q-Identities and affinized projective varieties, II. Flag varieties

In a previous paper we defined the concept of an affinized projective variety and its associated Hilbert series. We computed the Hilbert series for varieties associated to quadratic monomial ideals. In this paper we show how to apply these results to affinized flag varieties. We discuss various examples and conjecture a correspondence between the Hilbert series of an affinized flag variety and a modified Hall-Littlewood polynomial. We briefly discuss the application of these results to quasi-particle character formulas for affine Lie algebra modules.Comment: AMSTeX, 25 pages, 3 figure

A perspective on the control of FES-supported standing

This special section is about the control of electrical stimulators to restore standing functions to paraplegics. It addresses several important topics regarding the interactions of the intact central nervous systems (CNS) with the artificial control system. The topics are as follows: how paraplegics use their arms to help themselves stand up with functional electrical stimulation (FES); the user-driven artificial control of FESsupported standing up; a controller which is promising for the control of sitting down; the application of reinforcement machine learning for the controllers of standing up; arms-free\ud standing with voluntary upper body balancing and artificially controlled ankle stiffness; and cognitive feedback in balancing. This Commentary introduces the papers in this section and relates them to earlier research

Holographic graphene in a cavity

The effective strength of EM interactions can be controlled by confining the fields to a cavity and these effects might be used to push graphene into a strongly coupled regime. We study the similar D3/probe D5 system on a compact space and discuss the gravity dual for a cavity between two mirrors. We show that the introduction of a conformal symmetry breaking length scale introduces a mass gap on a single D5 sheet. Bilayer configurations display exciton condensation between the sheets. There is a first order phase transition away from the exciton condensate if a strong enough magnetic field is applied. We finally map out the phase structure of these systems in a cavity with the presence of mirror reflections of the probes - a mass gap may form through exciton condensation with the mirror image

Education as a positional good for marked-based reforms of state schooling: paper presented at the ECER 2000-conference in Edinburgh 20 - 23 September 2000

Analyses of market-based reforms of state schooling have occasionally acknowledged positional elements in parental demand, but none has fully examined their nature and implications. Contrary to the normal predictions of orthodox economic analysis, competition in positional markets can result in inefficient outcomes. Predominantly relying upon recent British experience, we examine the extent to which compulsory schooling can be viewed as a positional good and explore its implica-tions for policy. In particular, we consider whether policies targeting increases in parental choice assist a rise in the overall level of educational attainment. --schooling choice,educational markets,positional good,status competition

Practical application of pseudospectral optimization to robot path planning

To obtain minimum time or minimum energy trajectories for robots it is necessary to employ planning methods which adequately consider the platform’s dynamic properties. A variety of sampling, graph-based or local receding-horizon optimisation methods have previously been proposed. These typically use simplified kino-dynamic models to avoid the significant computational burden of solving this problem in a high dimensional state-space. In this paper we investigate solutions from the class of pseudospectral optimisation methods which have grown in favour amongst the optimal control community in recent years. These methods have high computational efficiency and rapid convergence properties. We present a practical application of such an approach to the robot path planning problem to provide a trajectory considering the robot’s dynamic properties. We extend the existing literature by augmenting the path constraints with sensed obstacles rather than predefined analytical functions to enable real world application

A Laboratory for Relevance: Findings and Recommendations from the Arts Innovation Fund

Starting in 2006, a group of leading California arts institutions set out to innovate with new ways of working in the 21st century. With support from the Arts Innovation Fund of The James Irvine Foundation, they approached the challenge of innovation in a variety of ways, with a wide range of objectives and results. Across the board, the experimentation process prompted organizational reflection and change. Most grantees developed new levels of adaptive capacity, an attribute that many thought leaders believe will be essential for arts organizations, and the arts sector as a whole, to thrive into the future. After a strategic qualitative review of the innovation projects pursued by organizations participating in the Arts Innovation Fund, the Slover Linett evaluation team offers the following report with its insights and recommendations

Changing Sources of Magma Generation Beneath Intra-Oceanic Islands Arcs: An Insight From the Juvenile Kohistan Island Arc, Pakistan Himalaya

The Kohistan arc, situated in the Pakistan Himalaya, is a Cretaceous intraoceanic island arc which was initiated during the northward movement of the Indian Plate. The arc was sutured to Asia at ca. 100 Ma. It was subsequently tilted northward when underplated by Indian continental crust during the early stages of India–Asia collision. Deep erosion of this tilted section provides a spectacular section through the whole arc sequence and offers a profound insight into the mechanisms of early stages of arc formation. Geochemical analysis and rare earth element modelling of basaltic sequences which date from the intraoceanic stages of arc development allow identification of three main magma source types in the mantle beneath the juvenile arc. The ‘E-type’ Kamila Amphibolites, with a MORB-type chemistry, form the intraoceanic basement to the arc. The ‘D-type’ Kamila Amphibolites are the earliest of the arc volcanic rocks. These were extracted from a primitive spinel-bearing mantle source, above a north-dipping subduction zone. The stratigraphically younger basalts of the Jaglot Group and Ghizar Formation of the Chalt Volcanic Group were derived from partial melting of a garnet-bearing source at greater depth. The Hunza Formation of the Chalt Volcanic Group contains the youngest mafic volcanic rocks of the intraoceanic arc. Although coeval with the Ghizar Formation of the Chalt Volcanic Group, they were generated by melting of a depleted, spinel-bearing mantle source rock and were erupted into a spatially and temporally restricted back-arc basin developed behind the volcanic front. The Chalt Volcanic Group was therefore formed from two different, adjacent, mantle source regions active at the same time. Results of REE modelling are consistent with models for intraoceanic arc formation in which the earliest volcanic rocks are derived from shallow level spinel-bearing peridotite, and later ones from a deeper garnet-bearing source. This is consistent with the melt region becoming deeper with time as subduction continues. A two-stage model is proposed for the back-arc basalts of the Hunza Formation in which a mantle source, depleted from a previous melting event, is underplated beneath the arc and later remelted during decompression as a consequence of extension and rifting of the arc