Abstract Wilson loop diagrams are an important tool in studying scattering amplitudes of SYM $N=4$ theory and known by previous work to be associated positroids. In this paper, we study the structure positroids, as well denominator integrand defined each diagram. We give algorithm derive Grassmann necklace positroid directly from diagram, a recursive proof that dimension these cells is thrice n...

The metric dimension problem was first introduced in 1975 by Slater [35], and independently by Harary and Melter [16] in 1976; however the problem for hypercube was studied (and solved asymptotically) much earlier in 1963 by Erdős and Rényi [10]. A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of...

Trust has been found to be important for integrating suppliers ́ knowledge in new product development (NPD). Different degrees of trust have different consequences for NPD. This paper investigates the effects of trust for capturing supplier knowledge in NPD in different situations. Two different NPD collaborations, identified as polar cases, are studied. The findings indicate differences in know...

[This article examines whether trust or fiduciary law provides potential ‘stolen wages’ plaintiffs with a strong basis for a claim over money in bank accounts that previous governments held on the plaintiffs’ behalf. It also considers the broader issue of whether governments owed a fiduciary duty flowing from their obligations under general ‘protective’ legislation to prevent such workers from ...

Conformal field theory (CFT) is important in modern particle physics in various contexts. The most powerful tool in the 2-dimensional CFT is the operator product expansion (OPE). The OPE between the energy-momentum tensor and an operator extracts its conformal weight. We find it interesting to consider the similar issue with respect to the Wilson loop in a conformally invariant Yang-Mills theor...

Starting with intersecting M2-branes in M-theory, the IIA supertube can be found by S compactification followed by a boost to the speed of light in the 11th dimension. A similar procedure applied to DonaldsonUhlenbeck-Yau instantons on C, viewed as intersecting membranes of D = 7 supersymmetric Yang-Mills (SYM) theory, yields (for finite boost) a new set of 1/4 BPS equations for D = 6 SYM-Higgs...

Recently, it was shown by Jevicki, Kazama and Yoneya (JKY) that the SuperYang-Mills theories (SYM) in D ≤ 4 can reproduce the conformal symmetry of the near-horizon geometry of the D-brane solutions. However, the eikonal approximation they used is not sufficient for analyzing the conformal symmetry in SYM. We carry out the 1-loop calculation beyond the eikonal approximation for D = 1 SYM (i.e.,...

We introduce a novel and exciting research area: symmetrising levels of consistency to produce stronger forms of consistency and more efficient mechanisms for establishing them. We propose new levels of consistency for Constraint Satisfaction Problems (CSPs) incorporating the symmetry group of a CSP. We first define Sym(i, j)-consistency, show that even Sym(1,0)-consistency can prune usefully, ...