hamiltonian cycle problem, using different models of computations and especially the probabilistic and quantum ones. Starting from the classical probabilistic approach of random walks, we take a step to the quantum direction by involving an ad hoc designed Quantum Turing Machine (QTM), which can be a useful conceptual project tool for quantum algorithms. Introducing several constraints to the graphs, our analysis leads to not-exponential speedup improvements to the best-known algorithms. In particular, the results are based on bounded degree graphs (graphs with nodes having a maximum number of edges) and graphs with the right limited number of nodes and edges to allow them to outperform the other algorithms