In this work we present RESCU, a powerful MATLAB-based Kohn-Sham density functional theory (KS-DFT) solver. We demonstrate that RESCU can compute the electronic structure properties of systems comprising many thousands of atoms using modest computer resources, e.g. 16 to 256 cores. Its computational efficiency is achieved from exploiting four routes. First, we use numerical atomic orbital (NAO) techniques to efficiently generate a good quality initial subspace which is crucially required by Chebyshev filtering methods. Second, we exploit the fact that only a subspace spanning the occupied Kohn-Sham states is required, and solving accurately the KS equation using eigensolvers can generally be avoided. Third, by judiciously analyzing and optimizing various parts of the procedure in RESCU, we delay the O(N 3 ) scaling to large N , and our tests show that RESCU scales consistently as O(N 2.3 ) from a few hundred atoms to more than 5,000 atoms when using a real space grid discretization. The scaling is better or comparable in a NAO basis up to the 14,000 atoms level. Fourth, we exploit various numerical algorithms and, in particular, we introduce a partial Rayleigh-Ritz algorithm to achieve efficiency gains for systems comprising more than 10,000 electrons. We demonstrate the power of RESCU in solving KS-DFT problems using many examples running on 16, 64 and/or 256 cores: a 5,832 Si atoms supercell; a 8,788 Al atoms supercell; a 5,324 Cu atoms supercell and a small DNA molecule submerged in 1,713 water molecules for a total 5,399 atoms. The KS-DFT is entirely converged in a few hours in all cases. Our results suggest that the RESCU method has reached a milestone of solving thousands of atoms by KS-DFT on a modest computer cluster.
A quantum computer (QC) can solve many computational problems more efficiently than a classic one. The field of QCs is growing: companies (such as DWave, IBM, Google, and Microsoft) are building QC offerings. We position that software engineers should look into defining a set of software engineering practices that apply to QC's software. To start this process, we give examples of challenges associated with testing such software and sketch potential solutions to some of these challenges.
BackgroundProtein structure comparison is a fundamental task in structural biology. While the number of known protein structures has grown rapidly over the last decade, searching a large database of protein structures is still relatively slow using existing methods. There is a need for new techniques which can rapidly compare protein structures, whilst maintaining high matching accuracy.ResultsWe have developed IR Tableau, a fast protein comparison algorithm, which leverages the tableau representation to compare protein tertiary structures. IR tableau compares tableaux using information retrieval style feature indexing techniques. Experimental analysis on the ASTRAL SCOP protein structural domain database demonstrates that IR Tableau achieves two orders of magnitude speedup over the search times of existing methods, while producing search results of comparable accuracy.ConclusionWe show that it is possible to obtain very significant speedups for the protein structure comparison problem, by employing an information retrieval style approach for indexing proteins. The comparison accuracy achieved is also strong, thus opening the way for large scale processing of very large protein structure databases.
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