Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

An Electromagnetic Tracker System for the design of a dental superstructure

Nowadays, different techniques are available for manufacturing full-arch implant-supported prosthesis, many of them based on an impression procedure. Nevertheless, the long-term success of the prosthesis is highly influenced by the accuracy during such process, being affected by factors such as the impression material, implant position, angulation and depth. This paper investigates the feasibility of a 3D electromagnetic motion tracking system as an acquisition method for modeling such prosthesis. To this extent, we propose an implant acquisition method at the patient mouth, using a specific prototyped tool coupled with a tracker sensor, and a set of calibration procedures (for distortion correction and tool calibration), that ultimately obtains combined measurements of the implant’s position and angulation, and eliminating the use of any impression material. However, in the particular case of the evaluated tracking system, the order of magnitude of the obtained errors invalidates its use for this specific application.

Electromagnetic tracker feasibility in the design of a dental superstructure for edentulous patients

The success of the osseointegration concept and the Brånemark protocol is highly associated to the accuracy in the production of an implant-supported prosthesis. One of most critical steps for long-term success of these prosthesis is the accuracy obtained during the impression procedure, which is affected by factors such as the impression material, implant position, angulation and depth. This paper investigates the feasibility of 3D electromagnetic motion tracking systems as an acquisition method for modeling full-arch implant-supported prosthesis. To this extent, we propose an implant acquisition method at the patient mouth and a calibration procedure, based on a 3D electromagnetic tracker that obtains combined measurements of implant’s position and angulation, eliminating the use of any impression material. Three calibration algorithms (namely linear interpolation, higher-order polynomial and Hardy multiquadric) were tested to compensate for the electromagnetic tracker distortions introduced by the presence of nearby metals. Moreover, implants from different suppliers were also tested to study its impact on tracking accuracy. The calibration methodology and the algorithms employed proved to implement a suitable strategy for the evaluation of novel dental impression techniques. However, in the particular case of the evaluated electromagnetic tracking system, the order of magnitude of the obtained errors invalidates its use for the full-arch modeling of implant-supported prosthesis.

Assessment of Laparoscopic Skills Performance: 2D Versus 3D Vision and Classic Instrument Versus New Hand-Held Robotic Device for Laparoscopy

Introduction and Objectives. Laparoscopic surgery has undeniable advantages, such as reduced postoperative pain, smaller incisions, and faster recovery. However, to improve surgeons’ performance, ergonomic adaptations of the laparoscopic instruments and introduction of robotic technology are needed. The aim of this study was to ascertain the influence of a new hand-held robotic device for laparoscopy (HHRDL) and 3D vision on laparoscopic skills performance of 2 different groups, naïve and expert. Materials and Methods. Each participant performed 3 laparoscopic tasks—Peg transfer, Wire chaser, Knot—in 4 different ways. With random sequencing we assigned the execution order of the tasks based on the first type of visualization and laparoscopic instrument. Time to complete each laparoscopic task was recorded and analyzed with one-way analysis of variance. Results. Eleven experts and 15 naïve participants were included. Three-dimensional video helps the naïve group to get better performance in Peg transfer, Wire chaser 2 hands, and Knot; the new device improved the execution of all laparoscopic tasks (P < .05). For expert group, the 3D video system benefited them in Peg transfer and Wire chaser 1 hand, and the robotic device in Peg transfer, Wire chaser 1 hand, and Wire chaser 2 hands (P < .05). Conclusion. The HHRDL helps the execution of difficult laparoscopic tasks, such as Knot, in the naïve group. Three-dimensional vision makes the laparoscopic performance of the participants without laparoscopic experience easier, unlike those with experience in laparoscopic procedures.