Most classical constructions of low-discrepancy point sets are based on generalizations of the one-dimensional binary van der Corput sequence whose implementation requires non-trivial bit-operations. As an alternative we introduce the quasi-regular golden ratio sequences which are based on the fractional part of successive integer multiples of the golden ratio. By leveraging results from number...

For a graph G, let fij be the number of spanning rooted forests in which vertex j belongs to a tree rooted at i. In this paper, we show that for a path, the fij’s can be expressed as the products of Fibonacci numbers; for a cycle, they are products of Fibonacci and Lucas numbers. The doubly stochastic graph matrix is the matrix F = (fij)n×n f , where f is the total number of spanning rooted for...

Several methods to perform exact computations on real numbers have been proposed in the literature. In some of these methods real numbers are represented by innnite (lazy) strings of digits. It is a well known fact that, when this approach is taken, the standard digit notation cannot be used. New forms of digit notations are necessary. The usual solution to this representation problem consists ...

In this paper, we give a pedagogical introduction to several beautiful formulas discovered by Ramanujan. Using these results, we evaluate a Ramanujan-type integral formula. The result can be expressed in terms of the Golden Ratio.

We propose a simple modification of a well-known Random Walk algorithm for solving the Satisfiability problem and analyze its performance on random CNFs with a planted solution. We rigorously prove that the new algorithm solves the Full CNF with high probability, and for random CNFs with a planted solution of high density finds an assignment that differs from the planted in only ε-fraction of v...

Gait is known to be an effective behavioral biometric trait for the identification of individuals. However, clothing has a dramatic influence on the recognition rate. Researchers have attempted to deal with this issue of clothing by segmenting parts of the gait images based on anatomical proportions. However, the clothing proportion is not the same as the anatomical proportion, as clothing is d...

The golden ratio primal-dual algorithm (GRPDA) is a new variant of the classical Arrow--Hurwicz method for solving structured convex optimization problems, in which objective function consists sum two closed proper functions, one involves composition with linear transform. same as and popular (PDA) Chambolle Pock, GRPDA full-splitting sense that it does not rely on any subproblems or system equ...