Consistency of Concave Regression with an Application to Current-Status Data

We consider the problem of nonparametric estimation of a concave regression function F. We show that the supremum distance between the least square s estimatorand F on a compact interval is typically of order(log(n)/n)2/5. This entails rates of convergence for the estimator’s derivative. Moreover, we discuss the impact of additional constraints on F such as monotonicity and pointwise bounds. Then we apply these results to the analysis of current status data, where the distribution function of the event times is assumed to be concave.

Pressure from the vacuum of confined spinor matter

Charged spinor matter field is quantized in a spatial region bounded by two parallel neutral plates. The most general set of boundary conditions ensuring the confinement of matter within the plates is considered. We study a response of the vacuum of the confined matter to the background uniform magnetic field which is directed orthogonally to the plates. It is proven that, in the case of a sufficiently strong magnetic field, the vacuum pressure onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates.

Influence of quantized massive matter fields on the Casimir effect

Charged massive matter fields of spin-0 and spin- 1/2 are quantized in the presence of an external uniform magnetic field in a spatial region bounded by two parallel plates. The most general set of boundary conditions at the plates, that is required by mathematical consistency and the self-adjointness of the Hamiltonian operator, is employed. The vacuum fluctuations of the matter field in the case of the magnetic field orthogonal to the plates are analyzed, and it is shown that the pressure from the vacuum onto the plates is positive and independent of the boundary condition, as well as of the distance between the plates. Possibilities of the detection of this new-type Casimir effect are discussed. Read More: http://www.worldscientific.com/doi/10.1142/S0217732315500996

Casimir effect with quantized charged spinor matter in background magnetic field

We study the influence of a background uniform magnetic field and boundary conditions on the vacuum of a quantized charged spinor matter field confined between two parallel neutral plates; the magnetic field is directed orthogonally to the plates. The admissible set of boundary conditions at the plates is determined by the requirement that the Dirac Hamiltonian operator be self-adjoint. It is shown that, in the case of a sufficiently strong magnetic field and a sufficiently large separation of the plates, the generalized Casimir force is repulsive, being independent of the choice of a boundary condition, as well as of the distance between the plates. The detection of this effect seems to be feasible in the foreseeable future.

CAD/CAM fabrication accuracy of long- vs. short-span implant-supported FDPs

OBJECTIVE To compare the precision of fit of long-span vs. short-span implant-supported screw-retained fixed dental prostheses (FDPs) made from computer-aided-design/computer-aided-manufactured (CAD/CAM) titanium and veneered with ceramic. The null hypothesis was that there is no difference in the vertical microgap between long-span and short-span FDPs. MATERIALS AND METHODS CAD/CAM titanium frameworks for an implant-supported maxillary FDP on implants with a flat platform were fabricated on one single master cast. Group A consisted of six 10-unit FDPs connected to six implants (FDI positions 15, 13, 11, 21, 23, 25) and group B of six 5-unit FDPs (three implants, FDI positions 21, 23, 25). The CAD/CAM system from Biodenta Swiss AG (Berneck, Switzerland) was used for digitizing (laser scanner) the master cast and anatomical CAD of each framework separately. The frameworks were milled (CAM) from a titanium grade V monobloc and veneered with porcelain. Median vertical distance between implant and FDP platforms from the non-tightened implants (one-screw test on implant 25) was calculated from mesial, buccal, and distal scanning electron microscope measurements. RESULTS All measurements showed values <40 μm. Total median vertical microgaps were 23 μm (range 2-38 μm) for group A and 7 μm (4-24 μm) for group B. The difference between the groups was statistically significant at implant 21 (P = 0.002; 97.5% CI -27.3 to -4.9) and insignificant at implant 23 (P = 0.093; -3.9 to 1.0). CONCLUSIONS CAD/CAM fabrication including laboratory scanning and porcelain firing was highly precise and reproducible for all long- and short-span FDPs. While all FDPs showed clinically acceptable values, the short-span FDPs were statistically more precise at the 5-unit span distance.

Bilateral deep brain stimulation: the placement of the second electrode is not necessarily less accurate than that of the first one.

BACKGROUND Deep brain stimulation (DBS) is recognized as an effective treatment for movement disorders. We recently changed our technique, limiting the number of brain penetrations to three per side. OBJECTIVES The first aim was to evaluate the electrode precision on both sides of surgery since we implemented this surgical technique. The second aim was to analyse whether or not the electrode placement was improved with microrecording and macrostimulation. METHODS We retrospectively reviewed operation protocols and MRIs of 30 patients who underwent bilateral DBS. For microrecording and macrostimulation, we used three parallel channels of the 'Ben Gun' centred on the MRI-planned target. Pre- and post-operative MRIs were merged. The distance between the planned target and the centre of the implanted electrode artefact was measured. RESULTS There was no significant difference in targeting precision on both sides of surgery. There was more intra-operative adjustment of the second electrode positioning based on microrecording and macrostimulation, which allowed to significantly approach the MRI-planned target on the medial-lateral axis. CONCLUSION There was more electrode adjustment needed on the second side, possibly in relation with brain shift. We thus suggest performing a single central track with electrophysiological and clinical assessment, with multidirectional exploration on demand for suboptimal clinical responses.

Search for satellites near comet 67P/Churyumov-Gerasimenko using Rosetta/OSIRIS images

Context. The European Space Agency Rosetta mission reached and started escorting its main target, the Jupiter-family comet 67P/Churyumov-Gerasimenko, at the beginning of August 2014. Within the context of solar system small bodies, satellite searches from approaching spacecraft were extensively used in the past to study the nature of the visited bodies and their collisional environment. Aims. During the approaching phase to the comet in July 2014, the OSIRIS instrument onboard Rosetta performed a campaign aimed at detecting objects in the vicinity of the comet nucleus and at measuring these objects' possible bound orbits. In addition to the scientific purpose, the search also focused on spacecraft security to avoid hazardous material in the comet's environment. Methods. Images in the red spectral domain were acquired with the OSIRIS Narrow Angle Camera, when the spacecraft was at a distance between 5785 km and 5463 km to the comet, following an observational strategy tailored to maximize the scientific outcome. From the acquired images, sources were extracted and displayed to search for plausible displacements of all sources from image to image. After stars were identified, the remaining sources were thoroughly analyzed. To place constraints on the expected displacements of a potential satellite, we performed Monte Carlo simulations on the apparent motion of potential satellites within the Hill sphere. Results. We found no unambiguous detections of objects larger than similar to 6 m within similar to 20 km and larger than similar to 1 m between similar to 20 km and similar to 110 km from the nucleus, using images with an exposure time of 0.14 s and 1.36 s, respectively. Our conclusions are consistent with independent works on dust grains in the comet coma and on boulders counting on the nucleus surface. Moreover, our analysis shows that the comet outburst detected at the end of April 2014 was not strong enough to eject large objects and to place them into a stable orbit around the nucleus. Our findings underline that it is highly unlikely that large objects survive for a long time around cometary nuclei.