Multiclass Data Segmentation using Diffuse Interface Methods on Graphs

We present two graph-based algorithms for multiclass segmentation of high-dimensional data. The algorithms use a diffuse interface model based on the Ginzburg-Landau functional, related to total variation compressed sensing and image processing. A multiclass extension is introduced using the Gibbs simplex, with the functional's double-well potential modified to handle the multiclass case. The first algorithm minimizes the functional using a convex splitting numerical scheme. The second algorithm is a uses a graph adaptation of the classical numerical Merriman-Bence-Osher (MBO) scheme, which alternates between diffusion and thresholding. We demonstrate the performance of both algorithms experimentally on synthetic data, grayscale and color images, and several benchmark data sets such as MNIST, COIL and WebKB. We also make use of fast numerical solvers for finding the eigenvectors and eigenvalues of the graph Laplacian, and take advantage of the sparsity of the matrix. Experiments indicate that the results are competitive with or better than the current state-of-the-art multiclass segmentation algorithms.Comment: 14 page

Ternary Bismuthide SrPtBi2: Computation and Experiment in Synergism to Explore Solid-State Materials

A combination of theoretical calculation and the experimental synthesis to explore the new ternary compound is demonstrated in the Sr-Pt-Bi system. Since Pt-Bi is considered as a new critical charge-transfer pair for superconductivity, it inspired us to investigate the Sr-Pt-Bi system. With a thorough calculation of all the known stable/metastable compounds in the Sr-Pt-Bi system and crystal structure predictions, the thermodynamic stability of hypothetical stoichiometry, SrPtBi2, is determined. Followed by the high-temperature synthesis and crystallographic analysis, the first ternary bismuthide in Sr-Pt-Bi, SrPtBi2 was prepared and the stoichiometry was confirmed experimentally. SrPtBi2 crystallizes in the space group Pnma (S.G. 62, Pearson Symbol oP48), which matches well with theoretical prediction using an adaptive genetic algorithm (AGA). Using first-principles calculations, we demonstrate that the orthorhombic structure has lower formation energies than other 112 structure types, such as tetragonal BaMnBi2 (CuSmP2) and LaAuBi2 (CuHfSi2) structure types. The bonding analysis indicates the Pt-Bi interactions play a critical role in structural stability. The physical properties measurements show the metallic properties with low electron-phonon interactions at the low temperature, which agrees with the electronic structure assessment.Comment: 12 pages, 7 figure