Similarity-Aware Spectral Sparsification by Edge Filtering

In recent years, spectral graph sparsification techniques that can compute ultra-sparse graph proxies have been extensively studied for accelerating various numerical and graph-related applications. Prior nearly-linear-time spectral sparsification methods first extract low-stretch spanning tree from the original graph to form the backbone of the sparsifier, and then recover small portions of spectrally-critical off-tree edges to the spanning tree to significantly improve the approximation quality. However, it is not clear how many off-tree edges should be recovered for achieving a desired spectral similarity level within the sparsifier. Motivated by recent graph signal processing techniques, this paper proposes a similarity-aware spectral graph sparsification framework that leverages efficient spectral off-tree edge embedding and filtering schemes to construct spectral sparsifiers with guaranteed spectral similarity (relative condition number) level. An iterative graph densification scheme is introduced to facilitate efficient and effective filtering of off-tree edges for highly ill-conditioned problems. The proposed method has been validated using various kinds of graphs obtained from public domain sparse matrix collections relevant to VLSI CAD, finite element analysis, as well as social and data networks frequently studied in many machine learning and data mining applications

Self-adaptive Multiprecision Preconditioners on Multicore and Manycore Architectures

Abstract. Based on the premise that preconditioners needed for scien-tific computing are not only required to be robust in the numerical sense, but also scalable for up to thousands of light-weight cores, we argue that this two-fold goal is achieved for the recently developed self-adaptive multi-elimination preconditioner. For this purpose, we revise the under-lying idea and analyze the performance of implementations realized in the PARALUTION and MAGMA open-source software libraries on GPU architectures (using either CUDA or OpenCL), Intel’s Many Integrated Core Architecture, and Intel’s Sandy Bridge processor. The comparison with other well-established preconditioners like multi-coloured Gauss-Seidel, ILU(0) and multi-colored ILU(0), shows that the twofold goal of a numerically stable cross-platform performant algorithm is achieved.

The great turn-of-the-century housing boom

This article explains the recent high levels of residential investment and rates of homeownership.Home ownership ; Housing - Finance ; Housing - Prices

The Analysis of Actors in the Making of the Budget Revenue of Regional Cost

This article is the result of research on the analysis of the policy making of the budget revenues and shopping area of Makassar city fiscal year 2009. One part of this research use approach to the actors and the relationships between actors in policy making. Within the framework of the system of policy making of Budget income and Expenditure area (Budgets) Makassar city, this research is the description of the analysis of the local government and actors People\u27s Representative Council District Makassar city as policy makers in making Grant Makassar cit

Cultural Perspectives of Associating Music With the Giftedness in Saudi Arabia

In the literature, performing music is regarded as a manifestation of giftedness. However, the legitimacy of this activity has been the topic of much debate among Islamic scholars since performing music first began. This paper aims to explore whether Saudis’ conceptions of music are shaped by interpretation of religious law and dogma or by Western understandings of giftedness. A total of 14 teachers and Mosque Imams participated in this study. The findings showed that, although most in the teachers group personally admitted that music is part of the giftedness domain, for religious reasons, everyone in the teachers and Mosque Imams’ group did not appreciate performing music. However, the participants showed significant appreciation for songs (i.e., recitation/ lyrics) without musical instruments

Macroeconomic Determinants of Consumer Lending in Saudi Arabia

This paper empirically investigates the macroeconomic variables that influence consumer lending in Saudi Arabia using quarterly data for the period of 1996-2017. The Johansen and Juselius (1990) multivariate cointegration test were used to examine the impact of banks liquidity, interest rate, oil prices and GDP per capita on consumer lending. The test results indicate the existence of the long-term relationship and the empirical results show that consumer lending is positively influenced by a change in banks liquidity, growth in oil prices and GDP per capita. Contrary to expectation, the interest rate was positive and significant. The modified Granger causality test in Error Correction Model framework reports bidirectional causality from banks liquidity to consumer lending and vice versa, while unidirectional causality from GDP per capita and interest rate to consumer lending. The main finding of the paper is to encourage the monetary authority to allow for a gradual phase-out of restrictions on the number of personal loans as well as enhancing consumer protection mechanism to prohibit unfair contractual terms in the agreements

Magnetic domain studies in gadolinium

The domain structure of gadolinium has been observed and investigated. The wet colloid techniquehas been used f o r observation at temperatures down to 240K. The dry colloid technique has been used forthe observation of the patterns formed at low temperatures below 240K. Various specimens of gadoliniumof different sizes have been used to investigate the changes of domain structure with crystal shape andsize. All the crystals except one were obtained from the Centre for Materials Science University of Birmingham,and were high purity. At 273K patterns on planes containing the c-axis showed parallel l80 walls, with the development o f reverse domains. The effect of the crystal thickness on the size of the domain structure has been observedon the basal plane at 273K. This is discussed and found to agree with an. expression due to Kaczer. The effect on the patterns of reducing the temperature has been studied. The domain structure has been observed at 77K, where the easy directions lie on a cone around the c-axis, on all prepared surfaces. The zero field basal plane pattern shows complex wall structure, while planes containing the c-axis show a system of domains parallel to the c-axis. The effect of applying a magnetic field on the domain structure has been observed and is discussed. The lengths of daggers of reverse magnetization and the widths of their bases were found to be in direct proportion at both temperatures 77K and 216k.An interpretation of the pattern Is given for the two range of temperature, where the c-axis is easy and for the easy cone region. A model is given for the patterns observed at 77K and its limitations discussed. Possible types of walls and magnetization direction are also discussed on the basis of the known magnetic properties of the material