We design, analyze and test a golden ratio primal–dual algorithm (GRPDA) for solving structured convex optimization problem, where the objective function is sum of two closed proper functions, one which involves composition with linear transform. GRPDA preserves all favorable features classical (PDA), i.e., primal dual variables are updated in Gauss–Seidel manner, per iteration cost dominated b...

We determine the maximal set of moves for 2-pile take-away games with prescribed P -positions (bαnc, bβnc) for n ∈ Z≥1 where α ∈ (1, 2) is irrational, 1/α+1/β = 1. This was done in [3] for the special case α = golden ratio. We generalize the infinite Fibonacci word to an infinite wordW with alphabet Σ = {a, b}, in which α replaces the golden ratio, and we analyze the set {s ∈ Z≥0 : W(s) = b, W(...

An observation was made in this research regarding the fact that the signatures of isotropic charge distributions in silicon nanowire transistors (NWT) displayed identical characteristics to the golden ratio (Phi). In turn, a simulation was conducted regarding ultra-scaled n-type Si (NWT) with respect to the 5-nm complementary metal-oxide-semiconductor (CMOS) application. The results reveal tha...

We propose a new declustering scheme for allocating uniform multidimensional data among parallel disks. The scheme, aimed at reducing disk access time for range queries, is based on Golden Ratio Sequences for two dimensions and Kronecker Sequences for higher dimensions. Using exhaustive simulation, we show that, in two dimensions, the worst-case (additive) deviation of the scheme from the optim...

Fragment-based drug discovery (FBDD) is complementary to high-throughput screening. The approach has two key stages: identifying the starting fragment hit to be developed and generating the lead compound from the starting fragment hit. Here, we provide an overview of FBDD and introduce two indices originally developed at Astellas Pharma. The first is related to the size ratio of fragment hits t...

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 infinite (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...

Given a finite set of real numbers A, the generalised golden ratio is the unique real number G(A) > 1 for which we only have trivial unique expansions in smaller bases, and have non-trivial unique expansions in larger bases. We show that G(A) varies continuously with the alphabet A (of fixed size). What is more, we demonstrate that as we vary a single parameter m within A, the generalised golde...

UNLABELLED This study aimed to investigate the association of facial proportion and its relation to the golden ratio with the evaluation of facial appearance among Malaysian population. This was a cross-sectional study with 286 randomly selected from Universiti Sains Malaysia (USM) Health Campus students (150 females and 136 males; 100 Malaysian Chinese, 100 Malaysian Malay and 86 Malaysian Ind...