Borel-de Siebenthal theory for affine reflection systems

We develop a Borel-de Siebenthal theory for affine reflection systems by classifying their maximal closed subroot systems. Affine reflection systems (introduced by Loos and Neher) provide a unifying framework for root systems of finite-dimensional semi-simple Lie algebras, affine and toroidal Lie algebras, and extended affine Lie algebras. In the special case of nullity $k$ toroidal Lie algebras, we obtain a one-to-one correspondence between maximal closed subroot systems with full gradient and triples $(q,(b_i),H)$, where $q$ is a prime number, $(b_i)$ is a $n$-tuple of integers in the interval $[0,q-1]$ and $H$ is a $(k\times k)$ Hermite normal form matrix with determinant $q$. This generalizes the $k=1$ result of Dyer and Lehrer in the setting of affine Lie algebras

Twisted Demazure modules, fusion product decomposition and twisted Q--systems

In this paper, we introduce a family of indecomposable finite-dimensional graded modules for the twisted current algebras. These modules are indexed by an $|R^+|$-tuple of partitions \bxi=(\xi^{\alpha})_{\alpha\in R^+} satisfying a natural compatibility condition. We give three equivalent presentations of these modules and show that for a particular choice of \bxi these modules become isomorphic to Demazure modules in various levels for the twisted affine algebras. As a consequence we see that the defining relations of twisted Demazure modules can be greatly simplified. Furthermore, we investigate the notion of fusion products for twisted modules, first defined in \cite{FL99} for untwisted modules, and use the simplified presentation to prove a fusion product decomposition of twisted Demazure modules. As a consequence we prove that twisted Demazure modules can be obtained by taking the associated graded modules of (untwisted) Demazure modules for simply-laced affine algebras. Furthermore we give a semi-infinite fusion product construction for the irreducible representations of twisted affine algebras. Finally, we prove that the twisted $Q$-sytem defined in \cite{HKOTT02} extends to a non-canonical short exact sequence of fusion products of twisted Demazure modules

The increasing importance of economic conditions on fertility

This paper investigates whether there has been a fundamental change in the importance of economic conditions on fertility. Through the 1980s econometric studies had found at best a mixed, neutral or negative effect of economic conditions on fertility. Notably, Butz and Ward (1979) concluded that fertility was counter-cyclical, with fertility falling in good times, as the opportunity costs of childbearing rose. More recently, there have been signs that fluctuations in fertility have been pro-cyclical, with good economic times being associated with higher birth rates, and the recent recession with lower birth rates. In this paper, we use panel methods to study short term changes in aggregate fertility and economic measures in OECD countries from 1976-2008. We find indeed that fertility became positively associated with good economic conditions. Furthermore, the increasing importance of economic conditions was detected for both tempo and quantum.economic conditions, total fertility rate

Gate induced monolayer behavior in twisted bilayer black phosphorus

Optical and electronic properties of black phosphorus strongly depend on the number of layers and type of stacking. Using first-principles calculations within the framework of density functional theory, we investigate the electronic properties of bilayer black phosphorus with an interlayer twist angle of 90$^\circ$. These calculations are complemented with a simple $\vec{k}\cdot\vec{p}$ model which is able to capture most of the low energy features and is valid for arbitrary twist angles. The electronic spectrum of 90$^\circ$ twisted bilayer black phosphorus is found to be x-y isotropic in contrast to the monolayer. However x-y anisotropy, and a partial return to monolayer-like behavior, particularly in the valence band, can be induced by an external out-of-plane electric field. Moreover, the preferred hole effective mass can be rotated by 90$^\circ$ simply by changing the direction of the applied electric field. In particular, a +0.4 (-0.4) V/{\AA} out-of-plane electric field results in a $\sim$60\% increase in the hole effective mass along the y (x) axis and enhances the $m^*_{y}/m^*_{x}$ ($m^*_{x}/m^*_{y}$) ratio as much as by a factor of 40. Our DFT and $\vec{k}\cdot\vec{p}$ simulations clearly indicate that the twist angle in combination with an appropriate gate voltage is a novel way to tune the electronic and optical properties of bilayer phosphorus and it gives us a new degree of freedom to engineer the properties of black phosphorus based devices.Comment: 8 pages, 8 figure

Was Levinas an Antiphilosopher? Archi-ethics and the Jewish Experience of the Prisoner

This paper explores Levinas’s Carnets de captivité and Écrits sur la captivité in light of Badiou’s category of ‘antiphilosophy’. We make four movements: firstly, a description of what antiphilosophy is; secondly, an explanation of why the category of antiphilosophy is important to a reading of Levinas; thirdly, an exposition of the antiphilosophical elements of the Carnets and Écrits on captivity; and fourthly, we situate our reading of the notebooks within the larger context of Levinas’s post-captivity work.

The Idea of Sustainable Development in Public Administration

This article introduces the Focus Issue on Sustainable Development by first discussing the environmental problems caused by unsustainable development and then the shortcomings caused by a piecemeal approach to policy development and implementation. The idea of sustainability appears to fit well with other core values of public administration, which is a consistent theme throughout each of the articles in this issue. Definitions of sustainability are discussed, followed by two relevant models. Finally, each article in the focus issue is introduced

Velocity Correlations in Dense Gravity Driven Granular Chute Flow

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time \dt used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size and grain stiffness, and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, \hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.Comment: 21 pages, 16 figure

Identities of the multi-variate independence polynomials from heaps theory

We study and derive identities for the multi-variate independence polynomials from the perspective of heaps theory. Using the inversion formula and the combinatorics of partially commutative algebras we show how the multi-variate version of Godsil type identity as well as the fundamental identity can be obtained from weight preserving bijections. Finally, we obtain a new multi-variate identity involving connected bipartite subgraphs similar to the Christoffel-Darboux type identities obtained by Bencs

HapTree-X: An Integrative Bayesian Framework for Haplotype Reconstruction from Transcriptome and Genome Sequencing Data

By running standard genotype calling tools, it is possible to accurately identify the number of wild type and mutant alleles for each single-nucleotide polymorphism (SNP) site. However, in the case of two heterozygous SNP sites, genotype calling tools cannot determine whether mutant alleles from different SNP loci are on the same chromosome or on different homologous chromosomes (i.e. compound heterozygote)