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.
This paper explores solutions for enabling efficient supports of position independence of pointer-based data structures on byteaddressable None-Volatile Memory (NVM). When a dynamic data structure (e.g., a linked list) gets loaded from persistent storage into main memory in different executions, the locations of the elements contained in the data structure could differ in the address spaces from one run to another. As a result, some special support must be provided to ensure that the pointers contained in the data structures always point to the correct locations, which is called position independence. This paper shows the insufficiency of traditional methods in supporting position independence on NVM. It proposes a concept called implicit self-contained representations of pointers, and develops two such representations named off-holder and Region ID in Value (RIV) to materialize the concept. Experiments show that the enabled representations provide much more efficient and flexible support of position independence for dynamic data structures, alleviating a major issue for effective data reuses on NVM. CCS CONCEPTS • Hardware ! Memory and dense storage; • Computer systems organization ! Architectures; • Software and its engineering ! Compilers; General programming languages;
Xu [Jianwei Xu, J. Phys. A: Math. Theor. 45 405304 (2012)] generalized geometric quantum discord [B. Dakic, V. Vedral, andČ. Brukner, Phys. Rev. Lett. 105 190502 (2010)] to multipartite states and proposed a geometric global quantum discord. Almost at the same time, Hassan and Joag [J. Phys. A: Math. Theor. 45 345301 (2012)] introduced total quantum correlations in a general N-partite quantum state and obtained exact computable formulas for the total quantum correlations in a N-qubit quantum state. In this paper, we pointed out that the geometric global quantum discord and the total quantum correlations are identical. We derive the analytical formulas of the geometric global quantum discord and geometric quantum discord for two-qubit X states, respectively, and give five concrete examples to demonstrate the use of our formulas. Finally, we prove that the geometric quantum discord is a tight lower bound of the geometric global quantum discord.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.