On symmetric commutator subgroups, braids, links and homotopy groups

In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for braid and surface groups.Comment: 24 pages, 1 figur

Flux rope proxies and fan-spine structures in active region NOAA 11897

Employing the high-resolution observations from the Solar Dynamics Observatory (SDO) and the Interface Region Imaging Spectrograph (IRIS), we statistically investigate flux rope proxies in NOAA AR 11897 from 14-Nov-2013 to 19-Nov-2013 and display two fan-spine structures in this AR. For the first time, we detect flux rope proxies of NOAA 11897 for total 30 times in 4 different locations. These flux rope proxies were either tracked in both lower and higher temperature wavelengths or only detected in hot channels. Specially, none of these flux rope proxies was observed to erupt, but just faded away gradually. In addition to these flux rope proxies, we firstly detect a secondary fan-spine structure. It was covered by dome-shaped magnetic fields which belong to a larger fan-spine topology. These new observations imply that considerable amounts of flux ropes can exist in an AR and the complexity of AR magnetic configuration is far beyond our imagination.Comment: 8 pages, 8 figures, Accepted for publication in A&

Evaluation of ASTER GDEM ver2 using GPS measurements and SRTM ver4.1 in China

The freely available ASTER GDEM ver2 was released by NASA and METI on October 17, 2011. As one of the most complete high resolution digital topographic data sets of the world to date, the ASTER GDEM covers land surfaces between 83°N and 83°S at a spatial resolution of 1 arc-second and will be a useful product for many applications, such as relief analysis, hydrological studies and radar interferometry. The stated improvements in the second version of ASTER GDEM benefit from finer horizontal resolution, offset adjustment and water body detection in addition to new observed ASTER scenes. This study investigates the absolute vertical accuracy of the ASTER GDEM ver2 at five study sites in China using ground control points (GCPs) from high accuracy GPS benchmarks, and also using a DEM-to-DEM comparison with the Consultative Group for International Agriculture Research Consortium for Spatial Information (CGIAR-CSI) SRTM DEM (Version 4.1). And then, the results are separated into GlobCover land cover classes to derive the spatial pattern of error. It is demonstrated that the RMSE (19m) and mean (-13m) values of ASTER GDEM ver2 against GPS-GCPs in the five study areas is lower than its first version ASTER GDEM ver1 (26m and -21m) as a result of the adjustment of the elevation offsets in the new version. It should be noted that the five study areas in this study are representative in terms of terrain types and land covers in China, and even for most of mid-latitude zones. It is believed that the ASTER GDEM offers a major alternative in accessibility to high quality elevation data

Flexible protein folding by ant colony optimization

Protein structure prediction is one of the most challenging topics in bioinformatics. As the protein structure is found to be closely related to its functions, predicting the folding structure of a protein to judge its functions is meaningful to the humanity. This chapter proposes a flexible ant colony (FAC) algorithm for solving protein folding problems (PFPs) based on the hydrophobic-polar (HP) square lattice model. Different from the previous ant algorithms for PFPs, the pheromones in the proposed algorithm are placed on the arcs connecting adjacent squares in the lattice. Such pheromone placement model is similar to the one used in the traveling salesmen problems (TSPs), where pheromones are released on the arcs connecting the cities. Moreover, the collaboration of effective heuristic and pheromone strategies greatly enhances the performance of the algorithm so that the algorithm can achieve good results without local search methods. By testing some benchmark two-dimensional hydrophobic-polar (2D-HP) protein sequences, the performance shows that the proposed algorithm is quite competitive compared with some other well-known methods for solving the same protein folding problems

Enhanced collectivity in neutron-deficient Sn isotopes in energy functional based collective Hamiltonian

The low-lying collective states in Sn isotopes are studied by a five-dimensional collective Hamiltonian with parameters determined from the triaxial relativistic mean-field calculations using the PC-PK1 energy density functional. The systematics for both the excitation energies of $2^+_1$ states and $B(E2;0^+_1\to 2^+_1)$ values are reproduced rather well, in particular, the enhanced E2 transitions in the neutron-deficient Sn isotopes with N<66. We show that the gradual degeneracy of neutron levels 1g7/2 and 2d5/2 around the Fermi surface leads to the increase of level density and consequently the enhanced paring correlations from N=66 to 58. It provokes a large quadrupole shape fluctuation around the spherical shape, and leads to an enhanced collectivity in the isotopes around N=58.Comment: 5 pages, 4 figures, accepted for publication in Physics Letters