Geometric Algebra to Model Uncertainties in the Di

Authors: Rafael Alves Carlile Lavor

Publish Date: 2016/03/21

Volume: 27, Issue: 1, Pages: 439-452

PDF Link

Abstract

The discretizable molecular distance geometry problem DMDGP is related to the determination of 3D protein structure using distance information detected by nuclear magnetic resonance NMR experiments The chemistry of proteins and the NMR distance information allow us to define an atomic order v 1ldotsv n such that the distances related to the pairs v i3v iv i2v iv i1v i for i 3 are available which implies that the search space can be represented by a tree A DMDGP solution can be represented by a path from the root to a leaf node of this tree found by an exact method called branchandprune BP Because of uncertainty in NMR data some of the distances related to the pairs v i3v i may not be precise values being represented by intervals of real numbers underlined i3ioverlined i3i In order to apply BP algorithm in this context sample values from those intervals should be taken The main problem of this approach is that if we sample many values the search space increases drastically and for small samples no solution can be found We explain how geometric algebra can be used to model uncertainties in the DMDGP avoiding sample values from intervals underlined i3ioverlined i3i and eliminating the heuristic characteristics of BP when dealing with interval distances

Keywords: