Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Cognitive Changes During the Grief Process

Although many authors have used the term grief work since Lindemann (1944) first coined it, there has been no systematic investigation of the nature of this phenomenon. This study sought to delineate the cognitive and interpersonal events that occur during grief events and grief resolution. It was hypothesized that grief work involves the creation of a new relationship with the deceased, and that this would be manifested in a variety of styles of grief. Men and women who had been widowed within the previous two years were identified through newspaper obituaries and recruited as subjects. Sixty subjects completed two process measures. The Grief Work Survey measured recent behaviors and thoughts concerning the loss. The Attitude Toward Grief Survey measured attitudes toward loss and grief. Subjects also completed forms designed to measure a number of prebereavement variables and to assess the degree of grief resolution. In addition an unstructured interview was conducted. On the Grief Work Survey, subjects reported that they thought about their loss quite frequently. However, the loss was only rarely mentioned by other people and subjects stated that they only rarely discussed the loss with others. This pattern of behavior contrasted sharply with subjects\u27 attitudes toward grief. Subjects reported on the Attitudes Toward Grief Survey that under optimal conditions grief is shared with other people. In order to determine styles of grieving, a hierarchical clustering of subjects was conducted based on responses to the Grief Work Survey. When clusters were based on the entire form, four clusters emerged. These were labeled nongrievers, overwhelmed grievers, stiff upper lip grievers and emotionally expressive grievers. The overwhelmed and stiff upper lip clusters stood out as showing significantly poorer outcomes. There were few differences among groups on prebereavement variables. In a second attempt to determine styles of grief responses to the Grief Work Survey were factor analyzed. Four factors emerged. These appeared to lie along two dimensions: public-private and pain-comfort. Factor scores for each subject on each factor were calculated and these were correlated with the various pre-bereavement and outcome measures. The pain factors were found to be correlated with bad outcome. A long terminal illness was correlated with a private pattern of grief work. Finally, older women who reported high marital satisfaction were found to engage most frequently in behaviors which loaded highly on the comfort factors. Behavior during the unstructured interview was reported. Implications concerning a cognitive theory of grief and concerning appropriate therapeutic interventions for the bereaved were discussed

Overview of SERI's high efficiency solar cell research

The bulk of the research efforts supported by the Solar Energy Research Institute (SERI) High Efficiency Concepts area has been directed towards establishing the feasibility of achieving very high efficiencies, 30% for concentrator and more than 20% for thin film flat plate, in solar cell designs which could possibly be produced competitively. The research has accomplished a great deal during the past two years. Even though the desired performance levels have not yet been demonstrated, based on the recent progress, a greater portion of the terrestrial photovoltaics community believes that these efficiencies are attainable. The program will now allocate a larger portion of resources to low cost, large area deposition technology. The program is currently shifting greater emphasis on to the study of crystal growth in order to provide the understanding and tools needed to design a large area process

Comprehensive Trauma-Informed Care for the Whole Community: The Whole Child Initiative Model

The Whole Child Initiative (WCI) is a decade-long blueprint for sustainable and comprehensive community-wide change. To be successful, community-wide sustainable change must embrace a common vision, language, and common experiences to bridge the contrasting community structures, environments, and scopes of work. The Whole Child Initiative uses data, shared goals, and aligned supports ensure that every youth is safe, supported, engaged, healthy, and challenged in the community-at-large. We make the case that a population health or public health approach is needed to sustainable change in communities and the WCI model is described. Among other important outcomes, researchers have found social and emotional health of youth significantly improves across the community using the WCI approach

Accelerating BST Methods for Model Reduction with Graphics Processors

Model order reduction of dynamical linear time-invariant system appears in many scientific and engineering applications. Numerically reliable SVD-based methods for this task require O(n3) floating-point arithmetic operations, with n being in the range 103 − 105 for many practical applications. In this paper we investigate the use of graphics processors (GPUs) to accelerate model reduction of large-scale linear systems via Balanced Stochastic Truncation, by off-loading the computationally intensive tasks to this device. Experiments on a hybrid platform consisting of state-of-the-art general-purpose multi-core processors and a GPU illustrate the potential of this approach

Divergent Reactions to Convergent Strategies: Investor Beliefs and Analyst Reactions During Technological Change

An important outcome of technological change is industry “convergence,” as a new technology spurs competition between established firms from different industries. We study the reactions of securities analysts, as important sources of institutional pressures for firms, to the similar product/market strategies undertaken by firms from different prior industries responding to industry convergence. Our empirical setting is the convergence between the wireline telecommunications and cable television industries in the period following the advent of voice over Internet protocol technology. Controlling for firm financial performance and capabilities, we find that analysts were consistently more positive toward the cable firms than toward the wireline telecom firms. Our findings further show that this divergence in reactions arises from differences in existing investor expectations and preferences concerning how firms create value; stocks owned by investors with a greater preference for growth receive more positive reactions than those owned by investors with a greater preference for margins. However, this divergence in reactions shrinks over time as convergence unfolds and as investors shift their shareholdings in response to misalignment between their preferences and firms\u27 strategic changes. Reactions from analysts—reflecting inertial expectations of investors—may persist for a time despite changes to firms\u27 strategies, thus creating challenges for some firms in responding to technological change and industry convergence while legitimating and enabling similar responses from their competitors