Two A5 modular symmetries for Golden Ratio 2 mixing

Two 'Golden Ratio' indices in fragment-based drug discovery.

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...

Problem of Erdös – Vershik for Golden Ratio

Golden Ratio Sequences for Low-Discrepancy Sampling

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...

A Golden Ratio Notation for the Real

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 ...

Detecting Modular ACU Structural Symmetries

We present an efficient encoding of order-sorted modular ACU terms into colored directed graphs. Then, by computing the automorphism groups of the encoded graphs, we are able to extract modular ACU structural symmetries both inside a term and across a set of terms. Finally, we show how the computed symmetries can be applied to the optimization of the equational generalization algorithms for mod...