The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Towards W b bbar + j at NLO with an automatized approach to one-loop computations

We present results for the O(alpha_s) virtual corrections to q g -> W b bbar q' obtained with a new automatized approach to the evaluation of one-loop amplitudes in terms of Feynman diagrams. Together with the O(alpha_s) corrections to q q' -> W b bbar g, which can be obtained from our results by crossing symmetry, this represents the bulk of the next-to-leading order virtual QCD corrections to W b bbar + j and W b + j hadronic production, calculated in a fixed-flavor scheme with four light flavors. Furthermore, these corrections represent a well defined and independent subset of the 1-loop amplitudes needed for the NNLO calculation of W b bbar. Our approach was tested against several existing results for NLO amplitudes including selected O(alpha_s) one-loop corrections to W + 3 j hadronic production. We discuss the efficiency of our method both with respect to evaluation time and numerical stability.Comment: 14 pages, 3 figure

Perception Of Visual Speed While Moving

During self-motion, the world normally appears stationary. In part, this may be due to reductions in visual motion signals during self-motion. In 8 experiments, the authors used magnitude estimation to characterize changes in visual speed perception as a result of biomechanical self-motion alone (treadmill walking), physical translation alone (passive transport), and both biomechanical self-motion and physical translation together (walking). Their results show that each factor alone produces subtractive reductions in visual speed but that subtraction is greatest with both factors together, approximating the sum of the 2 separately. The similarity of results for biomechanical and passive self-motion support H. B. Barlow\u27s (1990) inhibition theory of sensory correlation as a mechanism for implementing H. Wallach\u27s (1987) compensation for self-motion. (PsycINFO Database Record (c) 2013 APA, all rights reserved)(journal abstract