[en] Evaluation of the cerebellum and vermis is one of the integral parts of the fetal cranial anomaly screening. The aim of this study was to create a nomogram for fetal vermis measurements between 17 and 30 gestational weeks. This prospective study was conducted on 171 volunteer pregnant women between March 2013 and December 2014. Measurements of the fetal cerebellar vermis diameters in the sagittal plane were performed by two-dimensional transabdominal ultrasonography. Optimal median planes were obtained in 117 of the cases. Vermian diameters as a function of gestational age were expressed by regression equations and the correlation coefficients were found to be highly statistically significant (P < 0.001). The normal mean (± standard deviation) for each gestational week was also defined. This study presents the normal range of the two-dimensional fetal vermian measurements between 17 and 30 gestational weeks. In the absence of a three-dimensional ultrasonography, two-dimensional ultrasonography could also be used confidently with more time and effort

[en] We enumerate the labelled and unlabelled d-regular maps on two-dimensional oriented surfaces of arbitrary genus g. The case of d-regular maps with a single face is considered separately in more detail.

[en] This paper presents a new approach to automatic three-dimensional (3D) cephalometric annotation for diagnosis, surgical planning, and treatment evaluation. There has long been considerable demand for automated cephalometric landmarking, since manual landmarking requires considerable time and experience as well as objectivity and scrupulous error avoidance. Due to the inherent limitation of two-dimensional (2D) cephalometry and the 3D nature of surgical simulation, there is a trend away from current 2D to 3D cephalometry. Deep learning approaches to cephalometric landmarking seem highly promising, but there exist serious difficulties in handling high dimensional 3D CT data, dimension referring to the number of voxels. To address this issue of dimensionality, this paper proposes a shadowed 2D image-based machine learning method which uses multiple shadowed 2D images with various lighting and view directions to capture 3D geometric cues. The proposed method using VGG-net was trained and tested using 2700 shadowed 2D images and corresponding manual landmarkings. Test data evaluation shows that our method achieved an average point-to-point error of 1.5 mm for the seven major landmarks. (paper)

[en] We give an algorithm for counting self-avoiding walks or self-avoiding polygons of length n that runs in time on 2-dimensional lattices and time on d-dimensional lattices for d  >  2. (paper)

[en] The exotic electronic band structures of Ruby and Star lattices, characterized by Dirac cone and nontrivial topology, offer a unique platform for the study of two-dimensional (2D) Dirac materials. In general, an ideal isotropic Dirac cone is protected by time reversal symmetry and inversion, so that its robustness against lattice distortion is not only of fundamental interest but also crucial to practical applications. Here we systematically investigate the robustness of Dirac cone in a Ruby lattice against four typical lattice distortions that break the inversion and/or mirror symmetry in the transition from Ruby to Star. Using a tight-binding approach, we show that the isotropic Dirac cones and their related topological features remain intact in the rotationally distorted lattices that preserve the inversion symmetry (i-Ruby lattice) or the in-plane mirror symmetry (m-Ruby lattice). On the other hand, the Dirac cones are gapped in the a- and b-Ruby lattices that break both these lattice symmetries or inversion. Furthermore, a rotational unitary matrix is identified to transform the original into the distorted lattice. The symmetry-protected Dirac cones were also verified in photonic crystal systems. The robust Dirac cones revealed in the non-mirror symmetric i-Ruby and non-centrosymmetric m-Ruby lattices provide a general guidance for the design of 2D Dirac materials. (paper)

[en] We present a two-dimensional particle–particle–particle-mesh (P³M) algorithm with an optimized Green’s function and adaptive softening length for gravitational lensing studies in N-body simulations. The analytical form of the optimized Green’s function $\stackrel{^<!--\; ^\; -->}{G}(\mathit{k})$ is given. The softening schemes (S) are studied for both the particle-mesh (PM) and the particle–particle (PP) calculations in order for accurate force calculation and suppression of the particle discreteness effect. Our method is two orders of magnitude more accurate than the simple PM algorithm with the poor man’s Green’s function (∝ 1/k ²) at a scale of a few mesh cells or smaller. The force anisotropy is also much smaller than the conventional PM calculation. We can achieve a force accuracy better than 0.1% at all scales with our algorithm, which makes it an ideal (accurate and fast) algorithm for microlensing studies. When we apply the algorithm to computing weak and strong lensing quantities in N-body simulations, the errors are dominated by the Poisson noise caused by particle discreteness. The Poisson noise can be suppressed by smoothing out the particle distribution, which can be achieved by simply choosing an adaptive softening length in the PP calculation. We have presented a criterion to set the adaptive softening length. Our algorithm is also applicable to cosmological simulations. We provide a python implementation P3Mlens for this algorithm.

[en] The tunable two-dimensional photonic crystals band gap, absolute photonic band gap and semi-Dirac point are beneficial to designing the novel optical devices. In this paper, tunable photonic band gaps structure was realized by a new type two-dimensional function photonic crystals, which dielectric constants of medium columns are functions of space coordinates. However for the two-dimensional conventional photonic crystals the dielectric constant does not change with space coordinates. As the parameter adjustment, we found that the photonic band gaps structures are dielectric constant function coefficient, medium columns radius, dielectric constant function form period number and pump light intensity dependent, namely, the photonic band gaps position and width can be tuned. we also obtained absolute photonic band gaps and semi-Dirac point in the photonic band gaps structures of two-dimensional function photonic crystals. These results provide an important theoretical foundation for design novel optical devices.

[en] We propose a workable scheme for generating a bulk valley pump current in a silicene-based device which consists of two pumping regions characterized by time-dependent strain and staggered potentials, respectively. In a one-dimension model, we show that a pure valley current can be generated, in which the two valley currents have the same magnitude but flow in opposite directions. Besides, the pumped valley current is quantized and maximized when the Fermi energy of the system locates in the bandgap opened by the two pumping potentials. Furthermore, the valley current can be finely controlled by tuning the device parameters. Our results are useful for the development of valleytronic devices based on two-dimensional materials. (paper)

[en] Two-dimensional hexagonal boron nitride (h-BN) as an emerging nanomaterial exhibits unique physicochemical properties, making it suitable candidate for a wide spectrum of applications. However, due to its poor functionality, the processability of this nanomaterial is low. In this work, we report on a straightforward and scalable approach for the functionalization of h-BN by nitrene [2 + 1] cycloaddition at room temperature. The triazine-functionalized h-BN (Trz-BNs) showed a high reactivity toward nucleophiles, through which post-modifications are performable. The post-modification of Trz-BNs by L-cysteine was studied using cyclic voltammetry and differential pulse voltammetry. Taking advantage of the scalable and straightforward functionalization as well as ability of triazine functional groups for the controlled post-modifications, Trz-BNs is a promising nanoplatform for a wide range of future applications. (paper)

[en] In this paper, spintronic properties of a mono-layer GaTe under biaxial and uniaxial strain is investigated. Here, spin properties of two structures of GaTe, one with mirror symmetry and the other with inversion symmetry, is studied. We have also calculated the band structure of GaTe with and without spin–orbit coupling to find out the importance of spin–orbit interaction (SOI) on its band structure. We find band gap can be modified by applying spin–orbit coupling in the presence of strain. We explore Mexican-hat dispersion for different structures and different strain. We find Mexican-hat can be tuned by strain however some cases shows any Mexican-hat. We calculate spin-splitting in conduction and valence band in the presence of strain where the structure with inversion symmetry doesn’t show any splitting. We find in some cases, GaTe indicates Rashba dispersion that can be adjusted by strain. The amount of Rashba parameters may be in the order of other reported two-dimensional materials. (paper)