Lattice rules are a quasi-Monte Carlo method, an alternative to the Monte Carlo method for multidimensional numerical integration. The measures of performance that we estimate by simulation can be seen as the values of integrals in large dimensions. Therefore, instead of the usual Monte Carlo method, one can use lattice rules in simulation. In this paper, we compare these rules to the Monte Car...

Several different families of quaternary codes related to Reed-Muller binary linear codes can be found in the literature. Two definitions of such families are denoted as ZRM−(r,m) and {RMs(r,m)}. In the current paper ZRM−(r,m− 1) and {RMs(r,m)} codes are shown to be equal exactly for s = 0 (0 ≤ s ≤ bm−1 2 c). Therefore, for the above-mentioned value of s, Z4-linear Reed-Muller codes with the sa...

In this paper we introduce a family of planar, modular and self-similar graphs which have small-world and scale-free properties. The main parameters of this family are comparable to those of networks associated to complex systems, and therefore the graphs are of interest as mathematical models for these systems. As the clustering coefficient of the graphs is zero, this family is an explicit con...

We present a dynamic off-equilibrium method for the study of continuous transitions, which represents a dynamic generalization of the usual equilibrium cumulant method. Its main advantage is that critical parameters are derived from numerical data obtained much before equilibrium has been attained. Therefore, the method is particularly useful for systems with long equilibration times, like spin...

The BO neutral, cationic, and anionic molecular species have been painstakingly studied through multireference configuration interaction and single reference coupled cluster methods employing basis sets of quintuple cardinality. Potential energy curves have been constructed for 38 (BO), 37 (BO(+)), and 12 (BO(-)) states and the usual molecular parameters have been extracted most of which are in...