Two-level Chebyshev filter based complementary subspace method: pushing the envelope of large-scale electronic structure calculations

We describe a novel iterative strategy for Kohn-Sham density functional theory calculations aimed at large systems (> 1000 electrons), applicable to metals and insulators alike. In lieu of explicit diagonalization of the Kohn-Sham Hamiltonian on every self-consistent field (SCF) iteration, we employ a two-level Chebyshev polynomial filter based complementary subspace strategy to: 1) compute a set of vectors that span the occupied subspace of the Hamiltonian; 2) reduce subspace diagonalization to just partially occupied states; and 3) obtain those states in an efficient, scalable manner via an inner Chebyshev-filter iteration. By reducing the necessary computation to just partially occupied states, and obtaining these through an inner Chebyshev iteration, our approach reduces the cost of large metallic calculations significantly, while eliminating subspace diagonalization for insulating systems altogether. We describe the implementation of the method within the framework of the Discontinuous Galerkin (DG) electronic structure method and show that this results in a computational scheme that can effectively tackle bulk and nano systems containing tens of thousands of electrons, with chemical accuracy, within a few minutes or less of wall clock time per SCF iteration on large-scale computing platforms. We anticipate that our method will be instrumental in pushing the envelope of large-scale ab initio molecular dynamics. As a demonstration of this, we simulate a bulk silicon system containing 8,000 atoms at finite temperature, and obtain an average SCF step wall time of 51 seconds on 34,560 processors; thus allowing us to carry out 1.0 ps of ab initio molecular dynamics in approximately 28 hours (of wall time).Comment: Resubmitted version (version 2

The endoribonucleolytic N-terminal half of Escherichia coli RNase E is evolutionarily conserved in Synechocystis sp. and other bacteria but not the C-terminal half, which is sufficient for degradosome assembly

Escherichia coli RNase E, an essential single-stranded specific endoribonuclease, is required for both ribosomal RNA processing and the rapid degradation of mRNA. The availability of the complete sequences of a number of bacterial genomes prompted us to assess the evolutionarily conservation of bacterial RNase E. We show here that the sequence of the N-terminal endoribonucleolytic domain of RNase E is evolutionarily conserved in Synechocystis sp. and other bacteria. Furthermore, we demonstrate that the Synechocystis sp. homologue binds RNase E substrates and cleaves them at the same position as the E. coli enzyme. Taken together these results suggest that RNase E-mediated mechanisms of RNA decay are not confined to E. coli and its close relatives. We also show that the C-terminal half of E. coli RNase E is both sufficient and necessary for its physical interaction with the 3'-5' exoribonuclease polynucleotide phosphorylase, the RhlB helicase, and the glycolytic enzyme enolase, which are components of a "degradosome" complex. Interestingly, however, the sequence of the C-terminal half of E. coli RNase E is not highly conserved evolutionarily, suggesting diversity of RNase E interactions with other RNA decay components in different organisms. This notion is supported by our finding that the Synechocystis sp. RNase E homologue does not function as a platform for assembly of E. coli degradosome components

Chebyshev polynomial filtered subspace iteration in the Discontinuous Galerkin method for large-scale electronic structure calculations

The Discontinuous Galerkin (DG) electronic structure method employs an adaptive local basis (ALB) set to solve the Kohn-Sham equations of density functional theory (DFT) in a discontinuous Galerkin framework. The adaptive local basis is generated on-the-fly to capture the local material physics, and can systematically attain chemical accuracy with only a few tens of degrees of freedom per atom. A central issue for large-scale calculations, however, is the computation of the electron density (and subsequently, ground state properties) from the discretized Hamiltonian in an efficient and scalable manner. We show in this work how Chebyshev polynomial filtered subspace iteration (CheFSI) can be used to address this issue and push the envelope in large-scale materials simulations in a discontinuous Galerkin framework. We describe how the subspace filtering steps can be performed in an efficient and scalable manner using a two-dimensional parallelization scheme, thanks to the orthogonality of the DG basis set and block-sparse structure of the DG Hamiltonian matrix. The on-the-fly nature of the ALBs requires additional care in carrying out the subspace iterations. We demonstrate the parallel scalability of the DG-CheFSI approach in calculations of large-scale two-dimensional graphene sheets and bulk three-dimensional lithium-ion electrolyte systems. Employing 55,296 computational cores, the time per self-consistent field iteration for a sample of the bulk 3D electrolyte containing 8,586 atoms is 90 seconds, and the time for a graphene sheet containing 11,520 atoms is 75 seconds.Comment: Submitted to The Journal of Chemical Physic

Privacy Preserving Utility Mining: A Survey

In big data era, the collected data usually contains rich information and hidden knowledge. Utility-oriented pattern mining and analytics have shown a powerful ability to explore these ubiquitous data, which may be collected from various fields and applications, such as market basket analysis, retail, click-stream analysis, medical analysis, and bioinformatics. However, analysis of these data with sensitive private information raises privacy concerns. To achieve better trade-off between utility maximizing and privacy preserving, Privacy-Preserving Utility Mining (PPUM) has become a critical issue in recent years. In this paper, we provide a comprehensive overview of PPUM. We first present the background of utility mining, privacy-preserving data mining and PPUM, then introduce the related preliminaries and problem formulation of PPUM, as well as some key evaluation criteria for PPUM. In particular, we present and discuss the current state-of-the-art PPUM algorithms, as well as their advantages and deficiencies in detail. Finally, we highlight and discuss some technical challenges and open directions for future research on PPUM.Comment: 2018 IEEE International Conference on Big Data, 10 page

Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellman-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8,0) boron-nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of accuracy required in a practical DFT calculation