Automatic Brain Tumor Segmentation using Cascaded Anisotropic Convolutional Neural Networks

A cascade of fully convolutional neural networks is proposed to segment multi-modal Magnetic Resonance (MR) images with brain tumor into background and three hierarchical regions: whole tumor, tumor core and enhancing tumor core. The cascade is designed to decompose the multi-class segmentation problem into a sequence of three binary segmentation problems according to the subregion hierarchy. The whole tumor is segmented in the first step and the bounding box of the result is used for the tumor core segmentation in the second step. The enhancing tumor core is then segmented based on the bounding box of the tumor core segmentation result. Our networks consist of multiple layers of anisotropic and dilated convolution filters, and they are combined with multi-view fusion to reduce false positives. Residual connections and multi-scale predictions are employed in these networks to boost the segmentation performance. Experiments with BraTS 2017 validation set show that the proposed method achieved average Dice scores of 0.7859, 0.9050, 0.8378 for enhancing tumor core, whole tumor and tumor core, respectively. The corresponding values for BraTS 2017 testing set were 0.7831, 0.8739, and 0.7748, respectively.Comment: 12 pages, 5 figures. MICCAI Brats Challenge 201

K\"ahler-Ricci Flow on Projective Bundles over K\"ahler-Einstein Manifolds

We study the K\"ahler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_\Sigma \oplus L)$ over compact K\"ahler-Einstein manifold $\Sigma^n$. Assuming the initial K\"ahler metric $\omega_0$ admits a U(1)-invariant momentum profile, we give a criterion, characterized by the triple $(\Sigma, L, [\omega_0])$, under which the $\mathbb{P}^1$-fiber collapses along the K\"ahler-Ricci flow and the projective bundle converges to $\Sigma$ in Gromov-Hausdorff sense. Furthermore, the K\"ahler-Ricci flow must have Type I singularity and is of (\C^n \times \mathbb{P}^1)-type. This generalizes and extends part of Song-Weinkove's work \cite{SgWk09} on Hirzebruch surfaces.Comment: revised version for publication, to appear in Trans. Amer. Math. So

A New Species of \u3ci\u3eHydrochara\u3c/i\u3e (Coleoptera: Hydrophilidae) from the Western Great Lakes Region

A new species Hydrochara simula (Coleoptera: Hydrophilidae) is described from Wis- consin and separated from other western Great Lakes species by a key. It is similar to H. obtusata (Say) and H. soror Smetana, but males can be easily recognized by a dorso-basal concavity of the aedeagus. Females can be distinguished from H. obtusata and H. soror by the more elongate penultimate segment of the maxillary palpus and other less consistent characters

Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these algebras (including as examples the symmetric groups and generalised blob algebras) are tautologically equal to the associated $p$-Kazhdan-Lusztig polynomials, provided that the characteristic is greater than the Coxeter number. We hence give an elementary and more explicit proof of the main theorem of Riche-Williamson's recent monograph and extend their categorical equivalence to cyclotomic Hecke algebras, thus solving Libedinsky-Plaza's categorical blob conjecture