Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules

We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dimensional smooth functions over the unit cube as they achieve the near optimal order of convergence. The main problem addressed in this paper is to find an efficient way of computing the worst-case error. A general algorithm is presented and explicit expressions for base~2 are given. To obtain an efficient component-by-component construction algorithm we exploit the structure of the underlying cyclic group. We compare our new higher order multivariate quadrature rules to existing quadrature rules based on higher order digital nets by computing their worst-case error. These numerical results show that the higher order polynomial lattice rules improve upon the known constructions of quasi-Monte Carlo rules based on higher order digital nets

Educational Mobile Robots In Cloud-Based Framework For Laboratory Environment

This article describes the development of architecture cloud-based for control different robotic platform to be used as an interdisciplinary teaching tool integrated in the curriculum. The results obtained with this educational approach for control robotic platform shown that a practical-learning approach usage in conjunction with highly motivating topics and promotes academic success and improves theoretical concepts comprehension. Students increased knowledge and skills during the problem resolution and achieved a real solution according their options. Moreover, this approach provides students an extensive learning experience on current technologies, architectures, modules and programming languages

Educational Mobile Robots In Cloud-Based Framework For Laboratory Environment

This article describes the development of architecture cloud-based for control different robotic platform to be used as an interdisciplinary teaching tool integrated in the curriculum. The results obtained with this educational approach for control robotic platform shown that a practical-learning approach usage in conjunction with highly motivating topics and promotes academic success and improves theoretical concepts comprehension. Students increased knowledge and skills during the problem resolution and achieved a real solution according their options. Moreover, this approach provides students an extensive learning experience on current technologies, architectures, modules and programming languages

Parallel Pseudorandom Number Generation Using Additive Lagged-Fibonacci Recursions

. We study the suitability of the additive lagged-Fibonacci pseudorandom number generator for parallel computation. This generator has a relatively short period with respect to the size of its seed. However, the short period is more than made up for with the huge number of full-period cycles it contains. We call these different full-period cycles equivalence classes. We show how to enumerate the equivalence classes and how to compute seeds to select a given equivalence class. The use of these equivalence classes gives an explicit parallelization suitable for a fully reproducible asynchronous MIMD implementation. To explore such an implementation we introduce an exponential sum measure of quality for the additive lagged-Fibonacci generators used in serial or parallel. We then prove the first non-trivial results we are aware of on this measure of quality. 1. Introduction. In Knuth's well known exposition on pseudorandom number generation [5], several methods of generation are considered..

On the Security of Diffie-Hellman Bits

Boneh and Venkatesan have recently proposed a polynomial time algorithm for recovering a "hidden" element α of a finite field IFp of p elements from rather short strings of the most significant bits of the remainder modulo p o