On the Convergence of (Stochastic) Gradient Descent with Extrapolation for Non-Convex Optimization

Extrapolation is a well-known technique for solving convex optimization and variational inequalities and recently attracts some attention for non-convex optimization. Several recent works have empirically shown its success in some machine learning tasks. However, it has not been analyzed for non-convex minimization and there still remains a gap between the theory and the practice. In this paper, we analyze gradient descent and stochastic gradient descent with extrapolation for finding an approximate first-order stationary point in smooth non-convex optimization problems. Our convergence upper bounds show that the algorithms with extrapolation can be accelerated than without extrapolation

Evidence of the side jump mechanism in the anomalous Hall effect in paramagnets

Persistent confusion has existed between the intrinsic (Berry curvature) and the side jump mechanisms of anomalous Hall effect (AHE) in ferromagnets. We provide unambiguous identification of the side jump mechanism, in addition to the skew scattering contribution in epitaxial paramagnetic Ni$_{34}$Cu$_{66}$ thin films, in which the intrinsic contribution is by definition excluded. Furthermore, the temperature dependence of the AHE further reveals that the side jump mechanism is dominated by the elastic scattering

Half Metallic Bilayer Graphene

Charge neutral bilayer graphene has a gapped ground state as transport experiments demonstrate. One of the plausible such ground states is layered antiferromagnetic spin density wave (LAF) state, where the spins in top and bottom layers have same magnitude with opposite directions. We propose that lightly charged bilayer graphene in an electric field perpendicular to the graphene plane may be a half metal as a consequence of the inversion and particle-hole symmetry broken in the LAF state. We show this explicitly by using a mean field theory on a 2-layer Hubbard model for the bilayer graphene.Comment: 4+ pages, 4 figure

4-{(Z)-(sec-Butyl­amino)(phen­yl)methyl­ene}-3-methyl-1-phenyl-1H-pyrazol-5(4H)-one

In the title compound, C21H23N3O, the dihedral angles formed by the pyrazolone ring with two phenyl rings are 10.38 (8) and 76.94 (6)°. The sec-butyl­amino group is disordered over two positions, with refined site-occupancy factors of 0.730 (4) and 0.270 (4). The compound could potentially be ligand stabilized in the solid state in a keto–enamine tautomeric form. The amine functionality is involved in an intra­molecular N—H⋯O hydrogen bond, while weak inter­molecular C—H⋯O and C—H⋯N hydrogen bonds participate in the formation of the crystal structure

Endoglin Is Essential for the Maintenance of Self-Renewal and Chemoresistance in Renal Cancer Stem Cells.

Renal cell carcinoma (RCC) is a deadly malignancy due to its tendency to metastasize and resistance to chemotherapy. Stem-like tumor cells often confer these aggressive behaviors. We discovered an endoglin (CD105)-expressing subpopulation in human RCC xenografts and patient samples with a greater capability to form spheres in vitro and tumors in mice at low dilutions than parental cells. Knockdown of CD105 by short hairpin RNA and CRISPR/cas9 reduced stemness markers and sphere-formation ability while accelerating senescence in vitro. Importantly, downregulation of CD105 significantly decreased the tumorigenicity and gemcitabine resistance. This loss of stem-like properties can be rescued by CDA, MYC, or NANOG, and CDA might act as a demethylase maintaining MYC and NANOG. In this study, we showed that Endoglin (CD105) expression not only demarcates a cancer stem cell subpopulation but also confers self-renewal ability and contributes to chemoresistance in RCC