Cocharacter-closure and spherical buildings

Let $k$ be a field, let $G$ be a reductive $k$-group and $V$ an affine $k$-variety on which $G$ acts. In this note we continue our study of the notion of cocharacter-closed $G(k)$-orbits in $V$. In earlier work we used a rationality condition on the point stabilizer of a $G$-orbit to prove Galois ascent/descent and Levi ascent/descent results concerning cocharacter-closure for the corresponding $G(k)$-orbit in $V$. In the present paper we employ building-theoretic techniques to derive analogous results.Comment: 16 pages; v 2 17 pages, exposition improved; to appear in the Robert Steinberg Memorial Issue of the Pacific Journal of Mathematic

G-complete reducibility in non-connected groups

In this paper we present an algorithm for determining whether a subgroup H of a non-connected reductive group G is G-completely reducible. The algorithm consists of a series of reductions; at each step, we perform operations involving connected groups, such as checking whether a certain subgroup of G^0 is G^0 -cr. This essentially reduces the problem of determining G-complete reducibility to the connected case.Comment: 14 page

Toward a Constitutional Kleptocracy: Civil Forfeiture in America

Leonard Levy, the legal historian who has written a number of highly regarded historical studies on various provisions of the United States Constitution, has added to his impressive oeuvre a new study of civil and criminal forfeiture. A License to Steal brings together a discussion of English legal history, a review of a number of Nineteenth Century and late Twentieth Century Supreme Court forfeiture decisions, accounts of actual applications of civil and criminal forfeiture, and a summary and critique of legislative proposals that have been made for reform of the civil forfeiture provisions of the federal drug statute. There is more space devoted in the book to civil than criminal forfeiture because, as Levy explains, criminal forfeiture was not widely used throughout most of the country\u27s history. Levy discusses criminal forfeiture primarily to contrast it with civil forfeiture, which affords virtually none of the procedural protections that are taken for granted in criminal prosecutions. What emerges clearly and forcefully in this book is that civil in rem forfeiture proceedings have been used - and increasingly are being used - as an expedient to circumvent the usual protections accorded to defendants in criminal proceedings, and to augment federal, state, and local treasuries. Drawn primarily from secondary sources, A License to Steal is footnoted throughout and contains an excellent bibliography

Predicting and Evaluating Software Model Growth in the Automotive Industry

The size of a software artifact influences the software quality and impacts the development process. In industry, when software size exceeds certain thresholds, memory errors accumulate and development tools might not be able to cope anymore, resulting in a lengthy program start up times, failing builds, or memory problems at unpredictable times. Thus, foreseeing critical growth in software modules meets a high demand in industrial practice. Predicting the time when the size grows to the level where maintenance is needed prevents unexpected efforts and helps to spot problematic artifacts before they become critical. Although the amount of prediction approaches in literature is vast, it is unclear how well they fit with prerequisites and expectations from practice. In this paper, we perform an industrial case study at an automotive manufacturer to explore applicability and usability of prediction approaches in practice. In a first step, we collect the most relevant prediction approaches from literature, including both, approaches using statistics and machine learning. Furthermore, we elicit expectations towards predictions from practitioners using a survey and stakeholder workshops. At the same time, we measure software size of 48 software artifacts by mining four years of revision history, resulting in 4,547 data points. In the last step, we assess the applicability of state-of-the-art prediction approaches using the collected data by systematically analyzing how well they fulfill the practitioners' expectations. Our main contribution is a comparison of commonly used prediction approaches in a real world industrial setting while considering stakeholder expectations. We show that the approaches provide significantly different results regarding prediction accuracy and that the statistical approaches fit our data best

Semisimplification for Subgroups of Reductive Algebraic Groups

Acknowledgements: We are grateful to Brian Lawrence for his questions, which motivated this paper, and for his comments on an earlier draft.Peer reviewedPublisher PD

Cocharacter-closure and spherical buildings

Let k be a field, let G be a reductive k-group and V an affine k-variety on which G acts. In this note we continue our study of the notion of cocharacter-closed G(k)-orbits in V . In earlier work we used a rationality condition on the point stabilizer of a G-orbit to prove Galois ascent/descent and Levi ascent/descent results concerning cocharacter-closure for the corresponding G(k)-orbit in V . In the present paper we employ building-theoretic techniques to derive analogous results