Very recently, a new concept called multiplicative differential and the corresponding c-differential uniformity were introduced by Ellingsen et al. (IEEE Trans. Inform. Theory 66(9), 5781–5789 2020). A function F(x) over finite field GF(pn) to itself is said have δ, or equivalent, differentially (c,δ)-uniform, when maximum number of solutions x ∈GF(pn) F(x + a) − cF(x) = b, a,b,c ∈GF(pn), c≠ 1 ...

In this paper, we establish a deterministic error bound for estimating a functional of the solution of the integral transport equation via random walks that improves an earlier result of Chelson generalizing the Koksma-Hlawka inequality for nite dimensional quadrature. We solve such problems by simulation, using sequences that combine pseudorandom and quasirandom elements in the construction of...

Infinitely divisible random vector without Gaussian component admits representations of shot noise series. Due to possible slow convergence of the series, they have not been investigated as a device for Monte Carlo simulation. In this paper, we investigate the structure of shot noise series representations from a simulation point of view and discuss the effectiveness of quasi-Monte Carlo method...

The Hermite radial basis functions (HRBFs) implicits have been used to reconstruct surfaces from scattered Hermite data points. In this work, we propose a closed-form formulation to construct HRBF-based implicits by a quasi-solution approximating the exact solution. A scheme is developed to automatically adjust the support sizes of basis functions to hold the error bound of a quasi-solution. Ou...

The Hermite radial basis functions (HRBFs) implicits have been used to reconstruct surfaces from scattered Hermite data points. In this work, we propose a closed-form formulation to construct HRBF-based implicits by a quasi-solution approximating the exact solution. A scheme is developed to automatically adjust the support sizes of basis functions to hold the error bound of a quasi-solution. Ou...

This self-contained tutorial surveys the state of the art in quasi-Monte Carlo rendering algorithms as used for image synthesis in the product design and movie industry. Based on the number theoretic constructions of low discrepancy sequences, it explains techniques to generate light transport paths to connect cameras and light sources. Summing up their contributions on the image plane results ...

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...

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...