Minimizing Communication in Linear Algebra

In 1981 Hong and Kung proved a lower bound on the amount of communication needed to perform dense, matrix-multiplication using the conventional $O(n^3)$ algorithm, where the input matrices were too large to fit in the small, fast memory. In 2004 Irony, Toledo and Tiskin gave a new proof of this result and extended it to the parallel case. In both cases the lower bound may be expressed as $\Omega$(#arithmetic operations / $\sqrt{M}$), where M is the size of the fast memory (or local memory in the parallel case). Here we generalize these results to a much wider variety of algorithms, including LU factorization, Cholesky factorization, $LDL^T$ factorization, QR factorization, algorithms for eigenvalues and singular values, i.e., essentially all direct methods of linear algebra. The proof works for dense or sparse matrices, and for sequential or parallel algorithms. In addition to lower bounds on the amount of data moved (bandwidth) we get lower bounds on the number of messages required to move it (latency). We illustrate how to extend our lower bound technique to compositions of linear algebra operations (like computing powers of a matrix), to decide whether it is enough to call a sequence of simpler optimal algorithms (like matrix multiplication) to minimize communication, or if we can do better. We give examples of both. We also show how to extend our lower bounds to certain graph theoretic problems. We point out recently designed algorithms for dense LU, Cholesky, QR, eigenvalue and the SVD problems that attain these lower bounds; implementations of LU and QR show large speedups over conventional linear algebra algorithms in standard libraries like LAPACK and ScaLAPACK. Many open problems remain.Comment: 27 pages, 2 table

Exploring the Relationship between U.S. Jamaican Immigrants’ Cultural Beliefs and Conflict Management Styles as These Correlations are Related to Their Perceived Job Satisfaction and Job Performance

Immigrant numbers in developing and first world countries are increasing, and immigrants are bringing with them to the host country their set of attitudes, customs, habits, interests and traditions. Due to this influx of immigrants, conflict situations between employees are on the rise and are more difficult to resolve when compared to conflicts that are within the same cultural groups. If organizations are better able to understand the relationship between the cultural beliefs and conflict management styles of employees, they can help them utilize conflict management styles in specific situations to result in increased job satisfaction and job performance. This collected papers dissertation explored the relationship between U.S. Jamaican immigrants’ cultural beliefs, and conflict management styles related to perceived job satisfaction and job performance. There were two studies completed in fulfillment of this collected papers dissertation. STUDY #1: The purpose of this structured literature review was to systematically examine the literature on conflict management style and perceived job satisfaction and job performance. STUDY #2: The purpose of this cross-sectional, explanatory study was to examine the relationship between the cultural beliefs and conflict management styles of U.S. Jamaican immigrants, and their job satisfaction and job performance in the workplace. Quantitative data were examined in two stages using SPSS 23. In the first stage, descriptive statistics were used. Second, a moderated regression analysis and linear regression were done. It was found in study #1, that the two conflict management styles that were associated with increased job satisfaction and job performance with were integrating and compromising conflict management styles (Zhang et al., 2015). In study #2, it was found that the dominant conflict management style for U.S. Jamaican immigrants was collaborating. However, the only conflict management style that was found to be a significantly positive moderator for the relationship between job satisfaction and job performance was compromising conflict management style. This finding is consistent with the finding from Study #1, where Zhang et al. (2015) found that employees who use compromising conflict management style were more satisfied and had higher levels of job performance

Capturing the spark: PISA, twenty-first century skills and the reconstruction of creativity

Creativity has fascinated scholars for generations, and its identification as one of the key ‘twenty-first century skills' necessary for economic growth has led to renewed interest. This creates two challenges for the OECD: its flagship Programme of International Student Assessment (PISA) does not directly measure creativity. Secondly, the increased importance attached to creativity has highlighted claims that high performers on PISA are largely nations stereotyped as lacking creativity. This challenges PISA's self-proclaimed status as the premier global benchmark for evaluating and comparing the quality of school systems and weakens its capacity to deliver its core mission; to identify ‘best practices' which ensure economic prosperity. We explore these challenges and examine both how the OECD has responded to them and is moving to include creativity in PISA 2022. We argue that, while a precise definition of creativity has defied scholars for centuries, the indications are that the OECD's metric will focus on a narrow, convergent and easily-measured conception associated with cognitive competencies and linked to enhancing human capital. In this way, the ‘messiness’ around the polysemic concept will be simultaneously both exploited and threatened, as new, measurable versions displace alternatives

Prospects for lithium-ion batteries and beyond-a 2030 vision.

It would be unwise to assume ‘conventional’ lithium-ion batteries are approaching the end of their era and so we discuss current strategies to improve the current and next generation systems, where a holistic approach will be needed to unlock higher energy density while also maintaining lifetime and safety. We end by briefly reviewing areas where fundamental science advances will be needed to enable revolutionary new battery systems

Calcium supplements and cancer risk : a meta-analysis of randomised controlled trials

Peer reviewedPublisher PD

Effect of calcium supplements on risk of myocardial infarction and cardiovascular events : meta-analysis

Peer reviewedPublisher PD

Analytical performance assessment of a novel active mooring system for load reduction in marine energy converters

This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.Reliability and storm survival of Marine Energy Converters are critical to their commercial development and deployment. The Intelligent Active Mooring System (IAMS) is a novel device intended to minimise extreme and fatigue loading in mooring lines through a non-linear load–extension curve that is variable in operation to adjust to the prevailing metocean conditions. An analytical model of IAMS, validated by physical model tests at the Dynamic Marine Component test facility at the University of Exeter, is used in a numerical simulation of the performance of IAMS as part of the mooring system of the South West Mooring Test Facility buoy. A 10 m length of IAMS can reduce the rms line tension in normal operating conditions by up to 21% and the peak line tension in storm conditions by up to 21% when compared to braided nylon mooring lines. Peak line tension reductions of over 50% can be achieved if a longer IAMS unit is used. The resulting mooring system can be optimised to give load reductions in a wide range of metocean conditions; while variable pre-tension could be used for tidal range compensation or to ease access for installation and maintenance.The work reported here is part of a joint project between AWS Ocean Ltd., Teqniqa Systems Ltd. and the University of Exeter. The project was funded in part by the Technology Strategy Board (now Innovate UK) grant number 101970