Implicit-factorization preconditioning and iterative solvers for regularized saddle-point systems

We consider conjugate-gradient like methods for solving block symmetric indefinite linear systems that arise from saddle-point problems or, in particular, regularizations thereof. Such methods require preconditioners that preserve certain sub-blocks from the original systems but allow considerable flexibility for the remaining blocks. We construct a number of families of implicit factorizations that are capable of reproducing the required sub-blocks and (some) of the remainder. These generalize known implicit factorizations for the unregularized case. Improved eigenvalue clustering is possible if additionally some of the noncrucial blocks are reproduced. Numerical experiments confirm that these implicit-factorization preconditioners can be very effective in practice.

When smoke gets in our eyes: The multiple impacts of atmospheric black carbon on climate, air quality and health

With both climate change and air quality on political and social agendas from local to global scale, the links between these hitherto separate fields are becoming more apparent. Black carbon, largely from combustion processes, scatters and absorbs incoming solar radiation, contributes to poor air quality and induces respiratory and cardiovascular problems. Uncertainties in the amount, location, size and shape of atmospheric black carbon cause large uncertainty in both climate change estimates and toxicology studies alike. Increased research has led to new effects and areas of uncertainty being uncovered. Here we draw together recent results and explore the increasing opportunities for synergistic research that will lead to improved confidence in the impact of black carbon on climate change, air quality and human health. Topics of mutual interest include better information on spatial distribution, size, mixing state and measuring and monitoring. (c) 2006 Elsevier Ltd. All rights reserved.

Implicit synthesis

In this reply to Neal and Hesketh and to the commentators, we argue that implicit knowledge is partly abstract and can be usefully defined by the criteria of both metaknowledge and intentional control. We suggest that the pattern of dissociations supports a claim of separate implicit and explicit learning modes. According to our characterization, implicit learning leads to knowledge that is not automatically represented as knowledge by the learning process; instead, the presence of knowledge has to be inferred by the subject (partial explicitation) if metaknowledge is gained at all. During explicit learning, knowledge is automatically labeled as knowledge by the learning process, so that metaknowledge comes immediately and to the fullest extent. Finally, we suggest that implicit knowledge may to some degree apply regardless of intention.