Approximate Capacities of Two-Dimensional Codes by Spatial Mixing

We apply several state-of-the-art techniques developed in recent advances of counting algorithms and statistical physics to study the spatial mixing property of the two-dimensional codes arising from local hard (independent set) constraints, including: hard-square, hard-hexagon, read/write isolated memory (RWIM), and non-attacking kings (NAK). For these constraints, the strong spatial mixing would imply the existence of polynomial-time approximation scheme (PTAS) for computing the capacity. It was previously known for the hard-square constraint the existence of strong spatial mixing and PTAS. We show the existence of strong spatial mixing for hard-hexagon and RWIM constraints by establishing the strong spatial mixing along self-avoiding walks, and consequently we give PTAS for computing the capacities of these codes. We also show that for the NAK constraint, the strong spatial mixing does not hold along self-avoiding walks

Bis(1,10-phenanthroline-κ2 N,N′)(sulfato-κ2 O,O′)cobalt(II) butane-2,3-diol monosolvate

In the title compound, [Co(SO4)(C12H8N2)2]·C4H10O2, the Co2+ ion has a distorted octa­hedral coordination environment composed of four N atoms from two chelating 1,10-phenanthroline ligands and two O atoms from an O,O′-bidentate sulfate anion. The dihedral angle between the two chelating N2C2 groups is 83.48 (1)°. The Co2+ ion, the S atom and the mid-point of the central C—C bond of the butane-2,3-diol solvent mol­ecule are situated on twofold rotation axes. The mol­ecules of the complex and the solvent mol­ecules are held together by pairs of symmetry-related O—H⋯O hydrogen bonds with the uncoordinated O atoms of the sulfate ions as acceptors. The solvent mol­ecule is disordered over two sets of sites with site occupancies of 0.40 and 0.60

Complete initial solutions for iterative pose estimation from planar objects

Camera pose estimation from the image of a planar object has important applications in photogrammetry and computer vision. In this paper, an efficient approach to find the initial solutions for iterative camera pose estimation using coplanar points is proposed. Starting with homography, the proposed approach provides a least-squares solution for absolute orientation, which has a relatively high accuracy and can be easily refined into one optimal pose that locates local minima of the according error function by using Gauss-Newton scheme or Lu's orthogonal iteration algorithm. In response to ambiguities that exist in pose estimation from planar objects, we propose a novel method to find initial approximation of the second pose, which is different from existing methods in its concise form and clear geometric interpretation. Thorough testing on synthetic data shows that combined with currently employed iterative optimization algorithm, the two initial solutions proposed in this paper can achieve the same accuracy and robustness as the best state-of-the-art pose estimation algorithms, while with a significant decrease in computational cost. Real experiment is also employed to demonstrate its performance