Numerical analysis of a Neumann boundary control problem with a stochastic parabolic equation

This paper analyzes the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where an additive noise occurs in the Neumann boundary condition. The convergence is established for general filtrations, and the convergence rate $O(\tau^{1/4-\epsilon} + h^{1/2-\epsilon})$ is derived for the natural filtration of the Q-Wiener process

Extremely large magnetoresistance in topologically trivial semimetal α\alpha-WP2_2

Extremely large magnetoresistance (XMR) was recently discovered in many non-magnetic materials, while its underlying mechanism remains poorly understood due to the complex electronic structure of these materials. Here, we report an investigation of the $\alpha$-phase WP$_2$, a topologically trivial semimetal with monoclinic crystal structure (C2/m), which contrasts to the recently discovered robust type-II Weyl semimetal phase in $\beta$-WP$_2$. We found that $\alpha$-WP$_2$ exhibits almost all the characteristics of XMR materials: the near-quadratic field dependence of MR, a field-induced up-turn in resistivity following by a plateau at low temperature, which can be understood by the compensation effect, and high mobility of carriers confirmed by our Hall effect measurements. It was also found that the normalized MRs under different magnetic fields has the same temperature dependence in $\alpha$-WP$_2$, the Kohler scaling law can describe the MR data in a wide temperature range, and there is no obvious change in the anisotropic parameter $\gamma$ value with temperature. The resistance polar diagram has a peanut shape when field is rotated in $\textit{ac}$ plane, which can be understood by the anisotropy of Fermi surface. These results indicate that both field-induced-gap and temperature-induced Lifshitz transition are not the origin of up-turn in resistivity in the $\alpha$-WP$_2$ semimetal. Our findings establish $\alpha$-WP$_2$ as a new reference material for exploring the XMR phenomena.Comment: 18 pages, 12 figure

Nonrigid Registration of Brain Tumor Resection MR Images Based on Joint Saliency Map and Keypoint Clustering

This paper proposes a novel global-to-local nonrigid brain MR image registration to compensate for the brain shift and the unmatchable outliers caused by the tumor resection. The mutual information between the corresponding salient structures, which are enhanced by the joint saliency map (JSM), is maximized to achieve a global rigid registration of the two images. Being detected and clustered at the paired contiguous matching areas in the globally registered images, the paired pools of DoG keypoints in combination with the JSM provide a useful cluster-to-cluster correspondence to guide the local control-point correspondence detection and the outlier keypoint rejection. Lastly, a quasi-inverse consistent deformation is smoothly approximated to locally register brain images through the mapping the clustered control points by compact support radial basis functions. The 2D implementation of the method can model the brain shift in brain tumor resection MR images, though the theory holds for the 3D case