Finite Schur filtration dimension for modules over an algebra with Schur filtration

Let G be GL_N or SL_N as reductive linear algebraic group over a field k of positive characteristic p. We prove several results that were previously established only when N 2^N. Let G act rationally on a finitely generated commutative k-algebra A. Assume that A as a G-module has a good filtration or a Schur filtration. Let M be a noetherian A-module with compatible G action. Then M has finite good/Schur filtration dimension, so that there are at most finitely many nonzero H^i(G,M). Moreover these H^i(G,M) are noetherian modules over the ring of invariants A^G. Our main tool is a resolution involving Schur functors of the ideal of the diagonal in a product of Grassmannians.Comment: 22 pages; final versio

Pragmatism, Education, and the Problem of Pluralism

The concept of pluralism is of central importance in contemporary moral and political education, where a crucial aim is to promote acceptance of the life choices of others and to teach tolerance towards diversity of values. However, this promotion of pluralism suffers from two immediate difficulties. Firstly, the concept of pluralism has proved somewhat elusive, and it is far from clear that its various uses are congruent. Secondly, there is a long-standing criticism against ethical and political pluralism which maintains that pluralist views are difficult if not impossible to defend without succumbing to dreaded relativism. In this article, I will firstly distinguish an educationally interesting form of pluralism and then, drawing from thinkers in the tradition of philosophical pragmatism, attempt to meet the criticism that such pluralism has no interesting philosophical defense.Peer reviewe

Endoplasmic reticulum stress-induced apoptosis in the development of diabetes: is there a role for adipose tissue and liver?

Diabetes mellitus (DM) is a multifactorial chronic metabolic disease characterized by hyperglycaemia. Several different mechanisms have been implicated in the development of the disease, including endoplasmic reticulum (ER) stress. ER stress is increasingly acknowledged as an important mechanism in the development of DM, not only for β-cell loss but also for insulin resistance. Accumulating evidence suggests that ER stress-induced apoptosis may be an important mode of β-cell loss and therefore important in the development of diabetes. Recent data also suggest a role of ER stress-induced apoptosis in liver and adipose tissue in relation to diabetes, but more extensive studies on human adipocyte and hepatocyte (patho)physiology and ER stress are needed to identify the exact interactions between environmental signals, ER stress and apoptosis in these organs

Quantum Electrodynamics of the Helium Atom

Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and radiative corrections to the Schr"odinger energy. Average values of these operators can be calculated using a variational Schr"odinger wave function.Comment: 23 pages, revte

M5-branes from gauge theories on the 5-sphere

We use the 5-sphere partition functions of supersymmetric Yang-Mills theories to explore the (2,0) superconformal theory on S^5 x S^1. The 5d theories can be regarded as Scherk-Schwarz reductions of the 6d theory along the circle. In a special limit, the perturbative partition function takes the form of the Chern-Simons partition function on S^3. With a simple non-perturbative completion, it becomes a 6d index which captures the degeneracy of a sector of BPS states as well as the index version of the vacuum Casimir energy. The Casimir energy exhibits the N^3 scaling at large N. The large N index for U(N) gauge group also completely agrees with the supergravity index on AdS_7 x S^4.Comment: 44 pages, 1 figure, v4: ref added, clarified weak/strong coupling behaviors of large N free energy, minor improvements, version to be published in JHE

Producing valid statistics when legislation, culture, and medical practices differ for births at or before the threshold of survival: Report of a European workshop

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Exploring Curved Superspace

We systematically analyze Riemannian manifolds M that admit rigid supersymmetry, focusing on four-dimensional N=1 theories with a U(1)_R symmetry. We find that M admits a single supercharge, if and only if it is a Hermitian manifold. The supercharge transforms as a scalar on M. We then consider the restrictions imposed by the presence of additional supercharges. Two supercharges of opposite R-charge exist on certain fibrations of a two-torus over a Riemann surface. Upon dimensional reduction, these give rise to an interesting class of supersymmetric geometries in three dimensions. We further show that compact manifolds admitting two supercharges of equal R-charge must be hyperhermitian. Finally, four supercharges imply that M is locally isometric to M_3 x R, where M_3 is a maximally symmetric space.Comment: 39 pages; minor change

Predatory Bacteria: A Potential Ally against Multidrug-Resistant Gram-Negative Pathogens

Multidrug-resistant (MDR) Gram-negative bacteria have emerged as a serious threat to human and animal health. Bdellovibrio spp. and Micavibrio spp. are Gram-negative bacteria that prey on other Gram-negative bacteria. In this study, the ability of Bdellovibrio bacteriovorus and Micavibrio aeruginosavorus to prey on MDR Gram-negative clinical strains was examined. Although the potential use of predatory bacteria to attack MDR pathogens has been suggested, the data supporting these claims is lacking. By conducting predation experiments we have established that predatory bacteria have the capacity to attack clinical strains of a variety of ß-lactamase-producing, MDR Gram-negative bacteria. Our observations indicate that predatory bacteria maintained their ability to prey on MDR bacteria regardless of their antimicrobial resistance, hence, might be used as therapeutic agents where other antimicrobial drugs fail. © 2013 Kadouri et al

Orientifolds and the Refined Topological String

We study refined topological string theory in the presence of orientifolds by counting second-quantized BPS states in M-theory. This leads us to propose a new integrality condition for both refined and unrefined topological strings when orientifolds are present. We define the SO(2N) refined Chern-Simons theory which computes refined open string amplitudes for branes wrapping Seifert three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new invariants of torus knots that generalize the Kauffman polynomials. At large N, the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined topological strings on an orientifold of the resolved conifold, generalizing the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define and solve refined Chern-Simons theory for all ADE gauge groups