Amplitude Relations in Non-linear Sigma Model

In this paper, we investigate tree-level scattering amplitude relations in $U(N)$ non-linear sigma model. We use Cayley parametrization. As was shown in the recent works [23,24] both on-shell amplitudes and off-shell currents with odd points have to vanish under Cayley parametrization. We prove the off-shell $U(1)$ identity and fundamental BCJ relation for even-point currents. By taking the on-shell limits of the off-shell relations, we show that the color-ordered tree amplitudes with even points satisfy $U(1)$-decoupling identity and fundamental BCJ relation, which have the same formations within Yang-Mills theory. We further state that all the on-shell general KK, BCJ relations as well as the minimal-basis expansion are also satisfied by color-ordered tree amplitudes. As a consequence of the relations among color-ordered amplitudes, the total $2m$-point tree amplitudes satisfy DDM form of color decomposition as well as KLT relation.Comment: 27 pages, 8 figures, 4 tables, JHEP style, improved versio

Covariant Hamiltonian boundary term: Reference and quasi-local quantities

The Hamiltonian for dynamic geometry generates the evolution of a spatial region along a vector field. It includes a boundary term which determines both the value of the Hamiltonian and the boundary conditions. The value gives the quasi-local quantities: energy-momentum, angular-momentum and center-of-mass. The boundary term depends not only on the dynamical variables but also on their reference values; the latter determine the ground state (having vanishing quasi-local quantities). For our preferred boundary term for Einstein's GR we propose 4D isometric matching and extremizing the energy to determine the reference metric and connection values.Comment: 6 pages, contribution to the Proceedings of the Second LeCosPA Symposium "Everything about Gravity", Taipei, 14-18 Dec., 201

Modifying the DPClus algorithm for identifying protein complexes based on new topological structures

<p>Abstract</p> <p>Background</p> <p>Identification of protein complexes is crucial for understanding principles of cellular organization and functions. As the size of protein-protein interaction set increases, a general trend is to represent the interactions as a network and to develop effective algorithms to detect significant complexes in such networks.</p> <p>Results</p> <p>Based on the study of known complexes in protein networks, this paper proposes a new topological structure for protein complexes, which is a combination of subgraph diameter (or average vertex distance) and subgraph density. Following the approach of that of the previously proposed clustering algorithm DPClus which expands clusters starting from seeded vertices, we present a clustering algorithm IPCA based on the new topological structure for identifying complexes in large protein interaction networks. The algorithm IPCA is applied to the protein interaction network of Sacchromyces cerevisiae and identifies many well known complexes. Experimental results show that the algorithm IPCA recalls more known complexes than previously proposed clustering algorithms, including DPClus, CFinder, LCMA, MCODE, RNSC and STM.</p> <p>Conclusion</p> <p>The proposed algorithm based on the new topological structure makes it possible to identify dense subgraphs in protein interaction networks, many of which correspond to known protein complexes. The algorithm is robust to the known high rate of false positives and false negatives in data from high-throughout interaction techniques. The program is available at <url>http://netlab.csu.edu.cn/bioinformatics/limin/IPCA</url>.</p