Unlocking of time reversal, space-time inversion and rotation invariants in magnetic materials

Time reversal (T ) and space inversion are symmetries of our universe in the low-energy limit. Fundamental theorems relate their corresponding quantum numbers to the spin for elementary particles: Tˆ2 = (PˆTˆ)2 = −1 for half-odd-integer spins and Tˆ2 = (PˆTˆ)2 = +1 for integer spins. Here we show that for elementary excitations in magnetic materials, this “locking” between quantum numbers is lifted: Tˆ2 and (PˆTˆ)2 take all four combinations of +1 and −1 regardless of the value of the spin, where T now represents the composite symmetry of time reversal and lattice translation. Unlocked quantum numbers lead to new forms of minimal coupling between these excitations and external fields, enabling novel physical phenomena such as the “cross-Lamor precession”, indirectly observable in a proposed light-absorption experiment. We list the magnetic space groups with certain high-symmetry momenta where such excitations may be found.

Deformation corrected workflow for maxillofacial prosthesis modelling

The purpose of this article is to describe a deformation corrected workflow for maxillofacial prosthesis modelling based on the improved Laplace and iterative closest point–based iterative algorithms. For incomplete maxillofacial data with local deformed symmetrical features, the Laplace algorithm with rotation invariants was demonstrated that the operations can recover the local deformation while preserving the surface geometric detail; the M-estimation iterative closest point–based iterative algorithm integrated with the extended Gaussian image ensures the precision of the symmetry plane, making the outer point having almost no effect on the minimum process. The additional experiments also verified the ability of deformation corrected maxillofacial prosthesis modelling. Case study confirmed that this workflow is attractive and has potential to design the desired maxillofacial prosthesis for correcting the deformed oral soft tissue. The results of this study improve the quality of maxillofacial prostheses modelling. This technique will facilitate modelling of maxillofacial prostheses while helping the patients predict the effect before the prosthesis is manufactured. In addition, this deformation corrected workflow has great potential for improving the development of maxillofacial prosthesis modelling software.

Gaussian-Geometric Moments and its Application in Feature Matching

Since the 7 famous Hus invariants had been introduced in 1960s, the moment invariants play an important role in image analysis and pattern recognition. In this paper, we propose a new moment called Gaussian-Geometric moment, and derived their translation and rotation invariants. One significant conclusion drawn is that the rotation invariants of Gaussian-Geometric moments have the identical forms to those of geometric moments.The Gaussian-Geometric moments and the geometric moments both can represent the image information, difference is that the Gaussian-Geometric moment can represent the center information of an image and the geometric moments represent the edge information of an imageonly. This is particularly evident in the performance of high order ones. Another important property of Gaussian-Geometric moments is that it has a scale parameter which allows choosing the best scale to represent the interest region of an image. A detailed comparison has been made to test the feature matching capability between the proposed moments and the geometric moments. The results show that the proposed moments perform much better than the geometric ones.