The QRD and SVD of matrices over a real algebra

Recent work in the field of signal processing has shown that the singular value decomposition of a matrix with entries in certain real algebras can be a powerful tool. In this article we show how to generalise the QR decomposition and SVD to a wide class of real algebras, including all finite-dimensional semi-simple algebras, (twisted) group algebras and Clifford algebras. Two approaches are described for computing the QRD/SVD: one Jacobi method with a generalised Givens rotation, and one based on the Artin-Wedderburn theorem.Comment: Uses elsarticle.cl

Adaptive Orthogonal Matrix-Valued Wavelets and Compression of Vector-Valued Signals

Wavelet transforms using matrix-valued wavelets (MVWs) can process the components of vector-valued signals jointly, and thus offer potential advantages over scalar wavelets. For every matrix-valued scaling filter, there are infinitely many matrix-valued wavelet filters corresponding to rotated bases. We show how the arbitrary orthogonal factor in the choice of wavelet filter can be selected adaptively with a modified SIMPLIMAX algorithm. The 3×3 orthogonal matrix-valued scaling filters of length 6 with 3 vanishing moments have one intrinsic free scalar parameter in addition to three scalar rotation parameters. Tests suggest that even when optimising over these parameters, no significant improvement is obtained when compared to the naive scalar-based filter. We have found however in an image compression test that, for the naive scaling filter, adaptive basis rotation can decrease the RMSE by over 20%

IceCube Science

We discuss the status of the kilometer-scale neutrino detector IceCube and its low energy upgrade Deep Core and review its scientific potential for particle physics. We subsequently appraise IceCube's potential for revealing the enigmatic sources of cosmic rays. After all, this aspiration set the scale of the instrument. While only a smoking gun is missing for the case that the Galactic component of the cosmic ray spectrum originates in supernova remnants, the origin of the extragalactic component remains as inscrutable as ever. We speculate on the role of the nearby active galaxies Centaurus A and M87.Comment: 19 pages, 8 figures; Talk at Discrete 08, Valencia, Spai

Cellular allometry of mitochondrial functionality establishes the optimal cell size

Eukaryotic cells attempt to maintain an optimal size, resulting in size homeostasis. While cellular content scales isometrically with cell size, allometric laws indicate that metabolism per mass unit should decline with increasing size. Here we use elutriation and single-cell flow cytometry to analyze mitochondrial scaling with cell size. While mitochondrial content increases linearly, mitochondrial membrane potential and oxidative phosphorylation are highest at intermediate cell sizes. Thus, mitochondrial content and functional scaling are uncoupled. The nonlinearity of mitochondrial functionality is cell size, not cell cycle, dependent, and it results in an optimal cell size whereby cellular fitness and proliferative capacity are maximized. While optimal cell size is controlled by growth factor signaling, its establishment and maintenance requires mitochondrial dynamics, which can be controlled by the mevalonate pathway. Thus, optimization of cellular fitness and functionality through mitochondria can explain the requirement for size control, as well as provide means for its maintenance

The utilisation of health research in policy-making: Concepts, examples and methods of assessment

The importance of health research utilisation in policy-making, and of understanding the mechanisms involved, is increasingly recognised. Recent reports calling for more resources to improve health in developing countries, and global pressures for accountability, draw greater attention to research-informed policy-making. Key utilisation issues have been described for at least twenty years, but the growing focus on health research systems creates additional dimensions. The utilisation of health research in policy-making should contribute to policies that may eventually lead to desired outcomes, including health gains. In this article, exploration of these issues is combined with a review of various forms of policy-making. When this is linked to analysis of different types of health research, it assists in building a comprehensive account of the diverse meanings of research utilisation. Previous studies report methods and conceptual frameworks that have been applied, if with varying degrees of success, to record utilisation in policy-making. These studies reveal various examples of research impact within a general picture of underutilisation. Factors potentially enhancing utilisation can be identified by exploration of: priority setting; activities of the health research system at the interface between research and policy-making; and the role of the recipients, or 'receptors', of health research. An interfaces and receptors model provides a framework for analysis. Recommendations about possible methods for assessing health research utilisation follow identification of the purposes of such assessments. Our conclusion is that research utilisation can be better understood, and enhanced, by developing assessment methods informed by conceptual analysis and review of previous studies

The Daemo crowdsourcing marketplace

The success of crowdsourcing markets is dependent on a strong foundation of trust between workers and requesters. In current marketplaces, workers and requesters are often unable to trust each other’s quality, and their mental models of tasks are misaligned due to ambiguous instructions or confusing edge cases. This breakdown of trust typically arises from (1) flawed reputation systems which do not accurately reflect worker and requester quality, and from (2) poorly designed tasks. In this demo, we present how Boomerang and Prototype Tasks, the fundamental building blocks of the Daemo crowdsourcing marketplace, help restore trust between workers and requesters. Daemo’s Boomerang reputation system incentivizes alignment between opinion and ratings by determining the likelihood that workers and requesters will work together in the future based on how they rate each other. Daemo’s Prototype tasks require that new tasks go through a feedback iteration phase with a small number of workers so that requesters can revise their instructions and task designs before launch

Prototype tasks: Improving crowdsourcing results through rapid, iterative task design

Low-quality results have been a long-standing problem on microtask crowdsourcing platforms, driving away requesters and justifying low wages for workers. To date, workers have been blamed for low-quality results: they are said to make as little effort as possible, do not pay attention to detail, and lack expertise. In this paper, we hypothesize that requesters may also be responsible for low-quality work: they launch unclear task designs that confuse even earnest workers, under-specify edge cases, and neglect to include examples. We introduce prototype tasks, a crowdsourcing strategy requiring all new task designs to launch a small number of sample tasks. Workers attempt these tasks and leave feedback, enabling the requester to iterate on the design before publishing it. We report a field experiment in which tasks that underwent prototype task iteration produced higher-quality work results than the original task designs. With this research, we suggest that a simple and rapid iteration cycle can improve crowd work, and we provide empirical evidence that requester “quality” directly impacts result quality