Nonlocal Flow of Convex Plane Curves and Isoperimetric Inequalities

In the first part of the paper we survey some nonlocal flows of convex plane curves ever studied so far and discuss properties of the flows related to enclosed area and length, especially the isoperimetric ratio and the isoperimetric difference. We also study a new nonlocal flow of convex plane curves and discuss its evolution behavior. In the second part of the paper we discuss necessary and sufficient conditions (in terms of the (mixed) isoperimetric ratio or (mixed) isoperimetric difference) for two convex closed curves to be homothetic or parallel.Comment: 23 page

Semi-Supervised Domain Adaptation with Source Label Adaptation

Semi-Supervised Domain Adaptation (SSDA) involves learning to classify unseen target data with a few labeled and lots of unlabeled target data, along with many labeled source data from a related domain. Current SSDA approaches usually aim at aligning the target data to the labeled source data with feature space mapping and pseudo-label assignments. Nevertheless, such a source-oriented model can sometimes align the target data to source data of the wrong classes, degrading the classification performance. This paper presents a novel source-adaptive paradigm that adapts the source data to match the target data. Our key idea is to view the source data as a noisily-labeled version of the ideal target data. Then, we propose an SSDA model that cleans up the label noise dynamically with the help of a robust cleaner component designed from the target perspective. Since the paradigm is very different from the core ideas behind existing SSDA approaches, our proposed model can be easily coupled with them to improve their performance. Empirical results on two state-of-the-art SSDA approaches demonstrate that the proposed model effectively cleans up the noise within the source labels and exhibits superior performance over those approaches across benchmark datasets. Our code is available at https://github.com/chu0802/SLA .Comment: Accepted by CVPR 202

Surface and Edge States in Topological Semi-metals

We study the topologically non-trivial semi-metals by means of the 6-band Kane model. Existence of surface states is explicitly demonstrated by calculating the LDOS on the material surface. In the strain free condition, surface states are divided into two parts in the energy spectrum, one part is in the direct gap, the other part including the crossing point of surface state Dirac cone is submerged in the valence band. We also show how uni-axial strain induces an insulating band gap and raises the crossing point from the valence band into the band gap, making the system a true topological insulator. We predict existence of helical edge states and spin Hall effect in the thin film topological semi-metals, which could be tested with future experiment. Disorder is found to significantly enhance the spin Hall effect in the valence band of the thin films