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

Analysis and visualization of Arabidopsis thaliana GWAS using web 2.0 technologies

With large-scale genomic data becoming the norm in biological studies, the storing, integrating, viewing and searching of such data have become a major challenge. In this article, we describe the development of an Arabidopsis thaliana database that hosts the geographic information and genetic polymorphism data for over 6000 accessions and genome-wide association study (GWAS) results for 107 phenotypes representing the largest collection of Arabidopsis polymorphism data and GWAS results to date. Taking advantage of a series of the latest web 2.0 technologies, such as Ajax (Asynchronous JavaScript and XML), GWT (Google-Web-Toolkit), MVC (Model-View-Controller) web framework and Object Relationship Mapper, we have created a web-based application (web app) for the database, that offers an integrated and dynamic view of geographic information, genetic polymorphism and GWAS results. Essential search functionalities are incorporated into the web app to aid reverse genetics research. The database and its web app have proven to be a valuable resource to the Arabidopsis community. The whole framework serves as an example of how biological data, especially GWAS, can be presented and accessed through the web. In the end, we illustrate the potential to gain new insights through the web app by two examples, showcasing how it can be used to facilitate forward and reverse genetics research. Database URL: http://arabidopsis.usc.edu

The scale of population structure in Arabidopsis thaliana

The population structure of an organism reflects its evolutionary history and influences its evolutionary trajectory. It constrains the combination of genetic diversity and reveals patterns of past gene flow. Understanding it is a prerequisite for detecting genomic regions under selection, predicting the effect of population disturbances, or modeling gene flow. This paper examines the detailed global population structure of Arabidopsis thaliana. Using a set of 5,707 plants collected from around the globe and genotyped at 149 SNPs, we show that while A. thaliana as a species self-fertilizes 97% of the time, there is considerable variation among local groups. This level of outcrossing greatly limits observed heterozygosity but is sufficient to generate considerable local haplotypic diversity. We also find that in its native Eurasian range A. thaliana exhibits continuous isolation by distance at every geographic scale without natural breaks corresponding to classical notions of populations. By contrast, in North America, where it exists as an exotic species, A. thaliana exhibits little or no population structure at a continental scale but local isolation by distance that extends hundreds of km. This suggests a pattern for the development of isolation by distance that can establish itself shortly after an organism fills a new habitat range. It also raises questions about the general applicability of many standard population genetics models. Any model based on discrete clusters of interchangeable individuals will be an uneasy fit to organisms like A. thaliana which exhibit continuous isolation by distance on many scales

Heat tolerance in a wild Oryza species is attributed to maintenance of Rubisco activation by a thermally stable Rubisco activase ortholog

• The response of photosynthesis and plant growth to short periods of supra-optimal heat was tested in rice (Oryza sativa) and two wild Oryza species from the Australian savanna, O. meridionalis and O. australiensis. The mechanism of heat tolerance in the wild species was explored, particularly focusing on the heat-labile protein Rubisco activase (RCA). • We compared leaf elongation rates, net photosynthesis and Rubisco activation state at moderate (28°C) and high temperature (45°C). Sequence analysis followed by enzyme kinetics of RCA was used to identify structural differences and thermal stability. • Oryza australiensis was the most heat-tolerant species. Rubisco activation state was positively correlated with leaf elongation rates across all three species at four times following exposure to 45°C. Oryza australiensis had multiple polymorphisms in the RCA primary protein sequence, and the protein was thermally stable up to 42°C relative to RCA from O. sativa which became inhibited at 36°C. • We attribute the heat tolerance of growth and photosynthesis in these wild species to thermal stability of RCA, enabling Rubisco to remain active. Because thermal stability of RCA in O. australiensis co-occurs with reduced enzyme specific activity, an increased RCA to Rubisco ratio is required in vivo to maintain high Rubisco activation

The Depth and Dynamics of Context: Tracing the Sources and Channels of Engagement and Disengagement in Students' Response to Literature

In this article, we analyze one coauthor's 12th-grade English class, focusing on a small group of students who interpreted the character of Gertrude in Hamlet through a body biography, a life-sized human outline that students filled with words and images that represented their understanding of the character. We analyze the body biography production as a function of the social context of activity and then analyze the processes of composition involved in their production. Analysis of the data reveals that (a) the students exhibited different degrees of commitment to and involvement in the group task, (b) the degree of equity in productivity and social relations varied within the group in accordance with these different degrees of engagement, and (c) the inequity in social relations and contributions to the group product belied the degree to which the final interpretive product met the teacher's assessment criteria. We conclude with a reconsideration of the notion of engagement that includes attention to both the immediate social relations within the classroom and the histories of engagement that students bring to class.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline