Mid-sagittal plane and mid-sagittal surface optimization in brain MRI using a local symmetry measure

This paper describes methods for automatic localization of the mid-sagittal plane (MSP) and mid-sagittal sur-face (MSS). The data used is a subset of the Leukoaraiosis And DISability (LADIS) study consisting of three-dimensional magnetic resonance brain data from 62 elderly subjects (age 66 to 84 years). Traditionally, the mid-sagittal plane is localized by global measures. However, this approach fails when the partitioning plane between the brain hemispheres does not coincide with the symmetry plane of the head. We instead propose to use a sparse set of profiles in the plane normal direction and maximize the local symmetry around these using a general-purpose optimizer. The plane is parameterized by azimuth and elevation angles along with the distance to the origin in the normal direction. This approach leads to solutions confirmed as the optimal MSP in 98 percent of the subjects. Despite the name, the mid-sagittal plane is not always planar, but a curved surface resulting in poor partitioning of the brain hemispheres. To account for this, this paper also investigates an opti-mization strategy which fits a thin-plate spline surface to the brain data using a robust least median of squares estimator. Albeit computationally more expensive, mid-sagittal surface fitting demonstrated convincingly better partitioning of curved brains into cerebral hemispheres. 1

Comparative Hybrid Hartree-Fock-DFT Calculations of WO2-Terminated Cubic WO3 as Well as SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) Surfaces

We greatly acknowledge the financial support via the ERAF Project No. 1.1.1.1/18/A/073. Calculations were performed using Latvian Super Cluster (LASC), located in the Center of Excellence at Institute of Solid State Physics, the University of Latvia, which is supported by European Union Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-Teaming Phase 2 under Grant Agreement No. 739508, project CAMART.We performed, to the best of our knowledge, the world’s first first-principles calculations for the WO2-terminated cubic WO3 (001) surface and analyzed the systematic trends in the WO3, SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) surface ab initio calculations. According to our first principles calculations, all WO2 or TiO2-terminated WO3, SrTiO3, BaTiO3, PbTiO3 and CaZrO3 (001) surface upper-layer atoms relax inwards towards the crystal bulk, while all second-layer atoms relax upwards. The only two exceptions are outward relaxations of first layer WO2 and TiO2-terminated WO3 and PbTiO3 (001) surface O atoms. The WO2 or TiO2-terminated WO3, SrTiO3, BaTiO3, PbTiO3 and CaTiO3 (001) surface-band gaps at the Γ–Γ point are smaller than their respective bulk-band gaps. The Ti–O chemical bond populations in the SrTiO3, BaTiO3, PbTiO3 and CaTiO3 bulk are smaller than those near the TiO2-terminated (001) surfaces. Conversely, the W–O chemical bond population in the WO3 bulk is larger than near the WO2-terminated WO3 (001) surface.---//---This work is licensed under a CC BY 4.0 license.ERAF Project No. 1.1.1.1/18/A/073; Institute of Solid State Physics, University of Latvia as the Center of Excellence has received funding from the European Union’s Horizon 2020 Framework Programme H2020-WIDESPREAD-01-2016-2017-TeamingPhase2 under grant agreement No. 739508, project CAMART²