In this paper, we propose a Parallel Hybrid Direct-Iterative Eigensolver for Hermitian Eigenvalue Problems without tridiagonalization, denoted byPHIDE, which combines direct and iterative methods.PHIDEfirst reduces a Hermitian matrix to banded form, then applies a spectrum slicing algorithm to the banded matrix, and finally computes the eigenvectors of the original matrix via backtransformation. Compared with conventional direct eigensolvers,PHIDEavoids tridiagonalization, which involves many memory-bound operations. InPHIDE, the banded eigenvalue problem is solved using the contour integral method implemented in FEAST, which may yield slightly lower accuracy than tridiagonalization-based approaches. For sequences of correlated Hermitian eigenvalue problems arising in density functional theory (DFT),PHIDEachieves an average speedup of$1.22\times$over the state-of-the-art direct solver in ELPA when using 1024 processes. Numerical experiments are conducted on dense Hermitian matrices from real applications as well as large sparse matrices from the SuiteSparse and ELSES collections.

In this paper, we propose some efficient data redistribution algorithms for redistributing matrices from 1D or 2D irregular format to block cyclic data distribution (BCDD) format, which can be much faster than the BLACS routinePXGEMR2D. These algorithms can be used to combine direct methods with iterative methods. The proposed algorithms divide the communication into two phases: one for processes in the same column and the other for processes in the same row, and the whole data redistribution task is divided into several independent sub-communications. The communication time can be reduced a lot compared with BLACS. Performance results show that our algorithms can be$2\times$–$5\times$faster than the BLACS routinePXGEMR2Dwhen using 4096 processes and the experiments are performed on Tianhe-2A supercomputer.

Process-Oriented Guided Inquiry Learning (POGIL) activities are used in many undergraduate courses. Their utilization in Computer Science courses is very useful in the delivery of fundamentals of computer science. The site https://cspogil.org/contains many such activities. Currently, there is limited amount of research published involving both POGIL and Security. As such we feel that this area is wide open for contributions. In this work we create a POGIL activity designed to introduce some fundamental Cybersecurity concepts to undergraduate computer science/information technology/information systems students enrolled in non-security-focused courses. The learners will get exposure to essential application security risks and reflect upon the concepts introduced. Through this POGIL activity students get exposed to exercises involving the first seven of the The Open Web Application Security Project (OWASP) Top 10 Application Security Risks. We use PRE/POST survey methods to collect data from these courses and investigate students' engagement and knowledge gains resulted from this activity.

The article reviews the basics of the variable precision rough set and the Bayesian approaches to data dependencies detection and analysis. The variable precision rough set and the Bayesian rough set theories are extensions of the rough set theory. They are focused on the recognition and modelling of set overlap-based, also referred to as probabilistic, relationships between sets. The set-overlap relationships are used to construct approximations of undefinable sets. The primary application of the approach is to analysis of weak data co-occurrence-based dependencies in probabilistic decision tables learned from data. The probabilistic decision tables are derived from data to represent the inter-data item connections, typically for the purposes of their analysis or data value prediction. The theory is illustrated with a comprehensive application example illustrating utilization of probabilistic decision tables to face image classification.

This paper reports our experiences with the application of the hierarchy of probabilistic decision tables to face recognition. The methodology underlying the classifier development for our experiments is the variable precision rough sets, a probabilistic extension of the rough set theory. The soft-cut and probabilistic distance-based classifier method, the related theoretical background, including the feature extraction technique based on the principal component analysis, and some experimental results are presented. © 2011 Wiley Periodicals, Inc.