Constructing Sobol' sequences with better two-dimensional projections

Direction numbers for generating Sobol' sequences that satisfy the so-called Property A in up to 1111 dimensions have previously been given in Joe and Kuo [ACM Trans. Math. Software, 29 (2003), pp. 49–57]. However, these Sobol' sequences may have poor two-dimensional projections. Here we provide a new set of direction numbers alleviating this problem. These are obtained by treating Sobol' sequences in d dimensions as (t, d)-sequences and then optimizing the t-values of the two-dimensional projections. Our target dimension is 21201

Component-by-component construction of good intermediate-rank lattice rules

It is known that the generating vector of a rank-1 lattice rule can be constructed component-by-component to achieve strong tractability error bounds in both weighted Korobov spaces and weighted Sobolev spaces. Since the weights for these spaces are nonincreasing, the first few variables are in a sense more important than the rest. We thus propose to copy the points of a rank-1 lattice rule a number of times in the first few dimensions to yield an intermediate-rank lattice rule. We show that the generating vector (and in weighted Sobolev spaces, the shift also) of an intermediate-rank lattice rule can also be constructed component-by-component to achieve strong tractability error bounds. In certain circumstances, these bounds are better than the corresponding bounds for rank-1 lattice rules

A fast 3-D object recognition algorithm for the vision system of a special-purpose dexterous manipulator

A fast 3-D object recognition algorithm that can be used as a quick-look subsystem to the vision system for the Special-Purpose Dexterous Manipulator (SPDM) is described. Global features that can be easily computed from range data are used to characterize the images of a viewer-centered model of an object. This algorithm will speed up the processing by eliminating the low level processing whenever possible. It may identify the object, reject a set of bad data in the early stage, or create a better environment for a more powerful algorithm to carry the work further

Naturalness of scale-invariant NMSSMs with and without extra matter

We present a comparative and systematic study of the fine tuning in Higgs sectors in three scale-invariant NMSSM models: the first being the standard $Z_3$-invariant NMSSM; the second is the NMSSM plus additional matter filling $3(5+\bar{5})$ representations of SU(5) and is called the NMSSM+; while the third model comprises $4(5+\bar{5})$ and is called the NMSSM++. Naively, one would expect the fine tuning in the plus-type models to be smaller than that in the NMSSM since the presence of extra matter relaxes the perturbativity bound on $\lambda$ at the low scale. This, in turn, allows larger tree-level Higgs mass and smaller loop contribution from the stops. However we find that LHC limits on the masses of sparticles, especially the gluino mass, can play an indirect, but vital, role in controlling the fine tuning. In particular, working in a semi-constrained framework at the GUT scale, we find that the masses of third generation stops are always larger in the plus-type models than in the NMSSM without extra matter. This is an RGE effect which cannot be avoided, and as a consequence the fine tuning in the NMSSM+ ($\Delta \sim 200$) is significantly larger than in the NMSSM ($\Delta \sim 100$), with fine tuning in the NMSSM++ ($\Delta \sim 600$) being significantly larger than in the NMSSM+.Comment: 31 pages, 22 figures, published versio