A framework for deflated and augmented Krylov subspace methods

We consider deflation and augmentation techniques for accelerating the convergence of Krylov subspace methods for the solution of nonsingular linear algebraic systems. Despite some formal similarity, the two techniques are conceptually different from preconditioning. Deflation (in the sense the term is used here) "removes" certain parts from the operator making it singular, while augmentation adds a subspace to the Krylov subspace (often the one that is generated by the singular operator); in contrast, preconditioning changes the spectrum of the operator without making it singular. Deflation and augmentation have been used in a variety of methods and settings. Typically, deflation is combined with augmentation to compensate for the singularity of the operator, but both techniques can be applied separately. We introduce a framework of Krylov subspace methods that satisfy a Galerkin condition. It includes the families of orthogonal residual (OR) and minimal residual (MR) methods. We show that in this framework augmentation can be achieved either explicitly or, equivalently, implicitly by projecting the residuals appropriately and correcting the approximate solutions in a final step. We study conditions for a breakdown of the deflated methods, and we show several possibilities to avoid such breakdowns for the deflated MINRES method. Numerical experiments illustrate properties of different variants of deflated MINRES analyzed in this paper.Comment: 24 pages, 3 figure

People's revolution or state imposition?

My aim in this study is to develop more theoretically informed praxis - and practically informed theory - about two seminal questions: "What is the good life?", and "How we are to live together?" This thesis explores community and development through the lens of a small Community Building Demonstration Project that was conducted in Melbourne's Northern suburbs between 2001 and 2005. This project, at the time, was promoted by the State Labor Government as a radical strategy that would overcome deeply entrenched social problems. I argue that we are indeed in a predicament that does not easily lend itself to deductive-positivist methods of problem solving. Given that 'reality' can be interpreted in many ways, and knowledge itself is coloured by the interests of powerful groups, how best are we to investigate from within the frame of our own culture? Questions of the social are deeply implicated with those of the environmental, economic and cultural, thus part of the research challenge is to circumscribe a methodology that is appropriate to asking questions about how we are to work together towards the human good. The thesis progressively contextualizes the hidden connections between the day-to-day lived experiences of those in the project and broader factors at the regional, national, and ultimately global political-economic levels. The research re-views the history of Western expansionism over the globe, firstly in the form of the colonial 'adventure', and more recently the efforts to 'develop' the Third World, in what has come to be accepted as 'modernism' and 'progress', but most typically at the cost of community. The research necessarily grapples with the contemporary litany of fashionable ideas like social capital, the Third Way, 'joined-up' government, and Participatory Rural Appraisal. The questioning throughout the thesis of the holistic relationship between the 'personal' and the 'political' leads to various propositions about dealing with our predicament, ranging from how we may seek more respectful interpersonal relationships, to how a community-based committee might represent local interests, as well as what guiding philosophies of the state may be consistent with the goals of such 'development'. As the nature of the predicament becomes clearer, I begin to focus on the question of the opportunities for personal agency given the seemingly overwhelming structures that surround us. The empirical study of the Community Building project reveals the contradictions and dialectics that occur when change is attempted in such a milieu. It shows the interplay of contradictions when imposition meets resistance, and what opportunities there are there to work in the space between these dialectics. It finally reveals other possibilities for understanding and acting, or for 'other discourses' that we might use to make a better future together

Classes of general H-matrices

[EN] Let M(A) denote the comparison matrix of a square H-matrix A, that is, M(A) is an M-matrix. H-matrices such that their comparison matrices are non-singular are well studied in the literature. In this paper, we study characterizations of H-matrices with either singular or non-singular comparison matrices. The spectral radius of the Jacobi matrix of M(A) and the generalized diagonal dominance property are used in the characterizations. Finally. a classification of the set of general H-matrices is obtained.Bru, R.; Corral Ortega, C.; Gimenez Manglano, MI.; Mas Marí, J. (2008). Classes of general H-matrices. Linear Algebra and its Applications. 429(10):2358-2366. doi:10.1016/j.laa.2007.10.030S235823664291

Inverse M-matrices, II

AbstractThis is an update of the 1981 survey by the first author. In the meantime, a considerable amount has been learned about the very special structure of the important class of inverse M-matrices. Developments since the earlier survey are emphasized, but we have tried to be somewhat complete; and, some results have not previously been published. Some proofs are given where appropriate and references are given for others. After some elementary preliminaries, results are grouped by certain natural categories

Open Problems in DAOs

Decentralized autonomous organizations (DAOs) are a new, rapidly-growing class of organizations governed by smart contracts. Here we describe how researchers can contribute to the emerging science of DAOs and other digitally-constituted organizations. From granular privacy primitives to mechanism designs to model laws, we identify high-impact problems in the DAO ecosystem where existing gaps might be tackled through a new data set or by applying tools and ideas from existing research fields such as political science, computer science, economics, law, and organizational science. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the wider research community to join the global effort to invent the next generation of organizations

Mechanics of Reversible Unzipping

We study the mechanics of a reversible decohesion (unzipping) of an elastic layer subjected to quasi-static end-point loading. At the micro level the system is simulated by an elastic chain of particles interacting with a rigid foundation through breakable springs. Such system can be viewed as prototypical for the description of a wide range of phenomena from peeling of polymeric tapes, to rolling of cells, working of gecko's fibrillar structures and denaturation of DNA. We construct a rigorous continuum limit of the discrete model which captures both stable and metastable configurations and present a detailed parametric study of the interplay between elastic and cohesive interactions. We show that the model reproduces the experimentally observed abrupt transition from an incremental evolution of the adhesion front to a sudden complete decohesion of a macroscopic segment of the adhesion layer. As the microscopic parameters vary the macroscopic response changes from quasi-ductile to quasi-brittle, with corresponding decrease in the size of the adhesion hysteresis. At the micro-scale this corresponds to a transition from a `localized' to a `diffuse' structure of the decohesion front (domain wall). We obtain an explicit expression for the critical debonding threshold in the limit when the internal length scales are much smaller than the size of the system. The achieved parametric control of the microscopic mechanism can be used in the design of new biological inspired adhesion devices and machines

Myogenin Regulates Exercise Capacity and Skeletal Muscle Metabolism in the Adult Mouse

Although skeletal muscle metabolism is a well-studied physiological process, little is known about how it is regulated at the transcriptional level. The myogenic transcription factor myogenin is required for skeletal muscle development during embryonic and fetal life, but myogenin's role in adult skeletal muscle is unclear. We sought to determine myogenin's function in adult muscle metabolism. A Myog conditional allele and Cre-ER transgene were used to delete Myog in adult mice. Mice were analyzed for exercise capacity by involuntary treadmill running. To assess oxidative and glycolytic metabolism, we performed indirect calorimetry, monitored blood glucose and lactate levels, and performed histochemical analyses on muscle fibers. Surprisingly, we found that Myog-deleted mice performed significantly better than controls in high- and low-intensity treadmill running. This enhanced exercise capacity was due to more efficient oxidative metabolism during low- and high-intensity exercise and more efficient glycolytic metabolism during high-intensity exercise. Furthermore, Myog-deleted mice had an enhanced response to long-term voluntary exercise training on running wheels. We identified several candidate genes whose expression was altered in exercise-stressed muscle of mice lacking myogenin. The results suggest that myogenin plays a critical role as a high-level transcriptional regulator to control the energy balance between aerobic and anaerobic metabolism in adult skeletal muscle

Careers in ecstasy use: do ecstasy users cease of their own accord? Implications for intervention development

<p>Abstract</p> <p>Background</p> <p>Ecstasy (MDMA, 3, 4-methylenodioxymethamphetamine) use is widespread in the Netherlands, with a lifetime prevalence of 4.3%, and two-thirds of dance party visitors being ecstasy users. However, research into Dutch ecstasy use patterns is lacking. In addition, recent studies suggest that ecstasy users cease their use automatically, which implies that interventions would do better to better focus on the promotion of harm reduction strategies than on inducing cessation. The current study addresses this process of ecstasy cessation.</p> <p>Methods</p> <p>32 participants from the Dutch dance scene were interviewed, and the results were systematically analysed using NVivo.</p> <p>Results</p> <p>Most ecstasy users had started to use out of curiosity. During use, users applied a host of harm reduction strategies, albeit inconsistently and sometimes incorrectly. Most users appeared to cease ecstasy use automatically because of loss of interest or changing life circumstances (e.g. a new job or relationship).</p> <p>Conclusion</p> <p>It appears that cessation of ecstasy use is largely determined by environmental variables and not by health concerns. This supports the idea that health promotion resources are better spent in trying to promote consistent and correct application of harm reduction practices than in trying to induce cessation.</p