The Hartree-Fock-Bogoliubov equation for the ground states of even-even atomic nuclei is solved using the canonical representation in the coordinate space for zero range interactions like the Skyrme force. The gradient method is improved for faster convergence to the solutions under constraint of orthogonality between canonical orbitals. Necessity of the cut-off of the pairing interaction is sh...

In this paper, we present an extension of the state-of-theart normalized graph cut method based on asymmetry of the affinity matrix. We provide algorithms for classification and clustering problems and show how our method can improve solutions for unequal and overlapped data distributions. The proposed approaches are based on the theoretical relation between classification accuracy, mutual info...

We analyze several heuristics for nding a maximum planar subgraph of a nonplanar graph. The problem is NP-hard, although heuristics which perform well in practice have been reported. In particular, we compare the two principle methods, based on path addition and vertex addition, respectively , with an incremental method, a \cycle packing" approach, and a branch-and-cut algorithm. For the incre-...

A new class of solutions to Laplacian growth (LG) with zero surface tension is presented and shown to contain all other known solutions as special or limiting cases. These solutions, which are time-dependent conformal maps with branch cuts inside the unit circle, are governed by a nonlinear integral equation and describe oil fjords with non-parallel walls in viscous fingering experiments in Hel...

Recursive spectral bisection (RSB) is a heuristic technique for finding a minimum cut graph bisection. To use this method the second eigenvector of the Laplacian of the graph is computed and from it a bisection is obtained. The most common method is to use the median of the components of the second eigenvector to induce a bisection. We prove here that this median cut method is optimal in the se...