Quasi-random (also called low discrepancy) sequences are a deterministic alternative to random sequences for use in Monte Carlo methods, such as integration and particle simulations of transport processes. The error in uniformity for such a sequence of N points in the s-dimensional unit cube is measured by its discrepancy, which is of size (log N) N-Ifor large N, as opposed to discrepancy of si...

Owing to the symmetry between drive–response systems, discussions of synchronization performance are greatly significant while exploring dynamics neural network systems. This paper investigates quasi-synchronization (QS) and quasi-uniform (QUS) issues systems on fractional-order variable-parameter networks (VPNNs) including probabilistic time-varying delays. The effects system parameters, proba...

We demonstrate a one-to-one correspondence between idempotent closure operators and the so-called saturated quasi-uniform structures on category C. Not only this result allows to obtain categorical counterpart P of Császár-Pervin quasi-uniformity P, that we characterize as transitive compatible with an interior operator, but also permits describe those topogenous orders are induced by The P⁎ P−...

We characterize probabilities in Bayesian networks in terms of algebraic expressions called quasi-probabilities. These are arrived at by casting Bayesian networks as noisy AND-OR-NOT networks, and viewing the subnetworks that lead to a node as arguments for or against a node. Quasiprobabilities are in a sense the “natural” algebra of Bayesian networks: we can easily compute the marginal quasi-p...

The probabilistic roadmap (PRM) planner is a popular method for robot motion planning problems with many degrees of freedom. However, it has been shown that the method performs less well in situations where the robot has to pass through a narrow passage in the scene. This is mainly due to the uniformity of the sampling used in the planner; it places many samples in large open regions and too fe...

Two moving mesh partial differential equations (MMPDEs) with spatial smoothing are derived based upon the equidistribution principle. This smoothing technique is motivated by the robust moving mesh method of Dorfi and Drury [J. Comput. Phys., 69 (1987), pp. 175–195]. It is shown that under weak conditions the basic property of no node-crossing is preserved by the spatial smoothing, and a local ...

We present deterministic sequences for use in sampling-based approaches to motion planning. They simultaneously combine the qualities found in many other sequences: i) the incremental and self-avoiding tendencies of pseudo-random sequences, ii) the lattice structure provided by multiresolution grids, and iii) lowdiscrepancy and low-dispersion measures of uniformity provided by quasi-random sequ...

We consider planar systems driven by a central force which depends periodically on time. If the force is sublinear and attractive, then there is a connected set of subharmonic and quasi-periodic solutions rotating around the origin at different speeds; moreover, this connected set stretches from zero to infinity. The result still holds allowing the force to be attractive only in average provide...

Appendix A: Properties of EDS grids In this appendix, we characterize the dispersion of points, the number of points, and the degree of uniformity of the constructed EDS. Also, we discuss the relation of our results to recent mathematical literature. A.1 Dispersion of points in EDS grids We borrow the notion of dispersion from the literature on quasi-Monte Carlo optimization methods; see, for e...

Monte Carlo is one of the most versatile and widely used numerical methods. Its convergence rate, O(N~^), is independent of dimension, which shows Monte Carlo to be very robust but also slow. This article presents an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques. Accelerated convergence for Monte Ca...